Re: Einstein's (1905) time dilation derivation

eleaticus:

Buy a high school algebra book.

First, a rehash of Einstein's (1905) time dilation derivation, and then
further applications of the same technique that will demonstrate the
obvious: if you apply valid technique to garbage equations (such as
t'=g(t-vx/cc)) you get garbage out.

We examine Einstein's time dilation derivation from his t' = g(t-vx/cc),
using his very own technique.
--------------------------

A. Albert demonstrated the moving system time coordinate, t', at the moving
origin:

t'=g(t-vx/cc)

He substituted vt for x (from x=vt, describing the stationary system
location, x, of the moving origin), and using B=vv/cc):

t'=g(t-v(vt)/cc) = g(t-Bt) = gt(1-B) = t*sqrt(1-B)

t' = t*sqrt(1-B)

Yep, that says dilation, because sqrt(1-B) is always less than 1.000. Thus,
the equation says it takes more stationary system time units (t) than it
does moving system time units (t') to mark the same time interval (from t0=0
to whatever value of t is involved).
-------------------------------

B. But, these t' (and x' and y' and z') values are supposed to be as seen
by the stationary system, so why are we looking at t' anywhere than at the
observing stationary system's origin?

t'=g(t-vx/cc)

At the origin x is always zero:

t'=g(t-0) > t, because g is always greater than 1.000 if the velocity is not
zero.

Obviously, there is not time dilation, there is time contraction. The
equation says it takes more moving system time units (t') than stationary
system units. That is time contraction/speeding, not time dilation/slowing.

For instance, if g=3 (and g=gamma is always greater than or equal to one) we
have t'/3=t, meaning that it takes three times as many moving system units
as it does stationary system units to measure the interval. Dilation says it
takes fewer.
---------------------------

C. But, hey, what about our stationary system observers in the other
direction from the nosing origin?

t'=g(t-vx/cc)

Being superstitious we might always have an observer at location x=-7:

t'=g(t+7v/cc).

Wow!

Talk about time contraction!

That is, if g=3, for example, t' is even more than 3t, far more as compared
to t' at x=0.

That's time contraction/speeding, not time dilation/slowing.
--------------------------------

D. So, you can conclude anything you like about moving system time if you
use Albert's reasonable technique. But I suggest that if you accept
Albert's ridiculous t'=g(t-vx/cc) you should examine it from the viewpoint
of the thematic observer at x=0.
----------------------------

E. If you use the obvious and traditional way to measure time intervals:

T' = t'.b - t'.a.

t'.b = g(t.b - vx/cc)
t'.a = g(t.a - vx/cc)

t'.b - t'.a = g(t.b-t.a)= gT= T'

That is contraction, folks.
----------------------------

F. Einstein's technique - looking at t' at some particular (but maybe
changing) x-location - is valid, but the conclusion depends on what
x-location you use. A valid techniques yields contradictory results?
Garbage In, Garbage Out. And the garbage is the BEER (Basic Equations of
Einstein's Relativity), t'=g(t-vx/cc) being one of the BEER.

(c)eleaticus
ee-lee-AT-i-cus
http://eleaticus.blog-city.com


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