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. 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.