Is thinking...

That the origin of matter and energy is that of the curvature of spacetime itself. Have a sufficiently large enough curvature and you can create matter and energy, this is what Einstein's equations predict..

But equally, matter especially is a late low energy phenomena; the appearance of matter is therefore described by the low energy epoch called Geometrogenesis. Maybe matter did not appear from the big bang, but energy did. Einstein once taught us that there is really no such thing as matter - it was all just various forms of energy.

If this is the case, maybe matter is not fundamental. Maybe energy is. Equally, maybe geometry is not fundamental so a final theory will not be concerned with matter or geometry, this would mean it is not concerned with space as we usually recognize it every day in our lives.

The latter has already been questioned by Fotini Markoupoulou.

So if matter comes from geometry and eminated from the curvature of a reasonably early universe, then were did space itself come from?

I think Fotini is correct. She believes that the final theory of physics will be concerned with no geometry. That space essentially does not exist.


So maybe space, matter and geometry are all concerned with the same topic, in that we will find that none of them will describe our final theory. We shall tackle some of these idea's later - such as whether a no-space no-time model can fit into this idea. The idea that timelessness exists would imply in relativity that no space really exists either, since both are unified relativitistically. This is in the same kind of light I treated my no-time no-energy Cosmological Problem. The very fact that we seem to have no Global description of time given in the Wheeler de Witt equation must imply an undefined non-conserved energy for a universe. Thus the absence of geometrical space would imply there is no geometrical time, that the vanishing time derivative in the WDW-equation gives us light to assume other idea's, such as the no-energy postulation as well. It is a cosmological assumption that all the negative particles equally cancel out the positive charges in the vacuum.

So, just like feet on a centipede, they are all conjoined by one body.

The absence of space, must imply the absence of matter and geometry, would include the absence of time which would naturally assume the absence of energy. So maybe energy is not as fundamental as we think?

Maybe the four ''fundamental'' ingredients for a vacuum like ours, those including space, time, matter and energy are all but fascets of one theory hinting at an illusion.

I will get Fotini's paper later today and I will talk about this further.

First of all, we should tackle what kind of theory geometrogenesis implies: It means the materialistic organization space; the configuration of matter giving rise to geometrical bodies.


If Markopoulou is right, then it seems she predicts something quite odd usually - the notion that space, is not a fundamental object, that in fact, physics seems to be hinting at a space with no geometry.

What we are challenged with is rooted from a relaltivistic discipline. It teaches our mind to think of time as being a dimension of space, the fourth dimension of space to be exact. It is an imaginary leg which is orientated 90 degrees from the real leg on the spacetime triangle. Time is as invariant as space was, then that neither of them could be seperated. It also implied time was primal, that it had some kind of unique meaning in the beginning of everything.

However, even with these predictions that Einstein's theory made on these things, there was an unusual glitch in his equations. Some of them, those concerned with global measurements have no time description. Called Timelessness in general relativity, it is considered a ''problem'' for physicists. If the timeless solutions to Einstein's equations is implying that the universe is timeless, then there are some interesting symmetries which are obtained from other sources of work.



If all the negative matter cancels out every positive peice of matter, such as the zero-energy universe. In particular interest, it is in fact the Minkowski metric (the four dimenensional manifold) which implies zero energy. The reason why the Minkowski metric implies the null energy condition [1] will require only a few steps. We begin with an equation which has been selected because it is a result of the Schwarschild's metric

E = Mc^2 - \frac{Gm^2}{2R}

According to this equation, when M=0 the energy is also zero, but you obtain the metric itself. So this is classed as the null energy condition.

Interestingly though, I have already elaborated on a time-energy problem concerning how if there is a vanishing time then there is no way to translate a universal symmetry with any energy, the equivalent to energy being conserved.

Alone, we have seen that time and energy have some problems if they are to be understood fully.


But as I mentioned earlier, Fotini has described a universe without space. Albeit, she does this to achieve merit in her opinion that time can be saved, but she still raises an interesting argument in favor of Geometrodynamical models. [2],[3]

The first paper linked to, involves the spaceless theory, but makes mention of her quantum graphity model. The second paper is on the paper which first speculated quantum graphity.

It is really from this point I have been wondering whether the fact that physics seems to be implying a no-space, no-time and no-energy universe, (where energy and matter in this sense can be freely exchanged) there is still the evidence that Geometrogenesis predicts matter as a low energy phenomenon, one which appeared when there was some geometry involved.


Julian Barbour seems to be important to mention here.

He constructed a theory which would describe motion from a timeless theory [4]. He tackles his questions with a series of simple equations which seem to contain the relevant data without the description of time. He assumes that we should concentrate on the right hand side of the equation which does not contain the time variable and deal with observable quantities, which he says, is the way physics should work.

One of his final equations are described as:

v_i=\frac{\delta d_i}{\delta t} = \sqrt{\frac{2(E-V)}{\sum_i M_i(\delta d_i)^2}} \delta d_i

He rids the equation of the time description by using the fact that the speed of a body [i]is not the ratio of it's displaceent to an abstract time increment but to which involves displacements of all the bodies in the system. By doing this, he rids his use of time describing motion. Most interesting of all, is that his theory predicts that time is no longer measured by particular individual motions, but by a sum of all the motions.


It might seem like a stretch in believing that all the factors which make our theory, those being of space, matter, energy and time as being illusions, yet I say that in hindsight that the fact all these things are called into question more of as a clue. It might be one which could hold some merit if one wanted to construct a theory of everything, but if it states that time, energy, space and matter are all absent, how do you approach such a theory?

It seems that we require new parameters that do not vanish. Here I am taking use of Julian Barbour's approach in creating an equation which ridded itself of a time variable, but also contained dynamics which would still successfully decribe the system.

Perhaps our final approach will be one which is similar.

We might find that all those ingredients are insufficient to describe everything, so we must consider alternatives.





[1] http://arxiv.org/pdf/gr-qc/0605063v3.pdf

[2] http://fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf

[3] http://arxiv.org/pdf/0801.0861v2.pdf

[4] http://www.platonia.com/nature_of_time_essay.pdf


ps. I have more to state, more thoughts on these illusions of physics. I will share them as the week passes us by.

Maybe just as a side note, a few weeks back I created a mass-flow equation. The design was to basically measure a mass-flow rate, which necesserally includes the passage of a time over some part of a geometry.

The equation which was of interest to me, was a mass flow equation I frivoulously derived with no merit behind why it was derived, only to achieve the dimensions required. I arrived at this equation:

\dot{\chi} = (\frac{\partial \mathcal{L}}{\partial \dot{q_i}} \cdot d_) \nabla^2

The matter field \chi can be thought of any matter field. You may freely chose to replace \chi with any or all the matter fields, each piece of matter with their own individual clocks.

\sum^{k}_{k=1} \dot{M}_k \hat{S}_{k} = \nu_i

where \nu is the net rate of flow of entropy. A classical field version again of a mass flux is given by

\dot{\chi} = (\frac{\partial \mathcal{L}}{\partial \dot{q_i}} \cdot d_) \nabla^2

where the dot represents a multiplication, not a dot product, which has been mistaken before.

Plugging in \nu_i gives

\sum^{k}_{k=1} \dot{\chi}_k \hat{S}_{k} = \sum^{k}_{k=1} (\frac{\partial \mathcal{L}}{\partial \dot{q_i}} \cdot d_)_k \nabla^2 \cdot \hat{S}_k = \dot{M}_{k}(\hat{-K_B \sum_i P_i In P_i})_k

where P_i is the probability.

Assuming that information can actually leave a universe, this equation works for it describes the mass flux in and out of the system.

Using Julian Barbours approach, where he considers each particle with a mass M as having recording the ticking of time. There maybe atleast one matter field we may use in physics to describe a mass flow/flux.

If so, we have a mass flux with individual constituents with their own dynamical clocks. For particles like an electron, this is not a bad idea. To me, it seems clear that one can derive his timeless equations and be plugged in to the existing values.

Light following a geodesic as predicted by general relativity best explains and predicts what is observed. Non-geometric Newtonian gravity and refractive gravity both do not accurately predict the bending of light as it passes a massive object like the sun but space-time curvature does.

A unified field theory based on geometry is then required.

Albert Einstein wrote what appears to be an interesting paper on the unification of gravity and electromagnetism:

http://www.alexander-unzicker.de/rep0.pdf



Unified Field Theory of Gravitation and Electricity
Albert Einstein
translation by A. Unzicker and T. Case

[...]

The applied method can be characterized as follows. First, I looked for the formally most simple expression for the law of gravitation in the absence of an electromagnetic field, and then the most natural generalization of this law. This theory appeared to contain Maxwell’s theory in first approximation.
In the following I shall outline the scheme of the general theory (§ 1) and then show in which sense this contains the law of the pure gravitational field (§ 2) and Maxwell’s theory (§ 3).


If what we call gravity is actually the curvature of space-time, and it appears to be so, then it seems likely that the path to unifying gravity with the other fundamental forces of nature would entail a geometric approach.

:shrug::shrug::shrug:

Heisenberg uncertainty is a form of the geometric Cauchy Schwarz inequality law - AKA the triangle inequality. There is also a time-energy uncertainty derived from the Heisenberg uncertainty principle.

http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality#Physics

Such hopeful clues exist and possibly they will help us to discover the geometric laws of the unified field theory :D

The equation which was of interest to me, was a mass flow equation I frivoulously derived with no merit behind why it was derived, only to achieve the dimensions required. I arrived at this equation:

\dot{\chi} = (\frac{\partial \mathcal{L}}{\partial \dot{q_i}} \cdot d_) \nabla^2

The matter field \chi can be thought of any matter field. You may freely chose to replace \chi with any or all the matter fields, each piece of matter with their own individual clocks.

\sum^{k}_{k=1} \dot{M}_k \hat{S}_{k} = \nu_i

where \nu is the net rate of flow of entropy. A classical field version again of a mass flux is given by

\dot{\chi} = (\frac{\partial \mathcal{L}}{\partial \dot{q_i}} \cdot d_) \nabla^2

where the dot represents a multiplication, not a dot product, which has been mistaken before.

Plugging in \nu_i gives

\sum^{k}_{k=1} \dot{\chi}_k \hat{S}_{k} = \sum^{k}_{k=1} (\frac{\partial \mathcal{L}}{\partial \dot{q_i}} \cdot d_)_k \nabla^2 \cdot \hat{S}_k = \dot{M}_{k}(\hat{-K_B \sum_i P_i In P_i})_k

where P_i is the probability.

Assuming that information can actually leave a universe, this equation works for it describes the mass flux in and out of the system.The equation has been thoroughly (http://sciforums.com/showthread.php?t=111942&page=7) shredded, so much so you even admit it was just something you randomly made up one drunken evening, yet here you are inserting it into ever more elaborate claims.

Why are you piling on more and more claims on an equation which is nonsense, both physically and mathematically? Just because you've heeded one of several comments about it, ie you now say its not a dot product but a scalar product, doesn't make it mathematically meaningful, it's still nonsense.

On January 19 (http://sciforums.com/showpost.php?p=2892208&postcount=140) you make a load of excuses why no one should pay attention to it, yet on February 3rd (http://sciforums.com/showpost.php?p=2899231&postcount=3) you're still talking about it?

This is why people think you're actively dishonest. You complain how James and I shouldn't be giving your 'equation' too much attention, it was just the result of a drunken evening, yet you then go and post it again and again.

And your desperate desire to throw in more and more expressions for things gives your ignorance away, namely in your expression for entropy. Ignoring the fact you suddenly produce probabilities from nowhere, without justification, definition or derivation, you write In, ie that is a capital i and then a lower case n. It's a mistake someone utterly unfamiliar with entropy or even basic calculus might make if they just looked at the equations because, as with many fonts, there's little distinction between a capital i and a lower case L, ie I vs l.

It isn't In, it is \ln. It's the standard expression for the natural logarithm, which is lower case l followed by lower case n. There's even a LaTeX symbol for it, \ln . The fact you don't even know notation so basic it's used in A Level classes shows, yet again, the laughable nature of your attempts to look like you're doing something meaningful.

If you insist on posting BS at least be clear about it. Don't try to dress it up as if you're working on developing published material or formal mathematics. How many years of this are you going to do?

The equation has been thoroughly (http://sciforums.com/showthread.php?t=111942&page=7) shredded, so much so you even admit it was just something you randomly made up one drunken evening, yet here you are inserting it into ever more elaborate claims.

Why are you piling on more and more claims on an equation which is nonsense, both physically and mathematically? Just because you've heeded one of several comments about it, ie you now say its not a dot product but a scalar product, doesn't make it mathematically meaningful, it's still nonsense.

On January 19 (http://sciforums.com/showpost.php?p=2892208&postcount=140) you make a load of excuses why no one should pay attention to it, yet on February 3rd (http://sciforums.com/showpost.php?p=2899231&postcount=3) you're still talking about it?

This is why people think you're actively dishonest. You complain how James and I shouldn't be giving your 'equation' too much attention, it was just the result of a drunken evening, yet you then go and post it again and again.

And your desperate desire to throw in more and more expressions for things gives your ignorance away, namely in your expression for entropy. Ignoring the fact you suddenly produce probabilities from nowhere, without justification, definition or derivation, you write In, ie that is a capital i and then a lower case n. It's a mistake someone utterly unfamiliar with entropy or even basic calculus might make if they just looked at the equations because, as with many fonts, there's little distinction between a capital i and a lower case L, ie I vs l.

It isn't In, it is \ln. It's the standard expression for the natural logarithm, which is lower case l followed by lower case n. There's even a LaTeX symbol for it, \ln . The fact you don't even know notation so basic it's used in A Level classes shows, yet again, the laughable nature of your attempts to look like you're doing something meaningful.

If you insist on posting BS at least be clear about it. Don't try to dress it up as if you're working on developing published material or formal mathematics. How many years of this are you going to do?

Well, I posted that specific post just to see if you would bite.

Didn't take much now did it.

As for the ''In'' part, you might as well call it basic, which it is. It's obviously my latex.

Light following a geodesic as predicted by general relativity best explains and predicts what is observed. Non-geometric Newtonian gravity and refractive gravity both do not accurately predict the bending of light as it passes a massive object like the sun but space-time curvature does.

A unified field theory based on geometry is then required.

Albert Einstein wrote what appears to be an interesting paper on the unification of gravity and electromagnetism:

http://www.alexander-unzicker.de/rep0.pdf



If what we call gravity is actually the curvature of space-time, and it appears to be so, then it seems likely that the path to unifying gravity with the other fundamental forces of nature would entail a geometric approach.

:shrug::shrug::shrug:

We also require that time takes to move from one place to another, but if timelessness exists, then the same dichotemy presents itself.

Space is not fundamental. Geometrodynamics proves this well.

Well, I posted that specific post just to see if you would bite.

Didn't take much now did it.

Are you saying you knowingly posted something you knew to be false, in order to throw out some troll-bait?

Please explain your comment in detail, because you may be banned for this.

Well, I posted that specific post just to see if you would bite.

Didn't take much now did it.Firstly I didn't even reply for several days, so it's not like I'm chomping at the bit to point out your ignorance. Secondly I don't believe you, given you have repeatedly posted nonsense and only admitted it when your back is against the wall because so many problems have been highlighted.

It's always some excuse with you. You can't say "I was wrong, I don't understand this stuff", instead you come out with "It was the result of a drunken evening" or "I typed up something I'd printed out ages ago and forgot it wasn't me who wrote it" or "I was troll baiting".

As James has said, 'troll baiting' in that form is itself trolling. Whatever your motivation, be it to try to con others into thinking you're not ignorant or be it to elicit a response from me, you post knowingly false material which you try to present as viable discussion. You're spreading misinformation. Regardless of whether or not you do it deliberately it's extremely dishonest and shows you're willing to mislead others just to entertain yourself.

