The Large Hadron Collider can accelerate protons to 99.9999991% the speed of light. Why can’t we reach 100%?
In: Physics
Protons have mass. Any matter with mass cannot move at the speed of light or faster, as far as we understand.
It’s a fundamental aspect of our universe.
Using special relativity the formula for the energy of a proton can be found as E = γmc^2. Where m is the mass of the proton and c is the speed of light. γ is an interesting number called the ‘Lorentz factor’ and depends on the speed of the proton.
The Lorentz factor with a speed of zero is equal to 1 and for slow, everyday speeds is basically still equal to 1. This is the familiar E = mc^2 equation and tells you how much energy a particle (like our proton) has when it is stationary, due its mass alone.
As you might expect, as you accelerate this proton faster its energy increases. It now has kinetic energy too. If you’ve done any physics you might be familiar with the equation KE = 1/2 mv^2 for kinetic energy, but really this is an approximation that only works for speeds much slower than c. Instead we stick to γmc^2 to describe the total mass and kinetic energy of the proton.
The problem now is that rather than simply increasing with the square of speed like our old formula for kinetic energy, the gamma factor, and therefore the energy, actually starts to increase much more rapidly as you get close to the speed of light. So to go from 99.991% to 99.992% is a lot more energy than you’d otherwise expect. As you get closer and closer to c, smaller increments in speed require much larger increments in energy in such a way that reaching c would require an infinite amount of energy.
Picture it this way: accelerating the proton is like rolling a ball along a path that represents the speed of our proton. We can roll the ball to any point along our path, except that it has an end, the speed of light. As you get toward the end the hill gets steeper and steeper until it may as well be a vertical wall that goes on forever. You can roll the ball as high up as you like but you can never reach the top
Literal ELI5: The faster you go, the more energy you need to got ‘a little bit more fast’.
Eventually, the speeds get fast enough that we don’t have enough energy to make it go faster, even though it’s still less than the speed of light.
The faster something is going, the more energy it takes to accelerate it even more.
I don’t know the real costs involved, so these are just toy example numbers, but imagine:
* you turn on the LHC. It uses electricity to speed up protons.
* you spend 1000 euros of electricity to bring the proton from stationary to 50% of the speed of light (c).
* you spend another 1000 euros to bring the proton up another 25%, so 75% of c.
* then another 1000 euros to go up another 12.5% to 87.5% of c.
* then another 1000 euros to go up 6.25% to 93.75% of c
* and you can repeat this, spending 1000 euros to get half of the remaining way to c, but never quite reahing c
There is a lot more to it than that (like maybe higher speeds take more energy to maintain, so the cost of each step might increase. Or maybe the highest speed depends on how large a collider you build, etc etc).
However, I think that example gives the basic feel of it.
As you get closer and closer to 100%, it takes more and more energy to obtain smaller and smaller increases. It would literally take infinite energy to go to 100%.
… that is, for particles that have mass. Particles that have no mass (e.g. photons) do travel at 100% the speed of light.
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