The Wheeler-Feynman Absorber Theory

When I first wrote this article my definition of Radiation Resistance was incorrect.

While updating my Mass and Charge article in 2017 I realised that Radiation Resistance is not electrical resistance in the normal sense but the 'resistance to acceleration' of free electrons in a transmitter aerial. It appears as soon as current starts to change. This indicates that it is a local effect within the aerial itself. It cannot be caused by interaction with the receiving aerials (as proposed in the Wheeler-Feynman Absorber Theory) for two reasons. Any such interaction would have to be immediate and coherent. However, there will be a time delay in any feedback from a receiver aerial due to the distance between the transmitter and receiver aerials. Also, these feedback signals may not be in phase with one another and not coherent when arriving at the transmitter due to the different distances between the transmitter and various receivers.

I now propose that Radiation Resistance is due to Self-inductance in the transmitter aerial. When the free electrons accelerate, relative to the electrical presence of the excess protons which surround them, they experience a force opposing their motion as described in the Self-inductance topic in my Mass and Charge article.

I have left my original article unchanged to show my train of thought at the time and because I still consider my critique of the Wheeler-Feynman Absorber Theory to be valid.

The theory

The Wheeler-Feynman Absorber Theory is described in John Gribbin's book 'Schrödinger's Kittens' as an attempt to explain 'radiation resistance'. This term originated in radio technology. The medium into which the aerial is radiating can be said to be equivalent to a circuit of resistance R. R can be calculated from the input power and current to the aerial.

This is the relevant excerpt from John Gribbin's book 'Schrödinger's Kittens' (page 238):

'It works like this. When an electron vibrates, ..., it attempts to radiate by producing a field which is a time-symmetric mixture of a retarded wave propagating into the future and an advanced wave propagating into the past. As a first step in getting a picture of what happens, ignore the advanced wave and follow the story of the retarded wave. This heads out into the future until it encounters an electron which can absorb the energy being carried by the field. The process of absorption involves making the electron that is doing the absorbing vibrate, and this vibration produces a new retarded field which exactly cancels out the first retarded field. So in the future of the absorber, the net effect is that there is no retarded field. But the absorber also produces a negative-energy advanced wave travelling backwards in time to the emitter, down the track of the original retarded wave. At the emitter, this advanced wave is absorbed, making the original electron recoil in such a way that it radiates a second advanced wave back into the past. This ‘new’ advanced wave exactly cancels out the ‘original’ advanced wave, so that there is no effective radiation going back into the past before the moment when the original emission occurred. All that is left is a double wave linking the emitter and the absorber, made up half of a retarded wave carrying positive energy into the future and half of an advanced wave carrying negative energy into the past (in the direction of negative time). Because two negatives make a positive, this advanced wave adds to the original retarded wave as if it too were a retarded wave travelling from the emitter to the absorber.'

Problems

I have considered this scenario from the classical viewpoint (with many electrons radiating a wave front), from the quantum viewpoint (with individual electrons emitting photons), and from the strange hybrid viewpoint, as used above, where the radiation is described in terms of waves but no allowance is made for attenuation with distance. I reached the same conclusion in each case.

That is, there are at least two major flaws in the theory as described by John Gribbin. I have highlighted the relevant passages in the text.

1. Replace the statement 'ignore the advanced wave and follow the story of the retarded wave' with 'ignore the retarded wave and follow the story of the advanced wave'. This is a perfectly valid thing to do if the interaction is time-symmetric. Then, using the same argument, you arrive at the conclusion that the emitter radiates only to an absorber in its past.

I consider that this flaw alone is enough to cast serious doubt on the idea. However, the second flaw is worth mentioning as it points the way to an alternative conjecture.

2. The statement 'At the emitter, this advanced wave is absorbed, making the original electron recoil' implies that the recoil cancels out the effect of the original motion of the emitter. This is wrong. The reaction (the recoil) of the emitter to the motion of the second electron would be in addition to the original motion of the emitter, causing an additional retarded wave to propagate into the future. This positive feedback would initiate a 'race condition', and the motion of both the emitter and the absorber would instantaneously increase to… an infinite value.

An alternative conjecture

Instead of starting with the motion of an isolated electron (the emitter), consider the interaction between two electrons (A and B) as a whole. That is, two events (a cause and an effect) linked by a link entity (a wave or photon).

Space-time diagram of an interaction between two charges

If you consider time to go 'forwards', the motion of A is the cause and the motion of B is the effect. If you consider time to go 'backwards', the motion of B is the cause and the motion of A is the effect. If the interaction is time-symmetric either viewpoint is valid.

The link entity can be considered to operate in either direction. The 'recoil' is not in addition to the original motion of A. The recoil is the original motion of A, so there is no positive feedback and no race condition, and there is no propagation either side of the interaction.

Moreover, in the direction in space-time in which the link entity acts, both time and space have a value of zero. (Due to time dilation and space foreshortening) This supports the notion that an interaction should be viewed as a whole.

The arrow of time

If electrical interactions are time-symmetric, time can be considered to flow in either direction (when considering purely electrical interactions). This means that the past and the future must exist 'all the time', and leads to the conclusion, unpopular with many people, that free will is an illusion. If this is unacceptable you must conclude the opposite; that the past, as well as the future, is 'not fixed' which could be even less acceptable.

Either one of the above conclusions is true or the interactions between charged particles are not time-symmetric. Is there a way out of this dilemma? (Not forgetting that the interactions between charged particles might not be time-symmetric and one of the above conclusions could still be true.)

All known charged particles have mass as well as charge. Interactions between masses are not time-symmetric. (For example, the suck-blow phenomenon.) The universe itself is not time-symmetric. It is, after all, expanding, perhaps open-endedly. The interaction between the charges of two electrons is vastly greater than the interaction between their masses, but it appears that the effect of their masses cannot be ignored. So, interactions between charged particles might not be time-symmetric after all.

The Wheeler-Feynman Absorber Theory

The theory

Problems

An alternative conjecture

The arrow of time

More questions