tar Posted June 30, 2017 Posted June 30, 2017 So is there any miniscule amount of length contraction/time dilation that the pellet will undergo in the direction of fire that would not occur in the vertical direction, that could be measured and determined shorter and quicker for the pellet that traveled?
swansont Posted June 30, 2017 Posted June 30, 2017 So is there any miniscule amount of length contraction/time dilation that the pellet will undergo in the direction of fire that would not occur in the vertical direction, that could be measured and determined shorter and quicker for the pellet that traveled? Not measurable at these speeds. The effect is of order 10^-11
Delta1212 Posted June 30, 2017 Posted June 30, 2017 So is there any miniscule amount of length contraction/time dilation that the pellet will undergo in the direction of fire that would not occur in the vertical direction, that could be measured and determined shorter and quicker for the pellet that traveled? Even if it could be measured, any relativistic effects in the horizontal direction wouldn't effect the vertical motion, which is still the same for both pellets.
tar Posted June 30, 2017 Posted June 30, 2017 Except how can the pellet experience less time in one direction than the other? If you fired a highly polished and reflective spherical pellet through an evacuated track, to a very tiny degree it should look like an oblate spheroid to the rest frame, right? Could you not aim various lasers from various angles at a point in the track where the pellet will cross, and judge by the landing spots of the reflections, on screens very far from the pellet, for leverage, the oblateness?
Delta1212 Posted June 30, 2017 Posted June 30, 2017 Except how can the pellet experience less time in one direction than the other? If you fired a highly polished and reflective spherical pellet through an evacuated track, to a very tiny degree it should look like an oblate spheroid to the rest frame, right? Could you not aim various lasers from various angles at a point in the track where the pellet will cross, and judge by the landing spots of the reflections, on screens very far from the pellet, for leverage, the oblateness? Time dilation affects the time experienced by the bullet as compared with other frames, not the velocity that other frames see it moving at.
Strange Posted June 30, 2017 Posted June 30, 2017 (edited) If you fired a highly polished and reflective spherical pellet through an evacuated track, to a very tiny degree it should look like an oblate spheroid to the rest frame, right? Could you not aim various lasers from various angles at a point in the track where the pellet will cross, and judge by the landing spots of the reflections, on screens very far from the pellet, for leverage, the oblateness? In principle yes (although I have no idea what this has to do with the subject). And this is confirmed by experiments in particle accelerators. Edited June 30, 2017 by Strange
imatfaal Posted June 30, 2017 Posted June 30, 2017 If you fired a highly polished and reflective spherical pellet through an evacuated track, to a very tiny degree it should look like an oblate spheroid to the rest frame, right? Could you not aim various lasers from various angles at a point in the track where the pellet will cross, and judge by the landing spots of the reflections, on screens very far from the pellet, for leverage, the oblateness? In principle yes (although I have no idea what this has to do with the subject). And this is confirmed by experiments in particle accelerators. I am not convinced you and Tar are right there. The sphere is length contracted but very odd things happen when you "look" at it - light (very fast as it is) still has a finite transfer time, and when you are "looking" at something which is moving at a sizeable fraction of the speed of light one must not think of transmission as instantaneous. If I have remembered correctly a sphere being observed will appear to be a sphere rotating (the direction of rotation is as if it is rolling along a floor and we are looking through the floor). The phenomenon is called Penrose-Terrell rotation. NB this is just what the sphere looks like to an observer - it is actually flattened
Strange Posted June 30, 2017 Posted June 30, 2017 Sigh. You are absolutely right. Again. I had forgotten about Terrell rotation. But, as you say, even though it ends up not looking oblate, it is. As shown by scattering in particle accelerators. http://math.ucr.edu/home/baez/physics/Relativity/SR/penrose.html
Mordred Posted June 30, 2017 Posted June 30, 2017 (edited) Nice..that link happens to have a decent breakdown of the SO(2) doublecover. Though obviously not as detailed as I personally would like 😎 Edited June 30, 2017 by Mordred
swansont Posted June 30, 2017 Posted June 30, 2017 Except how can the pellet experience less time in one direction than the other? If you fired a highly polished and reflective spherical pellet through an evacuated track, to a very tiny degree it should look like an oblate spheroid to the rest frame, right? Could you not aim various lasers from various angles at a point in the track where the pellet will cross, and judge by the landing spots of the reflections, on screens very far from the pellet, for leverage, the oblateness? Not measurable at these speeds. The effect is of order 10^-11
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