Such actions make your complains about other people being mean or unkind hypocritical. You're willing to mislead people to give yourself a chuckle. Mind you, if you find humour in your actions I think you should take a long look at yourself. Actually I think you should do that anyway.


As for the ''In'' part, you might as well call it basic, which it is. It's obviously my latex.Excuses excuses. It's a mistake common to people who haven't really worked with logs before. If this were a once off I'd give you the benefit of the doubt but your 'latex errors' are so frequent and basic they cannot all be typos, they are further evidence of how little you actually do.

Are you saying you knowingly posted something you knew to be false, in order to throw out some troll-bait?

Please explain your comment in detail, because you may be banned for this.

No, I wasn't troll baiting at all.

I am still under the impression the equation could have merit without the limit I previously had on it.

Now, it has been with difficult task for me to actually get alphanumeric to engage in a topical debate. Because of this, I wondered what would do it.

It has been a previous thought of mine that the equation could hold merit and as you will see, the equation has been applied to something in that post. I wondered how long it would be before alphanumeric actually took a bite of the subject.

I still want him to try and participate in the OP, not wholey with the topics which he thinks he is impervious to mistakes, which is demonstratably false.

Plus, how can I derail my own thread... or more to the point, why?

We also require that time takes to move from one place to another, but if timelessness exists, then the same dichotemy presents itself.

Space is not fundamental. Geometrodynamics proves this well.

Let me expand on this, the other day my taxi arrived and I quickly wrote the above.

A particle takes time to move from one point to another, but timelessness persists in GR, and we are told to take it seriously by some scientists. One however is applied to a local time whereas the other is more of an application to a global time, described by a Global Wave Function.

Global Time has problems. It simply does not exist. However papers I have read suggest that perhaps the absence of a Global Time is often taken for granted and that perhaps the absence of a Global Time must indicate some kind of singularity. Actually, there are existing proofs of this (if memory serves, by George Ellis).

Now geometry, is all fine and well in General Relativity but we have failed to find an appropriate quantum theory of General Relativity, which must imply that GR breaks down as you get to the understanding of High Energy Physics.

In light of this, Geometrodynamics states a very obvious truth then. That Geometry is a concern of a low energy epoch where matter dominated the universe (the place where fixed clocks can tick off time according to Julian Barbour). The high energy epoch is were geometry no longer exists and the geometrical vision of Einstein is under threat.

Heisenberg uncertainty is a form of the geometric Cauchy Schwarz inequality law - AKA the triangle inequality. There is also a time-energy uncertainty derived from the Heisenberg uncertainty principle.

http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality#Physics

Such hopeful clues exist and possibly they will help us to discover the geometric laws of the unified field theory :D

That is actually a very interesting approach! Some one who uses their imagination I see :)

The reason why that approach could be important, is because the uncertainty principle dominates the condition known as the Big Bang, the applications are huge. I even speculated that maybe space (required) to expand initially not because of any negative energy density, but maybe because particles where so ''confined'' that to remain as compact at the big bang would almost certainly violate the Uncertainty Principle.

Mind you, how do you speak of geometry still, at the big bang?

Dare I say, maybe big bang is what is crippling the unified approach rather than GR necesserily meaning to break down. GR may not need to break down, if our approach did not involve a big bang. There are already scores of problems concerning the big bang.

No, I wasn't troll baiting at all.Now you're contradicting yourself.


I am still under the impression the equation could have merit without the limit I previously had on it.Except it had been explained to you why it was flawed in several ways and you yourself told us not to pay any attention to it. So why are you posting it again? Are you now claiming people should pay attention to it? You can't have it both ways.


Now, it has been with difficult task for me to actually get alphanumeric to engage in a topical debate. Because of this, I wondered what would do it.There can't be any 'topical debate' if you're dishonest and posting knowingly false things.


I still want him to try and participate in the OP, not wholey with the topics which he thinks he is impervious to mistakes, which is demonstratably false.Where did I claim to be impervious to mistakes? Stop being so dishonest and lying so blatantly. Doing so only demonstrates you aren't really looking for a discussion, you just want an excuse to spout nonsense. Sorry, I'm not going to feed your desire to delude yourself.

Now you're contradicting yourself.

Except it had been explained to you why it was flawed in several ways and you yourself told us not to pay any attention to it. So why are you posting it again? Are you now claiming people should pay attention to it? You can't have it both ways.

There can't be any 'topical debate' if you're dishonest and posting knowingly false things.

Where did I claim to be impervious to mistakes? Stop being so dishonest and lying so blatantly. Doing so only demonstrates you aren't really looking for a discussion, you just want an excuse to spout nonsense. Sorry, I'm not going to feed your desire to delude yourself.

I took the flaw that the limit kind of redefines the world line in such a way that it cannot be good form. I've accepted that. But the rest of your quibbles lie marginely on the fact I had no basis for its derivation, I only sought to balance dimensions.

Anyway, since you won't participate I have no choice now but to block you. I've tried and failed.

I took the flaw that the limit kind of redefines the world line in such a way that it cannot be good form. I've accepted that. But the rest of your quibbles lie marginely on the fact I had no basis for its derivation, I only sought to balance dimensions.I gave multiple reasons why it was mathematically nonsense. That alone should have been enough for you not to try to build on it. Instead you ignored them all and ignored the fact you have absolutely no physical justification for such an expression to mean anything by your own admission. You repeatedly complained that James and I shouldn't be slating you for the equation because you'd just made it up one drunken evening. Now you're building on it, trying to pass off your work as something related to actual physics. That's hypocritical, dishonest and deceitful.


Anyway, since you won't participate I have no choice now but to block you. I've tried and failed.What is there to participate in? When you have fundamental flaws in your claims pointed out you make excuses and tell people not to take any heed of the claims but then you turn right around and start piling more and more things on top of those claims.

How can anyone participate in an honest discussion if you're not only unable to be honest but are actively deceitful? You can't complain I'm not willing to play ball when I'm the one using actual maths/physics pointing out the fundamental problems in your claims, claims you admit are the product of a drunken evening.

You don't want people to talk about your 'work' when they are showing it to be flawed but then you want to talk about your work. You want to be immune from criticism or correction, which simply isn't going to happen.

I gave multiple reasons why it was mathematically nonsense. That alone should have been enough for you not to try to build on it. Instead you ignored them all and ignored the fact you have absolutely no physical justification for such an expression to mean anything by your own admission. You repeatedly complained that James and I shouldn't be slating you for the equation because you'd just made it up one drunken evening. Now you're building on it, trying to pass off your work as something related to actual physics. That's hypocritical, dishonest and deceitful.

What is there to participate in? When you have fundamental flaws in your claims pointed out you make excuses and tell people not to take any heed of the claims but then you turn right around and start piling more and more things on top of those claims.

How can anyone participate in an honest discussion if you're not only unable to be honest but are actively deceitful? You can't complain I'm not willing to play ball when I'm the one using actual maths/physics pointing out the fundamental problems in your claims, claims you admit are the product of a drunken evening.

You don't want people to talk about your 'work' when they are showing it to be flawed but then you want to talk about your work. You want to be immune from criticism or correction, which simply isn't going to happen.

How about participating in a discussion of the OP, and divert your attention from the equation. It is not the only thing that has been discussed.You act like it is.

In an approach according to a paper I linked previously in the past, it was customary as a reparamaterization of the Wheeler de Witt equation to reconfigure time as \chi = \tau, so the matter field was now acting as a clock.

The Total Hamiltonian for a universe is given by the WDW-Hamiltonian

H_{WDW}=H_T=H_{\phi, h_{\mu \nu}} - H_0 [1]

where h_{\mu \nu} is a metric perturbation. The equation of interest is

|\psi> = |\phi_a> |\chi_{\phi, h_{\mu \nu}}> [2]

Using a proceedure of seperation of variables, we obtain

(H+V(a)|\psi_a> = E|\psi> [3]

and

(H + V(\chi)_{\phi h_{\mu \nu}})|\chi_{\phi, h_{\mu \nu}}> = E|\chi_{\phi h_{\mu \nu}}> [4]

The potential terms in these equations are equal to

V(a) = a^2-g^2a^4 [5]

and

V(\chi) = \chi^2 - g^2\chi^4 [6]

Going back to eq. [4] we have

(H+(\chi^2-g^2\chi^4))|\chi_{\phi, h_{\mu \nu}}> = E|\chi_{\phi h_{\mu \nu}}> [7]

Because of continuity of eigenvalues, one should state that as (\chi_{\phi, h_{\mu \nu}}) \rightarrow \phi then the interaction term (\chi^2-g^2c^4) \rightarrow 0 goes to zero.

A potential solution to this equation is

|\psi> = \phi + \frac{1}{E - H_0} \cdot (\chi^2- g^2\chi^4)|\psi> [8]

where \cdot is multiplication. Whilst this is a potential solution, a problem exists. A serious problem in the form of a singularity exists in (E-H_0) since E is an eigenvalue of H_0.

There is one distinct way of making this singularity to normally disappear. One way is to make the denominator slightly complex i\epsilon. Instead, I am going to use a different approach.

To avoid the singular existance of this mathematical object, we are going to substitute E for a result of the Schwartzchild Metric

Mc^2 - \frac{Gm^2}{2R} [9]

This changes our equation in such a drastic way, it rids us of the singularity in our equation. No longer does (E-H_0) hold, because the null energy condition states that as M=0 all we are left with is the metric.

So we have a correspondance between (Mc^2 - \frac{Gm^2}{2R}) and H_0 in which if you imply a nullified energy condition you obtain a solution to avoid the singularity problem.

Interestingly, it does not only imply that our matter field \chi no longer has any mass, but it also means we have no radiation fields either.

Let's look at the original Hamiltonian in a different way, now accounting for systems of many particles if one desired but for simplicity we will assume particles i and j.

For N-particles (2 in our case), we can have

\{ \sum_{i} H(i) + \sum \frac{1}{r_{ij}} \} = E \psi

where r_{ij} calculates the distance between i and j. If we represent this in a Hilbert Space, the configuration space looks like

H= \sum_i H_i + \sum_{k \in I} h_k

where h_k is a hermitian operator. I is the set of interactions \{i,j\} \equiv k and naturally can form a direct tensor Hilbert space \mathcal{H}_3 = \mathcal{H}_1 \otimes \mathcal{H}_2.

This is already beginning to be like a theory which deals with no geometry. Indeed, a Hilbert Space are often called ''points'' which describe abstractly the configuration space. This is the similar approach Markoupoulou attempts to make in her Graphity model. She takes Hilbert Spaces and describes their interactions in such a model without resorting to geometry.

In tackling my theory of the cosmological energy-time problem, I considered first of all a question which has plauged observer-physics; How can the universe have an energy? To have an energy, someone would need to be sitting outside of the universe to view it's energy content. That or someone would need to sit until the very last moment of existence and maybe they will be fortunate enough to measure an energy.

Smolin states:

"We didn't know how, in the language we were working in, to put in the notion of causality" in LQG, Smolin says. Markopoulou Kalamara found that by attaching light cones to the nodes of the networks, their evolution becomes finite and causal structure is preserved. But a spin network represents the entire universe, and that creates a big problem. According to the standard interpretation of quantum mechanics, things remain in a limbo of probability until an observer perceives them. But no lonely observer can find himself beyond the bounds of the universe staring back. How, then, can the universe exist?'' [1]

This was a passage from a webpage describing her newest works in attempting to view space as having no geometry, it is only the configuration of matter which gives rise to the geometrical assembly of observables, that fundamentally, geometry was to be banished. Einstein's theory then, cannot assume that geometry will exist when unification of GR with QM is achieved.

With this, I extended the question in terms of conservation of energy, whether the universe possessed one. In light of the energy problem of an observer to define the wave function, a number of other ''facts'' of physics seemed to agree there was no energy at all.

There was the no-energy condition of universes, where every peice of energy and matter all mathematically reduced to zero. And more prominently, there was the infamous of Time Problem of QM, the issue of the vanishing time derivative in the WDW equation. The WDW equation is in fact obtained from quantizing Einstein's field equations.

Interestingly one approach Markoupoulou uses is spin network theory in Quantum Loop Gravity.

Someone here called Khan mentioned the uncertainty principle in relation to geometry.

Well a similar approach can be found in spin networks. Each point or ''unit'' as they are called, represent geometric points in space and must obey the triangle inequality (the same example khan used). In an abstract sense, my Hilbert space demonstration (Markoupoulou's approach also) is an attempt to describe the configuration space of a spin network in terms of Hilbert Spaces.

The geometry is then emergent from well-positioned particles called the spin network.

[1] http://www.mlahanas.de/Greeks/new/Kalamara.htm

In my solution to the Singularity (E-H_0) where we make the matter-energy content vanish, is akin to making the matter langrangian equal zero \mathcal{L}_M then what is left over is the Einstein-Hilbert action.

S=\frac{1}{4\pi G}\int d^4x \sqrt{-g}(R - 2\Lambda) + \int d^4x \sqrt{-g}\mathcal{L}_M

What is left over from my quantity is the metric itself.

In the EH action, the quantity left over makes it perfect to describe the gravitational field itself, even without the presence of matter. The right hand side of this equation

\nabla R^{\mu \nu} = \frac{1}{2}\nabla_{\mu}g^{\mu \nu}R

says that if it is equal to zero, then there is no matter in the universe. But should this imply there is zero curvature? Gravity takes a new appearance as gravitational waves. They have no mass but they can ripple spacetime and cause curvature.

I propose that matter came from such curvature. These gravitational waves might be so ellusive now that we may never see one. It must have occurred when the universe had cooled sufficiently to allow geometry to be translated then from the positions of particles in a spin network.

We remove geometry, but there is also the remaining time problem. Well, time may then be a late phenomena, atleast one which can be translated successfully by measuring the motion of particles, thus requiring geometry and the notion of matter. But if time does not exist period, then neither should matter, or any real geometry. It is all just a quantized set of spaces.

Then what of the no-energy proposal? There is still the problem of whether the universe could even have an energy without a global time translation.

Hypothetically speaking - before the big bang - also called the "pre-bang" era - instead of a singularity, all the forces of nature along with all matter energy, space and time, could have been unified into a single substance that was existing in a highly symmetrical yet unstable state. It underwent spontaneous symmetry breaking and the universe was born.

http://en.wikipedia.org/wiki/Gravitational_singularity



Both General Relativity and Quantum Mechanics break down in describing the Big Bang, but in general quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths.


:shrug::shrug::shrug:

Hypothetically speaking - before the big bang - also called the "pre-bang" era - instead of a singularity, all the forces of nature along with all matter energy, space and time, could have been unified into a single substance that was existing in a highly symmetrical yet unstable state. It underwent spontaneous symmetry breaking and the universe was born.

http://en.wikipedia.org/wiki/Gravitational_singularity



:shrug::shrug::shrug:


You make a lot of shrugs, but you must have a good idea, to make mention of the things you have, how indepth these subjects are.

For instance, it is true; the ''quantum gravity'' as it has been dubbed - the single fasceted side of a four-edged coin - the unification of gravity with EM and weak and strong nuclear forces.

Yet saying reality appeared because this force was unstable, seems too folly for me. There must be mechanisms involved, it is surely not enough to say that it was unstable (no dig at you). In relativity, there is an old question - what came first, matter or curvature?

The answer must be curvature. So we can answer where matter came from - the appearance of energy itself is much more primal according to Geometrogensis. There was, at a point, a beginning of spacetime where energy eminated from a singularity. There is a contradiction with the pre-bang era.

Assuming that relativity is taken seriously, then one cannot speak about time or space assuming this is pre-bang. Unless one assumes that space and time has always existed.

