Originally posted by sonhouse
I know c is the speed limit of course. But I was thinking about two light beams traveling towards each other. If you had timers at some point where the beams were far apart and clocked say a single photon passing each detector coming from the two beams, so 2 photons are detected simultaneously then following that beam as they come closer together, and a sec ...[text shortened]... nd set makes the same kind of measurement, wouldn't it show the two beams coming together at 2c?
Ok. Lets say we have two light sources pointed at each other floating
in a vacuum in empty space.
And we are sitting dead centre between the two light sources and
both the light sources and us are all stationary relative to one another
and in the same reference frame [R1].
Then from our perspective in R1 we 'see' the light from Light Source 1 [LS1]
heading towards us at c.
We also 'see' the light from Light Source 2 [LS2] heading towards us from
the other direction at -c.
The combined closing velocity of the two light beams as measured in
R1 is indeed 2*c.
However that's ok because we are not observing anything in our reference frame
that has a velocity greater than c. Which is what SR prohibits.
And it doesn't matter if you now start moving the observer with respect to R1,
because as you know regardless of your reference frame you always observe
light travelling at c. And so the closing speed will always be 2*c and never greater.
It gets slightly tricky if you try to fly along with the light beam AT c.
Because that is basically what SR specifically prohibits.
AT c time dilation becomes infinite and time stops, and also distance becomes infinitely
contracted. Which kinda prevents talking about concepts like velocity.
From every other reference frame such that the observers velocity is < c you
will observe all light beams travelling at c, you observe all objects with mass travelling
at < c . And no closing speed between 2 objects/ light beams, will exceed 2*c .