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 Originally Posted by Renton
If two light particles are on a direct colliding course, are they relatively (to each other) moving at 2x the speed of light?
This is dipping your toe into the realm beyond physics. I can only answer this in terms of taking a limit of 2 objects approaching each other at a velocity that approaches the speed of light (others may do better).
The relevant outcome is that they only appear to be approaching each other at 2x the speed of light in a stationary reference frame. They do not view each other as moving faster than the speed of light.
Example:
Ongie is approaching me from the left at 99% the speed of light and Renton is approaching me from the right at 99% the speed of light. (The equation is much simplified if they are approaching at the same speed, but this is a minor tweak to make a simplified example.)
In my reference frame, they are approaching each other at 1.98 the speed of light.
In either of their reference frame, I appear to be approaching them at 99% the speed of light, and beyond me they see the other approaching at:
2*beta/(1 + beta^2) = 2*0.99/(1 + 0.99^2) = 1.98/(1 - 0.9801) =
99.994 950 % the speed of light, which is still less than the speed of light.
To talk about photons, I take the limit as beta goes to 1, and the result of the equation is clearly
2*1/(1 + 1^2) = 2/2 = 1.
So 2 photons approaching each other see a photon traveling at the speed of light coming toward them... or do they?
This is where it gets really fun. As anything approaches the speed of light, the gamma factor approaches infinity. This means that they experience infinite space contraction, infinite time dilation, and infinite mass increase.
Good thing photons have no mass, that gets us cleanly out of that universe ending debacle. Whew.
Infinite space contraction: the entire universe appears as an infinitely thin disk, which photons pass through short ways.
Infinite time dilation: none of the clocks in the universe tick, in fact time is completely frozen from the photons' reference frames.
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