Does Hoyle C field violate conservation of energy-momentum?

[bcrowell]

That theorem forbids interaction in a Hamiltonian formulation which means you can't use canonical quantization. I'm not sure, but maybe you can quantize such theories using path integrals.

EDIT:
Yeah, I found it. But I haven't read it! The abstract says it uses a S-matrix.

I guess I'm really confused now. Isn't it true that E&M can also be quantized using a Hamiltonian? If it can also be expressed as a direct field, wouldn't that be a counterexample to CJS?

 

[ShayanJ]

I guess I'm really confused now. Isn't it true that E&M can also be quantized using a Hamiltonian? If it can also be expressed as a direct field, wouldn't that be a counterexample to CJS?

It seems to me your problem is with the CJS theorem itself. I quote a good statement of the theorem from Eric Gourgoulhon's special relativity in general frames:

according to a theorem established by D.G. Currie, J.T. Jordan and E.C.G. Sudarshan (1963), the conditions
(i) Invariance of the Hamiltonian structure under the action of the Poincare group.
(ii) Using the spacetime coordinates of the particles as canonical coordinates.
are not compatible, except if there is no interaction between the particles. This result has been called the no-interaction theorem.

I also should note that he explains this in the context of such direct interaction theories. The point is, the structure of the actions are very different for Maxwell EM+charged particles and charged particles with direct interaction. In the former the coordinates of the particles only couple to field variables while in the latter they should couple to each other. The CJS theorem says that such direct coupling causes an inconsistency. But there is nothing wrong with the coupling of coordinates to field variables.

 

[bcrowell]

I guess it's going to be hard (for me at least) to figure out what's going on without reading the Davies article, which I don't have access to.

 

[bcrowell]

I realized something that I hadn't noticed before. Hawking and Ellis have this:

"[The weak energy condition] will not hold for the 'C'-field proposed by Hoyle and Narlikar (1963). This again is a scalar field with m zero, only this time the energy-momentum tensor has the opposite sign and so the energy density is negative. This allows the simultaneous creation of quanta of positive energy fields and of the negative energy 'C'-field."

This looks wrong to me. The C field has the stress-energy tensor of a perfect fluid with *zero* energy density and negative pressure. Classically, it doesn't patch up conservation of energy-momentum by making enough negative energy to cancel out the positive energy of the newly created atoms. There is no negative energy. So my mental pictures of an unfilled Dirac sea were all wrong, I guess.

I think this sort of makes sense because if the C field compensated for the creation of atoms simply by canceling out their energy with negative energy, then every region of space at all times would have zero energy density, which is not what we observe.