Re: Can time dilation be computed with just the Lorentz transformation and no other assumptions?
- From: jem <xxx@xxxxxxx>
- Date: Thu, 31 Jul 2008 09:27:46 -0400
Shubee wrote:
On Jul 29, 4:10 pm, Edward Green <spamspamsp...@xxxxxxxxxxx> wrote:On Jul 22, 11:03 am, Shubee <e.Shu...@xxxxxxxxx> wrote:
On Jul 22, 8:27 am,EdwardGreen<spamspamsp...@xxxxxxxxxxx> wrote:So little time, so much to learn, so much assurance that whatever IOn Jul 22, 8:27 am, Shubee <e.Shu...@xxxxxxxxx> wrote:So how would you prove that the Lorentz transformation implies timeWhat assumptions, if any, must be added to the Lorentz transformationNone.
in order to compute time dilation for a clock-carrying traveler?
Shubee http://www.everythingimportant.org/relativity/special.pdf
dilation without presupposing more than just the Lorentz
transformation?
write is unlikely to influence your point of view or enrich mine.
Nonetheless, I don't want to seem to shirk the question.
(1) The Lorentz transformation is presumed to be between at least one
frame where physics appears "normal" or "simple" (for example, in
which Newton's laws hold in the low velocity limit) and other frames,
wherein physics looks just the same.
[I guess that is an additional assumption beyond simply saying "the
Lorentz transformation" without commentary or context. So you win, if
you like.]
(2) t', written in terms of the (unprimed) variables which we may take
to pertain to the (first) observer, is ticking along more slowly than
t. t', however, by (1), is a time coordinate which is just as natural
to a comoving observer as our time coordinate is to us. His watches
keep it, his metronomes tick it, he keeps his appointments by it, and
he is in every way satisfied with its performance as "time".
That's what is meant by "time dilation". That's _it_. That's all
there is to it. There isn't any more. Lorentz invariance -- which is
a shorthand way of saying "Lorentz transformation and the context
built into (1)" -- implies time dilation.
Meanwhile, time keeps ticking away, and I am wasting it.
Edward,
It's not clear to me why the Lorentz transform can't be reduced to the
Galilean transform by resetting clocks and rescaling distance measures
and clock rates
It can. So what? Does it surprise you, mathematician Shooby, that the form of a transformation can change when its variables are redefined?
according to the recipe on page 11 of.
http://www.everythingimportant.org/relativity/special.pdf and
equations (48) to (58).
How do you answer this riddle?
Shubee
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