# Double-slit experiment - a couple of questions

1. Sep 16, 2008

### Pastel

Hi. I've just started learning about quantum mechanics, and I find the whole subject very interesting. I have read about the double-slit experiment, and I didn't understand a couple of things.
Assuming one were to fire one particle at a time at the diffraction slit:
- will all particles pass through the double-slit thingy, or will some remain on that board without passing through the slits?
- I understand electromagnetic waves do not really carry energy, but merely determine where the particle will land. Is that correct?
- Photons travel at the speed of light, right? So would it be possible to determine the trajectory of a photon by calculating the time that passes between emission and reception? So that you would know which slit it passed through?
- Do the aforementioned waves travel at the speed of light as well? If so, how does it make sense that they can interfere with each other, when they fall on the screen at different times?
- If the waves and the photons travel at the speed of light, and if you can determine the time between emission and reception, then some photons should be determined to have passed through the nearest slit to the point where they 'land'. But in order for particles to determine where they land, they should need information from the diffracted waves from both slits, yet the wave from the slit farther away shouldn't even have reached the reception screen by that time. How can this be explained?

2. Sep 16, 2008

### RandallB

NO, the percentage of open area though the board determines how many will pass.
NO
NO
That’s the point - it is a paradox. Resolving a paradox is how science moves forward to a better understanding of reality and how the world really works.
In one of two ways:
First; consider Niels Bohr where he identified a solution that is as complete as reality can allow meaning other interpretations may match but can never be more complete than QM. To understand this you will need to have a clear understanding of 1) Copenhagen Interpretation and 2) Non-Local (start with a thread search here) to see how this resolves the paradoxes by declaring the questions you raise irrelevant and do not need to be answered because that cannot be answered. Don’t just ask “how’s that” no one can give you an answer if you do not take the time to learn and fully understand "Copenhagen" and "Non-Local".

Or Second; you can consider the Einstein EPR claim that Copenhagen QM cannot be complete because it is not “Realistically Local” and a more complete[\b] should be, but has not yet been, found. If you accept this then the paradoxes have not been resolved and the only answer possible to any of your questions is “We Don’t Know” until the EPR paradox has been resolved.

Has the EPR paradox been resolved or not; yes or no?
Most say Yes a few like me think No, a differance of opinion and separate from your question; but makes a differance as to how (or if) your questions can be answered.
- - To build your own opinion as to who is correct, Bohr or Einstein, I suggest you start by searching threads for keyword Entanglement, Bell Proof, or EPR.

3. Sep 16, 2008

### Pastel

Thanks for the answer. I admit I don't know a lot about QM - I was just asking some questions about things I thought I should know before I delve deeper.
Still,
could you maybe explain this one? Where was I wrong? (I don't doubt that I was, I just want to understand these things better).

4. Sep 16, 2008

### DrChinese

Welcome to PhysicsForums, Pastel!

With Quantum Mechanics, simple intuitive explanations are difficult (perhaps impossible) to come by. We talk about waves and particles, but those terms should be considered as useful approximations within the context of a formal mathematical apparatus (often simply referred to as the QM formalism). All of the simple (or what some call "naive") models (i.e. like the ideas you propose) have been ruled out experimentally as impossible. The double slit is one such experiment, but there are many others equally surprising.

On the other hand, the mathematical formulas have remained more or less intact for 80 years and have been found to work nicely, even in complex and otherwise confusing situations. But the formulas do not map well to visual models or classical concepts of reality akin to what we see around us. This has confounded and confused physicists from Einstein to today. Yet it is hard to argue with what works (QM).

I would recommend that you spend some additional time learning about the subject now, don't worry so much about trying to put things in terms of your everyday experience. You will quickly discover that the quantum world plays by some very different rules. Learn a bit about the Heisenberg Uncertainty Principle, virtual particles, electron orbitals and EPR. Those will give you a better idea of what we are dealing with.

Good luck,

-DrC

5. Sep 16, 2008

### RandallB

Just to keep the logic simple consider the energy lost from a battery and the mechanical energy created from an electromagnetic motor. The only accounting for that transfer of energy is though the motion and interaction of electromagnetic waves defined by continuous electromagnetic fields. I know of no other rational explanation for how an electromagnetic motor works.

Just to know from what level of science you are coming from?
- Did you already know that about motors; but had neglected to include that in your thinking when you approached Quantum Issues. If so don’t do that you do not need to ignore what you know about physics to work on QM it is compatible with it within the rules of Copenhagen-HUP.

