General relativity with infinite speed of light?

[mersecske]

Are there any consistent theory in which the speed of light is infinity,
but the space-time is curved?
Let us imagine a history of mankind in which GR is invented before special relativity (SR).

 

[Passionflower]

Are there any consistent theory in which the speed of light is infinity, but the space-time is curved?

There is a difference between a theory and a fantasy. If it is not based on reality it is not a theory. Since the speed of light is not infinite this is simply a fantasy.

 

[arkajad]

"Are there any consistent theory in which the speed of light is infinity"

There is such. You may like to check http://arxiv.org/abs/arXiv:gr-qc/9604054" by Christian Rueede and Norbert Straumann. Also search for "Newton-Cartan" and "Galilei general relativity". This way you will find further references.

 

[arkajad]

There is a difference between a theory and a fantasy. If it is not based on reality it is not a theory. Since the speed of light is not infinite this is simply a fantasy.

Not necessarily. For instance you may think that the speed of light may be irrelevant for gravity. That it is relevant is just an assumption justified by a long and mostly successful use of GR. But this fact must not be taken as a "no-no" for trying other assumptions, even if at first look you don't like them.

 

[mersecske]

There is a difference between a theory and a fantasy. If it is not based on reality it is not a theory. Since the speed of light is not infinite this is simply a fantasy.

Do you think that Newtonian theory is fantasy?
NO! Newton theory is a real theory,
and describes the real world in the regime v << c.
The above mentioned theory (GR without SR)
can describe also the real world in a suitable regime,
for example gravitational Doppler effect is a situation,
where we don't need SR but GR is needed

 

[Passionflower]

Are you thinking that special relativity is fantasy?
NO! Special relativity is a real theory,
and describes the real world in the regime v << c.

I don't know what you are talking about but last time I checked the speed of light is finite, in fact it is exactly:

299792458 m / s

 

[arkajad]

The question is why the value of the speed of light should affect gravity? It is an assumption of GR that it does. But other assumptions and models are not excluded, and other theories are being tried.

 

[Passionflower]

The question is why the value of the speed of light should affect gravity? It is an assumption of GR that it does. But other assumptions and models are not excluded, and other theories are being tried.

Yes they are excluded because the speed of light is not infinite, as is established by experiment.

 

[arkajad]

They are not excluded, because they do not claim that the speed of light is infinite. They claim that it is irrelevant for a theory of gravity. Speed of light enters Maxwell's equation. And it can be well what it is. But equations for the gravitational field is something else.

 

[JesseM]

There is a difference between a theory and a fantasy. If it is not based on reality it is not a theory. Since the speed of light is not infinite this is simply a fantasy.

Theoretical physicists sometimes investigate theories known to be incompatible with observation if it illuminates the mathematical properties of more realistic theories...for example, considering the 2+1 dimensional analogue of general relativity, or adding an extra time dimension to M theory which may reveal some symmetries which are hidden in the ordinary version. For a simpler example consider the exercise of http://www.physics.princeton.edu/~mcdonald/examples/mechanics/lee_ajp_43_434_75.pdf , which results in a transformation which has an adjustable parameter in the place of c which can either be given an infinite value (in which case the transformation reduces to the Galilei transformation of Newtonian physics) or a finite value (in which case it reduces to something like the ordinary Lorentz transformation).

 

[arkajad]

Quoting from http://image.sciencenet.cn/upload/blog/file/2010/8/201081019170575880.pdf" :

"As may be recalled, there is a space-time formulation of Newtonian gravitational theory originally provided by Cartan [7], and further studied independently by Friedrichs [14] and Trautman [40], in which the Newtonian version of the equivalence principle is directly incorporated into the geometrical description. (See Ref. 12 for an up-to-date account.) The Cartan geometric formulation of Newtonian gravitational theory is indeed the appropriate one for taking into account the subtleties of (what remains of) the principle of general covariance and the principle of equivalence. (For example, the Newton-Cartan space-time of a constant non-zero Newtonian gravitational field has an identical geometry to that of the zero gravitational field, but it differs from a non-uniform Newtonian field which produces tidal effects.) It has been pointed out by Christian [8] that the Newton-Cartan framework provides a valuable setting for exploring some of the fundamental problems of unifying quantum theory with gravitational theory without, at this stage, the more severe difficulties of general relativity having to be faced. Christian argues that this framework indeed sheds important light on the role of gravity in the measurement problem.
As it turns out, the criterion for quantum state reduction that we shall be led to here is independent of the value of the speed of light c."

