Much to my surprise, the the speed of light (in a vacuum) being a constant - regardless of the frame of reference - was not a consequence of the theories of relativity, but relativity is dependent on the actual previous measurements that SoL is a constant.
If I’ve got that right, please explain how “practical” measurements of the SoL work. Anything that I could do to verify the SoL (in any direction) given a few hundred euros worth of equipment would be amazing.
You could do a crude measurement cheaply by calculating when the moon will pass in front of a star, then measuring the time this is observed on earth.
More accurate measurements can be made by means of a rotating mirror experiment, such as was done in 1850 by Fizeau and Foucault. The idea is to send light reflected off a rotating mirror along a longish path, then measure how much the mirror has rotated (and thus how much time has elapsed) when the light returns.
The result works out fairly close to a billion feet per second.
Note that c (as in E = mc[sup]2[/sup]) is a common abbreviation for the speed of light.
As usual, Wikipedia to the rescue. You can do it for the cost of a decent telescope by observing the moons of Jupiter and noticing the differences between the expected period when earth is closer to Jupiter and when the planets are farther. This method was used by Danish astronomer Ole Romer in 1676.
If you want to do the experiment entirely on the surface of the earth, you can use the Fizeau-Foucault method [extremely simplified explanation]: shine a beam of light through a toothed wheel, reflect it off a distant mirror, and adjust the wheel speed so that the returning beam passes or is blocked by the tooth. [See the linked page for a more coherent explanation.]
The original Wiki page also describes modern techniques such as interferometry and using an oscilloscope.
thank you both commasense and Xema but because of lack of sobriety or just plain stupidity (or both) I don’t really understand the Fizeau-Foucault method, though I’ve read about it before. Can you please provide a brief sketch of how this aparatus works? I’m off to bed soon, so no rush 
If you had two synced atomic clocks, maybe you could rig one up to a lightning rod, and another a mile away to a photoreceptor. Program one clock to stop when lightning hits the rod, and the other to stop when it detects the lightning flash. Calculate the time discrepancy over the distance, and you should be able to measure it close enough.
There’s some cost there, and the set up is a Pain in the Ass™, but hey, that’s science. 
Picture a mirror on a shaft, rotating at a high speed. Light from a bright source that reflects off this mirror when it’s at one particular angle proceeds to a fixed mirror a long way off, which reflects it back again. By the time it returns, the mirror has rotated a bit. You use a telescope to pick up the second reflection off the rotating mirror, and measure the angle through which it has moved.
The “time of flight” of the light will be the time it took for the mirror to rotate the measured number of degrees: TimeOfFlight = MeasuredChangeInMirrorAngle / RateOfRotation
The speed will then be twice the distance to the fixed mirror divided by the time of flight.
Let’s say you’re able to rotate the mirror at 10,000 rpm - that’s 60,000 degrees/second. Let’s further say that you need an angle change of at least 2 degrees to be sure of a decent measurement. Since we know C is around 300 million meters/sec, we divide that by 30,000 deg/sec yielding a distance of 10000m. Thus, the fixed mirror would need to be located at least 5km away.
Back in 1850, Foucault used a much greater distance between mirrors - probably implying he couldn’t achieve impressive rotation speeds.
You can use a telescope to concentrate light from a bright star and use that light to send a beam out through the teeth of a rotating wheel, and to a distant mirror which sends the light back to the wheel again. You look through the wheel teeth at another location to see the returning light. At low speed, you have to be an integer number of tooth spaces away so you have spaces for the beam to leave through and return through. As you spin the wheel faster, though, you have to move your position along the periphery of the wheel to alter the timing of the teeth, because the light is taking some time to make its journey. You can use this dependence of the brightest position on the wheel speed, and the distance to the mirror, to calculate the speed of light.
If you pick a star that the Earth is traveling towards in its orbit to do the experiment, and then six months later repeat the experiment using the same star, the Earth will now be moving away from it, and there will be a difference in your speed toward the star of twice the Earth’s orbital velocity. If your measured speed of light differs by this much between the two tests, you will have found that the light moves at different speeds - but if, as would actually happen, you get the same result in both cases, you know the light reaches you at the same speed independent of your own motion.
I still have a yellowed wad of notes from when, in a physics class, we derived E = m c^2 from the observation that the speed of light is constant, as you note in your OP. Not that I remember it now…
I’m not entirely sure the microwave oven method is legit. I suspect the documented frequency of the microwave was derived from knowing the wavelength and the speed of light to begin with, rather than someone directly measuring it.
I couldn’t remember completely, but a book on relativity I got in sixth grade said that the speed of light was actually derived from using already existent equation. I want to say they had something to do with a Maxwell.
A quick Googling for “maxwell speed of light” got me this Wikipedia article.The relevant paragraph:
I believe he created an equation to demonstrate this, and that that equation did not have velocity as a variable, leading Einstein to hypothesize that the speed of light was constant, regardless of velocity.
