Your Quantum Mechanical Eye

3 Dec

Terry Bollinger, 2014-12-02

Some Reflections on Reflections

Centuries ago, Isaac Newton realized that something very odd was going on when light reflects from a smooth surface.

What concerned him was the phenomenon of partial reflection. Sir Newton asked in effect, “When you shine a beam of light at an angle on a pool of water, some of the light reflects, and some enters the water. So how does each particle of light ‘decide’ whether to reflect or not to reflect?” (Remarkably, Newton believed light to be particles, not waves. Later physicists reversed that view to “light is only waves,” but Newton seems to have been strangely prescient on this point, anticipating a view that did not recover popularity again until quantum mechanics emerged centuries later.)

Here is another puzzling feature of light:

If light truly is composed of tiny, particle-like packages called photons, how do those individual photons manage to reflect smoothly off of the surface of something like a mirror? After all, if the mirror is composed of wildly vibrating atoms and molecules, so shouldn’t a very light particle like a photon get kicked all over the place by those vibrations? How does the photon “figure out” that it needs to reflect in a way that is determined not by the motions of individual atoms, but by the overall shape of the mirror?

The answers to all such questions is a bit surprising. Light can accomplish remarkable feats of smooth, nearly lossless redirection precisely because photons are not part of our everyday classical world. When it comes to behaviors such as reflection and refraction, photons and light in general behave in way that can only be understood in terms of quantum mechanics.

Tales of the All-Seeing Photon

Reflection and refraction are non-classical because they requires every photon to be aware, in some all-knowing way, the “average” shape and composition of the enormously larger classical surfaces and bodies of mirrors and lenses. Even worse, because special relativity forbids the photon from seeing a truly instantaneous view of the surface, this averaging must to some degree takes place not just over space, but also over time.

If the idea that a single photon must have such an all-reaching ability to “sound out” its classical-scale surroundings, consider this: Does light change the way it reflect or refracts is it gets dimmer, or does it stay constant? For example, if you keep cutting the brightness of a light source in half, does the pattern of light that it produces after reflection or refraction change? The answer is no of course. If you shine a light through a glass, the pattern of bright areas just gets dimmer as the light grows dimmer. It would seem very surprising indeed if the pattern itself changed!
Yet that very constancy is a problem, because it means that every fraction of the light, no matter how dim, must somehow “know” how to create the pattern after it passes through the glass. Thus even when the light becomes so dim that no more than one photon emerges from it at a time, each of those photons will still need on average to produce the same pattern seen using a bright light.

But how is that even possible? How can a single photon “know” the layout of the entire glass in a way that allows it to replicate the light pattern produced by a much stronger light source?

Have Wave, Will Travel

The answer is that each photon carries its “wave” with it, in the form of Feynman’s path-integral exploration of every possible path from point A to point B. If you could somehow “fill in” a large number of these paths with real photons that are identical to each other, you would find yourself back in the same situation you get with a laser. What is truly amazing is that no matter whether the paths have real energy or not, they always combine through the path integral (which includes that critical concept of phase cancelling) to give the same light-bending or light-reflecting result. Very strange!

This “wave of photons that never were” that is attached to every photon is what saves the day in terms of how light can reflect evenly from a mirror surface at room temperature. Just as with ocean waves, the small deviations due to irregularities and thermal motion do add to the overall reflection, but in ways that for the most part are small, random, and in the far-field, self-cancelling. Only a very small subset of the reflected signals along specific paths end up reinforcing each other instead of cancelling each other, forming the various reflections and refractions we associate with classical optics.

Quantum Sight vs Classical Blindness

But it’s all an illusion. We like to think that the photons in a laser beam are moving along a straight path, but even there most folks know that as the beam gets narrower, the direction of those photons becomes more uncertain. What is really happening there is that the illusion of billiard-ball like motion simplicity is being slowly stripped away, and the “I want to explore everything!” aspect of the true quantum mechanical photon is being revealed. The reality is pretty remarkable: Every photon coming out of the source must “sniff out” all the possible paths ahead of it, using its “wave of photons that never were,” to decide what it will end up doing. Anything less would make the photon subject to the tiniest variations of any atom or electron in its path.

