Re: Time dilation mirrors perpendicular to motion


xxein@xxxxxxxxxxxxx wrote:
Sue... wrote:
Zinc Potterman (delete 123's to reply) wrote:
In James Hartle's book Gravity (An introduction...) he runs through the
maths of deriving time dilation from a pair of mirrors aligned parallel
with their motion.
He then sets the same problem for a pair of mirrors aligned perpendicular to
their motion
i.e at the front and back of a rocket e.g
I have struggled with this for many hours and can't progress. Also searched
the net.
Does anyone know of a clear exlanation/derivation of time dilation for this
configuration please.

Since your book is about gravity, you might choose avoid some of
the rigour of derivng a 4 space:
http://farside.ph.utexas.edu/teaching/em/lectures/node113.html
... and try jumping right into the deep water

<< Spacetime in general relativity
In general relativity, it is assumed that spacetime is curved
by the presence of matter (energy), this curvature being
represented by the Riemann tensor. In special relativity,
the Riemann tensor is identically zero, and so this concept
of "non-curvedness" is sometimes expressed by the statement
"Minkowski space is flat."

Many space-time continua have physical interpretations
which most physicists would consider bizarre or unsettling.
For example, a compact spacetime has closed, time-like
curves, which violate our usual ideas of causality (that is,
future events could affect past ones). For this reason,
mathematical physicists usually consider only restricted
subsets of all the possible spacetimes. One way to do this is
to study "realistic" solutions of the equations of general relativity.
Another way is to add some additional "physically reasonable"
but still fairly general geometric restrictions, and try to prove
interesting things about the resulting spacetimes. The latter
approach has led to some important results, most notably the
Penrose-Hawking singularity theorems. >>
http://en.wikipedia.org/wiki/Spacetime

It is a long swim by either route and I caution that many are
dissappointed at end of journey to find they have more a
quantitative calculating formalism that is not very illustrative
of underlying mechanisms. The rubber *** analogy is
really misleading but it is a long journey to get to the higher
level of abstraction where you can attach any real meaning
to 'curvature of space-time'.

Sue...





Zinc

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xxein: Good reply. At least you resist the myth.

All I am saying is that you are able to think beyond the box --- not
that it is the correct thinking. At least you are trying to
investigate from what you think is a viable perspective.

Iow, you seem to attach a physicallity to the issue instead of just a
subjectively measured math concept. There is hope for you.

I wish I could say more, but I'll give you some time renegotiate your
thoughts into your final say. We know that it won't be complete, but
it is impossible for us to be complete. We just try harder instead of
being sheep.

X: Just be as honest as you can with what you can think.

Thanks, :-) IOW
<< So I have just one wish for you--the
good luck to be somewhere where you are free to maintain
the kind of integrity I have described, and where you do not
feel forced by a need to maintain your position in the organization,
or financial support, or so on, to lose your integrity. May you
have that freedom. -- Richard Feynman >>
http://www.physics.brocku.ca/etc/cargo_cult_science.html
http://www.quackwatch.org/01QuackeryRelatedTopics/pseudo.html

Sue...




http://www.physics.brocku.ca/etc/cargo_cult_science.html

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