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Meir Achuz

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It is not a paradox, unless you don't understand it.

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russ_watters

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Currently, there are 24 GPS satellites circling the globe (plus, iirc, 4 spares) at various orbital inclinations. Each contains a clock(actually, 3 clocks, iirc) superior to the ones used in the 1971 experiment and since each is going ~40x faster and flying 10x higher than the planes in the 1971 experiment, the Relativistic effects are far more pronounced. The GPS system verifies the predictions of Relativity to an extremely high precision.

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Almost all authors agree there is no paradox - but there is much disagreement as to why.

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ahrkron

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There are different ways to explain the effect, but there is no disagreement on the fact that it comes from relativity.yogi said:Almost all authors agree there is no paradox - but there is much disagreement as to why.

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I believe that yogi is attributing properties to clocks that they simply don't have, and that his search for a "physical" explanation of their behavior is based on the faulty assumption that two clocks following a different path "should" both read the same time when they next meet. There is no reason to suppose that clocks have or should have this property, though in older Newtonian theory clocks did have this property.

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Sometime back on another thread I raised the question re the mechanism that produced actual time differences - you posted a short explanation which much intrigued me - then the thread went off in a different direction. I would appreciate your reiteration of that idea - and perhaps some additional embellishment.

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Hurkyl

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Suppose I had marked two spots on the floor, and I had drawn two different paths that led from the first spot to the second, one a straight line, and the other a semicircle.

I find two people who happen to have devices that measure the length of a path, and set them on each path. They roll their device along their path. I claim that the devices will give different readings: the device rolled along the semicircle will measure a greater distance than the device rolled along the straight line.

Would you object that I have not given a physical mechanism that produced an actual difference in the measurements of the devices? Would you take this as a flaw of Euclidean geometry, and any physics based upon it?

The situation with clocks is similar. Wait, that's misleading... it's

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"Laws of nature are the same to every inertial observer".yogi said:

This is the basic postulate of SR. The value of the interval (or the speed of light, c) has to remain constant to every observer, no matter what their relative speed is. Otherwise laws of nature would be chaotic.

For this to be valid, time and distance can't be the same to every observer, but are relative concepts that depend on the relative speed of the observers.

btw. hi I'm new here. Sorry if I don't write perfect english, I'm finnish

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Hurkyl

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The same way that a measuring tapes "know" to give different readings when they measure different paths: the measuring tapes measure length, so when they measure paths with different lengths, they give different readings.how does a clock that is put in uniform motion wrt to another clock to which it has been synchronized know at what rate to run?

In the same way, clocks measure proper time. So, if used to measure two paths along which the proper time is different, the clocks will measure different durations.

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Hurkyl

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If you're going to make these sorts of objections, you had better sayHurkyl - that is a description - I find no fault with the description, but it is not an explanation

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DrGreg

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I have two rulers (measuring rods) and lay one in a north-to-south direction and the other in a northeast-to-southwest direction. How does the second ruler "know" to measure distance travelled northeastwards instead of distance travelled northwards ?yogi said:how does a clock that is put in uniform motion wrt to another clock to which it has been synchronized know at what rate to run?

(The question is, of course, rhetorical. This is another way of saying what Hurkyl just said.)

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As for temporal changes - there is a permanent record - relatively moving clocks log different times, and this time differential can be ascertained when the two clocks are brought to rest in the same frame as per Hafele-Keating. Time dilation is not an fleeting phenomena - this is the significance of Einsteins explanation of the physical effects described in part IV of his 1905 paper - and that is the element that distinquishes SR from all the assertions that it was Poincare or Lorentz or somebody else who should be accorded recognition for the concept - Einstein stuck his neck out and predicted actual time dilation. No one else had the courage to go that far.

My question remains - perhaps it is a consequence of spatial motion relative to Minkowski Spacetime - the problem with this interpretation is that it smacks of a preferred global reference frame.

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russ_watters

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Thereyogi said:The contraction is real only in the sense that the measurements are real, There is nopermanentphysical change as Lorentz proposed to save the ether. [emphasis added]

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Hurkyl

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Given two different trajectories in space-time, the proper time along those paths is generally unequal. Thus, the time measured by clocks traversing each trajectory will generally be different.

P.S. when length measurements of the same "object" are conducted in two different frames, what is actually measured is different for each frame. Thus, just like the clocks, different paths have different proper lengths, and thus the results of the measurement are different.

P.S. when length measurements of the same "object" are conducted in two different frames, what is actually measured is different for each frame. Thus, just like the clocks, different paths have different proper lengths, and thus the results of the measurement are different.

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What is interesting about the development of the conclusions in part IV of the 1905 paper is the shift from observational symmetry with regard to length contraction, to the conclusion that temporal differences are real - and consequently they are "one way" since at the end of the experiment A cannot read more than B and at the moment and in the same frame B cannot read more than A. This all comes with very little comment.

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Hurkyl

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Yes it does: the paths they took are different. The paths have different proper times. Clocks measure proper time.but does this reveal anything about why the two moving clocks do not run at the same rate.

Let's try this from the top.

Space-time is four-dimensional. We have a metric on space-time: the measure of a straight line segment is given by, in any inertial frame: (using the +--- convention, and units where c = 1)

d(P, Q)² = (Δt² - Δx² - Δy² - Δz²)

And through the methods of calculus, we can turn this into an infinitessimal metric which can be used to measure

A bit of work shows that d(P, Q)² is independent of the inertial reference frame used to compute it, thus the metric is a "pure" geometric object -- we can speak of its value without referring to any sort of coordinate system.

When d(P, Q)² > 0, we say that the line segment PQ is

This terminology also applies to curves through space-time where the metric does not change sign.

Now, if we have a point-like object travelling through space-time, its trajectory is a time-like curve, called its

A

So, if I have two (time-like separated) points in space-time, and two clocks follow two different worldline (segments) joining the two points, then they've measured the metric along two entirely different curves, and it should be clear that the circumstances would have to be very special for the readings to be the same.

(Note that in this discussion of travelling points and clocks, I've not invoked a single mention of any sort of coordinates!)

We can draw space-like curves in space-time, and also ask about the lengths of these things.

Measuring the length of an actual object is another question all together. Suppose we have a one-dimensional object travelling through space-time. It traces out a two-dimensional shape through space-time, called its

Now, it doesn't make sense to ask about the length of a two-dimensional shape! However, I can ask about the proper length of a

Now, I'll step back to an inertial reference frame: when we ask about the length of an actual (one-dimensional) object, what we really mean is that we want to compute the proper length of a

Different inertial reference frames have different hyperplanes of simultaneity, and thus will use different cross-sections when measuring the length of a one-dimensional object.

Inertial reference frames are also good for selecting cross-sections of worldlines as well (a.k.a. a point on the worldline). Given a worldline and two values of coordinate time (or hyperplanes of simultaneity, if you prefer), we can speak of the segment of the worldline between those

Note that time dilation is always with respect to

It

This is all

edit: fixed mistake involving the metric

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Hurkyl

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You're right. Except for when I wrote down the formula, I was thinking of d(P, Q)², and not d(P, Q).

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Hurlyl - very good tutorial - I will comment tomorrow when not so tired.

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russ_watters

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dgoodpasture2005, time dilation is observed in clocks that have **no mechanical parts whatsoever**. It is also the same in all clocks capable of measuring it - if it were some sort of "clock effect", different clocks in the same frame would not necessarily agree.

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