Understanding Double Slit interference and Uncertainty

[John Morrell]

I've recently been doing some learning about the double slit experiment and a bit about how, qualitatively, quantum electro dynamics works. Something that I wondered about for a long time was how momentum could be conserved in these systems when we assume that a particle could land in any number of positions. I kept thinking; couldn't we do the double slit experiment and just measure the velocity of the particle before it reaches the slits so that we know which one it goes through and where it hits after that? Then I realized that the uncertainty principle states that we can't know both the position and velocity beyond a certain uncertainty.

I just want to check if this is a correct interpretation of this principle. Is it fair to look at the double slit experiment as a result of our fundamental uncertainty about where the particle is and where it's moving? Is it possible to get similar results by assuming particle-like motion where we just don't know where the particle starts or which direction its moving?

Note, I'm not saying that this is why the double slit experiment works the way it does. I just want to know if this is a valid alternative way of modeling it.

 

[zonde]

Then I realized that the uncertainty principle states that we can't know both the position and velocity beyond a certain uncertainty.

I just want to check if this is a correct interpretation of this principle.

This is not quite right interpretation of uncertainty principle nowadays. There is no principal limit to accuracy with which you can measure position and momentum of single particle but you can't predict position and momentum beyond certain limit i.e. it is not possible to prepare a state (ensemble of particles) such that position and momentum does not show some spread in observed values.

 

[Karolus]

The alternative way is to Feynman, as far as we know. The particle along a well defined path from the source to the plate ... a path? no .. different paths, to be honest endless ... what? everyone imaginable compatible with the constraints of equipment ... all ... all and all together.

 

[bhobba]

Note, I'm not saying that this is why the double slit experiment works the way it does. I just want to know if this is a valid alternative way of modeling it.

Well the double slit is surprisingly an advanced topic.

At the beginner level you use a wrong Idea - the wave particle duality - its wrong, was overthrown at least by 1926 when Dirac came up with his transformation theory that generally goes by the name of QM these days, but you need to start somewhere.

Then using the formalism of standard QM you have the following explanation:
https://arxiv.org/abs/quant-ph/0703126

But even that is wrong from an even more advanced standpoint:
https://arxiv.org/abs/1009.2408

And to make matters worse even the above is wrong from the very advanced view - we have professors that post here who even criticize it.

Sometimes physics is like that - maddening isn't it.

At your level , since this is an I level and not an advanced level thread, simply use the first link I gave - you can come to grips with the more advanced stuff layer. If it was an advanced level thread I would let the professors and other professional physicists talk about and simply listen. I understand it to the level of the second paper - beyond that it gets a bit over my head.

Thanks
Bill

 

[John Morrell]

Hey thanks for the help guys! In a way this sort of this is kind of maddening because I'm actually an engineering student and I don't know if I'll ever have time to really thoroughly understand this sort of thing in the way that a real professional course of study would let me. But It's nice to know that at least I can keep asking and pick it up one misguided question at a time.

 

[PeroK]

Hey thanks for the help guys! In a way this sort of this is kind of maddening because I'm actually an engineering student and I don't know if I'll ever have time to really thoroughly understand this sort of thing in the way that a real professional course of study would let me. But It's nice to know that at least I can keep asking and pick it up one misguided question at a time.

It's also worth pointing out that the uncertainty in position and momentum actually relates to the three spatial components separately. There is an uncertainty relation between the x-components of position and momentum; between the y-components; and, between the z-components. But, there is no uncertainty relation between the x-component of momentum and the y-component of position, say.

 

[John Morrell]

Do you mean that the direction, like the unit vector of the x y and z momentum, is unchanging (unless of course the particle interacts with something else)? The direction it travels is essentially constant?

 

[bhobba]

Do you mean that the direction, like the unit vector of the x y and z momentum, is unchanging (unless of course the particle interacts with something else)? The direction it travels is essentially constant?

Since the kinetic energy remains constant the change in momentum at the slit due to the uncertainty principle is reflected in a change in direction.

See the first paper I posted.

Thanks
Bill