The Limits of Knowledge, Part I: Point of View

Science will not do your homework for you.

Some questions can be answered by science:  “What happens when I add an acid to a base?” and “What happens if I stick this fork into a wall socket.” Others, such as “Does God exist, and if so, why is He not running the Universe to my liking?” and “What is good? What is evil? Does this make me look fat?” can not.

In the ancient world, a business card reading “philosopher” gave one license to inquire into everything, and I mean everything. Aristotle (the Philosopher) wrote on topics ranging from ethics to politics to zoology to cosmology. For any question he had an answer.

But job descriptions change. Part of the evolution of natural philosophy, under nascent scientists such as Francis Bacon and Galileo, was to drop some questions, for example teleology (“for what purpose”), and  focus solely on reproducible, material observations.

Science is about limitations, but limitation is the source of the power of science. Indeed, the history of the physical and mathematical sciences in the twentieth century includes not only discovering the vastness of the cosmos and the infinitesimal secrets of the atom, but also making shocking discoveries what we cannot know.

I’ll be writing a series of posts about some of the essential limitations we have discovered, ranging from the precise uncertainty defined by Heisenberg, to the butterfly-fueled rampages of chaos theory, to the weird mathematical backstabbing of Gödel’s theorems. Look for these in weeks to come.

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Today I start by writing about Einstein’s relativity.  Einstein did not completely invent relativity–Galileo actually anticipated many of the ideas, and Lorentz and Poincare worked out much of the math before a cocky young patent clerk (3rd class) came on to the scene. But Einstein was the one who tied it all up neatly. And he did it by focusing on what we cannot know.

First, a step backwards. One of the great triumphs of Newton was to assume the laws of physics are universal–that the same laws on Earth acting on an apple apply to the moon and to the most distant stars. This is a radical departure from Aristotle, who envisioned a layered, hierarchal universe, with the Earth flawed and decaying and the celestial sphere perfect and unchanging. (A brilliant SF reimagining of an Aristotelian universe is Vernor Vinge’s award-winning novel A Fire Upon the Deep, in which the laws of the universe do depend where you are.)

Einstein assumed that laws of physics are independent of motion; in other words, that you cannot do an experiment to determine absolute motion.  This is a fairly modest generalization of Newton’s relativity, and even Galileo postulated this principle.

But mix in another seemingly innocuous assumption and everything suddenly gets weird.

It was long thought that light, as a wave, required a medium that, well, waved, in the same way water waves required water and sound waves required air. But Maxwell’s equations (1865) predicted electromagnetic waves–confirmed by Hertz’s 1887 experiment producing radio waves–and light took its place on the electromagnetic spectrum. The problem is, one would expect math terms in Maxwell’s equations expressing motion relative to the “luminiferous ether”–and there was no such term. Either Maxwell’s equations were incomplete….

Or not.

Maxwell’s equations give the speed of light, in terms of the electric permittivity and the magnetic permeability. Einstein took Maxwell’s equations seriously, in particular that the speed of light was fixed for everyone. From this he was able to derive astonishing consequences. Time and space are not rigid but stretch and shrink. Mass and energy can be interchanged, with the conversion rate of c2.

Every observer has his or her own personal “rest frame”–with a “normal” clock, a “normal” ruler, and so on. All the weird effects of relativity are somebody else’s problem; it’s their clock that runs slow, their spaceship that is squished, and so on.

Not everything is relative. There are invariants to the theory, quantities all observers can agree one: the speed of light, c, for one, and the rest mass of objects for another. Furthermore, the changes are not arbitrary, but dictated precisely by the mathematics of the Lorentz transformation.

It’s not “just a theory.” All the math is backed up by lots and lots of experimental confirmation, including nuclear energy (woo-hoo! E = mc2!) and the slowing of fast-moving subatomic clocks, to name just two.

I’ve just described Einstein’s theory of special relativity. Here “special” means specific circumstances of linear, constant motion. It took Einstein eleven years to extend his ideas to the theory of general relativity, which includes acceleration and gravity.

Once again, general relativity is based upon a fundamental limit to what we can know: You cannot do an experiment to distinguish between acceleration and gravity. That is, if you are locked in a small space and something is tugging you toward the floor, there is no device (aside from, oh, a window) you can invent that can distinguish between being on the surface of a planet, or being inside an accelerating spaceship.

This “you cannot do X” statement also has observable, testable consequences. Gravity bends light, slows down time, and swallows hapless astronauts in black holes for eternity.  There are even ways to parameterize theories of gravity, with various “post-Newtonian parameters” that allow one to dial continuously between Newtonian gravity and Einsteinian general relativity, and to date every observation yields values consistent with general relativity.

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What does this mean for SF? Aside from the inconvenience of a cosmic speed limit  making interstellar travel an enormous headache?

First, it helps remind us that real science often has surprising limitations.  Good SF world-building uses consistent and often intuition-defying limitations to give the illusion of real science. Even if one has a faster-than-light travel, for example, one might postulate it won’t work in a gravity well. Or it only works starting from a gravity well.

Second, effective rubber science in SF is based less upon minutiae of science facts and more upon basic principles, much like Einstein’s “you cannot determine X” dicta. Damon Knight relates how in a story he justified human immortality not through subtleties of biochemistry, but noting that long-lived species also tended to have stretched out adolescences–and his immortals effectively stretched out human adolescence indefinitely.

Finally, it’s a sober reminder of how surprising and unexpected the universe is.  Many philosophers have expected, even demanded that the universe to be entirely comprehensible. Conversely, like rebellious teenagers getting tattoos, the postmodernists, have tried to be uber-fashionable by going from there are limits to knowledge and truth to there is no knowledge or truth, and suggesting that western science is merely a cultural creation.

But who could have imagined that space and time are flexible, not in rubbery dream-logic fashion, but with the cold precision measureable by stopwatch and rule? What cultural assumptions could have lead to the marching lock step of photons in a laser, and the stubborn don’t-invade-my-space of electrons in an atom?  What sane person would have dreamt that mundane algebra could conceal and cover-up truths like some bizarre conspiracy theory?

No, this is the universe speaking to us, and we should listen.

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