Reply #9: Einstein wasn't thinking in terms of information

[caraher]

Prior to Einstein, the equations one usually learns when working with special relativity - mainly the Lorentz transoformations - were already known. There were many conjectures regarding length contraction, fewer regarding time dilation, and no good theoretical umbrella to put everything under. Earlier, Maxwell developed a highly successful theory of electricity and magnetism, that indeed predicted the existence of electromagnetic waves that travel at the speed of light.

What Einstein did was put a bunch of pieces together through a fresh way of looking at these puzzle pieces. On the basis of declaring that all inertial references frames are equally valid and taking the speed of light (in vacuum) to be constant in all of them, Einstein could make sense of a variety of seemingly-disparate theoretical puzzles and experimental results.

The tie-in with "information" is somewhat indirect, and has to do with how Einstein revolutionized how we look at time. The basic principle is that, using Lorentz transformations, we can always relate the time between a pair of events as measured in one reference frame to the time between the same two events as measured in any other frame. These measurements do not agree in general; however, there is a well-defined time-ordering of events in certain circumstances.

Basically, two events in spacetime separated such that something moving slower than the speed of light could be present at both have the same temporal order in every inertial reference frame. On the other hand, events that are spatially separated such that something would need to move faster than lightspeed in order to be present at both have an ambiguous temporal order - in some reference frames, A occurs before B, while in other reference frames, B occurs before A.

Because the usual notion of causality is that causes must always precede effects, there's a big problem if events A and B could have causal influences on one another - we'd have the embarrassing circumstance of future events causing past events (at least as seen in some reference frames). The language of information is perhaps a more modern way of talking about this - we can equate causal influence with a transfer of information. In any case, Einstein basically stipulates that one cannot allow causal influences - i.e. information - to travel faster than the speed of light because he wants to preserve the usual notions of causality.

This is why, in many previous reports of superluminal phenomena, one frequently finds statements to the effect that although something can be said to travel faster than the speed of light, a more careful analysis shows that no *information* travels superluminally. That's because the most important thing the "speed limit" accomplishes is to ensure that causal relationships cannot be formed between events whose time ordering is ambiguous. So long as you can't use it to send a signal, you don't upset the causal applecart! This helps make the nonlocality of quantum mechanics less threatening to relativity - while on most accounts of "wavefunction collapse" you have a "spooky action at a distance," this phenomenon cannot be used to send a signal faster than the speed of light - and thus does not threaten the causal order.

In the end, I don't think it's as simple as replacing the "speed of light" with some very similar value for "the speed of neutrinos" because relativity's foundation is not really the notion one starts with the speed of the fastest phenomenon that can carry a signal and scale everything else to it. In relativity, time measurements are about things like synchronizing clocks in motion relative to one another, and to get that right, as a matter of oft-repeated experimental fact, you need to use the speed of light to get the correct numbers - and not the speed of light plus the tiny extra bit reported for the neutrino speeds OPERA reported. It's a small difference, but large enough that numerous precision measurements over the past few decades would have noticed a discrepancy.

Thanks for the post - it got me to think more carefully about "what is special about light?" in relativity. There's more to it that what I wrote, but I think in the end it really does come down to experiment (even though there are also powerful purely theory-driven reasons to give light a privileged role).