Physics Question

[CeeTee]

I remember doing a physics problem in college that demonstrated that if you compared an object moving through space at close to the speed of light with an object standing still on earth, time on earth would advance at a much faster pace than it would for the object traveling at such a high speed in space. So lets say hypotheticaly An object moving at the edge of light speed moves away from the earth for 2 years and then returns home, thats 4 years total. In that 4 year time frame many hundreds even thousands of years may have passed on earth. Does anyone know the mathematical formula for solving this problem ? If so could you explain it to me because I have forgotten how to do it over the years.

:)

[A_Non_Ymous]

Re: Physics Question

I remember doing a physics problem in college that demonstrated that if you compared an object moving through space at close to the speed of light with an object standing still on earth, time on earth would advance at a much faster pace than it would for the object traveling at such a high speed in space. So lets say hypotheticaly An object moving at the edge of light speed moves away from the earth for 2 years and then returns home, thats 4 years total. In that 4 year time frame many hundreds even thousands of years may have passed on earth. Does anyone know the mathematical formula for solving this problem ? If so could you explain it to me because I have forgotten how to do it over the years.

:)

The conditions you seem interested in modelling aren't stated with a considerable
amount of scientific rigor, but I think I understand what you're asking. Let's try
the simple approach: I can refresh your memory about the equation from the
Special Theory of Relativity that relates to time. If T is the subjective time on Earth in
your scenario, and T' is the subjective time on your space vehicle, v is the velocity
of the vehicle and c is the speed of light:

T = T' / Sqrt [ 1 - (v^2 / c^2)]

It's not quite as simple as that sounds, because presumably, you cannot
reach the (implied) high value of v instaneously. Presumably, you had to
accelerate for some period of time to reach your target velocity. When
we add acceleration for a long period of time into the mix, things start
to become more complex. Let's not talk about renormalizing your velocity
as v approaches c.

All this is with reservations until enough of the conditions emerge to be
certain what you're after. :)

LSN

[Caliburn]

Also, it begins getting horribly complicated if you cross any areas with any significant gravity because this slows down time as well.

[A_Non_Ymous]

Also, it begins getting horribly complicated if you cross any areas with any significant gravity because this slows down time as well.

Indeed. That's one consideration I was trying to skirt here. If he wants time
dilation, some entertaining things could be done with intense gravitational
fields. Getting his space craft out of said field intact is left as an
exercise for the reader. ;)

Based on the nature of his question, I didn't want to complicate
the picture by dragging in General Relativity. I gather the poster wanted
a "simple" answer, or what passes for one. Otherwise, it might be best
to refer him to Misner, Thorne, and Wheeler or Wald on GR.

LSN