## Quantum Spacetime Points & General Covariance

 Quote by atyy What do you mean by LET? Is it SR in a particular inertial frame?
In LET, the aether frame is one particular inertial frame. So? Are you saying LET aether can never be physical?

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 Quote by stglyde In LET, the aether frame is one particular inertial frame. So? Are you saying LET aether can never be physical?
OK, if you define LET as SR in a particular inertial frame, ie. the LET aether is a particular inertial frame, then by definition the theory is equivalent to SR.

It is not so much that the LET aether frame is not "physical" as that it is not unique. The moment you have one LET aether frame, LET itself predicts that you have an infinite number of LET aether frames, all equally "physical". The equivalent statement in SR are that there is infinite number of Lorentz inertial frames, all equally preferred.

Anyway, since you define LET as SR, let's just use the term SR to include LET.

 Quote by atyy OK, if you define LET as SR in a particular inertial frame, ie. the LET aether is a particular inertial frame, then by definition the theory is equivalent to SR. It is not so much that the LET aether frame is not "physical" as that it is not unique. The moment you have one LET aether frame, LET itself predicts that you have an infinite number of LET aether frames, all equally "physical". The equivalent statement in SR are that there is infinite number of Lorentz inertial frames, all equally preferred. Anyway, since you define LET as SR, let's just use the term SR to include LET.
Is the main reason "LET itself predicts that you have an infinite number of LET aether frames, all equally "physical"" is because when one uses a length contracted and time dilated ruler and clock in any frame to measure your length and time, they would see you as similarly length and time contracted, hence one may just say as well that there is "infinite number of Lorentz inertial frames, all equally preferred?".

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 Quote by stglyde Is the main reason "LET itself predicts that you have an infinite number of LET aether frames, all equally "physical"" is because when one uses a length contracted and time dilated ruler and clock in any frame to measure your length and time, they would see you as similarly length and time contracted, hence one may just say as well that there is "infinite number of Lorentz inertial frames, all equally preferred?".
I'm not sure about all technical details, but that is the essential idea. Technically, we say the laws of physics (even written in a single inertial frame) have Poincare invariance.

 Quote by atyy I'm not sure about all technical details, but that is the essential idea. Technically, we say the laws of physics (even written in a single inertial frame) have Poincare invariance.

"V -> Velocity with respect to (wrt) the aetherial background (CMBR)
v -> Velocity of a second moving object (Frame), again wrt the aetherial frame
dv -> net differential speed

LET and SR "are not 'identical' Lorentz says that velocity is dv = V - v and SR says dv = v. In SR one arbitrarily assumes a rest frame and in Lorentz's theory they do not. In Lorentz's theory it is ALWAY dv and in SR v relative to one's choice. Since the transform used only dv as in Sqrt(1 - [dv/c]^2) the computed results are the same. Also, since dv is squared the sign (as in direction relative to V) is masked but actually important. There is NO symmetry in LET, the faster you move the more phyically time slowly and contracted you are, period! Finally, where in LET is relative simultaniety mentioned???"

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 Quote by stglyde I'm trying to study the best approaches to quantum gravity and especially the interactions of quantum and the metric. But first let us settle about the so called "spacetime points". What is the proof that spacetime points can't be composed of any substance but purely an abstract. The often arguments are that general covariance and diffeomorphism invariance require the spacetime points are not composed of any substance or something that can be tracked in time. I want to know all the proof of this from actual experiments. Is there any or all just a theoretical reasoning based on beauty and symmetry with no actual experimental justifications?
I'm not arguing with you, I just don't completely understand the bolded sentence in your post and would like a little clarification as to what you are saying.

Are you referring to the socalled Hole Argument? Are you saying that according to the (often cited) Hole Argument diffeo invariance implies that spacetime points don't have physical existence?

 Quote by marcus I'm not arguing with you, I just don't completely understand the bolded sentence in your post and would like a little clarification as to what you are saying. Are you referring to the socalled Hole Argument? Are you saying that according to the (often cited) Hole Argument diffeo invariance implies that spacetime points don't have physical existence?

"It [the hole argument] is incorrectly interpreted by some philosophers as an argument against manifold substantialism, a doctrine that the manifold of events in spacetime are a "substance" which exists independently of the matter within it. Physicists disagree with this interpretation, and view the argument as a confusion about gauge invariance and gauge fixing instead."

PeterDonis said: "In other words, the hole argument does not show that general covariance is inconsistent with spacetime being a "real thing". All it shows is that GR is a gauge theory."

So it doesn't have to do with the Hole Argument. Unless you want to say it is indeed?
What is your comment about "general covariance and diffeomorphism invariance require the spacetime points are not composed of any substance or something that can be tracked in time". Do you agree with it or disagree and why? Thanks.

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