I Why is the Uncertainty principle inherent to particles?

[Phys12]

If we have a particle, say, an electron and we shoot it straight through an empty box. This box is surrounded by light sources on its two sides:

So, if you consider the above cube, if we shoot a particle in a straight line such that it crosses the face ABEF and it crosses the face HGDC through their center. And we keep an array of light sources in the faces BCGF and ADHE in the middle along the side BC and AD respectively. The light sources are high energy and hence, smaller wavelength to be able to reflect off the electron.

If we have the setup above, light would bounce off the electron on the two sides and when it does, we'll detect exactly where the electron is. Since we have these waves coming from both the directions, it wouldn't change the momentum of the particle. We could measure the position of the particle at a specific instant, do the same measurement at a different instance and then divide the change in position by change in time to get the velocity and hence, the momentum, correct?

Edit: Oops! Title didn't really match the elaboration.
So, if we can get a high enough energy light, wouldn't we be able to measure the position and the momentum at the same time with uncertainties less than h bar/2? How exactly is it the case that we're not limited by our instruments, but the inherent nature of the universe doesn't allow for such precise measurements?

 

[phinds]

Precision isn't the problem. Repeatably is. Whatever answer you get for the first electron, the next one won't act exactly the same.

 

[PeroK]

If we have a particle, say, an electron and we shoot it straight through an empty box. This box is surrounded by light sources on its two sides:
View attachment 220835
So, if you consider the above cube, if we shoot a particle in a straight line such that it crosses the face ABEF and it crosses the face HGDC through their center. And we keep an array of light sources in the faces BCGF and ADHE in the middle along the side BC and AD respectively. The light sources are high energy and hence, smaller wavelength to be able to reflect off the electron.

If we have the setup above, light would bounce off the electron on the two sides and when it does, we'll detect exactly where the electron is. Since we have these waves coming from both the directions, it wouldn't change the momentum of the particle. We could measure the position of the particle at a specific instant, do the same measurement at a different instance and then divide the change in position by change in time to get the velocity and hence, the momentum, correct?

Edit: Oops! Title didn't really match the elaboration.
So, if we can get a high enough energy light, wouldn't we be able to measure the position and the momentum at the same time with uncertainties less than h bar/2? How exactly is it the case that we're not limited by our instruments, but the inherent nature of the universe doesn't allow for such precise measurements?

One problem is that the measurement of position as the electron exits the box may influence its momentum at that time.

In any case, the uncertainty principle is a statistical law and does not relate to one-off measurements on a single particle.

If you search my recent posts for "HUP" for more on this.

 

[mfb]

The uncertainty principle is not about measurements. The particles do not have an exact position and momentum, so attempts to measure both will return some value - but what exactly you get is random, and if you repeat it you'll get something else (even for the same particle, if you repeat position and momentum measurements).

Unrelated to that:

Since we have these waves coming from both the directions, it wouldn't change the momentum of the particle.

It would. The electron would randomly scatter one photon from one side if you get a useful position measurement.

 

[Demystifier]

The uncertainty principle is not necessarily inherent to the particle. It is inherent to the wave function of the particle. How exactly the particle is related to it's wave function, that's a matter of interpretation on which there is no consensus among experts. In some interpretations the particle and it's wave function are one and the same object (in which case the UP is inherent to the particle), but in other interpretations this is not so.

 

[Phys12]

One problem is that the measurement of position as the electron exits the box may influence its momentum at that time.

In any case, the uncertainty principle is a statistical law and does not relate to one-off measurements on a single particle.

If you search my recent posts for "HUP" for more on this.

Awesome! Thank you. I went through your posts and one of them says,

One interpretation of this is that if you prepare a state with a well-defined momentum, then that state will have a relatively large spread of position measurements; and, vice versa.

Can you please explain what you mean by "a state" in this context?

 

[phinds]

Awesome! Thank you. I went through your posts and one of them says,

Can you please explain what you mean by "a state" in this context?

The "state" is the condition that a particle is in. Depending on the particle it can include spin, momentum, position, etc.

What he's saying is the same thing I said in post #2

 

[Phys12]

The uncertainty principle is not necessarily inherent to the particle. It is inherent to the wave function of the particle. How exactly the particle is related to it's wave function, that's a matter of interpretation on which there is no consensus among experts. In some interpretations the particle and it's wave function are one and the same object (in which case the UP is inherent to the particle), but in other interpretations this is not so.

So when you say that in the interpretation where the particle and its wave are one and the same object, does the uncertainty arise from the fact that the wave function is probabilistic?

 

[Phys12]

The "state" is the condition that a particle is in. Depending on the particle it can include spin, momentum, position, etc.

What he's saying is the same thing I said in post #2

I see, so for a different particle you'd get different measurements. What if I take the same particle and run it through the experiment repeatedly? Does the uncertainty arise because we have a different particle?

 

[Phys12]

The electron would randomly scatter one photon from one side if you get a useful position measurement.

Why would it do that?

 

[phinds]

I see, so for a different particle you'd get different measurements. What if I take the same particle and run it through the experiment repeatedly? Does the uncertainty arise because we have a different particle?

No, the uncertainty exists because it is inherent in the nature of things. If you could in fact take exactly the same particle (and as far as electrons are concerned they ARE essentially exactly the same particle) and set it up in exactly the same way and then run the exact same experiment, you would get different results. That is the essence of the HUP, which is not a measurement problem

 

[Demystifier]

So when you say that in the interpretation where the particle and its wave are one and the same object, does the uncertainty arise from the fact that the wave function is probabilistic?

Not necessarily. The many-world interpretation is a counterexample.