Towards Ideas on a Quantum Theory of Gravity

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That's me done for the day, though I got to write a little on the Bianchi identities, the real revelation the last few days is how bad NotEinstein's physics is. The cutest remark he made was about the ''last two missing gamma matrices'' - this was the real ice breaker for me, I knew then he has no idea about my model, let alone the math.
 
NotEinstein said:
Aha, this is where the derivative of the Christoffel symbol enters the game! However, what is missing due to the notation here is that the derivatives are not taken on just the Christoffel symbols, but on some object that is unstated in this expression. Remember those missing indices I mentioned earlier? That are supposed to be contracted with a vector field that the covariant derivative is operating on. In other words, this unexplained rewritten formula is not taking derivatives of the object it's operating on into account, making it very suspect as to its correctness.

Let compare this with Reiku's own provided source, https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll3.html About halfway down (before eq 3.65), Carroll says "The actual computation is very straightforward. Considering a vector field $$V\scriptstyle \rho$$, we take", followed by a derivation. But note that Carroll gets a different answer than we have here.

If we assume the derivative-of-the-Christoffel-symbol clash is just a notational issue, we're still left with:
- A missing minus sign
- A missing Christoffel symbol pair (and its minus sign)
- A missing second term

In other words, this formula is plain wrong, as demonstrated by Reiku's own source. But, let's assume this is just some tex-mixup, and continue!


This is not just the Riemann tensor. Corroll is quite clear that only part of this expression is the Riemann tensor. Reiku mistakenly dropped various Riemann and all non-Riemann tensor contributions. In other words, this sentence is unambiguously incorrect. The formula looks like an inverse of an earlier formula, but in that case, the inequality is the wrong way around. Let's assume this is (another) typo, and soldier on!


Let's focus on the formula. We start with the Einstein tensor, with its indices explicitly stated.
The second term is the definition of the Einstein tensor.
The third term is an approximation that we haven't seen before. We recognize the commutator, but nowhere was that argued to be approximately equal to the Einstein tensor. I can only guess that this follows from the "and is just the Riemann tensor" statement (which is wrong). Worse, what was a tensor now suddenly has two unevaluated covariant derivatives! This is of course mathematically impossible.
The fourth term is just an expansion of the third term.
The fifth term follows from an earlier formula.
The sixth term is straight up non-sense. We've switch from a tensor to a scalar; no indices are present, and they cannot be, as all the terms in the expression are scalar-valued.
The seventh term follows from that totally-no-really-irrelevant formula at the start of the post. Let's just assume it's true, even though it looks like the Heisenberg uncertainty principle and we haven't been doing any quantum mechanics up to this point.

So in conclusion, what do we have? We've approximately related through an inequality the Einstein tensor (with indices noted) to a scalar value. Since a tensor is not a number, let's interpret this the mainstream way (I don't see any alternative?): we aren't talking about the tensor itself, but the value of all the elements in it. What consequences does this have?

Immediately obvious should be the lack of any non-positive values (term seven is a positive constant scalar, and each element is larger than that). If we assume a zero cosmological constant, we can translate the Einstein tensor directly into the stress-energy tensor. (See https://en.wikipedia.org/wiki/Einstein_field_equations#Mathematical_form ) All its elements will be positive too. So we end up with a spacetime where even empty space has a minimum energy density. We end up with a constant momentum density and momentum flux, even in empty space. We end up with a space that is always exerting pressure. But how large are these contributions? Well, I cannot tell, as the units don't match up. Term seven evaluates to $$1.896\times 10^{-19}\dfrac{m^8}{s^6}$$, which is no energy density units I've ever heard of. We can only conclude that various constants are missing in the last term of the formula, even though the presence of $$c$$ suggests they were put back in, so we can't trust the value that's given for term seven as it is written.

Note that playing with the cosmological constant won't help you much, as by compensating for one term, you're making the others worse due to the minus sign(s) in the metric.

