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quote:Originally posted by lightarrowThose explanations don't seem to solve the problem. Let's consider only those regions of the strings where they are straight and without acceleration: according to lenght contraction they should be shorter, but how it's possible if the pulleys are the same distance apart?My compliments to you, Solvay, that's a really interesting paradox!
quote:Originally posted by lightarrowMy compliments to you, Solvay, that's a really interesting paradox!
quote:Originally posted by lightarrowSo, how do you explain my previous question: a circular ring of some matter rotates at high speed. Then, according to lenght contraction, its circumference should shorten. Does it really happen? Does the radius shortens too?
quote:Originally posted by lightarrowSo, how do you explain my previous question: a circular ring of some matter rotates at high speed. Then, according to lenght contraction, its circumference should shorten. Does it really happen? Does the radius shortens too?If we can solve this, and it should be easier, we can probably solve Solvay's paradox.
quote:Originally posted by Solvay_1927I've managed to find some more info on the relativistic relationship between radius and circumference of a rotating disk/cylinder. It gives rise to the "Ehrenfest Paradox" (the resolution to which is not straightforward, it seems). For example, see:http://en.wikipedia.org/wiki/Ehrenfest_paradox
quote:Originally posted by Solvay_1927In this way angular momentum is conserved. My understanding is that angular momentum IS conserved in relativity, even though linear momentum isn't. (As far as I can remember, in relativity it's the "momentum-energy four-vector" that's invariant, rather than (linear) momentum in isolation or energy in isolation. But angular momentum IS invariant on its own. But please let me know if I've got that wrong.)
quote:Originally posted by another_someoneIf I understand the article correctly, in principle, the resolution looks quite obvious when one thinks about it. The actual argument seems to be say that assuming that the material has sufficient strength, there will be no contraction at all. If I understand what they are saying correctly, they work on the basis that length contraction only occurs if the material is not under strain (i.e. the material will try to contract, but if there is a counteracting force, then the material will not be able to contract). Since the bulk material is held in a rigid shape, therefore there is a force that prevents the contraction from happening, and all you see are increased stresses in the material rather than actual changes in the dimensions of the material.This would appear to me to mean that the forces an stationary observer sees in the bulk material trying to tear the ring or disc apart are different from the forces that someone fixed to the ring or disc would see. If this is case, and given that the point at which the ring will break apart should be the same no matter whom the observer is, it seems to imply that the strength of the material would have to appear to be different to the two observers.
quote:Originally posted by lightarrowIf you are assuming that Hook's law and F = m*a law are Lorentz-invariant, it's not so.
quote:Originally posted by another_someonequote:Originally posted by lightarrowIf you are assuming that Hook's law and F = m*a law are Lorentz-invariant, it's not so.I am not sure what you mean by the laws not being Lorentz-invariant.Clearly, F=M*A would be modified by the change in mass effected by relativity, but otherwise, are you saying that taking into account that change in mass, there are other relitavistic changes that invlaidte the direct proportionality?
quote:Originally posted by Solvay_1927The 50km track along which the twine has been pulled has 50 million miniature hammers along it, and these hammers are set to all snap shut at exactly the same time (at a time much greater than 50,000/59.96 seconds in the scenario you've just described, to ensure that Albert has definitely got well past the 50km mark)(Note: the hammers slam shut simultaneously according to my frame of reference.)And while the twine is trapped inside these hammers, you can trim off the excess twine from either end of the track.Now, when you prise open these hammers, the twine should be 50km long. But will there be 50,000,000 or 50,000,001 knots in it?
quote:Originally posted by Solvay_1927But is there a way to tell that, during his journey, we must have measured different "displacements in space"? Is there something that does the equivalent of a clock, but for indicating past dispacements in space rather than past displacements in time?Paul.
Chicken?Nah.Scared witless is a better description.No, I'm reading you Vern, but this is where I'm 'stuck' for the moment.Don't worry man, your time will come too Ps: are you saying that Einstein didn't accept Lorenz contraction as being 'real'?"It's either all space-time, or all matter distortion"