No computer stuff today.
Martin Gardner – writer, skeptic, recreational mathematician – died recently. As a teenager I would scour the back room of Casablanca Books looking for back issues of Scientific American for interesting Mathematical Recreation columns. Martin Gardner was one of the people whose work got me interested in mathematics, science and computing, so I’d like to dedicate today’s blog to his memory.
I was driving home late from dinner at a friend’s house the other day. It wasn’t raining, so the top was down, in keeping with my policy. As I merged onto the highway I glanced up and saw Vega, which made me happy. Of course. Who isn’t happy when they see part of the Summer Triangle? It makes me think of long moonless nights on the beach in my youth, watching for shooting stars and polar orbit satellites with my physicist friend John and our respective cousins.
Vega is only 25 light years away, hardly any distance at all astronomically speaking. And yet it appears as just a point of light in the sky. No matter what binoculars or telescopes you aim at it, Vega will not resolve into a disk. It’s just too small.
Or is it?
As I was driving home I started to think about the big picture of Vega; what is it really like? I want to consider not just Vega the highly localized, rapidly rotating mass of incandescent gas, but everything Vega was, is, and will be.
Vega is a young star, only 455 million years old, give or take a dozen million years. There were vertebrate fishes swimming in the oceans of the planet Earth when a sizeable ball of gas and dust falling towards its center attained sufficient mass and pressure to start thermonuclear fusion of its hydrogen. At that moment of ignition massless photons of many wavelengths started streaming symmetrically away from the center of the new star, along with charged particles like electrons, neutral neutrinos and so on.
The set of photons and other particles originating from the ignition of Vega forms a sphere. At the moment of ignition that sphere was relatively small, but of course immediately behind those first photons were more and more photons. We have an ever-expanding, (and increasingly tenuous) sphere of particles.
A scant twenty-five years later a new star lit up in the Paleozoic night sky; the sphere of photons had reached 25 light years in radius, forming a volume of about 4 * 10^50 cubic meters. Of course, some of those photons were intercepted by collisions with atoms in the interstellar medium, and each Vega photon is getting farther and farther apart from its nearest neighbor as it gets farther away from its creation.
That sphere’s diameter has grown inexorably by 36 billion metres every minute for the last 455 million years. The original sphere of ignition photons is now 910 million light years in diameter, encompassing not only our entire galaxy and its local group, but the entire supercluster. That outermost sphere has got to be exceedingly low density by now, but surely some of those photons and neutrinos and whatnot have survived. We can easily see visible light from galaxies billions of light years away through the Hubble Space Telescope; those photons are light from stars just like Vega, light that has travelled through the interstellar medium for billions of years only to fall onto the primary mirror of the Hubble.
The Earth is practically at the center of that sphere now, only 25 light years away from the center of a sphere almost a billion light years in diameter. Vega is not small; the entire object that is the light emitted by Vega is huge. The angular size of the surface of the star right now is tiny, but the angular size of the whole thing since its ignition is enormous. The reason it looks so small to me is a function of my limited perspective; I can deduce what some of the characteristics of the whole billion-light-year wide sphere of photons is like, but I can only see an infinitesimally tiny fraction of it. If I had sensors all over the galaxy and some ability to integrate their data into a coherent whole over a large time scale, my perspective of Vega would be quite different.
In short, Vega doesn’t look like a point because it is a point with respect to me; Vega looks like a point because I am a point with respect to it.