I couldn’t help it. At $5.50 for a matinee showing, I just had to hear it for myself. I recently went to see the newest Armageddon thriller to hit the big screen, 2012. I couldn’t resist because of this New York Times article about movie director Roland Emmerich and his tendency to destroy the world in his movies (Independence Day, The Day After Tomorrow). In particular, the article explains that in 2012 the earth tears itself apart when
A monster solar flare shoots invisible neutrinos into the earth’s core, cooking it like a Hot Pocket.
You have to love the Hot Pocket reference, but what drew me to see the movie was, of course, the neutrino as Hollywood star.
Sure enough, the film begins with an American scientist visiting a solar neutrino experiment located in a deep underground cavern in India. After being told by the physicist running the detector about the increases in rate they have witnessed recently (I think he said a factor of two increase in neutrino interactions in the detector, but I’m not positive), they opened the hatch on top of the detector and, sure enough, the liquid inside was boiling. Oh, wow.
I also recently saw Angels and Demons since it came out on video. In A&D, of course, as I blogged about forever ago, a small canister of antimatter is used as a weapon to threaten the Vatican City. In that post, I talked about the antimatter we produce everyday here at Fermilab and how it compares to the claims in the movie.
So, how accurate is the science of 2012? Well, not very, I’m afraid. First, it is absolutely true that the Sun produces tremendous numbers of neutrinos and that many of them hit the Earth. A common statistic to set the scale is that trillions of neutrinos from the Sun pass through the nail on your pinkie finger (about 1 sq. cm.) every second! That’s a lot of neutrinos, but the key is that they pass right through. And most of them pass right through the Earth’s core as well like it isn’t even there, moving on toward distant reaches of the galaxy with little to impede their journey.
I said most pass right through, because a small fraction of the neutrinos from the Sun certainly do interact with materials on Earth and deposit tiny amounts of energy. If they didn’t, then we would have no way of knowing they were there. I know the energy deposited by an interacting neutrino is impressively tiny, but I became curious about the temperature change that might be caused by a neutrino from the Sun interacting at Earth – exactly how far is it from making water boil?
So here’s the simplistic calculation that I did. The Super-Kamiokande neutrino detector in Japan is an enormous tank that holds about 25,000 tons of water. When a neutrino interacts with a hydrogen or oxygen nucleus in the water, the interaction gives off light which is detected. A neutrino from the sun typically contains around 10 MeV of energy. MeV is just a unit of energy measurement and 10 MeV is equal to about 16E-13 joules – a tiny amount. So I made the simplifying assumption that all of the energy from the neutrino goes into heat energy in the water to estimate the temperature increase of the water in Super-Kamiokande due to a single neutrino interaction. I used the specific heat formula from an old physics textbook:
change in Temperature = [(energy added) / (specific heat of H2O) x (mass H2O)]
T = (16E-13 J) / [(4180 J/kg*K) x (25,000,000 kg)] = 1.5E-23 K = 1.5E-23 degrees Celsius
Wow, okay, so assuming I didn’t screw that up (an enormous assumption) that indicates that each neutrino interaction increases the temperature of the water by about a 100 billionth of a trillionth of a degree. I think Super-Kamiokande sees about 4,000 solar neutrino events per year. So assuming no heat is dissipated (but it is), that’s an increase by 6E-20 degrees Celsius a year (0.00000000000000000006 C). You can see that it will take a whole lot more than a doubling of the solar neutrino rate to make a measurable change in the temperature of the detector, much less make water boil! I’m pretty sure we’re safe from this particular form of Armageddon.
I think seeing major players from our theories of fundamental physics, like neutrinos and antimatter, show up on the big screen is pretty fun. Its true that the science of these movie plots is usually far from accurate, but if it gets anyone asking questions like “Is antimatter real?”, or “What are neutrinos and do they really come from the Sun?”, then I’m not inclined to complain too loudly. Its interesting that, in these examples at least, the particles are all a threat to humans, but I suppose that’s Hollywood. For now, I’m inclined to keep thinking that “all press is good press”. Anyone know of a movie where subatomic particles magically save the world?