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This claim that 'nothing can travel faster than light' is sloppy, because you have to interpret what counts as a 'thing' in the word 'nothing'.
There's no problem at all with a phase velocity being faster than the speed of light. For example, an interference pattern can easily 'travel' faster than light, and the pattern might look like a 'thing'. Just think of two plane waves propagating at v and crossing at a shallow angle (say theta), then the intersection of the wavefronts 'travels' at a speed vp where vp = v/sin(theta/2). (I need for find an image of this). By making theta small vp can be as big as you like.
In a waveguide (such as an optical fibre) this is the phase velocity, but the more meaningful speed is the group velocity vg. The group velocity is the speed at which information can be transmitted, and is always less than v. In fact vg x vp = v^2.
My point is that the 'thing' that can't travel faster than light is information, which is the point I made before about the EPR paradox.
Of course all this probably irrelevant as far as the neutrino story is concerned. If particles are travelling faster than light and being detected, then presumably information could be transmitted using them. Still, it seemed like that at first sight with the EPR paradox yet when you analyse it carefully (which is way beyond my understanding but has been done by people who know) it turns out that you can't actually use it to send information faster than the speed of light.
My bet is that whatever the resolution of this latest neutrino story, it'll turn out that you can't send information faster than light.
This claim that 'nothing can travel faster than light' is sloppy, because you have to interpret what counts as a 'thing' in the word 'nothing'.
There's no problem at all with a phase velocity being faster than the speed of light. For example, an interference pattern can easily 'travel' faster than light, and the pattern might look like a 'thing'. Just think of two plane waves propagating at v and crossing at a shallow angle (say theta), then the intersection of the wavefronts 'travels' at a speed vp where vp = v/sin(theta/2). (I need for find an image of this). By making theta small vp can be as big as you like.
In a waveguide (such as an optical fibre) this is the phase velocity, but the more meaningful speed is the group velocity vg. The group velocity is the speed at which information can be transmitted, and is always less than v. In fact vg x vp = v^2.
My point is that the 'thing' that can't travel faster than light is information, which is the point I made before about the EPR paradox.
Of course all this probably irrelevant as far as the neutrino story is concerned. If particles are travelling faster than light and being detected, then presumably information could be transmitted using them. Still, it seemed like that at first sight with the EPR paradox yet when you analyse it carefully (which is way beyond my understanding but has been done by people who know) it turns out that you can't actually use it to send information faster than the speed of light.
My bet is that whatever the resolution of this latest neutrino story, it'll turn out that you can't send information faster than light.
2 comments:
The point about what counts as 'things travelling faster than the speed of light' is well made.
An even more accessible example is sweeping a laser across the moon - like sweeping the spot of a laser pointer across a distant wall, only a bit larger scale. You don't have to move the laser that fast to have the 'spot' zip across the moon's surface faster than the speed of light. From memory, if you have a laser about a metre long, you only need to have the end moving at about 1 m/s (2mph) to do this. Of course, there isn't actually a 'thing' on the moon that is moving - it's just a succession of photons hitting the surface at different times.
But I'm pretty sure neutrinos count as a thing. They are, as you say, particles, and even have non-zero (but very very small) mass.
My money is on this experiment - and the earlier (not statistically significant but interesting) result from Fermilab - pointing up an interesting (for some values of interesting) new source of systematic error in such experiments. I reckon there's an outside chance they're pointing the way to something really really interesting about the nature of neutrinos beyond the Standard Model. And almost no chance that they're violating Special Relativity.
Yes, thanks, the laser on the moon is indeed a very nice example.
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