Upfront Disclaimer - (as I’m sure will soon be apparent) I have essentially no knowledge or understanding of quantum physics. Still, I’m not gonna let that stop me from asking my question.
In Wheeler-Feynman Absorber Theory, it’s my ‘understanding’ that electromagnetic waves (or charges) can be either retarded or advanced, with the latter seemingly in violation of the basic principle of causality. However, according to the theory, no paradoxes ensue because the various waves all cancel out exactly and/or are totally absorbed by the other particles in the Universe.
My question has to do with the impact of the Uncertainty Principle on the ostensibly “exact” cancellation or absorption as mentioned above. Wouldn’t the Uncertainty Principle guarantee that the cancellation is not, and cannot ever, be exact? In other words, some small part of the advanced wave would ‘survive’ uncanceled. And, that would imply that the travel or transmission of at least some information is, potentially, in violation of causality. I think.
I am not trying to argue that any information transmitted or ‘surviving’ in this way would be useful or could be used to communicate backwards in time. My only point is that according to the way I am interpreting things, there should be some ‘leakage’ of information that would seem to violate causality.
No, the cancellation isn’t always exact, but the residual is so small as to be literally lost in the noise. Keep in mind that the uncertainty principle also applies to time measurements, as well as space measurements (specifically, the product of time uncertainty and energy uncertainty has a minimum possible value, similarly to position and momentum).
Not surprising. Still, the conclusion is a neat one, i.e. although not identifiable in the “noise”, there is nonetheless information arriving from the future. Extraordinary (if only in a ‘philosophical’ sense).
Hmm, I’m not sure I agree with this. I’m not too familiar with the Wheeler-Feynman idea, but it seems to me as if the argument ought to work just as well for ordinary spatial interference of waves. But there, you actually have places of total destructive interference, i.e. where the probability of detecting any light is exactly zero. The reason this is not in conflict with the uncertainty principle is that it’s the wave function that interferes, not any observable quantity.
From another point of view, uncertainty relations exist only between certain sets of quantities, called ‘conjugate’ or ‘complementary’ pairs. But interference depends only on the relative phase of the waves, which, as a single quantity, can be as definite as one likes (though the phase is a bit dicey as an observable in quantum mechanics).
Finally, uncertainty principles are only relevant in a measurement context, so they ought only matter for interference if, given the resulting wave, a measurement could be executed upon it such that one can infer information about two conjugate quantities going beyond the limit imposed by the uncertainty relations (in fact, Einstein suggested a thought experiment along these lines at Solvay, purporting to show that one can use an interference experiment to circumvent the uncertainty relations, and thus, that quantum mechanics doesn’t yield a complete description of physical reality; Bohr soon could expose the flaw in his reasoning, however).
But I haven’t really given this much thought, so I’d be happy to be corrected.
I think the simplest answer is that when you go into the quantum realm whatever it is that cancels out (the probability density of finding light at a point, the expectation density of making some sort of measurement on the electromagnetic field at a point, or something more esoteric) is not something that is a quantum mechanical observable anyway and therefore the uncertainty principle is not directly relevant in this way.
This is pretty much what HMHB has said, but I would just add that how you would interpret Wheeler-Feynman absorber theory in the context of quantum mechanics depends on how you mover from classical electromagnetism to quantum theory and the interpretations you make (as well as the possible problems that may be thrown up by those interpretations).
This does not address the OP’s question, but I suggest using energy-time uncertainty principles with caution. Energy and time are not conjugate variables like position and momentum. In most formulations time is a real number, measured precisely by a classical clock. It is possible to define energy-time uncertainty principles for specific systems, sometimes describing uncertainty in time, but sometimes merely the duration of the measurement. Most often, invocation of an energy-time uncertainty principle is essentially hand-waving.
Material waves, such as we are familiar with (ocean, sound, etc) have a sinusoidal energy profile that integrates to net zero. But I think indivdual wave/particles in the quantum realm must somehow have a different profile, otherwise it would always be darkest before the photon (or after it). Quantum interference must, I would expect, be based on alternate properties, like charge/color (for charged/colored particles), polarity or “spin”. Does everything have a living anti-particle to balance its energy? Does to universe have a net zero energy?
