Wednesday, February 18, 2015 4:43 AM

Just Six Numbers and Three Demensions

Wednesday, February 18, 2015 4:43 AM
Wednesday, February 18, 2015 4:43 AM

A second after the big bang, if Ω had varied from unity by more than one part in a million billion the universe would not still be expanding.

Forget those 1,000 things you need to do before you die. Concentrate instead on six impossible things that, as the White Queen advised Alice, you must try to believe before breakfast.

Just Six Numbers: The Deep Forces that Shape the Universe (Science Masters) by Martin Rees

Without them there would be no galaxies of stars, no chemistry, no people, no books and no breakfast. There is – there has been for decades – an almost absurd number of brilliantly readable books about why the universe is as it is, but this one just possibly might be my favourite: its basic idea is so simple, its structure so constrained, and yet – like the universe it describes – so rich with possibilities.

Some of the six numbers should already be familiar to anyone who reads about cosmology, though one is a complete surprise, not because the number is new, but because it is so familiar it had never occurred to me that it was a property that could be any different.

One can marvel, almost indefinitely, at the balance between the nuclear forces and the astoundingly feeble but ultimately inexorable power of gravity, giving us N, a huge number involving 36 zeroes, and nod gratefully each time one is told that were gravity not almost exactly 1036 times weaker then we wouldn't be here. One can gasp at the implications of the density parameter Ω (omega), which one second after the big bang could not have varied from unity by more than one part in a million billion or the universe would not still be expanding, 13.7bn years on.

But who'd have thought that we also needed D for dimension to equal three, because without that value the show would never have got on the road? We go up the stairs, down the hall or across the living room so often that we tend to imagine that those are the only imaginable dimensions, but there could have been just two, for instance, or perhaps four.

Had there been four dimensions, gravitational and other forces would have varied inversely as the cube of the distance rather than the square, and the inverse cube law would be an unforgiving one. Any orbiting planet that slowed for whatever reason in its orbit would swiftly plunge into the heart of its parent star; any planet that increased its speed ever so slightly would spiral madly into the cold and the dark.

Under the inverse square law, however, a planet that speeds up ever so slightly – or slows down – simply shifts to a very slightly different orbit. That is, we owe the stability of the solar system to the fact that spacetime has, on the macroscale, only three physical dimensions.

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