- If you did not know that; be sure to add more Classical Physics to your study. QM does not reject and replace basic physics it builds from that foundation by adding some addition principles.

6. Sep 19, 2008

### muppet

Here's the best way I can explain the 'paradox' of double slit (and get to the heart of QM more generally).
The "Wave" is not some physical thing pushing a particle along a trajectory, as was originally suggested. What the wave tells us is the probability that we will find the particle in some particular place, at some particular point in time. This variation with time accounts for the fact that we perceive things to be moving with velocities- the distance from some known starting point at which we are most likely to find it changes with time at a particular rate, which you can also determine using the wave function. It is this "wave function" that interferes with itself, and you don't treat the particle as a localised thing with definite properties until you measure those properties.

I should say now that what I just said is a loose translation of the mathematics of quantum mechanics into words. It doesn't necessarily follow that the particle doesn't exist, or doesn't have definite properties, prior to us looking for it. QM restricts itself to predicting the results of experiments; which it does extremely well! But it doesn't give us a particularly coherent picture of nature the way that Newton's second law describes particles accelerating in whatever direction you push them. Different groups of people have proposed various different such "pictures", and you'll find some pretty veherment disagreements about their various merits on here and elsewhere.

RandallB: Surely the EM fields in your motor are ultimately quantised?

Here's a question about this experiment for people versed in the maths of QM- one that, a little embarassingly, occured to me as I was thinking through an FAQ entry on it I told ZZ I'd do a while ago
The act of measurement is essentially described as a projection- picking out one particular state vector from the eigenbasis of whatever variable you're measuring. If you do this experiment with (say) electrons, and try and "catch" whatever slit the particle went through, you destroy your interference pattern- the particles line up behind the slits like bullets would. But what you've done here is measured the position, and it can't be simultaneously in an eigenstate of both the position and momentum operators. So why does it then carry on like a bullet in a straight line? Why doesn't its momentum carry it off whichever way it pleases?

The answer I've just come up with is that the average momentum in directions orthogonal to the axis perpendicular to the plane of the slits is zero. When you've measured the position of the particle in the direction of the width of the slits, that's what you're stuck with before momentum carries it anywhere else. Then, the standard deviation of lateral momenta about zero is given by the HUP to be on the order of hbar/(slit width). In the 'standard' experiment (without detectors over the slits) you have (to excellent approximation) a free electron wavefunction of e^ikx, which gives rise to an interference pattern because it's a diffracting wave. Is this right?

(The implication of this if correct of course is that Huygens' principle can be applied to our 'probability' waves... which would actually make quite good physical sense, by the standards of QM )

7. Sep 19, 2008

### Marty

No they don't. They spread out like waves.

It doesn't.

It does. You get a spread-out detection pattern on the screen with no maxima or minima.

8. Sep 19, 2008

### muppet

Huh. I got the idea that they did from Jim Al-Khalili's book- admittedly popsci, but the guy is a respected working physicist and he's quite explicit in the claim. Can I ask why you say that they don't?

9. Sep 19, 2008

### Marty

By which I'm understanding you mean to say "why don't they go like bullets and line up with the slits". Because if they did you would never get an interference pattern in the first place. The reason you get interference is because each of the two slits, taken separately, creates a spread-out patch on the screen. If you combine these patches THEY OVERLAP. That's where the interference takes place.

You can make slits big enough and far enough apart so that they effectively cast shadows of themselves on the screen. But you then you can't get an interference pattern. You only get an interference pattern when you squinch the slits down so small that they cause the waves to spread out behind them.

10. Sep 19, 2008

### muppet

That you should observe single-slit diffraction is what got me thinking about this in the first place...
Also, you say that they "spread out like waves" but that you don't see an interference pattern. Are you saying that they diffract or not?

11. Sep 19, 2008

### Marty

I don't know the techinical meaning of the word diffract, so I can't answer your question yes or no. I know that waves spread out if the slit is narrow enough. And that with one slit there are no interference bands.

12. Sep 19, 2008

### muppet

Ah... well that point is quite important!
Can I ask again if you've heard somewhere the specific, exact claim that if you do the two slit expt. and try and detect the slit through which the electron passes you observe the results you've described?

13. Sep 19, 2008

### Marty

I'm not basing this on any specific claims I've heard. I'm just sort of figuring it out as I go along. Sorry if I gave the impression that I knew what I was talking about.

