# Does action at distance in electromagnetism violate energyconservation

• hemalpansuriya
In summary, the conversation discusses a paradox involving two charges A and B separated at distance D. Charge B is attached to a spring and can move towards and away from charge A. When charge A is brought closer to charge B and then taken back to its original position, the work done in this process is zero due to conservative forces. However, if this action is done in a time interval less than D/c, charge B does not feel any force or reaction during this time. As the reaction force reaches charge B and causes it to oscillate, work is done on charge A, but charge B gains energy from the oscillation. The conversation also mentions a paper discussing the instantaneous propagation of the Coulomb force and experimental evidence supporting this assumption.
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 ?

meopemuk
hemalpansuriya said:
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!

meopemuk
hemalpansuriya said:
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.

vanhees71 and Delta2
Dale said:
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,

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.

meopemuk said:
Hi hemalpansuriya,

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.

weirdoguy and 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.

meopemuk said:
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.

hemalpansuriya said:
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.

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

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.

Last edited:
Dale said:
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.

weirdoguy
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.

weirdoguy
hemalpansuriya said:
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

## 1. What is action at a distance in electromagnetism?

Action at a distance in electromagnetism refers to the phenomenon where charged particles can interact with each other without physically touching. This is possible due to the existence of an electromagnetic field, which can exert forces on charged particles over a distance.

## 2. How does action at a distance violate energy conservation?

According to the law of energy conservation, energy cannot be created or destroyed, only transferred or converted. However, in action at a distance, the electromagnetic field is able to exert a force on a charged particle without any apparent transfer of energy, which seems to violate this law.

## 3. Is action at a distance a proven concept?

Yes, action at a distance is a well-established concept in electromagnetism, and it has been experimentally confirmed through various experiments and observations.

## 4. Can action at a distance be explained by other theories?

While action at a distance may seem to contradict the principle of energy conservation, it can be explained by the theory of relativity. According to this theory, the electromagnetic field and the charged particles are part of a larger system, and the energy is conserved within this system.

## 5. Are there any potential implications of action at a distance in electromagnetism?

The concept of action at a distance has played a crucial role in the development of modern physics, particularly in the understanding of electromagnetic interactions. It has also led to the development of technologies such as wireless communication and remote sensing, which rely on the ability of the electromagnetic field to act at a distance.

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