# GTR Vacuum vs Quantum Theory Vacuum: Speed of Light

• B
• Pikkugnome
I am wondering about the speed of light in GTR vacuum, since it predates quantum theory. It is surprising that the speeds should be the same, as the vacuums could be different. Are the speeds different, should they be, I have no idea.

#### Pikkugnome

What is the difference between the GTR vacuum and the vacuum of quantum theory? What is the speed of light in the vacuums, specifically what can be predicted and what must be measured?

Pikkugnome said:
What is the difference between the GTR vacuum and the vacuum of quantum theory?
Um, that they are two different theories?

I'm not sure what you are trying to get at here. Some more background about why you are asking the question, or some more specific scenario you are wondering about, would help.

Pikkugnome said:
What is the speed of light in the vacuums, specifically what can be predicted and what must be measured?
Our physical theories based on Lorentz invariance predict that there should be a finite invariant speed. Our measurements bear this out.

The actual numerical value of the finite invariant speed depends on your choice of units; in "natural" units, the numerical value of that speed is ##1## and it is dimensionless (has no units).

• jbriggs444
I am wondering about the speed of light in GTR vacuum, since it predates quantum theory. It is surprising that the speeds should be the same, as the vacuums could be different. Are the speeds different, should they be, I have no idea.

Pikkugnome said:
I am wondering about the speed of light in GTR vacuum, since it predates quantum theory. It is surprising that the speeds should be the same, as the vacuums could be different.
You seem to be confusing theoretical models with reality. GR and quantum theory are theoretical models. As I have already said, both of them agree that there should be a finite invariant speed. And as far as the numerical value of that speed, as I have already said, that depends on your choice of units; in natural units it is ##1##. It doesn't even make sense to ask whether GR or quantum theory predicts a particular value for the speed, since humans' choice of units is not something theories of physics can predict.

In reality, we observe that yes, there is a finite invariant speed. Its numerical value depends on our choice of units.

• malawi_glenn and Dale
c is a conversion factor between distance and time. In that sense it is like any other conversion factor - like a dozen. Don't you expect a "dozen" to be the same in GR as QM?

Pikkugnome said:
What is the difference between the GTR vacuum and the vacuum of quantum theory?
You've labelled this thread as B-level, but it's really an A-level question. Here's my attempt at an answer that's somewhere in between...

In flat (Minkowski) spacetime there's no difference between those vacua -- because QFT is constructed with Special Relativity as a foundation.

In any specific QFT, one constructs the (Fock) state space in terms of field modes (e.g., by a Fourier decomposition).

In a curved spacetime, it turns out that such a decomposition "here" (and the state space spanned by those field modes) is inequivalent to a (superficially similar) decomposition "there". In other words, the 2 state spaces are inequivalent -- in general one cannot express the vacuum (or any other mode) in one of those state spaces as a linear combination of modes from the other. One must use more advanced techniques to handle this (Birrel & Davies is the classic reference).

So the short (probably still puzzling) answer to your question is that, in curved spacetime, there is an infinity of inequivalent versions of the simplistic vacuum of ordinary (non-interacting) QFT.

If you really want to know more, google for "Bogoliubov transformation". (Alas, you'll need to become proficient in ordinary QFT first, for this to make much sense.)

strangerep said:
the short (probably still puzzling) answer to your question is that, in curved spacetime, there is an infinity of inequivalent versions of the simplistic vacuum of ordinary (non-interacting) QFT.
Note, though, that in the algebraic approach to QFT, all of these unitarily inequivalent constructions can be handled in a unified manner. So I think the jury is still out on exactly what the physical meaning is of the mathematical fact that unitarily inequivalent constructions exist.

PeterDonis said:
Note, though, that in the algebraic approach to QFT, all of these unitarily inequivalent constructions can be handled in a unified manner. So I think the jury is still out on exactly what the physical meaning is of the mathematical fact that unitarily inequivalent constructions exist.
The "physical meaning" is that the choice of mathematical framework (Fock space) is not quite right. Find the right structure and collect your Clay Institute prize. • Demystifier
Pikkugnome said:
What is the difference between the GTR vacuum and the vacuum of quantum theory? What is the speed of light in the vacuums, specifically what can be predicted and what must be measured?

General relativity is a metric theory of gravity, and the properties of the vacuum are just those properties needed to measure distances and times. To be more precise, if one is familiar with special relativity (which is highly advisable before attempting to tackle general relativity), the metric determines the invariant Lorentz interval.

I'm not sure how to describe the quantum vacuum formally, perhaps someone else can provide a better discussion. Informally, though, the quantum vacuum is full of virtual particles, while GR, being a classical theory, is not.

It is felt that quantum effects , when incorporated into General Relativity, may explain the cosmological constant, but at the moment we have no theory of quantum gravity. It's an oustanding unaswere question why the effects of the quantum vacuum are so small in General Relativity - naive approaches predict a much larger effect than is obsreved.

pervect said:
Informally, though, the quantum vacuum is full of virtual particles, while GR, being a classical theory, is not.
Ahem. It might be helpful to review Arnold Neumaier's insight articles on virtual particles.

• vanhees71, weirdoguy and PeroK
• vanhees71 and strangerep
Pikkugnome said:
I am wondering about the speed of light in GTR vacuum, since it predates quantum theory. It is surprising that the speeds should be the same, as the vacuums could be different. Are the speeds different, should they be, I have no idea.
Those theories complement each other to predict the very accurate experimental evidence.

According to SR, massless particles must move with the invariant speed ##v=c##.
##0 = m= \frac{E}{c^2} \sqrt{1-v^2/c^2}##
In GR, spacetime is locally flat. Therefore, SR is locally valid.

QFT, which is a relativistic theory, predicts together with the standard model the following: Unlike some other particles, photons don't interact with the Higgs-field, which exists everywhere in vacuum, and therefore don't have a mass.

As a consequence, light moves in vacuum with the speed ##c##.

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• vanhees71