Do Particles at LHC Travel Near Light Speed?

[Benplace]

If particles at the LHC are traveling very near the speed of light, are they affected by the slowness of time?
Also, how can they travel near the speed of light when the planet is rotating around the sun and the solar system is traveling around the galaxy and the galaxy is moving through space, wouldn't those put the particles over the universal speed limit?

 

[axmls]

Yes, time will go slower for the particles (this can be seen because particles that are going at such speeds decay slower than if they were at rest).

And no, a consequence of relativity is that velocities do NOT add like intuition suggests: 0.9c + 0.9c =/= 1.8c.

 

[Benplace]

Is that why when traveling on a train and you jump in the air you don't get slammed into the car behind you?

 

[axmls]

No, that's just a consequence of Newton's first law. In the case of the train, you and the train both have the same velocity. When you jump, there's no horizontal force on you that would slow you down, so you keep going horizontally with the same velocity (objects in motion will continue along their path unless acted on by an outside force).

What I mean is, in Newtonian mechanics, if I'm traveling in a car at 50 mph, and another car is traveling in the opposite direction going 50 mph, then we can add velocities directly and say that in my reference frame, I am at rest, and they're traveling at 100 mph. In relativity, however, velocities do not add like this. It just doesn't show for velocities low compared to the speed of light. Taking relativity into account, if I declare that I am at rest, the other car actually looks like it's going 99.9999999 mph as opposed to 100--in other words, velocity addition doesn't work the same in relativity.