Regarding relativity.  It is said that a person going at light speed
would not experience time, so I'm wondering what would happen in the
following scenario...

Let's say that there is a spaceship that can travel at the speed of
light, and this spaceship is placed in an orbit around a non-rotating
planet.  The orbit is such that it takes the spaceship one year (at
the speed of light) to go all the way around this planet.

Now, on that planet, let's place a very good hiker.  This guy will
circumvent the planet on foot, by boat, by bike, etc. also in one
year.

Now, the guys in the spaceship have a telescope that is looking right
at the guy on the planet (and maybe he has one looking back).  What I
don't understand is how the guys in the spaceship would not perceive
the passage of time, especially since, presumably, they would be able
to see the hiker making progress across the world.

I may have misstated this or missed something, but I trust you get the
idea.  How can time be relatively still for the spaceship, but a year
goes by for the hiker?

Can someone explain?

Part of the problem is the spaceship guys would have infinite mass and
be infinitely flat.

Ignoring that, they wouldn't be able to see the hiker 'cuz he wouldn't
be where they were looking as they woul dhave moved to a different
point over the planet. I suppose he could hang about for a while to
let his image get to the spaceship, but that would let you see part of
the problem...

I think the key is in the name of the theory - the light emitted from
the planet alters and time alters relative to the spaceship (on the
assumption that the spaceship it only just sub light speed, not *at*
light speed).


The only way I can begin to visualise (no pun intended) this scenario
is, if you imagine everything has a set amount of energy to expend on
moving through the four dimensions.

If you are moving at, say, 50 miles an hour through one of the 3
physical dimensions, most of your energy is used going through time at
1 second per second relative to your surroundings.

Should you, however, travel at approaching the speed of light then
most of your energy is going into 3 dimensional travel and there's
none left to carry on going forward in time relative to other things
that are travelling slowly, and can still put most of the energy into
going through time.

http://en.wikipedia.org/wiki/General_relativity


Anyway, watch "The Planet of the Apes" (original) and "Buck Rogers in
the 25th Century" and you will learn all you ever need to know.

I hear that's where Stephen Hawking picked all the stuff up that he goes on about ;)

Some hypothetical questions of this sort are answerable by pointing
out that the spaceship wouldn't be traveling at the speed of light.
The spacecraft is massive, and therefore in context of special
relativity it is forever confined to speeds less than c. The best it
can ever do is approach c, but not get to c.

   It's like this: Division by zero is "not allowed" in math class.
Why is that? It's because, as mathematician's would put it, division
by zero, x/0, is undefined. There's no meaning to it at all. But it is
meaningful to speak of the relationship x/n such that n approaches 0.
It can then be legitimately said that x/n approaches infinity as n
approaches 0. This is called the "limit" of the function x/n as n
approaches 0.

   In the same way it's meaningless to ask hypothetically of
circumstances in which observers are traveling at c. They can't travel
at c, and so there is no answer that matters in the real world.
According to SR, it's only meaningful to analyse observations from a
reference system which is approaching c as a limit.

   So no matter how close to c you'd care to propose for the orbiting
spaceship, it will be subject to the orderly passage of time.

   Another problem with your thought experiment is that it's not
special relativistic. It clearly involves non-linear travel, since it
asks about observations from a circularly orbiting platform. This
means that it's only properly addressed by general relativity, which
is capable of dealing with non-inertial circumstances. So we must ask,
what is the centripetal force acting on the spaceship to hold it to
its circular path?

   By the equivalence principle (upon which GR is founded), this
central force will be effectively equivalent to gravitation, and thus
will impart the same consequences that gravity induces. In particular,
the spaceship will be subject to time dilation due to gravitation
apart from the time dilation due to its tangential motion. Overall,
I'd say that for light itself (a massless object) to orbit circularly
at c, the centripetal force would be equivalent to the gravitational
field just barely above the event horizon of a black hole. Any massive
object would be orbiting the hole at an even higher altitude. But what
this means most importantly is that the planet & its hiker would then
be inside a black hole, relative to the orbiting ship, and would be
unobservable.

There is no problem with this at all. Allow me to change it a bit.
Imagine your hiker is walking around the equator of a planet holding a
laser straight up the entire time.

Just above the hikers head if you measure the lasers spot across a non
moving sheet of paper (relative to the planet) it will only be
slightly faster than his walking speed. Immesurably faster if it's
jsut a few inches above the laser. If you go much farther out the spot
will move closer and closer to the speed of light across the paper and
eventuialy you could calculate the speed of the dot as being much
faster than the speed of light. That's because motion of the spot
across the paper is not motion at all.

So there is actuialy a point where you cannot travel fast enough to
keep up with the hiker. There is also a point where you could and
still be right up against the speed of light. By the time the light
gets out to your ship the hiker would have gone around the world
several more times and the ship would be behind. It's all about where
you observe the hiker from.

Thank you all very much!  I know I'm a bit dense on this, but permit
me to ask it another way....

For the sake of this thought experiment, let's say that there is a
rope of infinite lightness (i.e., it would not be weighed down by it's
own weight at some point).  One end of the rope is held by the hiker,
and the other end is tied to the space ship.

Again, both will circumvent the planet in one year...one at the
equator, the other so far out as to be required to travel at light
speed in order to make the round in one year.

Well, it seems logical to me (again, I realize I must be missing
something) that the spaceship would be in something akin to
geostationary orbit above the hiker (granted, far, far, far above). 
That is, when the hiker has circumvented a quarter of the globe, so,
too, will the spaceship.

For the life of me, I don't see why that is not possible (setting
aside for a moment the notion/fact that a spaceship cannot go at the
speed of light).  And assuming it could be done, I don't see how a
year is a year is a year would not apply to BOTH the hiker and the
people aboard the spaceship.

Additional thoughts welcome (please be kind!)

The problem is that a year isn't a year. Time only matters to the
observer, it is not absolute. One hour on earth is not the same as an
hour on the moon (though it is extremely close). If the observers in
the space ship did not know about relativity, and they tried to
calculate the speed of the hiker (knowing planets circumference), they
would estimate the hiker moving much faster than he is actually
moving. The reason is that the time for the hiker may be a year, but
the time for the space ship guys approaches zero as they approach the
speed of light.

The Lorentz Factor = 1/(1-v^2/c^2)

This is essentially your increase in speed due to relativity, or can
be viewed as a reduction in time past. For 99% speed of light, you are
essentially travelling 50 times the speed of light, and the hiker
would appear to be travelling 50 times the speed he was really
travelling. For 99.9%, the factor is 500. The amount of energy
required to reach these speeds can be calculated with with speed times
the Lorentz (E ratio is L^2), not just by using Newtonian physics for
.99c and .999c

There is nothing wrong with your question. The answer is essentially
that time passage doesn't have to be the same for everyone. Didn't you
hear about that Russian spacecraft that orbited at very high speeds
with an accurate watch onboard that came back reading slow?