Double slit probability question

[ueit]

Initial momentum is unknown and it is not 0 at x=0 how did you assume that?! And you can't know if it is small either.

You are thinking about particles as projectiles, as if they are billiard balls. Photon for example can never be standing still by have 0 momentum at x=0.

I have defined X axis to be in the plane of the barrier, perpendicular on the direction of propagation of photons. The photons are not standing still but virtually all of their momentum is on Z.

All particles that arrive to the slits will have, by design, almost 0 momentum in the plane of the slits if the source is far away (the Sun for example). The distance traveled by the photons in 8 minutes is at most one half the distance between the slits, witch should be of the order of mm or smaller.

I am not assuming the particles are billiard balls, in fact I see this assumption as the most important misconception (unfortunately shared by Feynman himself) that stands against a logical understanding of this experiment. However, momentum in QM is still measured by repeated position measurements. This is how momentum is determined in particle accelerators. In our case the first position is given by the location of the source, and the second by the location of the slits.

Andrei

 

[ueit]

I never said you could measure a violation of momentum conservation. But I certainly reject the idea the particle is flying in a straight line like a little billiard ball, because we would see no interference if that were the case. How momentum might vary when we are not watching is unknown.

On the other hand, you cannot measure the initial position accurately AND expect to know much about initial momentum. Ditto with ending q and p.

You seem to imply that uncertainty principle does not let you know the position and momentum at the same time. This is a common misconception Heisenberg himself tried to fight. By performing a position measurement on a particle in a momentum eigenstate you can find out both position and momentum the particle had at the moment of measurement. The catch is that, following the position measurement, the momentum changed and you cannot predict its path.

Andrei

 

[DrChinese]

You seem to imply that uncertainty principle does not let you know the position and momentum at the same time. This is a common misconception Heisenberg himself tried to fight. By performing a position measurement on a particle in a momentum eigenstate you can find out both position and momentum the particle had at the moment of measurement. The catch is that, following the position measurement, the momentum changed and you cannot predict its path.

That interpretation of events would not be shared by everyone. I would say it could have a well defined momentum eigenstate at T=0 and a well defined position at T=1. But I would not agree it was in known p and q eigenstates at the same T=1, nor at any point in time.

 

[PeterDonis]

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