If the vacuum is a configuration space for matter which exist in Hilbert Spaces, described by spin networks that obey the uncertainty principle inequality triangle relationship, then it might be possible to describe the kind of universe I was planning for the last few years. That is, space and time as far as we can record it appeared from an unstable region where matter was compressed to increadible densities. The space between the existing objects did not exist, hence why space began to expand, so that new degrees of freedom could be experienced.

So how does the Cauchy-Schwartz Inequality work?

Well, any time you take the dot product of any two vectors then you cannot find anything larger than if you just multiplied the two vectors' lengths.

| <x|y>| \le |x||y|

Is the inequality. Remember then, that particles in the Spin neywork must obey this inequality. So what I am wanting to do, is retrieve the geometrical relationships in a space with no geometry!

God my brain hurts.

How about participating in a discussion of the OP, and divert your attention from the equation. It is not the only thing that has been discussed.You act like it is.I am not going to feed your desire to deceive people. You're talking about Hilbert spaces and metrics but you don't know the material, you're just parroting it.

I'd challenge you to do some questions on it but you've already failed to do stuff years simpler which James asked you.

But the way, your use of reparameterisations is wrong. Would you like to explain where? Go on, show you understand the stuff you're spouting. Last time I asked you and even pointed you at the relevant equations you couldn't notice a mistake so I won't hold my breath.

I am not going to feed your desire to deceive people. You're talking about Hilbert spaces and metrics but you don't know the material, you're just parroting it.

I'd challenge you to do some questions on it but you've already failed to do stuff years simpler which James asked you.

But the way, your use of reparameterisations is wrong. Would you like to explain where? Go on, show you understand the stuff you're spouting. Last time I asked you and even pointed you at the relevant equations you couldn't notice a mistake so I won't hold my breath.

You claim I am parroting known stuff yet equally state I am deceiving people.

That is a contradiction.


I am talking about Hilbert Spaces because I know how to apply it in theory. The work suggesting the solution to the equation solving the singularity is also my work. I simply chose to solve the equation in terms of the Lippman-Schwinger equation.

My use of reparameterisations is wrong? Guess where?

Well, considering I am using an identical approach as a paper I have followed in the past, you'd be best to clarify what the problem is.

So how does the Cauchy-Schwartz Inequality work?

Well, any time you take the dot product of any two vectors then you cannot find anything larger than if you just multiplied the two vectors' lengths.

| <x|y>| \le |x||y|

Is the inequality. Remember then, that particles in the Spin neywork must obey this inequality. So what I am wanting to do, is retrieve the geometrical relationships in a space with no geometry!

God my brain hurts.

I have many questions and speculations. I suspect that in order for a universe to maximize entropy it must have three expanded spatial dimensions and one entropic "time arrow" dimension. Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy. Universes with higher than three expanded spatial dimensions would have higher symmetry but would be unstable and would decay into a more stable configuration I am guessing. :shrug:



Von Newman entropy

http://en.wikipedia.org/wiki/Von_Neumann_entropy

Entropic Gravity

http://en.wikipedia.org/wiki/Entropic_gravity



Entropic gravity is a hypothesis in modern physics that describes gravity as an entropic force; not a fundamental interaction mediated by a particle, but a probabilistic consequence of physical systems' tendency to increase their entropy. The proposal has been intensely contested in the physics community.



Causal dynamical triangulations are beyond my understanding at this time :D

http://arxiv.org/pdf/1001.4581.pdf





...

I have many questions and speculations. I suspect that in order for a universe to maximize entropy it must have three expanded spatial dimensions and one entropic "time arrow" dimension. Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy. Universes with higher than three expanded spatial dimensions would have higher symmetry but would be unstable and would decay into a more stable configuration I am guessing. :shrug:



Von Newman entropy

http://en.wikipedia.org/wiki/Von_Neumann_entropy

Entropic Gravity

http://en.wikipedia.org/wiki/Entropic_gravity




Causal dynamical triangulations are beyond my understanding at this time :D

http://arxiv.org/pdf/1001.4581.pdf





...

Let me concentrate on this ''time presumption based on science'' which you have brought up.

I see the word ''entropy'' being raised.

In so many words, I think entropy is an inertial quantity rather than a relativistic one. The reasons why are actually quite simple. One reason is because only entropy is measured by the chronological account of the ''flux'' (aka. passage) of time. Time we should not forget then, is merely a calculational tool to derive semi-symmetries.

Semi

-symetries are creations of two boundary conditions. A good example is the Plank Time. It is bound by a beginning and end point and this is the quantized path to formulating a universal understanding of GR.

The cosmological side almost fades out, it is quite disturbing.

We are, it seems able to be forced by physics to suggest that the cosmological side of the universe, can only up to certain limit be unified. If that remaining half or whatever fraction has remained unanswered with remain as such, because of an incomplete theory we have so admirably followed to this point in our history.

If unification is to be achieved, then the cosmological approach of unifying an understanding of time and space into the world at large (General Relativity) then these relativistic relations will find new contraints on the theory predicting incredible new pictures, I predict.

But as far as entropy goes, my own speculations and years of studies seem to indicate, that time is only measured by observers, experiences yet what is called a ''local time'', measured in real coordinates. Since photons and other types of energy particles with no mass term face the same relativistic dynamics of Lorentz Invariance, then these particles without mass experience no time.

In a certain approach to unify this all, the matter field \chi I have speculated on in this post and others, could have a time description using a Julian Barbour Approach, one which had time invariant in the calculations, but using other solutions with avoided any time term but used observable quantities (an arguement he used in his own paper).

It will be calculated by the sum of all the particles, the primordial matter field \chi therefore is unique enough to have a name of it's own, which I will call the ''Origon Field'' from the latin word ''Origo'' meaning ''beginning'' and ''on'' from traditional nuclear-naming of particles such as, Prion, Gluon, Photon ect.

This field however could not be the field which originated at big bang, assuming it is correct.

It must be a low energy phenomenon, as a late epoch where the single matter field broke into many others. This was the origin of the spontaneous symmetry breaking, when the (if found) Higgs particle dressed energy into inertial matter particles. Fundamentally-speaking then, the Origon Field then is the explanation of inertial appearance in matter.

Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy.

Totally, Khan.

Geometrogenesis is the appearance of any necessery degrees of freedom to produce any kind of entropy in the geometric sense. One in a manner, could argue that entropy in a geometric sense could not happen at big bang, for obvious reasons. So did entropy fundamentally exist?

This is also why I said the Uncertainty Principle is the reason for the expansion of space because, as you said:

''Universes with less than three expanded spatial dimensions would be extremely stable but would not have the necessary degrees of freedom to produce maximal entropy.''

Which just to follow on, if there are no degrees of freedom then this violates the fundamental cornerstone of physics, the uncertainty principle - so in order for the universe to push back from where it began, a high quantum potential designated the further design of an expansion. Why, we can only look at the suspects.

You claim I am parroting known stuff yet equally state I am deceiving people.

That is a contradiction.No, it isn't. You parroted Susskind but since you didn't understand some of the things he said you miscopied or misexplained or misrepresented results he was writing down in that YouTube video.

Besides, passing off other people's explanations as your own is deceiving people, as you did with Susskind and James's questions.

Also when you do try to weave in your own nonsense you try to hide it within a discussion of some paper or video or bit of bookwork. Or you just don't clarify when you're talking about stuff you made up rather than referring to some paper, as is the case with your matter flow 'equation'.


I am talking about Hilbert Spaces because I know how to apply it in theory.Tell me, do you really believe yourself when you say such things or are you aware you're mistaken?


Well, considering I am using an identical approach as a paper I have followed in the past, you'd be best to clarify what the problem is. You say \chi = \tau and then have a V which is purely a function of \tau, ie time. No such quantum mechanical system exists.


The work suggesting the solution to the equation solving the singularity is also my work. I simply chose to solve the equation in terms of the Lippman-Schwinger equation.This is precisely what I'm talking about. You recently failed to do questions expected of high school students, stuff you should have just steam rollered. You failed utterly and made laughable excuses but rather than think "That made it so obvious I can't do this stuff perhaps I should stop" you've just started up another thread spewing out more buzzwords.

The Lippman-Schwinger equation pertains to eigenvalue/eigenstates of infinite dimensional operators, yet you struggled with 2x2 matrices (http://sciforums.com/showthread.php?t=112104&page=3).

Or how the equations involved in this area of quantum mechanics heavily relate to oscillations and peroidic functions, something you failed to even recognise in the high school example James asked you about. James asked you something I remember doing when I was 17, but you couldn't do it and yet now you're claiming to be presenting alternative approaches to quantum mechanics problems?

You clearly don't understand the nature of the singularity referred to in the system. It's a pretty standard one, encountered in bookwork for introductory courses in quantum mechanics so people can learn how to do with certain types of eigenvalue related problems. One method is to use high order perturbative expansions and another is to use complex integration and perturb the contour slightly. Both of them have very sound mathematical footing.

Let's consider your 'solution', to sub in an expression for E from the SC metric. You have no justification for that, beyond word association with 'singularity'. Beyond the fact they both pertain to quantities which look like 1/0 they are not related to one another, but you wouldn't get this if you can only buzzword match. Secondly the form E takes is dictated by the Hamiltonian, a principle fundamental and core to Hamiltonian mechanics. The expectation of the Hamiltonian is literally the expectation of the energy of a system. You cannot change the E's without changing H. Thirdly, even changing E or H or rewriting the form of E doesn't negate the fact the E in the expression is defined as an eigenvalue of H and therefore (H-E)|\psi\rangle = 0 is possible. Writing E = \textrm{something} doesn't avoid this any more than writing 0 = 1-1 doesn't magically make 1/0 = 1/(1-1) valid. Fourthly you end up claiming, via a series of unjustified non-sequitors, that you end up with a result which doesn't involve geometry. You used the SC metric! You made an explicit reference to a geometry. Now Markoupoulou might manage to use a standard method like the contour integral perturbation to get a result without reference to a geoemetry but you don't.

You also show you don't know how to use words properly. You write down a Hamiltonian (without justification or construction) and refer to it as a configuration space. No, a Hamiltonian is an operator on a space, not necessarily configuration space. You also say that "Indeed, a Hilbert Space are often called ''points'' which describe abstractly the configuration space". That isn't true either. Certain constructions/descriptions of certain configuration spaces can be described using Hilbert spaces but not all Hilbert spaces are configuration spaces (few even have physical interpretations!) nor are all configuration spaces Hilbert spaces. Nor does having a Hamiltonian imply you're working with a Hilbert space. Nor does having a Hilbert space imply there's a Hamiltonian. These concepts might be used together sometimes but they are constructions in and of themselves, they are not necessary or sufficient for one another. Heck, I've just spent the last fortnight considering Hamiltonians which aren't Hermitian. Or defined on a Hilbert space.

Clearly you read someone say something like "the ''points'' which describe abstractly the configuration space can be taken to be elements in a Hilbert space" but given you don't know the formal properties of such things or their proper applications in physics or mathematics you've tried to reword it. And like you do all too often when you try to reword things, you screwed it up.

I am in no doubt that you've honed your BS'ing skills enough to be able to con some non-physicists unfamiliar with your past but you're even more transparently dishonest now than you were 4 years ago. You've been increasing the level of complexity of the material you try to parrot but it just leads to ever more glaring abuses of terminology and non-sequitors. That's why I don't see any reason to engage you in actual discussion on the subject matter, you demonstrate that if left to your own devices you'll quite happily spout nonsense and be dishonest. I didn't force to you post that nonsense, just like I didn't force you to make post after post pushing your \dot{\chi} equation despite after you'd admitted it was a pile of nonsense you'd made up a drunken evening. Clearly you'll lie when you think you can get away with it. If you don't have enough respect for people who are looking for honest discussion, like khan seems to be, to be honest why should you expect to be treated kindly? If you piss on someone's shoes they'll not be very happy with you, particularly if you say "It's not me, it's raining" when they tell you to stop.

And additionally, you could apply yukawa couplings along the same line of using them in quantum theory to measure different particles masses. Equally, spontaneous symmetry breaking in the Higgs form, might be the correct mathematical approach to a different interaction.

Alpha numeric***

**** off.

For starters, I can easily state that E=something, when E has not been defined, for instance, AN. Secondly, since I can define E as the energy of the universe under the very simple assumptions based from the WDW equation, then you can define the rest as it naturally unfolds.

And for last, you obviously can't understand the nature of the problem if you think the universes energy can be solved in terms of high perturbative expansions, since, the universe can no longer be a steady expansion, yet is now exponential as it increases proportionally and relativistically at magnitudes of the speed of light.

I have came to some interest, in a different mathematical approach which satisfies, I think, the fluid density dynamics of a universe

If

\rho_{I} \bold{x}_i = T_{\alpha \beta}(\phi^{\alpha}_i \phi^{\beta}_j \cdot (x^{\mu}\tau)_i)

where \phi is some scalar field (here in hindsight, consider it the ground state mexican hat potential). \bold{x} is the four veclocity, so we are keeping our relativistic form.

The i's here are mathematical markers. Since the density at this point of the equation does not satisfy any inertial conditions by requisit, then as x^{\mu}_i\tau_i \rightarrow c where c is the speed of light, then \phi = 0.

In concordance to this mathematical motive, the coupling terms satisfy \delta_{ij}. Since \phi = 0 then this describes the ground energy of a photon. This therefore assumes that the inertial density is also zero \rho_I = 0.

If (x^{\mu}_i\tau)_i< c then the inertial couplings \psi(\phi_i, \bold{x}_i) at certain energy requirements.

Thus meeting these requirements, we can now state \phi in new terms when it acts as a fluctuations away from the ground state, so \phi \ne 0. We may assume, for the beauty of unity that \phi = 1.

Thus, what we end up with is an inertial term on the right hand side, where \phi couples with (x^{\mu}\tau)_i such that we can make (x^{\mu}\tau)_i vanish from the equation and allow the matter field to now be a a unit timelike vector which defined the world lines of some configurations of particles, then the energy-mass density of the universe would be the scalar field

\rho \bold{x}_i = T_{\alpha \beta} \chi^{\alpha} \chi^{\beta}

Which neglects the four velocity. I think this is an important realization that maybe the vanishing four-velocity parameter is in fact an indication of the breakdown of this equation.

I have came to some interest, in a different mathematical approach which satisfies, I think, the fluid density dynamics of a universe

If

\rho_{I} \bold{x}_i = T_{\alpha \beta}(\phi^{\alpha}_i \phi^{\beta}_j \cdot (x^{\mu}_i\tau)_i)

where \phi is some scalar field (here in hindsight, consider it the ground state mexican hat potential). \bold{x} is the four veclocity, so we are keeping our relativistic form.

The i's here are mathematical markers. Since the density at this point of the equation does not satisfy any inertial conditions by requisit, then as x^{\mu}_i\tau_i \rightarrow c where c is the speed of light, then \phi = 0.

In concordance to this mathematical motive, the coupling terms satisfy \delta_{ij}. Since \phi = 0 then this describes the ground energy of a photon. This therefore assumes that the inertial density is also zero \rho_I = 0.

If (x^{\mu}\tau)_i < c then the inertial couplings \psi(\phi_i, \bold{x}_i) at certain energy requirements.

Thus meeting these requirements, we can now state \phi in new terms when it acts as a fluctuations away from the ground state, so \phi \ne 0. We may assume, for the beauty of unity that \phi = 1.

Thus, what we end up with is an inertial term on the right hand side, where \phi couples with (x^{\mu}\tau)_i such that we can make (x^{\mu}\tau)_i vanish from the equation and allow the matter field to now be a a unit timelike vector which defined the world lines of some configurations of particles, then the energy-mass density of the universe would be the scalar field

\rho x_i = T_{\alpha \beta} \chi^{\alpha} \chi^{\beta}

Which neglects the four velocity. I think this is an important realization that maybe the vanishing four-velocity parameter is in fact an indication of the breakdown of this equation.

