What Happens When We Cover Up One Slit in the Double Slit Experiment?

[Mashulike]

My apologies - you are all probably bored to death with these kind of naive questions - but I'd appreciate an answer if someone knows a definite answer.

I'm thinking about the original double slit experiment - We fire one particle at a time at two slits and, as long as we don't detect which slit anyone particle goes through, then, over a period of time an interference pattern emerges on the screen.


I am assuming that in firing one particle at a time we don't always get an impact on the screen anyway. We are not aiming at either slit exclusively so presumably only some particles ever go through either slit. Or do they always find a way through? How would that happen - why would some particles not just collide with the divider and go no further?

Assuming this is the case (i.e. only a proportion of particles go through slits) we could alternately (or randomly?) cover up one or other of the two slits each time we fire a particle and have no way of knowing which slit anyone particle had passed through on its way to the screen. And in that case, would we get an interference pattern over time or not?

Thanks in anticipation

 

[dx]

if you cover up the slit each time, you know that the particle had to go through the other slit. this means that there are two separate distinguishable final states :

1. < particle at x, went through slit 1 |
2. < particle at x, went through slit 2 |

the distribution of the dots on the screen in this case would be the sum of the squares of the amplitudes of each possibility, i.e no interference. covering the slits alternately in effect is the same as doing N/2 hits with the one slit open and N/2 hits with the other slit open. only when there's no way to distinguish the final states do we get interference. if you cannot in principle determine which slit the particle went through, then the amplitude of the particle arriving at some point x on the screen would be the sum of the probabilities of it going through each of the slits.

 

[dx]

and no, they do not necessarily always find their way through. the distribution we observe on the screen is given by the ones that DO make their way through, i.e

$$| <x, through slit 1|s> + <x, through slit 2|s> |^2$$

this is an interference pattern. it is in no way effected by the ones that do no make it through because here we are considering the probability amplitudes for the different ways of making it through.

 

[peter0302]

The only way the experiment would work is if you could some how randomly - on a quantum level - close one slit or the other. There'd have to be no way of determining, or knowing, which slit it was, either before or after the fact. Then an interference pattern would show up. This is essentially a delayed choice experiment, contemplated by Wheeler, and has essentially been done. Google Experimental Realization of Wheeler's Delayed Choice Gedanken Experiment.

 

[Mashulike]

Thankyou both - and for taking the time to respond so quickly. That's helped me a lot - I'm off to Google the delayed choice experiment then ...