Is there a gravitational variant of the Schwinger limit?

[Giovanni Cambria]

Is there a gravitational variant of the Schwinger limit? I mean: a strong gravitational field can separate virtual dipoles with tidal forces. The force applied to the positron is different from that applied to the electron (though both are attractive) and, if this difference is high enough, the two particles can be separated permanently. Do you agree with this? Has this occurrence been studied in physics in the literature of the past? I have not found anything on the internet and it seems strange.

 

[PeterDonis]

The force applied to the positron is different from that applied to the electron

Do you mean the gravitational force? That's the same for both.

 

[Giovanni Cambria]

Why? Electron and positron have different positions.

 

[PeterDonis]

Electron and positron have different positions.

Virtual particles don't have well-defined positions.

 

[Giovanni Cambria]

So how can you say that gravity force is equal for both? If the position is not well defined how can you do this assertion? Be very dettailed please.

 

[PeterDonis]

So how can you say that gravity force is equal for both?

A better way to say it would be that "gravity force" isn't even well-defined for virtual particles. (In relativity, gravity isn't even a force anyway, it's just spacetime geometry.)

But in any case, "virtual particles" here really means just the vacuum. So a better way to ask the question I think you are asking is, can gravity polarize the vacuum? Googling on "gravity vacuum polarization" will turn up a number of papers investigating this.

 

[Demystifier]

A better way to say it would be that "gravity force" isn't even well-defined for virtual particles. (In relativity, gravity isn't even a force anyway, it's just spacetime geometry.)

In perturbative quantum gravity (which is non-renormalizable but still OK as effective theory), gravity is a force described by exchange of virtual gravitons in Feynman diagrams. In higher-order processes, even virtual particles can exchange virtual gravitons. So it is well defined, as long as one does not apply the effective theory at very high energies.

 

[Giovanni Cambria]

I was motivated by this: http://www.dailymail.co.uk/sciencet...k-hole-appears-travel-faster-speed-light.html
Maybe there is a simpler explanation but anyway is interesting.

 

[PeterDonis]

I was motivated by this

It's always better to read the actual paper than a media articles; the latter are notorious for over-hyping and misinterpreting things. The preprint on arxiv.org is here:

https://arxiv.org/abs/1412.4936

Nowhere does the paper claim that the gamma rays are coming from inside the horizon. It just says that the region from which they are coming happens to be smaller in size than the horizon radius of the hole. It's perfectly possible to have a region outside the horizon (for example, at the base of one of the jets emitted by a rapidly rotating hole, which appears to be the favored hypothesis in the paper) that is smaller than the horizon radius.

 

[Giovanni Cambria]

Yes you are absolutely right: there are far simpler explanations.
Anyway searching for the dailymail article i discovered this:
http://cerncourier.com/cws/article/cern/28606
<<Quantum effects such as vacuum polarization in gravitational fields appear to permit "superluminal" photon propagation and give a fascinating new perspective on our understanding of time and causality in the microworld.>>
I have not read it yet so i cannot say but it seems relevant: a correlation between superluminal photons and gravitational polarization of the vacuum was investigated in the past.

 

[PeterDonis]

a correlation between superluminal photons and gravitational polarization of the vacuum

The effect that article is talking about is not gravitational polarization of the vacuum; it's ordinary vacuum polarization, due to QED, in a curved spacetime instead of a flat spacetime.

 

[Giovanni Cambria]

Ok someone could explain better the crucial part: <<While the SEP may be consistently imposed in classical physics, somewhat surprisingly it is violated in quantum theory (see Further information). In quantum electrodynamics (QED), Feynman diagrams involving a virtual electron-positron pair influence the photon propagator. This gives the photon an effective size of the order of the Compton wavelength of the electron. If the space-time curvature has a comparable scale, then an effective photon-gravity interaction is induced. This depends explicitly on the curvature, in violation of the SEP. The photon velocity is changed and light no longer follows the shortest possible path.>>

 

[PeterDonis]

someone could explain better the crucial part

The basic idea is that, if you take any field theory (classical or quantum) that is written down assuming a flat spacetime, and try to use it in a curved spacetime, there will always be possible additional terms in the Lagrangian that couple to spacetime curvature. For example, MTW discusses this in relation to Maxwell's Equations; in flat spacetime, in 4-d tensor formalism, they look like this:

$$
\partial_c F^{ab} + \partial_b F^{ca} + \partial_a F^{bc} = 0
$$
$$
\partial_a F^{ab} = 4 \pi J^b
$$

