Most Successfull Illusion : Theory of SR

[xersan]

Most successful illusion: Theory of SR

The special theory of relativity has a very special place for history of mind. Because it has paradoxes; but, these paradoxes are accepted willingly. Paradoxes give a signal of failure. But mystic, fantastic conclusions of SR attend to our semantic necessity. And it has become philosophic idol. Brains have acquired blinkers. Even some simple wrongs cannot be perceived. For example:

In the formula of time dilation:

t’ = t / sqrt (1 – v2/c2)

The denominator is always small than 1. And t’ > t

In this case does the tempo of time become faster?

Does it require t’< t for time dilation ?

[Erasmus00]

Originally Posted by xersan

In the formula of time dilation:

t’ = t / sqrt (1 – v2/c2)

The denominator is always small than 1. And t’ > t

In this case does the tempo of time become faster?

Does it require t’< t for time dilation ?

t' is the proper time. Its the time the clock reads according to the observer moving in that frame. The proper time is bigger then the observed time t. This is what time dilation means. It only looks like a paradox because you're confusing the variables.
-Will

[xersan]

Originally Posted by Erasmus00

t' is the proper time. Its the time the clock reads according to the observer moving in that frame. The proper time is bigger then the observed time t. This is what time dilation means. It only looks like a paradox because you're confusing the variables.
-Will

If we consider a numerical example for v = 0.60 c and t = 10 sec:=====> t’ = 5 sec.

An observer in relative system reads the time 5 second when the observer on the reference system is reading the time 10 second from his own clock.

We can calculate the proper time for this numerical example:

The view of the relative clock comes to the reference observer for the time of (v.t/c)

t + vt/c = 10 sec =====> 1.60 t = 10 sec ===> t = 6.6666 sec

for the value of t = 6.6666 sec t’ = 3.333333 sec ===> Proper time is 3.3333 sec.

The reference observer reads 3.3333 second on the clock of relative system at the time of 10 referencesecond

Also proper time is always small than the time of reference system.

t’ must not be higher than t for time dilation.

You may say that 5 sec > 3.3333 sec. Yes, of course you are right. But you can perceive that it means, at the time of 5 relative second the reference observer can determine this time 3.3333 second.

I want to say If the familiar formula of tıme dilation is : t' = t / sqrt(1 - v2/c2)

This formula can not your result of time dilation

===> t' = 10 / 0.80 = 12.50 second ???????

[Qfwfq]

Originally Posted by Erasmus00

t' is the proper time.

No, t is. Any observer not at rest will see time intervals longer than proper time.

Still, as usual, I don't see Xersan's point at all.

[Qfwfq]

Originally Posted by xersan

If we consider a numerical example for v = 0.60 c and t = 10 sec:=====> t’ = 5 sec.

No, t' = 12.5 s.

[xersan]

Originally Posted by Qfwfq

No, t' = 12.5 s.

The formulas of SR don't give the value of proper time. t or t' are not proper time.

I want to say just the same thing with you. If the t' is 12.5 second, what is the value of t' = 5 sec obtained by Lorent'z equation?

[xersan]

We can think that: What time is it in reference system when it was observed the time of t’= 5 relativesecond ?

v.t = 0.60 . c .10 = 6. c

T = The duration of returning of the view of 5 relativesecond = vt/c = 6.c / c = 6 sec.

The time of observation for t’ = 5 sec is 16 reference second.

The reference observer reads 5 second on the relative clock at the time of his 16 referencesecodç

[Qfwfq]

Originally Posted by xersan

what is the value of t' = 5 sec obtained by Lorent'z equation?

With what equation?

[xersan]

Lorentz's equations: (From Einstein's book : Relativity, The Special and The General Theory 1916

x' = (x - vt) / sqrt(1 - v2/c2) ; y' = y ; z' = z

t' = (t - vx/c2) / sqrt(1 - v2/c2)

x = c.t ===> t' = (1 - v/c) t / sqrt(1 - v2/c2) (*)

Our numerical example : t' = (1 - 0.60) 10 / O.80 = 5 sec.

But Einstein had given also different formula for the < t' > : t' = t / sqrt(1 - v2/c2) (**)in his book (at the and of section 12). It ıs interesting, because he had calculated the value of unit < t > for the < t' = 1> . In my opinion he had been aware of dissimilar formulas and he had found resource to cache this point. Or an effort for compromising without close attention.

(*) This is genuine formula of theoryfor time dilation

(**) This is derived for perpendicular direction of lightclock.

Please analyse. Incredible.

[Qfwfq]

Originally Posted by xersan

x' = (x - vt) / sqrt(1 - v2/c2) ; y' = y ; z' = z

t' = (t - vx/c2) / sqrt(1 - v2/c2)

This is the coordinate transformation, a so-called Lorentz boost, for motion along the x axis at velocity v. You seem to be misapplying it, replacing an x with a t, apart from the fact that that isn't how the ratio between proper time and another observer's time is worked out. The appropriate way is:

t' = t / sqrt(1 - v^2/c^2)

Because each observer's time interval is the projection onto their time axis.