14. Sep 19, 2008

### muppet

Diffraction is the spreading out of a wave as it passes through an aperture: see http://en.wikipedia.org/wiki/Diffraction for an introduction. If you are coming to this discussion with a knowledge of the maths of QM, is this from a treatment of QM within a maths degree? As that's a pretty elementary concept for a physics student.
I also find the claim that you don't see an interference pattern for one slit interesting... as you categorically do observe it with light, so if true it would imply that there's a different underlying mechanism

EDIT in response to your post: I can see why what you're claiming would seem to make sense, as it's what got me thinking about this question in the first place. I hope it's becoming obvious that I've given the issue a little thought however, and I'm really looking for someone conversant with the maths (and preferably with the actual experimental results!!) to see if what I said above is correct.

15. Sep 19, 2008

### Marty

I guess I was wrong about that. When I think about it, I have to agree that under special conditions you can get very weak band patterns even from a single slit.

That wouldn't be me then.

16. Sep 19, 2008

### Marty

OK, I've reread your posts and I understand what you're saying here:

Yes, you DO see single-slit diffraction when you block one slit. But single-slit diffraction does not always give you band patterns. In fact, if the slits are the optimum geometry for double-slit diffraction, then there will be no bands when you block off either slit.

17. Sep 20, 2008

### RandallB

Are you claiming that quantized or not that the correct understanding is that “electromagnetic waves do not really carry energy” as pastel thought??
If so what is carring the energy though the motor?
The point Marty was making was that caricaturization has never been a good one.
Whenever electrons or photons go though an appropriate slit or double slit they never act like bullets they always produce a pattern. The question is what kind of pattern; Dispersion or Interference. Note that Interference Patterns always fit inside the boundaries of where the Dispersion Pattern would have been expected.
Yah I’d say you seem confussed – exactly where do you think “you categorically do observe” that?

18. Sep 20, 2008

### muppet

The original quote:
I don't pretend to know anything about QFT- is it correct to describe quantised fields as continuous? I can see based on a quick wikipedia that it could be, but I don't know.

I think he was really disputing that the results of that particular variant of the experiment were as I described them, to be honest.

Couldn't agree more. In my original post I described that the pattern resulting when a detector was in place was the same as what one would obtain if one fired bullets at the screen. Sorry if that wasn't clear- the whole point of my question was to establish exactly how such a pattern as we would normally associate with ballistic behaviour comes about.

Whenever you pass a beam of light through a single slit of width comparable to its wavelength. My point was that I'd be very suprised if the mechanism by which diffraction occurs was so radically different that you didn't see a similar effect performing a one-slit experiment with electrons, buckyballs, etc. I'm fairly certain, however, that there's nothing there that I need to be confused about- it'd be perfectly reasonable for someone who didn't know what diffraction was to suppose that you wouldn't get an intereference pattern with just one slit, even though you do.

19. Sep 21, 2008

### RandallB

NO you don't see a interference pattern with a single slit, just a dispersion pattern with a definable shape.

I think you are confused by the sharp edge diffraction interference in the shadow line of light passing a one-sided barrier. Sure that you can have a wide opening act as a two sided barrier with that shadowed line diffracting on both sides. And if you bring the barriers closer together to create a slit instead of an opening the sharp edge diffraction interference remains on both sides of the opening. You can even bring them together if you make the slit narrow enough.

Sure, that can change the shape of the dispersion pattern when a small enough slit width is used.
But that has nothing to do with the interference pattern that fits inside the dispersion pattern (without changing the dispersion pattern shape) caused by using two slits.
It is just a dispersion pattern shape and should not be misrepresented as a interference pattern.

20. Sep 21, 2008

### lightarrow

I've always called "diffraction" what you call "dispersion":

http://en.wikipedia.org/wiki/Dispersion_(optics)
http://en.wikipedia.org/wiki/Diffraction

Anyway, it's true that the interference pattern with the two slits has nothing to do with the spreading out of the particles from a small opening or slit but it's certainly true that there is also an interference pattern from a single slit, unless the slit's opening is so small (with respect to lambda) that you can only see the first bright band. When the two slits experiment is performed with such small slits, it's more simple to understand the difference between the case of a single slit open and two slits open.

In that case, the pattern formed with only one slit open is similar to the one obtained with bullets shoot at random against a wall with a small opening: you see them spread out in the last screen, even if the distribution is not exactly the same as with light or electrons and even if partcles like electrons and photons don't travel in a straight line, as bullets do.
I've written all this to try to clarify to the others, and not because I think that you don't know it ...