Gravitational Waves & Unification: Einstein's Remark?

[RAD4921]

It seem that if gravitational waves travel at C, that this is a hint that there is unification between gravity and electromagnetism. Didn't Einstein once remark about this?
Thanks RAD

 

[Symbreak]

There is a way we can conduct an experiement to test this hypothesis:

observe gravitational waves (GR) passing through a variable electromagnetic field (emf/v).

(the idea being, the displacement in the field caused by GR leads to the emf/v emmiting electromagnetic waves. The GR energy is transferred into light.)

... so somewhere along the line, is it possible to 'convert' GR into light?

 

[Hurkyl]

I thought Kaluza and Klein did unify EM with gravity.

 

[Symbreak]

They unified using a 5th spatial dimension 'wrapped up' in space. Superstring theory seems to be regarded as a better version.
But as far as I know, there is no mention of graviational/electromagnetic radiation unification?

 

[Hurkyl]

But as far as I know, there is no mention of graviational/electromagnetic radiation unification?

Wouldn't what we perceive as 4-D gravity waves and EM waves both be special cases of 5-D gravity waves?

 

[pervect]

I thought Kaluza and Klein did unify EM with gravity.

I thought there were some problems with KK theory, but I'm not sure of the details. Wiki says

However, a naive attempt to convert this interesting geometrical construction into a bona-fide model of reality founders on a number of issues, including the fact that the fermions must be introduced in an artificial way (in nonsupersymmetric models). A less problematic approach to the unification of the forces is taken by modern string theory and M-theory.

I suspect the people in the string forum (Beyond the standard model) might know more.

 

[Hurkyl]

Basically, I thought the only problem was that KK-theory was a classical theory, and not a quantum theory. Of course, I'm not an expert on this topic.

 

[selfAdjoint]

Basically, I thought the only problem was that KK-theory was a classical theory, and not a quantum theory. Of course, I'm not an expert on this topic.

Oskar Klein actually interpreted the compact cycle of KK theory as the quantum wave function, and used it to derive a quantum theory. I have read that he continued to work on this concept for years, right up to WWII, which ended so much and began so much in physics.

 

[Los Bobos]

It seem that if gravitational waves travel at C, that this is a hint that there is unification between gravity and electromagnetism.

If I walk with my dog at the same speed, am I a dog?

If I remember correctly Einstein worked on this unification in his late years, but I think KK theories were the best applicant. Anyways KK theories served as the starting point for string theories, which I have understood some people like.

I think that gravitational waves have little to do with this, but the fact that electromagnetism is very closely connected to the causal structure of spacetime might serve as motivation.

 

[pervect]

I seem to remember that KK theory predicted particles that don't actually exist, but I don't seem to be able to find the source, and I don't necessarily trust my recollection on this.

 

[Chris Hillman]

Speed of light in relativistic physics

It seem that if gravitational waves travel at C, that this is a hint that there is unification between gravity and electromagnetism.

There is a way we can conduct an experiement to test this hypothesis:

observe gravitational waves (GR) passing through a variable electromagnetic field (emf/v).

(the idea being, the displacement in the field caused by GR leads to the emf/v emmiting electromagnetic waves. The GR energy is transferred into light.)

... so somewhere along the line, is it possible to 'convert' GR into light?

RAD4921: it seems to me that this doesn't really concern UNIFICATION at all. Better to say that in relativistic physics, it is more or less inevitable that physical fields will be "updated" THERE and THEN to take account of changes HERE and NOW in the source of the field by signals traveling at (at most) the speed of light in vacuo. So Maxwell's theory of EM predicts "EM radiation" which travels at c, gtr (and related theories of gravitation) predicts "gravitational radiation" exists and travels at c, toy theories of scalar fields "coupled" in various ways to curvature predict "scalar radiation" which travels at the speed of c, and so on and on.

Symbreak: a "metric theory" of gravitation such as gtr more or less automatically "incorporates" other theories such as Maxwell's theory of EM or a scalar field theory, by allowing the energy of the EM field, or of the scalar field, to gravitate and thus to affect the spacetime geometry. Going the other way, it is more or less inevitable that gravitational radiation, which changes the spacetime geometry, will slightly change a distribution of charge, and thus can affect electromagnetic fields.

Similarly, a passing gravitational wave can affect the propagation of an EM wave. Indeed, without loss of generality, assuming they are not propagating parallel to each other, they can be treated as the collision of a gravitational and an EM wave, and the study of exact solutions answering to this description often have some initially surprising features! (See Griffiths, Colliding Plane Waves in General Relativty, Clarendon Press, 1991, for a very readable survey of this fascinating subject, unfortunately now 15 years out of date.)

Indeed, according to gtr, such effects can be literally "seen", in principle, in the presence of a single gravitational planar "sandwich wave". Imagine an inertial observer in a region of flat spacetime. Along comes a gravitational wave with planar wavefronts and some roughly sinusoidal oscillations as in MTW section 35.9. If the observer looks through approaching wavefronts at more distant objects (e.g. "constellations"), he sees no optical distortions--- of course not, or he would have advance warning of a signal approaching him at the speed of light! But if after the wave passes his location, he turns and looks through departing wavefronts at more distant objects, he will see optical distortions, as revealed by the nonzero expansion and shear scalars of the appropriate null geodesic congruence.

