[neilep (OP)]

Ok, so you're waiting at the station for the train home and here it comes, and there it goes !!  It was travelling 10mph less than the speed of light. Plenty of time for you to peruse every carriage and make lengthy notes of the contents therein !! This is true because someone told me !!


So, as it passes, you notice a boy throwing a ball the same direction as the travelling train and he throws the ball at 20mph !!  VOILA !!...the ball is now travelling 10mph faster than the speed of light !!


Thank you


You're welcome




So, whats wrong ? does the ball (from the perspective of you waiting for the train) travel faster or not than the speed of light ?


your thoughts ? wisdom ?

[Halc]

So, as it passes, you notice a boy throwing a ball the same direction as the travelling train and he throws the ball at 20mph !!  VOILA !!...the ball is now travelling 10mph faster than the speed of light !!

If he throws it at 20mph, then it is moving at 20mph, almost stopped.
If he throws it 20mph relative to the train, then you have to use Einstein's light velocity addition formula: https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

So the ball is essentially still going 10mph less than c relative to the guy on the platform, with negligible additional velocity.

[neilep (OP)]

So, as it passes, you notice a boy throwing a ball the same direction as the travelling train and he throws the ball at 20mph !!  VOILA !!...the ball is now travelling 10mph faster than the speed of light !!

If he throws it at 20mph, then it is moving at 20mph, almost stopped.
If he throws it 20mph relative to the train, then you have to use Einstein's light velocity addition formula: https://en.wikipedia.org/wiki/Velocity-addition_formula#Special_relativity

So the ball is essentially still going 10mph less than c relative to the guy on the platform, with negligible additional velocity.

Well there goes my Noble prize ! I was building a cabinet and everything too !!  hurrumpth !!

[evan_au]

It's even more extreme in the LHC:
- protons coming from the left at almost c
- protons coming from the right at almost c
- meet in the middle
- From the viewpoint of of the proton coming from the left, the proton coming from the right is (barely) still traveling at less than c.

[neilep (OP)]

It's even more extreme in the LHC:
- protons coming from the left at almost c
- protons coming from the right at almost c
- meet in the middle
- From the viewpoint of of the proton coming from the left, the proton coming from the right is (barely) still traveling at less than c.

phew !!  grasping it !!...why then do both the protons need to moving ? why not just the one ?

[Halc]

why then do both the protons need to moving ? why not just the one ?

It takes less (half) the energy to accelerate two particles up to a certain relative velocity than if you tried to put it all in one and hit a 'parked' photon.  It also centers the violence of a collision.

Picture trying to test-crash a pair of cars, except it really is expensive to get them up to speed since your only available method to move them is using sheep as reaction mass, so you (hopefully) want to minimize that.
To get a given energy collision, it takes half the sheep to get each car up to 1/2 V than it takes to get one car up to V, plus you have the benefit of the camera not needing to move when you photograph the collision.  Hit a parked car and the splatter scene just whizzes off screen, making it harder to capture the data with a bolted down camera.