Is E=MC2 the Complete Equation for Energy-Mass Relation?

[pmb_phy]

One last note: I hope I did not give the impression that c is not constant or that the photon's proper mass is not zero. This was never my intent. I was merely pointing out that the logic to which one applies to relativity requires certain postulates.

Pete

 

[reilly]

In QFT there are big differences between massless and massive particles, all due to no rest frame exists for massless particles. As anyone who has grappled with QED quantization, the difficulties of quantizing a massless spin 1 field are tougher than for a massive spin1 system, all due to the requirements of gauge invariance.

Pete is right about Proca, (see, also, Gross's and Weinberg;s QFT tomes for more about gauge invariance, masses and no masses). One can certainly generalize Maxwell by using a massive vector field, but I'd say there would undoubtedly be some controversy about nomenclature -- I'd suggest something like Generalized Maxwell Equations.

E&M with a mass would have an exp(-Mr) term, where M is dependent upon the rest mass, m. I would guess that atomic spectra computations might be another source for measuring any photon mass. (The Fourier Xform of the non-spin part of the massive E&B field will be of the Klein-Gordon eq. form, 1/(p*p + m*m) where p is momentum, m is photon mass.)

For a photon in flat space, mass=0, c= constant are equivalent. And, I believe with my little theorist's brain that indeed c=constant, the upper bound on photon mass is pretty small.
Regards.
Reilly Atkinson

 

[clj4]

Einstein's or Lorentz's derivations, or Maxwell's Eq.'s in vacuum are all elegant and profound -- but if they did not do well when exposed to Nature, we would not know much about them. And they are all based on the vacuum speed of light being constant for all inertial frames, so that they do well when confronted with experiments and observations

No one argues with that.

Pete is right -- we don't have a clue why c=constant for all intertial observers -- one could consider this equality a gift from Nature, but that doesn't say much.
Regards,
Reilly Atkinson

This is not what Pete asked. He asked textually:

Nobody knows why the speed of light is Lorentz invariant (i.e. remains unchanged by a Lorentz transformation, i.e. change from one inertial frame to another.

...which is an ill posed question. To an ill-posed question there is no right answer. We all know that.
Had he asked "why is that the speed of light is invariant to frame change" I would have answered differentlly , that Einstein had to postulate this in order to have all the pieces (experimental observation+Maxwell's theory) coalesce into a new, unitary theory. But he didn't ask that.

 

[rbj]

That is only true if one assumes that the photon's proper mass is zero, i.e. add the photon mass zero postulate of you define the term Maxwell's equations to be those equations of electrodynamics for which the proper mass is zero. Do you have the text Classical Electrodynamics - 3rd Ed. J. D. Jackson, Wiley Press (1999)? If so then please see Section 12.8 Proca Lagrangian; Photon Mass Effects page 600.

i don't have that book (indeed, i am not a physicist nor a graduate from physics, but an electrical engineer who got his fields course in the EE department), but the Maxwell's Equations that i am referring to are:

\nabla \cdot \mathbf{E} = 0

\nabla \cdot \mathbf{B} = 0

\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}} {\partial t}

\nabla \times \mathbf{B} = \frac{1}{c} \frac{\partial \mathbf{E}}{\partial t}

or similar. there is nothing in them that has anything to do with photons, photon mass, or any reference to particle-like properties of light. these are wave equations. it is true that if interpreted as being valid only in the frame of reference of the aether, then the wave speed would be c only in that frame of reference. but if, as Einstein thought, that the equations are equally valid for any intertial frame of reference, then c is the same for any of these frames of reference since there is no reason for it to be different.

the reason that the speed of sound is different for different moving observers is that you can tell if the medium (air) is moving past you at some velocity. then you can measure the speed of sound to be different upwind than downwind. but if there is no medium of propagation for E&M and if you cannot tell if a vacuum is moving past you or not, there may be no meaning to a velocity of a vacuum, then there is no reason for c to be different for one inertial observer than for any other inertial observer, even as they observe the same beam of light.

i disagree that no one knows why c is constant. i think Einstein told us why it is (and some of the consequences of that). or, at least, why it was most reasonable to make that presumption.

 

[pmb_phy]

This is not what Pete asked. He asked textually:

I am baffeled as to how you think that was a question.

At best it was a confusing definition since people assume that the Lorentz transformation is defined by an equation rather than by requirement. The requirement is invariance of c. The equation is that which is derived by requiromg c=const.

I got a response from J.D. Jackson on the QFT/photon mass question. I asked

Dear Dr. Jackson

I'm reading your EM text regarding the Proca Lagrangian and I was wondering if you could tell me whether or not a nonzero photon mass would change QFT. Does QFT require/postulate that the photon mass is zero?

Thanks

Peter M. Brown

Dr. Jackson responded with

Peter,
QFT is an umbrella category that labels any quantum theory with an infinite number of degrees of freedom, e.g., the normal modes of sound waves in a box. The Proca lagrangian is another example, as are the lagrangians of QED and QCD. If you question really is does QED require/postulate that the photon mass be zero, the answer is yes. My discussion of the Proca lagrangian is purely classical, but that lagrangian can be the basis of a QFT.

J. D. Jackson

Pete