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Speed of Light Measurement Using Ping
Thomas Colthurst writes "You've no doubt already read the story of ping,
but have you ever used it to measure the speed of light?" Here's a case where all that cat5 on college campuses can actually be used for education ;)
If you want a real experiment, measure the speed of light using Jupiter's moons. This was how the first accurate measurement was made. At least they'll be playing outside.
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It doesn't have to be a constant. See below.
Except for the fact that it actually gives the right answer for the speed of light -- reliably and reproducibly, to within a few percent. I wonder how that happened. Accident? Coincidence? Fudging the data? Incompetent error analysis? Wishful thinking? No, none of the above.
You really need to learn about statistical error analysis. This happens in every scientific experiment: there are always uncontrollable, unknown sources of error "that can throw the values off" -- be they fluctuations in OS response time, or in the temperature of a material, or air currents, or whatever is relevant to your experiment. (This case is just more extreme, where the errors are larger than the signal.)
However, that doesn't prevent you from analyzing the magnitudes of the errors and getting an accurate result bounded by error bars. In this case, if you take enough measurements, it's possible to extract a signal from the noise -- you just need to make sure that the signal-to-noise ratio is good enough.
I'm reminded of a trick for improving GPS accuracy: it's only accurate to some certain number of meters. But if you leave the receiver at the same location and carefully integrate the signal for a sufficiently long period of time (hours or days), you can actually get down to centimeter accuracy -- far beyond the theoretical "accuracy" of the equipment, even though random errors throw each individual measurement off by metters.
The reason is because the error goes like 1/sqrt(N) where N is the number of measurements. Take a lot of measurements, and you can reduce the error. (Up to a point, until the noise swamps the signal beyond any statistical chance of recovery. It isn't a magic trick for providing infinite accuracy.) I remember Jerry Pournelle, in his Chaos Manor column, talking about using a GPS unit this way to locate the exact best location for a solar eclipse (just for the heck of it, not that you really need to know it down to the last centimeter).
For that matter, this is the same reason why the LIGO instrument can use laser rangefinding to measure distances on the order of 1/1000 of the diameter of a proton. No, I'm not joking. 10^-18 meters. How can it do that, if that's far smaller than the size of an atom, if the mirror the beam is bouncing off of isn't even flat to that accuracy?
It can do that because it's measuring the average distance of lots of atoms (all the atoms in the mirror), so the same kind of 1/sqrt(N) argument applies. It's another counterexample to your first remark: the measured values don't have to be constant (due to a constant systematic error bias); they can fluctuate, as long as you've got a very accurate measurement of their average. Thus, the instrument will be able to detect the minute changes in distance that occur when a gravitational wave passes by and curves space along the beam line.
(Side note: LIGO II will be sensitive that it will actually be making macroscopic quantum measurements, running up against the Heisenburg uncertainty bound on position accuracy -- as applied to a 30-40 kg object, the mirror. It's a textbook problem to verify that the HUP bound on position for a macroscopic object is utterly tiny, but for the first time, we will be able to demonstrate its applicability on the macroscale directly.)
In all of the above cases, including the case under discussion here, this trick is only possible because the SNR was low enough to permit signal extraction from the noise. If the OS/system/hardware threw off the values by too wide a spread every time, then you wouldn't be able to do this -- but they don't. (In the LIGO case, the signal is so small that they have to do amazing noise reduction in order to pull out any signal at all. The observatory is so sensitive that it can track passing aircraft from the noise they make, since it vibrates the mirrors that the lasers are bouncing off of. Fortunately, they have all kinds of ways of subtracting out noise like that, so that the remaining unavoidable noise is absolutely tiny.)
In fact, in the case under discussion, the very errors you're claiming make the experiment "a waste of time", are what make the experiment work! (As was pointed out in the paper, and by other posters here.) If you always got a consistent "ping 1 ms" or whatever, that wouldn't tell you much, since the actual transit time is much less than 1 ms. But if there are some fluctuations due to random errors, then changing the physical round trip time will have an influence on the statistical distribution of those fluctuations. (i.e., the shape of the error bars -- or, more accurately, of the statistical distribution of error -- bounding a data point depends on where the data point is. Thus, the noise tells you about the signal!)
Incidentally, I'm reminded of some amateur radio astronomers being able to measure pulsar emission rates using homebuilt experiments. There's no way you can actually see the period signal directly, but with long integration times, some Fourier transforms, and a little signal processing... It's really amazing what you can do with a little signal processing! I'm pretty sure they weren't using anything as fancy as stochastic resonance, but imagine what they could do if they could apply this technique...