Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Koorosh on 05/05/2013 08:37:18
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when utilizing a generalized Lorentz transformation that are not constant, then one could break down an event into infinitesimal events until we get inertial(ity). Taking the positions vectors into consideration, then we could make linear transformations at each point and glue them together on a base. The arguments are, if we make a synchronized observation of a fast moving event, by changing the coordinate base constantly, there will be a contradiction on the observation compared to an stationary observer. On a whole both these observers could be seen as inertial while considering large distances to the event which makes the slightly rotating observer an inertial observer with good approximation
For full details see:
http://en.wikipedia.org/wiki/User:Koorosh.shahdaei/sandbox
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Either you will find time dilation and Lorentz contraction even when treating the relative motion as 'inertial' by splitting it into very small pieces, or you won't. If there is a scale to a frame of reference, assume Planck scale for that, then that is what you are questioning, although treating it as measured/compared relative a 'relative motion' instead, as I think. To me the question becomes one of how different scales will treat each other, comparing, and if Lorentz contractions/time dilations will matter from some smallest scale. But at those smallest scales I don't expect you to be able to measure any way, except in a theoretical manner, and your mathematics will break down there as I think.
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In other words, is it a smooth, or a 'bit' universe, we live in? Assuming your mathematics to stop giving you answer at Planck scale you can define it both ways, under it becoming 'smooth' as in continuous without seams and breaks, but also unmeasurably so, over it giving us quanta and discrete bits. But to get to that 'inertiality' you want, you will need to scale it down to where you can't get a answer, as I suspect.
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This is not really about the infinitesimal measurements itself, it just help us to compare two two observer, one stationary at a fixed point and the other with a slight rotation, the later won't see any time dilation or length contraction, it is mathematically selfconsitent as you would see. The infinitesimal part also help us to make symmetry transformation at each particular time (let say for now the local time of the observer) as proceeding. Hope it is clear.
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Well, to me it really is the question :) I might be one eyed there, but it will make one h* of a difference to your mathematics if we could find a way to test it.
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At least you agree that physical content are the same whether the observer is stationary or not and gauge part (non linear) can be excluded if applied, the two observer with negligible velocity would agree to LT, but in this case they won't.
What test do you suggest?
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That is a really good question :) We have NIST:s experiments, but they only get down to centimeters (time dilations). Also assuming that a Lorentz contraction is a complementary effect here. I'm still wondering what experiment one could use for testing that one? I've seen some astronomical observations getting down to very small scales, although inferring those mathematically instead of measuring directly, but that might be me not getting them straight. But I still think we need to find a experiment able to test if there is some scale from where relativity 'builds up'. Hogans Holometer is one test I know of, but it's been criticized from SR.
I suspect it must become astronomical evidence, as that is where we get the most energy interacting, meaning the smallest scales if thought of as waves? Maybe there are some better way though? A ideal experiment should be one easily reproducible.
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It also depends on what you think of as a 'rotation'. If you deem it 'illusionary' or real. I define it as real from a local definiton. you measuring. To define it otherwise presume one to have a way to prove experimentally that it is not. And as it is local experiments that have defined Lorentz contractions and time dilatations, one then will need to find some other way to define what a 'real experiment' should be, also invalidating all other experiments creating main stream physics, or prove them included in ones new theory. As Newtonian mechanics becomes something included in relativity.
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Indeed, it's been more then 100 year of dispute about relativity, but thinking of making a simple law or a few simple laws that can cover all physics, would be naive. As we go forward, we see more difficulties that can't be explained current physics, like: dark material, Higgs mechanism, Expanding universe, Gravity, big bang, bubble universe etc etc.
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Maybe you're right, myself I like to think of it as us not asking the right questions yet. If we find them I hope the simplicity will be seen. But it depends, you could also state that there are different regimes under which a theory fit, but so far science still try to find one answer covering it all. But as we can't get to Planck scale, neither to extreme temperatures, it's a tricky path to walk.