So what was the goal of all this? Let's look ahead to the first bit of the second post...


Maybe, maybe not, but the question bares no relation to the derivation we just went through. No particle has been postulated; we're still working with empty spacetime. Additionally, there's nothing that suggests any kind of self-gravitation: all we've done is given the elements of the Einstein-tensor a required minimum value. So this statement doesn't help us here, and we must conclude that part two is about something else, and part one stands on its own.

And as it stands, we've got a huge pile of probable typo's, undefined terms, copy-paste mistakes, and a bunch of incorrect statements. We're missing huge steps in the derivation, and thus it looks like assumptions are made left and right. In the end, we end up with a formula whose derivation is so obscured by all these issues, we can only take it as a postulate or assumption. Especially note how the critical "uncertainty relation" was just assumed to be true in the first place. Since all this post was trying to accomplish was relating that uncertainty to something metric-y, the entire post might just as well have succinctly stated:

"Let's assume: $$G_{ij} = [\nabla_i,\nabla_j] \approx [\nabla_i,\nabla_j] \geq \frac{c^3}{G \hbar}$$."

As the post currently stands, this is fully equivalent to it.
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Keep in mind it is very difficult to accurately copy down equations you do not understand. It is even more difficult to try to summarize an explanation of those equations when you do not even understand the real explanations in the first place. It reminds me of Simons Cat who was completely unable to talk sensibly about the equations he copied down and resorted to plagiarizing entire pages of text to explain the equations. I believe that is why he left our little group.
 
hahaha

you guys are funny. I can take you through the whole derivation, right down to each and every last thing we do, and you are protecting someone (most likely you on a fake account), who has no knowledge of commutators or even what differential notation looks like.


Blind leads the blind is true.
 
Geon said:
There are no typo's here, just one mistake, and that's you. No wonder you created a fake account, I'd be really embarrassed about now.
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I've figured it out!

Geon said:
Pulling it out of its differential notation form, what we really have is
$$[\nabla_i,\nabla_j] = \frac{\partial \Gamma_i}{\partial x^j} + \frac{\partial \Gamma_j}{\partial x^i} + \Gamma_i \Gamma_j$$
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Geon said:
$$-\frac{\partial \Gamma_j}{\partial x^{i}} + \frac{\partial \Gamma_{i}}{\partial x^{j}} + [\Gamma_i \Gamma_j]$$

is just


$$-\frac{\partial \Gamma_j}{\partial x^{i}} + \frac{\partial \Gamma_{i}}{\partial x^{j}} + \Gamma_i \Gamma_j - \Gamma_j \Gamma_i$$
Click to expand...

Compare the first quoted formula with the first expression in the second quote. Watch how a minus-sign is the same as no minus-sign. How commutator-brackets are the same as no commutator-brackets.

It's Orwellian notation! War is peace! Freedom is slavery! Ignorance is strength!

Also, you do realize you just called me (as a human being) a mistake? I "fucking seriously" hope that's (another) typo.
 
NotEinstein said:
Also, you do realize you just called me (as a human being) a mistake?
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Yes, you making this fake account and coming here acting authorative on matters of math you seem absolutely clueless about, was a mistake. Do I feel bad? No... far from it. You are a troll, you designed your account to derail this thread and try to undermine me.
 
Geon said:
Yes, you making this fake account and coming here acting authorative on matters of math you seem absolutely clueless about, was a mistake. Do I feel bad? No... far from it. You are a troll, you designed your account to derail this thread and try to undermine me.
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Why does that post start with "yes" when you clearly mean "no"? Oh right, Orwellian notation.

I don't see how it was a mistake? I mean, I haven't suffered any negative consequences (yet?).
And "designed" is a big word. You're not that special, Reiku.
 
NotEinstein said:
Why does that post start with "yes" when you clearly mean "no"? Oh right, Orwellian notation.