According to a quantum approach, if \mathcal{O} is some observable, then the operator is stationary and the state is time-dependent if

\frac{\partial}{\partial t} < \mathcal{O} > = \frac{1}{i\hbar}< \{ \mathcal{O}, \mathcal{H} \}>

If we take the derivative with respect to \rho and divide both sides of the equation with the derivative in respect of our time derivative,

\rho = T_{\alpha \beta} \chi^{\alpha}\chi^{\beta}

then we would have after quantizing our equation would yield, this time including our time derivative

\frac{\partial \rho}{\partial t} = \frac{1}{i\hbar} \{ H, \rho \}

This can be solved by Ehrenfest's Theorem. Best of all, this equation works for a mixed state, just like a matter field with many particles.

Hello again Reiku :D

I went and read some of your older postings and found this interesting question that you mentioned regarding the requirement of 3 spatial dimensions.

http://www.sciforums.com/showthread.php?t=79747


I suspect that the constants of physics arise as statistical regularities and are entropic in nature, for example, the Monte Carlo PI approximation:

http://www.chem.unl.edu/zeng/joy/mclab/mcintro.html

Gravity is possibly geometrically spherical-like and symmetric ...and electromagnetism would be transposition invariant and geometrically toroidal. is gravity an entropic phenomenon that is related to electromagnetism in some yet as undefined way? :shrug:

Hello again Reiku :D

I went and read some of your older postings and found this interesting question that you mentioned regarding the requirement of 3 spatial dimensions.

http://www.sciforums.com/showthread.php?t=79747


I suspect that the constants of physics arise as statistical regularities and are entropic in nature, for example, the Monte Carlo PI approximation:

http://www.chem.unl.edu/zeng/joy/mclab/mcintro.html

Gravity is possibly geometrically spherical-like and symmetric ...and electromagnetism would be transposition invariant and geometrically toroidal. is gravity an entropic phenomenon that is related to electromagnetism in some yet as undefined way? :shrug:

I'll need to read into this. To be honest, I know little about whether electromagnetism would be transposition invariant. Perhaps almost slightly embarrased to say, but I have never heard of a transposition quantity.

As for your theory personally, as arrogant as it might sound, I don't agree with but I think it is a promising approach for random physics theory. For people like me, we sit in the lonely camp outside the maintraim still believing in Einstein's dream.

In post 21, I qouted Smolin on the spin network I was approving in my own analysis:

Smolin states:

"We didn't know how, in the language we were working in, to put in the notion of causality" in LQG, Smolin says. Markopoulou Kalamara found that by attaching light cones to the nodes of the networks, their evolution becomes finite and causal structure is preserved. But a spin network represents the entire universe, and that creates a big problem. According to the standard interpretation of quantum mechanics, things remain in a limbo of probability until an observer perceives them. But no lonely observer can find himself beyond the bounds of the universe staring back. How, then, can the universe exist?'' [1]


Notice how also it preserves causality. This is the precurser of determinism, and hopefully, a global case. There is also a serious problem then with my model. If the matter field is not applied and we talk about high energy physics conditions, then causality could not be a quantum case. Causality must break down, since determinism is an occurance of geometrogenesis, according to all the facts.

This is another realization. It speaks of stating that determinism is something recorded by entropy. Entropy is a measure of physical changes in time. If this is correst, then radiation field where the matter field \chi=0 then there can be no passage of time. These so-called pure gravity theories then have still the looming question:

''Are pure gravity solutions of GR real physical phenomena?''

I'll need to read into this. To be honest, I know little about whether electromagnetism would be transposition invariant. Perhaps almost slightly embarrased to say, but I have never heard of a transposition quantity.

My brain hurts too Reiku. :shrug:

Einstein was developing the unified theory from the ideas of the non-symmetric field...

http://www.combat-diaries.co.uk/diary29/Link%2014%20Einstein.PDF




[...]

We postulate for the field equations of the non-symmetric field that they be transposition invariant. I think that this postulate, physically
speaking, corresponds to the requirement that positive and negative
electricity enter symmetrically into the laws of physics.

[...]





http://www.emis.de/journals/HOA/IJMMS/Volume6_4/140940.pdf




With so many covariant variables, it was impossible to choose them according to the relativism alone. To overcome this difficulty, Einstein introduced a very important concept, transposition invariance. This "transposition invariance" (or transposition symmetry) meant that when all A_ik were transposed (A^T _ik == A_ki) all equations were still applicable [2] Einstein supposed that field equations were transposition invariant. He thought that in physics this hypothesis was equivalent to the law that positive and negative electricity occurred symmetrically.

When someone says to me ''a non-symmetric field'' I think along the lines of symmetry-breaking. Now, if I followed you correctly before, you made a mention of symmetry-breaking as a mechanism involved in the creation of the universe.

I have a question for you;

If you think this is the case (which I cannot make my mind up on right now), then what symmetry existed at the big bang to actually break?

I mean, in other words, there must be in some assumption some kind of mathematical symmetry to speak about. Needless to say, this symmetry must have existed at the very first chronon of time, or even planck time if we wish to quantize the beginning.

Or are you assuming some pre-bang notion again, that there was some condition before the BB, in which case, if it was unstable, you must answer two more questions for me:

1) why was it unstable?

2) and how long had it been unstable for?

Perhaps for questions later, once one has evaluated possible answers to these questions, perhaps the priori question dominates everything, that being:

3) Where did all this ''unstable-ness'' come from?

Because in my mind, the idea of a pre-bang scenario does not answer, unless it can, where everything still came from.

In post 21, I qouted Smolin on the spin network I was approving in my own analysis:

Smolin states:

"We didn't know how, in the language we were working in, to put in the notion of causality" in LQG, Smolin says. Markopoulou Kalamara found that by attaching light cones to the nodes of the networks, their evolution becomes finite and causal structure is preserved. But a spin network represents the entire universe, and that creates a big problem. According to the standard interpretation of quantum mechanics, things remain in a limbo of probability until an observer perceives them. But no lonely observer can find himself beyond the bounds of the universe staring back. How, then, can the universe exist?'' [1]


Notice how also it preserves causality. This is the precurser of determinism, and hopefully, a global case. There is also a serious problem then with my model. If the matter field is not applied and we talk about high energy physics conditions, then causality could not be a quantum case. Causality must break down, since determinism is an occurance of geometrogenesis, according to all the facts.

This is another realization. It speaks of stating that determinism is something recorded by entropy. Entropy is a measure of physical changes in time. If this is correst, then radiation field where the matter field \chi=0 then there can be no passage of time. These so-called pure gravity theories then have still the looming question:

''Are pure gravity solutions of GR real physical phenomena?''

perhaps, if the above is also true, it might correspond alliances with the proof I gave that if the universe truely is timeless in a global sense, then conservation of energy cannot be measured mathematically. And if any measurement of energy cannot be translated in time (it's symmetrical conjugate quantity) then there can be no such thing as a fundamental entropy, only a late case, were clocks tick and matter field persist.

For starters, I can easily state that E=something, when E has not been defined, for instance, AN. Secondly, since I can define E as the energy of the universe under the very simple assumptions based from the WDW equation, then you can define the rest as it naturally unfolds.

(SORRY)

Going back to AN, missed something he said.

Yes I know AN, that changing E changes H. They both amount to the energy afterall. Stop trying to tell me things I don't know.

Also, that does not change the fact that it solves the problem, atleast by solving it with another problem.

Also, AN

''You write down a Hamiltonian (without justification or construction) and refer to it as a configuration space. No, a Hamiltonian is an operator on a space, not necessarily configuration space. ''

Well, you must have missed the r_{ij} which defines the distance between i and j. These can be considered ''points'' on a simple Hilbert space. The Hamiltonian is not supposed to be a representation of a configuration space only the former.

Clear?

When someone says to me ''a non-symmetric field'' I think along the lines of symmetry-breaking. Now, if I followed you correctly before, you made a mention of symmetry-breaking as a mechanism involved in the creation of the universe.

I have a question for you;

If you think this is the case (which I cannot make my mind up on right now), then what symmetry existed at the big bang to actually break?

I mean, in other words, there must be in some assumption some kind of mathematical symmetry to speak about. Needless to say, this symmetry must have existed at the very first chronon of time, or even planck time if we wish to quantize the beginning.

Or are you assuming some pre-bang notion again, that there was some condition before the BB, in which case, if it was unstable, you must answer two more questions for me:

1) why was it unstable?

2) and how long had it been unstable for?

Perhaps for questions later, once one has evaluated possible answers to these questions, perhaps the priori question dominates everything, that being:

3) Where did all this ''unstable-ness'' come from?

Because in my mind, the idea of a pre-bang scenario does not answer, unless it can, where everything still came from.

A Highly symmetric pre-bang state would be inherently unstable as there would be no entropic time arrow as we now experience.

http://en.wikipedia.org/wiki/Stephen_Hawking



In collaboration with Jim Hartle, Hawking developed a model in which the universe had no boundary in space-time, replacing the initial singularity of the classical Big Bang models with a region akin to the North Pole: one cannot travel north of the North Pole, as there is no boundary. While originally the no-boundary proposal predicted a closed universe, discussions with Neil Turok led to the realisation that the no-boundary proposal is also consistent with a universe which is not closed.


Once maximal entropy is reached for the universe there is also no arrow of time:

http://www.wired.com/wiredscience/2010/02/what-is-time/



Carroll: The arrow of time doesn’t move forward forever. There’s a phase in the history of the universe where you go from low entropy to high entropy. But then once you reach the locally maximum entropy you can get to, there’s no more arrow of time. It’s just like this room. If you take all the air in this room and put it in the corner, that’s low entropy. And then you let it go and it eventually fills the room and then it stops. And then the air’s not doing anything. In that time when it’s changing, there’s an arrow of time, but once you reach equilibrium, then the arrow ceases to exist. And then, in theory, new universes pop off.




When maximal entropy is reached in the universe there would be no more entropic arrow of time and that is also unstable. It is also a different type of symmetry condition. The universe then quantum jumps into a pre-bang condition or new universes are born depending on the theoretical model :shrug:

Since there is no arrow of time after maximal entropy and no arrow of time for the pre-bang era. There is no before or after for the universe. All versions would essentially exist simultaneously. :bugeye:

For starters, I can easily state that E=something, when E has not been defined, for instance, AN. Secondly, since I can define E as the energy of the universe under the very simple assumptions based from the WDW equation, then you can define the rest as it naturally unfolds.E is defined the moment you write down the Hamiltonian. They are not independent constructs, the Hamiltonian defines the energy.


And for last, you obviously can't understand the nature of the problem if you think the universes energy can be solved in terms of high perturbative expansions, since, the universe can no longer be a steady expansion, yet is now exponential as it increases proportionally and relativistically at magnitudes of the speed of light.Nice try, unfortunately in trying to say "You don't understand perturbative expansions and their role" you've shown you don't understand perturbative expansions and their role. The whole thing about the Lippmann-Schwinger equation (http://en.wikipedia.org/wiki/Lippmann%E2%80%93Schwinger_equation) involves altering a default Hamiltonian with a potential. S matrices are generally computed using expansions. In fact that's what Feynmann diagrams are, they are contributions to the perturbation. You're throwing in stuff to do with cosmology and expansion unnecessarily. The question is whether you're doing it because you think it's relevant or because you're trying to throw up a smoke screen.

Your waffling about bookwork expressions suggests it's a smoke screen. Let's consider one of them ....


According to a quantum approach, if \mathcal{O} is some observable, then the operator is stationary and the state is time-dependent if

\frac{\partial}{\partial t} < \mathcal{O} > = \frac{1}{i\hbar}< \{ \mathcal{O}, \mathcal{H} \}>Not true. What you've written down is the equation which describes the time evolution of an operator expectation value, yet you claim it's what follows if "the operator is stationary and the state is time-dependent". It's obvious to anyone who understands anything about this that if something is time independent then the time derivative vanishes so obviously what you say and the equation you provide don't quite gel. I imagine you've missed out a line or two from the source you're copying. What you really meant was "The equation for the time evolution of an operator's expectation value is....". If it's constant then \frac{\partial}{\partial t} \langle \mathcal{O} \rangle = 0.


If we take the derivative with respect to \rhoThere's no rho in the expression you gave. Again, I imagine you've skipped a few lines from where ever you're copying from. The fact you don't even realise what you're saying is obviously not in line with the expression you've given (seriously, no rho!) shows how mindlessly you're parroting this stuff. No one typing that off the top of their head would repeatedly make such mistakes.


and divide both sides of the equation with the derivative in respect of our time derivative,

\rho = T_{\alpha \beta} \chi^{\alpha}\chi^{\beta}That's not even a coherent sentence.


then we would have after quantizing our equationThe time dependence equation was already quantised. Don't you see the \hbar there? That's what it's for.


would yield, this time including our time derivative

\frac{\partial \rho}{\partial t} = \frac{1}{i\hbar} \{ H, \rho \}This is just the Heisenberg equation of motion for any operator. Seriously, it's such a basic result it's covered in any lecture course on quantum mechanics which covers time dependence and operators. The expression you equate \rho to has nothing to do with it, you've just written down an identity in the Heisenberg picture.


This can be solved by Ehrenfest's Theorem.No, Ehrenfest's theorem doesn't 'solve' that. It implies a closely related expression (more specifically the original time derivative equation you wrote down), since as stated immediately on its Wiki page (http://en.wikipedia.org/wiki/Ehrenfest_theorem) it is that equation with an additional term. Ehrenfest's theorem doesn't 'solve' a differential equation, it tells you how to quickly and easily construct one!


Best of all, this equation works for a mixed state, just like a matter field with many particles.Best of all it's a very basic and core result which you couldn't even state properly!


As for your theory personally, as arrogant as it might sound, I don't agree with but I think it is a promising approach for random physics theory. For people like me, we sit in the lonely camp outside the maintraim still believing in Einstein's dream.You sit in the 'lonely camp' because you refuse to learn anything properly. All you do is copy equations you don't understand and pass off other people's explanations and algebra as your own understanding.

I absolutely guarantee you'll never contribute to 'Einstein's dream' if you continue in this way.


Yes I know AN, that changing E changes H. They both amount to the energy afterall. No, the expectation value of the Hamiltonian is the macroscopic energy and the state energy is the eigenvalue of the Hamiltonian associated to the eigenstate being considered. You can construct E from H but not the other way around.


Stop trying to tell me things I don't know.Sorry but you don't know so much that it's hard to say anything without telling you something you don't know.


Also, that does not change the fact that it solves the problem, atleast by solving it with another problem.No, it doesn't.


Also, AN

''You write down a Hamiltonian (without justification or construction) and refer to it as a configuration space. No, a Hamiltonian is an operator on a space, not necessarily configuration space. ''

Well, you must have missed the r_{ij} which defines the distance between i and j. These can be considered ''points'' on a simple Hilbert space. The Hamiltonian is not supposed to be a representation of a configuration space only the former.

Clear?Wrong again. The terms in the Hamiltonian, r_{ij}, quantify the distance between particles. Obviously you don't see the difference there. The particles exist at points in a space. This space has an inner product on it and so you can promote it to a Hilbert space. The distances between points can be obtained via the use of the inner product but the output of the inner product is not an element in the Hilbert space so the distances do not belong to the space. Furthermore the Hamiltonian can depend on these distances but that doesn't mean it's in a Hilbert space. It acts on elements of the Hilbert space and it can depend on properties of states in the Hilbert space.

Also, you're the one who said "the configuration space looks like... [expression for Hamiltonian]" so if you're now saying the Hamiltonian isn't supposed to be a representation of a configuration space then you're contradicting yourself. Which statement are you going to stand by?

