Ehrenfest Theorem - Does Classical Mechanics Need Big Particles?

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Discussion Overview

The discussion revolves around the implications of Ehrenfest's theorem in the context of classical mechanics and quantum mechanics, specifically questioning whether classical behavior can emerge from a system of many small particles as opposed to requiring larger particles. The scope includes theoretical considerations and interpretations of quantum mechanics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that if expectation values in quantum mechanics follow classical equations of motion, then many small particles could behave classically.
  • Another participant counters that the law of large numbers implies statistical averages approach classical behavior, but individual particles remain quantum mechanically "weird."
  • A third participant agrees that while averages may conform to classical theory, individual measurements do not necessarily reflect this behavior.
  • It is proposed that the center of mass of a large number of particles may exhibit classical motion, although this is contingent on the interpretation of classical behavior.

Areas of Agreement / Disagreement

Participants express disagreement regarding whether classical behavior can be attributed to individual particles or only to statistical averages. There is no consensus on the necessity of large particles for classical mechanics.

Contextual Notes

Participants highlight the distinction between individual quantum behavior and statistical averages, indicating that assumptions about particle size and behavior may influence interpretations.

geoduck
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Since it's true in quantum mechanics that expectation values obey the classical equations of motion, then if you have a whole bunch of particles, would most of them behave classically?

I thought to get classical mechanics you needed big particles, but Ehrenfest's theorem says lots of small particles would do.
 
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No.

All you are talking about is the law of large numbers in that the statistical average tends towards the average as the number increases. Each individual particle is still fully QM weird.

Thanks
Bill
 
"would most of them behave classically?"

Ofcourse not, each is treated Quantum mechanically and will be so.

Finally under a statistical average, under many many measurements everything will tend obey the classical theory.

Bhobba please comment
 
That looks about right - provided you mean by everything will tend to obey the classical theory you mean the averages do - not individual measurements.

Thanks
Bill
 
exactly
 
If you have a lot of particles, then their centre of mass will move nearly classically.
 

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