## Wednesday, February 20, 2008

### Quantum Mechanics: The double slit experiment

See previous post: Particles and Waves

The Set-up

The double slit experiment is one of the most famous physics experiments of all time. It demonstrates that light has properties of both particles and waves.

Here's the set up. We point a laser at a plate. The plate has two slits in it. The light goes through the slits and hits a screen in the back. This results is what's known as an interference pattern. It looks like this:

When I first saw this, I thought, why are there so many bars? Shouldn't there only be two bars, one for each slit? To understand why the interference pattern appears, we have to understand two properties of waves.

Two Properties of Waves

The first important wave property is diffraction. Diffraction allows waves to move around obstacles. When you shout out, "Dinner time!" the whole family can hear you regardless of whether you have a direct line of sight to them. This is because sound can travel around corners, through doorways, and into people's ears. Whenever a wave goes through a doorway or a slit, the wave spreads out in all directions on the other side.

In a way, diffraction is the opposite of what we expect from particles. When we shoot a particle through a slit, we expect it to follow a very narrow path on the other side. The smaller the slit, the narrower the path will be. But when we shoot a wave through a slit, it will spread out in all directions on the other side. The smaller the slit, the more it will spread out. So when we shoot light through a slit, it's not going to just make a single spot on the screen, but will go in all directions.

The second important property of light is interference. If two identical waves go through each other, then their intersection will look like the sum of the two waves. Recall that all waves are fluctuations in something. A typical wave quickly alternates between a fluctuation up and a fluctuation down. That's why, in the above drawing, we represent the wave with alternating black and white lines. The black lines represent upward fluctuations and the white lines represent downward fluctuations.

If two intersecting waves both happen to be fluctuating up, then the sum will be a fluctuation up with twice the amplitude. This is called constructive interference. If one is fluctuating up while the other is fluctuating downwards, they will cancel each other out. This is called destructive interference.

Now that we have an idea of how waves behave, we can now predict the results of the double slit experiment. Some of the light will go through slit 1, and some through slit 2. After going through the slit the light will spread out in all directions. The light that went through slit 1 will interfere with the light that went through slit 2.

How can we tell from the diagram where the light will interfere constructively and destructively? Well, the light interferes constructively whenever both waves fluctuate up in the same place and time. The light interferes destructively when the waves are fluctuating in opposite directions at the same time. To make this clearer, I've shown the locations of constructive (red lines) and destructive interference (blue lines) in the picture below.
The result? We only see the spots where the light interferes constructively, and not destructively. Therefore, we will see alternating light and dark bars--the interference pattern.

The Particle Properties Emerge

The fact that we see an interference pattern is proof that light is a wave, right? But what about the proof that light is a particle? It had been shown by Einstein that light comes in little separate packets, called photons. What happens if we send one photon through the double slit? According to our previous analysis, the interference pattern requires that the wave go through both slits at the same time and interfere. But if we just have one photon, it can only go through one slit. After all, it can only hit one spot on the screen behind the slits.

But when this experiment is performed the interference pattern does appear. Each photon, of course, hits only one random spot on the screen. But if we shoot, one by one, a whole bunch of photons, then the sum of their landing points forms an interference pattern. That is, a photon is much more likely to land in a spot where there is constructive interference. The only way this can happen is if the photon is traveling through both slits at once and interfering with itself!

The conclusion is that light shares properties with particles and waves. Which of the two is it? Neither, of course.

Next page: The Quantum Measurement Problem. This is where Quantum Mechanics gets weird!

Anonymous said...

Very well-explained! I remember doing this experiment in high school, along with several related ones. Specifically, we did the same thing with one slit and observed an interference pattern around the edges of the strong white bar that resulted. Physics is cool!

miller said...

Ah yes, this experiment is actually possible with just one slit. That's because the slit is not infinitely small, and has a width.

Arjen Dijksman said...

Nice figures and a very good explanation.

It would be fair to say that some disagree on the conclusion: "The only way this can happen is if the photon is traveling through both slits at once and interfering with itself!". We could refer to John Bell who wrote in Six Possible Worlds of Quantum Mechanics (1986): "De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to me so natural and simple, to resolve the wave-particle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored."

miller said...

I assume you are talking about the Bohm interpretation? As far as I can tell, that's one of the less popular interpretations. Under that interpretation, I would also be incorrect in saying that light is neither a particle nor a wave--it is both.

Arjen Dijksman said...

Yes, in that interpretation, light is both a particle- and a wave- phenomenon. Not 'just' a wave or 'just' a particle.

In the quote, Bell talked about the 'pilot wave' picture, of which Bohm's interpretation is one (there are other ones). It is strange that this picture is unpopular. In my experience, laymen are very receptive to pilot-wave approaches. It demystifies the quantum weirdness of quantum interference experiments.

Blake Stacey said...

. . . but makes understanding entanglement, EPR experiments and so forth more difficult.

Blake Stacey said...

. . . and causes problems when you try to move from quantum mechanics to quantum field theory.

Arjen Dijksman said...

Yes, the Bohmian (deterministic) interpretation needs to be nonlocal in order to explain Bell's inequality violations. There are however other pilot wave interpretations that remain largely unexplored and which give an intuitive comprehension of entanglement experiments, cf. section 3 of my paper at materion.free.fr/OldVersion/physique/QMObservationMacroscopicArrows.pdf

MrEmbiggen said...

Hi,

Firstly thanks for the above description on this experiment. I'm heading up a book club in my bookshop that will be discussing the book Quantum Theory Cannot Hurt You by Marcus Chown and wondered whether or not there were any simple little/or no equipment experiments I could perform with the group to help illustrate a couple of quantum ideas like the wave interference one you just described?

And thanks again for this blog.
Cheers

miller said...

Sorry, I don't think I'm the best person to ask. I'm just a student, I don't have a whole lot of experience setting up these labs myself.

The physics forums suggest pointing a laser pointer at a hair or a CD.

MrEmbiggen said...

Ok thanks for the tip.

Anonymous said...

How come the photon can't just be a particle, and the light bounce back and fourth from the back of the intermediary wall where the slit is? How is this interference pattern 'observed' and can it be observed on the back of the slit's wall?

Below my simple diagram of what I'm wondering can happen with a single slit....

Source=Light Source
Wall= Intermediary 'Slit' wall
X = degree of strength of light as it refracts

| W |
| A XX
| L __/|
| L __/ |
| | __/ |
| | ___/ |
| |_/ |
| XXX_ |
| | \____ |
| | \____ |
| | \__ |
| | \|
SOURCE<------->>>-------<------XXXX
| | __/|
| | __/ |
| | __/ |
| | ___/ |
| |_/ |
| XXX_ |
| | \____ |
| | \____ |
| W \__ |
| A \|
| L XX
| L |

miller said...

I don't understand the question.