[Kryptid (OP)]

To the best of our particle accelerators' resolution, electrons appear to be point particles. A point is an object with no size, so it should be possible for a point to pass through a gap or hole no matter how small it is. However, we know that electrons don't behave in such a simple matter. They have wave-like properties and also obey Heisenberg's uncertainty principle.

Can an electron pass through a gap or hole that is smaller than its own wavelength? Would the uncertainty principle also put limits on how small of a hole it can pass through given that there is supposedly a limit on how small of a space you can confine a particle of a given energy? Making a physical hole that is on such a tiny scale might not be possible, so let's say I'm talking about a tiny wormhole mouth instead. If the wormhole was, say, 10,000 times smaller than the diameter of a proton, would that be too small for an electron to pass through?

[jeffreyH]

You appear to be ignoring the effects of a charged particle moving through an electric or magnetic field. How would this impact motion through the hole?

[Kryptid (OP)]

You appear to be ignoring the effects of a charged particle moving through an electric or magnetic field. How would this impact motion through the hole?

If the presence of such a field makes any difference, we can discuss that as well. It does make me wonder if the curved space inside of a wormhole's throat would actually make the electron's field lines loop around and interact with themselves in some manner.

[evan_au]

it should be possible for a point to pass through a gap or hole no matter how small it is

Radioactive decay tells us that you can tunnel through a barrier even if the barrier has no holes.
- Even with non-point particles like protons and neutrons
- In the case of a radioactive nucleus like U238, the strong nuclear force doesn't have holes, but the barrier does have a finite thickness, and there is a finite chance that a particle can tunnel through to the other side of that barrier.

So perhaps rather than worrying about the diameter of the hole, you should be looking at the length of the tunnel?

[Kryptid (OP)]

Radioactive decay tells us that you can tunnel through a barrier even if the barrier has no holes.
- Even with non-point particles like protons and neutrons
- In the case of a radioactive nucleus like U238, the strong nuclear force doesn't have holes, but the barrier does have a finite thickness, and there is a finite chance that a particle can tunnel through to the other side of that barrier.

So perhaps rather than worrying about the diameter of the hole, you should be looking at the length of the tunnel?

I hadn't even thought about tunneling. I suppose it does make sense to say that an electron can tunnel through a tiny wormhole. Would an electron have to rely on tunneling in order to make it through an ultra-microscopic wormhole like the kind I mentioned in the OP?

[Colin2B]

Photons are not supposed to pass through holes smaller than wavelength so presumably same should be true of electron. Although any charge or mag field at opening of wormhole would deflect electron.
This link suggests photons can pass through a smaller hole, but I’m not sure what they mean by pass through, certainly some photons would be on other side of barrier, but are they created there?
https://physics.aps.org/story/v4/st18

[evan_au]

pass through, certainly some photons would be on other side of barrier, but are they created there?

My impression from that article is that plasmons transfer the photon energy from one side of the metal plate to the other. The photon is then recreated on the other side of the slot, by the same mechanism which absorbed the photon in the first place.

For holes which are around 10% of a wavelength wide, they managed to get 80% transmission (in a computer model). Without the plasmons, they were expecting much lower transmission.

Note that electromagnetic waves are long, but they can be very "skinny".

When I was working on shielding for Radio-Frequency Interference, you could get significant transmission of 1 meter wavelength RFI through a doorjamb slot that was less than a millimeter wide - provided it was at least a meter long. To prevent this RFI leakage, you need to make electrical contact along the length of the doorjamb, so that any gaps are only a millimeter long, as well as only a millimeter wide.

See: https://en.wikipedia.org/wiki/Plasmon

[PmbPhy]

To the best of our particle accelerators' resolution, electrons appear to be point particles. A point is an object with no size, so it should be possible for a point to pass through a gap or hole no matter how small it is.

That is correct.

However, we know that electrons don't behave in such a simple matter.

Sure we do.

They have wave-like properties and also obey Heisenberg's uncertainty principle.

