Question about light beams aimed at each other:

sonhouse
Science 13 Dec '13 12:10
1. sonhouse
Fast and Curious
13 Dec '13 12:10
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 second set makes the same kind of measurement, wouldn't it show the two beams coming together at 2c?
2. 13 Dec '13 12:56
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]
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 .
3. sonhouse
Fast and Curious
13 Dec '13 13:25
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 ...[text shortened]... ass travelling
at < c . And no closing speed between 2 objects/ light beams, will exceed 2*c .
I was just thinking, if you DID get to c and time stopped, how could you get OUT from doing exactly c? There would be no way any equipment onboard your spacecraft that could do work! So you would be stuck at c forever. The whole universe would unravel and you would still be going at c.
4. 13 Dec '13 14:12
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?
In a relativistic sense, no information is transferred faster than c here, so there is no problem. In the frame of reference of the light beam, the other light beam is moving towards it at c.

If you use the same wavelength beams, you just get a standing wave. You can use this to make optical lattices and do nifty stuff.
http://en.wikipedia.org/wiki/Optical_lattice
5. Soothfast
0,1,1,2,3,5,8,13,21,
14 Dec '13 12:351 edit
Confucius say if pair of scissors the size of a galaxy is closed at 0.5c, then point of contact between two shears will accelerate to 2c and beyond.

No information is transmitted, though.
6. sonhouse
Fast and Curious
14 Dec '13 14:41
Originally posted by Soothfast
Confucius say if pair of scissors the size of a galaxy is closed at 0.5c, then point of contact between two shears will accelerate to 2c and beyond.

No information is transmitted, though.
Also that would be because no piece of the super scissors is going at c, just a moving intersection of matter sliding by one another.
7. Soothfast
0,1,1,2,3,5,8,13,21,
16 Dec '13 03:17
Originally posted by sonhouse
Also that would be because no piece of the super scissors is going at c, just a moving intersection of matter sliding by one another.
Now, what if I watched the point in space, 100 lightyears away, where the tip of the shears make contact as the giant scissors are closed. If the shears are perfectly rigid, and you open and close the handles in a patterned way in order to make the tip of the shears send a message in Morse code, would not information be transmitted faster than light?

I guess the answer is it's not possible, because "perfect rigidity" is not possible. The force that moves the atoms comprising the tips of the shears must be transmitted from the handles via the electrons of the intervening atoms, so in fact the shears will develop a bend that will move at something less than the speed of light. It would be like a wave traveling along a rope that's been given a shake at one end.