I don't see how it was a mistake? I mean, I haven't suffered any negative consequences (yet?).
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Origin came in here and made a big deal out of me not replying to you... are you origin? If you and origin is all there is replying to this post, who would give you negative criticism but me?

Are you expecting a moderator maybe, to moderate your actions?
 
And I am going to make a deal with the next person who doesn't call me by my user name.... I will simply ignore you. If you don't have the decency to call me by my 0perating name, you don't deserve my attention.
 
NotEinstein said:
I've figured it out!





Compare the first quoted formula with the first expression in the second quote. Watch how a minus-sign is the same as no minus-sign.
Click to expand...


Yes big deal, you found an equation drop a minus sign - if you were any honourable person, you would have checked every other form or way its been written to see if it was just a drop... but you didn't. A sign drop is about as much as you can follow.
 
Geon said:
Origin came in here and made a big deal out of me not replying to you... are you origin? If you and origin is all there is replying to this post, who would give you negative criticism but me?

Are you expecting a moderator maybe, to moderate your actions?
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Well, I suppose at some point a moderator will be involved, and my actions will be judged. Maybe then my "mistake" will finally be made clear to me.

Geon said:
Yes big deal, you found an equation drop a minus sign - if you were any honourable person, you would have checked every other form or way its been written to see if it was just a drop... but you didn't. A sign drop is about as much as you can follow.
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Thing is, I pointed it out multiple times. If that's "as much as I can follow", it clearly is more than you can muster!

Geon said:
And I am going to make a deal with the next person who doesn't call me by my user name.... I will simply ignore you. If you don't have the decency to call me by my 0perating name, you don't deserve my attention.
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And I will only refer to you as Geon from now on, as per your request.
 
Geon said:
Yes, you making this fake account and coming here acting authorative on matters of math you seem absolutely clueless about, was a mistake. Do I feel bad? No... far from it. You are a troll, you designed your account to derail this thread and try to undermine me.
Click to expand...

Interesting how you can state, with apparent knowledge, that NotEinstein has created a "fake account"... almost as though you know him already, as though from another name...

Perhaps it is time to give up the game...
 
Kittamaru said:
Interesting how you can state, with apparent knowledge, that NotEinstein has created a "fake account"... almost as though you know him already, as though from another name...

Perhaps it is time to give up the game...
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I explained who it may have been, goes by the name of Origin. He came in here, concerned that I brushed over NotEinstin. I mean, can you wonder why he may be concerned about that?
 
Geon said:
I explained who it may have been, goes by the name of Origin. He came in here, concerned that I brushed over NotEinstin. I mean, can you wonder why he may be concerned about that?
Click to expand...

A proficient sidestepping of the question, but ultimately meaningless.

If you claim this all to be one giant coincidence, then I would counter claim that I am the Queen of France.
 
Geon said:
Origin came in here and made a big deal out of me not replying to you... are you origin? If you and origin is all there is replying to this post, who would give you negative criticism but me?
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This is off topic but you brought it up and it is only right that it should be answered. I categorically state that NotEinstein and Origin are not the same poster.
See how easy that is?

Now it is your turn; are you and Reiku the same poster?
 
Kittamaru said:
A proficient sidestepping of the question, but ultimately meaningless.

If you claim this all to be one giant coincidence, then I would counter claim that I am the Queen of France.
Click to expand...

I don't quite follow you. What do you mean?
 
origin said:
Now it is your turn; are you and Reiku the same poster?
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Even if I was, why would it make a difference, what has he done? I am only concerned about the troll known as NotEinstein who is clear bent on disrupting my posts... along with you.

Even if it isn't you, it is someone here, because they created their account with the sole intention of posting in my thread and my thread only. And only you were concerned with me not answering NotEinstein, and only you have been in the background with similar comments about me ''being reiku.''
 
Geon said:
I am concerned about people like you who are manipulating places like this.
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(I thought I was the one concerned?)

Your concern is noted. What would you have me do to reduce this concern? (No joking, I am serious about this.)
 
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