Sum Over Histories

[Badly Shaved Monkey]

From this thread (http://forums.randi.org/showthread.php?p=1229343#p1229343)
Note that one way of looking at virtual particles is to imagine a particle moving forward in time and then going back in time a little bit and then going forward. Then the particle-antipartical creation could be called "causal," but it would be caused by something from the future. Many people do this, and it makes them happy. Of course, it goes against how people think of causality, as something going forward in time.

I think I have given this thread the correct title, but if I haven't, it is the idea that an interpretation of quantum mechanics is that anti-particles are particles going backwards in time.

The question I have is: I think I recall something to the effect of this interpretation meaning that the Universe just has one electron zipping back and forth in time to give all the apparent electrons we can detect. I think Feynman suggested it so I'm not sure whether that was his usual playful hyperbole or a literal possibility. Can someone elaborate?

[hammegk]

... something to the effect of this interpretation meaning that the Universe just has one electron zipping back and forth in time to give all the apparent electrons we can detect.
You should be more careful. You are going to give your buddies the homeopaths ideas. ;)

Cramer's transactional interpretation is also interesting: possible free-will anyone?

[hammegk]

oops ... dammit.. move along, nothing to see here.

[Badly Shaved Monkey]

You should be more careful. You are going to give your buddies the homeopaths ideas. ;)

Well we do stray into that territory where interpretations of QM are organised to encompass all the existing data but seem not to make falsifiable pedictions. Still, even if it's just a story I'd quite like to know the properties of this version of the story.

[Psi Baba]

From this thread (http://forums.randi.org/showthread.php?p=1229343#p1229343)


I think I have given this thread the correct title, but if I haven't, it is the idea that an interpretation of quantum mechanics is that anti-particles are particles going backwards in time.

The question I have is: I think I recall something to the effect of this interpretation meaning that the Universe just has one electron zipping back and forth in time to give all the apparent electrons we can detect. I think Feynman suggested it so I'm not sure whether that was his usual playful hyperbole or a literal possibility. Can someone elaborate?
I remember reading about these ideas in either Hawking's The Universe in a Nutshell or Timothy Ferris' The Whole Shebang. Feynman's idea is that the probability that a system in an initial state A will evolve to a final state B is given by adding up a contribution from every possible history of the system that starts in A and ends in B. Sum over histories. I'm not sure if that single electron idea is related to Feynman's theory, though maybe, like you suggested, one was intended to be a metaphor for the other. Or it might be more closely related to Hawking's Wave Function of the Universe theory or to string theory in general.

[Badly Shaved Monkey]

I remember reading about these ideas in either Hawking's The Universe in a Nutshell or Timothy Ferris' The Whole Shebang. Feynman's idea is that the probability that a system in an initial state A will evolve to a final state B is given by adding up a contribution from every possible history of the system that starts in A and ends in B. Sum over histories. I'm not sure if that single electron idea is related to Feynman's theory,

http://plato.stanford.edu/entries/causation-backwards/


"Richard Feynman once came up with the idea that the electron could go backwards in time as a possible interpretation of the positron (Feynman, 1949). In fact he imagined the possibility that perhaps there were only one electron in the world zig-zaging back and forth in time. An electron moving backwards in time would carry negative energy whereas it would with respect to our ordinary time sense have positive charge and positive energy. But few consider this as a viable interpretation today (Earman, 1967, 1976)."

[Badly Shaved Monkey]

http://www.physicsforums.com/showthread.php?t=23700

[Pragmatist]

From this thread


I think I have given this thread the correct title, but if I haven't, it is the idea that an interpretation of quantum mechanics is that anti-particles are particles going backwards in time.

The question I have is: I think I recall something to the effect of this interpretation meaning that the Universe just has one electron zipping back and forth in time to give all the apparent electrons we can detect. I think Feynman suggested it so I'm not sure whether that was his usual playful hyperbole or a literal possibility. Can someone elaborate?
It wasn't Feynman's idea it was John Wheeler's. Wheeler was Feynman's thesis adviser at Princeton in 1940. Feynman related a story of how Wheeler phoned him in the fall of 1940 and suggested that the reason why all electrons had the same charge and mass was because they were all the same electron. Basically Wheeler was suggesting that all possible time evolutions of an electron state represented all possible electrons (i.e. the multiple quantum outcomes for one wavefunction of one electron could be intepreted as the "futures" of all electrons. In order to balance this out, Wheeler also suggested that the process had to be balanced by the electron also moving backwards in time as a positron. Feynman immediately countered that there were more electrons than positrons so the theory didn't work, so Wheeler suggested that maybe the "missing" positrons were hidden inside protons.

