Re: How is the speed of light measured in a laboratory?

Hello Aditya,

You can read a lot about light-speed measurements at www.what-is-the-speed-of-light.com, of all places, or at the "Physics FAQ". I'll refer you there for details, but here's a quick overview:

There are lots of ways to measure the speed of light. An important early measurement (done first in the late 1800s, and still done by many undergraduate physics labs - perhaps you could do it yourself!) involves actually timing a light beam over a long distance. This is done by a clever arrangement with a rotating mirror; you can arrange to bounce a light beam twice off of a single rapidly-rotating mirror. If the light has to go a long distance between the first bounce and the second bounce, there is time for the mirror to turn slightly between the two bounces. You can measure the angle of turning accurately, since the beam will reflect the second time at a slightly different angle than the first time.

Modern methods take advantage of our ability to measure the frequency of light waves very precisely. We know that a light beam (most commonly, a laser), bouncing back and forth between two mirrors, will behave according to a very particular relationship between the distance, the frequency, and the speed of light. Measuring the distance and the frequency can tell you the speed. The setup is called an "interferometer", and there are endless variations on the details. I'm sorry I can't find a good Web reference! The idea is: light is a wave. Waves can interfere with one another: if you try to lay two waves (water waves, sound, light) on top of each other, they add up in interesting ways. In particular, if the "peaks" of one wave overlay the "dips" of the other wave, they can cancel out! And no wave at all will be observed at that spot. An interferometer is a pair of mirrors with a light wave bouncing back and forth between them. Now, this light wave will be "interfering" with itself every time it bounces back and forth - it's a matter of the timing of the bounces that determines whether the waves overlap and cancel one another (if the peaks and troughs coincide) or reinforce one another (if peak matches peak and trough matches trough). The timing, of course, depends on the speed. For as given set of mirrors and a given frequency of light, you can figure out where the peaks and troughs are and thus what sort of interference to expect. If the wave is reinforcing itself ("constructive interference") you'll see a lot of light in the cavity; if it is "destructively interfering" you will see less or none. The setup is really that simple: two somewhat-transparent mirrors facing each other, a laser beam shining in through one side, and a light-meter catching the leakage out of the other side. It all has to be very precisely aligned, though. This is a very brief picture; feel free to ask another question if you want a better explanation!

You ask whether it's possible to measure the speed of light without interfering with the light: no, not really. Certainly, to detect a photon you have to destroy it, so the flight-time of your light beam must end when it hits the detector. The setups I describe above all include mirrors, off of which the light bounces - if you want to avoid bouncing, you can do a "toothed wheel" or "Kerr cell" experiment, which are similar to the rotating-mirror experiment in principle, but can be done without mirrors. I'm not sure why you'd want to, though.

You also ask how we measure the speed of particles in an accelerator: Particle accelerators are designed and built by people who know the speed of light and the speeds of their particles very precisely. If you misunderstand the speeds, the particles will be in the wrong places at the wrong times, and the machine will not work - acceleration is a delicate process, with no room for errors! At the LEP accelerator at CERN in Geneva, for example, the precision is almost legendary - for example, the accelerator will not work properly if you fail to notice that the Earth's crust stretches slightly when the Moon is overhead, or when water levels in Lake Geneva are low! At LEP, electrons and positrons go around a 26-km loop, taking about 87 microseconds to go around. Every time an electron traverses the loop, it gets a "kick" - a big electric field that gives it more energy - which has to be precisely timed on the sub-nanosecond level. An electron can stay in this loop, getting kicked every few dozen microseconds, for as long as 20 hours. Additionally, there are measurements being done all over the accelerator - smaller and more accurate kicks to precisely shape the electron bunch - which are timed down to picoseconds. So, let's see, if a particle travels 26 kilometers in 87 microseconds and we can predict its arrival time within 1 picosecond, then we know the speed to an accuracy of 1 part in 100,000,000. That's more than enough accuracy to see that the electrons are going slower than light speed! And that's a very conservative estimate on my part.

It's true, though, that most detectors measure only energy and momentum. However, many experiments include "time-of-flight" sensors, or Cerenkov counters, either of which (directly or indirectly) measure particle speeds. Moreover, the usual energy/momentum/velocity relationships of Special Relativity are so well-established, it's difficult to come up with sensible theories that contradict them. Experiments along these lines are still worthwhile, though, and there are a few papers every year suggesting faster-than-light neutrinos, or a varying speed of light over the history of the Universe, or different "lightspeeds" for different particle families, or some such thing. So far all of these ideas have failed experimental tests, whereas Relativity has never failed in the slightest.

I'm happy with 299,792,498, myself. When I did the "rotating mirrors" experiment as a student, bouncing a laser beam 30 meters up and down a corridor and seeing the 100-nanosecond travel time, I got an answer quite near that (with large error bars of course); I don't have to take anyone's word for it!

-Ben Monreal