Understanding Probability and Particle Behavior in Double-Slit Experiments

[StevieTNZ]

Hi there,

If I fire four particles from a source to a screen, with a double-slit between and a detector, and each particle has 50% probability going through either slit, I'd find that 1 out of every two would go through slit 1?

But I could fire two particles towards the screen and they both go through slit 2, but then I decide not to fire anymore, so this shouldn't happen in theory as one needed to have gone through slit 1 for the 50% probability going through either slit to hold?

 

[Clever-Name]

That's not really how probability works... In general after thousands/millions/billions of trials the probability should converge upon 50%, but with only a 2 trial sampling you can't with any accuracy say what the probability of a system is.

For example, with a coin, you would assume there is a 50% probability of landing heads H or tails T. But if you flip a coin 8 times and you get:
H
H
H
H
T
H
T
H

You can't suddenly declare that probability is wrong or that your coin is rigged just because you got 75% heads and 25% tails. If you continued this experiment for thousands of more flips then the numbers would converge to 50-50, assuming there is an equal chance of heads and tails (i.e. the coin isn't rigged)
Now to address more specifically your understanding of the double-slit experiment you need to understand that the particle doesn't randomly pick which slit to go through, the particle is a 'wave-function' and it goes through both slits at the same time and interferes with itself (thus showing the interference pattern). If you only looked at individual slits and nothing else (i.e. the interference pattern on the screen) then you would see a distinct 50-50 pattern emerge (over time). This process collapses the wavefunction at the slit and not at the detector, thus ruining the interference pattern that you would normally see.

So in the case you're describing you can't generalize the process to '1 out of every two would go through slit 1', you have to say that each particles goes through both slits at the same time and interferes with itself.

 

[ibysaiyan]

What sets up the probability of the particles being 50% at the start ? also, I don't see what point you're tying to make here. Or is this a hypothetical scenario ?
EDIT: ah I have been beaten to it . I echo what the above post says.
-ibysaiyan

 

[mathman]

Hi there,

If I fire four particles from a source to a screen, with a double-slit between and a detector, and each particle has 50% probability going through either slit, I'd find that 1 out of every two would go through slit 1?

But I could fire two particles towards the screen and they both go through slit 2, but then I decide not to fire anymore, so this shouldn't happen in theory as one needed to have gone through slit 1 for the 50% probability going through either slit to hold?

If the particles are photons or electrons, it is more complicated because of quantum effects. In these cases, the particle (even if only one) acts like a wave and goes through both slits, with an interference pattern resulting.