Feynman told us that as photons and matter travel through space they take all possible paths. Some paths have greater probabilities than others, but all possible paths must be accounted for.


He also told us that once we define which path the photon or particle took all the other possibilities vanish immediately. This brings up many implications including faster than light information and something else.

We have shown that even though all the probabilities vanish in that instant the information doesn not in fact travel any faster than light. The information has to go back to its source before making its way to the other probabilities. That is my understanding anyway.


However, my question entails the still existing probabilities that are there before the photon is observed. Those probabilities are all there and all valid. I think of them as lines from a source to a destination. The density of lines is of course greatest along the shortest path (or shortest time) between the two points.

Until we pinpoint where the photon is, those other possibilities still exist. My cousin presented this question to me over Thanksgiving.

"Is it possible that all of those possibilities carry momentum and thus mass?" If this is possible then, "could that mass be the dark matter that everyone is looking for?"



As I understand it, probabilities are massless constructs. But they do exist. Are there answers to those questions?

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I am not an expert in quantum electrodynamics, but I think the concept you are searching for is that of the wave function of the photon. This is not so different from any wave function in quantum mechanics, so I think your questions could be posed for an electron in a box just as well. When you measure it, the wave function "collapses", and all those other probability amplitudes vanish. Note they are indeed amplitudes, not real probabilities, which means they are complex numbers with phases that can interfere with each other. Indeed, the reason photons take the quickest path is not that the paths are denser, it is that the possible paths don't destructively interfere the way they do for other trajectories. So it's all about the interference patterns embedded in the wave function, and to answer the question about the energy or momentum, yes, they do contribute to the energy of the photon in a way that is well described by quantum mechanics. However, in regions where the probability amplitudes destructively interfere, there is little contribution left, so there is not significant energy carried outside the straight-line path that connects the source to the place where the photon is detected. Note that before the photon is detected, this is not at all the case, as the photon amplitude at any given time might spread over a surface the size of a galaxy, or a universe. The wave function collapse is much faster than the speed of light-- when we detect a CMB photon, for example, it immediately cannot be detected by aliens a billion light years away. But this transports no information, as they weren't expecting that they would detect it!

that's right Ken. It has been a couple years since I took a Quantum class. Next fall I take Graduate Quantum. Now that you say it I do remember about the amplitudes and phases.


well, not the universe as it wouldn't have had time to get there yet. Now, since all those amplitudes still exist isn't it possible they carry momentum? Even if it is very small; there are lots of photons; and this could add up right?

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The CMB?
Sure, although energy is better at adding up without cancelling. But yes, the energy density of the CMB used to dominate the universe, early on. As one example, note that a formal plane wave fills all space with its amplitude, and to get its momentum and energy you need to integrate this amplitude over all space. But it's still just the energy and momentum of the photon, there's no "added stuff". All the rest cancels out as all phases are represented.

Not really. He made a mathematical model working that way, which is not the same as saying that's how the physical world really works.

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Yes, I think it would be more accurate to say the photon amplitudes take all paths, and then the amplitudes are added up to determine where the photon is likely to go in "reality".

ah, but they are just probabilities. the photon could actually be at one of the less probable places.

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why probability may not become a certain thing. i am still confuse on the phenomena of "probability".

You're not the only one.

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Yay!!! That matches my (relatively ignorant) interpretation!!!

-- Jeff, in Minneapolis

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Perhaps this is a good place to comment on the so-called "wave/particle duality" of elementary particles. I've never liked the statement that "sometimes things act like particles, sometimes like waves". That is selling quantum mechanics short, as if there was some ambiguity in which behavior you will see. But in fact, QM tells us that all particles, whether electrons or bowling balls treated as point objects, obey wave mechanics. Note this last sentence used both the words "particle" and "wave", but didn't sound like the two were somehow contradictory. By "obey wave mechanics" I mean that they move about by sending out probability amplitudes that are described by wave physics (the so-called "wave function"), but when they show up somewhere, it is as a particle, a discrete entity, that they are measured. In a sense, they all "exist" as particles, but "move" like waves. It's just that very short wavelength waves follow paths that we would call statistical trajectories (like pieces of a grenade in an explosion), and longer wavelength waves show the peaks and valleys of interference patterns. But it's not that the first is particle-like and the second is wave-like, they're both wavelike, they just have different wavelengths. The particle-like behavior is totally separate and not contradictory, and has to do with the discreteness of the entity in question.