# Quantum Mechanics and Electrodynamics/Electrostatics

• WWCY
In summary, the conversation discusses the uncertainty relation in quantum mechanics and how it contrasts with classical electrostatics/dynamics. The participant raises a question about the compatibility of assuming knowledge of both position and momentum in classical theory, and the reason why classical theory still holds up well despite this. The response explains that this is due to the small value of h, which allows for accurate preparation of position and momentum on classical scales.

#### WWCY

Hi all, I have a question relating to the title above.

The uncertainty relation tells us that an electron that is localised (in terms of its PDF) is space has a large uncertainty in momentum space. However in classical electrostatics/dynamics we seem to make attempts to do things like approximating the magnetic field caused by an electron moving at a given velocity from A to B.

Isn't this a little wonky since we are assuming that we know position and momentum at the same time? If so, is there a reason why classical theory still holds up pretty well (slight understatement)?

WWCY said:
If so, is there a reason why classical theory still holds up pretty well

Because h is small.

Dale

Because h is small.

Do you mind elaborating a little on what this means? I'm afraid I don't follow.

If h were zero, QM would look like classical physics.

WWCY said:
Isn't this a little wonky since we are assuming that we know position and momentum at the same time? If so, is there a reason why classical theory still holds up pretty well (slight understatement)?
As @Vanadium 50 said above, the reason it works is because h is small in terms of the scale where classical theory holds up well. Recall that the uncertainty principle does not merely tell us that we cannot know position and momentum at the same time, but it also puts specific constraints on our knowledge of position and momentum. Specifically: ##\sigma_x \sigma_p \ge \hbar/2##.

So if we have an electron whose velocity we prepare to an accuracy of 1 m/s then we simultaneously prepare its position to an accuracy of 58 microns. If it is a proton with the same velocity then we can also prepare its position to an accuracy of 32 nanometers. On classical scales that works OK.

WWCY
Dale said:
As @Vanadium 50 said above, the reason it works is because h is small in terms of the scale where classical theory holds up well. Recall that the uncertainty principle does not merely tell us that we cannot know position and momentum at the same time, but it also puts specific constraints on our knowledge of position and momentum. Specifically: ##\sigma_x \sigma_p \ge \hbar/2##.

So if we have an electron whose velocity we prepare to an accuracy of 1 m/s then we simultaneously prepare its position to an accuracy of 58 microns. If it is a proton with the same velocity then we can also prepare its position to an accuracy of 32 nanometers. On classical scales that works OK.

Thanks a lot!

## What is quantum mechanics?

Quantum mechanics is a branch of physics that studies the behavior of particles at the atomic and subatomic level. It describes how particles such as electrons and photons interact with each other and with electromagnetic fields.

## What is the difference between electrodynamics and electrostatics?

Electrodynamics and electrostatics are both branches of physics that study the behavior of electrically charged particles. However, electrodynamics focuses on the movement of charges and the effects of changing electric and magnetic fields, while electrostatics studies the behavior of stationary charges and the properties of electric fields in the absence of changing fields.

## How does quantum mechanics explain the behavior of particles?

Quantum mechanics explains the behavior of particles through the use of wave functions, which describe the probability of a particle being in a certain location or having a certain energy. It also introduces the concept of quantization, where particles can only exist in certain discrete energy levels rather than a continuous range of energies.

## What is the role of electromagnetism in quantum mechanics?

Electromagnetism plays a crucial role in quantum mechanics, as it is responsible for the interactions between charged particles and the creation and manipulation of electromagnetic fields. The principles of electromagnetism are incorporated into the equations and theories of quantum mechanics.

## What are some real-world applications of quantum mechanics and electrodynamics?

Quantum mechanics and electrodynamics have numerous applications in modern technology, such as the development of transistors and computer chips, lasers, and medical imaging devices. They also play a crucial role in understanding and developing quantum computing and communication technologies.