Would the double slit experiment still yield the same results if the electron were travelling really slowly?

Question

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!

Answer 1

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.

Answer 2

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.

Answer 3

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.