Invariance
Science is supposed to be about an objective world. Yet our observations are inherently subjective, made from a particular frame of reference, point of view. How do we get beyond this subjectivity to see the world as it truly is?
Through the idea of invariance. To have a chance of being objective, our theory of the world must at least be intersubjectively valid: It must take the same form for all observers, regardless of where they happen to be located, or when they happen to be doing their experiment, or how they happen to be moving, or how their lab happens to be oriented in space (or whether they are male or female, or Martian or Earthling, or…). Only by comparing observations from all possible perspectives can we distinguish what is real from what is mere appearance or projection.
Invariance is an idea of enormous power. In mathematics, it gives rise to the beauties of group theory and Galois theory, since the shifts in perspective that leave something invariant form an algebraic structure known as a "group."
In physics, as Emmy Noether showed us with her beautiful theorem, invariance turns out to entail the conservation of energy and other bedrock conservation principles—"a fact," noted Richard Feynman, "that most physicists still find somewhat staggering."
And in the mind of Albert Einstein, the idea of invariance led first to e = mc2, and then to the geometrization of gravity.
So why aren't we hearing constantly about Einstein's theory of invariance? Well, "invariant theory" is what he later said he wished he had called it. And that's what it should have been called, since invariance is its very essence. The speed of light, the laws of physics are the same for all observers. They're objective, absolute—invariant. Simultaneity is relative, unreal.
But no. Einstein had to go and talk about the "principle of relativity." So "relativity"—and not its opposite, "invariance"—is what his revolutionary theory ended up getting labeled. Einstein's "greatest blunder" was not (as he believed) the cosmological constant after all. Rather, it was a blunder of branding—one that has confused the public for over a century now and empowered a rum lot of moral relativists and lit-crit Nietzscheans.
Thanks, Einstein.
