# Photons “rate of fire”

I'm not sure if this makes any sense but, do photons "discharge" from a source at an infinite rate?

• Interesting and complicated question. I think you can take the energy emission rate and divide it by the average energy of each photon to get an average photo emission rate. I think the strangeness of quantum mechanics makes this only a classical view that isn't truly accurate though. – Brandon Enright Aug 26 '14 at 5:50
• Are you asking whether a photon is created instantaneously? That is, whether the system goes from no photon to one photon in zero time? – John Rennie Aug 26 '14 at 6:13
• Photons are subject to the uncertainty principle. If you try to measure a photon very "quickly", you will lose the information about its frequency/wavelength. In other words... there is really no way to assign an emission/absorption aperture to a photon. That's a property of the measurement device just as much as it is a property of the source that emits them. – CuriousOne Aug 26 '14 at 6:22
• I'm pretty sure the questioner is asking for a rate in # of photons / unit of time. en.wikipedia.org/wiki/Photon_counting – Brandon Enright Aug 26 '14 at 6:25
• @wtoh The apparent speed of the border of the laser dot on the surface of Moon is indeed faster than light, but no information is really transferred. Vsauce has a great recent video on this topic with links to nice visualizations of this. – Void Aug 26 '14 at 11:31

## 1 Answer

You are asking about the number of photons fired from a device such as a laser at a unit time. We cannot say what the precise number of photons would be at any interval due to a version of the Heisenberg uncertainty principle: $$\Delta E \Delta t \geq \frac{\hbar}{2}$$ It basically states we cannot suppress our uncertainty about energy fluctuations in time, such as in a light source, under a certain limit.

However, for any device we can say with certainty it will not fire an infinite number of photons in any time interval. Why? Because the probability of any distribution of "fire-per-time" can be non-zero for any number, but the total probability of all events has to be normalized, i.e. $$\sum_{i=1}^\infty P( i\; {\rm photons\; in\; given\;time \; interval }) = 1$$ The convergence of the sum has a necessary condition that $$P(\infty {\rm \; photons \; fired}) = {\rm lim}_{i\to \infty} P( i\; {\rm photons\; in\; given\;time \; interval }) = 0$$

That is, we are certain any device will not fire an infinite number of photons at any given time interval. Any photon rate of a physical source of light will thus be finite.

This is a formal analysis and could be in principle circumvented. But think about it in a different way. Say every photon is carrying a fixed finite energy. Then an infinite number of photons per unit time would mean an infinite amount of energy per unit time. This is obviously not a property of any possible physical device.

• The above seems like all jargon to me haha. Even though I'm no professor but I guess its illogical for light to carry an infinite amount of energy. Thanks for answering. – wtoh Aug 26 '14 at 11:37
• I guess that for the case you are thinking of, the completely sufficient answer is that the mean rate of photons has to be finite because the mean energy flux has to be finite. (There are some loopholes in this argument, though.) But quantum fluctuations are a weird thing - they cause particles to jump behind walls and all kinds of bizarre stuff, so it is important to ask whether they could cause an infinite rate, even if for a moment. – Void Aug 26 '14 at 11:50