Quote:
Originally Posted by Shark Bait
I have been listening to reports and reading articles about recent events at CERN's LHC.
Quote: At full power, trillions of protons will race around the LHC accelerator ring 11 245 times a second, travelling at 99.9999991% the speed of light. Two beams of protons will each travel at a maximum energy of 7 TeV (tera-electronvolt), corresponding to head-to-head collisions of 14 TeV. Altogether some 600 million collisions will take place every second.
So......
If two cars have a head on collision and they are both travelling at 100km/h, the combined speed of the impact is going to be 200km/h.
If two protons collide, travelling at 99.9999991% the speed of light they will NOT have a combined impact velocity that is faster than the speed of light. I have trouble visualising this as it seems to defy logic.
Science states that any object (or sub-atomic particle) cannot reach the speed of light as they have mass.
Any thoughts that can help make this clear would be greatly appreciated.
Thanks.
Stu.
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This is where mathematics helps in resolving this apparent defying of logic.
The
approach velocity of two cars travelling at 100 km/hr is in fact 200 km/hr.
The approach velocity is derived in special relativity by the equation
(u+v)/(1+uv/c^2) where u and v are the velocities of the objects moving towards each other.
For the two cars in the example 100 km/hr = 0.0000055c
In the equation the uv/c^2 term for the cars is (0.0000055cx0.0000055c)/c^2 = 1.008X10^-16 which is a very small number.
The approach velocity of objects travelling at speeds well below c is
(u+v)/(1+uv/c^2) = u+v as the uv/c^2 term is very small.
Hence the approach velocity of the two cars is 100 + 100 = 200 km/hr.
Suppose there are two objects travelling towards each other at 0.9c
Now the uv/c^2 term is no longer small and equals (0.9cx0.9c)/c^2 =0.81.
The approach velocity is (0.9c+0.9c)/1.81 = 0.995c.
The approach velocity can never exceed c.
For two photons approaching each other at c, uv/c^2 = 1, and the approach velocity is (c+c)/2 = c.
Regards
Steven