Neutrinos: fascinating webcast lecture Friday from the CERN OPERA chap. Lots of explaination of corrections and stuff. This might have been one of the questions (maybe the one about drilling a hole in the tunnel) but I would have thought that if these muon neutrinos exceeded light speed there would have been a shock-wave, usually given off as Cherenkov Radiation – the blue glow you see in nuclear rod cooling tanks as the neutrinos exceed the speed of light in the medium of water.
Satellites: Well, looks like UARS might have landed on (or at least very near to) North America anyway. Well done NASA for predicting that it wouldn’t land on North America, but they couldn’t predict where else it might not. I’m sure there’s a name for this type of prediction (answers on a postcard).
Economy : Everyone’s calling for united action. Quite what action and by whom remains to be seen. What a mess. DON’T PANIC ! China to the rescue.
Causality: Is the relationship between an event (the cause) and a second event (the effect), where the second event is understood as a consequence of the first. (Wikipedia).
I guess what we’re saying here is that Causality could be represented as a function with a non-negative time component. That is to say, an Event 1 (characterised by conditions E1 at time t1) causes Event 2 (conditions E2 at time t2) , by the transformation f(E, t).
The function presumably can take many forms, but will always take a positive finite amount of time. If it takes, or appears to take a negative amount of time then E1 will appear as an effect of E2. So the muon neutrino hitting the detector in Italy might appear to have caused the release of the muon neutrino in Switzerland, from the Italian’s perspective.
What if a faster-than-light neutrino was sent back to Switzerland when triggered by the arrival of the first , then a new Swiss FLT neutrino was released on the arrival of the Italian, and so on ?
Well, let’s assume that the trigger is instantaneous for the moment ie. no trigger delay. And for comparison let’s add beam of photons to the tunnel i.e. light, that go through the same routine as the neutrinos, with the initial Swiss photon sent at the same time as it’s neutrino counterpart.
On the first run, Swiss neutrino 1 arrives 7 nanoseconds before Swiss photon 1. Immediately Italian neutrino 1 is sent back 7 ns before Italian photon 1. Italian neutrino 1 now arrives in Switzerland 14 ns before Italian neutrino 1.
And so on.
Now, at the speed of light 730km (let’s say exactly and call it l) the photon should take 0.00243501789 seconds or 2,435,017.9 nanoseconds to cover the distance. In 1 second there should have been 410.6746 lengths covered, or Swiss photon 206 is 2/3rds on the way to Italy. Which number neutrino is in flight ? It’s also Swiss neutrino 206, about 849.51 metres ahead of the photon. So after 859.3189014843 seconds Swiss neutrino 352900 will be 730km ahead of Italian photon 352899.
Will continue later.
Update: Having thought a bit more, it would seem useful to arrange this neutrino pin-pong in the OPERA to lengthen the effective length of the experiment and therefore the apparent lag between neutrino and photon to beyond the length of potential timing errors, but I guess you’d need a particle accelerator in Italy to make the neutrinos ?