Relativity and matter by Pauli

[TrickyDicky]

I've recently had the oportunity to read the fantastic work Wolfgang Pauli did to summarize the theory of relativity for an encyclopedic article and I have a question about the final part of the article where Pauli addresses the problems of the theory to ultimately solve the problem of the structure of matter and stationary charges to conclude that no theory including GR has satisfactorily solved it.

One statements of Pauli that I would like to get some modern opinion about ( it has more to do with elctrodynamics but given the context I figured it fitted here)is the following:
"We therefore see that the Maxwell-Lorentz electrodynamics is quite incompatible with the existence of charges, unless it is supplemented by extraneous theoretical concepts".
I guess this has to do with the annoying problem of self-interaction that is confronted also by QFT.
Is this considered nowadays as a true inconsistence of classical electrodynamics?

 

[Mentz114]

There is no such problem in GR, ( Einstein-Maxwell equations ) where the electric fields contribute to the curvature. Perhaps the perceived inconsistency stated in "Maxwell-Lorentz electrodynamics is quite incompatible with the existence of charges," is because this contribution is ignored ?

 

[TrickyDicky]

There is no such problem in GR, ( Einstein-Maxwell equations ) where the electric fields contribute to the curvature.

Remember electric fields are produced not only by static charges but by time-varying magnetic fields also, and besides in relativity we usually use the electromagnetic tensor.
Anyway clearly there is such problem in GR (that is Pauli's point at the end of his article-book). Einstein-Maxwell equations assume a point charge singularity, and require to use the EM stress-energy tensor rather than the general Tab of the EFE and have to include the cosmological constant lambda(they are only valid in the absence of matter so they aren't of any help for what is inquired in the OP). There are no solutions of the EFE with stress-energy tensor for point particles or charges.

 

[WannabeNewton]

Could you quote the exact phrase? The issue of point particles/point charges in the electromagnetic and gravitational case for curved space-time backgrounds was dealt with in a rigorous manner by Wald and Sam Gralla across like 3 papers when discussing the back reaction forces in both electromagnetism and gravitation.

 

[TrickyDicky]

Could you quote the exact phrase? The issue of point particles/point charges in the electromagnetic and gravitational case for curved space-time backgrounds was dealt with in a rigorous manner by Wald and Sam Gralla across like 3 papers when discussing the back reaction forces in both electromagnetism and gravitation.

Hi,WN. What exact phrase? I'm not sure if you refer to Pauli's quote which I quoted exactly from his book "Theory of relativity" that you can find in the Look inside feature of Amazon.com (page 186), or are you referring to the post #3 last line?

 

[Bill_K]

"We therefore see that the Maxwell-Lorentz electrodynamics is quite incompatible with the existence of charges, unless it is supplemented by extraneous theoretical concepts"

From what I can see of the book online, Pauli is discussing the failed attempts by Abraham and Lorentz to build a stable electron purely from electromagnetism.

 

[TrickyDicky]

From what I can see of the book online, Pauli is discussing the failed attempts by Abraham and Lorentz to build a stable electron purely from electromagnetism.

He indeed is doing that at the beginning of that section, it is when justifying that the rigid electron of the Abraham theory is actually foreign to electrodynamics that he introduces the incompatibility between charges and electrodynamics. A more modern treatment of this is found here: http://philpapers.org/rec/FRIIIC

 

[Mentz114]

Remember electric fields are produced not only by static charges but by time-varying magnetic fields also, and besides in relativity we usually use the electromagnetic tensor.
Anyway clearly there is such problem in GR (that is Pauli's point at the end of his article-book). Einstein-Maxwell equations assume a point charge singularity, and require to use the EM stress-energy tensor rather than the general Tab of the EFE and have to include the cosmological constant lambda(they are only valid in the absence of matter so they aren't of any help for what is inquired in the OP). There are no solutions of the EFE with stress-energy tensor for point particles or charges.

Point taken.
Are you sure about the last line? The SET of the Reissner-Nordstrom solution looks like that of a point charge to me.

 

[WannabeNewton]

There are no mathematically meaningful solutions to the EFEs in which the SET is given by a delta function source representing the worldline of a time-like point particle. See the classic paper: http://prd.aps.org/abstract/PRD/v36/i4/p1017_1

 

[Mentz114]

There are no mathematically meaningful solutions to the EFEs in which the SET is given by a delta function source representing the worldline of a time-like point particle. See the classic paper: http://prd.aps.org/abstract/PRD/v36/i4/p1017_1

OK, that's good to know. So the RN electric field is sourced by a distribution of charge, not a point charge.

 

[TrickyDicky]

OK, that's good to know. So the RN electric field is sourced by a distribution of charge, not a point charge.

Not really. Again the Einstein-Maxwell equations of which the RN is a solution don't include the SET but the EM SET and are therefore not the full EFE, they model the exterior gravitational field of a point charge singularity. They can be considered a variant of Gab=0.

 

[Mentz114]

Not really. Again the Einstein-Maxwell equations of which the RN is a solution don't include the SET but the EM SET and are therefore not the full EFE, they model the exterior gravitational field of a point charge singularity. They can be considered a variant of Gab=0.

I'm not getting this, especially "...not the full EFE, ..." bit. I'll do some reading and watch this thread.

 

[WannabeNewton]

When writing down the Einstein-Maxwell equations for the RN metric, we are considering the energy-momentum tensor of a spherically symmetric Maxwell tensor in a spherically symmetric space-time; that is the only assumption that is made a priori; there is absolutely no mention of point charges or anything of the likes. The energy-momentum tensor associated with the Maxwell tensor is of course a specific type of energy-momentum tensor. It will turn out that the electromagnetic field takes the form $-\frac{Q}{r^{2}}$, in Schwarzschild coordinates, if we ignore the duality rotation that gives the magnetic monopole term, where $Q$ is the total charge of the spherically symmetric configuration (it will agree with the Komar integral for charge). This spherically symmetric configuration can be for example a charged static black hole.

EDIT: Mentz since you just got Wald, check out problem 3 of chapter 6.

 

[TrickyDicky]

When writing down the Einstein-Maxwell equations for the RN metric, we are considering the energy-momentum tensor of a spherically symmetric Maxwell tensor in a spherically symmetric space-time; that is the only assumption that is made a priori; there is absolutely no mention of point charges or anything of the likes. The energy-momentum tensor associated with the Maxwell tensor is of course a specific type of energy-momentum tensor.

In this kind of free space solutions the mass and charge are considered part of the boundary conditions either when used to model RN black holes or other charged objects.

When talking about singularities I was concentrating obviously on RN black holes.