Wikipedia:Reference desk/Archives/Science/2024 March 24

= March 24 =

Smallest electric current intensity
Can we consider that the smallest electrical intensity corresponds to one electron per second? Or is there another value? Malypaet (talk) 23:55, 24 March 2024 (UTC)
 * Surely one electron per hour is a smaller intensity than one electron per second. And one electron per day is smaller than that. I don't see that there's any meaningful definition of the "smallest electrical intensity". CodeTalker (talk) 01:53, 25 March 2024 (UTC)
 * Thanks, I hadn't seen things from that angle. The electron is a discrete quantity, but indeed the intensity also depends on time which is continuous. However, if we know the start date of this current, we still know the minimum intensity at a given date: an electron between these two dates. Malypaet (talk) 22:06, 25 March 2024 (UTC)
 * Imagine an infinitesimally thin plane the electron is passing through. Since it is a wave in the electromagnetic field, it is not possible to define when it passes through. But using the probability associated with the wave, we can consider the probability $$p(t)$$ that, at time $$t$$, it has already passed through. The intensity of the current would then be $$e\tfrac{\text{d}p(t)}{\text{d}t},$$ in which $$e$$ denotes the elementary charge. By slowing down the electron, this can be made (mathematically) arbitrarily small. Perhaps the wave packet started to move through when the first electrons came into being and has not made substantial progress since, the prognosis being that it will not even be halfway through at the end of time, $$10^{10^{10^{.^{.^.}}}}$$ eons into the future.  --Lambiam 12:00, 26 March 2024 (UTC)
 * My question was about physics, not math. An electron being a discrete quantity and matter also, in physics, an infinitely thin plane does not exist. Unless they are electrons in a vacuum. But since the measurement of intensity is done by material instruments, we return to discrete quantities. Physics is an experiment. Malypaet (talk) 21:55, 26 March 2024 (UTC)
 * Can you define the notion of the magnitude of the electric current represented by a single moving electron without appeal to mathematical concepts? If a regular stream of electrons moving at a certain velocity represents a certain current, an equally spaced stream at half that velocity will represent half that current. However you choose to define the magnitude of the current of a single electron, the same should hold for this single electron: halve its speed, and you halve its current. So now we should wonder, what is the smallest speed? --Lambiam 09:22, 27 March 2024 (UTC)
 * We can make that speed arbitrarily small, but Heisenberg tells us that we may have to increase the spacing of the stream. Which makes the current even lower. PiusImpavidus (talk) 17:06, 27 March 2024 (UTC)
 * So, the smallest strictly positive current you can measure depends on the time period over which you average it. Yes, an electron can be halfway through, in the sense that it is on both sides at the same time, but when we take a measurement, the wave will collapse and it will be on one side or the other. And taking such a measurement will affect the current. PiusImpavidus (talk) 17:01, 27 March 2024 (UTC)
 * The drift speed of electrons (or holes; i.e. charge carriers) that determines an electric current can in general be astonishingly slow. The current itself propagates at the speed of light since it is carried in the electric field between charge carriers. The way to get more current from a slow sparse electron flow is just to make your conductor thicker (see my first link: $I=nAvQ$) (even if by "electrical intensity" you use a definition resembling formal intensity, that'd again leave wire area in the numerator). And also, since the measured current itself wouldn't have anything much to do how many actual bits and pieces of moving electron in there (since what you're gonna be measuring/experiencing in practice is the interaction between the electrons), you can make this as slow as you want. Electric charge is (likely maybe asterisk) quantized, but current, power, intensity, etc are not. SamuelRiv (talk) 01:06, 31 March 2024 (UTC)