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Starts With A Bang

Throwback Thursday: Logic Is No Match For Science

Why the argument that “this idea is absurd” is no argument at all.

“He who loves practice without theory is like the sailor who boards ship without a rudder and compass and never knows where he may cast.” –Leonardo Da Vinci

Yesterday, I wrote a long response piece to Ben Carson’s remarks about the Big Bang, and about science in general. The general argument he gave is that science says a lot of absurd things, and that with the power of our minds — our logical, reasonable minds — all we need to do is think about these absurdities and we’ll realize they must be wrong.

One of the things I said was as follows:

[T]he natural world — and the natural Universe — [is] often counterintuitive. That doesn’t make it wrong! Nature reveals itself to us through scientific inquiry and investigation, which is all the more reason to listen to the story that the Universe tells us about itself, no matter what it says.

Image credit: Science Photo Library/Corbis.

This isn’t some new problem, mind you, that only came about with the advances of quantum mechanics, quantum field theory, general relativity, or some other “weird” idea. Science giving us counterintuitive results, results that we’d never arrive at using our limited experience and logic alone, is one of the most spectacular thing about the entire enterprise. If we want to learn about the Universe itself, we have to not only ask it questions about itself, but listen to its answers. And with that in mind, I’d like to throw it back — way back — to some 200 years ago.

Imagine yourself back in history, a hundred years after Isaac Newton. His treatises on a variety of topics — mathematics, astronomy, gravitation, mechanics and optics — had been verified better than any other scientific disciplines in history up to that point.

Image credit: Newton’s sketch of Halley’s Comet in the Principia, retrieved viahttp://plato.stanford.edu/entries/newton-principia/.

Many of these fields had been further developed as well: the periodicity of comets, the principles of least action, the development of multivariable calculus, and the use of the Newtonian reflector to discover additional planets in our Solar System. Newton’s theories and ideas not only served as a solid foundation for each of these fields, but that they often provided deep insights into the fundamental workings of the Universe when applied to new phenomena.

This was true for practically all of the aforementioned areas, but with one exception: the behavior of light.

Image credit: University of Iowa.

Newton was insistent that light behaved like a ray, refracting, diffracting and reflecting according to the laws he laid out in his important book: Opticks. Through this work, he was able to account for a whole host of phenomena, including the behavior of colors, all verifiable through experiment. Indeed, the first sentence of his book opened as such:

My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments.

Reason is well and good, of course, but sometimes your reason can’t account for the results your experiments give. 100 years after Newton, an experiment was performed that simply couldn’t be explained in accord with Newton’s conception.

Images credit: retrieved from http://genesismission.4t.com/Physics/Quantum_Mechanics/double_slit_experiment.html.

If you passed a beam of light through a single, narrow slit, you’d expect it to arrive on the other side, perhaps more intense towards the very center than at either end as you moved away. If you passed a beam of light through two slits, you’d expect two central peaks, each one fading away as you moved away from it. At least, that would be true if light were made of corpuscles, or particles.

But when the experiment was performed with these slits closely spaced together, you didn’t wind up seeing two peaks at all, but rather a great number of peaks, with dark spaces in between them.

Image credit: ©Tony Mangiacapre, viahttp://www.stmary.ws/highschool/physics/home/notes/waves/lightwave.htm.

This sort of phenomenon could not be accounted for with any ray-based (or corpuscular-based) theory of light, but rather required that light fundamentally behaved as a wave. When Thomas Young performed his double slit experiment in 1799, he recognized that this type of phenomenon could only result if — as others such as Huygens had theorized before — light was fundamentally behaving as a wave. This same pattern of interference, with constructive peaks and destructive minima, was familiar to anyone that had performed the analogous experiment with water waves.

Image credit: sketch by Thomas Young, 1803, scan and upload by Wikimedia Commons user Quatar.

But light also appeared to have corpuscular (or particle-like) properties as well. Newton’s treatise on Opticks, after all, was able to explain how light reflected and refracted perfectly, without treating light as a wave. The new revelation — and the new experimental results — didn’t invalidate the older ones at all. Quite to the contrary, if light really were a wave, it should show up in all instances that a wave-like behavior ought to evidence itself.

Image credit: Benjamin Crowell.

So the top theorists of the time, many of whom were enamored with the infallibility of Newton, set out to see if the idea that light was a wave led to any predictions that were absurd.

And in 1818, that’s exactly what the famed French mathematician and physicist Simeon Poisson set out to do.

He imagined what would happen if he had a source of light that emitted a single wavelength — assuming it was a wave, of course — and that it spread out as it left the source until it encountered a spherical object. The light that hit the sphere would either be absorbed or reflected away, and what you’d be left with was a ring of light showing up on the screen behind it.

Image credit: Auburn University.

But if light were truly a wave, you would get some very bizarre phenomena, some that you might expect and some that’s completely unintuitive. You might expect that you’d get a series of light-and-dark fringes outside the sphere, similar to the interference pattern observed in the double slit. But what no one expected was that Poisson’s calculations showed that at the very center of the shadow on the screen, there should be a single bright point, where the wave nature of light all constructively interfered at the most unlikely of places.

Image credit: Robert Vanderbei.

How absurd! And so, Poisson elegantly reasoned that the wave nature of light was a ridiculous notion, and must be wrong.

But Poisson committed the cardinal sin of theoretical, reason-based, logical hubris: he drew a conclusion without performing the crucial experiment at all! The circumstances of this were particularly maddening: this was at a competition sponsored by the French Academy of Sciences to explain the nature of light, and the entrant who proposed the wave theory — Fresnel — was basically laughed out of the room by Poisson, who had been selected to be one of the judges.

But the head of the committee stood up for the entrant and wouldn’t stand for Poisson’s dismissiveness, and decided to do what a scientist must do in good conscience. François Arago, who later became much more famous as a politician, abolitionist, and even prime minister of France, performed the deciding experiment himself, fashioning a spherical obstacle and shining monochromatic light around it. The result?

Image credit: Thomas Bauer at Wellesley.

The spot is real!

I myself have referred to this — like many others — as the Poisson spot in the past, but no longer shall I do so. From this point on, in honor of the scientist who actually put the science to the experimental test, it shall be known as the Spot of Arago!

Image credit: Thomas Reisinger Created using Google Sketchup 8.0, under c.c.-by-3.0; correction/modification by me.

What’s perhaps most amazing about this is that if you craft a perfectly circular obstacle, the intensity of light at the very center is actually equal to the completely unobstructed intensity, with small circular fringes around the spot itself!

Image credit: Thomas Reisinger. Created using GNUPlot, under c.c.a.-sharealike-3.0. The “wiggles” in the otherwise dark area are due to surface imperfections in the smoothness of the sphere.

So the next time you run across what appears to be a theoretical absurdity, either because you believe such a thing must be so or cannot be so, don’t forget the vital importance of putting it to the experimental test! It’s the only Universe we have, and no matter how solid the footing of our theoretical predictions, they must always be subject to the scrutiny of unrelenting and continuous tests. After all, you never know what secrets the Universe will reveal about itself until you look!


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