Unification of GR and classical E&M

[metrictensor]

It is my view that the road to a unified quantum theory of gravity and electromagnetism begins with unifying GR and E&M classically (i.e. a non quantum mechanical formulation). They show so may similarities that they may be more closely related than we think.

 

[dextercioby]

Interesting.Guess what,Theodor Kaluza thought of it 86 years ago and 79 years ago F.Klein approved giving mathematical consistency to his theory...

Yes,the two CLASSICAL fields have many things in common,but so many different.

Daniel.

 

[metrictensor]

Interesting.Guess what,Theodor Kaluza thought of it 86 years ago and 79 years ago F.Klein approved giving mathematical consistency to his theory...

Yes,the two CLASSICAL fields have many things in common,but so many different.

Daniel.

The two differences that come to mind right away are that gravity is only attractive and that there is no analog to the magnetic field in gravity. But just because these have not been detected does not rule out their existence. We need to keep the options open until they are explicitly rulled out.

 

[pervect]

The two differences that come to mind right away are that gravity is only attractive and that there is no analog to the magnetic field in gravity. But just because these have not been detected does not rule out their existence. We need to keep the options open until they are explicitly rulled out.

Theoretically, there is an analog to the magnetic field in gravity. This is sometimes called gravitomagnetism, and other times called frame dragging.

Some detailed study of the orbits of the Laegos satellites seems to confirm the theoretical predictions of gravitomagnetism/frame dragging, and Gravity Probe B should provide a more direct and precise measurement of this effect.

See for instance

http://www.phys.lsu.edu/mog/mog10/node9.html

for more details.

 

[selfAdjoint]

It is my view that the road to a unified quantum theory of gravity and electromagnetism begins with unifying GR and E&M classically (i.e. a non quantum mechanical formulation). They show so may similarities that they may be more closely related than we think.

This is what Einstein and Schroedinger were working on. http://www.einstein-schrodinger.com/ has carried the work farther and claims to have achieved a full EM field in the combined theory by careful choice of parameters.

 

[Chronos]

GR and EM cannot be unified classically.

 

[eNathan]

What if a new theory came along, that explains relativit, gravity, and EM, QM, and everything of that matter Maybe in 1000 years, til then, there must be a unification. Its like saying gravity and relativity have no unification, until it came along (Einstine). Perhaps the current theories make unification close to imposible, because they don't describe everything 100% accuratly. I am my opinion, there will be a unification, when the right theory comes along, but classicly, probally not.

 

[metrictensor]

GR and EM cannot be unified classically.

Not a very scientific statement.

 

[member 11137]

Not a very scientific statement.

Certainly yes, but a correct statement.
For a more complete explanation, it should be (for example) good to consider the mathematical difficulties encountered by the Theory of Spinors (TS) to connect with the GR. As one knows that the TS is an excellent tool to describe rotations and reversals, that the Faraday's tensor (the EM strength tensor; 4-D representation) accepts a (4-4) matrix representation that can be considered as the representation of a bivector and that this one is equivalent to an infinitesimal rotation... one can may be guess the end of this unsuccess story and understand the statement. Regards

 

[franznietzsche]

GR and EM cannot be unified classically.

Yes they can.

Kaluza-Klein, by extending GR to five dimensions you get Maxwell's equations as well.

Unless i am misunderstanding Kaluza-Klein?

 

[dextercioby]

The point is:do you understand this theory...??Altogether,not only the results...

Daniel.

 

[member 11137]

The point is:do you understand this theory...??Altogether,not only the results...

Daniel.

We certainly could have a long discussion as long as we would not have a common definition of the word "classical". If this word is a reference to a certain period of the history, this must be to the period +- 1890- 1920. EM theory was formulated in a 3-D space with consideration for the evolution of the things that is with consideration for the time. The GR is a kind of generalization of the Special Relativity which is introducing the time as an "adult" independant dimension in the discussion and we get with this a 4-D Theory. If we stop the history here, then the Klein-Kaluza Theory which is obviously an interesting generalization of the GR is no more classical. As you see just a question of definition concerning "classical"... Regards

 

[franznietzsche]

The point is:do you understand this theory...??Altogether,not only the results...

Daniel.

In a word: no. I'll admit that.

But if my understanding of what it means is incorrect, please reeducate me.

 

[dextercioby]

No,the result is okay.Indeed,Kaluza was able to write a Lagrangian action which,when reduced to 4D,would yield both H and Maxwell actions...


Daniel.

 

[franznietzsche]

We certainly could have a long discussion as long as we would not have a common definition of the word "classical". If this word is a reference to a certain period of the history, this must be to the period +- 1890- 1920. EM theory was formulated in a 3-D space with consideration for the evolution of the things that is with consideration for the time. The GR is a kind of generalization of the Special Relativity which is introducing the time as an "adult" independant dimension in the discussion and we get with this a 4-D Theory. If we stop the history here, then the Klein-Kaluza Theory which is obviously an interesting generalization of the GR is no more classical. As you see just a question of definition concerning "classical"... Regards

Classical in physics generally means non-quantized. Continous quantities and the like.

 

[dextercioby]

The K-K theory is very classical,simply because at 1919,the QM was inexistent...So yes,history decides,even not knowing what the theory itself was about...

Daniel.

 

[Chronos]

GR and EM cannot be unified classically.

Yes they can.

Kaluza-Klein, by extending GR to five dimensions you get Maxwell's equations as well.

Unless i am misunderstanding Kaluza-Klein?

