Ehrenfest Theorem - Does Classical Mechanics Need Big Particles?

[geoduck]

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.

 

[bhobba]

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

 

[sugeet]

"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

 

[bhobba]

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

 

[sugeet]

exactly

 

[Demystifier]

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