# Quantum Spacetime Points & General Covariance

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?

atyy
The corresponding problem in classical general relativity without matter is that there are no local observables. Because there is no prior geometry, there is no preferred frame of reference. Since all coordinate systems are equally good, when you say R(x), what does x mean? However, once you add matter the problem is solved in classical general relativity, as discussed in Eq 1.1 of http://arxiv.org/abs/gr-qc/9404053. This is also called "relational" since we used matter to define an absolute spacetime event.

How to define local or approximately local observables in quantum gravity is discussed in http://arxiv.org/abs/hep-th/0512200 and http://arxiv.org/abs/1105.2036. A particularly interesting case to study is AdS/CFT in which a theory on the boundary of spacetime is thought to define a theory of gravity in the interior or bulk. How can the boundary theory specify locality in the bulk? Some ideas are http://arxiv.org/abs/hep-th/0606141 and http://arxiv.org/abs/0903.4437.

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The corresponding problem in classical general relativity without matter is that there are no local observables. Because there is no prior geometry, there is no preferred frame of reference. Since all coordinate systems are equally good, when you say R(x), what does x mean? However, once you add matter the problem is solved in classical general relativity, as discussed in Eq 1.1 of http://arxiv.org/abs/gr-qc/9404053. This is also called "relational" since we used matter to define an absolute spacetime event.

How to define local or approximately local observables in quantum gravity is discussed in http://arxiv.org/abs/hep-th/0512200 and http://arxiv.org/abs/1105.2036. A particularly interesting case to study is AdS/CFT in which a theory on the boundary of spacetime is thought to define a theory of gravity in the interior or bulk. How can the boundary theory specify locality in the bulk? Some ideas are http://arxiv.org/abs/hep-th/0606141 and http://arxiv.org/abs/0903.4437.

What I want to understand is this. Even after Michelson-Morley Experiment has already refuted the ideas of an Aether. But Lorentz Ether Theories are still being explored by modern physicists. For example, in http://arxiv.org/abs/gr-qc/0401021

Isn't it that whatver is the complexities of aether. It still retains being a substance. But General Covariance and Diffeomorphism Invariance have shown there can't be an aether made of substance. So why so physicists still explore it?

Perhaps modern lorentz ether theories don't contain substance? If so, What kind of aether is it?

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atyy
What I want to understand is this. Even after Michelson-Morley Experiment has already refuted the ideas of an Aether. But Lorentz Ether Theories are still being explored by modern physicists. For example, in http://arxiv.org/abs/gr-qc/0401021

Isn't it that whatver is the complexities of aether. It still retains being a substance. But General Covariance and Diffeomorphism Invariance have shown there can't be an aether made of substance. So why so physicists still explore it?

Perhaps modern lorentz ether theories don't contain substance? If so, What kind of aether is it?

The result of the Michelson-Morley experiment got rid of the "non-relativistic aether", but replaced it with something called the metric, which is present at every point in spacetime. In special relativity, the metric is flat and not acted on by matter. In general relativity, matter tells the metric how to curve, and the metric tells matter how to move. So in some sense, the metric may be considered a thing - or in physics jargon - a "field". In particular, the metric is the gravitational field. The metric is distinguished from other fields such as the electromagnetic field in that it does not have localized energy and momentum. So in that sense it is not a thing.

Most curiously, there appears to be an aether consistent with general covariance and background independence. I think its predictions are different from general relativity, which has not yet been falsified. Nonetheless, it is interesting that such theories can exist mathematically. Here is a review by Ted Jacobson about such theories: http://arxiv.org/abs/0801.1547

There's a lot of 'ether theories' inspired from analogue gravity in condensed matter; basically, excitations in some condensed matter system (like a Bose-Einstein condensate or superfuild He-4) behave a lot like 'elementary' particles moving in curved spacetime -- they don't see the material of the condensate, it's their vacuum, since they're excitations of this material, and they propagate like (relativistic) particles in some metric. Essentially, special relativity and a gravitational field, and perhaps even the full general relativity, may emerge in such a setting, even though it's absent from the fundamentals (those systems being fully describable in the 'absolute', Newtonian space and time of the laboratory they're in). One such approach is Olaf Dreyer's 'http://arxiv.org/abs/gr-qc/0604075" [Broken] do something similar with their 'string-net liquids', but lack, I believe, the gravitational angle.

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The result of the Michelson-Morley experiment got rid of the "non-relativistic aether", but replaced it with something called the metric, which is present at every point in spacetime. In special relativity, the metric is flat and not acted on by matter. In general relativity, matter tells the metric how to curve, and the metric tells matter how to move. So in some sense, the metric may be considered a thing - or in physics jargon - a "field". In particular, the metric is the gravitational field. The metric is distinguished from other fields such as the electromagnetic field in that it does not have localized energy and momentum. So in that sense it is not a thing.

Most curiously, there appears to be an aether consistent with general covariance and background independence. I think its predictions are different from general relativity, which has not yet been falsified. Nonetheless, it is interesting that such theories can exist mathematically. Here is a review by Ted Jacobson about such theories: http://arxiv.org/abs/0801.1547

The paper is very complex. But let us just discuss the main general issue about general covariance. First. Up to what size scale has GR been tested already in the general covariance, diffeomorphism invariance, and background independent department? Maybe up to certain size or scale only and the article or main idea of covariant ether theories is that below a certain size, general covariance, diffeo invariance no longer work? Is this the main idea of it all?

atyy
The relevant test is usually that of local Lorentz invariance (LLI). This is only tested to a certain scale, and the theories hypothesize that LLI fails beyond that scale.

