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Grimble
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In http://www.bartleby.com/173/12.html" Einstein says the following:
But what is he saying here?
That 1 proper second in the reference frame K is equal to gamma proper seconds in the moving frame K0, leading to the conclusion that the seconds in K are larger than the seconds in K0 and that therefore the moving clock slows?
No it isn't that, for the proper seconds in K0 have been transformed by the application of the Lorentz Transformation equations into coordinate time (as we term it), so he is saying that 1 proper second in the reference frame K is equal to gamma coordinate seconds in the moving frame K0.
So Einstein is actually describing a conversion from one set of units to another; that conversion being performed using the Lorentz Factor.
And does the moving clock slow? Well, no, for what we see is that 1 unit of time in the reference frame K is equal to gamma coordinate units, so if anything one would say that the moving clock goes faster, albeit in smaller seconds.
Grimble
Let us now consider a seconds-clock which is permanently situated at the origin (x' = 0) of K'. t' = 0 and t' = 1 are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks:
t = 0
and [tex]t = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]
As judged from K, the clock is moving with the velocity v; as judged from this reference-body, the time which elapses between two strokes of the clock is not one second, but [tex] \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]
seconds, i.e. a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest.
But what is he saying here?
That 1 proper second in the reference frame K is equal to gamma proper seconds in the moving frame K0, leading to the conclusion that the seconds in K are larger than the seconds in K0 and that therefore the moving clock slows?
No it isn't that, for the proper seconds in K0 have been transformed by the application of the Lorentz Transformation equations into coordinate time (as we term it), so he is saying that 1 proper second in the reference frame K is equal to gamma coordinate seconds in the moving frame K0.
So Einstein is actually describing a conversion from one set of units to another; that conversion being performed using the Lorentz Factor.
And does the moving clock slow? Well, no, for what we see is that 1 unit of time in the reference frame K is equal to gamma coordinate units, so if anything one would say that the moving clock goes faster, albeit in smaller seconds.
Grimble
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