(In mathematical terms, this analysis involves an exact gravitational plane wave solution and a null geodesic congruence, "opposing" the wave vector field of the gravitational plane wave. In physical terms, this scenario involves a strong gravitational wave interacting with weak EM radiation, corresponding to the light from distant constellations or whatever. Needless to say, such a scenario, while fun and instructive to explore as an exercise in gtr, is probably rather hard to arrange in the real universe!)

So it is true that according to gtr, gravitational waves can affect EM waves and vice versa, and even that electromagnetic and gravitational radiation can be "partially interconverted". It turns out that these are very tiny effects--- but you had the right idea!

But again, this kind of mutual influence and partial interconversion is not the same thing at all as unification. In gtr, EM fields and hypothetical scalar fields are treated quite differently from the gravitational field. In a unification, these should somehow stand revealed as different aspects of the same thing, but that doesn't happen in gtr, where various sharp contrasts (in terms of physically observable behavior and mathematical treatment) between gravitational radiation and EM radiation (and between these and scalar radiation) tend to be even more striking than their similarities.

About "incorporation": if one accepts the principle that all forms of mass-energy gravitate, then it is more or less inevitable any good theory of gravitation will be rather generous about what it accepts as admissable forms of mass-energy. It can sometimes be helpful to think of relativistic gravitation theories such as gtr as analogous to thermodynamics, where we seek a theory telling us how energy transformations and transport works in very general terms, without needing to specify a theory of matter. In the same way, a gravitation theory should specify how gravitation works, without needing to specify a theory of matter, or a theory of some field which might also be contributing to the ambient mass-energy present in some location. And indeed, in gtr, to make specific predictions we might need to know something about the stress-energy tensor, but the theory itself happily accepts (almost too happily!) pretty much anything as a term contributing to the stress-energy, if you let it. This isn't really a defect, but a more or less inevitable feature of gravitation theories. My point is that any good gravitation theory will have to "incorporate" EM and other theories, even toy theories made up in school one day. Again, this is not the same thing at all as "unification".

(By the way, the very rough analogy between thermodynamics and gravitation may remind some of a rather specific analogy which turns out to be, apparently, much more than a mere analogy! C.f. "black hole thermodynamics", which has led to such intriguing concepts as optical and acoustical black holes, which may some day afford experimental verification of the existence of Hawking radiation, albeit associated with optical or acoustical holes, rather than the gravitational kind. Presumably the Nobel Prize committee will not quibble if this comes to pass, however! Certainly the optical Hawking radiation would be no less real than gravitational Hawking radiation, if either does indeed exist.)

Hurkyl: you already know about "ascent", in which one tries (roughly speaking) to obtain solutions of some kind (e.g. vacuum solutions) in four-dimensional gtr (or some comparable theory), with specified properties, by trying to extract such solutions from solutions of some kind, with specified properties, in higher dimensions (possibly in some theory other than n-D gtr). But you will probably be intrigued to learn (if you don't already know) that there is a kind of "dual" notion of"descent", in which, for example, one represents vacuum solutions having particular (rather restrictive) symmetry properties as solutions to the 3-D Einstein equations for an artificial type of scalar field. Since 3-D gtr is mathematically and physically quite different from 4-D gtr, the very possibility of making such a representation immediately implies that the originally sought symmetrical vacuum solutions can't exhibit (for example) gravitational radiation.

My point is that in addition to "unification" versus "incorporation" we find a third important theme: "representation" (parse that "re-presentation"), e.g. of 4-D special vacuum solutions as certain nonvacuum solutions in 3-D, and so on.

Chris Hillman

 

[Symbreak]

Chris: thanks for the info on 'Colliding Plane Waves in General Relativty' (http://www-staff.lboro.ac.uk/~majbg/jbg/book/Chap19.pdf ) .

The author makes no hint of implicit unification but it seems clear to me that this is necessary if we follow the GR-EMR connection to its conclusion.

Has it been considered that gravitational waves can be quantized into a form of graviton, so that we achieve a photon-graviton link, possibly unifying gravitation and electromagnetism?

 

[Chris Hillman]

Hi, Symbreak,

I commend you to textbooks which discuss in detail both the many analogies and the sharp differences between EM and gravitational radiation, which are profound. Specifically, you might try both Ohanian and Ruffini, Gravitation and Spacetime, and MTW. Studying the excellent discussion offered by these authors may help you appreciate why gtr certainly does not UNIFY EM and gravitational radiation; quite the contrary. You might also examine the problem book by Lightman et al., which offers some excellent problems intended to further explore this issue. This course of reading should also help you to answer your own question about photons and gravitons. (The short answer is: "yes, it has been considered, and no, naive quantization certainly does NOT yield a unification in the sense in which physicists use that term".)

Chris Hillman