I was listening to a podcast (Ask a Spaceman), and he was going on about how clocks register time more slowly when traveling faster than the “stationary” clock on earth. Brittanica.com says this:
“The clock paradox effect has been substantiated by experiments comparing the elapsed time of an atomic clock on Earth with that of an atomic clock flown in an airplane.”
But the clock on earth is moving. Sources vary, but it appears that the earth is traveling around the sun at about 66,000 MPH. I realize there are other variables (sun around the center of the gallery, galaxy towards the Great Attractor, etc), but for now, let’s just consider it’s course around the sun.
Suppose we have 2 atomic clocks set to the same time. One stays on earth and we launched one clock off of earth in the opposite direction of its rotation around the sun. It seems like that clock would register time faster since it would be going slower than the clock on earth (relative to it’s speed around the sun).
Going “slower” relative to what? Seems like you have a preferred frame of reference baked into your assumptions.
If your frame of reference is the clock on earth, the velocity effect will have the other clock seem to tick slower because it’s traveling at high speed away from your reference frame (the clock on earth, which is standing still and the other clock is moving away).
Likewise, from the perspective of the other clock, the clock on earth will seem to tick slower because it’s traveling at high speed away from its reference frame (in which the earth is moving away at high speed and it is standing still).
That is, until things circle around and they’re moving towards each other again.
This seems like a classic issue of properly defining the frame where you want to measure things from.
Notice the sun doesn’t matter here. Earth’s velocity relative to the sun is exactly that - relative to the sun. If you are measuring using the clock on earth as your frame of reference, referencing your own velocity against the sun is a contradiction.
If your reference is the sun, both clocks have equivalent velocity, so from the reference of the sun, both clocks around circling the sun and show the same time dilation effects due to velocity from the perspective of the sun.
Also, to complicate the issue, don’t forget there are gravitational effects in relativity as well. Having the second clock merely in orbit and not moving away from earth will have it tick faster from the perspective of the clock on earth, even without considering velocity. GPS accuracy relies on taking both velocity and gravitational corrections into account.
If you just have two observers with clocks moving relative to each other, at constant velocity, then the two observers will disagree over which one is slower. And as long as that’s all they do, it won’t matter that they disagree.
They only have to agree if they later come back together again. But in order for them to do that, they can’t both be going at constant velocity. One or both of them is going to have to turn around to make that possible. And so now there’s an asymmetry: The one who turned around will be behind the one who didn’t turn around.
It’s stated in my OP:
“It seems like that clock would register time faster since it would be going slower than the clock on earth (relative to it’s speed around the sun).”
I don’t see how this is possible. If one clock is on the earth, and one clock is travelling 66,000 mph in the opposite direction of earths rotation, wouldn’t that clock appear to be stationary from the sun’s point of view?
Maybe I misunderstand the clock experiment. I thought they had one clock on earth and jetted one around, when that clock came back, and the clocks were together again, the one that jetted around showed a lag. Is that not right?
Well, no. Earth is a tiny rock revolving around the sun. It’s constantly in motion from the perspective of an observer on the sun. If it wasn’t, it would fall directly into the sun due to gravity.
It’s exactly like the moon from earth. The moon is constantly revolving around earth.
It’s only from a perspective on earth itself that the clock is stationary.
I recently watched a dumb movie via MST3K (is there any other kind?). The premise was: Two spaceships, one in front, travelling close to speed of light. Three light-months behind, another spaceship that has crashed onto a planet.
First ship retraces its figurative 3 light-month steps, finds crashed ship. Inhabitants of crashed ship are dead, but male offspring is now grown up into a young man due to “time dilation.”
Except their version of time dilation is because the planet circles its sun more quickly than earth, so the years pass by more quickly. Nothing to do with relativity. I was SO ANNOYED.
But: according to relativity, how much of a time difference would there be with a 3-month “backtrack” at close to speed of light? Is that calculatable?
Uh… 3 months. Or do you mean that the 3 light-months was in another frame of reference and the forward spaceship was halfway across the galaxy when it turned around? (Due to length contraction/time dilation, you can get arbitrarily far in 3 months if you go fast enough, so that 20 years or whatever have passed on the planet by the time you get back.)
I think that the idea is that one ship is 3 light months ahead of the other ship, when it finds out that the other ship has crashed. It turns around and comes back to the crash site.
This has a number of issues, like how did anyone survive a crash at relativistic speeds, or even how a planet survived being hit at relativistic speeds, and also how much delta V the lead ship had to be able to make such a maneuver.
But, if you had those numbers, then you could work out the time experienced for all parties.
See, that would make so much sense, if they had just handwaved it as "Well, it was three months for us, but due to the distance/speed we travelled, 18 years have passed on this “stationary” planet. But nooooooo, it’s because of the speed of orbit.
Spoiler alert: one of the rescuing female crewmembers stays with the all-growed-up boy … and the name of the planet is EARTH.
The limit is to be at rest with respect to the proper motion of space itself. The closest approximation to this would be to be at rest with respect to the CMB. My understanding is that something that had been at rest wrt to the CMB since the beginning of the universe would have experienced about 30,000 years more than someone moving with the general motion of the Earth. I’d cite it, but I can’t find one right now, but that figure is something I’ve heard on a few podcasts of respectable physicists like Sean Carroll.
However, if you sent a probe out to “slow down” and come to rest wrt the CMB, you would watch its clock slow down as it sped away from you. When it returns, you will see that less time passed on it than passed for you.
What if we sent the probe to “slow down” and stay there and just transmit clock readings back to us? Does the transmission time and red shift alter the readings? I mean, if the probe says it is “now” x-time what is “now?”
Sorry if that is unclear (my fault). Let me know if if should try to be more clear or just give up.
The CMB, as far as we know doesn’t affect the predictions of special relativity. It just has the interesting effect of providing a frame of reference that is definable across the universe. But is otherwise unremarkable.
When you take the expansion of the universe into account the universe is expanding isotropicly around the CMB. But this is only meaningful in intergalactic space where there is expansion of space. Nearer to home it is just yet another undistinguished reference frame.
The clock experiment is a bit more nuanced. The original done by Hafele and Keating flew clocks both east and west as well as keeping two on the ground. The centre of the Earth defined the inertial frame of reference. This is partly because the centre has no net gravitational field. Whereas the surface of the Earth is not an inertial frame of reference because we are immersed in the gravitational field pulling us down.
The experiment has to take account of time dilation in the gravitational field (time speeding up with altitude) as well as relative motion. So both special and general relativity. The clock on the ground is moving in this analysis with the travelling clocks moving faster and slower depending on which way they moved relative to the Earth’s rotation.
The plane’s speed was low enough that the time dilation with altitude was very close to cancelling out the dilation with motion when opposing the Earths rotation. Faster planes would start to allow special relativity effects to dominate. But I doubt an SR-71 was available.
It just occurred to me to recommend Einstein’s Dreams by Alan Lightman. It doesn’t explain anything, but is a lovely set of somewhat surreal short stories set in universes where relativity meets daily life. Ages since I read it. I’ll should get it out again.
In order to come to rest wrt to the CMB, it would have to speed away from us at a fairly high speed, so we would see its clock tick at a slower speed. It would also see our clock tick at a slower speed.