# Where does quantum gravity starts ?

#### notknowing

Usually one thinks of quantum gravity effects becoming important at the scale of the Planck length. I have however some strong doubts about this because of the following.

In relativity, one uses "sticks" and clocks to be able to define events in spacetime. Consider for instance a light clock. Usually one uses light clocks in thought experiments but a thought experiment has only some validity as long as the experiment under consideration is feasible to be carried out. To build a light clock, you need two mirrors. These two mirrors must be made of solid material (preferentially metallic), so that each mirror is at least a few atoms thick. So, a real light clock would have a size of a least a few atom radii (and here I leave out already the difficult task of synchronising such a clock), which is much larger than the Planck length. Further, some other peculiar aspects come in: if you would make the spacing between the two mirrors very small, you effectively create a situation where the Casimir force sets in. In addition, the speed of light would no longer be c inbetween the plates (I have seen once a calculation of this effect). Such a clock would be thus essentially different from a macroscopic clock. Usually, one also neglects the time it takes for light to reflect on the surface of the mirror. For spaces which are separated far apart, this is a very good approximation but as the separation is decreased, this is no longer true. Reflection is due to the fact that the electric field associated with the electromagnetic wave sets the (outer) orbital electrons into oscillation, which in turns results in the re-emission of waves. Setting an electron into an oscillatory motion requires time because of the inertia of the electron.

So, if one thinks of how to set up spacetime coordinates, such that the points become very closely spaced, things become rather messy (even at atomic distances) and all the concepts of GR (clocks, synchronisation, etc.) seem to fall apart.

Any comments or thoughts are welcome.

Rudi Van Nieuwenhove

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#### jtbell

Mentor
So, if one thinks of how to set up spacetime coordinates, such that the points become very closely spaced, things become rather messy (even at atomic distances) and all the concepts of GR (clocks, synchronisation, etc.) seem to fall apart.
How is it then, that the combination of SR and QM in the form of QED especially, but also electroweak theory and QCD, has been so successful in agreeing with experiments on the atomic scale? If your argument has validity, surely we would have seen discrepancies by now!

#### vanesch

Staff Emeritus
Gold Member
I'd say that the OP has a point. What we can say, is that the more macorscopic model we have of GR can be "analytically continued" (that's a kind of hypothesis) on the atomic and subatomic scale, but frankly, we can't verify it the way the thought experiments in GR to find out the local metric are specified (and on the level of the radius of a nucleus, I wonder how one could even think of such a way in practice).

Now, locally, GR looks like SR in not too strong gravity fields, and the only thing we can say is that if we pretend that SR works also on this small scale (by extrapolating from what we do on larger scales), and combine it with some ideas from QM, to set up a QFT, that this gives us good results. There is indeed no direct way to test SR (let go GR) on subatomic scale. But it is not because we cannot test it directly, that it must necessarily fail: the mathematical structure can still be valid, without the possibility of using the usual constructions with meter sticks and so on. But you're right that this is extrapolation from what we macroscopically know. And maybe at some point it will break down, but this must not necessarily be the point where we cannot apply the usual constructions anymore.

#### Garth

Gold Member
Further, some other peculiar aspects come in: if you would make the spacing between the two mirrors very small, you effectively create a situation where the Casimir force sets in. In addition, the speed of light would no longer be c inbetween the plates (I have seen once a calculation of this effect).
Hi Rudi!

That is an interesting statement, do you have a reference?

As a note: Some time ago Turbo-1 made a similar starement in another thread and was shot down for introducing a private theory, however I found the question about how the velocity of light might be affected by the quantum vacuum a valid one to ask.

Garth

#### notknowing

Hi Rudi!

That is an interesting statement, do you have a reference?

As a note: Some time ago Turbo-1 made a similar starement in another thread and was shot down for introducing a private theory, however I found the question about how the velocity of light might be affected by the quantum vacuum a valid one to ask.

Garth
Hi Garth, it was a long time ago I had read about this, so I lost the specific reference. A quick search by Google gave me an interesting link however :
http://www.npl.washington.edu/AV/altvw43.html

I think also that some forums are too strict in relation to private theories. If one ONLY can ask questions on well-established published theories, how can one then expect progress to happen ? As far as I see it, a forum should not only be there as an educational tool for students in physcs but should also tolerate a certain level of challenge.

Rudi

#### notknowing

Hi Rudi!

That is an interesting statement, do you have a reference?

As a note: Some time ago Turbo-1 made a similar starement in another thread and was shot down for introducing a private theory, however I found the question about how the velocity of light might be affected by the quantum vacuum a valid one to ask.

