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Consider this. Due to Heisenberg‘s uncertainty principle, a particle that is localized in position space must be spread out in momentum space. In particular, this applies to photons, so a photon that is not spread out over the entire universe has no definite momentum.

This, as far as I understand, is the reason why atoms (who have discrete spectra) are actually able to absorb photons (the probability for two real numbers being exactly equal is zero).

Now imagine a narrow hole, together with a very fast shutter. If you were to shine monochromatic light on that shutter (e.g. a laser), and if you were to open that shutter for just a very brief moment, you would have light that is very localized in space. Thus, it would have to be very spread out in momentum space, i.e. it would be polychromatic.

Is that really possible? If so, has such an experiment ever been performed?

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  • $\begingroup$ this is not true , in the mainstream standard model " so a photon that is not spread out over the entire universe has no definite momentum." a photon is a point particle with an (x,y,z,t) four vector and an energy momentum four vector.. The HUP applies to the probability of measurement a particular (x,y,z,t) . It is not spread out as you imagine. $\endgroup$
    – anna v
    Commented Aug 25 at 13:08
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    $\begingroup$ By position/momentum of the photon being spread out I of course mean the wave function being spread out in position/momentum space. $\endgroup$
    – BlenderBender
    Commented Aug 25 at 13:24
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    $\begingroup$ Related: physics.stackexchange.com/q/524012/123208 & physics.stackexchange.com/q/311663/123208 & links therein. $\endgroup$
    – PM 2Ring
    Commented Aug 25 at 14:04
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    $\begingroup$ I voted to reopen this because I think it's perfectly mainstream. However, it may be a duplicate of one of the questions that PM 2Ring linked. $\endgroup$
    – benrg
    Commented Aug 26 at 1:14
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    $\begingroup$ Why did this get closed? What the OP describes is what Q switching does and we can indeed relate the bandwidth to the pulse duration. $\endgroup$
    – John Rennie
    Commented Aug 26 at 5:29

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It would be hard to do the experiment you describe using any form of mechanical shutter as the duration of the pulse has to be very short to significantly increase the bandwidth of the light. You'd need a pulse duration of around ten times the period or shorter to have a big effect, and since the frequency of light is of order $10^{14}$ to $10^{15}$ Hz you need a duration of well under a picosecond.

The closest I know of to your suggested experiment is Q switching in lasers although I don't think this can get much below a nanosecond. However it is still short enough to measurably affect the bandwidth.

It is possible, indeed routinely so, to generate very short laser pulses although whether this fits with your idea of the experiment you will have to decide. These ultrashort pulses do indeed have a greatly increased spread of frequencies.

We should note that although what you describe may seem strange to you it is a well know effect that has been understood for hundreds of years. Any signal can be Fourier transformed to calculate its frequency spectrum, and this applies to electromagnetic pulses just as it applies to any form of wave.

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    $\begingroup$ A short and sweet answer. I would have wrote the exact same. $\endgroup$
    – Ritzthephysibeast
    Commented Aug 26 at 7:17
  • $\begingroup$ Thanks! I just wanted to confirm my understanding, and your answer does precisely that. The effect, even though easy enough to predict and understand on the theoretical level, just seemed very surprising to me. I recognize that it may be very hard to realize in an experiment. $\endgroup$
    – BlenderBender
    Commented Aug 26 at 7:28
  • $\begingroup$ imo, your answer is fine as long as the laser is not monochromatic, but has a width in frequencies. Monochromatic means there is one color, which means one frequency which means a single frequency for the photons. $\endgroup$
    – anna v
    Commented Sep 1 at 19:57

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