Here is a link to a page showing the double slit experiment with electrons including a video. Maybe this will help: http://www.hqrd.hitachi.co.jp/em/doubleslit.html
(NOTE: The page wanted me to install a Japanese language font [or something] which I refused and the page worked just fine anyway.)
The way I understand it is that the “wave” behavior of the electron )or whatever particle is n question) is a probability wave - ie, a wave representing the probability of the electron performing a certain behavior. The probability wave is a distribution function that shows the probability of each possible behavior the electron can be performing. In the case of the double-slit experiment, the distribution function represents the chance of the electron of being in any distinct location. When you make a measurement (or an observation - the two are pretty much interchangeable), you now know where the electron is. The probability of it being where it is goes to one, and the probability of it being anywhere else goes to zero. Thus, the probability wave collapses onto a single point, that point being the particle.
Anyway, that’s how I understand it. I could be way off, but this explanation allows me to sleep at night, at any rate. 
Jeff
Other interesting observations:
[ul]
[li]If in this experiment, you had a way of noting every time an electron was fired, and every time one hit the backstop behind the double slit, you’d find that they leave and arrive just like they were particles, i.e. one leaves, one arrives. There aren’t any half-arrivals or double-arrivals or such. Note that if you were talking waves flowing through that you would see various amplitudes at each arrival spot, as opposed to there-or-not-there, as you’d expect with particles.[/li][li]If you picked one spot on the backstop behind the two slits and watched electrons arrive at that one spot, the arriving electrons would be very erratic, not in a steady stream. Although, if you counted the number arriving in a given spot for a minute, then counted for a second minute, the number arriving would be a similar number. I.e., when an electron hits the wall, it hits it at a random spot; it’s only after watching many hit that we would see the interferance pattern.[/li][li](this is a good one.) If, as an electron passes through one slit or the other, we detect which slit it went through, the interferance pattern goes away, and instead you see what you’d expect to see with particles, a smooth pattern with no interferance. As soon as you stop detecting which slit it went through, it goes back to having an interferance pattern.[/li][li](kindof a continuation of the last) suppose we think that our detector at the slits is influencing the path of the electrons. So we turn down our detector. As we turn it down, we detect less electrons (although they all still end up hitting the backstop), but each one we do detect is still detected in a binary fashion, there-or-not there. And every electron we detect will contribute to a particle-expected pattern, and every electron we don’t will contribute to a wave-expected pattern.[/li][/ul]
The wave is wave of PROBABILITY. Its not a wave in some sort of medium, like a wave in water is. For example, if you were throwing darts at a dart board, the probability of a dart ending up in a particular location could be predicted by circular geometry*. In the case of an electron, its probability of being at a particular location is predicted by wave geometry, and the complext math therein required.
(*Assuming the thrower is an intelligent thrower and actually aiming at the dart board.)
Yep, this is the probalistic interpretation of the wave function.
Not in the Copenhagen intepretation, it’s pretty explicit that the wave is a mathematical construct that has no “real life” counterpart.
I’m aware of that. I don’t believe I ever indicated it was in any way physical.
Your’re right I was overstating the point, it’s just that really it should be it’s probabilty of being in a certain location when it is measured as in CI it doesn’t have a postion until it’s measured.
How can an individual wave of probability cause interference with itself?
The individual wave becomes TWO waves when it passes through the slits. These two waves interfere with each other.
I thought it wasn’t a physical wave.
Light is a wave, it passes through the two slits and diffracts (or splits) and interferes with itself, this is not a suprising result at all from the experiment. The suprising (wel not anymore as this experiment gets done alot) is that when a single ‘indivisible’ wave packet goes through it interferes with itself.
It’s not. It’s a probability wave. Really, we probably shouldn’t even use the word “wave” to describe it, but no other word really fits as well.
So what is an electron? What about about it allows it to interfer with itself?
So what is an electron? What about about it allows it to interfer with itself?
So what is an electron? What about about it allows it to interfer with itself?
Sorry for the triple post with the double about.
An electron is also a wave (what’s happening here is that the wave function is becoming confused with the wave-particle duality), like any object with a wavelength given by De Broglie equation.
electrons and photons are waves in the physical sense, their wave function is not a wave in the physical sense.
The fact that it exists as a probability wave until it interacts with something. The interfering-with-itself aspect is just one of the fundamental properties of probability waves. There’s really no simple answer to “why” other than “it just does”. Perhaps the reason becomes obvious if you study the math involved, but I’m no quantum physicist.
Should of been clearer when you’re diffracting a single particle you can’t really consider as a De Broglie wave (though that will give you the interference pattern).