Particle Colliders and Future Tech

In today's comic we make the claim that to have a clear test of string theory you would need a particle collider the size of a galaxy. While that sounds like a ridiculous idea, we did at least do some baseline calculations, and I thought it would be good to go into it with a little more rigor.

This is all based on the wikipedia article on string theory which states:

There should be heavier copies of all particles corresponding to higher vibrational states of the string. But it is not clear how high these energies are. In the most likely case, they would be 10¹⁵ times higher than those accessible in the newest particle accelerator, the LHC, making this prediction impossible to test with any particle accelerator in the foreseeable future.

Without citing any sources, of course (thanks wikipedia contributors!), so maybe you can take that with a grain of salt. In any case, we can use this cautiously as an order-of-magnitude starting point.

Obviously when we talk about the utility of a particle accelerator for discovering new phenomena, the important quantity is the energy of the beam, not the physical size. But do the two scale together? Roughly, yes.


These data come from the list of hadron colliders that have information for both track length and beam energy on the wikipedia article listing particle accelerators. (A range is given for RHIC, so I took the maximum.) Running a trend line through the data gives us the average relationship between the two parameters, which in this case tells us:

Beam energy = 280.14 x Track length - 652.46

So if the LHC is capable of 7000 GeV and we want 10^15 times that, we're up to 7 x 10^18 GeV. (That's 7000 yotta electron-volts, for those of you keeping track.) Then we just solve the above equation for track length, and the result is roughly 2.5 x 10^16 km, or about 2600 lightyears. Of course, that's probably the circumference of a circle, so the actual diameter would be a factor of pi smaller, but you get the idea. It's big.

Maybe not as big as a galazxy, though, but hey, at this point who's counting?* It's about 26000 lightyears to the center of the Milky Way, but the Milky Way is actually pretty large among the galaxies in the Local Group. So maybe the size of a dwarf galaxy.

It would also be a terribly impractical machine. Not only because of the maintenance you would have to do along those 2600 lightyears of track, but also just the logistics of running it. If you started two beams at opposite ends of the track moving towards each other at nearly the speed of light, it would still take 1300 years for them to meet in the middle. And this all begins after you've waited 800 years for the signal to start to reach the opposite side of the ring. So maybe if you're lucky, you get one run of this thing every 2000 years, and just hope it doesn't break sometime in the middle because one of the hundreds of thousands of stars that it's lassoed up has orbited through the beam.

So in conclusion, no, it's not very realistic to build a particle collider to test string theory. If it were ever going to happen, we'd need some pretty significant engineering advancements first. But heck, maybe this is just the cost of finding the answer to life, the universe, and everything.


-Peter

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*I am, obviously.