Given you've been rereading my post and retorting anything you can when you think you've got a retort I'll assume you accept that the other points I raised are valid.

khan, if you haven't realised it yet if you're looking for informed discussion you're not going to get it from Reiku. Of course if you're looking for someone to throw buzzwords back and fore with and convince yourself you're 'living Einstein's dream' then knock yourself out.

khan, if you haven't realised it yet if you're looking for informed discussion you're not going to get it from Reiku. Of course if you're looking for someone to throw buzzwords back and fore with and convince yourself you're 'living Einstein's dream' then knock yourself out.




It is VERY tempting for me to take poetic license with buzzwords but I actually hope to learn from an informed discussion, yes. There is no nearby university where I can go to learn about tensor calculus, so, for the last few years, I have built up a large collection of books on the subject:

Leonard Susskind
The Black hole War

Kip S. Thorne
Black Holes & Time Warps

Lieber,Lillian R.
The Einstein Theory Of Relativity (1945)

http://www.archive.org/details/einsteintheoryof032414mbp

Ray A. d'Inverno,
Introducing Einstein's Relativity

Bernard F. Schutz,
A First Course in General Relativity

Robert M. Wald,
General Relativity,

Charles W. Misner, Kip S. Thorne, and John A. Wheeler,
Gravitation

Alan P. Lightman
William H. Press
Richard H. Price
Saul A. Teukolosky
problem book in relativity and gravitation

Paul A. Dirac,
General Theory of Relativity

David C. Kay,
Schaum's Outline of Tensor Calculus

Nils K. Oeijord
The Very Basics of Tensors

I have not read all of these books yet but I have them and I plan to keep reading them until I can master the concepts within :D

I made it through lecture 11 of this great online course:

http://www.youtube.com/playlist?list=PL6C8BDEEBA6BDC78D

Multivariable vector calculus is also extremely helpful to me:

http://www.youtube.com/playlist?list=PL4C4C8A7D06566F38

I wish to learn the facts of the universe ...and the facts of the universe are tensors.


...

Quantify the distance, define a distance, if this is about a single word, then so be it have it your way.

Given you've been rereading my post and retorting anything you can when you think you've got a retort I'll assume you accept that the other points I raised are valid.

Of course, hasn't that been the way with us since the dawn of time?

E is defined the moment you write down the Hamiltonian. They are not independent constructs, the Hamiltonian defines the energy.

But the Hamiltonian defines E as you said, then a vanishing E directly effects the Hamiltonian. Am I missing something?

Nice try, unfortunately in trying to say "You don't understand perturbative expansions and their role" you've shown you don't understand perturbative expansions and their role.

Yea, and I was under the impression perturbative expansions are not necesserily assumed to be exponential... are there any cosmological cases you can inform me about?

In fact that's what Feynmann diagrams are, they are contributions to the perturbation. You're throwing in stuff to do with cosmology and expansion unnecessarily. The question is whether you're doing it because you think it's relevant or because you're trying to throw up a smoke screen.

Well let me explain.

I am throwing these things in because I find them necessery, or ''relevant'' as you put it. Should there be a potential?

Well yes there should, the cosmological application of a potential often comes in the form a^2-g^2a^4. This potential is often seen in the Hartle-Hawking Cosmological models.

Why is expansion important? Well, as the universe expands, more energy is released into the vacuum. If my theory so far dictates that energy is not conserved in a universe, then the implication that the universe is now receeding faster than light is an indication the universe is using up more and more energy at an exponential rate. (The latter here was actually hypothesized by Michio Kaku). Secondly if it is releasing energy due to its superluminal expansion, then the energy increases but there is no time to measure it still because of the vanishing time derivative in the WDW equation, which you will notice, has no place in the Lippmann-Schwinger equation.

The only way to calculate time, would be to take the energy density of a universe \rho=T_{ab}\phi^a \phi^b use my idea that \bold{x}_i is the sum of all four-vector velocities of the field, then when a massless field obtains mass, we have

\rho \bold{x}_i =T_{ab}\vec{\chi}^a \vec{\chi}^b \cdot x^{\mu}_{i}\tau_i

This expresses the matter field as calculated in such a way it describes the world lines, of remember, the equation I first defined as \dot{\chi}. This can be seen most effectively in

\frac{\partial \rho}{\partial t} = T_{ab} \dot{\chi}^a \dot{\chi}^b

which when quantized,which is what was implied originally, yield your quantum terms

\frac{\partial \rho}{\partial t} = \frac{1}{i\hbar} \{H,\rho \}

It's obvious to anyone who understands anything about this that if something is time independent then the time derivative vanishes so obviously what you say and the equation you provide don't quite gel.

You've not read me right. I said time-dependant, not time independant.

The whole point is to find a way were the time derivative does not vanish. Quantize a field, let real matter particles act as clocks. What good is approaching a theory where the time derivative vanishes, thus only to end up with the theory you are trying to avoid?


ps. You said that when I said R_ij is the distance between particles, you said that was wrong, then explained it was the distance between particles. Confused...

It is VERY tempting for me to take poetic license with buzzwords but I actually hope to learn from an informed discussion, yes. There is no nearby university where I can go to learn about tensor calculus, so, for the last few years, I have built up a large collection of books on the subject:

Leonard Susskind
The Black hole War

Kip S. Thorne
Black Holes & Time Warps

Lieber,Lillian R.
The Einstein Theory Of Relativity (1945)

http://www.archive.org/details/einsteintheoryof032414mbp

Ray A. d'Inverno,
Introducing Einstein's Relativity

Bernard F. Schutz,
A First Course in General Relativity

Robert M. Wald,
General Relativity,

Charles W. Misner, Kip S. Thorne, and John A. Wheeler,
Gravitation

Alan P. Lightman
William H. Press
Richard H. Price
Saul A. Teukolosky
problem book in relativity and gravitation

Paul A. Dirac,
General Theory of Relativity

David C. Kay,
Schaum's Outline of Tensor Calculus

Nils K. Oeijord
The Very Basics of Tensors

I have not read all of these books yet but I have them and I plan to keep reading them until I can master the concepts within :D

I made it through lecture 11 of this great online course:

http://www.youtube.com/playlist?list=PL6C8BDEEBA6BDC78D

Multivariable vector calculus is also extremely helpful to me:

http://www.youtube.com/playlist?list=PL4C4C8A7D06566F38

I wish to learn the facts of the universe ...and the facts of the universe are tensors.


...

Well, I kind of learned something from you.

It had escaped my notice originally how important the triangle inequality was, when you started to speak about ''hidden gems'' concerning heisenbergs uncertainty principle and the inequality.

It was until afterwards I realized it was important since the spin network relies on keeping the inequality in its phase space.

Quantify the distance, define a distance, if this is about a single word, then so be it have it your way.No, it obviously isn't 'about a single word', it's about many words. Seriously, are you so desperate to reply with something that you'll misrepresent me on the same page as the post in question? I clearly explain in detail your many mistakes, including multiple terminology related ones, so to say it's about a single word is either moronic or trolling. There isn't any other option. Either you utterly fail to understand basic English narrative (in which case you have no hope of understanding published papers) or you're being deliberately obtuse.


Of course, hasn't that been the way with us since the dawn of time?Just to check a few examples, so you accept your 'solution' involves a geometry? You accept no such quantum system exists with the time parametrisation you gave.You accept the 'singularity' has nothing to do with space-time? Do you accept Ehrenfest's theorem doesn't 'solve' what you claim it did? Do you accept you just stated the Heisenberg equation of motion?

Explicit yes or no answers please.


But the Hamiltonian defines E as you said, then a vanishing E directly effects the Hamiltonian. Am I missing something?You make it sound like E is the fundamental parameter. It isn't. The Hamiltonian of a system is what it is. The energy of a system is defined by the expectation of the Hamiltonian in that state, ie E = \langle H \rangle_{\psi} \equiv \frac{\langle \psi | H | \psi \rangle}{\langle \psi | \psi \rangle}. Changing state may or may not change E. It won't change H. Although in the Heisenberg picture operators, rather than states, are time varying the Hamiltonian is constant. Can you tell me why? It relates to something you've said.



Yea, and I was under the impression perturbative expansions are not necesserily assumed to be exponential... are there any cosmological cases you can inform me about?What are you on about?! The perturbations we're talking about here have nothing to do with cosmology or exponential expansion in space-time. Yes, there's talk of perturbations and expansions pertaining to space-time in things related to the WDW equation but the perturbative expansions I gave examples of have nothing to do with them. You're showing you're just buzzword matching. Come on, try a little harder.


I am throwing these things in because I find them necessery, or ''relevant'' as you put it. Should there be a potential?Sorry but they aren't. I gave clear context and you've just thrown in something you might find if you googled for "Wheeler-De Witt equation, perturbations". In fact I just did precisely that and low and behold it returns things related to metric perturbations, not the sort I'm talking about here.

If you really want to do science you need to be more than a glorified search engine and word comparer.


Well yes there should, the cosmological application of a potential often comes in the form a^2-g^2a^4. This potential is often seen in the Hartle-Hawking Cosmological models.But the parameter isn't time, as you stated.


Why is expansion important?You're trying to grandstand. There's no need for you to explain the importance of expansion in cosmology to me. Rather than throw up another smoke screen try to actually justify your quantitative claims.


If my theory so far dictates that energy is not conserved in a universe, then the implication that the universe is now receeding faster than light is an indication the universe is using up more and more energy at an exponential rate.Firstly you don't have a 'theory', not in the scientific sense. You have something which hardly qualifies as a dubious hypothesis. It's a random guess.

Secondly you haven't considered any energy conservation. You haven't shown a violation of any of the energy conservation derivations. To use the theoretical physics phrase (so you can go Google) you haven't shown an anomalous current exists.

Thirdly the phrase "The universe is now receding faster than light" is ambiguous and poorly defined. I know what you're referring to but that isn't an excuse for being bad at explaining yourself.

Fourthly you haven't shown any exponential expansion rate. Expansion doesn't mean exponential. There's numerous 'regimes' of expansion in cosmology, depending on various factors like energy and matter densities.


(The latter here was actually hypothesized by Michio Kaku). But he did some actual work to reach the conclusion. If I just said

"Under the closure of the 3-form dH = 0 we obtain an exponential bifurcation of the Higgs potential, \mu \to \mu_{\pm}e^{\pm iEt}, which implies black hole entropy is proportional to its surface area"

then I wouldn't make it more valid by saying "Hawking agrees with that last result".


Secondly if it is releasing energy due to its superluminal expansion, then the energy increases but there is no time to measure it still because of the vanishing time derivative in the WDW equation, which you will notice, has no place in the Lippmann-Schwinger equation.Firstly you haven't justified any of that. Secondly time independence in a quantum system doesn't imply no dynamics occur. Dynamic equilibria of particle interactions are time invariant but dynamics occur all the time. For example, the quantum field theoretic vacuum's properties are time independent but there's always a frenzy of activity going on. Thirdly the L-S equation doesn't negate time dependence.


The only way to calculate time, would be to take the energy density of a universe \rho=T_{ab}\phi^a \phi^b use my idea that \bold{x}_i is the sum of all four-vector velocities of the field, then when a massless field obtains mass, we have

\rho \bold{x}_i =T_{ab}\vec{\chi}^a \vec{\chi}^b \cdot x^{\mu}_{i}\tau_i

This expresses the matter field as calculated in such a way it describes the world lines, of remember, the equation I first defined as \dot{\chi}.Reiku, do you really think I (or anyone who didn't sleep through high school) believes you did any such calculations? Firstly (notice how I keep listing multiple mistakes you make in just a single paragraph?) the expression you give for density is not a fully general or even clearly defined one. Secondly your definition of x_{i} is clumsy and sounds an awful lot like the definition of \mathbf{X} given here (http://en.wikipedia.org/wiki/Energy_condition#Some_observable_quantities). Looks like another example of you parroting something, trying to change it and mangling it into nonsense. So much for it being your idea. Not only is it not original, it's essentially plagiarised. If you're going to plagiarise, at least get it right. Thirdly your equation is mathematically meaningless since the index structure isn't consistent. Just like you have to get units right you have to get indices right and you have a spare \mu on the right hand side. You have a similar issue with the i index, your notation is ambiguous.

You keep making such mistakes, failing to make simple things consistent. It's a sign you're copying without understanding. Sure, everyone makes a slip up here and there but the frequency you do it is too high to be excusable as slip ups.


This can be seen most effectively in

\frac{\partial \rho}{\partial t} = T_{ab} \dot{\chi}^a \dot{\chi}^b How did you get that from the previous expression? Let's see the step by step derivation.


which when quantized,which is what was implied originally, yield your quantum terms

\frac{\partial \rho}{\partial t} = \frac{1}{i\hbar} \{H,\rho \}Except it doesn't, not from your expression. As I just explained, which makes me wonder why on Earth you're repeating a discredited approach, that equation is the Heisenberg equation for any time dependent operator. The problem is you have gone from a scalar quantity to an infinite dimensional operator, as well as pluck a Hamiltonian from nowhere.

Now while it might be possible to construct a GR system from some metric, construct an energy condition, deduce it's equations of motion, upgrade the fields to quantum fields and then obtain such an equation I am confident it's the sort of thing which takes a dozen papers and so much eye watering algebra you could see it from space. This is the realm of Hawking's work, stuff which is extremely complex. You don't just say "And you quantise" and magically a GR equation into one of the central QM equations.

You're just throwing out equations and expressions and hoping no one will call you on it. If you could really do this sort of GR or QFT you'd know just how ridiculous it is for you to be pretending to understand it based on just some pop science reading and a mediocre high school grasp of mathematics and physics.


You've not read me right. I said time-dependant, not time independant.Okay, I misread it. However, on rereading it I notice you made a different mistake. You said "if O is some observable, then the operator is stationary and the state is time-dependent if [equation]". The equation tells you how the expectation value varies in time. It applies when an operator is stationary and the state time dependent and is applies when the complete opposite is true. It's a picture independent equation. In the Dirac picture the states vary and the operators are fixed while in the Heisenberg picture it's the reverse. That's why the equation for the time dependence of an operator is the Heisenberg equation of motion. It isn't true in the Dirac picture.

The two different pictures are important and pretty simple concepts, covered almost immediately when covering operators. I guess you missed that YouTube video...


The whole point is to find a way were the time derivative does not vanish. Quantize a field, let real matter particles act as clocks. What good is approaching a theory where the time derivative vanishes, thus only to end up with the theory you are trying to avoid?What good is making stuff up and mangling other people's work, in an attempt it off as your own understanding? What good is just being dishonest and spouting equations and terminology you don't understand in an attempt to deceive people online?


ps. You said that when I said R_ij is the distance between particles, you said that was wrong, then explained it was the distance between particles. Confused...No, I said that the Hamiltonian (and thus terms in the Hamiltonian, including r_{ij}) is not a configuration space or points in a configuration space or anything like that. It's an operator which acts on elements of a space, which may or may not be a configuration space for some system. I never said the r_{ij} weren't distances. It would be much easier if you understood what a Hilbert space it, what states are, what operators are, what expectation values are, what any of this stuff is.

Let's do this one at a time shall we.

you stated a few things here: ''so you accept your 'solution' involves a geometry? You accept no such quantum system exists with the time parametrisation you gave.You accept the 'singularity' has nothing to do with space-time? Do you accept Ehrenfest's theorem doesn't 'solve' what you claim it did? Do you accept you just stated the Heisenberg equation of motion? ''

Let's start with, why you think it involves a geometry?

Just on the side while you answer my previous question:

you said near the end

''No, I said that the Hamiltonian (and thus terms in the Hamiltonian, including ) is not a configuration space or points in a configuration space or anything like that.''

But you stated something I stated and said it was wrong. Even if this is not what you implied, you really need to use your imagination AN. If two particles are seperated by a distance r_ij then the two particles must have positions in space somewhere. In a very loose, but still correct statement, that if particles are described by a Hilbert Space as I have demonstrated then we must be implying some kind of configuration space.

