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And I mean really slow.

I don't know how this would even be done, but just a thought experiment.

To explain why I ask this, the way I understand the phrase "we can't know the momentum and position of something at the same time" is that when things move really fast, its not only that we can't know where it is, its that it actually stops being in one place at a time, and spreads out over a space where it has different probabilities of being in different parts (if I'm wrong, I'd super appreciated a correction, just if there's math involved please go through it slowly, step by step).

So if we were to slow the electron down, would it then only be at a single place? If we were to somehow stop an electron from moving altogether, would that mean it would literally only be at a single place? Or would it somehow teleport between locations?

Finally, if we could accelerate a person to a really, really high speed, would they also stop being at a defined location while they are moving, and spread out with probabilities of being in different places at the same time?

Thanks!

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    $\begingroup$ Possible duplicate of Can an electron interact with itself to create interference? $\endgroup$ – WillO Aug 19 '18 at 12:54
  • $\begingroup$ @WillO better now? $\endgroup$ – Joshua Ronis Aug 19 '18 at 12:56
  • $\begingroup$ Shifting the momentum of an electron (or a person) has no effect on the uncertainty in position. $\endgroup$ – WillO Aug 19 '18 at 13:03
  • $\begingroup$ @WillO thanks for the answer. So then why when a person walks towards 2 doors, they can only walk through one? $\endgroup$ – Joshua Ronis Aug 19 '18 at 13:06
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    $\begingroup$ Planck's constant is very very small. $\endgroup$ – WillO Aug 19 '18 at 13:09
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If the electron was stopped what would you use to measure it's position? Anything, a photon for example, has its own uncertainty issues and so it's not just where something is, it's also how you perceive/sense it. It's the whole system (object + measuring device) that gives us the uncertainty.

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Velocity and uncertainty in velocity are two separate things.

The wavelength of an electron's position wavefunction is inversely proportional to the electron's velocity. So, if the electron is moving very slowly, its wavefunction has a very long wavelength. That wavelength is an indication of uncertainty in position, so an electron known to be moving very slowly could be found anywhere that its position wavefunction has a non-zero value.

Similarly, if the position of the electron is squeezed down to a very small region, the uncertainty in its velocity would be very large because the uncertainty in its position is very small.

The uncertainty in an electron's position is inversely proportional to the uncertainty in its velocity. If you know that an electron is moving very slowly, then you know its velocity with high certainty, and therefore its position can be known only with very low certainty. If you know it is moving very fast, you don't necessarily know its velocity with high certainty. But if you do know the velocity of a fast electron with high certainty, then again you can only know its position with low certainty. On the other hand if the fast electron's position at a given moment can be known with very high certainty, its (high) velocity can be known only to the amount of certainly allowed by the uncertainty principle.

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  • $\begingroup$ Okay, so we are kind of having the same conversation on 2 different posts, and I think I'm gonna delete this one and keep that one up instead, so you can answer there instead, but if I understand what you are saying, when the electron is moving very slowly its got a probability of being in a lot of places at the same time? While if its moving faster... its wavelength shrinks so that it's only at one place? $\endgroup$ – Joshua Ronis Aug 19 '18 at 20:41
  • $\begingroup$ GOT IT! I wasn't paying attention to the fact that when the wavelength shrinks, its not just a top wave that shrinks, its gor a frequency as well! So let me resay that. When its moving faster, its got a high probability of being at MORE definite places at the same time, and when its moving slower the probability of being at any of those places for sure further away from each other dies out, but it could be either at point A, or a tiny distance away from point A, with around the same probability! The probability wave becomes less steep (more spread out) but also there are less definite peaks! $\endgroup$ – Joshua Ronis Aug 19 '18 at 20:44
  • $\begingroup$ @JoshuaRonis: No, you have this entirely wrong. If an electron is in (something very close to) an eigenstate of momentum, then the probability distribution for its position is going to have a very high variance, and this is equally true whether the momentum is very small or very large. $\endgroup$ – WillO Aug 21 '18 at 16:16
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First of all lets clear up this misunderstanding of probabilities:

and spreads out over a space where it has different probabilities of being in different parts

........

and spread out with probabilities of being in different places at the same time?

There is no probability for a specific electron to be in different places at the same time. An electron is an elementary particle and when detected it is always found at a specific (x,y,z,t). More so for a person.

The probability which gives rise to the interference pattern in the double slit experiment can only be probed by accumulating a distribution of electrons scattering off the same double slits, as seen here. Individuals, elecrons or persons leave one footprint at (x,y,z,t) (well a person in a volume around but one can see the argument).

Now for the simple case of a particle, either an elementary one as an electron, or a composite quantum mechanical particle up to nanometer scales, one can use the de Broglie wavelength to intuit the dimensions and distances of the double slit so that interference patterns can accumulate. Here one can find a calculator which will give double slit set ups.. It is for light but the mathematics is the same for particles.

So if we were to slow the electron down, would it then only be at a single place? If we were to somehow stop an electron from moving altogether, would that mean it would literally only be at a single place?

Whenever we detect an electron on a screen, we stop it there and it is absorbed by the atoms and molecules of the detector, and within the accuracies of the dimensions of an atom it is in one place

Or would it somehow teleport between locations?

There is no teleportation, see above about probabilities. Each individual quantum mechanical entity when detected is at a specific (x,y,z,t) within the errors of the measurement and the method used.

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