A and B start out right next to each other, with precise, synchronized clocks. A starts moving faster than B, and later on they get back together. Relativity says that because A was moving faster, time slowed down, and when they compare clocks, less time will have elapsed on A’s clock than on B’s clock.
I think that is correct so far. So here is my question:
Who is to say that A was really moving faster than B? Maybe A was really staying still, and B was moving in the opposite direction! This is a major point of relativity, isn’t it?
So what’s the deal, here? If one clock can be shown to go slower than another, then wouldn’t it be possible to set up a system of clocks moving in various directions, and then figure out which one was really and truly motionless, relativity be damned?
I Don’t remember the stuff as well as I should, but I think a big factor is the inertial framework. If I understand you correctly, when they started going they each experienced acceleration, then one was accelerated more than the other. So you could actually tell that A was moving away from B, rather than vice versa, because within their shared inertial framework A experienced a greater acceleration. Their initial motion can be discounted and they can be said to be stationary relative to each other, but then a accelerates to get a head, then experiences - acceleration to get back. B doesn’t. Relativity always takes into account the inertial framework of the observers/objects.
I’m sure there’s more that could be said, but that’s what springs to mind as a basic answer.
I’m not sure if there is a correct way to explain it or if I can even do a good job.
What you’re talking about is an inertial frame of reference which applies to Newtonian physics. If you’re standing in a train car you’re in a different frame of reference than you would be on the ground. A game of ping pong played on the train would look “wrong” to an observer on the ground if the train were somehow invisible. etc. etc.
Relativity throws a few different rules on the idea of a frame of reference or even “fixed” space. I am not able to give a short explanation. If you can find a physics text the Mitchelson-Morley interferometer experiment will be a good place start.
I follow you, Woodja, so I’ll clarify my question.
A and B both start out in New York and end up in London. A flies at 600 mph relative to the earth, B flies at only 500 mph relative to the earth. When you add in the earth’s movement (through the solar system, galaxy, and universe) we don’t really know which is moving faster. We expect that A is moving faster, and that A’s clock will register less time. But let’s say that the earth is actually moving through the galaxy in a London-to-NY direction at 900 mph, and that explains our surprise when we find that A’s clock (which was moving at only 300 mph) really shows more time that B’s clock (which was moving at 400 mph).
I should not have given a half answer but I’m already in over my head so here goes. Relativity does some funny things with space/time and mass/energy that don’t make a whole lot of sense in Newtonian physics.
Imagine a flowing river with an anchored buoy in the middle. We have a motorboat that makes a run up a mile then back to the buoy. Now the boat makes a run across the river with a path exactly 90 degrees to the river flow one mile (it’s a big ass river) and back to the buoy. The second trip took longer because the had to travel the two miles relative to the earth but a longer distance in the moving water so it would not drift downstream. We can use the time difference between the two trips to calculate the speed of the river relative to land.
The MM experiment tried to do the same thing with light bounced off distant mountains to measure the speed of the earth through space. The velocity of the surface of the earth around its axis or around the sun should have been easily measurable with the doppler effect but the results showed no such effect of moving through any fixed frame of reference no matter what direction the earth was going. That didn’t make sense.
One possible explanation is that the earth is in fact fixed in the universe and everything moves around it. Call it a hunch but I don’t think so. What relativity says is that what appears to be the Doppler effect (rising/falling train whistle pitch) is not that but something that appears to be exactly like it because of the way moving objects play havoc with time and space.
It blows my fragile little mind every time I think about it but taken all together relativity makes sense.
My Jesus fish can beat up your Darwin fish but forgives it instead.
In order to compare the clocks, you have to bring them together. To compare the elapsed time, you have to bring them together at both the start and end times. They can’t both be moving at a uniform velocity; at least one of them is accelerating. If one of the clocks isn’t accelerating, it will run the quickest. If two of the clocks are not accelerating, but are moving relative to each other, they can only come together to be synchronized once, not twice, so you can’t get an ellapsed time from them.
I don’t think that’s the correct way of looking at it. Remember that from A and B’s point of view the motion they share is inconsequential. That is, the motion of the earth, the solar system the galaxy, etc. do not come into play because A and B exist within that inertial frame of reference. As far as they can tell they are totally at rest except when they are accelerating and decelerating (unless they look out the window). A accelerated up to 600 mph, then decelerated back down to 0 (or, if you like, decelerated down to 300 and then accelerated back up to 900), while B experienced less acceleration (decelerated down to 400 then back up to 900, a smaller delta V you’ll notice). Within their shared inertial framework A still went faster; regardless of what the rest of the universe was up to, A’s clock is slow compared to B, and both are slow compared to C, who stayed behind in New York (Lord knows why).
