[Shark Bait (Stu)]

Originally Posted by LAW

Don't forget that E^2=m^2.C^4 + p^2.C^2 (Which is just saying that E only = mc^2 in it's 'rest' state or 'non-relativistic' state.

The energy of the collision increases because of inertia, when protons are travelling at the speeds they are capable of reaching in the LHC their mass increases by (correct me if I'm wrong) a factor of 7000.

Thanks Murphy.

Good video. Every little bit of information helps put the pieces of the puzzle in their place.

Originally Posted by sjastro

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

Cheers Steven.

Thank you for taking the time to go through the explanation in detail. I now understand why people see 'beauty' in equations.

Originally Posted by Dave2042

Stu

If I could draw a distinction which is extremely important in modern physics.

This certainly defies 'common sense' or ordinary day-to-day intuition. However it doesn't defy logic, as all the maths and physics 'fits together' properly, and what we observe matches what the theory says we should.

The issue is that our ordinary intuitions are based on the fact that we only see (and have evolved to deal with) a tiny bit of the universe, being where things are medium-sized and move slowly. Outside that, when you think about it, there's really no reason for us to have reliable intuitions about things.

Apologies Dave.

I was stuck for a title. I agree that these questions go beyond what the majority can fully comprehend (me included). That is probably what makes it so interesting.