Indeed, but Kaluza-Klein does not unify GR and EM any more than Einstein-Maxwell and produces results that do not agree with observation. Einstein spent half his life trying to classically unify GR with EM without success. No modern theorists, AFAIK, seriously consider it possible. Of course you need to define what is 'classical' to lend any meaning to such a statement. I generally think of it as the pre-quantum physics era. Perhaps it would be more rigorous to define it as solutions possible using only the mathematical tools available before the later half of the 20th century.

The problem inherent to both GR and EM is they are incomplete. It is understandably difficult to unify theories that are themselves incomplete. Neither GR or EM are quantum theories, hence they are not considered theories of fundamental interactions, as are quantum theories. Maxwell's EM is an effective field theory or "classical" limit of a renormalizable quantum field theory - quantum electrodynamics [QED]. A renomalizable quantum field theory of gravity has not been found and there is no apparent way to unify EM and GR without a quantum theory of gravity. Bear in mind the only sucessful unification theory developed to date - GWS electroweak - came from QED. I seriously doubt any other successful unification theory will be achieved using a 'classical' approach. Perhaps string theory will ultimately triumph. But, you can hardly call string a classical approach with a straight face.

 

[franznietzsche]

Indeed, but Kaluza-Klein does not unify GR and EM any more than Einstein-Maxwell and produces results that do not agree with observation.

Ok, this i did not know. I had assumed that KK was simply not pursued because with the discovery of quantum mechanics, maxwell's equations would have been outdated(the 'classical' limit), and so unifying GR with Maxwell would have been moot.

A renomalizable quantum field theory of gravity has not been found and there is no apparent way to unify EM and GR without a quantum theory of gravity. Bear in mind the only sucessful unification theory developed to date - GWS electroweak - came from QED. I seriously doubt any other successful unification theory will be achieved using a 'classical' approach. Perhaps string theory will ultimately triumph. But, you can hardly call string a classical approach with a straight face.

I have read about good things coming in the field of loop quantum gravity, which surpisingly, i rarely ever hear mentioned here, while string theory is brought up all the time.

 

[Chronos]

There are a number of us here that are very interested in LQG, but, most discussions are inspired by recent advances. String advocates are less frequently so inspired, but more passionate.

 

[metrictensor]

There are a number of us here that are very interested in LQG, but, most discussions are inspired by recent advances. String advocates are less frequently so inspired, but more passionate.

This is a ridiculous statement. How can you say string advocates are more passionate? This is completely ill-logical.

 

[metrictensor]

Ok, this i did not know. I had assumed that KK was simply not pursued because with the discovery of quantum mechanics, maxwell's equations would have been outdated(the 'classical' limit), and so unifying GR with Maxwell would have been moot.



I have read about good things coming in the field of loop quantum gravity, which surpisingly, i rarely ever hear mentioned here, while string theory is brought up all the time.

LQG is very interesting and it seems that some comments here are made w/o knowledge of what LQG is doing. It is not like string theory in being an attempt to unify the 4 fundamental forces. It is only a quantum theory of gravity. The problem with quantum field theories, including QED, is that they are not background independent. As long as a theory assumes an independent background it will not be compatible with GR.

 

[selfAdjoint]

This is a ridiculous statement. How can you say string advocates are more passionate? This is completely ill-logical.

See the comments by Lubos Motl on any post at Not Even Wrong that disparage or even criticize string physics.

 

[jcsd]

It shouldn't be LQG vs. String physics, aftre all it may very well turn out that LQG is just a low energy approximation of string physics. It seems to me that for a theory with no supporting direct evidence string theory got a lot of exposure in the media which then in turn caused a backlash and now it seems fashionable to take pot shots at string theory, which is still a promising candidate for a TOE.

 

[metrictensor]

See the comments by Lubos Motl on any post at Not Even Wrong that disparage or even criticize string physics.

Obviously there will be passionate advocates of both sides. The point is that to make such a broad generalization is absurd.

Here is debate a on the virtues of LQG and ST. Although this is one isolated incident it is obvous who wins and is indicative of the old guard's thinking.

 

[metrictensor]

It shouldn't be LQG vs. String physics, aftre all it may very well turn out that LQG is just a low energy approximation of string physics. It seems to me that for a theory with no supporting direct evidence string theory got a lot of exposure in the media which then in turn caused a backlash and now it seems fashionable to take pot shots at string theory, which is still a promising candidate for a TOE.

LQG and string theory may also help one another. There are good qualities of each theory that the other does not have. For example, LQG is background independent while string theory is not. The techniques used by LQG to resolve this may be applicable.

As far as a low energy limit it is possible that LQG could come out of ST in this sense. What is important to understand is that they are not competing unified theories. LQG is simply a quantum theory of gravity. It does not address the standard model in the way ST does.

 

[Chronos]

Agreed. A background independent version of string theory would greatly improve its appeal. Even Witten has said as much. The attractive feature of LQG is its limited focus. A quantum theory of gravity is the first, and most important toward any TOE [that may or may not be out there]. Without quantum gravity, a TOE is an unattainable and useless effort. The perceived conflict between LQG and string is imaginary, IMHO.

 

[metrictensor]

Agreed. A background independent version of string theory would greatly improve its appeal. Even Witten has said as much. The attractive feature of LQG is its limited focus. A quantum theory of gravity is the first, and most important toward any TOE [that may or may not be out there]. Without quantum gravity, a TOE is an unattainable and useless effort. The perceived conflict between LQG and string is imaginary, IMHO.

The idea that LQG and ST are mutually incompatible is more a matter of opionion than fact. I would say that LQG is more realistic in that t does not postulate things like 11 dimentions or supersymetry. It is based only upon GR and QM.