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Ed Greenberg wrote:

> I think it's called the Clock Paradox (not to be confused with
> the Twin Paradox), so the first question is whether I've got the name
> right.  The paradox is as follows:
> We imagine two inertial frames in relative motion, e.g., two trains
> moving in opposite directions at the same constant speed. Applying SR
> (perhaps erroneously), we could conclude that each frame's clock must
> be going at a slower rate than the other frame's clock since each
> frame can be assumed to be the rest frame; i.e., by symmetry, each
> frame's clock can be argued as moving at a slower rate than the other
> frame's clock.
> So the second question is this: Is the
> foregoing conclusion truly paradoxical if the clocks haven't been
> juxtaposed?  That is, is there anything fundamentally awry with SR
> seeming to imply that each clock runs slower than its counterpart (on
> the other train) if the clocks are not brought together for a direct
> comparison?
> Now we can be fairly certain, using another argument, that both train
> clocks run at the '''same''' rate. To show this, we can compare each train
> clock with '''one''' ground clock. Each train clock will run slower than
> the ground clock (from the POV of the rest frame of the ground clock)
> as a function of the relative speed of the moving frame with the rest
> frame. Since the identical argument can applied to each clock moving
> with each train, it's clear that both train clocks run at the '''same'''
> rate (albeit slower than the ground clock) since the time warp doesn't
> depend on relative velocity of the frames, but only on their relative
> speeds.
> If the latter argument is correct, what is the flaw in the
> former argument showing that each train clock runs at a slower rate
> than its counterpart on the other train?
> Ed

You have heard the expression no doubt, that one bad JimScarver picture (not to scale) is worth a gazillion misspelled words.

In SR or QET you can use future cones of LightCones to help understand what is happening.

Each ReferenceFrame thinks the base of it's future cone, the space dimension, is level, and the time dimension vertical. But moving reference frames are titled with respect to on another.

So tilt your monitor sideways to see a moving frames point of view.

Two trains are traveling in opposite directions away from each other along the same track.


(Units should be light years and years or the speed of light is one mile per hour)

In SR each train thinks the others time dimension is for shortened since it is tilted with respect to their own. Each others time dimensions are tilted across each other space dimension so there is no paradox. We only think there is a paradox if we think someones clock is really running slow. NO clocks run slow, they all run at normal time. It is simply that space is a manifestation of time and moving trough space relative to something else advances your time relative to them.

Let's complete the the example.

Suddenly, at 2 years, train B changes direction and speeds toward train A. At about 7 by the station clock they crash and plow into the station.

Train A says it is only 5 by their clock since they experienced 2 years of station A space instead of station A time.

Each observer thinks the tracks are on their own baseline and expects other perceive time and space the same same as they do.

Now tilting so train A's path is vertical, we see that train A thinks that B's path started at about -2 years and he changed directions at -1 years. (B also thinks A started at -2 years). B's path experienced about 4 years of A's space instead of time (about 1 to the right, and 3 to the left). So B's time to the crash is just one hour.

Going back to the station perspective, A experiences about 6 years of station A space instead of time, still one hour. Any frames we choose have a self consistent experience.

In the QuantumEventTimeSpace model, all clocks run at normal speed. We know that the clocks at each end of the railway, although they are in the same reference frame are independent, and event ordering may be experienced either as time or space depending of your relative motion. Distance between objects is really the manifestation of the event orderings they disagree with.

Disagreement on event ordering go back to electron integration where "space" is manifest by the exchange of a photon (discrete state change information), generating two perspectives which both perceives that it received a photon from the other. Once an object see an event it is gone, and in the past whether it was a simultaneous interaction or not. The space between object is the measure of the number of event which they disagree on the ordering of. This defines the relation between time and space.

To picture this think of lights turning on simultaneously all along the tracks, each train sees the closest lights come on first. The distance between the trains is proportional to the number of lights they disagree on what order they came on. Take away the lights and there are still a gazillion events, light hitting the tracks, atoms interacting in the tracks, etc., which they perceive in a opposite ordering.

To move from one frame to another an object must cross an event ordering disagreement. This in effect, destroys the time delay that existed between the frames, advancing the object into the other frames future since only events orderings consistent with both the original frame and new frames are possible.

Ok, each clock generates events independently and both train clocks slip into the future with respect to the originating clock as they travel toward the opposite clock. If the trains only go the same distance at the same speed an encounter each other again their clocks will match.

All clocks are independent by t=d/c where the distance, d is an absolute value, moving relative to a clock advances your time relative to that clock, and there is no universal time reference frame or absolute clock.

How can you prove or disprove that there is no absolute clock? It seems to me, that we cannot do this. This is a situation where we could arbitrarily pick a reference frame as 'the absolute', or we can ignore it (if one were to say, exist) and it would not matter. This is a logical system that works equally with or without one.

And I think that one could argue, or choose to view, the universe itself as a clock. Since events are merely the tick-tock sequence of a timeline/clock, then the universe itself, taken as a whole, becomes one large and complex clock.

Jim, please note: I'm not out to prove an absolute clock or frame of time reference, I'm just asking, as this seems to be a logical case where it doesn't matter. All time lines are their own zero frame, and all other time lines are relative to their zero frame. Logically, it seems that we could just as easily pick Big Ben as the 'zero frame-line'. You know, name our zero point, just as was done with Longitudes on Earth. Is this just a matter of following Occum and his razor?

Good point Star. I will give a description of UMT (Universal mean time) when I have a minute to spare to show why it won't work very well at all. They have discovered a "special" frame of the cosmic background radiation. Since enerbody can "see" this frame it would be the most ideal, but it still would be very confusing. This has implications for physics in general and the philosophy of science. -- JimScarver

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