If we now try to use these equations in curved spacetime, we run into a problem. The standard recipe for doing this is to just change all partial derivatives to covariant derivatives; that would give this:

$$
\nabla_c F^{ab} + \nabla_b F^{ca} + \nabla_a F^{bc} = 0
$$
$$
\nabla_a F^{ab} = 4 \pi J^b
$$

The problem, though, is that ##F^{ab}## itself involves partial derivatives, since the field tensor is the exterior derivative of the 4-potential; i.e., in flat spacetime we have

$$
F^{ab} = \partial^a A^b - \partial^b A^a
$$

But if we apply the "partial to covariant derivative" rule to this and then substitute into, say, the second Maxwell Equation, we get:

$$
\nabla_a \left( \nabla^a A^b - \nabla^b A^a \right) = 4 \pi J^b
$$

Expanding this out gives

$$
\nabla_a \nabla^a A^b - \nabla_a \nabla^b A^a = 4 \pi J^b
$$

And now we can see the problem: covariant derivatives in curved spacetime do not commute, so there is an ambiguity in how we do the translation to curved spacetime above; we could have perfectly consistently included a curvature coupling term ##R^b{}_a A^a## (the commutator of the covariant derivatives ##\nabla^a A^b## and ##\nabla^b A^a##) to obtain

$$
R^b{}_a A^a + \nabla_a \nabla^a A^b - \nabla_a \nabla^b A^a = 4 \pi J^b
$$

There is no general rule for deciding which one is right; but the argument in the CERN article you linked to is basically that, other things being equal, we should expect that curvature coupling term to be there, and we should expect it to have a significant magnitude--significant enough to affect experimental results--when the spacetime curvature length scale is of the same order as the photon length scale, i.e., the Compton wavelength of the electron. The above was written in terms of the classical Maxwell Equation, but the same equation also turns out to be the field equation for the photon in QED (or, to put it another way, the same Lagrangian that gives rise to Maxwell's Equations in classical electrodynamics also gives rise to the photon propagator in QED). So we should expect the same curvature coupling term to be present if we do QED in curved spacetime.

 

[Giovanni Cambria]

The existence of this curvature coupling term has also other physical consequences I suppose. Do you know if some of these have been observed?

 

[PeterDonis]

The existence of this curvature coupling term has also other physical consequences I suppose. Do you know if some of these have been observed?

I don't think so, because spacetime curvature in all of the regions we can probe experimentally is so weak compared to the scale it would need to be for such curvature coupling effects to be significant. Spacetime curvature of the same scale as the Compton wavelength of the electron would correspond to a curvature about 40 orders of magnitude larger than the curvature in the solar system, and about 30 orders of magnitude larger than the largest curvatures we have any experimental evidence for, those associated with things like binary pulsars and the black hole mergers recently observed by LIGO.

 

[Giovanni Cambria]

30 orders of magnitude...ok I think the article we are talking about is not relevant for the discussion.
Some other question:
* do you know exactly when the GR equation reduce to the Gravitoelectromagnetism equations? What are the conditions for using Gravitoelectromagnetism instead of GR?
* There are conditions about the field intensity? (i'm concerned about those)
* There is an extension of Gravitoelectromagnetism to the quantum word? (i have found something but I'm not sure)
* And finally: for you this 'quantum Gravitoelectromagnetism' (if existent) is the right formalism to study the hypothetical phenomenon I talked about in the first post? (This phenomenon should be the topic of the discussion)

 

[PeterDonis]

What are the conditions for using Gravitoelectromagnetism instead of GR?

That gravity is sufficiently weak (or, equivalently, that spacetime curvature is sufficiently small). The solar system is an example of a region where this condition is met.

Also, you don't use gravitoelectromagnetism (GEM) "instead of GR". GEM is an approximation derived from GR; if you use GEM, you are using GR.

There is an extension of Gravitoelectromagnetism to the quantum word?

Not to my knowledge. Do you have a reference?

