QM Interpretation & Young's Exp: Electron Position Defined?

[MHD93]

According to the Copenhagen Interpretation, and considering Young's double slit experiment: Is what interferes the mathematical wave function flowing out the two slits but the electron itself takes a well defined path? Anyhow, I need a clearer idea about the position definition or interpretation, does an electron have a specified one at a time? more than one? none or unknown? what does the standard model mean by considering the electrons (and all leptons) point particles? Does the standard model, in that, disagree with the formal interpretation of QM?

If any of that is left unanswered formally, I ask you to share your personal ideas and answers that, you feel, most conveniently describe the answer.

 

[Simon Bridge]

The particle must pass through one or the other slit. That is as "well defined" as the trajectory gets. How it gets to the slits or to the screen is up for grabs... the straight line is an average path.

A particle like an electron has a position and a momentum at any time these are measured. The measurement introduces an uncertainty into this.

The slit, in a way, is a device for measuring the position (y) of the electron as it passes a location (x) in the apparatus. The narrower the slit the bigger the resulting minimum uncertainty in momentum. If there are two slits, the uncertainty also includes which slit the electron passed through - which can be expressed as a wave-function.

The standard model treats particles as points in much the same way as students treat planets and stars as points when they learn about gravity. It is the interactions that count.

The standard model does not disagree with the formal interpretation of QM - it is the formal interpretation of QM.

The questions you are asking are a big topic in QM and you'll find lots of different ideas.
It will help you to have more of a foundation - suggested reading/viewing:

Feynman lectures - he covers the concepts behind your questions more rigorously.
http://vega.org.uk/video/subseries/8

QM treatment of interference at slits
http://arxiv.org/pdf/quant-ph/0703126.pdf
... the authors treat the source+slits as a device that prepares the state of the wavefunction. In this approach, the wavefunction does not interfere with itself as it passes through the slits - it is a manifestation of the (often complicated) interaction of the particle with the material around the slits.

... aand: Scott Aaronson's discussion of quantum probability
http://www.scottaaronson.com/democritus/lec9.html