Just also to clear up a few loose ends:

''Reiku, do you really think I (or anyone who didn't sleep through high school) believes you did any such calculations? ''

In the paragraph you have stated, I was quite aware of the density relationship . Is there any reason why my own relationship does not hold? If so I will quite willingly forget those relationships. But I can assure you right now that x_i is not X since x_i is the four velocity. The four velocity (summed over all particles given by i) multiplied by the density gives you your matter field acting like a unit timelike vector. As our original field \phi acted on x^{\mu} \tau}, it created \chi the inertial matter field. Thus from

\rho = T_{ab}\phi^a\phi^b

multiply by the four velocity gives

\rho x_i = T_{ab}\phi^a\phi^b (x^{\mu}\tau)

The right hand side turns into T_{ab} \chi^a \chi^b

.... and here I realized I've made a mistake, I've dropped a term on the right hand side

because from there it should be, divide by \partial t on both sides and taking partial \rho gives

\frac{\partial \rho x_i}{\partial t}= \frac{ T_{ab} \chi^a \chi^b}{\partial t}

Which means my assumptions on Heisenberg equation don't apply. Ignore it now AN.

You say \chi = \tau and then have a V which is purely a function of \tau, ie time. No such quantum mechanical system exists.

Well, considering I never reparamaterized any of my equations and I mentioned it just for the sake of stating some possible solutions to the WDW equation, I will find the paper....


....right http://arxiv.org/PS_cache/hep-th/pdf/9503/9503073v2.pdf

Page 8-11 should suffice.

Let's do this one at a time shall we.

you stated a few things here: ''so you accept your 'solution' involves a geometry? You accept no such quantum system exists with the time parametrisation you gave.You accept the 'singularity' has nothing to do with space-time? Do you accept Ehrenfest's theorem doesn't 'solve' what you claim it did? Do you accept you just stated the Heisenberg equation of motion? ''

Let's start with, why you think it involves a geometry?

OOOooohhh right. I read back on your posts (end up ignoring half of it because you tend to write so much), that

via a series of unjustified non-sequitors, that you end up with a result which doesn't involve geometry. You used the SC metric! You made an explicit reference to a geometry.

That's ok.

You see, we haven't even applied the Hilbert Space or any spin networks. I recall reading that r_ij is also a metric, a special kind of one, but that must have missed you as well. Niether metric are related, as far as I can tell.

I qoute Markoupoulou

''Just as there are no waves in the
molecular theory, we will likely not find geometric degrees of freedom in the fundamental theory. By analogy with known physics, we should expect that the quantum theory of gravity is not a theory of geometry. I must emphasize that no geometry does not mean discrete or fuzzy geometry. It means that the most primary aspects of geometry, such as the notion of \here" and \there" will cease to make sense. In fact, we have been grappling with no geometry for a while, in the traditional quantum gravity settings.''

Now, quantum graphity actually admits metric solutions, the things which involve space, matter and geometry http://arxiv.org/pdf/0801.0861v2.pdf . The approach however, even though I have adopted and Markoupoulou uses, argue that geometry does not fundmantally.

Keep in mind also, that fundamentally it is argued that geometry does not exist, not that it does not exist at all. The world of high energy physics is related to permutation symmetries, no locality and no subsystems. Low energy states are concerned with geometry and subsystems and the like.

In my original representation to you, I used the LS-equation to solve the original energy hamiltonian of the universe with potential. I had no explicitely stated yet that this specific equation would describe no geometry. That is only achieved when you would begin to model your theory with a Hilbert Space. In this space, as Fotini puts it:

''Information before geometry. Having raised the possibility that geometry does not exist at the fundamental level, we now need to find a way to do physics without geometry. This may appear hard because all our physics is done with geometry. But we can use a relational and information theoretic language.''

An example is that she considers a finite relational universe with N constituents, a bit like my (summing over all the particles making a field approach) which she models as a network of N nodes (a,b...=1) with a Hilbert Space \mathcal{H}_{ab} attached to each link (ab). It is this model I am trying advocate.

I think it is the correct approach because it sufficiently describes high energy physics, low energy, geometry stuff exists, we know this. It is once you apply the following approaches could we possibly achieve some kind of quantized theory involving no geometry.

There is more I see, you said I pulled a hamiltonian from no where in the Heisenberg equation. Well, no, not really.

If you want to know where I had been heading with that, is that there is such a thing as a ''fundamental Hamiltonian'' which describes high energy states. Obviously it was fundamental because, as you yourself said, ''didn't you notice the hbar in there?''

Markoupoulou remarks in her own work

''It should now be clear that there are two possible notions of time: the time related to the g00 component of the metric describing the geometry at low energy and the time parameter in the fundamental microscopic Hamiltonian.''

So why should I not plug in a Hamiltonian in there? It was there to describe individual particles anywhere, world lines in fact to be more precise.

In an approach according to a paper I linked previously in the past, it was customary as a reparamaterization of the Wheeler de Witt equation to reconfigure time as \chi = \tau, so the matter field was now acting as a clock.

The Total Hamiltonian for a universe is given by the WDW-Hamiltonian

H_{WDW}=H_T=H_{\phi, h_{\mu \nu}} - H_0 [1]

where h_{\mu \nu} is a metric perturbation. The equation of interest is

|\psi> = |\phi_a> |\chi_{\phi, h_{\mu \nu}}> [2]

Using a proceedure of seperation of variables, we obtain

(H+V(a)|\psi_a> = E|\psi> [3]

and

(H + V(\chi)_{\phi h_{\mu \nu}})|\chi_{\phi, h_{\mu \nu}}> = E|\chi_{\phi h_{\mu \nu}}> [4]

The potential terms in these equations are equal to

V(a) = a^2-g^2a^4 [5]

and

V(\chi) = \chi^2 - g^2\chi^4 [6]

Going back to eq. [4] we have

(H+(\chi^2-g^2\chi^4))|\chi_{\phi, h_{\mu \nu}}> = E|\chi_{\phi h_{\mu \nu}}> [7]

Because of continuity of eigenvalues, one should state that as (\chi_{\phi, h_{\mu \nu}}) \rightarrow \phi then the interaction term (\chi^2-g^2c^4) \rightarrow 0 goes to zero.

A potential solution to this equation is

|\psi> = \phi + \frac{1}{E - H_0} \cdot (\chi^2- g^2\chi^4)|\psi> [8]

where \cdot is multiplication. Whilst this is a potential solution, a problem exists. A serious problem in the form of a singularity exists in (E-H_0) since E is an eigenvalue of H_0.

There is one distinct way of making this singularity to normally disappear. One way is to make the denominator slightly complex i\epsilon. Instead, I am going to use a different approach.

To avoid the singular existance of this mathematical object, we are going to substitute E for a result of the Schwartzchild Metric

Mc^2 - \frac{Gm^2}{2R} [9]

This changes our equation in such a drastic way, it rids us of the singularity in our equation. No longer does (E-H_0) hold, because the null energy condition states that as M=0 all we are left with is the metric.

So we have a correspondance between (Mc^2 - \frac{Gm^2}{2R}) and H_0 in which if you imply a nullified energy condition you obtain a solution to avoid the singularity problem.

Interestingly, it does not only imply that our matter field \chi no longer has any mass, but it also means we have no radiation fields either.

Let's look at the original Hamiltonian in a different way, now accounting for systems of many particles if one desired but for simplicity we will assume particles i and j.

For N-particles (2 in our case), we can have

\{ \sum_{i} H(i) + \sum \frac{1}{r_{ij}} \} = E \psi

where r_{ij} calculates the distance between i and j. If we represent this in a Hilbert Space, the configuration space looks like

H= \sum_i H_i + \sum_{k \in I} h_k

where h_k is a hermitian operator. I is the set of interactions \{i,j\} \equiv k and naturally can form a direct tensor Hilbert space \mathcal{H}_3 = \mathcal{H}_1 \otimes \mathcal{H}_2.

This is already beginning to be like a theory which deals with no geometry. Indeed, a Hilbert Space are often called ''points'' which describe abstractly the configuration space. This is the similar approach Markoupoulou attempts to make in her Graphity model. She takes Hilbert Spaces and describes their interactions in such a model without resorting to geometry.

The equation H= \sum_i H_i + \sum_{k \in I} h_k is actually an equation Markoupoulou uses very very early on in her paper on quantum graphity. It is a simple approach, and has similar undertones to \{ \sum_{i} H(i) + \sum \frac{1}{r_{ij}} \} = E \psi where r_{ij} calculates the distance between i and j.

Let us first of all, describe the interaction k = \{ij \} where i and j are our particle system. (Can be thought of as a configuration space). Let us now state that the interaction is determined by a potential governing a force between the two particles.

V= \sum^{N-1}_{i=1} \sum^{N}_{i+1} g(r_{ij})

The calculation of the interaction forces on all N-particles due to pairwise interactions involves a maximum of \frac{N(N-1)}{2} contributions. In markoupoulou's work, K_N is the complete graph onN vertices, i.e., the graph in which there is one edge connecting
every pair of vertices, so that there is a total of N(N- 1)=2 edges and each vertex has degree N- 1 [1]. So what I have done is explicitely describe that there is a force between two particles in my case, (I have defined the set of interactions) and in Markoupoulou's we can see that her total space state of the system is \mathcal{H} = \otimes \frac{N(N -1)}{2} \mathcal{H}_{ab}.

So for now, what I really require is a bit of imagination. A certain matter field in the low energy epoch could satisfy a flux of time. But what we will find at the high energy state, is a place where my matter field vanishes, including the geometrical space - time is a consequence of real bradyonic particles. The universe could have a time, if summing each of these particles up and allowing them to have clocks, in both my vision and Julian Barbours, then you can say only geometric time exists, since in spin networks, space exists but not spacetime.

[1] http://fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf

[1] http://fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf


Thanks for the interesting links Reiku.

Keep up the good work :bravo:

The equation H= \sum_i H_i + \sum_{k \in I} h_k is actually an equation Markoupoulou uses very very early on in her paper on quantum graphity. It is a simple approach, and has similar undertones to \{ \sum_{i} H(i) + \sum \frac{1}{r_{ij}} \} = E \psi where r_{ij} calculates the distance between i and j.

Let us first of all, describe the interaction k = \{ij \} where i and j are our particle system. (Can be thought of as a configuration space). Let us now state that the interaction is determined by a potential governing a force between the two particles.

V= \sum^{N-1}_{i=1} \sum^{N}_{i+1} g(r_{ij})

The calculation of the interaction forces on all N-particles due to pairwise interactions involves a maximum of \frac{N(N-1)}{2} contributions. In markoupoulou's work, K_N is the complete graph onN vertices, i.e., the graph in which there is one edge connecting
every pair of vertices, so that there is a total of N(N- 1)=2 edges and each vertex has degree N- 1 [1]. So what I have done is explicitely describe that there is a force between two particles in my case, (I have defined the set of interactions) and in Markoupoulou's we can see that her total space state of the system is \mathcal{H} = \otimes \frac{N(N -1)}{2} \mathcal{H}_{ab}.

So for now, what I really require is a bit of imagination. A certain matter field in the low energy epoch could satisfy a flux of time. But what we will find at the high energy state, is a place where my matter field vanishes, including the geometrical space - time is a consequence of real bradyonic particles. The universe could have a time, if summing each of these particles up and allowing them to have clocks, in both my vision and Julian Barbours, then you can say only geometric time exists, since in spin networks, space exists but not spacetime.

[1] http://fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf

Now I made mention before that r_{ij} was in fact a metric - well actually, that was not quite true. It is what mathematicians define as a semi-metric. Let's see why

Let X be a set of pair points i and j one gets the distance between them by ij.

Interestingly this all comes back to the Triangle Inequality. In fact, a semi-metric is allowed to violate the Triangle Inequality. So only certain solutions for the metric will allow a complete theory of spin networks in a quantum loop gravity framework (coupled with Geometrogenesis), since spin network (which is at the core of LQG) relies on pin-pointing the states of particles obeying the triangle inequality ie. a must be less than or equal to b+c, b less than or equal to a+c, and c less than or equal to a+b.

Now I made mention before that r_{ij} was in fact a metric - well actually, that was not quite true. It is what mathematicians define as a semi-metric. Let's see why

Let X be a set of pair points i and j one gets the distance between them by ij.

Interestingly this all comes back to the Triangle Inequality. In fact, a semi-metric is allowed to violate the Triangle Inequality. So only certain solutions for the metric will allow a complete theory of spin networks in a quantum loop gravity framework (coupled with Geometrogenesis), since spin network (which is at the core of LQG) relies on pin-pointing the states of particles obeying the triangle inequality ie. a must be less than or equal to b+c, b less than or equal to a+c, and c less than or equal to a+b.

Now, in fotini's model, if G is some graph in this spin network space of states. A Hamiltonian operator H will assign an energy E(G) = <\Psi_G|H|\Psi_G> to this graph.

The reason why fotini can describe it this way (she doesn't mention this) along with a few other things I have brought up so far, if A(G) are adjacent vertices and E(G) is the set of the edges, then it satisfies

(i,j) \in E(G)

Each vertex represents a spin-state on the graph. Thus we will begin to see Fotini's approach, that to each vertex i \in A(G) there can be associated a Hilbert Space

H_G = \otimes_{i \in A(G)} \mathcal{H}_i = \mathbf{C}^{2}^{\otimes N}

Which takes on remarkable similarities to Fotini's equation describing the total space state. Indeed, the equation above describes the total number of vertices in our Hilbert Space.

Thus, we come back to a familiar garl. The distance between two particles i and j are vertices i,j \in A(G) in fact apply to the least action principle; it will define a graph geodesic between these two points.

And this is why her model works.

Interestingly this all comes back to the Triangle Inequality. In fact, a semi-metric is allowed to violate the Triangle Inequality. So only certain solutions for the metric will allow a complete theory of spin networks in a quantum loop gravity framework (coupled with Geometrogenesis), since spin network (which is at the core of LQG) relies on pin-pointing the states of particles obeying the triangle inequality ie. a must be less than or equal to b+c, b less than or equal to a+c, and c less than or equal to a+b.



Minkowski space has a reverse triangle inequality.

http://en.wikipedia.org/wiki/Minkowski_space#Reversed_triangle_inequality


Some scientists believe that in order to truly understand and resolve the twins paradox, the general theory of relativity is needed.

http://www.youtube.com/watch?feature=player_embedded&v=jlJNsRZ4WxI

5:15 of this video

Now, in fotini's model, if G is some graph in this spin network space of states. A Hamiltonian operator H will assign an energy E(G) = <\Psi_G|H|\Psi_G> to this graph.

The reason why fotini can describe it this way (she doesn't mention this) along with a few other things I have brought up so far, if A(G) are adjacent vertices and E(G) is the set of the edges, then it satisfies

(i,j) \in E(G)

Each vertex represents a spin-state on the graph. Thus we will begin to see Fotini's approach, that to each vertex i \in A(G) there can be associated a Hilbert Space

H_G = \otimes_{i \in A(G)} \mathcal{H}_i = \mathbf{C}^{2}^{\otimes N}

Which takes on remarkable similarities to Fotini's equation describing the total space state. Indeed, the equation above describes the total number of vertices in our Hilbert Space.

Thus, we come back to a familiar garl. The distance between two particles i and j are vertices i,j \in A(G) in fact apply to the least action principle; it will define a graph geodesic between these two points.

And this is why her model works.

You truly are a crazy man. You've managed to string together a string of mathematical conjectures together with only tangential relevance...almost as if they were linked together on some page in a web-like fashion in a freely accessible source.

Let's start with, why you think it involves a geometry? What about my last answer to this did you not understand? You use the Schwarzchild metric. That's a geometry!


''No, I said that the Hamiltonian (and thus terms in the Hamiltonian, including ) is not a configuration space or points in a configuration space or anything like that.''

