Stephen A. Lawrence wrote: > > > Harry Veeder wrote: >> Stephen A. Lawrence wrote: >> >>> >>> Harry Veeder wrote: >>>> Could you use this method to test special relativity? >>>> i.e. to see if the speed of the em wave in the wire independent of the >>>> wire's motion. >>> I wish! Trouble is, to get a readable result you need to move the wire >>> really, really fast, and I don't see any way to do that. >>> >> >> Is 100,000 km/h fast enough? >> This is the speed of Earth as it orbits the Sun. >> >> Tests of special relativity make use of the this motion, but the results >> depend on interference effects. > > Actually those are attempts at finding an aether, rather than tests of > SR per se. SR predicts that it makes no difference how fast we're going > around the sun, so such experiments should come up null.
Strictly speaking it is simply an attempt to show that the the SR rules for adding velocities (the Lorentz transforms) do not cover all situations. > The problem is that the aether theories predict that, by going and > coming along the same path -- as you need to do to get back to the > detector -- the effect of motion through the aether will cancel to first > order (one way's fast, the other way's slow); the effect looked for is a > second order effect (second order in velocity through the aether). This is the situation when the emitter-detector and the reflector are moving together at the same speed. However, if the reflector and the emitter-detector are moving towards each other or away from each other at a given relative speed, on the return path the difference in signal speed will be magnified. > Consequently it's really, really small, and is checked for, as you say, > using interference effects with light; radio waves would have > wavelengths far too long to achieve sufficient sensitivity. > >> >> If the wire loop is elliptical instead of circular, special relativity >> says the speed of the em wave would be the same whether the major axis >> of the loop is aligned parallel or perpendicular to the direction of the >> Earth's motion. > > Exactly. But what I'd _really_ like to do is observe an effect > predicted by SR, rather than not observe an effect not predicted by SR. I am puzzled by this remark. I always thought a prediction of SR is that c is a constant (in a vacuum) . > (For one thing I find aether theories highly unconvincing, right off > the bat...) > SR makes some cool predictions, but they require horrible speeds to see. > For instance, the value of a resistor supposedly depends on how fast > it's moving relative to you -- it would be lovely to check that > prediction! A fast centrifuge, with slip rings for the electrical > connections, leaps to mind as one approach. > > But as usual the change in value goes as gamma (or maybe gamma^2, I'm > not sure about this one off hand), and > > g = sqrt(1/(1 - v^2/c^2)) > > or, in the low speed limit, > > g = 1 + (1/2)(v/c)^2 > > or, again for "low" speeds, > > v = c * sqrt(2(g-1)) > > If we want something easily detectable in a typical basement setup, we'd > want to have gamma vary by at least a tenth of a percent. But then we'd > need to have v/c on the order of 4%. And that's about 12,000 km/sec, > which is about 1000 times Earth-surface escape velocity; no present-day > centrifuge is going to come close to that, and slip rings are likely to > be awfully noisy at that speed, if they don't melt outright. :-( > > That v^2/c^2 term is a killer; we need to boost sensitivity by two > orders of magnitude to reduce the velocity by 1 order: to get an effect > of 0.001 %, or a ratio of 0.00001, we'd still need a velocity of 0.4% of > C -- 1,200 km/sec, or about 100 times escape velocity. The dictates of mathematics... :) Harry
