Need help please

[TRZ]

Could someone help explain a few things about the double-slit experiment? These are fairly basic questions and they may reflect very flawed assumptions on my part, so please pardon this in advance. Here is where I am confused:

 

1. When electrons are fired at the screen, my understanding is they travel as wave-particle (with qualities of both). Question is -- do the electrons essentially travel straight, but in a sine-wave type of pattern? Or is there some sort of wave expansion as the electronic shoots forward, like the wave pattern that that forms when a raindrop falls in a pool of water? Or does it travel in some other mode entirely?

 

2. When the electrons are fired one at a time, an interference pattern gradually starts to form. From wikipedia, this is because the electron interferes with itself because it's possible to travel through _both_ slits in some sort of probabilistic manner. Even if you accept the notion that the electron could be in 2 places at once, how would it be physically possible for any one electron to go through both? By that I mean, I would assume the variability in the position of the electron is exceedingly small, at a sub-atomic level. Whereas, the distance between the 2 slits is relatively wide by comparision. I don't see how from a spatial perspective the location could vary by enough distance to go through both.

 

Thanks in advance.

[Cap'n Refsmmat]

Quick answers:

 

1. The electrons don't physically wiggle up and down in a sine wave pattern, no. One interpretation is that the waves represent the probability of finding the electron in a certain location, rather than the electron's actual location. When you make a measurement to determine its actual position, the result you get will match the probabilities. You can see it in action in quantum minigolf:
2. The slits have to be fairly close together for this reason. The experiment will not work if the slits are too far apart.

[TRZ]

Thanks!

 

On #2, is there any way to think about the size of the area in which the electron might be found (in some probability), as it travels on its path? For instance I had always thought of an electron being within the size of an atom. But, in order to potentially pass through either of the 2 slits, there must be some probability of finding the electron in an area that is considerably larger than an atom, right?

 

Is there any way to put this range of potential locations into context? For example, within the head of a pin, or a grain of sand, or a dime, a tennis ball, etc?

 

 

 

 

[Cap'n Refsmmat]

The range of potential locations can be determined with the Uncertainty Principle:

 

[math]\Delta x\, \Delta p > \frac{\hbar}{2}[/math]

 

where [math]\Delta p[/math] is the uncertainty in momentum and [math]\Delta x[/math] the uncertainty in position. If you know the approximate velocity of the electrons you can determine the range of potential locations, but it varies with the electron's momentum.