But you stated something I stated and said it was wrong. Even if this is not what you implied, you really need to use your imagination AN. If two particles are seperated by a distance r_ij then the two particles must have positions in space somewhere. In a very loose, but still correct statement, that if particles are described by a Hilbert Space as I have demonstrated then we must be implying some kind of configuration space.You're simply not reading what I say. Or you just don't understand basic meaning of terminology like 'Hamiltonian'.

I know you can describe points in space using a Hilbert space, since you can define the dot product as your inner product. However, you said the Hamiltonian is described as a configuration space. No, th Hamiltonian ACTS on a space, which may sometimes (but not always) be a configuration space.

You're responding to things I never said. Whether it's an attempt to make it seem to the lay person you're retorting my criticisms or you're just plain ignorant I don't know.


Just also to clear up a few loose ends:

''Reiku, do you really think I (or anyone who didn't sleep through high school) believes you did any such calculations? ''

In the paragraph you have stated, I was quite aware of the density relationship . Is there any reason why my own relationship does not hold? If so I will quite willingly forget those relationships. But I can assure you right now that x_i is not X since x_i is the four velocity. The four velocity (summed over all particles given by i) multiplied by the density gives you your matter field acting like a unit timelike vector. As our original field \phi acted on x^{\mu} \tau}, it created \chi the inertial matter field. Thus from

\rho = T_{ab}\phi^a\phi^b

multiply by the four velocity gives

\rho x_i = T_{ab}\phi^a\phi^b (x^{\mu}\tau)

The right hand side turns into T_{ab} \chi^a \chi^b

.... and here I realized I've made a mistake, I've dropped a term on the right hand side

because from there it should be, divide by \partial t on both sides and taking partial \rho gives

\frac{\partial \rho x_i}{\partial t}= \frac{ T_{ab} \chi^a \chi^b}{\partial t}

Which means my assumptions on Heisenberg equation don't apply. Ignore it now AN.Jesus, where to start. As I said and which you obviously don't understand, your index structure isn't right. Nor does the third expression follow from the second. Nor does your last expression make sense. You don't 'divide by \partial t', dear god that isn't what differentiation is about! It seems you can't even take partial derivatives properly, you think there's division involved. This just shows how ridiculous your claims of doing work in this stuff is, you can't do things expected of 1st years yet you're claiming to be coming up with solutions to research level quantum cosmology!

You really have something wrong with you if you think you're doing anything other than being massively dishonest. And even if you're aware you're being dishonest the fact you continue to do it, despite being exposed as a hack repeatedly, says something else is wrong with you personality-wise.


Well, considering I never reparamaterized any of my equations and I mentioned it just for the sake of stating some possible solutions to the WDW equation, I will find the paper....


....right http://arxiv.org/PS_cache/hep-th/pdf/9503/9503073v2.pdf

Page 8-11 should suffice.Firstly you've done what you often do and that's show where you're getting all your equations from. Just as when you linked to that YouTube lecture which contained all the equations you were spouting, right down to dubious notation, you've shown your hand by linking to that paper.

The paper gives the proper context of all the stuff you've been throwing out. Your problem is you don't understand it so you don't know how to give snippets of it in a way which makes sense, hence why your 'results' are all over the place.

The potential is a functional of the scale factor, a not uncommon notion in cosmology because it's a much better and more 'universal' (in some sense) parameter to describe how things vary. In fact that is what the t=a thing refers to. In the equations the a is playing the role of a temporal coordinate because it's monotonic increasing so you can do a valid reparametrisation. It isn't that the original potential is a manifest function of time,

Considering how that entire section is about inner products, which are required in the definition of Hilbert spaces, and all of it flows from a Hamiltonian constraint it's a little odd you don't understand which is which and how they relate to one another. Oh wait, no it isn't, you don't understand any of it.


OOOooohhh right. I read back on your posts (end up ignoring half of it because you tend to write so much),No, you ignore it because you can't respond to the repeated demonstrations you're dishonest and a hack. Clearly from your little snippet replies when you think you can throw something back at me you do it, you don't pass up the chance.


via a series of unjustified non-sequitors, that you end up with a result which doesn't involve geometry. You used the SC metric! You made an explicit reference to a geometry.

That's ok.

You see, we haven't even applied the Hilbert Space or any spin networks. I recall reading that r_ij is also a metric, a special kind of one, but that must have missed you as well. Niether metric are related, as far as I can tell.'We'? You aren't doing anything but spewing out other people's work. It's plagiarism. You're passing off other people's explanations as your own understanding. You're not doing anything yourself. you're just mangling together any source you can and trying to con people into believing you're doing some of this stuff yourself. Spinning together multiple people's work and passing off their calculations as your own is plagiarism. You can't even get the meaning of a Hilbert space right. Sure, you can quote Wikipedia at me but it's obvious from this thread and others you don't recognise them when you see them, you don't know how they work or how things relate to them. You're still struggling with the relationship of the Hamiltonian to them, despite me explaining it on more than one occasion. And you're certainly not doing anything to do with spin networks. They're considered unpleasant by actual mathematicians, never mind someone with your level of mathematical ability.

To illustrate consider the second bit of the above quote. You say " I recall reading that r_ij is also a metric, a special kind of one, but that must have missed you as well. ". Can't you work it out for yourself? Surely you know the definition of a metric? Can't you check whether it's a metric or not? You're trying to convince people you're dealing with geometry-less quantum cosmology and you can't work out if something is a metric or not. Why don't you give it a shot, confirm or refute your assertion, precisely and clearly.

I am in no doubt you'll fail. You are, for all intents and purposes when it comes to this level of mathematical physics, innumerate.


Now, quantum graphity actually admits metric solutions, the things which involve space, matter and geometry http://arxiv.org/pdf/0801.0861v2.pdf . The approach however, even though I have adopted and Markoupoulou uses, argue that geometry does not fundmantally.Like I said, if you think you're spending your time wisely or doing something viable, as you imply when you say "I have adopted...", is anything other than utter dishonest you have a personality issue.


In my original representation to you, I used the LS-equation to solve the original energy hamiltonian of the universe with potential. No, you didn't. Do you think I can't remember the start of the thread? Are you really so desperate to lie you'll resort to this level of dishonesty?


I had no explicitely stated yet that this specific equation would describe no geometry. That is only achieved when you would begin to model your theory with a Hilbert Space. Speaking as someone with a PhD in non-geometric spaces I can attest to the fact you don't necessarily require a Hilbert space to construct a description of a system which doesn't contain any geometry. You quote someone saying that the notion of 'here' and 'there' no longer applies. That's precisely the type of space I have published work in regards to.

Hilbert spaces can be used and can allow for some very interesting stuff but they aren't essential. But this is somewhat beside the point, given you clearly can't do any of this stuff.


In this space, as Fotini puts it:

''Information before geometry. Having raised the possibility that geometry does not exist at the fundamental level, we now need to find a way to do physics without geometry. This may appear hard because all our physics is done with geometry. But we can use a relational and information theoretic language.''Again, speaking as someone with experience with non-geometric constructs the quote it not entirely accurate, there are ways of doing physics not only without making reference to an underlying geometry (that's just background independence) but actually having no geometry at all. Information theory didn't need to come into it.


An example is that she considers a finite relational universe with N constituents, a bit like my (summing over all the particles making a field approach)Summing over particles does not a field approach make. There's a little more to it. You must have skipped over that section of quantum mechanics when you jumped from high school to the Dirac equation.


which she models as a network of N nodes (a,b...=1) with a Hilbert Space \mathcal{H}_{ab} attached to each link (ab). It is this model I am trying advocate. You can advocate her work but to try to present yourself as working on similar stuff and that's why you're an advocate is just ridiculous.


I think it is the correct approach because it sufficiently describes high energy physics, low energy, geometry stuff exists, we know this. It is once you apply the following approaches could we possibly achieve some kind of quantized theory involving no geometry.Now you could have said all of that without having to be dishonest and pretend you're doing some of this yourself. You could have started a discussion on non-geometric constructs and talked about this person's work. Instead you peppered it with laughable, ridiculous, delusional claims about yourself and supposed work you're doing. What could have been a good honest discussion you instead used as a bandwagon to try to delude your ego.

And before you whine "Oh you just don't like someone else doing work close to your own!" or "You're jealous" or anything else equally laughable if you're so sure you've got a new approach, valid and unknown to the mainstream submit it to a journal. You clearly have the time to write this stuff up. You know sufficient LaTeX to do the algebra yourself. Tell you what, if you write it up on this forum and send it to me via PM I'll compile it using actual LaTeX and send you the completed .tex and .pdf files, all in the appropriate formatting for a relevant journal, like JHEP. Then you can submit it. Come on, you have no excuse if you really think you're onto something. I'm sufficiently confident you'll crash and burn that I'll help you, so you have no excuse like "I don't know how to make .tex files" or "I can't format it the way they want!".

Put up or shut up.


There is more I see, you said I pulled a hamiltonian from no where in the Heisenberg equation. Well, no, not really.

If you want to know where I had been heading with that, is that there is such a thing as a ''fundamental Hamiltonian'' which describes high energy states. Obviously it was fundamental because, as you yourself said, ''didn't you notice the hbar in there?''What are you on about? The Hamiltonian in the equation you quoted wasn't in any of your previous expressions, so it was a non-sequitor. I know how the equation itself is derived, as I said it's standard bookwork for an introductory course into QM. And having \hbar doesn't make something 'fundamental'. Time and again you're just jamming your foot in your mouth.


Markoupoulou remarks in her own work

''It should now be clear that there are two possible notions of time: the time related to the g00 component of the metric describing the geometry at low energy and the time parameter in the fundamental microscopic Hamiltonian.''

So why should I not plug in a Hamiltonian in there? It was there to describe individual particles anywhere, world lines in fact to be more precise.Wow, you really are desperate. Did you just look through her paper for something to do with a Hamiltonian so you could throw it out and hope it sticks. It was a non-sequitor because you did a bunch of things which made no mention of a Hamiltonian and then you suddenly pull one out of nowhere. Not only that but the equation you produce is sufficiently well known that it's obvious it doesn't follow from what you'd said. Now I can imagine that there's a paper you're copying from which goes into a lot more detail, explained itself properly, includes many other expressions, equations etc and actually does such a derivation. However, as you generally do, you failed to include sufficient things from the paper in your post to make your post coherent. You really need to learn this method of deception doesn't work on people who know physics. It might seem to you like "Wow, look at all those equations. Everyone will think I'm a genius" but to people who understand the equations its clear you're just pulling them from somewhere.

Seriously, any rational person would have learnt after the first half dozen times of being exposed as dishonest in this manner to stop doing it. Instead you carry on. Like I said in a previous post, you'll lie when you think no one will call you on it, showing you're deliberately deceptive. But even more daft you'll lie to me about physics I've corrected you on dozens of times before.

I'd carry on replying to the other post or two of yours where you post more Wiki/ArXiv lifted equations but I'm hungry so I'm going to eat something. You need to really look at yourself and change how you act because you're not all there upstairs if you think you're able to do this stuff or you're taken seriously by anyone who knows any physics or maths. Hopefully your professed belief you could handle an undergrad course with ease is just that, a professed belief and not an actual belief. You need to get a firmer grasp on reality. You're 27 for god sake. Do something constructive with your life.

What about my last answer to this did you not understand? You use the Schwarzchild metric. That's a geometry!

You're simply not reading what I say. Or you just don't understand basic meaning of terminology like 'Hamiltonian'.

I know you can describe points in space using a Hilbert space, since you can define the dot product as your inner product. However, you said the Hamiltonian is described as a configuration space. No, th Hamiltonian ACTS on a space, which may sometimes (but not always) be a configuration space.

You're responding to things I never said. Whether it's an attempt to make it seem to the lay person you're retorting my criticisms or you're just plain ignorant I don't know.

Jesus, where to start. As I said and which you obviously don't understand, your index structure isn't right. Nor does the third expression follow from the second. Nor does your last expression make sense. You don't 'divide by \partial t', dear god that isn't what differentiation is about! It seems you can't even take partial derivatives properly, you think there's division involved. This just shows how ridiculous your claims of doing work in this stuff is, you can't do things expected of 1st years yet you're claiming to be coming up with solutions to research level quantum cosmology!

You really have something wrong with you if you think you're doing anything other than being massively dishonest. And even if you're aware you're being dishonest the fact you continue to do it, despite being exposed as a hack repeatedly, says something else is wrong with you personality-wise.

Firstly you've done what you often do and that's show where you're getting all your equations from. Just as when you linked to that YouTube lecture which contained all the equations you were spouting, right down to dubious notation, you've shown your hand by linking to that paper.

The paper gives the proper context of all the stuff you've been throwing out. Your problem is you don't understand it so you don't know how to give snippets of it in a way which makes sense, hence why your 'results' are all over the place.

The potential is a functional of the scale factor, a not uncommon notion in cosmology because it's a much better and more 'universal' (in some sense) parameter to describe how things vary. In fact that is what the t=a thing refers to. In the equations the a is playing the role of a temporal coordinate because it's monotonic increasing so you can do a valid reparametrisation. It isn't that the original potential is a manifest function of time,

Considering how that entire section is about inner products, which are required in the definition of Hilbert spaces, and all of it flows from a Hamiltonian constraint it's a little odd you don't understand which is which and how they relate to one another. Oh wait, no it isn't, you don't understand any of it.

No, you ignore it because you can't respond to the repeated demonstrations you're dishonest and a hack. Clearly from your little snippet replies when you think you can throw something back at me you do it, you don't pass up the chance.

'We'? You aren't doing anything but spewing out other people's work. It's plagiarism. You're passing off other people's explanations as your own understanding. You're not doing anything yourself. you're just mangling together any source you can and trying to con people into believing you're doing some of this stuff yourself. Spinning together multiple people's work and passing off their calculations as your own is plagiarism. You can't even get the meaning of a Hilbert space right. Sure, you can quote Wikipedia at me but it's obvious from this thread and others you don't recognise them when you see them, you don't know how they work or how things relate to them. You're still struggling with the relationship of the Hamiltonian to them, despite me explaining it on more than one occasion. And you're certainly not doing anything to do with spin networks. They're considered unpleasant by actual mathematicians, never mind someone with your level of mathematical ability.

To illustrate consider the second bit of the above quote. You say " I recall reading that r_ij is also a metric, a special kind of one, but that must have missed you as well. ". Can't you work it out for yourself? Surely you know the definition of a metric? Can't you check whether it's a metric or not? You're trying to convince people you're dealing with geometry-less quantum cosmology and you can't work out if something is a metric or not. Why don't you give it a shot, confirm or refute your assertion, precisely and clearly.

I am in no doubt you'll fail. You are, for all intents and purposes when it comes to this level of mathematical physics, innumerate.

Like I said, if you think you're spending your time wisely or doing something viable, as you imply when you say "I have adopted...", is anything other than utter dishonest you have a personality issue.

No, you didn't. Do you think I can't remember the start of the thread? Are you really so desperate to lie you'll resort to this level of dishonesty?

Speaking as someone with a PhD in non-geometric spaces I can attest to the fact you don't necessarily require a Hilbert space to construct a description of a system which doesn't contain any geometry. You quote someone saying that the notion of 'here' and 'there' no longer applies. That's precisely the type of space I have published work in regards to.

Hilbert spaces can be used and can allow for some very interesting stuff but they aren't essential. But this is somewhat beside the point, given you clearly can't do any of this stuff.

Again, speaking as someone with experience with non-geometric constructs the quote it not entirely accurate, there are ways of doing physics not only without making reference to an underlying geometry (that's just background independence) but actually having no geometry at all. Information theory didn't need to come into it.

Summing over particles does not a field approach make. There's a little more to it. You must have skipped over that section of quantum mechanics when you jumped from high school to the Dirac equation.

