Natural Science Forum / Physics / Relativity / June 2006

It is impossible to observe light propagating parallel to your line of
sight.
Have you ever seen any moon light bound for Jupiter?

There is no logical explanation of a physical absurditiy.
If you want to derive a Lorentz correction use something
that can acutally be observed and confirmed by experiment.

<<... we shall see later that the full time-dependent Maxwell's
equations only allow information to propagate at the speed of
light (i.e., they do not violate relativity). How can these two
statements be reconciled? The crucial point is that the scalar
potential cannot be measured directly, it can only be inferred
from the electric field. In the time-dependent case, there are
two parts to the electric field: that part which comes from the
scalar potential, and that part which comes from the vector
potential [see Eq. (393)]. So, if the scalar potential responds
immediately to some distance rearrangement of charge density
it does not necessarily follow that the electric field also has an i
mmediate response. What actually happens is that the change
in the part of the electric field which comes from the scalar
potential is balanced by an equal and opposite change in the
part which comes from the vector potential, so that the overall
electric field remains unchanged. This state of affairs persists
at least until sufficient time has elapsed for a light signal to
travel from the distant charges to the region in question.
Thus, relativity is not violated, since it is the electric field,
and not the scalar potential, which carries physically
accessible information. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node45.html

"Retarded potential"
http://farside.ph.utexas.edu/teaching/em/lectures/node50.html

Sue...

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 sheet 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...

Suppose the distance between the mirrors (in the reference frame of the
mirrors) is L, the speed of the mirrors is v, and g = 1/sqrt(1-v^2/c^2).
 Then, due to length contraction, the distance between the moving
mirrors is L/g, and the speed of a horizontal light pulse relative to
the mirrors is c-v in the direction the mirrors are moving, and c+v in
the opposite direction.  Therefore the time for a light pulse to
complete a round trip between the mirrors is L/(g(c-v)) + L/(g(c+v)) =
2gL/c (i.e. a factor of g longer than the time taken in the reference
frame of the mirrors).

Hartle problem
-------------mirror 2
  ^
  |
  | light path
  |
  |
-------------mirror 1                     the two mirrors are moving up as
seen.

Most books cover the derivation of time dilation. As shown below
-------------mirror 2
  ^
  |
  | light path
  |
  |
-------------mirror 1                     the two mirrors are moving right
as seen.

Please can someone help with the basic maths. Or even start me off.
I'm sorry but can't understand a word of some previous contributors.
Are they genuine?
Zinc