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Q & A: adding relative speeds

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Most recent answer: 07/17/2015
Q:
if we have two particles traveling with speed near the light speed and both of them don't know about this and both of them calculate speed of light as it is for others(c) is this possible that one of them give enough energy to another one to reach the speed of light or more?! because none of them knows how much speed they have and for them they are in constant state .
- Amir (age 19)
arak,iran
A:
Nope. The relativistic velocity addition formula gives V= (v-u)/(1+uv/c2) where u and v are here the two velocities in one frame and V is the velocity of one of the things in the frame of the other. Even if v and u are opposite and near to c in magnitude, V still comes out less than c. E.g if u and v are each 0.9c, opposite, V = (1.8/1.81)c.

However, it's possible that I misunderstood your question. If so, write back.

Mike W.

(published on 12/21/2010)

Follow-Up #1: relative speed addition

Q:
A simple question I hope. I grasp that light moves at a fixed speed in a vacuum and that this is independent of the source. If you have headlights on a rocket, the light moves at c no matter how fast the rocket is going. One feature of relativity seems to be that everything can be examined in its own frame, as if it were at rest. So what happens when things are moving in opposite directions? Say, two light particles shooting away from the same light source in opposite directions, in a vacuum? If you examine one and consider it at rest, surely the particle shooting the other way is moving at a relative speed of 2c ? The two light particles could be rockets for all it matters, somehow propelled to near the speed of light. If they are even going at just over half the speed of light in opposite directions, surely they would appear to be going > c relative to each other?
- David Jones (age 39)
UK
A:

This is a common question, so I've linked to a previous answer. It is the breakdown of what we intutively feel is "surely"  true that makes relativity initially so surprising. We should just add that we have no description of how things look from the light's point of view. Relativity gives the rules for translating between frames in motion at up to c with respect to each other, but not at c itself. 

Mike W.


(published on 06/09/2013)

Follow-Up #2: relative speeds

Q:
This is probably an old question, but if 2 spaceships approach each other at say 0.6*speed of light, I know there is a formula to allow for time lengthening effects for the people sat on the ships so that their relative speed is some number less than the speed of light. However, if an observer sat on a stationary spaceship sees them both coming towards him from different directions, would the decline in distance from his perspective be reducing at a number greater than the speed of light and if so does this cause any weird effects?
- Nick (age 42)
UK
A:

It is an old question, but since I didn't find it in a quick search, we can't expect you to either.

Yes, each of those ships sees the other as moving at (1.2/1.36) c. And yes, the observer who sees them approaching equally from opposite directions sees their relative speed as 1.2c. That's perfectly consistent with relativity and leads to no weird effects.

My one quibble with your question is that you refer to one observer as "stationary". That word has no meaning in this context.

Mike W.


(published on 07/17/2015)

Follow-up on this answer.