January 17th, 2009

While we’re in high-falutin’ mode, let us consider a moment the limits to human knowledge of the cosmos. Please don’t go away! Stunning photo after the jump! No equations, no words of more than three syllables, and anyway I’m not an expert so I certainly get a lot of it wrong and you can have the fun of correcting me!

For Christmas I bought myself a 3-D puzzle, a star globe. The puzzle is made of 540 identical pieces of stiff curved plastic, forming 90 hexagons. Fortunately Ravensburger number the pieces on the back.

star globe.jpg

For 2,000 years, from Aristotle to Newton, educated people thought the heavens were a bigger version of my puzzle: a rigid shell into which the Puzzlemaker had stuck the stars on the inside. In the West a few independent spirits like the pre-Socratic Anaximander (sorry, four syllables, but it’s only a name), and the Elizabethan discoverer of magnetism William Gilbert, speculated that the stars were sunlike bodies floating in infinite space. Similar ideas were held by a minority Chinese school of astronomers called the Hsüan Yeh. Since none of them had any evidence for these crazy ideas, the celestial sphere idea was the more economical and deservedly popular.

More, no more difficult and with a better photo, below the jump.

Aristotle (following Eudoxus) clinched it by making the celestial shell the mechanism for the movements of the planets, Moon and Sun. The spinning Prime Mover transmitted motion to successive transparent shells inside it, carrying the moving bodies. How exactly this worked was left studiously vague on Underpants Gnomes lines, but huge effort went into identifying the shells to fit with observations of planetary motion. By Aristotle’s time these were already 55 (Metaphysics, XII.8). With better data, more and more invisible clockwork had to be fitted in, like Ptolemy’s epicycles. The more astronomers knew, the kludgier it all looked.

Enter Copernicus and Kepler to simplify things. But the first century-and-a-half of the Copernican revolution left the celestial sphere untouched. Newton, in the Principia, proved that the mass of a uniform shell would have no net gravitational effect on bodies near its centre, the solar system he was primarily concerned with. But that was just to protect his system from a possible objection. Late in life he investigated an Anaximander-type infinite universe. If the stars were all like the Sun, their brightness should decline with distance on the inverse square law. This gave him the first estimate of the distance to Sirius (far too high, as Sirius is really much brighter than our Sun). Halley produced the objection to an infinite cosmos now known as Olbers’ paradox: as you go outwards though successive shells of space, the number of stars in each should increase by the same ratio as the intensity of light from each star declines, so why isn’t the sky infinitely bright? Newton died before he could crack that one. The current answer is decidedly inelegant: rather than a transparent vacuum, space on the large scale is dilute smog.

Newton’s successors passed through the cracked shell of the celestial sphere into the dynamic and extended universe of our current understanding. Halley showed in 1718 that the star Aldebaran had a proper motion, i.e. relative to other stars, over a long period of observation. Galaxies were identified by Messier and the Herschels. (George III, not in fact the mad tyrant of American myth, paid Caroline Herschel a salary: perhaps the first recognized woman scientist since Hypatia.) Infinite space was back.

But now it’s out again. The now solidly established Big Bang theory means that the observable universe has a limit: the distance light can travel since it happened, 13.4 billion years ago. As it happens, we can detect in all directions the remarkably smooth cosmic microwave background radiation (CMB) from a mere 300,000 years after the Bang. And here’s a lovely map of it, from the Puzzlemaker’s perspective, made freely available by the MIT astrophysicist Max Tegmark :

microwave background globe.gif

You can get the other half from Tegmark’s site, pretty much the same, and a high-resolution version for a blowup of the blowup.

The Mark II celestial sphere really is the formal limit of our observational knowledge. It also curiously takes us back to Aristotle in two other ways.

This sphere is in a sense once more the Prime Mover: for it is an image from as near as we can get to the superhot birth of our universe, which as it cooled and expanded set in motion the processes that gave us all we see. The clockwork of the universe is however not an angelic perpetual motion machine, but a musical box running very slowly down.

We are also once again at the centre. The isotropy of the CMB – it’s very nearly the same in all directions – means that we are hardly moving in relation to it, a mere 550 km/sec. The Earth’s orbit round the Sun (30 km/sec), the Sun’s wanderings through our galactic arm (20 km/sec) and orbit of the galactic core (250 km/sec), the Milky Way’s head-on motion towards the Andromeda Galaxy (100-140 km/sec), are just insignificant jiggles at the cosmic scale. The earth’s yearly motion relative to the CMB rest frame (.002 light years, calculated from here) is two parts in a hundred trillion of the current CMB distance. In the 4.5 billion years of the Earth’s life, it has only moved 0.04% of the same. [Math corrected - I hope.] We humans are almost, though not quite, at the Aristotelian “still point of the turning world“.

However, there is no physical reason to think we are privileged observers; and it is physical dogma that we are not. The celestial sphere of knowing is merely a consequence of the fixed speed of light. The physicists suppose, like Anaximander, that the sphere is simply embedded in more, perhaps infinitely more, of the same – but they don’t know. The proposition could only be an inference from cosmological theories that satisfactorily explained the data from within the sphere, and we are not quite there yet. The alternative speculation is that the universe is topologically closed, like a doughnut, perhaps in extra dimensions, and WYSIWYG. The minds of non-mathematicians can’t really imagine this.

In theory we could get a message from galaxy IOK-1 in Coma Berenices, sent a mere 750 million years after the Bang and 12.9 billion light years away, to the effect:

Greetings from Trantor! Our advice to any civilisation listening is to stay alive as long as you can and go with the Hubble flow! And by the way, the universe is isotropic from here.

Since IOK-1 would be at the centre of its own celestial sphere of observation, offset from ours by half its diameter, the message would confirm the no-privileges dogma and the extension of the universe beyond our boundary of observation. But don’t hold your breath. I’m readier to believe in the outlandish SF technologies required to send messages with such power – modulating supernovae or tweaking black holes or something – than in the likelihood of such a society wanting to do any such thing. FWIW, my pet solution to the Fermi paradox – if there are aliens, why haven’t they phoned? – is that either technologically advanced civilisations implode quickly or they learn to live by the Golden Rule: and the latter prohibits random interference with other intelligent species.

Main source: John North, The Fontana History of Astronomy and Cosmology, 1994. But don’t blame him.

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