Double Slit Experiment -- Electron Interference

Why in a double slit experiment when electrons are fired one at a time do the results still show an interference pattern? What are the individual electrons interfering with?

Themselves. Quantum mechanics says that the electrons each pass simultaneously through both slits (and in fact, through every point in the universe, as bizarre as that sounds). In other words, the electron’s existence is “smeared out” in spacetime, and its exact location is indeterminate until an interaction occurs (remember Schroedinger’s Cat?), and it can interfere with itself until it interacts with the film beyond the slits.

No, what is this?

Doesn’t this violate parts of relativity?

Schroedinger’s cat is a thought experiment used to describe probability functions. The idea is you have a live cat sealed in a box along with a vial of poison, and a trigger consisting of an atom of a radioactive element that will release the poison if the atom decays. If you run the experiment so that there is precisely a 50-50 chance of the atom decaying and relasing the poison during a given time interval, Schroedinger say there must exist two quantum waveforms of kitty–one where it is alive, and one where it is dead, and these waveforms will only collapse into one possibility or the other when the lid is opened and kitty is observed (or some other means is used to determine kitty’s fate).

The electron passing through every point in the universe doesn’t violate Relativity, because no information is being sent faster than light. The electron can’t be observed at a distant point until sufficient time has passed for it to be there. It’s existence at various points is only a function of the probability of it having taken that path, and if it did take a path that took it out to, say, Alpha Centauri (despite the VERY long odds of it doing so), it would take ~8 years for it to travel from the electron source to the detector behind the slit.

Ok, so what makes the probability higher that the electron will end up where it will? If it takes every path, why is one path more probable (does this have something to do with paths canceling each other out)?

From what I understand, yes. That is the point of the “interference” concept… some wave troughs and crests cancel each other out, etc.

hehe… two slits (sorry, I couldn’t help it… I’ve been at work 13 straight hours)

IIRC Schroedinger created his thought experiment to call into question some of the disturbing results quantum mechanics suggests. Also, for my part, why doesn’t the kitty count as an observer. That is, iy doesn’t take me opening the box to cause the waveform to collapse and settle on dead cat or live cat…the cat itself as already observed the results.

As to the electron taking eight years to reach Alpha Centauri remember that if the electron moves at light speed (I don’t know that it does) then from the electron’s perspective it takes zero time to reach Alpha Centauri and zero time to get anywhere. So, in a sense, the electron is everywhere in the universe simultaneously.

[quote]
From what I understand, yes. That is the point of the “interference” concept… some wave troughs and crests cancel each other out, etc.[/auote]

But why do we see the pattern we do in the double slit experiement? Why is this pattern the most probable?

Because the electron gun is pointed toward the target. So while there is a non-zero chance that the electron will end up in some random direction, it is very likely that it will hit the target. But within the aim of the electron gun the probability of going though either slit is essentially the same because they are so close together.

So why don’t we see a pattern when electrons hit directly behind the the two slits and not the interference pattern?

To clarifiy:
If we had one slit open then we would see a pattern directly behind that slit. If we had the other slit open we would see a pattern directly behind that slit. But if we open does slits and fire the electrons one at a time, we get an interference pattern.

I take it the individual electron wave cancels itself out, but how? And why?

We get an interference pattern when both slits are open because the electrons (or photons or Buicks or whatever particle flavor you happen to be using) pass through both slits at the same time. It’s important to note as you conduct this experiment, that the point where each particle hits the detector shows a distict propensity for having passed through one slit over the other. It is only after many thousands or millions of single particles have been fired does the interference pattern build up, becoming more distinct and pronounced with continuing repetition.

But how does an individual electron go through both slits? Do some photons only go through one slit (the electrons at the outside of the pattern)?

Because each and every electron is a wave, in and of itself.

Picture a swimming pool with a screen across the middle which has two slits in it. You drop a rock in one side of the pool causing a wave, or ripple. When this wave hits the screen two new waves will be created on the other side of the screen with their origins at the slits. It’s these two waves which interfer with each other.

Well each individual electron is a wave which creates two new waves at the slits. So you get interference.

You’re still thinking of electrons as point particles, and they ain’t. Not entirely. Set up your double-slit experiment in a shallow bath. Make a single wave by dipping your finger in the water in from of the slits. Watch the other side of the slits, and you’ll see a wave emerging from each slit, to continue on til they hit the side of the container. It’s not exactly like that, but you get the basic idea.

Remember too that the more massive a particle is, the less wavelike its behavior. You’d have to run this experiment for much longer to get similar results with Buicks, than you do for electrons.

Ok, I think I understand how the wave goes through both slits. But why do we only get a probability of where the wave will end up? Does the wave go each wave differently sometimes? Why can’t we determine exactly were the wave will end up? Does this have to do with the Heisenberg Uncertainty Principle?

This should read:

Does the wave go each slit differently sometimes?

Quantum physics operates on the principle that all possibilities of an event are occuring simultaneously, however we see expected Newtonian results because those unseen possibilities are cancelling each other out.

In effect, quantum theory attempts to explain some bizarre experimental results (the electron double-slit diffraction pattern) in the context of Newtonian physics (where electrons are particles, not waves).

While you’re thinking about that…

Even more crazy is the fact that every time a particle with insufficient energy to penetrate a given substance collides with that substance, there is a very small (but nonzero) probability that the particle will penetrate that substance.

Think of it this way–you throw a baseball at a concrete wall at 30 miles per hour. You expect it to reflect. And yet, by the laws of quantum mechanics, it is theoretically possible for that baseball to phase through the concrete wall. If you could throw baseballs at concrete walls for all eternity, eventually you would see this happen. This blows my mind.

Apologies to Q.E.D. if he’s about to post the same thing.

Any time the position of the electron is measured, the “wave packet” is collapsed. This is just a fancy way of saying that it stops acting like a wave and acts like a particle instead. I’ve never really seen an adequate explanation of why this happens, except to say that any system you can think of which measures the electron also affects the electron. For instance, you might bounce light off of the electron, but when something is as small as an electron, hitting it with a photon is like hitting me with a car. It just changes things.

The screen on the other side of the two slit experiment is just a way of measuring the position of the electron. Up to the moment it reaches the screen the electron behaves like a wave and its position is determined by probability. The moment the electron reaches the screen its position is measured and this forces the electron become a particle which can only have a specific position (though that position must fit into the earlier probability scheme).

It is possible to run this experiment in such a way that you can measure which slit each electron passes through. But if you do this, then the electrons take on a particle nature at the slits and the resulting pattern is that of a one slit experiment. (Except you get two peaks, one for each slit.)