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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?

BlenderBender
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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.

John Rennie
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