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When a single photon hits a screen - it leaves a dot; and many dots of other photons later - an interference pattern emerges.

My question is about size of a single dot.

What are key factors varying this size? Is there any equation for it?

enter image description here

I saw a video once, where it's been said that a size of a such single dot is directly depended on Uncertainty principle (or may be it was the Planck constant - I'm not sure; energy of a single photon might be involved I suppose as well), and now I just can't find it.

I saw it quite a long time ago, so it might be my perception\memory issue, especially since searching in Google didn't helped at all.

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  • $\begingroup$ I have not heard of a screen that also detects photons. Screens and detectors are as far as i can tell still separate units. But nevertheless, the screen's pixels or a CRT-phosphor has dots that are lit up by the hardware it is built upon and is not proportional to the size of the photon. However the distance between the dots in relation to the resolution of the detector and how the detector measure a photon or packets of electrons are of interest in this case. $\endgroup$ – Natural Number Guy Nov 19 '19 at 1:58
  • $\begingroup$ @NaturalNumberGuy I always thought that photon literally reacts with a "pixel" by exciting electrons inside a pixel in a manner that electrons start emitting their own light. Thus, the distance between dots on a screen is not a question of resolution, since that distance only depends on a wavelength of a measured energy packet and a width of a slit (separation - in case of many slits). $\endgroup$ – Victor Novak Nov 20 '19 at 3:53
  • $\begingroup$ My question was, ultimately, how many "pixels" an individual photon can react with. And the answer provided by @GiorgioP is "just one, at all times - as far as we know" (at least for a $10^{-6}$ m wide "pixels"). $\endgroup$ – Victor Novak Nov 20 '19 at 3:59
  • $\begingroup$ I doubt "pixel-technology" and the double-slit experiment has anything in common. I might be false. If it really is true; then I am amazed on how long a pixel can be lit, and how they can control the time a photon takes to hit the detector and lit up the pixels that make up the interference pattern. In other means, it is in our days impossible to actually have control over a single photon or have a single photon act as a single pixel. For once it would be too small for us to observe, and secondly the double-slit experiment would have been solved and not been a mystery like today. $\endgroup$ – Natural Number Guy Nov 20 '19 at 5:52
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    $\begingroup$ Im no expert in double slit, but you can start here: techbriefs.com/component/content/article/tb/techbriefs/… There are different ways to detect photons. The problem is about how to reduce noise to detect photons. Nano-wires is one method, photon transistors is another. What experamentalists use I don't know. My guess in all of this, is that there is a fluid in space consisting of "quadrillion" tiny particles and their interactions create light/photons. When a photon is detected it causes an interference in this fluid such that the wave-behaviour disappear. $\endgroup$ – Natural Number Guy Nov 20 '19 at 21:14
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The smallest CCD pixels or typical silver grains in analog photography have size of roughly the same order of magnitude (about $10^{-6}$ m ). I would not say that the size of the element which captures the photon is bound by uncertainty principle or by Planck's constant. At least nowadays, size bounds seem to be related more to technological and economical issues.

If your question is about what could be inferred about the size of a photon on the basis of the size of the spot on the screen, I would say that the present days answer is: at least as small as the smallest detecting element we can build. However, there are other (indirect) ways we can obtain information about the effctive size of a photon. In particular, analysis of single photon scattering events is compatible with a point-like photon, i.e. intrinsic finite-size effects are undetectable with the present technology.

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  • $\begingroup$ I've must heard something wrong then. I'll add in first message that I actually saw that video long time ago! $\endgroup$ – Victor Novak Nov 17 '19 at 9:52

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