On Thursday 09 June 2005 08:52, Gunnar Gällmo wrote:

> --- Stephen Hodge
>
> <s.hodge@...> skrev:
> > OK, perhaps my introduction of the speed of light is
> > not very compelling --
> > I used it because it is taken as a given by modern
> > physics that nothing in
> > the universe can exceed the speed of light.

For a material object to exceed the speed of light (c) would
require more than infinite energy. The object would also go
backwards in time. It would have greater than infinite mass, and
imaginary length. Faster-than-light motion is not allowed, for
this and many other reasons.

> I think it says that *no information* kan exceed the
> speed of light.

That, too.

> In an expanding universe two galaxies
> can, at least according to some theories, go away from
> each other faster than light - but then they will be
> beyond each other's horizons, so you can't see one of
> them from the other.

Neither of the galaxies moves. The space between them increases
in size, at the rate of about 70 km/sec/megaparsec. Galaxies
more than about 4 gigaparsecs apart (about 12 billion light
years) have their distance increasing by more than 300,000
km/sec. Light from one galaxy, while moving toward the other at
c, continues to get further away from it and can never arrive
there.

> And then, in the case of immediate rebecoming, there
> is of course the difference between objective and
> subjective time.

The rate that time passes is different for different observers.
The effect is measurable for airplanes carrying atomic clocks,
and is an important factor in managing communications and GPS
satellites. Of course, truly subjective time, measured by mental
events, is far more variable.

> I don't think astronomers today like
> to speak at all about "simultaneity" over interstellar
> distances.

Physics since Einstein does not permit speaking about
simultaneity at all, except for events occuring at the same
location, such as collisions of two particles, considered from
the point of view of each separately. The chain of logic is

o The speed of light is measured to be the same for all
observers, regardless of their state of motion.

o There is therefore no such thing as absolute motion, only
motion of objects relative to each other.

o Construct a train car with mirrors at both ends, and stand in
the middle with a light. Flash the light. The flashes return
from both ends to meet in the center at the same time, so we can
calculate that the light reached the two mirrors at the same
time.

o However, for an observer outside the car, with the car moving,
the light does not reach the mirrors at the same time. It
reaches the mirror at the back end first, since that end is
moving toward it, while the front moves away from the light that
chases it.

o The light in both directions travels through one long interval
when moving forward, and one short interval, when moving
backward, but in the opposite order. The sum of one long and one
short section is equal in both cases, and the light does return
to the center at the same time, as seen by both observers.

o We get the same results in reverse if the train is still, and
the outside observer is moving (perhaps on another train). So
neither observer is the arbiter of simultaneity, and there is no
true simultaneity.

The same events happen at different times for different
observers. It is also impossible to say which event occured
first, if they are outside each others' light cones.

> Gunnar
>
>
> gunnargallmo@...

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