Quote:
Originally Posted by Brian W
Hi all, in my naive and simplistic world particle accelerators accelerate particles in opposite directions at very fast speeds until at just the right speed and time they collide and some really really neat stuff happens.
Here's where I need some educating; these particles are moving at close to the speed of light (?)... this means that when they collide they have a closing speed greater than the speed of light(?)... if the maxim that for every action there is an equal and opposite reaction applies in this case does that mean that what comes out of this collision is travelling at a speed greater than the speed of light?
Brian
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Brian,
You may have heard of the Lorentz transformations for time and distance in Special Relativity. These can be used to derive how velocities add up in Special Relativity.
They add up according to the equation:
u=(u'+v)/(1+(u'v/c^2))
u is the velocity relative to a centre of mass frame.
u' is the velocity of a particle.
v is the velocity of the frame of reference of the particle moving in the opposite direction.
Suppose the particles are moving towards each other at 0.99c.
The inituitive calculation is that the speed in the centre of mass frame should be u=0.99c+0.99c= 1.98c.
However it is found to be u=(0.99c+0.99c)/(1+(0.99c*0.99c)/c^2))
= 0.999949497c
Regards
Steven