Garth
I just found another reference (on arxiv) :
http://arxiv.org/PS_cache/hep-th/pdf/9408/9408016.pdf [Broken]

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#### vanesch

Staff Emeritus
Gold Member
I think also that some forums are too strict in relation to private theories. If one ONLY can ask questions on well-established published theories, how can one then expect progress to happen ? As far as I see it, a forum should not only be there as an educational tool for students in physcs but should also tolerate a certain level of challenge.
Well, PF decided to be essentially an educational tool. Progress is not to be made on forums - certainly not on PF. Progress is to be made in journals, conferences or elsewhere but not on PF. (except maybe in our independent research forum...)

This is the line that has been drawn. One can regret it, I sometimes do myself, but otherwise the crackpot pressure is so big that the educational value of the site quickly goes down, for a very doubtful benefit of non-peer-reviewed progress. It's the fault of the gazillions of deluded crackpots that the few very smart geniuses don't find a place anymore to say what they have to say.

#### notknowing

Well, PF decided to be essentially an educational tool. Progress is not to be made on forums - certainly not on PF. Progress is to be made in journals, conferences or elsewhere but not on PF. (except maybe in our independent research forum...)

This is the line that has been drawn. One can regret it, I sometimes do myself, but otherwise the crackpot pressure is so big that the educational value of the site quickly goes down, for a very doubtful benefit of non-peer-reviewed progress. It's the fault of the gazillions of deluded crackpots that the few very smart geniuses don't find a place anymore to say what they have to say.
I see your point (about the crackpot pressure) and I respect this.
Indeed progress is traditionally made in journals. On the other hand, internet has become such a practical tool for exchanging ideas between scientists, that this exchange (in my view) really can lead to new insights, and thus to progress.

#### Thrice

I've been on forums where they allow crackpots to post. What ends up happening is the intelligent & truly hard posts don't get any replies because everyone's working on the crackpots. Needless to say, I very much prefer what PF's done

#### Garth

Gold Member
I just found another reference (on arxiv) :
http://arxiv.org/PS_cache/hep-th/pdf/9408/9408016.pdf [Broken]
Forgive me for not taking your first reference seriously as it was to "Analog Science Fiction & Fact Magazine".

However the second Physics ArXiv reference was also published in Nucl.Phys. B437 (1995) 60-82.

Does this effect not bring the principles of SR/GR into question?

Have photons travelling faster than c between Casimir plates actually been measured in an experiment? Indeed would this experiment be technically feasible?

Garth

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#### notknowing

Forgive me for not taking your first reference seriuosly as it was to "Analog Science Fiction & Fact Magazine".

However the second Physics ArXiv reference was also published in Nucl.Phys. B437 (1995) 60-82.

Does this effect not bring the principles of SR/GR into question?

Have photons travelling faster than c between Casimir plates actually been measured in an experiment? Indeed would this experiment be technically feasible?

Garth
Indeed, I quickly realised that the first reference woulf not be very convincing :rofl: .
I'm rather sure that such an experiment has not been carried out and because the predicted effect is so small, it would not be in reach of present technology. However, I think one can trust the predictions of QED in this case.

#### JesseM

Well, according to this page on John Baez's site the Casimir effect cannot actually be used to send information across the gap faster than c, so it isn't really equivalent to an actual change in the constant c in this region.
The Casimir effect is a very small, but measurable force which exerts between two uncharged conducting plates when they are very close together. It is due to vacuum energy (see the Physics FAQ article on the Casimir Effect). A surprising calculation by Scharnhorst suggests that photons travelling across the gap between the plates in the Casimir effect must go faster than c by a very very small amount (at best 1 part in 10^24 for a 1 nanometre gap.) It has been suggested that in certain cosmological situations, (such as in the vicinity of cosmic strings if they exist) the effect could be much more significant. However, further theoretical investigations have shown that once again there is no possibility of FTL communication using this effect.
refs:
K. Scharnhorst, Physics Letters B236, 354 (1990)
S. Ben-Menahem, Physics Letters B250, 133 (1990)
Andrew Gould (Princeton, Inst. Advanced Study). IASSNS-AST-90-25
Barton & Scharnhorst, J Phys A26, 2037 (1993).

#### Chris Hillman

Another intellectual bloodsport?

PF decided to be essentially an educational tool. Progress is not to be made on forums - certainly not on PF. Progress is to be made in journals, conferences or elsewhere but not on PF.
And good moderation is the biggest strength of this forum, IMHO. Enjoy it while we have it folks!

I've been on forums where they allow crackpots to post. What ends up happening is the intelligent & truly hard posts don't get any replies because everyone's working on the crackpots. Needless to say, I very much prefer what PF's done
Exactly!

If you seek freewheeling high-stakes high-level discussion of topics of current research interest in physics, I suspect that your only option is graduate school in physics, followed by a respectable academic job and frequent attendance at international conferences.

