## Friday, July 06, 2007

### I Overturn 450 Years of Scientific Error

So one in five Americans believe the sun revolves round the earth. This is nowhere near enough. I, like most thinking people, have long felt that this whole Copernican thing has gone too far. It is perfectly reasonable to assume for the purposes of argument that that the earth revolves around the sun, but patently absurd to believe that it actually does. There is no still point in the universe from which to measure all other points so it is impossible to say that anything revolves round anything else. We choose to make the sun stand still, but we could equally well choose to halt the earth. Admittedly this would make the geometry of the solar system look a bit messy, but the universe is under no obligation to be adhere to our bourgeois, earthling standards of neatness. Bring back Ptolemy, I say; he was wrong too, but he lasted a lot longer than Copernicus. (Pick the bones out of that one, Gordon McCabe.)

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Blimey! So when the Beatles sang 'Here Comes The Sun" they were wrong! It's actually us that was coming, as the sun goes nowhere.

ReplyDeleteI'm confused.

Confused is good, Richard. If only Gordon Brown were more confused...

ReplyDeleteConfusion will be my epitaph. I'm with you on the GCF. Why is it clunking fists are never confused? That overbearing belief in the rightness of everything he does is what stops him from doing right.

ReplyDeleteYou've reminded me about Pirsig writing about William James's picnic outing.

ReplyDeleteJames is on an outing with some friends and one of them chases a squirrel up the trunk of a tree. As the friend approaches, the squirrel instinctively moves to the opposite side of the trunk. The friend moves around to try to see the squirrel but as he circled the tree, so the squirrel circled on the opposite side.

Afterwards the friends discussed whether the man went around the squirrel or not.

To be accurate, I don't think anyone thinks the sun stands still - that would be unthinkable.

If the universe is finite, it has a centre of mass. Isn't that the fixed point about which everything else moves?

ReplyDeleteAlso, there's a slight problem with Bryan's equality of viewpoint argument. Two people are on a fast moving roundabout, one seated at the centre, the other flying around on the perimeter. Each might claim to be still while the other moves but only one is flung off as the roundabout hurtles around.

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ReplyDeleteWill Blake's comment confuses me. This being the man who wrote, "If the doors of perception, everything will appaear as it is, infinite." The universe being part of what is is therefore not finite, but infinite.

ReplyDeleteSo if the universe were finite, then the fixed centre would work, but since infinity stretches forth from every imaginary point within theis infinity, then it doesn't work.

well, I guess possible if the universe behaved like a solid, Will Blake - but what if it was more like a fluid?

ReplyDeleteif the universe is not finite mass, where does all the new material come from - or where does it all go if you want to imagine it getting smaller?

ReplyDeleteSorry about the rendering of Blake's, "If the doors of perception were cleansed every thing would appear to man as it is, infinite." The corollary to this being, "If the doors of perception were dulled, everything will appear to man as it isn't, finite."

ReplyDeleteI've a short couple of pieces on how percpetion equates with this universe of external reality here, and here.

ReplyDeleteI'm not sure you aren't confusing mass with volume, andrew. ;o)

ReplyDeleteUp until three years ago, I thought everything revolved around me. Alas, two pieces of very strong empirical evidence came to light that blew my theory out of the water overnight and rocked the foundations of my establishment. I now revolve around two sons who never stop moving and make the geometry of my house look very messy indeed.

ReplyDeleteIan: solid, liquid, gas, plasma or silly putty, it doesn't matter, if it's finite it has a centre of mass.

ReplyDeleteAndrew: we must seriously consider the possibility that there is more than one Will Blake. Perhaps an infinite number, some of whom think the world is all the better for being finite (both outwards and inwards, otherwise how would we get anywhere?).

Will, you seem to be insisting we still dwell in the Newtonian world-view as opposed to the infinities opened up by Einstein & the boys. You're also saying, "If it's finite, then..." This is simply accepting this finite nature as a statement of truth from which we then create our version of reality which fits into this pre-conceived framework. Which would seem to be the kind of idea before reality thinking that led the Greeks to have such disquietude over things like Pi & the square root of 2, suggesting as they did that reality did not fit into elegant finite models.

ReplyDelete"So one in five Americans believe the sun revolves round the earth."

ReplyDeleteThat doesn't scare me at all. The fact that one in four Americans think Bush is doing a good job.... now that scares me!

Will Blake, old pal, I wasn't questioning whether it had a centre of mass but your reasoning that it must be fixed.

ReplyDeleteAndrew: Nothing classical about finite quantities. When physicists found a way of getting rid of the apparent infinities in quantum theory, they won Nobel prizes for getting pleasantly finite results (nobody having seen the infinitely heavy electrons the theory seemed beforehand to predict).

ReplyDeleteThe only infinities in Einstein's theories are when it goes wrong (eg at singularities - centre of a black hole, big bang) - or at least ceases to give sensible answers - which is generally taken as telling you that something new is needed.

Ian: What would make it move? It would have to be outside a (finite) universe which can only mean...

Andrew: Also, the Greek examples you give are mathematical. It's quite possible to manipulate symbols which have the properties of infinite quantities. But it's a leap of faith to then think they correspond to something physical.

ReplyDeleteAndrew: Also, the Greek examples you give are mathematical. It's quite possible to manipulate symbols which have the properties of infinite quantities. But it's a leap of faith to then think they correspond to something physical.