 

[mersecske]

I don't know what you are talking about but last time I checked the speed of light is finite, in fact it is exactly:

299792458 m / s

Sorry, I mean Newtonian theory instead of SR, but its the same.
I am talking about special relativity which is not good in describing gravitation,
therefore you can say that its just a fantasy :) ?

 

[arkajad]

I am talking about special relativity which is not good in describing gravitation,

Special relativity was not invented for describing gravitation. Similarly you could say that gravitation is not good in describing quantum phenomena. So what? Different frameworks are invented for different purposes.

 

[Dale]

Are there any consistent theory in which the speed of light is infinity,
but the space-time is curved?

It would help if you clarified: Do you mean "consistent with observation" or "self-consistent".

The Newton Cartan formulation that arkajad mentioned is just a geometrical reformulation of Newtonian gravity, so it doesn't mention c at all. It is self-consistent, but it is not consistent with observation since it is just a reformulation of Newtonian gravity and therefore makes all of the same wrong (and right) predictions.

AFAIK, there is no theory of gravity consistent with observation that does not use a finite c.

 

[mersecske]

Special relativity was not invented for describing gravitation. Similarly you could say that gravitation is not good in describing quantum phenomena. So what? Different frameworks are invented for different purposes.

Yes, and GR without SR was not invented for describing gravitation with system with large velocities!

I mean "self-consistent".

(But I think, that we have nothing consistent with all observations yet)

 

[mersecske]

But Newton Cartan theory predict the right formula for gravitational Doppler-effect, or doesnt?

 

[Dale]

But I think, that we have nothing consistent with all observations yet

What observation is inconsistent with GR?

 

[mersecske]

I mean that GR is not the theory of everything, but this is not the subject of this post

 

[arkajad]

But Newton Cartan theory predict the right formula for gravitational Doppler-effect, or doesnt?

Newton-Cartan theory is not dealing with light. Maxwell's theory is. Similarly GR tells you nothing about Maxwell equations and propagation of electromagnetic waves. You need a separate theory of electromagnetism. Then, when you have both, you can try to relate the structure of one to the structure of the other.

 

[Dale]

I mean that GR is not the theory of everything, but this is not the subject of this post

For clarity, do you understand:
a) GR is self-consistent and also consistent with observation
b) Newton Cartan is self-consistent and not consistent with observation

 

[arkajad]

a) GR is self-consistent and also consistent with observation

Apparently not all experts consider it as being self-consistent, and not all experts consider it as being consistent with observations. But it is true that the set of physicists that claim both is non-empty.

 

[Dale]

Yes, there are few (if any) fields of human endeavor where agreement is complete, and even experts can be wrong.

 

[bcrowell]

But Newton Cartan theory predict the right formula for gravitational Doppler-effect, or doesnt?

I don't see how it could. In Galilean relativity, simultaneity is absolute, so clocks can't run at different rates, and you can't have kinematic or gravitational time dilation. Note that Newton-Cartan is just a different way of mathematically describing Newtonian gravity; it isn't a separate theory. Newtonian gravity (i.e., Newton's laws of motion plus Newton's law of gravity) does not say anything about light. You can't just stick Maxwell's equations into Newtonian mechanics, because then you get a system that's not mathematically self-consistent. So if you really wanted to rigorously check my assertion that Newtonian gravity can't possibly get gravitational Doppler shifts right, you would first have to define the laws governing electromagnetism.

 

[Passionflower]

I don't see how it could. In Galilean relativity, simultaneity is absolute, so clocks can't run at different rates, and you can't have kinematic or gravitational time dilation. Note that Newton-Cartan is just a different way of mathematically describing Newtonian gravity; it isn't a separate theory. Newtonian gravity (i.e., Newton's laws of motion plus Newton's law of gravity) does not say anything about light. You can't just stick Maxwell's equations into Newtonian mechanics, because then you get a system that's not mathematically self-consistent. So if you really wanted to rigorously check my assertion that Newtonian gravity can't possibly get gravitational Doppler shifts right, you would first have to define the laws governing electromagnetism.

Doesn't Newton-Cartan include gravitational time dilation?

 

[arkajad]

Quoting from http://arxiv.org/abs/gr-qc/9610036"

"In particular, as far as the comparison of the theory with experiments using light rays is concerned, the Newton-Cartan theory must be supplemented by the usual Lorentz-covariant electrodynamics instead of its corresponding Newtonian limit. This may be done by introducing an ether concept in a way also suggested by Trautman [23].
Thus it appears that presently there is no practical need to employ the Newton-Cartan road to post-Newtonian corrections."