I'm not sure how seriously they took the single electron idea, it was certainly just a hypothesis. They worked together later on a theory involving wave propagation that went both forward and backward in time, it was called the Wheeler-Feynman Absorber theory. But they later abandoned it and I seem to recall Feynman once saying it was a dead end hypothesis.

The positron/time thing isn't as arcane as it first appears. The story starts in 1928 with Paul Dirac who in the course of developing a relativistic quantum theory of the electron came up with a mathematical solution that implied the existence of negative energy states equivalent to the positive energy states of the electron. At that time it seemed absurd, but subsequently when anti-matter was discovered it all made sense - the negative energy state version of the electron was the positron.

Now in "normal" processes time runs forwards and energy and momentum are always positive (in magnitude). In order to make sense (in particular to ensure conservation and causality) of negative energy/momentum you can simply reverse the direction of time and they will then become "positive" (relatively speaking). So anti-matter is the physical interpretation of the meaning of negative energy states and time reversal is the way in which you can handle such situations with the "normal" mathematical machinery developed for positive states without violating conservation laws and/or causality. Whether that literally means time reversal in the practical sense as we understand "time" is another question probably best left to the philosophers! :)

In sum over histories, the idea is to chart all possible ways in which a particular "event" can occur and then to derive and sum the amplitudes of each possible way. In doing this, time reversal is allowed, so it's permissible to chart events occuring backwards in time and sum in their amplitudes just as if they were regular "forward" events. But there is no special significance to doing this, again it's just part of the machinery developed to allow the construction of appropriate path integrals.

I just remembered that Feynman mentioned this in his Nobel Lecture: (http://nobelprize.org/physics/laureates/1965/feynman-lecture.html) here is a relevant extract:

As a by-product of this same view, I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, "Feynman, I know why all electrons have the same charge and the same mass" "Why?" "Because, they are all the same electron!" And, then he explained on the telephone, "suppose that the world lines which we were ordinarily considering before in time and space - instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future we have the wrong sign to the proper time - to the proper four velocities - and that's equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron." "But, Professor", I said, "there aren't as many positrons as electrons." "Well, maybe they are hidden in the protons or something", he said. I did not take the idea that all the electrons were the same one from him as seriously as I took the observation that positrons could simply be represented as electrons going from the future to the past in a back section of their world lines. That, I stole!

[Badly Shaved Monkey]

Thanks

[Soapy Sam]

I've wondered the same about photons.
After all, if a photon is moving at lightspeed, time does not pass for it at all, so there seems nothing to prevent it being everywhere at once. Why postulate more than one? (Multiply ye not thy entities, sayeth the FSM).

The problem with thinking about stuff like this is that unless you understand the mathematics, it's impossible to tell complete nonsense from notions which are actually quite profound.

Hence, I suppose, the confidence with which people claim authority for improbable ideas by chanting the mantra "It's Quantum, inn'it?"

EG- I was quite taken with BSM's comment elsewhere that maybe everything tries to move at c, but is prevented by mass. That sounds like sense to me. But I just don't know how to tell.

[Badly Shaved Monkey]

EG- I was quite taken with BSM's comment elsewhere that maybe everything tries to move at c, but is prevented by mass. That sounds like sense to me. But I just don't know how to tell.

Thanks, Soapy. But also thanks for making me think about it again, because I didn't quite hit the nail on the head then and I've now remembered the proper concept which is even more beautiful.

Still with apologies to physicists if I get my jargon muddled.

Everything travels at the speed of light, but objects of non-zero rest mass divert some of their travel along the time axis whereas a zero rest mass object like a photon does not travel in time.

In other words, there is a trading of translation across distance, which photons do as fast as is possible, for a translation across time. So if I sit and a photon passes me it flies away in space as fast as possible, but an object sitting with me is travelling in time as fast as possible with no movement in space. An object with mass is moving with some combination of the two.

I really could do with a physicist to tidy that up, please. Maybe with some maths to go with it.

[Soapy Sam]

I can grasp spacetime as a 4 way hyperspace, but where do all the other space-like dimensions of string theory fit in? Is the photon moving in those , too? And are there other timelike dimensions? If not, why not? I'm paying my taxes. I demand a properly equipped universe.

[Badly Shaved Monkey]

I can grasp spacetime as a 4 way hyperspace, but where do all the other space-like dimensions of string theory fit in? Is the photon moving in those , too? And are there other timelike dimensions? If not, why not? I'm paying my taxes. I demand a properly equipped universe.

Bump, for Soapy.