3 ms·

I am not sure I follow. Here is my attempt to respond to what you raised but feel free to redirect me if I misunderstood. The following is a (simplified, abstr

I am not sure I follow. Here is my attempt to respond to what you raised but feel free to redirect me if I misunderstood. The following is a (simplified, abstracted) way to measure an arbitrary energy value. 1. Set the system up so that the carrier of the energy is a photon (e.g. let the two-level system decay[1] or use some form of transduction or whatever). 2. Send that photon to pass by two semi-transparent mirrors at a certain (continuously parameterized) distance between each other. 3. If the photon passes through both mirrors (as detected by a photon detector at the other side), it means its energy is equal to some known constant divided by the distance between the mirrors. If it does not pass it means it has a different energy. 4. Repeat the experiment many times as you slowly vary the distance between mirrors. I guess in point 4 there is an issue that you need to repeat the experiment with a new realization of your photon each time. Does that have bearing on the initial point being discussed? You are probably seeing this at this point, but just for completeness: this technique is no different from tuning a musical instrument with a tuning fork. I papered over some details about whether we want to detect transmission or reflection and exactly what type of transparency the mirrors need to be, etc. [1] Funnily, the usual way in which someone would prove that decay can happen at all does rely on the existence of a continuous spectrum of energies. This is the same topic I raised above when citing Quantum Optics textbooks.

lisper 2y ago
> this technique is no different from tuning a musical instrument with a tuning fork. Yes, I get that. But there are two problems. First, you cannot tune an instrument precisely. Precise tuning of a real musical instrument isn't even a meaningful concept because any wave with finite temporal extent has non-zero bandwidth. It's the same with energy. The exact same uncertainty relationship between frequency and time produces the Heisenberg uncertainty relation between energy and time, so it is not possible to produce an isolated photon at a known time with a known energy. The best you can do is produce a lot of photons so you don't have to wait forever for one of them to arrive at your detector. So the problem with the setup you describe is that in step 2 the concept of "that photon" is not well defined. Second... > I guess in point 4 there is an issue that you need to repeat the experiment with a new realization of your photon each time. Yes, that too. But you need to do more than that: in order to get a meaningful result you'd need to produce photons with the same energy, i.e. you'd need to use a laser or some other kind of tuned cavity. But it is not meaningful to identify individual photons emitted from a laser because they are identical bosons.

lisper 2y ago

> this technique is no different from tuning a musical instrument with a tuning fork. Yes, I get that. But there are two problems. First, you cannot tune an instrument precisely. Precise tuning of a real musical instrument isn't even a meaningful concept because any wave with finite temporal extent has non-zero bandwidth. It's the same with energy. The exact same uncertainty relationship between frequency and time produces the Heisenberg uncertainty relation between energy and time, so it is not possible to produce an isolated photon at a known time with a known energy. The best you can do is produce a lot of photons so you don't have to wait forever for one of them to arrive at your detector. So the problem with the setup you describe is that in step 2 the concept of "that photon" is not well defined. Second... > I guess in point 4 there is an issue that you need to repeat the experiment with a new realization of your photon each time. Yes, that too. But you need to do more than that: in order to get a meaningful result you'd need to produce photons with the same energy, i.e. you'd need to use a laser or some other kind of tuned cavity. But it is not meaningful to identify individual photons emitted from a laser because they are identical bosons.