# Double slit experiment

1. Jul 5, 2010

### rabbitrabbit

question about the double split experiment.

So detectors placed at the slits create the wave function collapse of the photon! why doesn't the actual slit experiment itself create the wave function collapse?

2. Jul 5, 2010

### Gear.0

That's the biggest mystery.
We know that if you let the experiment run on it's own you get interference, but if it is observed which hole it goes through then you get no interference.

The difference between the two is that the former leaves no record of which slit the particle actually went through. However, as soon as we perform the experiment in such a way that you gain knowledge of exactly which slit it goes through then you don't get interference.

It's a very odd behavior, but it's sort of like as long as it is impossible for us to know which slit it goes through, it essentially goes through BOTH (the wavefunction does), however, if we run the experiment in such a way that we gain knowledge of a particle going through a particular slit then that is exactly what happens it appears that it really does go through JUST that one slit instead of both.

We say the wavefunction collapses upon being "measured" so the above arguments lead many to believe that the thing that constitutes a "measurement" is a conscious observer. Because technically the slit walls know which slit the particle goes through, so why doesn't it collapse? Perhaps because the slit wall isn't a conscious observer.

But this is a problem in quantum mechanics, nobody knows what exactly a "measurement" is and what exactly causes the wavefunction to collapse.

3. Jul 5, 2010

### rabbitrabbit

thanks Gear.0 you clarified it do a degree! Measurement/record is the key there.

4. Jul 7, 2010

### Salman2

It is known that the wave properties of a single photon have a region of coherence that extends for ~ 1-2 meters in any direction. However, the particle properties of a single photon is ~ 10^-11 cm. A similar situation exists for a single electron, the wave properties are larger than the particle properties (not at same ratio as photon, but still larger).

So my question, has anyone conducted the two-slit experiment by adjusting the distance between the slits in a systematic manner ? So, for photon, have the slits 5 m apart, 1 m apart, 0.1 m apart, 0.00001 m apart, 0.0000000000001 m apart --an experimental design that would bracket the largest and smallest coherent wave and particle properties of the photon ? Would the exact same pattern be predicted no matter what the distance between the slits, all other experimental variables being held constant ?

5. Jul 7, 2010

### Gear.0

I don't know what you mean by the "region of coherence that extends for 1-2 meters".

As far as I know this totally depends on certain conditions. Could you have perhaps been reading something on uncertainty, in which the momentum was well known but then the position isn't known very well in which case it could have a wavefunction extending over large areas?

The only thing I can think that you would mean by the region of coherence is basically where it's position is defined by the wavefunction. If that is what you mean, then yes it totally depends on the experiment and can be well under 1m. We can basically narrow it down as much as we want, only limited by our experimental equipment. It could very well be on the scale of nanometers or picometers, it's not always fixed and usually a lot more defined than 1-2 meters.

As for the double slit experiment yes, things like that have been done, and there is an equation:
$$d sin(\theta) = m \lambda$$
I think that's it. "d" is the distance from the slits to the wall, "theta" is the angle between the normal and the line joining the m'th maximum bright fringe and the slits, "m" is just an integer number that indexes which maximum you are talking about on the interference pattern, and "lambda" is of course the wavelength of the particles you are using.
So "m" and "lambda" are basically the same regardless of distance, but if "d" is very large, then you can see that "sin(theta)" has to be extremely small, so that the bright fringes overlap and are indistinguishable.

Basically there really is no difference other than the question of whether or not you can notice interference.
Other than that the same principles apply at all scales.

6. Jul 7, 2010

### Salman2

Gear.O--thanks for your reply. The information on photon wave region of coherence I read about would be in relation to your comment "position is defined by the wavelength".

But, I am not sure the equation you provided helps with my question. Please see this two-slit experiment design:

http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html

My question is not related to the "d" distance in your equation (the distance from the barrier to the wall), it is related to the distance "between the two slits" on the barrier.

So, are there experiments where this "distance between slits" is experimentally changed but all other factors held constant ?

Given that the of wave to particle dimensions of the photon range ~ 10^9 units as relates to "position", it would be interesting to see what two-slit patterns result if the "distance between slits" is experimentally changed. So, if the slits are 5.0 m apart (or 1.0 m, or 0.5 m, or 0.01 m) on the barrier will we see the exact same interference pattern on the wall as if the slits are 0.0000000001 m apart (which is near the particle position dimension for the photon)? Are you aware of any publications I can read on this topic ? Thank you.

7. Jul 7, 2010

### Cthugha

Well, yes of course there are such measurements. In fact this is what the double slit experiment is measuring. The interference pattern you see depends strongly on the spatial coherence properties of the light used and therefore also on the coherence volume. If the relative phase of the light beams at the two slits is well defined, you see an interference pattern. If it is random you will not see an interference pattern. Having a well defined phase relationship at two positions is basically just another meaning of spatial coherence. Accordingly, for a given light source at a fixed position, the fringe visibility of the interference pattern will be reduced if the slits are placed further apart.
However, this will also depend on the distance between your light source and your screen. If this distance is short the light source is extended and the distance from on end of the source to the slit will be different from the distance from the other end of the source to the slit. Accordingly the phase becomes less well defined. If you increase the distance between light source and double slit, the opposite effect happens and your interference pattern visibility will increase. This is why light from distant stars has high spatial coherence.

8. Jul 7, 2010

### Gear.0

I apologize Salman2.
"d" actually is the distance between the slits :D
Sorry for the mistake. The distance to the wall is already incorporated into finding "theta".

9. Jul 7, 2010

### Salman2

Gear.O: Thanks for all the help.