SRian 'events' versus SRian dilation: ROFFLMFAO!

Time dilation can be summarized by the common T' = T/gamma, where T is the
'stationary' system elapsed time and T' is the purported 'moving' system
time elapsed time between two events.

Because gamma (=g) is always greater than or equal to one, that equation
says it takes fewer moving system time units to measure the elapsed time
that it does stationary system time units.

In "Tree Paradox" I applied that relationship directly to illlustrate the
poverty of SR's (Special Relativity's) time dilation concept.

As expected, because there almost alway is a contradiction between the BEER
(Basic Equations of Einstein's Relativity) and SR dogma, a polite post was
made by an spr reader that presented without explicitly saying so that one
should examine time dilation in terms of 'events'.

Well, let's examine time dilation (and spatial contraction) in terms of
those events.

The respondent presented one of the BEER and discussed a "time-like"
situation, one where the spatial distances involved are small compared to
the time 'distances'.

In particular, he let x1 and t1 describe the 'event' "axe begins cutting a
tree at one end (down the middle)" and x2 and t2 as the event "axe has cut
all the way down the tree length".

Using the BEER's t'=g(t-vx/cc), he gave:

t1' = g(t1 - v x1 /cc)
t2' = g(t2 - v x2 /cc)

Which, of course, are the wrong equations for that setup, what with the x
values both being the stationary system x-value for the cutting edge of the
axe. (You'd undertand better if you knew the axe just 'sat' there as the
tree ran into it.)

Hence, the two events are at a single location at different times, whish is
how he described the time-like situation:

t1' = g(t1 - v x1 /cc)
t2' = g(t2 - v x1 /cc).

Thus, the time-like moving system elapsed time is:

T' = t2' - t1' = g(t2- v x1 /cc) - g(t1 - v x1 /cc),

and that reduces to:

T' = g(t2 - t1) = gT,

just the opposite of the SR-dogmatic dilation: T'=T/g..

For this time-like-events situations there is, thus, by SR's very own BEER,
time contraction. It takes more moving system time units than it does
stationary system units to measure the elapsed time between events.

(Need I say "ROFFLMFAO!"?)

But what about "space-like" events intervals?

Here, his equations are appropriate (as much as any application of the
ridiculous BEER):

t1' = g(t1 - v x1 /cc)
t2' = g(t2 - v x2 /cc)

Perhaps the time it takes for an object to travel from one end of a road to
the other end.

T' = t2' - t1' = g(t2- v x2 /cc) - g(t1 - v x1 /cc),

which gives us

T' = g(t2 - t1 - v x2/cc + v x1 /cc) = gT - g(v x2 /cc - v x1 /cc)

T' + g(v x2 /cc - v x1 /cc) = gT.

Note that in the standard setup x2 > x1 when v>0 and the left side of the
equation actually is greater than T'

When v<0 x2 is still greater than x1 and the v x2 - v x1 difference is still
positive.

Hence, the space-like setup results in a computation of even more time
contraction than does the time-like situation.

ROFFLMFAO!

Please refer to "Einstein's dilation derivation: ROFFLMFAO!" showing how
Einstein's own (1905) derivation of the dilation effect from t'=g(t-vx/cc)
also can be used to derive the obvious time contraction effect from
t'=g(t-vx/cc).

eleaticus
ee-lee-AT-i-cus


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Relevant Pages

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