Re: The real paradoxes in SR.

To Time Lord:

You wrote: Typically people think that the time dilation formula
should
apply equally to the Twin Paradox. However, SR shows, when it's
correctly applied, that the twin on Earth views the traveling twin's
clock as dilated and the traveling twin views the trip as Lorentz
contracted. The time dilation formula says that time is dilated for
_colocal_ events. Earth and Alpha Centauri are not colocal in the
spacecraft's frame. Thus the time dilation formula does not apply to
the traveling twin.

Hi. I applaud your efforts to defeat these anti-relativity
arguments. I do a bit of it myself. But what you say above is not
quite correct. The time dilation formula does indeed apply to both
twins. Assume A is the Earthbound twin and B is traveling. The
Lorentz transformation for twin A's perspective shows us what B's
clock is reading by comparing A's time to B's. In this case, B's
clock will be compared with an A synchronized clock at B's location.

tB = (tA - vxA/cc)/(1-(v/c)^2)^.5

Since B is traveling at a constant v, xA = vtA so

tB = (tA - v(vtA)/cc)/(1-(v/c)^2)^.5

tB = tA(1-(v/c)^2)^.5)/(1-(v/c)^2)^.5 = tA(1-(v/c)^2)^.5

Since (1-(v/c)^2)^.5 < 1, then B's clock has passed less time than
A's.

Now, B can do the same thing; that is, he can compare a synchronized
clock in his frame next to A's clock.

tA = (tB - vxB/cc)/(1-(v/c)^2)^.5

-xB = -vtB so

tA = tB(1-(v/c)^2)^.5

Again, I B compares a local B clock to A, he sees A time dilated.

The next questionis whether B agrees with A's observation above. This
means B looks at an A clock in his own vicinity which means that xB =
0.

tA = (tB - vxB/cc)/(1-(v/c)^2)^.5 for xB=0 becomes

tA = (tB - 0)/(1-(v/c)^2)^.5 = tB/(1-(v/c)^2)^.5 or,.

tB = tA(1-(v/c)^2)^.5

The result is identical to our first equation so the theory is self
consistent. The phenomenon is explained by the fact that clocks
synchronized in one frame are not synchronized in a relatively moving
frame.

I hope this helps. There are no paradoxes.

.

Relevant Pages

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