The current limits to which LLI have been tested are reviewed in http://arxiv.org/abs/gr-qc/0502097 .

Theories of quantum gravity that break LLI must satisfy current bounds to be viable and are usually discussed by people studying such theories, eg. http://pirsa.org/index.php?p=speaker&name=Ted_Jacobson.

The relevant test is usually that of local Lorentz invariance (LLI). This is only tested to a certain scale, and the theories hypothesize that LLI fails beyond that scale.

The current limits to which LLI have been tested are reviewed in http://arxiv.org/abs/gr-qc/0502097 .

Theories of quantum gravity that break LLI must satisfy current bounds to be viable and are usually discussed by people studying such theories, eg. http://pirsa.org/index.php?p=speaker&name=Ted_Jacobson.

Thanks. Without adding more papers in which I can't understand them 100% because I'm not a full physics graduate and don't know all the math. Please confirm using simpler words if the punchline of it all is that it is still possible that Aether can still lurk at the very tiny scale where lorentz violations are observed and general covariance violated. But isn't it that Aether is supposed to be defined as medium of light which is debunked already. Or is Aether defined as simply a medium that may not have anything to do with medium of light and it is hiding in the very small?

Another thing. About General Covariance and spacetime points. If experiments can determine that large scale spacetime are general covariant, does it make sense at smaller scale, it is not generally covariant. Please show an example or analogy in daily life where this is possible.. without referring to any of the papers (or new ones). Thanks.

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Rereading all the papers and reflecting on them. So the key is local lorentz invariance. How about this scenerio. Supposed near the planck scale, lorentz invariance were violated. Supposed further than it was found out that all planck scale are connected to one another across the universe establishing an absolute space and time. And lorentz invariance are emergence.. meaning special relativity are large scale effect. How does it makes sense then? Can't you make planck scale the preferred frame such that that twins can establish identical time even hundreds of light years away? Why not? (others welcomed to share too, thanks)

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atyy
Please confirm using simpler words if the punchline of it all is that it is still possible that Aether can still lurk at the very tiny scale where lorentz violations are observed and general covariance violated.

Well, I'm no expert either (I'm a biologist), but the statement seems right if you delete "and general covariance violated".

It is much better to talk about local Lorentz invariance violations.

A direct to the point questions is thus. If local lorentz invariance violations were detected.. does it mean there is Absolute Space and Time hidden in the microscopic sector? If not. What is relevance of the the preferred frame in lorentz violations?

The result of the Michelson-Morley experiment got rid of the "non-relativistic aether", but replaced it with something called the metric, which is present at every point in spacetime. In special relativity, the metric is flat and not acted on by matter. In general relativity, matter tells the metric how to curve, and the metric tells matter how to move. So in some sense, the metric may be considered a thing - or in physics jargon - a "field". In particular, the metric is the gravitational field. The metric is distinguished from other fields such as the electromagnetic field in that it does not have localized energy and momentum. So in that sense it is not a thing.

Most curiously, there appears to be an aether consistent with general covariance and background independence. I think its predictions are different from general relativity, which has not yet been falsified. Nonetheless, it is interesting that such theories can exist mathematically. Here is a review by Ted Jacobson about such theories: http://arxiv.org/abs/0801.1547

atyy.. how do you think Gravity Aether Theory is related to Lorentz Ether Theory? Is GAT like GR what LET is to SR? That is.. is GAT a LET that include gravity like GR an SR that contains gravity and curved spacetime? If LET was true, does it mean GAT was true?

And if LET and GAT (Gravity Aether Theory) was true. Does it mean the Pilot waves have to be true?

atyy
atyy.. how do you think Gravity Aether Theory is related to Lorentz Ether Theory? Is GAT like GR what LET is to SR? That is.. is GAT a LET that include gravity like GR an SR that contains gravity and curved spacetime? If LET was true, does it mean GAT was true?

And if LET and GAT (Gravity Aether Theory) was true. Does it mean the Pilot waves have to be true?

What do you mean by LET? Usually I define LET as special relativity in a particular Lorentz inertial frame.

What do you mean by LET? Usually I define LET as special relativity in a particular Lorentz inertial frame.

Do you prefer Ohm's Law or an Apple Ipad? Ohm's law may be identical to Ipad but an Ipad is better.. hence LET may be better although you prefer SR (I know they have identical prediction like Ohm's law and Ipad have similar prediction in the electronic circuits).

atyy
Do you prefer Ohm's Law or an Apple Ipad? Ohm's law may be identical to Ipad but an Ipad is better.. hence LET may be better although you prefer SR (I know they have identical prediction like Ohm's law and Ipad have similar prediction in the electronic circuits).

If you don't define your terms, I won't know what you are talking about.

If you don't define your terms, I won't know what you are talking about.

Ohm's Law are models of the circuits. In the same sense that SR is a model of physical contraction in LET. Also note in: http://metaresearch.org/cosmology/gravity/gps-twins.asp [Broken]

"We note in passing that the effect that SR expects accelerations or frame changes to have on remote clocks would constitute an instantaneous action at a distance, a violation of the causality principle."

But LET does this naturally. Hence LET is preferred. But let's not argue about this. I'm just asking if LET and Gravity Aether theory (GAT) are related in that GAT requires LET (meaning the ether needs to be there).

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atyy
What do you mean by LET? Is it SR in a particular inertial frame?

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?

atyy
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.

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?".

atyy
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.

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???"

marcus
Gold Member
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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?

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.

atyy