Wave/Particle duality: Light

Classical mechanics gives us two things, waves and particles. Particles are the touchy feely massy stuff that has momentum and displacement and all that lovely stuff, but generally is, and remains as is. Light is not that. Light is a wave, and can be diffracted, deflected and generally interfered with. I may have understated the complexity somewhat but that doesn't really matter, because as any A level physics student can tell you, that ain't quite the case, is it?

We don't even have to wear uniform any more, we basically know everything.

In 1801, Thomas Young sought to answer the question as to what light really was. He did so by developing one of the most boring experiments ever thrust upon teenagers the world over that involved lasers, or more likely, a filament light bulb shone through a slit. Given that this is 1801, I think we can make a pretty sound wager as to which we're talking about here. The set up was thus: Light would be shone through two slits, and the pattern on a screen beyond the slits would be recorded. If light was made up of particles, the pattern would be a bell curve of intensity. If light was a wave, a diffraction pattern would appear.

As it turned out, Young found the second pattern. so it was settled. Light was a wave. Decades later, a guy called Maxwell would formulate his wave equation from which could be determined the speed of light; a nippy 3x10⁸ ms^-1.

I mentioned before that around the turn of the century, there was this problem going around regarding Black bodies and the light radiated from them. If you applied classical physics, or Maxwell's equation it come out as nonsense at large frequencies. It took Max Planck receiving a bunch of experimental data to get things going. He came up with the idea that light was made up of little packages of energy, or quanta.

Like many great, and even more awful theories, this wasn't taken particularly seriously at first, because let's face it, for all our talk of free thinking and empiricism, there are some physicists who are horribly stuck in their ways. Planck did nonetheless have his supporters in this particular idea. Einstein used it to great effect with his work on the photoelectric effect.

In short, this involved firing electrons between an anode and cathode, but making it somewhat difficult for the electron to reach the anode, though messing with the charges. It was supposed that if you increased the intensity of a light source aimed at the cathode the electrons would drink in the rarefied energy of the waves and have an easier time of it. This proved not to be the case. Indeed, the energy of the electrons seemed to be entirely independent of the intensity.

So, Einstein thought, if this Planck fellow is right, what does that mean? If we're firing individual particles, by increasing the intensity we're just firing more particles of the same energy. However if we were to increase the frequency, these little wave packets get more energy, and at some specific energy value the electrons hit by this energy would have enough to escape the surface of the cathode.

10 years later, a guy called Millikan would actually experimentally verify this, earning Einstein a Nobel prize.

So, light is made of little bundles of energy. That's nice. Can you smash other things with it? What a curiously violent question, imagined audience member. But yes, as it turns out you can.

Robert Holly Compton, the most amazingly named man ever to sport a toothbrush moustache observed what happened when you fire X-rays at electrons. Modelling x-rays as waves, one would expect the wave to just travel through the electron, moving it a little, like some twat reading his £129 Kindle in a pool.

"I'm not even reading it, this one is just to keep the sun out of my eyes."

Instead what we find is the electron moves as if something has collided with it, while there now exists a wave with a longer wavelength than the one previous. Compton, following on from Einstein by adopting Planck's "light is quantised" theory, worked out that what was happening was the photon would collide with the electron, give it some energy, while of course losing that same energy. This would result in a moving electron and a lower energy photon, moving at an angle to each other because conservation of momentum.

So there we have it. Hard proof of that wave exhibit particle-like properties. Because fuck you I won't do what you tell me.

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Notes: A (Very) Brief Introduction to Quantum Mechanics

In an uncharacteristic act of efficiency, I have finally gotten around to organising my notes into a fashion approaching orderly. So, I thought to myself, why not do some revision while the notes are out? So here we are. What shall we do? I'm feeling a in bit of a quantum stuff kind of mood. I'll just change the title there and let's get on with it, shall we?

I don't think I've delved much into QM at all here, so here is a quick comparison with it and the classical kind.

