On 2/1/2020 10:28 PM, Alan Grayson wrote:
On Saturday, February 1, 2020 at 11:12:01 PM UTC-7, Brent wrote: On 2/1/2020 6:45 PM, Alan Grayson wrote:On Saturday, February 1, 2020 at 3:04:16 PM UTC-7, Brent wrote: On 2/1/2020 12:11 PM, Alan Grayson wrote:On Saturday, February 1, 2020 at 6:49:40 AM UTC-7, John Clark wrote: On Sat, Feb 1, 2020 at 7:41 AM Alan Grayson <[email protected]> wrote: />But what if the CMB _is_ the local clock? / I'm not sure what you mean by that, but if all the hemispheres of the CMB look about the same to you then you'd know you're motion was about the same as the average motion of matter in the universe, if the hemispheres looked radically different then you'd know you were moving at a different speed than most matter in the universe. But so what? If you and I want to compare our local clocks the only relevant factors are our relative speed (Special Relativity) and the relative gravitational fields (General Relativity) we're in, how the CMB looks to either of us is irrelevant. As Brent said "/it's called relativity theory for a reason/". Einstein and even Galileo said if you're in a sealed room moving at a constant velocity you can't tell if you're moving or not, but you don't need to invoke the CMB to know that if you look out a window on a moving train you can see that there is a lot more stuff outside that window than inside the train, and so you could determine you're moving relative to most of the stuff around you. And if I was in a smaller train than you on a parallel track that was moving even faster than you compared to most of the stuff around us then the only thing you would need to know to figure out the time dilation is our relative motion. And both of our local clocks will be different not just from each other but also different from the clock on the station platform. /> How could it manifest time dilation, compared to a clock in some moving frame, if its "clock" reading doesn't change? AG / I don't understand the question. You never see your local clock rate change, you observe other people's local clock rate change. Everything always seems normal to you, it's other people's clocks that behave oddly. John K Clark When you use the Lorentz transformation to calculate the slower clock rate in another frame, what you get is the real clock rate in that frame. It's what the other observer measures, even though that observer notices nothing different. IOW, the calculation of the other observer's clock rate is not just an appearance, but what is experienced by the other observer. Now suppose we have an observer moving wrt the CMB, and the other observer at rest wrt the CMB, what I was calling the local clock. The local clock rate never changes, but it should according to relativity, from the pov of the observer in motion wrt the CMB. AGI think it is unfortunate that the idea of time dilation and length contraction was ever introduced. Just compare time dilation to ordinary Doppler shift. We don't make a big deal of the oscillator appearing slower when it's going away from us. We didn't invent a "frequency contraction" and puzzle over it. We just see it is just a temporal-geometric effect and the oscillator didn't do anything, it didn't slow down or speed up. When someone measures the frequency of an oscillator they would never attribute the measured value to the oscillator without correcting for Doppler due any relative motion that was present. Relativistic effects should be looked at the same way. Time dilation is not a clock slowing down compared to your stationary clock. It is the relativistic Doppler effect due to the two clocks measuring time in different directions. It should not be attributed to the clocks, any more than Doppler shift is changing an oscillator. It's just the paths they take thru spacetime and each one correctly measures duration along their path. How one looks from a different frame is interesting from the standpoint of instruments and measurements, but that's so you can correct for the spatio-temporal effects of motion and curvature, or you can invert the relation and infer the motion and curvature from the effects. But it should be kept clear that the motion and curvature are not effecting anything locally, they are only a relative effect of the intervening space and motion. Brent But the doppler effect is apparent only; it's what the observer receiving the signal measures or perceives; not what is reality for, say, the engineer of the passing train. In contrast, IIUC, the LT tells us what the observer in the transformed coordinate system actually measures, and experiences. AGThe observer in which transformed system? The system of the observer who is moving relative to the thing observed? The Doppler shift tells you what that observer actually measures and experiences. Do you think the engineer on the train (assuming it's closed) hears the Doppler shift? The Lorentz transform tells you what is measured in system by someone in a relatively moving system. It's exactly analogous. Having made an observation of a moving system you can use the inverse transformation to predict what observed moving with the system will see. BrentI don't think so. Not an exact analogy. CMIIAW, but the LT gives the observer using the transformation, what the other frame observer will actually measure; its real value.
Same as when he measures the frequency of a radio wave. It's a real value he measures. But it's not a property of the transmitter. The transmitter isn't affected by this measurement.
What the doppler effect gives is NOT what the train engineer measures or hears, which doesn't change while he moves with constant velocity, but what an observer external to the train measures, which depends on whether the train is coming toward him or receding. Motion in space-time gives the actual total elapsed time of, say, the traveling twin, at any point along his path, namely, the proper time. AG
Right. And the train engineer hears the actual pitch of his whistle at every point along his track. And people on other trains really do hear it differently.
But the simpler analogy for the twin paradox is the example of the car odometers I gave earlier.
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