So, as you read this text give some credit and thanks to the omnipresence and dominance of quantum mechanics in controlling light, because without it you would be completely blind. That is not in any way an exaggeration. A fully classical photon would never “see” the overall shapes of your cornea and lens, and so would have no idea where to head. Instead, it would dive into some random spot in a maelstrom of fast-vibrating molecules, a storm of complexity that to the photon would look and feel like the most gigantic, fast-moving, and convoluted pinball machine ever created. The chances of any photon passing through that monster machine would fall to zero, and you would be plunged into total darkness.

Photosynthesis, Quantum Computing, and Waves That Never Were

I must now mention a delightfully ironic twist on quantum clarity versus classical opacity.

In 2007, a team of researchers at the University of Chicago under Greg Engel postulated the then-radical idea that in photosynthesis, the chloroplast is somehow able to transfer energy from light to the right location for further processing with something like 97% efficiency, which is a phenomenally high figure for a bunch of random-looking proteins and affiliated compounds. Their explanation? Quantum computing. Somehow, the chloroplasts were using quantum mechanics in a way that enabled them to compute the best possible path for transferring energy from antenna-like chlorophyll molecules to a reaction center that would then convert that energy into an energy-storing chemical bond.

But how would that work? As it happens, the concept of quantum computing includes two distinct components, and that distinction is very important for cases like this.

The first and (heh!) more mundane component of quantum computing is the same effect I’ve just described for photons. That is, you can get a single particle to perform interesting and useful forms of computation simply by making careful use of its “wave of particles that never were.” That is because these waves not only can “see” complex shapes, objects, and features in classical space, but can also summarize the implications of those features in ways that are computationally interesting and useful. None of this would be possible if the photons were truly just isolated billiard-ball like particles, so this is indeed a form of quantum computing.

You are making good use of this variety of quantum computing right now, since without it you would not be able to organize the photons from your electronic device to form readable images on your retina. The particular quantum computation being done is more commonly call a Fourier transform, and it is enabled by the ability of the cornea and lens of your eye to “persuade” incoming photons to perform the right kind of summation. That summation in turn become a very high probability of the photon relocating itself in real space, specifically to form that image on the back of your eye. Voila! Sight via quantum computing, done so easily that we neglect to notice just how much computation is required to accomplish it.

The second component of quantum computing is the odd one (heh!), a little thing called entanglement. Entanglement enables quantum computing to leap from just “powerful” (e.g. making Fourier transforms very easy) to “astronomical,” (e.g. breaking every encryption code ever devised). Alas, entanglement is also far beyond the scope of what is needed to explain reflection and refraction, so that is a topic for some other time.

Part I of Quantum Computing as Good Lens Design

If you look at how the Engel team invokes the need for quantum computing to explain efficient energy transfers in chloroplasts, it is readily apparent that only the simpler wave-that-isn’t-really-there variety of computing is needed. That is, it needs the particles that carry the energy to “see” the entire path in front of them, and that path must in turn follow some set of larger-scale relationships that entice the particle to perform a useful function, in this case transferring concentrated energy from one physical location to another.

Does all of that sound familiar? Yep, it is the same type of quantum computation going on in your own eye: It is a focusing lens. The only significant difference is that instead of photons, the chloroplasts use more compact form of energy called an “exciton” to carry the energy. As with photons, these quasiparticles have their own clouds of “excitons-that-never-were” that can “see” the shape of the proteins and compounds around them, and so use them to calculate their final destination in the chloroplast.

Curiously, this remarkable ground-breaking work by the Engel team remains controversial in many quarters. Why? Oddly enough, it is because most molecular biologists have for decades accepted as a given the premise that “biological matter is too warm for quantum mechanics to be relevant.” In reality, if this were true there would be no such thing as eyes in animals, since the only way that photons can even traverse the complexity and thermal vibrations of biological lenses is by being quantum mechanical in nature.

Eventually this will all get cleared up conceptually, and the role of quantum mechanics in room temperature biology will be understood more clearly. Simply re-interpreting quantum biology as a matter of “clever lens design” for a variety of lightweight particles, including photons and quasiparticles such as excitons and phonons, could help make the field more analytic and less mystical-sounding. In any event, it should be fascinating and insightful to watch this emerging field of quantum biology grow and expand.

A Final Thought

Here’s a final thought to keep in mind: The next time you look at anything that reflects or transmits light, stop and contemplate for a moment the fact that you are directly observing human-scale quantum mechanics in action. That is because the only way any photon can navigate its way through such a complicated and thermally active classical-scale object is by using its remarkable cloud of photons-that-never-were to see the overall shape and form of that object in advance. That is… truly remarkable!


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