Monday, September 6, 2010

Resolve to the Twins Paradox – Frame of Origin

I have read many arguments concerning the issue of the famed “Twin Clock Paradox”. Very many arguments go through considerably complex explanations so as to defend Special Relativity or dispute it. But the explanation is actually much simpler.

In every proposed twins paradox, there is a Frame of Origin. The frame of origin is where the twins were at rest with respect to each other and to where they return. In the original scenario, that was “the Earth” and is referred to as “the inertial frame”.

It is called “the inertial frame” because it is the one frame declared “inertial; not movable”. But the issue comes to mind as to how either frame can be considered the one that isn’t moving. SR declares that such a notion is irrelevant. But if it is ignored, an apparent paradox arises.

So as to clear up the picture a bit, let’s presume that neither twin stands perfectly still, but rather one twin (Twin A) just very minutely drifts away from the Frame of Origin while the other twin (Twin B) takes off in his ultra fast rocket. This is merely to provide distinction and reveal that there are always 3 frames involved.

And further, so as to get away from the complexities of gravitation issues, lets put them out in space originally standing on a small floating space station far away from any gravity field.

The time dilation factor is always applied to whichever one leaves the Frame of Origin.

Twin B gets in his rocket and rockets away. Twin A gets into his rocket and sticks ores out his windows and begins to row hoping to catch a few gas particles drifting by from Twin B’s exhaust.

If we apply the time dilation to the one doing all of the serious moving, Twin B’s clock will run slower and he will age less. We cannot simply reverse the reasoning and say that it is all relative because Twin A is not moving away from the Frame of Origin.

That is pretty much the end of the story, but…

Some scenarios remove any sign of the Frame of Origin so as to make their point clear. The problem is that in every case, there must always be a Frame of Origin where their clocks were staying in sync whether anything is standing as a sign of it or not. If two items are moving away from each other, there must be a frame indicating a synchronized clock situation. The issue becomes how to find out where that frame would be.

If the ships merely see nothing but each other separating, they might not know which is accelerating from the Frame of Origin, but that is only a matter of their awareness. If they later find that one has greater time dilation than the other, it can be deduced as to which was accelerating more from the Frame of Origin.

If they see no difference in their clocks, then they can deduce that they were both leaving the Frame of Origin merely in different directions.

Without determining the Frame of Origin, the Twins cannot know which of them will age more until they meet again.

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