 

[Giovanni Cambria]

That gravity is sufficiently weak

Ok so it's not usable at all for a gravitational analog of the Schwinger limit. As I feared.

Not to my knowledge. Do you have a reference?

I do not know if the link is relevant: http://harvard.voxcharta.org/tag/gravitoelectromagnetism-gem-theory/

 

[PeterDonis]

I do not know if the link is relevant

Unfortunately, I don't think so, because these papers don't look like actual published papers in peer-reviewed journals; they look like people's personal speculations posted on arxiv and nowhere else (and unreliable speculations at that--see below). For example, one of the papers I see there is "Quantized gravitoelectromagnetism theory at finite temperature"; arxiv PDF is here:

https://arxiv.org/pdf/1605.07207.pdf

This paper's first paragraph makes this claim: "The similarity between Newton’s law and Coulomb’s law lead Maxwell [1] to formulate a theory of gravitation". The reference [1] given is to this paper:

J. C. Maxwell, Phil. Trans. Soc. Lond.155, 492 (1865)

It appears that somebody has actually scanned this paper by Maxwell (yes, the Maxwell) and put it online; here is the link:

http://www.bem.fi/library/1865-001.pdf

And what is the title of this paper? "A Dynamical Theory of the Electromagnetic Field". In other words, this is the classic paper where Maxwell first published Maxwell's Equations, for electromagnetism, not gravity.

In other words, the claim in the "Quantized gravitoelectromagnetism" paper, which I quoted above, is simply false. That makes me extremely skeptical that what they are doing is worth reading.

 

[Giovanni Cambria]

Thank you for the analysis: anyway Gravitoelectromagnetism is not useful for me so i will not bother about extensions.
Eliminated Gravitoelectromagnetism for me there is another possible approach and that's the latest question i will pose to you: I do not know if the theory is peer reviewed or not but...what do you think about https://arxiv.org/ftp/gr-qc/papers/9909/9909037.pdf (Polarizable-Vacuum (PV) representation of general relativity)?
It's an isomorphism between Maxwell in curved spacetime in vacuum and Maxwell in flat spacetime with a polarizable medium of variable refractive index...

 

[PeterDonis]

what do you think about...

It's a different way of representing the math of GR. It doesn't make any different physical predictions. This kind of interpretation was developed by, among others, Sakharov (the Soviet nuclear physicist and dissident) in the 1960's (MTW has a brief discussion). I couldn't say whether it has any relevance for what you're interested in.

 

[Giovanni Cambria]

Yes because PV assumes only: "matter polarizes vacuum". There are no explanations about how this happens...I will wait for a published, peer reviewed extension of PV that include a mechanism that explains how matter polarizes vacuum...
(like: Heaviside/Jefimenko (GEM) gravity + evanescent sea of dipoles. Gravity makes the sea of dipoles denser etc.)
Maybe more traditional theory, like quantum gravity, could be the way to go but I do not have years to study them so I prefer to wait the theory above.
Thank you for the patience.

 

[Olorin]

Hi Giovanni, in order for the Schwinger effect to be effective, you need a medium made of "unlike" charges. This works for EM interactions as vacuum pairs satisfy the "unlike" charge criteria ( positive and negative electric charges). In order for a gravitational Schwinger mechanism to be effective you would need a vacuum made of "unlike" gravitational charges, that is you would need repulsive gravitational interaction between matter and antimatter pairs ( antimatter particles bearing an opposite gravitational mass with respect to matter particles). This is the Hajdukovic hypothesis that you can further explore in this paper for example: https://hal.archives-ouvertes.fr/hal-01253534/document

 

[Giovanni Cambria]

Hi, I think matter and antimatter respond to gravity in the same way but the experiments will reveal if I'm correct or not. The idea I explore has no relation with the Hajdukovic hypothesis and is also different from the Hawking radiation. (there is no need of an event horizon: only a strong gravitational field and the associated tidal forces)

 

[Giovanni Cambria]

finally, by simply looking for "pair production tidal forces", I found the following article:

https://www.sciencedirect.com/science/article/pii/S0370269317307888

I do not have the right background to understand the content but some sentences are clear to me and it seems extremely relevant to the discussion.

Honestly I do not understand if the presence of a event horizon is necessary for energy conservation or not and, if so, why... if someone could explain I would be grateful.