would the LHC blow up your hand? I do the math

Recently I found myself in the unenviable position of having to do some math. After crying at some length on the impossible difficulty of multiplying numbers together, I braced myself, buckled down... and had Google do all the work for me.

The question at hand was a Hacker News article on what would happen if you stuck your hand into the Large Hadron Collider. As those who have followed the link will have found out, the result is a youtube video of several physicists being asked a somewhat complicated technical question, and prevaricating wildly in the manner of scientists being unexpectedly presented with a hard question, and expected to provide a nontechnical answer.

I found the question interesting. I have some experience in guessing at questions like these, and immediately set about multiplying some truly colossal numbers by other gigantic numbers.

First, let's assume the LHC is operating at its design limits, for a full 7 teraelectronvolts per proton. That's 1.12 microjoules, which is not a lot for a macroscopic object, but a really alarmingly colossal amount for an elementary particle.

Each beam has 2,808 pulses. Each pulse contains 1.15*10^11 protons. A hundred and fifteen billion protons. Now let's do the math.

(1.12*10^-6)*2*2808*(1.15*10^11) = 352,235,520 joules.

That there's a lot of energy. But let's translate that into a more useful form than "very large number". A stick of dynamite, weighing .25 kilograms, releases 2.1 megajoules of energy when it explodes. 352/2.1 = 168 sticks of dynamite, or 42 kilograms total.

Thus, the naive answer to "what would happen if you stick your hand into the LHC?," is, "your hand would explode, and you would die." However, there's more going on with a beam of hyperenergetic protons, and assuming that all the energy of the beam would just instantly turn into heat in your hand is optimistic.

Well, not optimistic. You know what I mean.

A 7 TeV proton is very, very energetic. A lesser proton, when accelerated into human flesh, would caroom off assorted carbon, hydrogen, and nitrogen atoms, until it came to rest, thereby transferring all of its energy to the target.

But a 7 TeV proton would be so fast, and so massive[1], that it might easily shrug off the paltry electric fields of the massed atoms making up the hand, and pass through the hand without damaging it at all. However, it is moving very, very fast, and will traverse the entire 27 kilometer ring once every 100 microseconds. The odds are good it will eventually strike hand.

But once it does, it would be nothing like the thermal impact of a less energetic proton. When it hit, it would fly apart, shatter violently, and spew subatomic shrapnel in a wide cone from the point of impact. Some of this debris would strike other hand-atoms, provoking other, secondary reactions, but most would waste their energy outside the hand. More's the pity. How much energy would end up in the hand, as thermal energy? I don't know.

But direct impacts, and the secondary impacts, yea, unto the fifth generations; are not the whole story.

Energetic particles emit photons when deflected by magnetic fields. When they're deflected by other particles, it's called bremsstrahlung radiation, and when it's a macroscopic magnetic field, as produced by, say, the superconducting containment magnets on the LHC, it's called synchrotron radiation. Both bremsstrahlung and synchrotron radiation tend to be quite energetic, in the X-ray range[2] and would contribute to the total heat load without ever striking a hand atom. How much? I don't know.

Here we are, some 600 words later, and I still don't have any hard answers. A full answer would most likely require actual work, as well as some modelling that doesn't much resemble the kind of cocktail napkin math I am so fond of.

But while losing your life is in question, you would most definitely lose the hand.

[1]: Relativistic effects become very, very apparent at these scales. Mass-energy equivalence is not an abstract concept for a subatomic particle traveling very close to the speed of light. The faster it moves, the heavier it gets. A 7 TeV proton is about 7100 times more massive than a proton at rest.

[2]: Amusing science fact: X-rays and gamma rays are the same thing, that is, high-energy photons. The difference between the two are how they are produced. Gamma rays are made by nuclear reactions, and X-rays are made by particle accelerators, such as the LHC, cathode ray tubes,[*] and X-ray tubes. This is, of course, because they were discovered using different methods; and only later discovered to be the same damn thing, after everything had been named.

[*]: Why yes, cathode ray tubes produce X-rays. Why did you think they were made of leaded glass?