## Tuesday, September 27, 2011

### More OPERA II

Some people need to see the pretty pictures, so let us draw the full pink line for tachyons.
Although I have not worried about the correct scaling for the curve, the only essential adjustment to relativity is the existence of a minimum $v > c$, given by $\Delta v/c = 2.5 \times 10^{-5}$. If photons always travel at the same local speed, why not particles of very small rest mass.

1. Sorry, just a quick clarification. What is this crazy theory exactly? I follow a bunch of different physics blogs (including this one), and it's unclear to me what the theory is. Sorry if I've just missed it...

2. Philosopher, if you are not a physicist and/or not reading the literature, I'm afraid you cannot expect a two line answer to your question.

3. FYI, Dennis Overbye linked to you from the New York Times.

4. What's unique about neutrinos is that they are the only particle whose speed we've accurately measured that **does not** participate in electromagnetic interactions.

The next non-electromagnetic particle whose speed we can expect to measure is the graviton (through the speed of gravity waves). I'm betting that they're going to go a lot faster than c.

5. Yes, Mitchell. Believe it or not, the New York Times link did result in a not insubstantial increase in blog traffic.

Carl, as I have said many times before, I do not believe in gravitational waves. Neutrinos are a lot more interesting, because they exist.

6. The simplest interpretation of the curve, though definitely wrong, might be worth stating.

It's the straightforward combination of two proposed explanations regarding OPERA's observations: neutrinos are tachyons, and photons have a small mass. The high-energy asymptote for the pink curve is the true relativistic speed-limit, and standard light-speed (corresponding to delta-v/c = 0, in your graph) is something like 1/1.025 =approx 0.975 of the true speed-limit.

But this is definitely wrong, because if the true speed-limit was *that* much greater than measured light-speed, then all measured relativistic effects would be palpably different, e.g. the variation in measured lifetime of unstable particles at different momenta, or the slowdown of atomic clocks in gravitational fields, or anything to do with gravitational red-shift, or anything to do with relativistic binding energies.

7. I can think of two more hypotheses, but they will require modifications of relativity that I don't know how to realize.

One option: measured light-speed is the true relativistic speed-limit, neutrinos are tachyons, but they are an odd sort of tachyon which asymptotes to the new minimal superluminal speed rather than to c.

The other option: there are two special speeds - call them c1 and c2 - and two types of Lorentz transformation, and the asymptote in the diagram is for c2 > c1. So photons move at c1, and tachyonic neutrinos asymptote to c2.

8. I thought of yet another possibility. :-) Measured light-speed is the relativistic speed-limit, neutrinos are tachyons that asymptote to light-speed at high energies, and the data point from OPERA around 43 GeV is due to some interaction. You might even be able to fit it by supposing neutrino oscillations between different imaginary masses.