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

In summary, the Copenhagen Interpretation states that a particle like an electron has a position and momentum at any given time, but the measurement of these quantities introduces uncertainty. In Young's double slit experiment, the slit acts as a device for measuring the position of the electron, leading to a wave-function that includes the uncertainty of which slit the electron passed through. The standard model treats particles as points and does not disagree with the formal interpretation of QM. However, there are various ideas and interpretations within QM, and it is important to have a strong foundation in the subject before delving into these topics. Suggested reading includes Feynman lectures and articles on QM treatment of interference at slits and quantum probability.
  • #1
MHD93
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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.
 
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  • #2
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
 
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FAQ: QM Interpretation & Young's Exp: Electron Position Defined?

1. What is the significance of Young's double-slit experiment in quantum mechanics?

The double-slit experiment conducted by Thomas Young in the early 1800s demonstrated the wave-like behavior of light, which later played a crucial role in the development of quantum mechanics. It showed that light behaves as both a particle and a wave, laying the foundation for the concept of wave-particle duality.

2. How does the double-slit experiment relate to the position of electrons in quantum mechanics?

The double-slit experiment can also be applied to electrons, which are particles with wave-like properties in quantum mechanics. It illustrates the concept of superposition, where an electron can exist in multiple states at the same time, until it is observed. This experiment also shows how the act of measurement can affect the position of an electron.

3. What are the different interpretations of quantum mechanics?

There are several interpretations of quantum mechanics, including the Copenhagen interpretation, the Many-Worlds interpretation, and the Pilot-Wave interpretation. Each offers a different perspective on the fundamental principles of quantum mechanics, such as wave-particle duality and the role of measurement in determining the state of a particle.

4. How does the Copenhagen interpretation explain the position of electrons in quantum mechanics?

The Copenhagen interpretation states that the position of an electron is not well-defined until it is measured. Before measurement, the electron exists in a superposition of all possible positions, and it is only when it is observed that its position becomes certain. This interpretation highlights the role of the observer in determining the state of a particle in quantum mechanics.

5. Can the position of an electron ever be precisely determined in quantum mechanics?

According to the Heisenberg uncertainty principle, it is impossible to simultaneously know the exact position and momentum of a particle. This means that the position of an electron can never be precisely determined in quantum mechanics. The best we can do is calculate the probability of finding the electron at a certain position, based on its wave-like behavior.

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