The HUP is a statement about the wavefunction itself before it interacts with a macroscopic system. It has nothing to do with the spatial extension of a particle. That it does appears to be a large misconception in quantum mechanics.

Can an electron pass through a gap or hole that is smaller than its own wavelength?

Of  course. Analyze Thomson's double slit experiment and you'll find that's the case there.

Would the uncertainty principle also put limits on how small of a hole it can pass through given that there is supposedly a limit on how small of a space you can confine a particle of a given energy?

No, because no such limit exists. Exactly what is it that you think the HUP says anyway?

[chiralSPO]

Others have touched on most aspects of this answer, but I am still compelled to contribute a few points:

First, one is certain to run into trouble when trying to think of electron-scale phenomena with macro-scale terminology. At the atomic scale there really isn't anything akin to what we think of as solid. Solids, after all, are merely collections of huge numbers of small particles behaving in such a way that their aggregate positions, motions, interactions, and forces appear to be a solid object--the primary forces involved in the bench I currently occupy preventing me from falling through are the electromagnetic forces (attributed to both the charge and spin of electrons and nuclei). If we consider the interaction of a single electron (rather than my rear end), then it is no longer accurate to consider the bulk aggregate of these charged particles, and must instead look at individual interactions (even if it is very many).

At the (sub)atomic scale, everything is "fuzzy" or "foamy". There are no well-defined (as we would think of them in our macro-scal world) boundaries, positions, times etc. This is partly due to HUP, and partly due to the fact that everything is constantly moving (even at 0 K).

Second, electrons (and other particles) can tunnel through "barriers" even with no "hole," so I would say there is no lower limit to the size of a hole required for an electron to pass. However, the time required for an electron to tunnel might be very long (the actually tunneling even is effectively instantaneous, but if the probability of it occurring is small, then it will probably only happen very rarely--this is exactly like half-lives for radioactive nuclei). Electrons can also move classically through barriers provided they have enough energy to do so.

[Kryptid (OP)]

Sure we do.

I know they behave like point particles in some circumstances, but doesn't their wave-like character come into play in other circumstances?

The HUP is a statement about the wavefunction itself before it interacts with a macroscopic system. It has nothing to do with the spatial extension of a particle. That it does appears to be a large misconception in quantum mechanics.

I have to admit that I've heard contradictory things about the HUP. One reference will say that particles do have absolute location and momentum but we can't know what they are exactly because any attempt to measure them disturbs the system, while another reference will say those properties are truly indeterminate whether you have interacted with the particle or not.

Of  course. Analyze Thomson's double slit experiment and you'll find that's the case there.

Alright, thanks for that.

No, because no such limit exists. Exactly what is it that you think the HUP says anyway?

I remember reading something on Wikipedia about a "preon paradox" which says that the electron could not be composed of more fundamental particles because confining them to a volume within the classical electron radius would force their uncertainty in mass to exceed the mass of the electron. Or something. It's easily possible that I misinterpreted what I read. I figured that meant that the HUP put a limit on how small of a volume you could confine a particle of a certain energy to.

[yor_on]

I'll see if I can find it but I seem to remember a new way of describing tunnelings, and didn't it get a prize too? As in overlaid wave patterns, geometric?? Sorry, I read about it though, maybe someone else recognize it?
=

And Kryptid http://hyperphysics.phy-astr.gsu.edu/hbase/uncer.html discuss Particle Confinement " The uncertainty principle contains implications about the energy that would be required to contain a particle within a given volume. The energy required to contain particles comes from the fundamental forces, and in particular the electromagnetic force provides the attraction necessary to contain electrons within the atom, and the strong nuclear force provides the attraction necessary to contain particles within the nucleus. But Planck's constant, appearing in the uncertainty principle, determines the size of the confinement that can be produced by these forces. Another way of saying it is that the strengths of the nuclear and electromagnetic forces along with the constraint embodied in the value of Planck's constant determine the scales of the atom and the nucleus. "