# acceleration of particles - thought experiment

The Large Hadron Collider accelerates particles to 99,9999991 % of the speed of light. And I understand that you need infinite amount of energy to accelerate it to the speed of light. What would happen if the Collider was vertical and you could use the force of gravity - would that change something? I understand that light has no mass and therefore no acceleration is possible - but the particle accelerated has a mass and therefore gravity should have an accelerating effect, or am I wrong?

Your reasoning is correct in theory, but flawed in magnitude. Placing the Large Hadron Collider vertically would have little to no effect on the final velocity of the particle. Since the particles fired through the collider are nearly massless, the potential energy of the particles is very, very small. The corresponding increase in final velocity will be insignificant compared to the final velocity in either case.

In addition, as Kyle Kanos points out, building the collider vertically would present some severe engineering challenges, which easily would wipe out any minimal gains in terms of increasing maximum particle velocity.

Since the collider is a big circle, even if you mounted it vertically it would make no difference, because half of the time, the particle would have to oppose the gravity. But the other answers are also correct in that the magnitude of any effect due to gravity is too small to make a difference anyway.

• yes but when it is slowed by gravity you only need a finite amount of energy to keep the speed constant until the particle reaches freefall, where the additional acceleration comes to play. Mar 7, 2015 at 9:55
• @Bobulou if you need to add extra energy to get the proton up over the top of the hill so that you get back the exact same amount of extra energy when it comes down the other side, then what have you gained? Might as well just leave the ring where it is, and add the extra energy. Unfortunately, the amount of extra energy that you are talking about is so small compared to what they are already using that I doubt their instruments could even measure it. Mar 7, 2015 at 17:03
• What would happen if you reach those 99,9999991 % of the speed of light at the top? Mar 8, 2015 at 7:21

It really won't help much. It's the weakest of the fundamental forces, and it can't be used to overcome fundamental issues regarding the speed of light without some exotic features (wormholes, negative masses) which we don't have good access to on Earth.

• Plus the support structure needed for a ~few km long linac might be a bit extreme. Mar 6, 2015 at 21:39
• But velocity is constant for any mass, or am I wrong? So no matter ho small the particle is it has a mass and therefore a velocity of 9,8 m/s^2 in freefall. Mar 7, 2015 at 9:50
• @Bobulou: You are correct if you replace "velocity" with "acceleration", and with the caveat that we're talking about "close to the surface of the Earth." Even in totally classical mechanics, you would need a path of length $1/2 g (c/g)^2$, about 10000 times the orbital radius of Neptune, to get to speed $c$. If you factor in the $1/r^2$ dependence of the force law, it turns out that there's a parameter called the "escape velocity" which is the speed of a particle which falls into earth from an infinite distance, which is only 0.003% the speed of light. It just won't help much. Mar 9, 2015 at 2:56