# Conservation of energy in the LHC

1. Nov 6, 2014

### tonyxon22

If I understand the basics correctly, the idea behind the Large Hadron Collider is to discover de Higgs boson. To do this, they accelerate protons to 99,99999% the speed of light.

I think it was Einstein who said that no particle with mass can ever reach the speed of light, there is a physical barrier that prevents that to happen.

So one thing that I think to understand but I'm not sure is: when protons get very close to the speed of light, they get heavier and heavier. This suggests that there are more and more Higgs bosons somehow "getting attached" to the proton to make it heavier, so it can never be accelerated to the speed of light.

This way, when they force a collision between two protons at almost the speed of light (loaded with Higgs bosons) but in oposite directions, they expect to break them down and find somewhere a Higgs boson, which is probable because there were so many.

Is this correct?

If it's not, my next and main question makes no sense at all...

How is the conservation of energy respected in a system of an accelerating proton if, besides the energy you somehow input (probably via magnetic field) to accelerate the particle making it gain kinetic energy, there is mass "appearing" out of nowhere through the Higgs bosons?

2. Nov 6, 2014

### Staff: Mentor

No. We're just trying to concentrate a whole bunch of energy in one place at the moment of the collision, in hopes of getting enough energy to produce a Higgs boson. We do this by colliding the fastest-moving protons that we can come up with.

The mass isn't appearing from nowhere. We're adding energy to the particles as we accelerate them (with electrical and magnetic fields, as you surmised) and that energy has mass via Einstein's $E=mc^2$.

3. Nov 7, 2014

### tonyxon22

But isn't that energy introduced to the system in the form of kinetic energy (speed of the protons)? When you say "that energy has mass" makes me think of new particles that were not there before..

Also, it's not true that the protons get heavier when approaching the speed of light?

4. Nov 7, 2014

### Staff: Mentor

Energy can convert into particles (google for "pair production").

The relationship between matter and energy is in some ways analogous to the relationship between ice and water: if the temperature changes, some water may turn into ice or vice versa, but the total amount of H2O is conserved.

Not true, at least as from the point of view of the protons. Consider that right now you are moving at 99.99% of the speed of light relative to some observer somewhere... But that doesn't make you any heavier.

What is true is that the total amount of energy in a system depends on the relative speed between the system and the observer. For example, we can say that a .1 kg bullet is moving at 1000 meters/second when it strikes a 1000 kg elephant at rest. Or we can describe the exact same situation as if the bullet is at rest while the elephant approaches the bullet at 1000 meters/second. We will, of course, calculate different kinetic energies in the two cases. This doesn't violate conservation of energy because every observer sees that energy is conserved; they just start with different values of the conserved quantity.

So if the numerical value of the total energy of a system depends in part on its speed relative to the observer, and if energy has mass according to $E=mc^2$, then we conclude that the total mass of a system depends on its speed relative to the person to measuring it.

5. Nov 7, 2014

6. Nov 7, 2014

### Staff: Mentor

If by that you mean e=.5mv^2, that's the whole point here: that equation doesn't work at relativistic speed. It is no longer a reflection of the actual input energy required to get to that speed.

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