In the comments following the silly accelerator poll, onymous wrote:
[T]he point of the LHC isn’t to discover the Higgs. No one in their right minds would build a 14 TeV pp collider if their only goal was to discover the Higgs.
While it’s true that the ultimate goal of the LHC is to discover more exotic particles that may or may not exist (blah, blah, supersymmetry, blah) most of the hype has focussed on the Higgs, which is the one thing they’re pretty sure they’ll find (comments later in that thread notwithstanding). This is one of the potential problems with the way the machine has been marketed, but that’s a whole different topic.
I did want to pick up on one thing, though, that relates to this question in a slightly different way, and that’s the big difference between the masses of the particles being sought and the machines that are used to look for them. Looking at the rumors that kicked this off, after all, they’re talking about a Higgs boson with a mass of around 150 GeV. The Tevatron, where they’re doing these experiments, already has an energy of around 2000 GeV (or 2 TeV), a full factor of ten bigger than the mass of the particle they’re trying to create. The LHC, when it eventually reaches its full energy, will be another factor of almost ten bigger than that.
So, why do you need such a big accelerator to look for such a small particle? If the goal is just to have enough energy to create the Higgs by converting the energy of the colliding particles into mass (E = mc2, baby), why do you need more than a few hundred GeV?
There are lots of ways to answer this, but they mostly come down to one thing: while the colliding particles may have a huge amount of energy, you almost never get to use all of it.
Here’s a classical analogy that, while not perfect, will get you the basic idea. If you’ve ever played pool, you know that it’s possible to send the cue ball into a stationary ball (the eight ball, say, because I’m sure you’re an excellent pool player, and are winning the hypothetical game) in such a way that the cue ball stops, and the eight ball moves off in exactly the direction that the cue ball was headed, at just about the speed that the cue ball had immediately before the collision.
Of course, if you’ve ever played pool, you also know that this is a little tricky to do. It’s not impossible by any means– even a mediocre player like me can manage it– but it takes some care, especially if the eight ball is at the far end of the table. If you don’t hit it exactly right, the eight ball will go off at a bit of an angle from the cue ball’s original path, and the cue ball will keep moving along a path that’s deflected in the opposite direction (the angle between the two will be very close to ninety degrees, as it happens).
When you hit the the shot perfectly, all of the kinetic energy of the cue ball (less a little bit that’s carried off as sound, or converted into an infinitesimal increase in the temperature of the two balls) gets transferred to the eight ball. When you’re a little bit off, the energy transferred to the eight ball is a bit less than the total, and the cue ball keeps some of its original kinetic energy. When the shot is a little bit off, the eight ball is moving a little slower than when you hit it correctly, and the cue ball is still moving a little bit.
Now, try to do the same thing with golf balls (you don’t need to hit them with a cue– feel free to just roll them with your hands). Golf balls are a lot smaller than billiard balls, and as a result, your aim has to be a whole lot better. It’s very difficult to get golf balls to collide in exactly the right way to have the moving one transfer all of its kinetic energy to the stationary one– most of the time, they’ll hit at an angle, and both will be moving. The amount of the original energy transferred to the target ball will, in general, be less than that with billiard balls.
Now, imagine doing the same thing with protons. And you get some idea of what’s going on.
This analogy is far from perfect– for one thing, the collisions between billiard balls or golf balls are what physicists call “elastic” collisions, in which the kinetic energy after the collision is the same as the kinetic energy after the collision. These sorts of collisions happen with protons, too, but they’re not particularly interesting. What particle physicists are after is the inelastic collisions, in which some of the initial kinetic energy gets turned into rest mass energy of new particles.
The basic idea, though, carries over. In order to convert all of the kinetic energy of the original colliding protons into rest mass energy of new particles, you would need to be incredibly lucky. The vast majority of the time, only a small fraction of the kinetic energy of the colliding particles will get turned into mass, with the rest of it remaining kinetic energy of the stuff that was already there.
That’s why you need a 2000 GeV accelerator to look for a particle with a mass equal to 150 GeV. It’s extremely rare to get 200 GeV worth of new stuff out of a 2000 GeV collision. I don’t know a good estimate of this, but we’re probably talking one-in-a-billion type odds, given the tiny bit I know about particle physics. (Anybody with actual knowledge, please let me know the real odds).
And that’s also a big part of why the LHC has a much better chance of finding the Higgs than the Tevatron does– the higher the collision energy, the better the chance of getting a given amount of new stuff. The odds of getting 10% of the kinetic energy out as new particles don’t get any better, but if you increase the collision energy by a factor of ten, you only need 1% of the collision energy to create the particles you’re after. That happens considerably more often, which means that a peak-performance LHC will see vastly more events with 200GeV worth of new particles than a peak-performance Tevatron (even if they both used the same number of protons in the beam, which they probably don’t).
So, if you’ve ever wondered why they need huge accelerators to detect relatively light particles, that’s (one of) the reason(s). At least, that’s how I would explain it to the dog…