Exploring the Speed of Light with LQG Theory

[metrictensor]

I think the solution to this question of why the speed of light is measured the same by all inertial observers can be answered by background independent theories such as LQG.

 

[marcus]

I think the solution to this question of why the speed of light is measured the same by all inertial observers can be answered by background independent theories such as LQG.

I am curious about how you draw that conclusion

it is an interesting thought
and moreover a big idea that probably needs to be broken down into easier-to-understand ones

I believe that background independent theories of spacetime geometry
(such as LQG) have NOT YET provided a reason, but you foresee that some background independent theory will in future be able to explain why c is the same for all.

(so far, it is more like people know that is the case so they construct theories which accommodate it----are compatible with c being the same from all points of view. or so i think. then it is a "post-diction" so to speak)

here is a general question to think about in this connection

WHICH PHYSICAL QUANTITIES ARE THE SAME WHEN MEASURED BY ALL
(nice) OBSERVERS?

each of us can decide what nice means, Lorentz-equivalent, inertial, whatever

It is an interesting question too, maybe background independent quantum gravity will have something to say about.

IS C THE ONLY INVARIANT QUANTITY?

or, for instance, is hbar (a small angular momentum) the same no matter who measures it?

or is maybe some small curvature associated with the cosmological constant also an invariant?

or is maybe the Planck length the same length from all perspectives!

how can we reconcile the claims of more than one quantity to be invariant?

we practically have fits just arranging for c to be the same to all observers, if we want yet another will this be the straw that breaks the computer's back?

sorry if too speculative.

let us hear your reasons why you think background independent model of spacetime might answer questions about c invariance and such like matters

 

[metrictensor]

First I present my argument on why LQG could provide an answer to the question as to the invariance of c in inertial frames. Secondly, I present my view as to why the question has not been answered up to this point. Last I summarize.

When I first encountered the idea that c is the same for all inertial observers it seemed very weird. But this was based on a particular assumption about the nature of space and time as being absolute. I then read that in GR spacetime and the gravitational field can be thought of as the same entity and all we really have are fields interacting with fields. If gravitational and E&M fields interact perhaps they interact in such a way that c is the same for all inertial observers. I basically looked at the question and asked why does it seem so strange and I concluded this was due to a particular view of space and time. If all we have a field interacting with fields then, at least for me, the question does not seem so strange and possibly solvable.

As far as I know there is no quantum theory of the E&M field that is defined on curved spacetime. All QFT is defined on a flat Minkowski spacetime. This in itself should be an obvious indication that the theory is not complete. Rovelli addresses this issue when he talks about the fact that the abundance of experimental data from the 60's on kept physicists busy without looking at fundamental questions in detail. Today there is not much experimental data to work with and there is a greater effort put into exploring more fundamental issues of physics. So the reason the question on the speed of light has not been answered is that QED is not a background independent theory and therefore the tools to address the question are not available.

There are many things in physics that really have no explanation (as far as I know). Why do systems appear to seek a state of minimal energy? Why do objects follow geodesics? Perhaps, based on how the EM field interacts with the gravitational field, the speed of light being the same enforces some general physical principle like energy conservation or minimal action? We can't answer this question until we have a background independent quantum theory of gravity and an understanding of how this interacts with the EM field. Your guess is as good as mine but from what I understand it is worth a look.

 

[Chronos]

I'm not sure the Planck length would necessarily be invariant, but the Planck energy might qualify. In any case, I think you must have at least two invariant constants to establish covariance.

 

[metrictensor]

In relation to your question of the Plank lengh being "invariant" LQG does contain the idea that there is a smallest length (whether it is the Plank length or not). An objection can be raised that this length could be Lorentz contracted but according to Rovelli (he wrote a paper on this) this is not a problem. I don't know the technical details but know he addresses the issue. It makes sense to me that if spacetime and gravity are the same entity and you want a quantum theory of the gravitational field then spacetime must be quantized.

Along these lines perhaps the invariance of the speed of light is a result of the quantum nature of light and EM field excitations. Perhaps if this were not the case then energy quantization would be violated. Again these are very rough thoughts I have only come up with today without too much time to contemplate. I like to put things out here to see what other have to say and stimulate thought. But the invariance of the speed of light has been something I have long struggled with to understand. I have asked physicists and, although there have been some good attempts, I have never gotten what I consider a satisfactory answer. My basic motivation for thinking there could be an answer to the question is that now we have a new paradigm that does away with the ideas that led to strangeness (in my mind) of the invariance of light.

I think you bring up a good point about invariants in general. The question of light might just be a particular case of a more general question.

 

[metrictensor]

If we consider the three constants that make up the Plank length what do we find. If seems that c is the only one related to a particular thing in the sense that we say light moves. G and h_bar measure the strength of interactions between massive objects and put a limit on our knowledge of physical systems respectively. Are we looking at c in the wrong way? Should it be more in line with the way G and h_bar are understood? The thing is light can be detected and seen. Can the same be said of G and h_bar. Of course they can all be measured but that is not what I an getting at.

Consider an object in free fall. We see the object and know there is something moving which could be analogous to light. The fact that it falls at 9.81 m/s^2 is not something we can see. It is not an entity in the same sense as the falling object. Nonetheless, we can measure this acceleration and determine it is a constant. This is similar to G and h_bar.

 

[selfAdjoint]

The obvious way to replace c in the Planck computations with a strength parameter as you suggest would be to use alpha, the fine structure constant, aka the coupling constant of EM. Of course this brings in the charge on the electron.

 

[metrictensor]

The obvious way to replace c in the Planck computations with a strength parameter as you suggest would be to use alpha, the fine structure constant, aka the coupling constant of EM. Of course this brings in the charge on the electron.

Thanks. This may turn out to be helpful.