Wednesday, October 23, 2013

In Which I Correct Newton and Mach

Newton arrived eventually at the idea of Absolute Space, the idea that space was a thing independent of matter. It was a needful idea in order to explain why, say, a bucket full of water, suspended from a rope and set to spinning, would transfer the spin from rope to bucket to water – yet when the bucket stopped spinning in one direction (the rope having rewound itself taut to the other extreme), the water would continue its whirlpool spin even as the bucket moved in the opposite direction. Trust me, it’s a problem, answered by Newton: motion must be relative to some greater context, and by extension, to the universe itself.

Leibnitz had argued that there was no space without matter, any more than there can be no alphabet without letters – it must be occupied to exist at all; an empty set is not a set at all: a null set is a mathematical conceit, having no actual reality. The spinning bucket with its concave water befuddles this conception. Ernst Mach came along two and a half centuries later and said that spin, which is what the discussion is all about, is dependent on how much matter there is in the universe. If you spin like an ice-skater you feel your arms pulled outward – not as a function of vision or of balance, but as a centrifugal quality inherent in matter. Mach said that if there were less matter in the universe, your arms would be flung out less. If there were no other matter in the universe, a “null” set universe, your arms would not move out at all.

I’m simplifying, of course.

 Well. We know this spin is not a function of local gravity, because whether as an ice-skater on earth or as an astronaut in zero gravity, if you are set to spinning, your arms are flung out. Centrifugal force manifests universally -- or at least under all testable circumstances.  Mach’s idea would have it that an astronaut set to spinning in our universe would have more centrifugal force than a similar astronaut in a universe in which there was only a single star. Which is to say, the mass of the universe, the amount of overall (not merely local) gravity, determines the perception or manifestation of spin. I see this as wrong on the face of it -- how much mass there is in the universe should have no bearing on the result from how much energy is put into a system to make it spin. X amount of energy would manifest as X amount of centrifugal response. No? I’m no mathematician, but this reasoning seems more to do with logic. Confounded of course by the fact that we are dealing with impossibilities -- there is no universe with only one star, so how can we decide upon an equivalence of X input energies? Would Joules or ergs be absolute, or proportional, relative to another cosmos? Maybe it’s an imponderable, or maybe there’s the math for it. I don’t know. But such maths would be based on suppositions. So I believe.

Newton said that even in an empty universe of absolute space, there would be a distinction between you stationary and you spinning. Mach said there would be no difference. This is all very fine and well. Where I must interject, object & correct is here: in an empty universe containing only you, how could you start spinning in the first place? From a static state, some other agent is required to provide the acceleration force – whether a passing alien or a springboard rock or a handheld rocket gun.

The term spin never got defined up front. Putting aside all considerations of torque and angular momentum and relative motion, spin requires the input and transfer of energy. Newton wound up the rope, which spun the bucket, which got the water moving. Spin requires a relationship between, uh, entities … energy, matter, space, what you will. Since matter and energy are equivalents, we should be able to say that matter requires other matter/energy in order to start spinning. As for what the ultimate reference point of spin would be, well, gravity is a universal field, as is the virtual foam of quantum mechanics. There is no need of an empty absolute space, because there is no such thing as emptiness. Newton of course anticipated Einstein, re relativity.

Of course all these thoughts have been thought before, and questions answered.  I'm surely traveling old ground. But discovery is relative.  Delight, Dear Reader, in my joy.


No comments: