Classical electron uncertainty

In summary, the article describes a way to prepare an electron with accurately known position and momentum using a classical trap.
  • #1
AndreiB
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In quantum mechanics it is impossible to prepare an electron in a state where both position and momentum are known with arbitrary accuracy. In classical physics such states do exist, but can they be prepared?

If we assume that the electron is a classical particle (small ball of charge) can we imagine an experiment, consistent with the laws of classical electromagnetism, that leaves the electron with a arbitrarily well known position and momentum?
 
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  • #3
vanhees71 said:
Sure, why not?
Can you provide an example?
 
  • #4
In classical electron theory you describe point particles as points in phase space as any classical point-particle theory. It's of course evident that this is an approximation, and there is no fully consistent relativistic dynamics of interacting point particles. The best you can come up with, using quantum theory of open systems (quantum Langevin equations), is an effective theory which boils down to the Landau-Lifshitz equation of motion. See, e.g.,

G. W. Ford et al, Phys. Rev. A 37, 4419 (1988)
 
  • #5
vanhees71 said:
In classical electron theory you describe point particles as points in phase space as any classical point-particle theory. It's of course evident that this is an approximation, and there is no fully consistent relativistic dynamics of interacting point particles. The best you can come up with, using quantum theory of open systems (quantum Langevin equations), is an effective theory which boils down to the Landau-Lifshitz equation of motion. See, e.g.,

G. W. Ford et al, Phys. Rev. A 37, 4419 (1988)
As far as I know, Born-Infeld theory is consistent. But is it really necessary to think of an experiment in the relativistic regime?
 
  • #6
I'm not sure, but isn't Born-Infeld theory ruled out by experiments?
 
  • #7
vanhees71 said:
I'm not sure, but isn't Born-Infeld theory ruled out by experiments?
I don't know about that, but it does not matter. It's a thought experiment. Let's assume, for the sake of the argument that the theory is true. Can you imagine an experiment that allows you to prepare an electron with accurately known position and momentum?
 
  • #8
Put the electron in a trap and let it radiate away its energy until it has stopped in the center of the trap. Done.
 
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  • #9
Vanadium 50 said:
Put the electron in a trap and let it radiate away its energy until it has stopped in the center of the trap. Done.
What kind of trap?
 
  • #10
An electron trap.
 
  • #11
Vanadium 50 said:
An electron trap.
If you are referring to a Penning trap, the electron does not remain stationary in the middle.
 
  • #12
Paul trap, Penning trap whatever.

AndreiB said:
the electron does not remain stationary in the middle.

And why? Quantum mechanics!

In a Penning trap, typically the cyclotron motion is in its ground state. It has energy ½ħω which it can't radiate away. Because of quantum mechanics.

Classically, it can have any energy it wants and will radiate it away until it is arbitrarily close to zero.
 
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  • #13
Vanadium 50 said:
In a Penning trap, typically the cyclotron motion is in its ground state. It has energy ½ħω which it can't radiate away. Because of quantum mechanics.

Classically, it can have any energy it wants and will radiate it away until it is arbitrarily close to zero.
In this paper the particle motion in a penning trap is treated classically:

Penning traps as a versatile tool for precise experiments in fundamental physics
K. Blaum, Yu.N. Novikov, G. Werth
Contemporary Physics, 51: 2, 149 -- 175 (2010)

https://arxiv.org/abs/0909.1095

At page 6 we read:

" we obtain three independent motional modes as shown in figure 3: (i) a harmonic oscillation along the z-axis with frequency ωz, (ii) a circular radial cyclotron motion with frequency ω+ slightly reduced compared to the free particles cyclotron frequency ωc and (iii) a circular radial magnetron or drift motion at the magnetron frequency ω- around the trap center."

So, even classically, the particle will move inside the trap. I guess that the energy of the particle is taken from the external fields, this is why the particle does not stop.
 
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  • #14
That paper does not support your point.
It's not nice to post a 78-page paper that ends up not supporting your point.

For the third time, classical motion produces classical radiation, which causes energy loss, slowing the particle. The paper itself shows this energy loss in equation (21), so it is kind of disingenuous to pretend it doesn't exist.
 
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  • #15
The topic in this thread is not really EM. It is how to shoot entire QM with one bullet from behind through the back into the eye.

Please remember that our credo is "Science as taught at universities."

This thread is closed.
 
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Related to Classical electron uncertainty

1. What is classical electron uncertainty?

Classical electron uncertainty refers to the principle in quantum mechanics that states it is impossible to know the exact position and momentum of an electron at the same time. This is due to the wave-particle duality of electrons, where they can behave as both a particle and a wave.

2. How does classical electron uncertainty affect our understanding of electrons?

Classical electron uncertainty challenges our traditional understanding of particles as having a fixed position and momentum. It suggests that electrons exist in a state of probability and can only be described by a wave function, rather than having a definite location and velocity.

3. What is the Heisenberg uncertainty principle and how does it relate to classical electron uncertainty?

The Heisenberg uncertainty principle is a fundamental principle in quantum mechanics that states the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This principle is closely related to classical electron uncertainty, as it is the mathematical expression of the uncertainty of an electron's position and momentum.

4. Is classical electron uncertainty a limitation of our technology or a fundamental property of nature?

Classical electron uncertainty is a fundamental property of nature that arises from the wave-particle duality of electrons. It is not a limitation of our technology, but rather a principle that cannot be overcome or measured with complete accuracy.

5. How does classical electron uncertainty impact the behavior of electrons in materials and devices?

Classical electron uncertainty plays a crucial role in the behavior of electrons in materials and devices. It explains phenomena such as quantum tunneling and the uncertainty in energy levels of electrons in atoms. It also affects the precision and accuracy of electronic devices, as the uncertainty in the position and momentum of electrons can lead to errors in calculations and measurements.

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