## Monday, October 3, 2011

### Even More Superluminal Musings

In my last post I promised the next one would have some stuff about quantum mechanics and the apparently superluminal neutrinos. Well, here it is a week later, and still no post. This is mostly because my ideas that I mentioned turned out to be of little interest after I thought about them some more, and then I got kind of busy with school and stuff. But since I promised a post, I might as well share what I was thinking about.

To start off with, relativity does not actually say that nothing can travel faster than the speed of light, c. It just says that no information can travel faster than that speed (and also nothing with mass, but since anything with mass carries information, that's almost a sub-case). In fact, in a beam of light composed of multiple 'wave-packets', you can measure the speed in several different ways, and some of those ways will give you speeds greater than c. They can't be used to carry any information, though. Spacetime itself is also thought to be able to expand faster than c (you just can't move faster than c through spacetime...which always leaves me feeling a bit confused).

You're probably asking yourself at this point, what does this have to do with quantum mechanics? A lot, as it turns out, because moving faster than the speed of light is not unknown in QM. One example has to do with the phenomenon known as entanglement. In the right circumstance, two particles can be created together such that they become entangled. What this means is that if one is measured to have a certain attribute, the other will have the exact opposite attribute. The usual example is that if one is measured to have 'spin up', the other will be measured to have 'spin down'. Spin up and spin down are extremely complicated to explain, and don't mean exactly what you would expect in classical mechanics. Just accept that the particles, when measured, can be either one or the other, but not both, and not anything in between, and which state it is is completely 50/50. The "when measured" part is important, because according to QM the particles aren't actually in either state before you measure them. Your act of measurement causes one to take on one state, and the other to take on the other. The interesting thing is that it happens, as far as we can tell, instantaneously.

Say you take one particle (without measuring it) and give the other one to a friend (again without measuring it), and you both take them far apart from each other. Then, at an agreed-upon time, you both measure your particles. Despite them not having a fixed orientation (spin up or spin down) before measurement, measuring one will instantly "collapse" the other into having the other orientation, so that they always have opposites. What's interesting is that you can have the two particles far enough apart that there's no way the second one could "know" the value measured for the first one utilizing any sort of subluminal communication. I.e, if you measure the two particles 20 nanoseconds apart, but it would take light 100 nanoseconds to move between them, there's no way for information to be exchanged according to relativity, and no way for the second particle to know what value to give when measured. And yet it happens. Always when the experiment is performed, the two particle have opposite spins, and the only conclusion is that they are "communicating" instantly. The reason this doesn't violate relativity is because no information can be exchanged this way -- you don't know what the value of your particle will be before you measure it, so there's no way to send a signal to your friend measuring the second particle, because he simply gets the opposite of what you have. If he measures a +1 every time you measure a -1 and vice versa, it does no good if you measure a random set of plus and minus ones.

Anyway, the other way that QM allows for faster-than-light travel is called tunneling. Tunneling is strange and a bit freaky, because there's no analog for it in classical mechanics or our everyday experiences. Imagine a particle trapped at the bottom of a potential well, by which I mean that the particle is repulsed from the sides, and doesn't have enough energy to escape. If the particle is unobserved, it exists as a sort of probability wave, and this wave can sort of leak through the sides of the well if there are areas of lower energy on the other side (think a well dug into the top of hill. The area at the bottom of the hill is of lower potential energy than the bottom of the well). This leakage is highly dependent on several factors, and almost always extremely small -- but what it says is that if the particle is suddenly measured, it has a chance of being found outside the potential well despite not having enough energy to get out. Again, this happens instantaneously, as far as we can tell, but again it can't be used to send information because it all depends on measuring the particle in the first place, and it may or may not be in the well when you do.

After that extremely long roundabout explanation, my initial thought was that the neutrinos were somehow tunneling as they made their way through the Earth's crust, causing them to appear to travel faster than light. After some thought, I decided this wasn't feasible for several reasons.

1. Tunneling depends on repulsion, and neutrinos aren't electrically charged (their name means "little neutral one" in Italian). They only interact via the weak nuclear force and gravity. Gravity doesn't repulse, and the weak force, as its name suggests, is much, much weaker than electromagnetism, which is where all known tunneling comes from. I'm not even sure it would be possible to induce tunneling with the weak force. It also depends on the particle being confined -- if it's just flying through space and meets an obstacle, it can simply ricochet off and never bother with tunneling.

2. Neutrinos hardly ever interact with matter. Whether or not they can tunnel is a moot point if they can pass through the Earth without interacting with a single atom of it, and billions do every second. So even if they could (which they probably can't), they probably wouldn't.

3. Tunneling is by its nature extremely rare for any single particle. Given that the scientists at OPERA have made multiple measurements (thousands, in fact) of the neutrinos that appear to be superluminal, it's extremely improbable that they were all tunneling, especially in light of the above two points.

What will most likely happen is that some measurement or combination thereof will be found to be in error, although it might require improvements to our measuring technology first. I haven't heard anything about the experiment since the initial buzz, but I'll keep an eye out for news, and keep you guys updated on the eventual conclusion of this (although if it does turn out to be superluminal motion, I hardly think you'll need me to tell you about it). A hui hou!