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]
<javascript:>> 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. AG
I 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
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