Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Alan McDougall on 05/09/2008 09:49:45

Greetings forum,
I am sure many are aware of this event and the many questions around it
The Large Hadron particle collide in Switzerland is to be switched on Wednesday with much speculation in the media (eg create a black hole that will swallow the earth nonsense.
Hadron is just another word for Proton and these protons are going to be accelerated to as near as possible to the speed of light in opposite directions
The question is if these particles are accelerate within a tad of light speed in opposite direction, would they then collide at greater than the speed of light??
Regards
Alan

Greetings forum,
I am sure many are aware of this event and the many questions around it
The Large Hadron particle collide in Switzerland is to be switched on Wednesday with much speculation in the media (eg create a black hole that will swallow the earth nonsense.
Hadron is just another word for Proton and these protons are going to be accelerated to as near as possible to the speed of light in opposite directions
The question is if these particles are accelerate within a tad of light speed in opposite direction, would they then collide at greater than the speed of light??
if v_{1} is proton_{1} speed and v_{2} is proton_{2} speed (regardless of the sign, that is, in modulus) then the relative speed V is not v_{1} + v_{2} but:
V = (v_{1} + v_{2})(1 + v_{1}v_{2}/c^{2})
This formula is always true, at every speed. Try to compute V for several speeds v_{1} and v_{2}, low and near or equal to c.
Edit: of course the formula is not valid for protons only [:)]

Light arrow,
So relativity still holds true, so if I could assume the Hadrons were spaceships they would still observe each other as approaching one another at less than light speed.
What about the observer subject synchronised to the microwave back ground
Alan

What about the observer subject synchronised to the microwave back ground
It will apply when they are launched in opposite directions at equal speeds relative to any inertial frame.
I'm not sure what your particular 'frame' actually means but I think you are trying to say 'the real stationary, Cartesian, frame of the universe' or something like that. But it is not a proper concept, these days. Any inertial frame will do  although there will always be some tiny influence of GR in practice. Even then the limit of c applies.

Hi, just stumbled on this site and thought I'd jump in!
If you are standing still (compared to earth's surface) and watching two particles approach each other, you will see one moving right at almost c, and the other moving left at almost c.
Now imagine you are moving with one of the particles so that from your point of view, it is stationary. You see the other particle approaching you and measure its speed relative to you, and you find it is still less than c, rather than 2 x c as you'd expect.
How can these both be true at the same time? When you are moving with respect to another object, the space between you and the object 'contracts' (from the maths of special relativity). Therefore the distance you measure between the two particles is a lot shorter if you are travelling with one of the particles than if you are standing still in the lab.
Example: If, when travelling with one particle, the distance measured between the pair is 25% of that measured in the lab, their measured relative speed will be 25% of that you measure in the lab.
Edit: Alan, to answer your question about the observer, they will observe each particle moving (relative to them) at nearly c. The relative speed they will measure between the two particles to be almost 2c, and that's fine. You are not seeing anything moving at greater than c relative to you at any point in this process, and that's what counts!
Richard

Richard
A warm welcome
Edit: Alan, to answer your question about the observer, they will observe each particle moving (relative to them) at nearly c. The relative speed they will measure between the two particles to be almost 2c, and that's fine. You are not seeing anything moving at greater than c relative to you at any point in this process, and that's what counts!
Of course they are moving at near light speed like two bullets approaching each other on a fatal head on collision course , relativity does not permit them to exceed light speed Physic's sometimes makes no sense. God does play dice and he cheats at times.
Strangly if they were receding from each other at 99.9 C they would see that, if of course given they could observe and calculate that
Regards

Richard
A warm welcome
Strangle if they were receding from each other at 99.9 C they would see that, if of course given they could observe and calculate that
Regards
Thanks for the welcome Alan!
If they were approaching or receding from each other at a speed you measure in the lab as 99.9% of c, this same length contraction/time dilation effect would mean that one particle still sees the other moving at a slower speed, about 7080% of c.
It's not an effect which switches on when the relative speed exceeds c, the same applies (just on a very small scale) when you consider two cars approaching each other. Their relative speed will always be measured as larger if you stand by the side of the road than if you are in one of the cars, just by an immeasurably small amount!
Richard