Archive: If you think you understand this, then you don't

First posted 21 Oct 2003. Not much to add or change now. My 'favourite' interpretation is that of Julian Barbour, which I'll share as a separate post.

Is light a wave or a particle? If your answer is, 'Who cares?' you may have a point, but you probably want to read a different post or visit a different blog. It seems that our answer is that we cannot be sure, but that light behaves in some ways as if it were the first and in others as if it were the second, and this duality is just one example of the counter-intuitive, but unprecedentedly accurate, conclusions quantum mechanics helps us reach.

The title of this post recalls famous physicist Richard Feynman, who said that anyone who thinks he understands quantum mechanics doesn't. Feynman admitted that he didn't really understand it.

Double slit
The famous (at least among physicists) double slit experiment at its most basic shows that light behaves as a wave. Point a lamp towards a photographic plate, but on its way, have it pass through a single vertical slit in a screen. Consider the lamp plus the slitted screen to be the 'light source' - in modern times we can replace this set with a laser. Now, erect another screen between the light source and the photographic plate, and cut two parallel vertical slits in it.

Some of the light shone at the screen passes through the left slit and some through the right. Like the ripples created by two pebbles dropped a few feet apart in a pond, the light coming through one slit interferes with the light coming through the other. As the light reaches the plate, at some points two 'peaks' of the ripples overlap and reinforce each other. At other points, two 'troughs' reinforce each other. In between different levels of reinforcement or canceling out occur. The visual result is a series of vertical white and black 'stripes' with varying grey bits in between. This is called an interference pattern, and it serves as great evidence that light does in fact behave as a wave. Seems simple enough. This experiment discredited Newton's 'corpuscular' theory of light in a single sweep.

Photo-electric effect - Einstein lays a foundation for the quantum revolution
But in the early 20th century, Einstein showed that when light was shone on a certain metallic surface, it knocked electrons from the surface like bullets chipping a stone wall. The brighter the light the more electrons are knocked free, but the brightness has no effect on the speed with which the electrons travel when knocked loose. Rather, the higher the frequency of the light, (moving up from red to violet) the greater the velocity (and therefore energy) of the electrons knocked loose. This all showed light to behave as a particle. Hmm, getting confusing...

Moreover, when performed across a range of light frequencies, it also verified Planck's quantum hypothesis - showing that the possible sizes of the energy 'transfers' to the dislodged electrons were not continuous, but rather discrete (quantum) levels. Photons (as light particles came to be known) below a minimum frequency (and hence energy level) for a given metal will not knock any electrons free, no matter how high the intensity of the light shone.

Photons and the double-slit experiment
Eventually, scientists were able to ‘shine’ light in smaller and smaller amounts, culminating in the ability to fire individual photons (they can do the same with electrons and get the same results). Here is where things take a very strange turn.

Turning back to the double-slit experiment, when photons are fired one at a time at the photographic plate, via the slits in the screen, the result is not a distribution like one would see when bullets are fired through gaps in one wall at a target on another wall, with light 'dots' concentrated in the areas aligned with the bullets’ possible trajectories. Instead, you get just the same interference pattern as in the original double slit experiment, only now built up slowly as more and more photons are fired one after another. Whoaaaa. Wait a minute!

So…the individual particles of light behave in a probabilistic, wave-like manner. Each particle seems to know what the others have done and to ‘interact’ with them, even though each is not fired until the previous one has already hit the plate. Viewed another way, each photon has a probability function, with a certain likelihood for landing in different places on the plate. But the photons do not 'pick' any one place. Each 'spreads itself out' on the plate according to that function. Another question is, how do the photons 'know' that both slits are there? Yes. This is headache material.

'Collapse' of the probability function
Now, even stranger, when you set up a contraption to measure and register when a photon passes through either the left or the right slit, the pattern on the plate is not the interference, wave-like one, but rather the bullet-type one that you might have expected based on common sense. What has happened?

It seems that as long as we don’t know which slit a particle passes through, each photon fails to ‘commit’ to one or the other, instead behaving probabilistically, as described above. But by measuring which slit a photon passes through, we force it to commit to one slit or the other and thereby to a single, bullet-like point of impact with the plate.

But we all know that photons don't think and that they don't 'commit'. We can't rely on such metaphors. How do we really describe what is happening? You may find the answer a bit disappointing. Although, the theory of quantum mechanics can model this behaviour mathematically and predict the behaviour of microscopic particles with unparalleled accuracy, scientists cannot agree how to explain this aspect of our world. Many refuse to even take up the challenge, defining it as within the domain of philosophy rather than science.

Interpretations
Various interpretations of this quantum mechanical outcome have been put forward, ranging from ones requiring an infinite number of dimensions in the universe to ones that question the existence of concrete properties independent of their observation by intelligent beings. The truth is that, theoretically, any number of interpretations are consistent with the mathematics and the observations with which they correspond so well.

The problem, for those of us who trust common sense, is that none of them correspond with it. We shouldn't be shocked by this. Our common sense was formed by our experiences in life, none of which deal with phenomena at the microscopic level. Like Einstein's theory of relativity, which only leads to different predictions than Newton's classical physics at velocities approaching the speed of light, quantum theory deals with the world at scales completely outside our direct experience.

No hidden variables
Still, many are uncomfortable with the lack of a satisfactory explanation of the unquestionable maths behind quantum theory. Einstein hoped that the theory of quantum mechanics was simply incomplete and that once we discovered other variables at play, the ‘uncertainty’ (I'll write some other time on Heisenberg's Uncertainty Principle) would disappear. Detailed experimental tests of John Bell's theorem suggest that no such variables could supplant quantum uncertainty. We may just have to celebrate quantum mechanics' great predictive powers and live, perhaps uneasily, with the uncertainty that it ascribes to the microscopic world.