Classical Mechanics

• The Newtonian sort. You have a particle with a position in space and a momentum. These are things that can be measured, calculated, and ultimately known.
• Generally it's applied to objects at a more macroscopic scale, stuff we can see around us, moving at reasonable velocities.
• It's therefore obvious to us and somewhat intuitive. You throw a ball, it moves as you'd expect with the energy you transfer into it. That ball hits your inattentive friend in the face and you can kind of predict that energy is going to be transferred into your friend's face as the ball comes to an abrupt halt.

Quantum Mechanics

• The position of a particle can be known if it is measured, but doing so means we cannot measure it's momentum to a similar degree of accuracy. This isn't so much that we don't have the equipment to do it as it is that the maths just doesn't work out.
• Here we are generally dealing with things on a more atomic scale, and not of things of our everyday ken.
• Subsequently you can expect it to be somewhat counter-intuitive.

The next thing you must understand is that it is a theory. It is a framework that allows us to make predictions and calculations on things beyond our aforementioned ken, but it must still be backed up by experiment. It has also thus far never been proven wrong. So, a pretty sound model, wouldn't you say?

This has nothing to do with anything in this post.

A quick history

Back in the 19th century there were some physical problems going about. Gustav Kirchoff had proven the concept of a black body, an object that absorbs all light, and thus would appear black to an observer. He also proved that the energy emitted E depends only on the temperature T and the frequency v of the emitted energy. He challenged physicists to find the specific function that could describe this.

Many attempts were made but it was not until Planck, following a visit from fellow physicist Heinrich Rubens in 1900, came up with the idea that light could be broken into separate "quanta" that things really got underway. Quick rundown time.

1905, Einstein (Big hair, kind of a big deal, you know the guy) was working on the photoelectric effect and realised that while electromagnetism wasn't working too well, Planck's idea about quanta might be a better bet. This realisation earned him the 1921 Nobel prize, which I imagine was nice for him.

1913, Neils Bohr made some pretty groundbreaking work regarding the spectral lines of Hydrogen. This was opposed by the old fuddyduddies, but the younger guys, Rutherford, Einstein and the like were pretty impressed by it all.

1924, Bohr et al propose more stuff. This all tuns out to be wrong, but it does provide plenty of precious precious experimental data.

1925, Heisenberg publishes a paper demonstrating that the observation of the position of a particle would ultimately change it's momentum. In doing so he uses matrices, shocking everyone who thought that matrices were solely the domain of those mathsy wankers.

1926, Paul Dirac fully derives Planck's law, and the idea of causality in physics is slowly being abandoned. Regarding collision Max Born wrote:

One does not get an answer to the question, What is the state after collision? but only to the question, How probable is a given effect of the collision? From the standpoint of our quantum mechanics, there is no quantity which causally fixes the effect of a collision in an individual event.

Later Einstein would write a letter to Born where he would spawn the famously paraphrased assertion:

Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secret of the Old One. I am at all events convinced that He does not play dice.

Now, I ask you, who the devil decided that "God does not play dice" was a better summary that "The Old One does not play dice"? It's right there in the quote guys. How the Almighty did you fuck that one up?

Anyway, Einstein continues to prove himself a belligerent old sod by arguing extensively about the matter. This is not really a bad thing, as in his eyes the theory's foremost supporters were basically sitting back and going "Well, that's that. Everything is shiny." Einstein was really just loudly explaining that he just didn't get it, and shouldn't we really be ironing out these questions before declaring the work done? He didn't want the Uncertainty Principle to become physics' "A wizard did it". 

This kicked off a series of arguments and thought experiments that came to be known as the Bohr-Einstein debates.

 "It is wrong to think the task of physics is to find out how nature is," said Bohr. Einstein disagreed. "What we call science," he said, "has the sole purpose of determining what is."

So, experiments were done, theories were made, and this has continued ever since. It is still our best theory for what happens at inconceivably small scales, and working with it hasn't made our quantum dependent electronics blow up (Note: I'm referring to basically all popular electronics. Reading this? Thank quantum mechanics.)

That'll do for now I think. I hope you find yourself intrigued, or at the very least a little more informed. That's all we ask here at EP.  Late'

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