How does Feynman Sum Over Histories make sense?

[Astralos]

How does Feynman "Sum Over Histories" make sense?

Hi. I am new to Quantum Physics and this forum as well. I was reading The Grand Design, by Stephen Hawking, and came upon the "Alternative Histories" theory in Quantum Mechanics.

My questions are:

1.) How is it possible that a particle can assume a superposition, such that it takes all paths simultaneously? How can something be in two places at once?

2.) What does it mean by "all paths"? Are there an infinite number of paths? If a particle is to go from point A to point B, a distance defined as 1.0 meters, would one of its possible paths involve going around Jupiter twice, coming back, circling the Earth one million times, and then landing at point B? What determines the possible paths? If there are an infinite possible number of them, then my assertion about Jupiter should be correct.

3.) Can you please explain the theory in simple terms? And then give an example?

4.) If this theory is correct, does that mean that the universe has no definite history, but experienced all histories?


Please answer at least one of the four questions. Thank you so much for your help. This is really intriguing me.

 

[Polyrhythmic]

1.) That's quantum mechanics. A particle has no definite location, only probabilities of measuring it somewhere.
2.) This probably refers to the path integral concept. It is a technique which works by summing over all possible paths through phase space (position and momenta) while only the ones most likely due to energetic reasons contribute (simply put).
3.) As an example, if you take a particle moving from A to B, you get quantum mechanical contributions from paths which deviate from the classical path the particle would take.
4.) I guess that depends much on the interpretation of quantum mechanics, which I don't want to go into (since it is useless to me, quantum mechanics works well as a physical theory and that's enough).

I guess that since you are new to Quantum Mechanics, you should take a look at some introductory texts to the subject. This will certainly help you to get an idea of the concepts that emerge in this theory.

 

[San K]

Hi. I am new to Quantum Physics and this forum as well. I was reading The Grand Design, by Stephen Hawking, and came upon the "Alternative Histories" theory in Quantum Mechanics.

My questions are:

1.) How is it possible that a particle can assume a superposition, such that it takes all paths simultaneously? How can something be in two places at once?

2.) What does it mean by "all paths"? Are there an infinite number of paths? If a particle is to go from point A to point B, a distance defined as 1.0 meters, would one of its possible paths involve going around Jupiter twice, coming back, circling the Earth one million times, and then landing at point B? What determines the possible paths? If there are an infinite possible number of them, then my assertion about Jupiter should be correct.

3.) Can you please explain the theory in simple terms? And then give an example?

4.) If this theory is correct, does that mean that the universe has no definite history, but experienced all histories?


Please answer at least one of the four questions. Thank you so much for your help. This is really intriguing me.

i am a layman and not a physicist...that said...

the possible paths are within the narrow band of the light's "width"

this is what the maths is saying...with a very high degree of accuracy

what happens in reality is anybody's guess...there are various hypothesis...

3. example could be light reflecting, and refracting, off a glass plate

 

[Fredrik]

1.) How is it possible that a particle can assume a superposition, such that it takes all paths simultaneously? How can something be in two places at once?

The theory doesn't say that a particle takes all paths. It just says that all paths from the emission event to a possible detection event contributes to the amplitude of the particle being detected at that event. The amplitude is a complex number whose squared modulus equals a probability. The theory doesn't attempt to tell you what the particle is really doing. It only tells you how to calculate probabilities of detection events.

2.) What does it mean by "all paths"? Are there an infinite number of paths? If a particle is to go from point A to point B, a distance defined as 1.0 meters, would one of its possible paths involve going around Jupiter twice, coming back, circling the Earth one million times, and then landing at point B? What determines the possible paths? If there are an infinite possible number of them, then my assertion about Jupiter should be correct.

Yes, infinitely many. Yes, including paths that go a million times around Jupiter, and also including paths through spacetime that correspond to velocities faster than the speed of light. The contribution from a typical path is canceled out by the contribution from another, so most paths (all of those weird ones) can actually be ignored in the calculation.

The exact details of what "all paths" should mean is a complicated mathematical problem that's still hasn't been solved for all types of problems. (Quantum field theories with interactions are especially problematic).

3.) Can you please explain the theory in simple terms? And then give an example?

No one has done a better job doing that than Feynman himself, in his book "QED: The strange theory of light and matter" and the lecture series that the book was based on. The book is cheap and I highly recommend it. The videos of the lectures are available here.

4.) If this theory is correct, does that mean that the universe has no definite history, but experienced all histories?

That's a possibility that can't be ruled out, but no one knows what this really means. Only another theory can explain that, and QM is still the best one we have.

 

[Astralos]

That was SO helpful. I'll read Feynman's book and look into this further. Please, if anyone could give me any more information, even if it does not pertain to the question, that would be wonderful. This is changing the way I think...

 

[phinds]

I'm new to all this too and one thing that I have found invaluable is to NOT try to apply classical mechanics to subatomic events. It will make your head hurt and serves no useful purpose since it actually DOESN'T apply. It took me a while to get past the point of running off screaming obscenities at the utter outrageousness of it things like the fact that the position of a subatomic particle is undefined just before a measurement gives a position. That is, I don't have too much trouble with the fact that the position is undefined UNTIL you measure it, but what bends my minds is that once you measure it and have some reasonable idea where it was at the moment you measured it, you have NO IDEA where it was one plank time prior to that. Newton's head would explode.

 

[Astralos]

I'm new to all this too and one thing that I have found invaluable is to NOT try to apply classical mechanics to subatomic events. It will make your head hurt and serves no useful purpose since it actually DOESN'T apply. It took me a while to get past the point of running off screaming obscenities at the utter outrageousness of it things like the fact that the position of a subatomic particle is undefined just before a measurement gives a position. That is, I don't have too much trouble with the fact that the position is undefined UNTIL you measure it, but what bends my minds is that once you measure it and have some reasonable idea where it was at the moment you measured it, you have NO IDEA where it was one plank time prior to that. Newton's head would explode.

Your response was very entertaining to read :)