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anticorncob28
Post  Post subject: Adding rotations to symmetries of the universe  |  Posted: Wed Aug 02, 2017 8:50 pm
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Joined: Thu May 05, 2016 10:31 pm
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Location: Nebraska, USA

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We know that the laws of physics are the same in any non-accelerating, non-rotating frame of reference. What if we also added that they are the same in any rotating frame so long as the rate of rotation is constant?
Special relativity would have to go- the speed of light would clearly increase in any rotating frame of reference, and I doubt if any transformations of time and space could resolve that.
The equation F = ma would have to change. The best alternate I've found so far is F = m(a + d^2a/dt^2), which only works if the rotation speed is one radian per unit of time. I suppose that's okay.
I believe that any such universe would have to be completely unpredictable in nature. The orbit of earth around the sun would be a valid reference frame, which in turn implies the moon's orbit around earth is a valid reference frame, and any object around the moon, added on with any constant velocity, with any extra rotations, etc.
Eventually this would lead to that any path whose coordinates can be described as a sum of sines and cosines multiplied by linear functions would count as a "still" frame of reference from which all laws of physics remain valid.
We know from Fourier series that every continuous function can be approximated as closely as we wish using these sums (provided periodicity, but we have even more wiggle room here). So if you let go of an object after giving it a force, you would have no idea what it's going to do. If our universe had this symmetry, we would not exist.
Any other thoughts?

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