Twin paradox

I join my question with Jim's. How does relative speed decide what clocks run slow, we still need to know how fast each clock is actually going with respect to the light speed: As often claimed, the speed of light is independent of observer velocities, thus in empty space there is no way of knowing which clock physically runs slower than the other from a SR traveling observer point of few. Can a traveling object measure it's own speed with respect to the light speed? I think that Nature only knows how fast things are traveling through space, and as a result, it imposes restriction on the traveling object. Shouldn't we use a frame traveling with light speed as a reference instead of frames at rest? We simply do not know what rest means. From an LR point of view, Earth is a massive object, and is likely to travel slower through space than fast orbiting GPS satellites, so the clock slowing of these satellites is more likely. In any case, intuitively, I just want to take a prefered reference frame.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Jim]: The relative motion detail is not at all clear to me. How would this kind of motion effect two clocks going the same speed in the opposite direction?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

You have just put your finger on the "paradox" part of the twin's paradox. How indeed? Two answers are available.

(1) In Einstein's special relativity, each inertial frame has its own time. That does not mean simply that time passes at different rates in different frames. The larger effect is what I call "time slippage", which means that when any two inertial frames are compared, either frame will judge that nearby parts of the other frame are experiencing time near the present; that receding parts of the other frame are experiencing time in the past; and that approaching parts of the other frame are now experiencing time in the first frame's future.

When this convoluted picture is worked out, it means that, because time is everywhere different depending on your frame and your speed relative to other frames, it is easily possible for two clocks with a relative speed to each determine that the other is ticking slower than itself. That is what SR is all about.

Part of what SR predicts -- namely that clocks in moving frames do appear to slow down -- has been verified beyond a reasonable doubt in numerous experiments, several of which are sketched in cartoon fashion in our presentation on "Gravitational force vs. gravitational potential" at < metaresearch.org/cosmology/gravity/gravity.asp >. However, fortunately, the SR interpretation is not the only one to make the same prediction.

(2) In Lorentzian relativity, the local gravity field is the "preferred" frame in which clocks tick fastest. For other clocks, it is not their speed relative to each other that matters, but rather the speed of each relative to the preferred frame. Locally, that preferred frame is the "Earth-centered inertial" frame, a reference frame centered on the Earth that does not share the Earth's rotation.

So in LR, if both clocks move in different directions at the same speed relative to the ECI frame (for example, two satellites in the same orbit moving in opposite directions), then each of those two clocks will agree with the other about both time and clock rates.

I know this stuff can be confusing, and even experts disagree among themselves about how to explain things like the twin's paradox. But the essence of the two leading theories can be briefly summarized this way:
* In SR, relative motion alters time itself.
* In LR, motion relative to the local gravity field alters the rate of ticking of clocks, but nothing happens to "time". -|Tom|-

The fact that two clocks moving at the same speed and in opposite directions keep the same time is a very interesting detail and is a paradox itself isn't it? How can time be measured the same at two different locations?

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Jim]: How can time be measured the same at two different locations?<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I lost you. All clocks on Earth are at different locations but are synchronized to read the same time. GPS clocks in a variety or orbits are now synchronized to do the same.

Among the many ways that clocks can be synchronized are these two:
* Each clock can signal the other about its time reading. That signal travels a known distance at a known speed, so the travel delay of the signal is also known.
* One clock can be physically transported to another and back again, so the two compared at convenient intervals.
What is puzzling you about this? -|Tom|-

We seem to have taken a different fork in the road. I was refering to two clocks going the same speed in opposite directions and keeping the same time. If they are moving apart they are in different locations somewhere in the universe and still in sinc while the local time is not the same in both places.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[Jim]: I was refering to two clocks going the same speed in opposite directions and keeping the same time. If they are moving apart they are in different locations somewhere in the universe and still in sinc while the local time is not the same in both places.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

I mentioned two clocks moving in opposite directions only in connection with LR, so I will assume your question is be to answered in an LR context.

In LR, the "local time" is the same everywhere in the universe. Time is unaffected by anything. Clock rates change with speed relative to the local gravity field. The two clocks I mentioned have the same speed relative to the local gravity field (direction does not matter), so they tick at the same rate.

What do you mean by "the local time is not the same in both places"? Or were you thinking about SR instead of LR? -|Tom|-