That said, there is a part of it that I’m not sure is right. Maybe the clocks will read the same, because though A went faster, B went longer, so there was longer for any putative time dilation to occur. I don’t remember the specifics well enough, and I don’t have any references handy.
If I may skip past all the posts in this thread and respond directly to Keeves’ first post…
To put it simply, you have already given yourself the answer when you stated your question. At the moment you said “A starts moving faster than B”, you have assumed the position of a stationary observer in the inertial reference frame where A and B were synchronized at first. So who is to say A was moving faster than B? It’s you of course. That’s also why you can’t say A was stationary and B was moving in the opposite direction (unless you lie to yourself of course).
So the deal is, you can gather as many clocks as you want, send them out at various speeds, directions, and take different routes. When they return to you, so long as you have remained stationary in your own inertial reference frame, then all the clocks you have sent out will be slowed in comparison to that clock you have carried with you. Those clocks that have been slowed the most will be the ones that have traveled the fastest overall. Those that have been slowed the least will be the ones closest to your definition of motionless.
With regard to the OP, I was reading “The Elegant Universe” by Brain Greene and there, at least as far as I can tell with my limited grasp of physics an example of this with two observers. Greene uses the example of two astronauts floating in the void (no reference point) with clocks on their chests that pass each other in space. In one example, one astronaut is stationary and one is moving; in the other scenario both are moving towards each other and then they pass and move apart. In both cases, if you were one astronaut and observing the other, you would still see the same thing-another astronaut approaching with a clock on his chest that draws near and then passes you. No matter whether you were stationary or moving-both see the same thing.
I don’t have the book with me, but I remember it has to do with how the information of the clocks is transmitted to the other observer. I’m over my head here, but if you’re the moving astronaut and you’re reading the clock of the stationary astronaut as you recede, his clock appears to run slower-but you would think it runs faster, since he’s stationary. Something like it takes the information from his clock longer and longer to reach you, so his clock ticks slower from your perspective but yours runs a the right speed since it moving at the same speed you are. A third observer next to the stationary astronaut would see your clock running slower and his as normal.
Greene only used two observers/astronauts to keep it simple for the laymen like me and I’d still have to reread it. Some of the physics guys could expand on this for multiple observers, I’m sure.
The main point of general relativity though is that you can use any frame of reference, inertial or noninertial, A’s or B’s, and the results will still be the same (one will be “older” than the other) of course.
This may not help, but as Feynman puts it, there is always a preferred frame of reference implied when this question is asked. You can’t ask it without one.
It’s a neat question, because it shows a lot about our models for understanding the universe, and even our imperfect perception of motion.
An observer standpoint is always implied. There’s no question without one. Once there’s a standpoint there’s no question about which clock is moving and which is still, or the relative motions of both clock’s.
In short, the question you are trying to ask, can’t actually BE asked, so it doesn’t need answering.
I’m sure that helped a lot.
If you think about it for a while it kind of comes to you in one of those “A-Ha!” experiences.
General relativity denies the need for preferred reference frames. The results are the same no matter which reference frame you use, inertial or noninertial. So, pick one, the answer is the same no matter which one you pick.
He means that one of the frames of reference is used as the standard against which the other is measured. You stay on earth, your twin goes to Alpha Centauri and back. Earth is the preferred frame. It has nothing to do with an absolute preference.
The answer has already been given several times, but it may be worth trying to clarify a bit more.
The situation you describe is not symmetrical. In order for the two clocks to start together, then move apart, then come back togeteher, there must be acceleration. The acceleration allows us to unambiguously detect which one will run slower.
If there was no acceleration, and at some time the clocks happened to be in the same place at the same time and indicate the same time reading, then they would be separated at all other times and could not be compared without transmitting a signal. In this circumstance, the result of the comparison will differ depending on which reference frame you use for your calculations. IOW, if you calculate in A’s reference frame, clock B will be slower and vice versa.
Okay, I think Scylla’s explanation made more sense then mine. It’s * all * in your * mind *, Keeves
RM Mentock is correct about the choice of reference frames too. It’s just that non-inertial reference frames have the tendency to become troublesome in calculations, so they aren’t usually employed.
Good morning all. RM Mentock’s links, as posted last night at 10:51pm, are as satisfying and complete as I am interested in. Thank you for posting them.
Anyone who passed over them without bothering to click, you’re missing out on something good!
You musta knocked off a piece there. I don’t have a copy of that book, but isn’t it just six of the Lectures on Physics? Which six? Anybody know?
<font color=#DCDCDC>Jack Nicholson/Karen Black
rocks</font>
