- #1
Tomer
- 202
- 0
Hey all,
this may sound dumb, but this question has been bothering me for a while now.
So we know that moving objects (or people!) measure time moving slowly compared to objects in rest (to them). We also know that distances appear to shrink.
Now, first this question: if we send a person to the nearest star, say, 5LY away, and he'll travel very rapidly (0.999c), which correlates to gamma ~22, he'd experience (theoretically) both time dilation and space contraction, right? So for us on Earth it would take t = (5/0.999) Y years to get there, right?
I'm having trouble calculating how long it would take him, in his system, because of these two effects. I couldn't understand if they cancel out, or add up, or are equivalent (that is, if he'll get there, according to his clock, after the same amount of time, t, or after t/22, or after t/22^2). I know well the lorentz transformations but I can't really define the event here. Is it "the person arrived the star"? If it is, when I'm trying to calculate it like I understand it, I get this strange result:
Earth system: x = 5LY, v =0.999c => t = 5/0.999 Y
But then:
x' = gamma * (x-vt) = ~22 * (5 -0.999 * (5/0.999) ) = 0 LY!
I don't get it at all :-)
My second question is: How does it feel like to be a photon? If space shrinks asymptotically to zero, does it "feel" like it's everywhere all the time? Another extraordinarily posed question, I know :-\
I hope I made some sense - I've had a little relativity when studying mechanics a few years back, I believe I could at least answer the first question alone back then (although probably just by using formulas like a robot), but I'm apparently very rusty :-)
Thanks a lot!
Tomer.
this may sound dumb, but this question has been bothering me for a while now.
So we know that moving objects (or people!) measure time moving slowly compared to objects in rest (to them). We also know that distances appear to shrink.
Now, first this question: if we send a person to the nearest star, say, 5LY away, and he'll travel very rapidly (0.999c), which correlates to gamma ~22, he'd experience (theoretically) both time dilation and space contraction, right? So for us on Earth it would take t = (5/0.999) Y years to get there, right?
I'm having trouble calculating how long it would take him, in his system, because of these two effects. I couldn't understand if they cancel out, or add up, or are equivalent (that is, if he'll get there, according to his clock, after the same amount of time, t, or after t/22, or after t/22^2). I know well the lorentz transformations but I can't really define the event here. Is it "the person arrived the star"? If it is, when I'm trying to calculate it like I understand it, I get this strange result:
Earth system: x = 5LY, v =0.999c => t = 5/0.999 Y
But then:
x' = gamma * (x-vt) = ~22 * (5 -0.999 * (5/0.999) ) = 0 LY!
I don't get it at all :-)
My second question is: How does it feel like to be a photon? If space shrinks asymptotically to zero, does it "feel" like it's everywhere all the time? Another extraordinarily posed question, I know :-\
I hope I made some sense - I've had a little relativity when studying mechanics a few years back, I believe I could at least answer the first question alone back then (although probably just by using formulas like a robot), but I'm apparently very rusty :-)
Thanks a lot!
Tomer.