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Imagine that you have 2 devices in a room (say 2 identical smartphones) and you video-call one another. Once connected, you arrange them in such a way that the outer (not the selfie) camera of the first records the screen of the second (which now projects what the first is recording). What should be projected by now is a pattern of recursively nested images (one inside the other)(Droste effect). Due to the processing time of the camera and the finite speed of light, each image should be slightly shifted in time.

If you can count $N$ images, then this time $t_d$ (time_delay) between the $1$st and the $N$th image should be equal to $Nt_p+ N\frac{2d}c$ where $t_p$ the processing delay, $d$, the path-distance from the first device to the corresponding satelite and $c$, the speed of light through the corresponding media. In $t_p$ parameter, all the processing times are included, but if the procedure is repeated 2 or more times, while the $t_p$ parameter remains unchanged, a least squares fitting can be applied from the slope of which you can figure the speed of light, canceling the $t_p$ term out, or else you can(?) look it up so that you obtain a first order linear equation with only one unknown parameter, $c$.

Is such a scenario realistic in order to measure the speed of light? If it is, under which conditions?

(e.g.
(1) you need to use a communication satelite?
(2) you have to repeat some million times in order to perform averaging due to the wireless network noise (can this noise be canceled out?)?
(3) you should use a cetain kind of internet conection or moon-planted internet?)

possible important parameters: refresh rate of the screen (aka of each device), fps of the camera, dimensions of the (ccd?) camera, resolution and dimensions of the screen, brightness of the screen, correspondance of pixels to length unit, path-distance (and perhaps other parameters like atmospheric density) from the device to the satelite and back,

things you may do:

  • switch on and of a light source (light bulb, or led), or
  • use a laser (or a laser pulse of known duration, power),
  • use the screen recorder of the device(s)
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  • $\begingroup$ There is a much easier method of measuring the speed of light by using resonance to set up the 1st harmonic of a standing wave between microwave mirrors, based on the equation $c=f\lambda$. $\endgroup$
    – David White
    Jan 3, 2019 at 1:09
  • $\begingroup$ Thank you, I can also set up the second harmonic etc right? In that case I can measure λ. And I find f knowing the power and the planck constant, h? The thing is, I am not doing that for fun, it is a tournament challenge that asks if one can measure the sol exploiting the Droste effect $\endgroup$
    – POL
    Jan 3, 2019 at 11:56
  • $\begingroup$ You can measure any harmonic, but how do you know which harmonic you are measuring? Answer: start with the reflectors very close together and slowly move them apart. The first resonance occurs at the first harmonic. Also, you know the frequency because you know the characteristics of the circuit that is generating the microwaves. Regarding the Droste effect, you have no way of precisely knowing the time delay associated with the electronics of the cameras that you are using. $\endgroup$
    – David White
    Jan 3, 2019 at 15:34
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    $\begingroup$ @POL by the way, begging "help me ASAP, you are my last chance" kind of doesn't work with strangers on the internet, but sounds a little strange. $\endgroup$
    – Marcus Müller
    Jan 3, 2019 at 18:10

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Welcome to physics stack exchange. You came to the right place. Your method requires that you know the delay due to processing to an accuracy of the order of a a few clock pulse lengths. On a smart phone this is in practice impossible to achieve as many system activities are going on that affect the performance more or less randomly.

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  • $\begingroup$ If I repeat 10^6 times and perform averaging? $\endgroup$
    – POL
    Jan 3, 2019 at 11:51
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    $\begingroup$ @POL lol, no. The processing delay uncertainty is so much larger than the time light travels between two screens that are within camera view... you're trying to measure the thickness of a hair by putting a randomly selected whale right next to it. Whales come in all shapes and sizes. And it's very hard to measure the thickness of whale + hair one million times and get a good measurement of the hair thickness, because a) you don't know how thick the whale is, and b) the whale breathes and turns around and c) you've found the least practical way of measuring thicknesses (or the speed of light). $\endgroup$
    – Marcus Müller
    Jan 3, 2019 at 18:01
  • $\begingroup$ Thank you very much for your clarity. Could i instead use optical fibers connection? ie: not use wireless network, but optical fibers instead, so i can control delay and distance traveled by the wave, without messing up with noises and whales. Or use wireless connection outside the earth atmosphere, say using a satellite on the moon and the 2 devices in a spaceship? thanks again $\endgroup$
    – POL
    Jan 4, 2019 at 20:15

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