There’s a fundamental constant that describes the strength of electric forces, and another fundamental constant that describes the strength of magnetic forces. Maxwell realized that, based on the way that electric and magnetic fields interact, it should be possible to produce waves of electric and magnetic fields, and the speed of the waves is determined by those two constants. So if you measure those two constants, then you can calculate the speed of electromagnetic waves (otherwise known as light). Since those two constants don’t say anything about what reference frame you’re in, the speed you derive from them also doesn’t depend on your reference frame.
I used to have students do the Fizeau method in our Optics Lab. I think the apparatus is actually cheaper than “a few hundred Euros”, but for some reason the websites with the price tags won’t come up on my screen right now.
Incidentally, there was an interesting article in American Journal of Physics many years ago pointing out bthat most textbooks got it wrong about Roemer, giving incorrect and disagreeing values for his speed of light.
You’re probably right — I just thought it was cute.
The Galilean-satellites method is on my list of The Big Three Coincidences of the Universe. (There may be others as intriguing, as improbable, and as important, but these are the ones that have struck me as such.
Any schoolkid can quote off the Sun-Earth distance in miles: 93 million. Now, remember that this is therefore the radius of the Earth’s orbit, and double it to get the diameter: 186 million miles. The speed of light being (to the same level of accuracy) 186,000 MPS, this means that Earth’s orbit has a diameter of 1000 light-seconds. Observation of anything not on or orbiting Earth taken six months apart will differ by 1000 seconds. Things with precise enough periodicity can be used to measure the speed of light and prove this out in consequence. (It’s not an artefact of the measuring system; in metric, SOL is roughly 300,000 kps, and Earth’s orbit is juast about 300,000,000 km across.)
(For what it’s worth, the other two Great Coincidences on my list are (1) that we happen to live at an epoch when the apparent (angular) diameters of the visual disks of the Sun and Moon are nearly precisely the same, resulting in total eclipses (as opposed to transits or occultations, if one were significantly larger than the other. And (2) nuclear power is possible because one nuclide that undergoes chain-reaction fission when concentrated ('fissionable") naturally exists in sufficient quantity to make mining and extracting it feasible not as a gram-weight laboratory curiosity but in commercial or strategic quantities. (Other fissionable nuclides exist but only in trace quantities naturally or owing to artificial production.) That lone nuclide, U-235, has a half-life about ten times what most threories of nucleus structure would have predicted – just long enough to allow it to survive in the slightly-below-1% concentration in nstural uranium ores that makes its production feasible.)
Polycarp, absolutely nice coincidences. I had the sun and moon one, but my other two are that Fahrenheit and Celsius temperatures coincide nearly at the freezing point of mercury (which is just a kind of scale irony or something), and that the number of pascals in a psi is almost exactly the same as some other damn thing I can’t remember. Mine are sucky…
At the risk of further hijacking, it’s also a nice coincidence that we live in an era in which there’s an easily visible star almost directly above Earth’s north pole.
I imagine that the demonstration of constancy of the speed of light that you’re thinking of is the Michelson-Morley experiment. This is a very different thing from measuring the speed of light (it’s not like they measured the speed in two different reference frames and saw that they were the same, which would be hard to do unless you could travel really fast). Also, I’ve read the claim that this result was not so important for inspiring relativity theory.
Polycarp, I’ve long been intrigued and pleased by the Moon/Sun/Eclipse coincidence, which is unique in our solar system, as far as I know. We got lucky on that one since it leads to spectacular solar eclipses.
The fact that the diameter of the Earth’s orbit is 1000 light seconds to a fraction of a percent is absolutely a coincidence of our unit system. Obviously it doesn’t depend on whether we use kilometers or miles, since it has units of time. We accidentally chose one of our units of time so that it comes out close to a power of 10, this does not impress me at all, but it does aid the memory.
Of course we got even luckier with the choice of kilometers as a unit of length, since the speed of light is within a fraction of a tenth of a percent of 300,000 km/s.
When I attended a summer physics program in my high school years (yes, I was and am a “nerd”), I believe we estimated the wavelength of a laser by passing its emission through a diffraction grating and measuring the spread of the resultant emission over a known distance (length of the lecture hall). However, from what I can find on the design of lasers cause them to emit at a certain wavelength, not period, and thus you really don’t get anywhere through this measurement, thus if this experiment was billed as a way to measure the speed of light (which I’m fairly sure it was), it fails.
I think you can use interferometry to determine the period of a laser, but my brain isn’t working well enough to determine if it’s really just wavelength.
Yes, glowacks, I can’t think of any way the laser and grating experiment would give you speed. I think you could be ignorant of the fact that laser light was a time periodic thing - in other words, the nature of light itself - and still deduce some relationships between the grating and the laser. You wouldn’t need to appreciate that time was passing during the experiment.