Heisenberg Uncertainty: simple explanation required please

In summary: The HUP is a consequence of the axiome that the commutator between a position and a momentum operator is the unit operator.)In summary, the Heisenberg Uncertainty Principle states that there is a limit to how precisely we can measure both the position and momentum of a particle at the same time. This applies to the interaction between light and electrons, as the measurement of the light's direction also affects the measurement of the electron's momentum. Therefore, we cannot know with certainty where or with what angle a photon hits an electron due to the uncertainty principle.
  • #1
cemtu
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TL;DR Summary
it is said that just because you can not know from where the light hit electron; you can not know the direction of the momentum of scattered electron. I do not understand the reason why we can not know from where or with what angle a photon hits an electron!
why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??
 
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  • #2
cemtu said:
Summary:: why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??

why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??

I don't see the connection between this question and the HUP. The HUP gives a relation between the standard deviations of momentum and position measurements of a particle in any state:
$$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$
 
  • #3
PeroK said:
I don't see the connection between this question and the HUP. The HUP gives a relation between the standard deviations of momentum and position measurements of a particle in any state:
$$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$
it is said that just because you can not know from where the light hit electron; you can not know the direction of the momentum of scattered electron. I do not understand the reason why we can not know from where or with what angle a photon hits an electron!
 
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  • #4
cemtu said:
it is said that just because you can not know from where the light hit electron; you can not know the direction of the momentum of scattered electron. I do not understand the reason why we can not know from where or with what angle a photon hits an electron!
To measure the direction that something was traveling, we need some sort of detector. For example, we could have a screen with a hole in it, and a piece of photographic film behind the hole. A particle hits the film and leaves a dot on the film; we draw a line from the dot back to the hole and that tells us the path of the particle.

In the language of quantum mechanics, the interaction with the hole has measured the momentum of the particle as it passed through the screen and the interaction with the film has measured the position as it reached the film.

However, there’s a catch. The hole in the screen and the dot on the film both have non-zero size so there are many lines that I can draw between the two, and they aren’t exactly parallel (compare the line between the right-hand side of the dot and the left-hand edge of the hole with the line between the left-hand side of the dot and the right-hand edge of the hole). So we haven’t exactly measured the angle, there’s some uncertainty in our result. The quantum mechanical uncertainty principle says that that uncertainty cannot be reduced all the way to zero.
 
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Likes Klystron, PeroK and cemtu
  • #5
thank you Nugatory!
 
  • #6
Well, in non-relativistic QM a give uncertainty (say, the momentum of a given electron) can be made as small as desired. The product of uncertainties of variables that are linked by the HUP does have a lower limite that can't be made smaller.
 

Related to Heisenberg Uncertainty: simple explanation required please

1. What is Heisenberg Uncertainty?

Heisenberg Uncertainty, also known as Heisenberg's Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to know with absolute certainty both the position and momentum of a subatomic particle at the same time.

2. Why is it called "uncertainty"?

It is called "uncertainty" because it describes the inherent limitations in measuring and predicting the behavior of particles at the quantum level. This means that there will always be a degree of uncertainty in our knowledge of a particle's position and momentum.

3. How does Heisenberg Uncertainty relate to the wave-particle duality?

Heisenberg Uncertainty is closely related to the wave-particle duality of quantum particles. This principle suggests that particles can exhibit both wave-like and particle-like behavior, and that the more accurately we measure one aspect (such as position), the less accurately we can measure the other (such as momentum).

4. What are the implications of Heisenberg Uncertainty in the real world?

Heisenberg Uncertainty has several implications in the real world. It means that at the quantum level, we cannot have complete knowledge of a particle's properties, and our measurements will always have some degree of error. This also has implications for technology, as it limits the precision of certain measurements and the development of certain technologies.

5. Can Heisenberg Uncertainty be overcome?

No, Heisenberg Uncertainty is a fundamental principle in quantum mechanics and cannot be overcome. It is an inherent part of the behavior of particles at the quantum level and has been confirmed through numerous experiments. However, scientists have developed techniques to minimize the effects of uncertainty and improve our understanding of quantum particles.

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