New look at Youngs experiment

[Iforgot]

My comment is with regards to Young's double slit experiment showing how diffraction patterns disappear when you measure which slit the electron passes through.

The standard interpretation is that the electron wave propagates through both slits, unless you measure which slit it passed through. Once you measure it, you force it to pass through one specific slit. No component passes through the other slit, and there is no "two source like terms" to interfere with each other, and produce a diffraction pattern.

My comment
Q: How (when I say how, I mean show/describe me the math) does measuring which slit the electron passes through force it into pass through one slit?

A: Consider Young's system. We identify which slit the electron passes through by using a laser monitoring each slit. If part of the laser beam is scattered (which we can detect), we know the electron entered that specific slit. The electron is treated as a free particle with wave vector k.

Now treat the laser as a small travelling/standing wave perturbation potential in the Schrodinger equation. Similar perturbation potentials (Kronig Penny Model, and free electron gas in a metal) have already shown (using time dependent perturbation theory) how a perturbation of this form causes the electron to transition from a momentum eigenstate with wave vector k into two a super position of different momentum eigenstates with wave vectors k+q and k-q, where q is the laser wave vector. This scattering process iterates over and over again until the electron is in a superposition of momentum eigenstates with wave vectors k-n*q where n is an integer spanning -infty to +infty.

As shown in any intro quantum textbook, as the electron wave-function broadens in k-space, it narrows in r-space. That is, the light forces the electron spatial distribution to narrow and have a well defined position.

implications: If one knew the exact state of a system, one could predict how/where an electron would localize. And the universe is, again, deterministic?

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I am assuming some one has thought of this before. Any one know who?

 

[DrChinese]

My comment is with regards to Young's double slit experiment showing how diffraction patterns disappear when you measure which slit the electron passes through.

The standard interpretation is that the electron wave propagates through both slits, unless you measure which slit it passed through. Once you measure it, you force it to pass through one specific slit. No component passes through the other slit, and there is no "two source like terms" to interfere with each other, and produce a diffraction pattern.
...

implications: If one knew the exact state of a system, one could predict how/where an electron would localize. And the universe is, again, deterministic?

Now, how did you get a deterministic system with simultaneous knowledge of p & q? We already know that you can follow one or the other - but not both.

 

[Iforgot]

Simultaneous knowledge momentum and position is not a perquisite for determinism. If so, how could we ever predict any wave motion? E.g. an electromagnetic wave of the form Sin(k*x-w*t) isn't spatially localized but has a (relatively) well defined momentum (+/- hk).

 

[DrChinese]

Simultaneous knowledge momentum and position is not a perquisite for determinism. If so, how could we ever predict any wave motion? E.g. an electromagnetic wave of the form Sin(k*x-w*t) isn't spatially localized but has a (relatively) well defined momentum (+/- hk).

I guess we have different definitions for determinism. Probability amplitudes evolve "deterministically" but do not lead to definite outcome predicitions. Momentum can evolve deterministically as well, but who can predict where such particle is? I can't.

 

[Iforgot]

Probability amplitudes evolve "deterministically" but do not lead to definite outcome predicitions. Momentum can evolve deterministically as well, but who can predict where such particle is? I can't.

That's my point! If you you know the exact initial conditions of the system, you could simulate the behavior using some PDE solver. In some region space, the probability amplitude will sum to 99.999999%. If that region is small enough, we say the wave-function has "collapsed"

My point is "wave function collapse" isn't a magical word. It happens because of the interactions between light and an electron. The outcome of this interaction can be calculated and predicted using time dependent perturbation theory, as I described in the first post.

 

[DrChinese]

My point is "wave function collapse" isn't a magical word. It happens because of the interactions between light and an electron.

No, that would not be a fair statement. Here are 3 things that imply or confirm that is not the case:

1. Entangled particle pairs exhibit the same behavior (respecting the HUP) when you observe Alice alone. This implies that it is not the physical interaction which causes collapse in a classical manner as you imply.

2. Commuting observables are not limited as non-commuting observables are. Why is that?

3. Although collapse may occur with a pair of non-commuting observables, other observables may not be affected in some cases. This too implies that it is not the physical interaction which causes collapse in a classical manner.

 

[Iforgot]

In response

1) Funny you should bring up entanglement. It is the eventual topic to which I want to apply this technique. BTW, do you know any good math based books introducing entanglement paradoxes?

2&3) Ummm... Don't understand. Can you express this question in equations? Maybe give an example?

 

[DrChinese]

2&3) Ummm... Don't understand. Can you express this question in equations? Maybe give an example?

There are experiments for hyper-entangled particle pairs, such as the following:

Experimental realization of hyper-entangled two-photon states
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"We report on the the experimental realization of hyper-entangled two photon states, entangled in polarization and momentum. These states are produced by a high brilliance parametric source of entangled photon pairs with peculiar characteristics of flexibility in terms of state generation. The quality of the entanglement in the two degrees of freedom has been tested by multimode Hong-Ou-Mandel interferometry. "

http://arxiv.org/abs/quant-ph/0406148

After a while, you realize that the physical interaction of the first measurement leaves the second observable in a superposition state. How can that be, if in fact the interaction with the measuring device causes something resembling a classical collapse? I realize this experiment is pretty complex and this conclusion is not easily recognized in the reference. Nonetheless, I think you will be able to sense that the polarizers do not affect the momentum entanglement themselves. They would need to, in order for your idea about Young's experiment to be valid since there are versions of Young in which polarizers are used to determine the which-path.

 

[Iforgot]

let's back track.

By what mechanism does a measurement cause a wave function to collapse?

I.e. What are the equations describing the transition between a some superposition, to a collapsed state?