posted
I was kicking around some ideas for alternative laws of physics in a boring class the other day, and one thing I came up with was this : Suppose the Universe was an accelerated frame of reference? (Alternative formulation : Every object experiences a force proportional to its mass, in some particular direction.) It might make an interesting gimmick for a science-fiction story, if you could figure out ways it would affect life on Earth. For example, the air would be thinner on one side of the planet, and the planet would be an ovoid. But then it struck me that the first problem would be whether the planetary orbit was stable or not.
There is one obvious simplification here : We can ignore any force component perpendicular to the plane of the ecliptic, since the Sun and the Earth will accelerate at the same rate in that direction, and this motion does not affect the orbit.
The obvious analogy is a weight on a string, which you swing in with the axis of rotation horizontal. In this case, there does exist a stable orbit, which any child can achieve by adjusting the tension in the string according to the orbital position. The question is, does there exist a path such that the force of gravity, plus my theoretical universal force, is exactly sufficient to maintain the Earth in that path?
I tried doing this by adding a term
V' = -r cos theta
to the usual gravitational Lagrangian, but the equations turn out to be very hairy. Does anyone see an obvious symmetry principle that would either stabilise or destabilise the orbit? Otherwise I may have to resort to (shudder) Mathematica.
Posts: 10645 | Registered: Jul 2004
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posted
Umm, I don't post detailed Mormon theology subjects here. Why should you get away with stuff you feel you maybe should post on Mathematica?
Posts: 11017 | Registered: Apr 2003
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posted
Mathematica the solver-of-differential-equations-program. To the best of my knowledge there is no forum called Mathematica.
As for posting it here, I thought people might find it interesting to work out the consequences of such a Universe, or come up with variations. You don't have to work out a solution to have fun with such a thought experiment, that was just something to get the discussion started. Though I realise I may have chosen my thread title a bit badly.
Posts: 10645 | Registered: Jul 2004
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posted
Actually, absolutely nothing would be different. In fact, we might as well already live in that universe. The only difference between the force you're talking about and gravity is that gravity becomes weaker the farther from a source object you get. Nothing in the universe would ever notice a static gravity-like force, because that force would act on every particle to the same degree.
As an illustration of this concept: humans can easily withstand 500 G's of acceleration, provided that said acceleration is actually due to gravity, and the human is in freefall. This works because every part of the human experiences the exact same acceleration (or close enough that the difference is negligible), so there is no difference in the resultant movement between, say, the toenails and the liver. As far as the human is concerned, he might as well be experiencing no acceleration whatsoever; it's that rapidly approaching ground that's going to ruin his day, and that only because it doesn't affect the entire body all at once.
posted
My God, you're right. How did I miss that? That's what comes of trying to sit in the rest frame of the Sun when that frame is accelerated.
Posts: 10645 | Registered: Jul 2004
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posted
I can still rescue my orbital question with a bit of *cough* creative editing, though. My hypothetical force is carried by a particle which couples to inverse momentum. The Sun, therefore, is not as strongly affected as the Earth.
Posts: 10645 | Registered: Jul 2004
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posted
I always thought the fact that inertia is the same as gravity is very weird. What is inertia? What's so special about a non-accelerating reference frame? How does it make any sense to say the universe isn't acclerating (because there has to be something for it to be accelerating relative to, and the universe is by definition everything.)
The only vaguely reasonable explanation I ever heard was Mach's principle, that says (I think) that somehow intertia results from the sum total of the gravity of all the stars and galaxies combined. As far as I know, that's not part of any viable theory of cosmology now, though, that is currently under consideration as a Theory of Everything. Can any physicists tell me more?
Posts: 6246 | Registered: Aug 2004
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posted
Inertia is not the same as gravity. Acceleration is the same as gravity (or rather, is indistinguishable from gravity).
Posts: 15770 | Registered: Dec 2001
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posted
I do know what you're referring to though, you're thinking of the question as to why inertial mass is the same as gravitational mass. I think several of the current theories of everything do address this, though I'm not up enough to explain specifics.
Posts: 15770 | Registered: Dec 2001
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