The above was just one opinion of 1996. There are other opinions as well. People are searching and researching.

 

[mersecske]

Using the equivalence principle you can calculate the gravitational Doppler without using specrel,
you can simply combine the equivalence principle to the standard Doppler in inertial frame.

 

[bcrowell]

Using the equivalence principle you can calculate the gravitational Doppler without using specrel,
you can simply combine the equivalence principle to the standard Doppler in inertial frame.

The gravitational redshift is gy/c². In a universe with infinite c, the gravitational redshift is zero.

In a universe with finite c, then I don't think your argument works, because you have to define how light propagates, and that is logically equivalent to assuming SR.

 

[mersecske]

c can be finite, but its not a limit velocity and does not affect the theory
in Newtonian theory light can be studied also

(Strictly speaking all theories are fiction, and only measurements are true)

 

[bcrowell]

in Newtonian theory light can be studied also

Then you would need to spell out what theory of electromagnetism you have in mind. It can't be Maxwell's equations, which are logically incompatible with Galilean relativity.

 

[arkajad]

"... which are logically incompatible with Galilean relativity. "

Let me recall: "This may be done by introducing an ether concept in a way also suggested by Trautman [23]."

 

[bcrowell]

"... which are logically incompatible with Galilean relativity. "

Let me recall: "This may be done by introducing an ether concept in a way also suggested by Trautman [23]."

I didn't say that there can be no theory of E&M in Galilean relativity. I just said that mersecske needed to specify what theory it was, and that it couldn't be Maxwell's equations. If it's an ether theory, that's fine.

 

[arkajad]

Well, then let me quote more:

"Newton-Cartan theory must be supplemented by the usual Lorentz-covariant electrodynamics instead of its corresponding Newtonian limit. This may be done by introducing an ether concept in a way also suggested by Trautman [23]."

That is there are Maxwell's equations and ether theory - both, working together in a tandem.

 

[bcrowell]

Well, then let me quote more:

"Newton-Cartan theory must be supplemented by the usual Lorentz-covariant electrodynamics instead of its corresponding Newtonian limit. This may be done by introducing an ether concept in a way also suggested by Trautman [23]."

That is there are Maxwell's equations and ether theory - both, working together in a tandem.

Since 1905, the standard interpretation of Maxwell's equations has been that they describe physics without an ether. It might be interesting to know what Trautman had in mind, but the Trautman paper is in an out of print book that can't be viewed through amazon or google books, so it appears that it would be difficult for us to have a discussion of it here, unless everyone involved in the discussion was willing to go to a university library and find the book.

 

[arkajad]

Well, if you are interested, you may like to read the review and some philosophically oriented discussion "http://philsci-archive.pitt.edu/archive/00001096/00/Rynasiewicz.doc" " .

 

[bcrowell]

Thanks, arkajad, for posting the link to the Rynasiewicz paper. That's very helpful. It includes a summary of the Trautman construction.

If I'm understanding Rynasiewicz correctly, then essentially the Trautman construction is an aether theory with no unification of E and B, it has E and B frame-invariant, it has a finite speed of propagation of light, and it has been falsified by experiments such as the Michelson-Morley experiment. Rynasiewicz claims that it correctly encapsulates pre-1905 ideas about electromagnetism. It has both a Galilean metric and a Minkowski metric hidden in it. Both of these metrics are flat, so it really doesn't address mechanics in the way that Newtonian mechanics or Newton-Cartan gravity does; in particular, it can't provide a description of mass (either gravitational or inertial). Since it's only a theory of electromagnetism, it doesn't include the ability to discuss clocks. (You can't build a clock out of photons.) Since there are no clocks, the theory seems not to address the question of whether the Galilean metric or the Minkowski metric is the one that gives the correct description of time, e.g., whether or not time dilation exists. To my mind, then, the theory's incompleteness means that it doesn't constitute a counterexample to my claim that the standard interpretation of Maxwell's equation is right: Maxwell's equations are incompatible with Galilean relativity. It seems to me that what Trautman, Earman, and Rynasiewicz are debating is not whether Maxwell's equations are incompatible with Galilean relativity. I think they're discussing something much more restrictive: whether or not there even exist interesting and historically relevant examples of physical theories in which space is absolute.

Would you disagree with any of the above in factual terms, or only in interpretation?