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jaketodd
Gold Member
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Does the math of the Feynman path integral dictate particles taking many paths or is that just an english language gloss-over?
Thanks,
Jake
Thanks,
Jake
ansgar said:all paths contribute, we don't know and can not know which path the particle took
jaketodd said:But some paths have a greater probability than others, correct?
IttyBittyBit said:Why don't you get the answer from the father of the path integral himself?
In QED: The Strange Theory of Light and Matter, Feynman explains, in a highly accessible way, what path integrals are and how they relate to QED. You can find that book in just about any library.
If you want nuts-and-bolts explanations there is no easy way other than learning about quantum field theory.
My understanding is that Feynman did not care much for interpretation anyway. "Shut up and calculate!"
As first said by Mermin :)FireBones said:My understanding is that Feynman did not care much for interpretation anyway. "Shut up and calculate!"
Frame Dragger said:@jaketodd: He did, but that doesn't mean it isn't useful or worth learning.
jaketodd said:I didn't say learning about the path integral and related things isn't useful or worth learning. I was saying that I think Feynman didn't publicly support the implications of the math that his path integral stated, and therefore he is not the person to get the proper interpretation from.
jaketodd said:Doesn't it all come down to the math in the end? If the math says a particle takes infinitely many paths, then that's what is happening if it's correct regardless of the shrink wrap you put around it. However, a good question would be: "Is there a different way to mathematically reproduce the same results (and therefore the same accuracy) without the infinitely many paths being built into the math?" Or, am I wrong and that interpretation is not built into the math?
jaketodd said:Isn't the path integral the best we have in terms of what happens on that scale? Could it be the best we will ever have given the inherent uncertainty in quantum theory? If not, is it not reasonable to think what would be an improvement on it would contain the ideas of the math of the path integral and then the something else?
Thank you,
Jake
FireBones said:My understanding is that Feynman did not care much for interpretation anyway. "Shut up and calculate!"
ansgar said:yes, each path is weighted with exp(-i/hbar * S ) where S is the classical action but since we can't tell which path the particle took, we must add these probabilites coherently
jaketodd said:Does the math of the Feynman path integral dictate particles taking many paths or is that just an english language gloss-over?
edpell said:The idea that a particle diffuses from point A to point B via all the paths available and favors those with least "resistance" seem beautiful and simple. Why the strong objection?
jaketodd said:Doesn't it all come down to the math in the end? If the math says a particle takes infinitely many paths, then that's what is happening if it's correct regardless of the shrink wrap you put around it. However, a good question would be: "Is there a different way to mathematically reproduce the same results (and therefore the same accuracy) without the infinitely many paths being built into the math?" Or, am I wrong and that interpretation is not built into the math?
Frame Dragger said:and then apparently coalesce at B
edpell said:I think we need to stop thinking in terms of points. QM wise it is not at a point A it is more a blob around A and it does not go to point B it is more a blob around B. If it starts and stops as a blob why would we think it would take one infinity thin path from blob volume A to blob volume B?
Frame Dragger said:Stephen Hawking for one, makes a very convincing argument for a "Sum Over All Histories" aka Path Integral for particles, but without unification... who knows?
edpell said:I am not take up on QM; what does "without unification" mean? Thanks.
edpell said:All paths seem a lot like LQG (Loop Quantum Gravity). That is a foam of quantized spacetime. So I guess the question is how big is the object (say an electron) relative to the plank spacetime interval? It almost seem like some kind of temperature comes in here to make the position of the electron (if point like) uncertain (diffuse). Or at least a QM zero point energy that makes the electron not point like.
We should keep in mind Feynman's all paths is effectively all paths very close to the classical path far away paths oscillate so fast that they cancel.
Frame Dragger said:If a particle can "test" all paths, why doesn't it TAKE all paths?
edpell said:Super good question.
I do not know. It is great to know that there are still areas in physics still to be understood. :)