Does action at distance in electromagnetism violate energyconservation

[hemalpansuriya]

Consider two charges A and B separated at distance D. charge B is attached on spring and can move towards and away from charge A. Now charge A is brought closer to charge B and then it is taken back to its original position. Work done in this process is zero because of conservative forces. If this action is done in time interval less than D/c, then charge B does not feel any force or reaction during this time. Now as this reaction force reaches to charge B, it will oscillate. In this process work done on charge A is zero but charge B is having energy due to oscillation. Is energy conservation violated in this retarded action ?

 

[russ_watters]

Consider two charges A and B separated at distance D. charge B is attached on spring and can move towards and away from charge A. Now charge A is brought closer to charge B and then it is taken back to its original position. Work done in this process is zero because of conservative forces. If this action is done in time interval less than D/c, then charge B does not feel any force or reaction during this time. Now as this reaction force reaches to charge B, it will oscillate. In this process work done on charge A is zero but charge B is having energy due to oscillation. Is energy conservation violated in this retarded action ?

Of course not. Where is it written that energy conservation must apply instantaneously across a distance? As long as you remember where you put it, it's accounted for!

Heck, my car has been sitting in my garage with the engine off for two hours and it's still giving off heat!

 

[Dale]

charge A is brought closer to charge B and then it is taken back to its original position. Work done in this process is zero because of conservative forces.

Work done in the process is nonzero because of the radiation produced.

 

[hemalpansuriya]

Work done in the process is nonzero because of the radiation produced.

Oscillation energy produced at charge B is also depends on magnitude of charge B. Because more charge, more force and hence more oscillating amplitude of charge B. We can take as much large magnitude of charge B as we want. This does not affect radiation energy at charge A, but it will increase energy of oscillation of charge B. So, radiation energy can not account for whatever energy is produced at the charge B.

 

[meopemuk]

Hi hemalpansuriya,

I like your paradox. A similar setup was discussed in

A. Kislev, L. Vaidman, "Relativistic causality and conservation of energy in classical electromagnetic theory", Am. J. Phys. 70 (2002), 1216; arXiv:physics/0201042v1

But I don't think the authors did a good job at providing a solution.
Eugene.

 

[hemalpansuriya]

Hi hemalpansuriya,

I like your paradox. A similar setup was discussed in

A. Kislev, L. Vaidman, "Relativistic causality and conservation of energy in classical electromagnetic theory", Am. J. Phys. 70 (2002), 1216; arXiv:physics/0201042v1

But I don't think the authors did a good job at providing a solution.
Eugene.

Yes, I have also gone through it. But I am not convinced with author's solution. I believe that for this problem classically energy can not be conserved. I don't have any further quantum mechanical explanation.

 

[meopemuk]

Here is another relevant paper:

W. Engelhardt, "Relativity of Time and Instantaneous Interaction of Charged Particles", Am. J. Mod. Phys. 4 (2015), 15.

It discusses exactly the same setup with two charges as proposed by you. The author seeks the resolution of this paradox in assuming the instantaneous propagation of the Coulomb force. There is experimental evidence that this assumption may have some validity:

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, "Measuring propagation speed of Coulomb fields", Eur. Phys. J. C, 75 (2015), 137. arXiv:gr-qc/1211.2913v2.

Eugene.

 

[hemalpansuriya]

Here is another relevant paper:

W. Engelhardt, "Relativity of Time and Instantaneous Interaction of Charged Particles", Am. J. Mod. Phys. 4 (2015), 15.

It discusses exactly the same setup with two charges as proposed by you. The author seeks the resolution of this paradox in assuming the instantaneous propagation of the Coulomb force. There is experimental evidence that this assumption may have some validity:

R. de Sangro, G. Finocchiaro, P. Patteri, M. Piccolo, G. Pizzella, "Measuring propagation speed of Coulomb fields", Eur. Phys. J. C, 75 (2015), 137. arXiv:gr-qc/1211.2913v2.

Eugene.

According to this author, interactions are instantaneous, which we know it can not be true. As light also have finite speed, Coulomb interactions can not be instantaneous. The only way is, energy is not conserved.

 

[Dale]

We can take as much large magnitude of charge B as we want. This does not affect radiation energy at charge A, but it will increase energy of oscillation of charge B.

Don't forget the self force on an accelerating classical point particle. That is the problem with all such analyses.

So, radiation energy can not account for whatever energy is produced at the charge B

Please show your work.

Poynting’s theorem guarantees that this claim is false. The self force is essentially a free variable which can always be set to satisfy Poynting’s theorem.

 

[hemalpansuriya]

Please show your work.

Any arbitrary large value of charge B does not increase the energy radiated by charge A. But , having larger value of charge B will produce large amount of oscillating energy. So, we can not have equal amount of energy transfer here. Moreover, radiated energy from charge A does not even reach to charge B, because charge B is placed in line with acceleration vector of charge A. Energy radiated by any charge in line of its acceleration vector is simply zero.

 

[Dale]

Handwaving is not showing your work.

Your handwaving neglects both the self force at B and also Poynting’s theorem. Show your work including both. You are making an exceptionally strong claim with an exceptionally weak justification.

Also, since the problems with classical point particles are well known it would be more convincing to use something more realistic.

 

[vanhees71]

Yes, I have also gone through it. But I am not convinced with author's solution. I believe that for this problem classically energy can not be conserved. I don't have any further quantum mechanical explanation.

I've not followed the argument in the paper yet, but in classical electromagnetic theory energy is always strictly conserved. You only have to carefully take into account the total energy-momentum-stress tensor.

 

[Dale]

This thread is closed for now. Please PM me with your work to reopen it.