Forgive me for not taking your first reference seriuosly as it was to "Analog Science Fiction & Fact Magazine".
This is another example illustrating why one should be very wary about what you read on the InterNet.

In the course of writing a regular column for Analog, John Cramer, a physicist on the faculty of the University of Washington, has written about many fields rather far removed from his field of expertise, so it shouldn't be surprising that some of these articles are quite misleading. As an exercise, curious students can attempt to spot howlers in this collection: http://www.npl.washington.edu/AV/av_index.html#5

#### notknowing

Well, according to this page on John Baez's site the Casimir effect cannot actually be used to send information across the gap faster than c, so it isn't really equivalent to an actual change in the constant c in this region.
From the arxiv paper : http://arxiv.org/PS_cache/gr-qc/pdf/0107/0107091.pdf [Broken]
I quote the following statement, which is in contrast to the above:

"In contrast, the Scharnhorst effect, which predicts that in a cavity with perfectly reflecting boundaries, photons can travel at a speed slightly larger than c, is an extremely tiny phenomenon, well below our capabilities for experimental verification. It is nevertheless of fundamental theoretical importance, in that here it seems to be the actual signal speed that it is modified."

I have not yet found a real journal paper though which confirms the above statement. In the arxiv paper which I mentioned earlier (which was also published) : http://arxiv.org/PS_cache/hep-th/pdf/9408/9408016.pdf [Broken]
calculations show that an electric field also causes a slight change in the speed of light. This effect would possibly be easier to verify (measure) because one could make a large experimental set-up, consisting of long (say 100 meter) parallel strips of conductors onto which one applies a large voltage such as to create a strong electric field between them. The whole has of course to be carried out in a vacuum (long evacuated tube). Then one could send a signal (very short light pulse) one way, reflect it on a mirror at the other end, and record the arrival time at its starting point. Using an accurate atomic clock, it could then maybe within reach to find a deviation from c.

Rudi

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#### JesseM

From the arxiv paper : http://arxiv.org/PS_cache/gr-qc/pdf/0107/0107091.pdf [Broken]
I quote the following statement, which is in contrast to the above:

"In contrast, the Scharnhorst effect, which predicts that in a cavity with perfectly reflecting boundaries, photons can travel at a speed slightly larger than c, is an extremely tiny phenomenon, well below our capabilities for experimental verification. It is nevertheless of fundamental theoretical importance, in that here it seems to be the actual signal speed that it is modified."
This paper also says that if you use multiple pairs of parallel plates moving at relativistic speeds relative to one another, this effect would potentially allow for genuine causality violations, ie sending a signal into the past. The authors invoke Hawking's chronology protection conjecture to prevent this, but they say that "Planck scale physics comes into play" in trying to analyze exactly how causality violations would be prevented (which I guess supports the point of this thread that Planck-scale physics can't be disentangled from the physics of larger scales). I'm a little skeptical about the idea that ordinary QED would lead to the possibility of causality violations since I've only seen the issue brought up in the context of weird spacetimes in GR, but it's certainly possible they're right...too bad this paper has not been peer-reviewed.

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#### turbo

Gold Member
Einstein claimed in his book "Relativity: The Special and General Theory" that the speed of light in a vacuum is not a constant, but is variable. From Chapter 22:

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its result hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).
http://www.bartleby.com/173/

He elaborated on this in his Leyden address (1920) and his essay "On the Ether" (1924), but his contemporaries were too pleased with the mathematical model of curved space-time to pay much attention to his thoughts on the reality of the vacuum (the ether).

#### JesseM

Einstein claimed in his book "Relativity: The Special and General Theory" that the speed of light in a vacuum is not a constant, but is variable.
Steve Carlip suggests in his article Is The Speed of Light Constant? that Einstein was just talking about the coordinate speed of light in some global coordinate system such as Schwarzschild coordinates, which does not contradict the fact that the speed of light in a locally inertial coordinate system is still always c, which is what modern physicists would mean when they say "the speed of light is constant" in GR.
Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book "Relativity: the special and general theory" he wrote: . . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity.

The problem here comes from the fact that speed is a coordinate-dependent quantity, and is therefore somewhat ambiguous. To determine speed (distance moved/time taken) you must first choose some standards of distance and time, and different choices can give different answers. This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c.

In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.

If general relativity is correct, then the constancy of the speed of light in inertial frames is a tautology from the geometry of spacetime. The causal structure of the universe is determined by the geometry of "null vectors". Travelling at the speed c means following world-lines tangent to these null vectors. The use of c as a conversion between units of metres and seconds, as in the SI definition of the metre, is fully justified on theoretical grounds as well as practical terms, because c is not merely the speed of light, it is a fundamental feature of the geometry of spacetime.

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