Relativistic Velocity Addition
Most recent answer: 02/08/2011
- Christopher (age 15)
Falmouth, ME USA
You've done what we've all done when first introduced to special relativity--come up with what seems to be an obvious paradox. In the future, it's a good check of your understanding to make sure what you're saying doesn't imply that you can go faster than the speed of light in any reference frame, but these thoughts mean you're thinking and thinking is always a good thing!
The first thing to know is that velocity addition is different in special relativity. Galilean velocity transformations are as follows:
A man on a train going velocity u with respect to the earth walking velocity v with respect to the train's floor will be traveling s = u+v with respect to the earth.
For trains going and people going slowly compared to the speed of light, c, this is approximately correct. Special relativity tells us that, in fact, the person will be traveling
Hence, if you actually carried out this calculation for your individual situation, you would find that the person in the limousine in the train in the rocket ship would indeed be going less than c.
To answer the second part of your question, you would not split into two different people. Remember that relativity only means that people in different inertial frames (a frame of reference that is not accelerating) will witness their own version of events. There is no absolute frame of reference to compare different accounts of events. For instance: if I'm on earth watching you zoom by at, oh, say, 0.8*c on a fancy space ship, I would see you move in very slow motion. You, on the other hand, since you're traveling at a constant velocity, would be perfectly legitimate in saying that I and the entire planet Earth were the ones moving past you at 0.8*c. So you would see me move in very slow motion. Well, who's right? The answer is: we both are. It sounds insane, and obviously paradoxical, but it actually isn't.
Hope that somewhat answers your question. I know it can be confusing. There are plenty of great resources available online and in print.
Those might be a couple of places to start.
Best of luck!
On your last question, no you wouldn't turn into pure energy. In fact, from your own point of view you're still at rest, even if some things are whizzing past you. /mbw
(published on 02/08/2011)
Follow-Up #1: Experimental proofs of the relativistic velocity addition formula
- David Martin (age 43)
In my field, high energy physics, the most obvious examples are proton accelerators such as the Tevatron at Fermilab or the Large Hadron Collider at CERN in Geneva Switzerland. Protons at these accelerators are constrained to move in a circular path by means of magnets. Every time they come around you give them an impulsive swat which increases their energy and momentum. At very low energies, much smaller than the rest mass of a proton, they pick up speed according to the Galilean non relativistic formula you are used to. But as they gain more and more energy they eventually reach the terminal velocity of the speed of light. This can be measured quite precisely and agrees with the relativistic formula.
(published on 12/10/2014)