Uncertainty principle and electromagnetic field

In summary, the conversation discusses the uncertainty principle and its application to particles in different electromagnetic fields. While the uncertainty in position and momentum may vary for a particle in a potential, the lower bound set by the principle is always upheld. The uncertainty principle applies to preparation procedures and measurements, and is not affected by dynamics or time-energy relations.
  • #1
relativityfan
75
0
hi,

I have a question about the uncertainty principle.

if an electron is in attractive OR repulsive electromagnetic field, is its uncertainty about its position lower than if it is a free electron?

I believe particles are more random, with a higher entropy when there is less interaction.
Am I right?
 
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  • #2
The Heisenberg uncertainty principle gives you a lower bound of the "uncertainty in position space" times "uncertainty in momentum space".

If you have an electron in a certain potential you have to solve for the wave function and calculate the two uncertainties explicitly. It can very well be that one uncertainty is rather small, whereas the other one becomes large. But the lower bound as specified in the Heisenberg uncertainty principle is never violated.

A simple state which minimizes the uncertainty relation is the ground state of the harmonic oscillator. You can by no means reduce the uncertainty.
 
  • #3
Adding to the above: Uncertainty relations concern preparation procedures of quantum states. They also apply to possible measurements at a given time. They have nothing to do with the dynamics. They deal with kinematical variables.

Time-energy uncertainty relation is somewhat different - it has its own treatment. It has been discussed elsewhere. But this is not what you are concerned with.
 

FAQ: Uncertainty principle and electromagnetic field

1. What is the uncertainty principle?

The uncertainty principle is a fundamental concept in quantum mechanics that states that it is impossible to know the exact position and momentum of a particle at the same time. This means that the more precisely one of these quantities is known, the less precisely the other can be known.

2. How does the uncertainty principle apply to electromagnetic fields?

The uncertainty principle also applies to electromagnetic fields, as they are made up of particles called photons. This means that it is impossible to know both the exact position and momentum of a photon at the same time. The uncertainty principle also applies to other properties of electromagnetic fields, such as energy and time.

3. What is the relationship between the uncertainty principle and Heisenberg's uncertainty principle?

The uncertainty principle is often referred to as Heisenberg's uncertainty principle, named after the physicist Werner Heisenberg who first proposed it. However, Heisenberg's uncertainty principle specifically refers to the uncertainty between position and momentum, while the uncertainty principle encompasses a broader range of properties, including energy and time.

4. How does the uncertainty principle affect our understanding of the behavior of particles and fields?

The uncertainty principle has significant implications for our understanding of the behavior of particles and fields at the quantum level. It means that we can never have complete knowledge or control over these systems, and that there will always be some level of uncertainty in our measurements and observations.

5. Can the uncertainty principle be violated or overcome?

No, the uncertainty principle is a fundamental principle of quantum mechanics and has been extensively tested and proven through experiments. It cannot be violated or overcome, as it is a fundamental property of particles and fields at the quantum level.

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