How to Build Your Own Quantum Entanglement Experiment (2013)

It was a metal ruler with the distance markers raised. He put the ruler on a table, reflected a laser off the ruler onto the blackboard and got a diffraction pattern, marked the positions of the lines of the diffraction pattern with some chalk, marked the position of the ruler on the table, and then turned off the laser.

Then using the ruler he measured the distance from the mark on the table to the blackboard, and measured the spacing of the lines in the diffraction pattern. It was then a short bit of math later and he had the speed of light.

Of course he had to use the frequency of the laser in that calculation, and the frequency of the laser was almost certainly calculated using the speed of light so in all likelihood all his demonstration actually did was verify that the frequency of the laser was really what the manufacturer said it was.

That then raises the question of whether there is a way we can determine the frequency of visible light without knowing the speed of light.

We could do it for radio probably fairly easily by a method I'll describe below but I don't know if that could be pushed all the way to visible light. On the other radio might be good enough. A 2.4 GHz radio wave has a wavelength of around 12.5 cm. I'd guess that it would be practical to build something that could make a diffraction pattern with that and let you then calculate the speed of the wave just like my professor did, albeit you'd need a lot more room than we had in the lecture hall.

Here's how I'd go about trying to get a radio wave around 2.4 GHz without knowing the speed of light or using anything that depends on knowing the speed of light.

First, I'd build two variable electronic oscillators and adjust them to match the frequency of the D right above middle C on my piano. That's 293.665 HZ.

Then I'd tune one of the oscillators up until it is twice the frequency of the other. You can build circuits that can detect when one oscillator is twice the frequency of another. You can even use those to build feedback circuits to adjust the tuning of the second oscillator to keep it exactly twice the first if either drifts a little due to things such as temperature changed.

Then tune the first to be twice the second. Keep doing this. If you can do this enough to get 23 doublings you'll end up at 2.46 GHz.

You probably can't actually do that with the original two oscillators, at least if you start off with simple EE 101 circuits. You might have to build more sophisticated oscillators along the way.

Actually, it might be best to build 23 oscillators instead of swapping, so you can have the complete chain of frequency doublings available, with each oscillator locked to twice the frequency of a neighbor by a feedback circuit.

To extend this all the way to visible light you'd need 37 to 44 doublings, depending on which piano note you use as your reference.

37 halvings brings visible light down to 2900-5800 Hz. The notes F#7-C8, 2959.96-4186.01 Hz, (82-88 on the standard 88 key piano) are in that range. You can halve visible light up to 44 times and remain in piano range. 44 halvings bring you to 23-45 Hz. The notes A0-F1, 27.5-43, 6535 HZ, (keys 1-9) are in that.

I don't think we have nearly as much flexibility with light as we do with radio when it comes to making variable oscillators and with making things that can detect when one light source is a frequency that is an integer multiple of another, so I don't know if it this method could be extended far enough.

Nevertheless, there is almost a half of century since it began to be possible to measure directly the frequency of lasers.

Nowadays, the frequency of the lasers is what is known, by measurement, and their wavelength is computed using the speed of light.

Before the speed of light became a conventional constant, there was a wavelength that determined the unit of length and a frequency that determined the unit of time.

At that time, measuring the speed of light was done by measuring both the wavelength and the frequency of a laser, as ratios to the standard of wavelength and to the standard of frequency.

Now, when the speed of light is a conventional constant, what the experiment described by you did, is measuring the length of a ruler using a laser of known frequency, and verifying that the measured length is the same as the length marked on the ruler.

The measurement of the frequency of lasers is done using a special kind of laser, which produces pulses of light, not continuous light, and which can be tuned so that there is a precise ratio between the frequency of the light and the repetition frequency of the pulses. (This kind of lasers are called by the not very explicit name "optical frequency combs")

The repetition frequency of the pulses is in the MHz to GHz range, so it can be compared with the frequency of other oscillators using electronic counters.

The frequency of the light can be compared with the frequency of other light sources using various optical interference methods (taking advantage of the fact that periodic pulses of light have a specter with a very large number of equidistant spectral lines, some of which will be close in frequency to the frequency that must be measured). So in the end, the ratio between the frequency of any low-frequency oscillator and the frequency of any light source can be determined.

If you wanted to perform most or all of the experiments it will probably cost you at least a few thousand dollars (and a few months' time), but the authors have done a great job with the presentation and content and clearly know their stuff.