Mathematical Relationships: Exploring Time Dilation and Speed Travel

[richnfg]

Hello! :)

A few questions out of pure interest here that I figured someone on the forum will probably be able to help me with.

Just wondering, in terms of maths, has there been any relationship found between the speed that you are traveling and the difference in time (from how it slows down)? So, say I wanted to travel at 99% of the speed of light for 2 years, would there be any 'equation' that could tell how many years in the future you actually are?
I'm guessing there is no real experimental data to play with, but it just crossed my mind.

I'm pretty new to this subject, so it could turn out I have no idea what I'm on about.

:P

Rich

 

[HallsofIvy]

Hello! :)

A few questions out of pure interest here that I figured someone on the forum will probably be able to help me with.

Just wondering, in terms of maths, has there been any relationship found between the speed that you are traveling and the difference in time (from how it slows down)? So, say I wanted to travel at 99% of the speed of light for 2 years, would there be any 'equation' that could tell how many years in the future you actually are?
I'm guessing there is no real experimental data to play with, but it just crossed my mind.

I'm pretty new to this subject, so it could turn out I have no idea what I'm on about.

:P

Rich

You understand, don't you, that this is a physics problem, not a mathematics problem?
Yes, there is such a formula, developed in physics, that, like any formula is written in mathematics terminology. It is, if I remember properly, that it is
$$t'= t\sqrt{1- \frac{v^2}{c^2}}}$$
But you have to be careful how you interpret that. That says, that, as spaceship A passes plane B with speed v (relative to the planet), while people on planet A have "t" years pass, they will observe the people on spaceship A aging only t' years. Of course, since velocity is relative, people on spaceship A will see planet B passing them at speed v and will observe exactly the opposite.

The difficulty with your scenario is that, while you say "travel at 99% of the speed of light for 2 years", you don't say whether that 2 years is measured in the spaceship or on a frame of reference that the ship is traveling at 99% the speed of light. Of course, in the "spaceship" frame of reference, the ship is not traveling at all.

Also I have no idea what you mean by "many years in the future you actually are? "
I can't think of any frame of reference in which you will have appeared to move into the future- well any faster than the rest of use do- "one day at time"! Relative to the spaceship frame of referenence, there will be no change in the flow of time. Relative to any frame of reference in which the spaceship has non-zero speed, time will have slowed down.

 

[cesiumfrog]

Moreover, this is just introductory "special relativity" and is explained at length in any cheap text on that subject (or on general physics even).

 

[russ_watters]

...and there is a mountain of experimental data to go on. See the GPS thread for a practical SR problem to practice on...

 

[yogi]

For a one way experiment, the most commonly cited experimental data is the decay times of high speed particles. So if you traveled for two years at .99c you would be two years older - us folks back home would be a lot older - you can use the formula cited in post #2 to figure out just what that number is. The story is a bit more complicated in that it is necessary to specify initial conditions - you need to start from a common reference frame and synchronize all clocks - otherwise an ambiguity is created as to who is doing the moving and consequently who is accumulating the greater number of years.

 

[liskawc]

Just wondering, in terms of maths, has there been any relationship found between the speed that you are traveling and the difference in time (from how it slows down)?
Rich

time doesn't slow down actually ... it stays the same its just that its just that time isn't an aboslute parameter at high speeds :
per say you would make yourselft a new parameter that is absolute then that parameter would show different times in the system taht travels near c (or is near a big mass)