Requiem for Classical Physics

We finally got to the beginnings of quantum mechanics today in our physics class.  Today, for me, classical physics died; but I’ve also discovered how incredibly exciting modern physics is going to be.  See, I knew about most of this stuff, like the uncertainty principle, and wave-particle duality and whatnot, but it just doesn’t mean as much to you until a professor – after telling you the truth all year and answering all your questions – simply can’t give you anymore answers.

For those of you who aren’t physicists – and for my own benefit of writing out the notes in my head – I’ll explain this problem in the simplest terms that I can here.  You probably won’t get the full effect of this problem unless you’ve actually taken a class on it, though.  And if you are a physicist, and I get something wrong, well… sorry.  I’m just an undergrad.

The Double Slit Experiment

Light – not just visible light, but also radio, microwave, infrared, ultraviolet, X-ray, and gamma ray – is a wave.  You may already know this.  It’s definitely a special kind of wave, but it is a wave. So just like dropping two pebbles a pond, we can shoot a laser through two very small slits in a board and the light wave coming from each slit will interfere with light from the other slit.

2-D representation of electromagnetic wave (light) interference from a double slit.

You can see this roughly in the first image; and it happens (you can work it out if you like) that this interference pattern defines straight lines where the waves interfere constructively (two maxima on top of each other) and destructively (two minima on top of each other).  When this light hits the wall, then, it doesn’t illuminate the wall evenly; it creates a diffraction pattern, which looks like the patterns in the second image.

Several different diffraction patterns from a double slit experiment. The size of the pattern depends on the slit separation, width, and distance from the slit to the projection screen.

So you might say – “Okay, fair enough.  Light’s a wave and it interacts with other light waves.  I haven’t taken much physics and I understand what’s going on; what’s the big deal here?”.  Well, here’s big deal number one.  It turns out that light is also a particle, called a photon.  Photons have no mass and move at the speed of light, and they’re critical to how physics works.  ”Are you sure?”, you might ask, “Because this wave thing works well enough, and I don’t see how particles could interfere like waves.”

Photons

Time lapse image of photons on a detector screen. With more photons, the probability density function of the diffraction patterns reveals itself.

Well, nobody thought they could before the 20th century. But here’s some proof that light really is a particle; you can have a light with a very low intensity that only emits a few photons per second.  Take a look at the image to the right.  This is a time lapse image of a light detector screen (like photo film) where the bright spots are photon hits on the screen.

Initially, the pattern looks pretty random.  But as we get more and more light, the pattern we saw in the other images reveals itself.  So it seems that even though the photons come one at a time, the wave interference pattern still occurs.  This is the first step into the concept of wave-particle duality.

You might suggest that we put photon detectors inside our double slits so we know which slit the photon is going through and where it should end up.  It turns out, however, that nature is a fickle trickster, so to speak, because the diffraction pattern disappears.

Let me say that again; as soon as we try to measure what’s happening with the photons between the laser light and the projection screen, the entire refraction pattern disappears, and it’s as if we were just shining a light at the wall the way we classically think of it happening.

This is because measuring the light interferes with it, messing up the entire wave pattern and scattering it, so it looks like light from a flashlight instead of the perfectly coherent light that comes from a laser.

Keep suggesting ways to avoid this, and I’ll keep telling you how you’re messing with the light.  It just doesn’t work.  We can’t know what’s happening between the laser and the screen, and we don’t know where the light will hit the screen until it does.  In a way of speaking, the light exists everywhere at once from the slits to the screen until it gets to the screen… at which point it’s forced to isolate into a single position that we observe as the photon collision with the screen.

Matter Waves

Big deal number two – mass refracts exactly like light.  It just so happens that mass is also a wave.

Electron diffraction pattern through a round slit.

“Whoa!”, you might say (that’s what I said), “hold on a second.  I’m made of matter, but I don’t diffract when I walk through a doorway; isn’t that basically the same thing?”.  Well, yes, and it just so happens that you do diffract when you walk through a doorway.  But to avoid mathematics on what was going to be a fairly short blog post, I’ll just say that the diffraction is absurdly negligible.  But much smaller things like electrons and even atoms diffract noticeably (with the right detection equipment).  If you shoot electrons through a diffraction grating like a crystal, the atomic lattice works just like the double slit board and you will observe a diffraction pattern.  Strange, but true.

You would think that since we’re using matter and not light, we can actually watch the electrons going through the air… right?

Wrong.  Watching the electrons going through the air means that we need to shine light on them (to see them), which would interfere with the photons (because light actually has momentum).  So we can do this… but the pattern collapses.  You can try to think of any other way to observe the electrons, but the fact of the matter is that it won’t work.  For us to get the information, something has to interfere with our sensory organs which was affected by – and, thus, reciprocally affected – the electrons, so the pattern collapses.  All we can know is what happens at the end.  This is the basic version of the uncertainty principle, although formally it involves the relation between observing mass and momentum.

Metaphyiscs

If you’re still reading this, you might have some philosophical questions lined up.  The uncertainty principle was most certainly (no pun intended?) something that had to be dealt with philosophically.  The idea that light affected matter and wasn’t simply a vehicle for sensory observation certainly, to my knowledge, impacts several philosophers’ takes on perception and space.  The Kantian view is certainly out, as I see it; space, in this case, is not simply a medium for sensory transaction, because it definitely cannot transmit a sensory experience of this mysterious waveform between the slits and the screen.  If we cannot sense it, does it exist?  For now, this problem is probably better answered over coffee than over a lab table.  

Perhaps this is best approached from the views of eastern mysticism.  In a way, this whole mystery seems like a zen koan – contradictory (wave or particle?), seemingly illogical – but it makes perfect sense when enlightened to the secret of the koan.  We just need to be enlightened.  Either way, the mystery of wave-particle duality has caught me today, and I’m looking forward to my future as a physicist.

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