Twins Paradox - but with a different spin

[PAllen]

Well I guess you have shown that "moving clock is a slow clock" leads to serious difficulties. Well done. This is not sarcasm. Clearly the twins must see the clocks to run identically, and they should see the other's clock as slower.


Let's say you see a moving clock. So it's a slow clock. Well that's ok. But it's also ok to decide that the clock is actually still, and you are moving, which means that the clock runs normally.

The two revolving clocks are both non-inertial, and can readily detect this with local experiments (accelerometers). Thus, neither can use laws in their inertial form to interpret the clock of the other (including the simple rule that clock moving relative to me is running slow), and the Lorentz transform cannot be used between coordinates in which each stays stationary.

See post #20 and #23.

 

[jartsa]

The two revolving clocks are both non-inertial, and can readily detect this with local experiments (accelerometers). Thus, neither can use laws in their inertial form to interpret the clock of the other (including the simple rule that clock moving relative to me is running slow), and the Lorentz transform cannot be used between coordinates in which each stays stationary.

See post #20 and #23.

Well I guess you can use the rule that a clock moving relative to you runs slowly, anytime you never meet with the clock again.

You can't use the rule if you are also doing any kind of checking that the clock really did run slow.

Fine rule indeed. This is sarcasm.

I have a theory about the source of all the confusion: the rule that a clock moving relative to you runs slowly.

 

[ghwellsjr]

Well I guess you can use the rule that a clock moving relative to you runs slowly, anytime you never meet with the clock again.

You can't use the rule if you are also doing any kind of checking that the clock really did run slow.

Fine rule indeed. This is sarcasm.

I have a theory about the source of all the confusion: the rule that a clock moving relative to you runs slowly.

The rule is that a clock moving relative to an inertial Frame of Reference runs slowly. Any number of clocks can be moving or be stationary according to that FoR. It doesn't matter what the relative speed is between them but unless they start out together and end up together, the rates of the clocks will change depending on your selected FoR.

I wouldn't propose or even suggest your own rule on this forum, it's a good way to get yourself banned. This forum is for learning the established theory of relativity. If you don't want to learn and instead promote your own private theory, you are not abiding by the rules you agreed to when you signed up. Just a friendly word of caution...

By the way, if you choose to learn relativity, your confusion will vanish.

 

[jartsa]

The rule is that a clock moving relative to an inertial Frame of Reference runs slowly. Any number of clocks can be moving or be stationary according to that FoR. It doesn't matter what the relative speed is between them but unless they start out together and end up together, the rates of the clocks will change depending on your selected FoR.

I wouldn't propose or even suggest your own rule on this forum, it's a good way to get yourself banned. This forum is for learning the established theory of relativity. If you don't want to learn and instead promote your own private theory, you are not abiding by the rules you agreed to when you signed up. Just a friendly word of caution...

By the way, if you choose to learn relativity, your confusion will vanish.

Here is my own rule: If you think a clock just seems to be moving, because you are moving yourself, then you must stick to that idea, until you feel an acceleration.

If you thought you were standing still before an acceleration, then after an acceleration you must be not standing still.

 

[ghwellsjr]

Here is my own rule: If you think a clock just seems to be moving, because you are moving yourself, then you must stick to that idea, until you feel an acceleration.

If you thought you were standing still before an acceleration, then after an acceleration you must be not standing still.

That's not such a bad rule--I don't think it's the sort of rule that will get you banned--but it's not precise. Here's the way you should think of it:

It doesn't matter whether you think you or the clock is moving, you must choose a Frame of Reference and say whose moving in that frame. If you choose a frame in which you are at rest, then the clock is moving (and experiencing time dilation). If you choose a frame where the clock is at rest, then you are moving and experiencing time dilation (although you won't be able to discern that). You could also pick a frame that was kind of half way between the motion of you and the clock and then you both would be moving and experiencing time dilation although not as much as in the first two cases.

Any time you accelerate from a position of rest within a Frame of Reference, then of course you will be moving in that Frame of Reference.

If you just always think in terms of a Frame of Reference, then you'll have no problem telling who's moving and who's not. Many times people assume a FoR without actually explicity saying so, like when they say "from my point of view" or "in my frame" but the problem is when the use that terminology and then at the same time switch to "in the clock's frame" and imply that you are not in the clock's frame and it is not in your frame. Everything and everybody is in every frame you want to consider and you don't want to share parameters between two frames without clearly saying which frame they apply to.

 

[jartsa]

Do we know the relative velocity that a spinning twin sees, when looking at the other twin?

There is a formula into which we can plug the velocity, and then the formula produces the rate of a clock that is seen by a twin looking at the other twin's clock.

Relativistic Doppler shift is the name of the formula.

 

[plbeale]

Here is an article about an experiment that shows the time shift between two atomic clocks, one stationary and one flown around the world, that were reunited at the stationary lab and compared.

http://www.npl.co.uk/news/time-flies

According to this article, and others I have found, the relative speed causes the traveling clock to run slower and the difference in gravity causes the stationary clock to run slower, because gravity is stonger on the ground. The net effect is that the traveling clock has gained time relative to the stationary clock on the ground, because the effect of gravity, in this experiment, is more pronounced than the effect due to the speed.