# Particle energy question

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Hi.

I have this question, not even sure if this is the right forum.

I was having a discussion about the technical implementation of the LHC and got into an argument I have no idea how to settle.

I claimed that a particle of non-zero/non-negligible mass can be accelerated via electromagnets (as it happens in reality). In my view, as the particle approaches c, apparent mass increases and it eats up more energy as it accelerates - allowing a virtually infinite amount of energy to be pumped into the particle. Not infinite, but close to. I'm thinking that the energy pumped into the magnets has to go somewhere.

The person I'm having the argument claims that once an amount of energy has been stored into the particle, that's it, and no more. As the particle reaches (almost) c, the energy that particle can deliver being mass multiplied by speed squared. It is unclear if the speed he speaks of is c or very close to.

I can't tell which is right, does the particle increase in mass, never reaching c and accumulating energy or does at some point the particle just go up in smoke (EM?) and that's it, the magnets simply stop drawing energy as the system becomes saturated?

Thanks.

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According to modern mainstream physics there is no theoretical limit for the kinetic energy of a particle. Any particle will still move with a speed <= c regardless of kinetic energy. Saying that an increase in mass was responsible for this effect (v<=c regardless of kinetic energy) is a popular explanation amongst laymen; and at least not completely wrong (I personally dislike it, though). Particles are either stable (will not decay or transform into something else without the influence of another particle) or unstable (spontaneously transform into something else). The kinetic energy or speed of a particle does not influence that.

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That makes sense. If it doesn't increase in mass, what does it increase in, if anything?

Several sources seem to suggest that it's inertia that changes, which makes some sense (breaks F=ma), while others suggest that the "simple way" is (as you suggested) to just increase mass and keep to the old (breaks simple definition of mass). And then there's the curved space time explanation. I think it's called curved because it's over my head.

Would the next-step-from-laymen be an increase in inertia, or it has no simple intuitive explanation and it's all in some transformation somewhere I'd best leave untouched?

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That makes sense. If it doesn't increase in mass, what does it increase in, if anything?

Energy, kinetic energy in particular . A bit of velocity too, but at some point the increase in velocity becomes negligible.

And then there's the curved space time explanation. I think it's called curved because it's over my head.

Curved spacetime has nothing to do with the question I can assure you (spacetime has, but only the non-curved one is relevant).

Would the next-step-from-laymen be an increase in inertia, or it has no simple intuitive explanation and it's all in some transformation somewhere I'd best leave untouched?

Sadly, my experience teaching/explaining relativity, particularly to non-physicists, is pretty much non-existent. I could tell you that the relation between energy and velocity for a particle with mass m you know, $E_{kin} = \frac 12 m \vec v^2$, is simply not correct and that the correct relation is $E_{kin} = \left( \frac{1}{ \sqrt{ 1 - \frac{\vec v^2}{c^2} } } - 1\right) mc^2$ (where m is non-increasing with velocity in this formula). But that will not really help understanding anything I'm afraid. At least from that you can verify that for any kinetic energy however large, the velocity leading to this energy is smaller than c. And that any kinetic energy, however large, can be achieved even when the speed is limited to be <c.

Edited by timo
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I get it, actually.

Looking from the other end of the math, a very small increase in v (when it is close to c), results in the whole sqrt() becoming even closer to zero. With all other things being fixed, the kinetic energy shoots up like a cork. It's much clearer when being plotted as a function of requirements (to me).

Thanks.

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The following graph might also be helpful too:

As one can clearly see, there is a vertical asymptote at v=c, as the kinetic energy of a particle increases.

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