ReplyDeleteMy patience is finite, that's for sure. But as long as you explain to the little darlings why daddy is cross it's ok. On the other hand, the number of ways in which a two-year old can wind you up is infinite. So how can the infinite coexist and interact with the finite within a closed system of rewards and punishments without causing an acceleration in the rate of entropy?

ReplyDeleteEvenin' all.

ReplyDeleteIn the Fridemann-Robertson-Walker models of general relativistic cosmology, (the models which are considered to describe our own universe), the spatial universe is represented to be homogeneous, and isotropic about each point in space. One consequence of this is that matter is uniformly distributed through space. This means that at any point in space, for a coordinate system centred at that point, that point will be the centre of mass in that coordinate system. Such a universe, then, has no unique centre of mass.

Note also that a Friedmann-Robertson-Walker model can possess an infinite spatial volume. There is no reason to think that our own universe has finite spatial volume.

The Ptolemaic models were capable of representing astronomical observations with arbitrary accuracy because they unwittingly used the mathematics of Fourier series. Any cyclical phenomenon can be described by Fourier series. The accuracy to which you describe it can be chosen by the number of terms you include in your Fourier series. When Ptolemaic astronomers added extra epicycles to accurately describe, say, the retrograde motions of the planets, they were unwittingly adding extra terms to their Fourier series.

Ah Gordon. At last. So am I right?

ReplyDeleteIf you're in one reference frame, with the Earth at the centre of the coordinates, and another object, the Sun, appears to be going around you, then you can switch to a reference frame in which the Sun is at the centre of coordinates, and the Earth appears to be going around the Sun, and vice versa. So there is a symmetry here, and only things invariant under a change of reference frame are supposed to be objective.

ReplyDeleteSo you're right on that level, the purely kinematical level, where only motion, and not the forces at work, are considered. However, once dynamics enter the fray, you lose the symmetry. The Sun is far more massive than the Earth, hence:

(1) Under the representation provided by Newtonian gravity, the Sun exerts a force on the Earth far greater than the force the Earth exerts on the Sun.

(2) Under the representation provided by general relativity, the Sun creates space-time curvature far greater than that created by the Earth.

Under either representation, there is an asymmetry here between the two reference frames.

Note also that the Sun and Earth, considered as a joint system, actually rotate about their common centre of mass. The Sun orbits a point which, because the Sun is so much larger than the Earth, lies within the surface of the Sun. Nevertheless, this point is displaced from the centre of the Sun. Astronomers use this same 'wobble' of distant stars to infer the mass of planets outside our own solar system.

"So one in five Americans believe the sun revolves round the earth."

ReplyDeleteThat's 20% terrifying and 80% reassuring.

Gordon: Very interesting. Just to see if I understand a little of what you say about the universe in more homely terms...

ReplyDeleteThe centre of mass of a hollow sphere isn't on the spherical surface but at its centre. Since the sphere is actually in 3D, there's no difficulty. However, if we were limited to living on the 2D spherical surface, any points not on the surface, including the centre of the sphere, wouldn't be accessible to us.

If we then tried to work out the centre of mass of the surface, we'd find that each and every position on the surface is the centre of mass from the point-of-view of someone at that position.

The universe as a whole is then like a 4D surface in space-time (is it a closed surface?). If the surface was within a 5D space then its centre of mass would lie within the 5D space but not within the universe. However, since we are limited to living within the 4D surface, we find that, like the spherical example, each position is a "centre-of-mass".

Is that sort of right?

Exactly Will.

ReplyDeleteThe 4-dimensional universe could be a 'closed' manifold (what topologists would call 'compact'), but there's no reason why it must be, and in most general relativistic cosmologies, it isn't.

The 3-dimensional 'slices' of space-time can be either compact or non-compact (e.g., the spatial universe could be a 3-dimensional sphere or 3-dimensional Euclidean space).

Gordon: I'm relieved.

ReplyDeleteA question occurs to me. The assumption of uniformity seems to be important in leading to everywhere being a centre-of-mass. I'd guess that it's assumed mainly because it makes the equations easier to solve. If the assumption was removed, might there be only one c-of-m?

Michael wrote:

ReplyDeleteThat's 20% terrifying and 80% reassuring.If I told you that 100% of those 20% always vote and at most 25% of those 80% usually vote, would that be a toss-up between terrifying and reassuring, 95% terrifying, or 75% "This way madness lies?"

The assumption of uniformity is there so that the cosmological models agree with astronomical observations. On the length scales represented in the cosmological models, the distribution of galaxies does appear to be uniform.

ReplyDeleteIt's perfectly possible to devise general relativistic models which do have a unique centre of mass. For example, the Schwarzschild models for a star or black hole most definitely have a unique centre of mass. It's just that these models are not considered to represent the entire universe.

I intend entering this post and comments for the Nobel Prize.

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ReplyDeleteYou might have better luck with the Ig Nobel prize, Bryan.

ReplyDeleteOr nobbly prize.

ReplyDeleteGordon: Isn't there a bit of a problem - maybe a contradiction - between applying observations of the part of the universe we can see to the whole thing and also assuming that it's infinite?

Or to put it another way, what observation could possibly show the universe to be infinite (rather than possibly larger than seen so far)?