You can advocate her work but to try to present yourself as working on similar stuff and that's why you're an advocate is just ridiculous.

Now you could have said all of that without having to be dishonest and pretend you're doing some of this yourself. You could have started a discussion on non-geometric constructs and talked about this person's work. Instead you peppered it with laughable, ridiculous, delusional claims about yourself and supposed work you're doing. What could have been a good honest discussion you instead used as a bandwagon to try to delude your ego.

And before you whine "Oh you just don't like someone else doing work close to your own!" or "You're jealous" or anything else equally laughable if you're so sure you've got a new approach, valid and unknown to the mainstream submit it to a journal. You clearly have the time to write this stuff up. You know sufficient LaTeX to do the algebra yourself. Tell you what, if you write it up on this forum and send it to me via PM I'll compile it using actual LaTeX and send you the completed .tex and .pdf files, all in the appropriate formatting for a relevant journal, like JHEP. Then you can submit it. Come on, you have no excuse if you really think you're onto something. I'm sufficiently confident you'll crash and burn that I'll help you, so you have no excuse like "I don't know how to make .tex files" or "I can't format it the way they want!".

Put up or shut up.

What are you on about? The Hamiltonian in the equation you quoted wasn't in any of your previous expressions, so it was a non-sequitor. I know how the equation itself is derived, as I said it's standard bookwork for an introductory course into QM. And having \hbar doesn't make something 'fundamental'. Time and again you're just jamming your foot in your mouth.

Wow, you really are desperate. Did you just look through her paper for something to do with a Hamiltonian so you could throw it out and hope it sticks. It was a non-sequitor because you did a bunch of things which made no mention of a Hamiltonian and then you suddenly pull one out of nowhere. Not only that but the equation you produce is sufficiently well known that it's obvious it doesn't follow from what you'd said. Now I can imagine that there's a paper you're copying from which goes into a lot more detail, explained itself properly, includes many other expressions, equations etc and actually does such a derivation. However, as you generally do, you failed to include sufficient things from the paper in your post to make your post coherent. You really need to learn this method of deception doesn't work on people who know physics. It might seem to you like "Wow, look at all those equations. Everyone will think I'm a genius" but to people who understand the equations its clear you're just pulling them from somewhere.

Seriously, any rational person would have learnt after the first half dozen times of being exposed as dishonest in this manner to stop doing it. Instead you carry on. Like I said in a previous post, you'll lie when you think no one will call you on it, showing you're deliberately deceptive. But even more daft you'll lie to me about physics I've corrected you on dozens of times before.

I'd carry on replying to the other post or two of yours where you post more Wiki/ArXiv lifted equations but I'm hungry so I'm going to eat something. You need to really look at yourself and change how you act because you're not all there upstairs if you think you're able to do this stuff or you're taken seriously by anyone who knows any physics or maths. Hopefully your professed belief you could handle an undergrad course with ease is just that, a professed belief and not an actual belief. You need to get a firmer grasp on reality. You're 27 for god sake. Do something constructive with your life.

The remarks you make on the post with the math, it's ok, I'm dropping all that anyway.

Now moving on, yes I did see the metric part of your explanation. You will need to read further that I have answered this queery. Anything you don't understand with any of the following posts which answer this, I am sure you will not hesitate to ask.

Anyway, I had the theory that space was not fundmental independant of Fotini - I based it on all the nullified conditions of energy, time and matter - advocating Fotini's paper is just one example that the approach should be made. Just so happens her simple mathematical model works best in my mind. I will answer the rest tomorrow if there is indeed anything worth replying to.

You truly are a crazy man. You've managed to string together a string of mathematical conjectures together with only tangential relevance...almost as if they were linked together on some page in a web-like fashion in a freely accessible source.

Yes I know.

Crazy? Isn't there a fine line between smart and insanity?

You know, I web these things together because I see their relevances in my head.

AN

In case you missed it, I have took the liberty of (gathering all the parts of the post which answers your question on the metric)

OOOooohhh right. I read back on your posts (end up ignoring half of it because you tend to write so much), that

via a series of unjustified non-sequitors, that you end up with a result which doesn't involve geometry. You used the SC metric! You made an explicit reference to a geometry.

That's ok.

You see, we haven't even applied the Hilbert Space or any spin networks. I recall reading that r_ij is also a metric, a special kind of one, but that must have missed you as well. Niether metric are related, as far as I can tell.

I qoute Markoupoulou

''Just as there are no waves in the
molecular theory, we will likely not find geometric degrees of freedom in the fundamental theory. By analogy with known physics, we should expect that the quantum theory of gravity is not a theory of geometry. I must emphasize that no geometry does not mean discrete or fuzzy geometry. It means that the most primary aspects of geometry, such as the notion of \here" and \there" will cease to make sense. In fact, we have been grappling with no geometry for a while, in the traditional quantum gravity settings.''

Now, quantum graphity actually admits metric solutions, the things which involve space, matter and geometry http://arxiv.org/pdf/0801.0861v2.pdf . The approach however, even though I have adopted and Markoupoulou uses, argue that geometry does not fundmantally.

Keep in mind also, that fundamentally it is argued that geometry does not exist, not that it does not exist at all. The world of high energy physics is related to permutation symmetries, no locality and no subsystems. Low energy states are concerned with geometry and subsystems and the like.

In my original representation to you, I used the LS-equation to solve the original energy hamiltonian of the universe with potential. I had no explicitely stated yet that this specific equation would describe no geometry. That is only achieved when you would begin to model your theory with a Hilbert Space. In this space, as Fotini puts it:

''Information before geometry. Having raised the possibility that geometry does not exist at the fundamental level, we now need to find a way to do physics without geometry. This may appear hard because all our physics is done with geometry. But we can use a relational and information theoretic language.''

An example is that she considers a finite relational universe with N constituents, a bit like my (summing over all the particles making a field approach) which she models as a network of N nodes (a,b...=1) with a Hilbert Space attached to each link (ab). It is this model I am trying advocate.

I think it is the correct approach because it sufficiently describes high energy physics, low energy, geometry stuff exists, we know this. It is once you apply the following approaches could we possibly achieve some kind of quantized theory involving no geometry.

Now I can't remember off the top of my head which equation I have used uses a metric, but I am almost sure none of my original equations have tackled a theory without geometry simply because we have not set into motion all these required works which will, in the end remove geometry and describe high energy reality.

The equation H= \sum_i H_i + \sum_{k \in I} h_k is actually an equation Markoupoulou uses very very early on in her paper on quantum graphity. It is a simple approach, and has similar undertones to \{ \sum_{i} H(i) + \sum \frac{1}{r_{ij}} \} = E \psi where r_{ij} calculates the distance between i and j.

Let us first of all, describe the interaction k = \{ij \} where i and j are our particle system. (Can be thought of as a configuration space). Let us now state that the interaction is determined by a potential governing a force between the two particles.

V= \sum^{N-1}_{i=1} \sum^{N}_{i+1} g(r_{ij})

The calculation of the interaction forces on all N-particles due to pairwise interactions involves a maximum of \frac{N(N-1)}{2} contributions. In markoupoulou's work, K_N is the complete graph onN vertices, i.e., the graph in which there is one edge connecting
every pair of vertices, so that there is a total of N(N- 1)=2 edges and each vertex has degree N- 1 [1]. So what I have done is explicitely describe that there is a force between two particles in my case, (I have defined the set of interactions) and in Markoupoulou's we can see that her total space state of the system is \mathcal{H} = \otimes \frac{N(N -1)}{2} \mathcal{H}_{ab}.

So for now, what I really require is a bit of imagination. A certain matter field in the low energy epoch could satisfy a flux of time. But what we will find at the high energy state, is a place where my matter field vanishes, including the geometrical space - time is a consequence of real bradyonic particles. The universe could have a time, if summing each of these particles up and allowing them to have clocks, in both my vision and Julian Barbours, then you can say only geometric time exists, since in spin networks, space exists but not spacetime.

[1] http://fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf


So, last night I was a buisy boy - I was babysitting, but when the kids went to sleep my mind started racing on my model again.

Beginning to Create a Spaceless Model

So, I began from where I started off. I had went and defined a set of interactions by k \equiv (i,j). I determined this by stating that the interaction is determined by a potential governing a force between the two particles.

This was described by

V = \sum^{N-1}_{i=1} \sum^{N}_{i+1} g(r_{ij})

Something I never explained, yet no one asked anyhow, what g stood for. It is a coupling on the distance between the two particles i and j, so it measures the force at any given moment in time by a simple integral method. It is constant for certain forces like charge which do not change for particles but the magnitude does proportional to changes in the distance. So a fixed distance implies a constant coupling. Naturally, different particles have different charge values, so the coupling just seemed appropriate, much like how a yukawa coupling measures the different particles masses in Heirarchy model.

The force then between two particles can be given as

F_{ij} = - \frac{\partial V (r_{ij})}{\partial r_{ij}} \hat{n}_{ij} where

\hat{n}_{ij} is the unit vector. Perhaps as a little interesting snippet, if one concentrates on the right hand side and take the dot product of the unit vector with a Pauli Matrix (designed to account for a two-spin network), then square, you end up with

- \frac{\partial^2 V^2 (r_{ij})^2}{\partial^2 r_{ij}^2} (\hat{n}_{ij} \cdot \sigma_{ij})^2 = - \frac{\partial^2 V^2 (r_{ij})^2}{\partial^2 r_{ij}^2} \begin{bmatrix} n_3 & n_{-} \\ n_{+} & -n_3 \end{bmatrix}^2

Now, from our equation above, we can define a motion for a single particle. To do this, we require two more equations:

M_ia_i = \sum^{N}_{j=1, j \ne i} F_{ij}

which describes the motion of particle i and for particle j we have

M_ja_j = \sum^{N}_{i=1, i \ne \j} F_{ij}

So how do you involve spin in these equations?

Remember, particles i and j can be replaced by spin networks in an abstract sense, since there are N-state amount of particles; in entropy-related equations, the N-state amount of particles is defined by

- \ell og \frac{1}{N} = N

Where we clearly have (i = 1... N) and (j = 1... N). These can take on new appearances, we usually denote with an uparrow-downarrow notation which describes a particle, for instance i which is either in an up-state or a down-state of spin.

These become the on-off nodes in Fotini Markoupoulou-Kalamari's graphity/geometrogenesis model.

Now that we have defined the interaction as a force, we can now concentrate on new parameters such as the electric charge force between two particles i and j.

If each particles (i,j) is described by a charge (q_i,q_j) then the equation describing the electric charge force between two particles is given as

F_{q_{ij}} = \sum^{N}_{i,j}\frac{q_i q_j}{r_{ij}}

I have more work. Requires a bit more time to latex it all.

Now, in fotini's model, if G is some graph in this spin network space of states. A Hamiltonian operator H will assign an energy E(G) = <\Psi_G|H|\Psi_G> to this graph.

The reason why fotini can describe it this way (she doesn't mention this) along with a few other things I have brought up so far, if A(G) are adjacent vertices and E(G) is the set of the edges, then it satisfies

(i,j) \in E(G)

Each vertex represents a spin-state on the graph. Thus we will begin to see Fotini's approach, that to each vertex i \in A(G) there can be associated a Hilbert Space

H_G = \otimes_{i \in A(G)} \mathcal{H}_i = \mathbf{C}^{2}^{\otimes N}

Which takes on remarkable similarities to Fotini's equation describing the total space state. Indeed, the equation above describes the total number of vertices in our Hilbert Space.

Thus, we come back to a familiar garl. The distance between two particles i and j are vertices i,j \in A(G) in fact apply to the least action principle; it will define a graph geodesic between these two points.

And this is why her model works.

Deriving Markoupoulou's Hamiltonian Assiging an Energy to the Graph

I personally don't know if Markoupoulou had officially derived her Hamiltonian which assigns the energy to the Graph, given as E(G), but there is a specific way, using a traditional equation

Since each pauli matrices can take on either eigenvalues of +1 or -1, remaining hermitian of course (real objects) pertaining to observable quantities, means that we can plug in any of the eigenvalues it permits, which it turns out according to the dimensions of space, there are six eigenvectors all in all.

The energy assigned by the Hamiltonian, is an observable. To derive Fotini's relationship, one can begin with

\bar{\mathcal{M}} = E(G) = \sum_i <i|\psi_G> <\psi_G|H|i>

Rearranging yields

= \sum_i <i|\psi_G|H|i><i|\psi_G>

the |i><i| disappears since it is the unit matrix which is just unity 1, then we are left with the expectation

E(G) = <\psi_G|H|\psi_G>

And viola!



I still have more to write, but I need to calculate things a little further before I am bold enough to post it.

My next approach is to apply a spin network, in a unique way. I am going to run it by some people first before I post it. I don't want to give ammo to the bazuka of math that AN lives by. I have not even studied a math course any higher than college. Maybe some will marvel at the fact that I am trying to apply this model to rather (complex) mathematics. I am atleast trying.... or you will end up in AN's camp. A filled camp here at sciforums, where if you have not passed the necessery degree's, why even speak about the subject?

I won't hold back though. Anyone who knows me now well enough will know I won't hold back on a thought or two ;)

Ok... so here it goes...

Spin has close relationships with antisymmetric mathematical properties. An interesting way to describe the antisymmetric properties between two spins in the form of pauli matrices attached to particles i and j we can describe it as an action on a pair of vectors, taking into assumption the vectors in question are spin vectors.

This is actually a map, taking the form of

T_x M \times T_x M \rightarrow \mathcal{R}

This map of an action on a pair of vectors. In our case, we will arbitrarily chose these two be Eigenvectors, derived from studying spin along a certain axis. In this case, our eigenvectors will be along the x and z axes which will always yield the corresponding spin operator.

(d \theta \wedge d\phi)(\psi^{+x}_{i}, \psi^{+z}_{j})

with an abuse of notation in my eigenvectors.

It is a 2-form (or bivector) which results in

=d\theta(\sigma_i)d\phi(\sigma_j) - d\phi(\sigma_j)d\phi(\sigma_i)

This is a result where \sigma_i and \sigma_j do not commute.


The mapping itself can be identified not only with the vector fields, but every differentiable function of that manifold M - this itself determined a unique vector field which is generally called the Hamiltonian vector field.


ps... AN please be brutally kind :P I know next to nothing about symplectic manifolds. I only know what led me to the above. Something is telling me that the points in this post might have some problems. I don't know yet... I'll need to see what the master of math says.

Now I can't remember off the top of my head which equation I have used uses a metric, but I am almost sure none of my original equations have tackled a theory without geometry simply because we have not set into motion all these required works which will, in the end remove geometry and describe high energy reality.Are you being deliberately obtuse or are you actually struggling to understanding English? I've told you several times that you explicitly use the SC metric (http://www.sciforums.com/showpost.php?p=2901015&postcount=20).


ps... AN please be brutally kind :P I know next to nothing about symplectic manifolds. I only know what led me to the above. Something is telling me that the points in this post might have some problems. I don't know yet... I'll need to see what the master of math says.I'm not even going to bother. You've obviously just pulling as much bullshit out as you can. You deliberately admit you haven't got any knowledge on this stuff and you go so far as to leave a message on my vistors wall to try to get me to reply.

You're trolling and you're being very obvious about it, just copying massives of expressions from elsewhere. No one thinks you can do any of this mathematics. If you believe you understand it then you have a real honest to god personality issue. I think you have something wrong with you anyway, as no one of sound mind would spend the years and massive effort to lie so often to the same people, each time hoping to convince them.

Like I said, you're 27 and you're spending your time doing this? You need to do something with your life or else you'll be exactly where you are now when you're 40 and you'll have amounted to nothing.

Moderator note: Reiku has been banned for 2 weeks for trolling, for pretending to knowledge he doesn't have, and for suspected plagiarism.