uspol joke
That would be surprisingly nonxenophobic.
re: trans stuff
@munin What does shot day mean?
Yes, sum-up amplitudes and take argument of that. (And it might be brighter/dimmer in different directions. I haven't figured out what will happen if I e.g. take a bunch of sources with positions taken from a Gaussian and with polarisations picked uniformly from a sphere.)
The other thing I wanted to point out is that this is not the thermodynamic case, where the information on which particle went where is there, but unretrievable without investing lots of entropy. In this case the information about source of the particular photon you captured doesn't exist.
Not exactly average phase, but something along these lines.
The reason I say along these lines instead of exactly that is quibbles around the difference between "there's literally no way to distinguish" and "our description considers these equivalent".
BTW. If the source is not monochromatic (as it never is), the notion of in phase becomes weird and complicated.
I think I figured it out in the meantime.
Assume a star is a collection of ideally monochromatic point sources. Then you can clearly see how they will interfere with each other at infinity in a particular direction. The net phase you observe there will be a function of phases of these sources, which avoids the "where does the timeshift asymmetry come from" problem. (Also, amusingly, the "you can't emit polarisationful wave in all directions" seems to still be the case, so there will be a line along which nothing gets emitted. If we allow the sources some bandwidth, this restriction disappears because it doesn't apply across different frequencies.)
Re "which photons we actually see": the question is ill-formed, because they interfere with each other.
I don't think this is what matters for visibility of beats. I would rather expect that what matters is relationship between 1/deltafrequency and time period you are integrating over. I'm not sure what's the effective time period eyes-as-EM-receiving-apparatus are integrating over, but it can't be more than ~1/60s. (If we had more resolving power in wavelength I could also estimate based on that, but alas.)
If I'm right and my naive estimate is roughly correct, sadly seeing beats with one's own eyes would require narrower spectra than any laser I know of (IIUC tens of kHz is already extremely narrow).
BTW an easier way of adjusting the frequency (if we had something with a narrow enough emission spectrum to start with) would be to put it in a magnetic field to split the excited state (see Quantum Light Dimmer in https://www.iypt.org/problems/problems-iypt-2024/).
@_thegeoff If you want to think in terms of photons, then I guess uncertainty principle on transverse directions might be relevant (as it's the source of diffraction limits).
Ah, this surely also relies on the size of the receiver, because it seems to be a consequence of the diffraction limit.
Yeah, I'm labouring under the same confusion. (It started from wondering what it would take to get visible beats: that would require absurdly narrow peaks (~single Hz wide) at a distance of less than ~40Hz. But then, if we somehow had that, what would determine the time offset of beats, assuming the star is large and emitting noncoherently across its surface?)
Perhaps thinking of a classical planar wave (and what can be observed about it in finite time) will be helpful here.
> Sorry for not being clearer: I was thinking more of the spatial coherence than spectral.
Or, actually, to be more precise, I was wondering how similar the situation is to a multitude of emitters emitting at different frequencies, esp. as far as phase coherence between them would manifest. (For non-spatially coherent sources the obvious answer is that you have all the possible phases coming from different directions.)
> The spectral lines are all single wavelengths when emitted
That's certainly wrong: the excited states would be stable if they were energy eigenstates. Are you saying that rotational Doppler smear is much larger than this?
> Further complicated by interstellar hydrogen clouds absorbing different wavelengths depending on their relative velocity, causing the "Lyman-alpha forest", which is a great name for a prog-rock band.
TIL. Thank you very much. Do I UC that this basically applies a filter (so can shift peaks only insofar they are not ideal Dirac deltas)?
Sorry for not being clearer: I was thinking more of the spatial coherence than spectral.
You might wish to look up time delays involved in using melatonin first: I don't remember what they are but I do remember that they sounded unintuitive to me.
Unless I get distracted, I will probably try to make loudnesses of different frequencies to scale.
Now that I think of it: do stars produce coherent light from our POV?
It sounds useful as a source of poison and a component of a trap.
I'm surprised to hear beats, given that I don't think I've seen destructive interference of nearby peaks in spectrum ever. Where does this difference come from?
@_thegeoff Huh, what? I meant that the fillings are usually made from thin (<2mm iirc) layers of a resin that the dentist shapes (or, for the first one, allows surface tension to shape) in a prepared hole in a tooth and solidifies with a UV lamp.
making something solid with light... doesn't that also include (the currently most typical) dental fillings? :)
Eh, też jest https://github.com/osmandapp/OsmAnd/issues/15058
Niby nie jakieś bardzo straszne (ktoś ma log który dla każdego klienta ma historię trójek (czas, adres IP, jakie mapy ściągał) niepowiązaną z niczym innym), ale konwersacja na tym bugu nie napawa mnie wiarą w rozsądek ludzi od osmand (zarówno dlatego, że oznaczyli komentarze gościa zgłaszającego jako "abuse" jak i dlatego, że przez pierwsze ileśtam stron nie przyznali, że czasami to może jakieś informacje wyciekać, nawet jeśli zgłaszający to przerysowuje) :(
(Sytuacja kiedy ten ID zwiększa wyciek to np. taka, w której po zbiorze IP i czasów ściągania map można kogoś zidentyfikować.)
Jednocześnie argument za tym ID jest trochę bez sensu: jeśli chcemy limitować ile _uczciwy klient_ ściąga, to spowodujmy żeby klient po prostu ściągając zgłaszał ile już danego np. dnia ściągnął, albo wysyłajmy ID które się zmienia codziennie.
I enjoy things around information theory (and data compression), complexity theory (and cryptography), read hard scifi, currently work on weird ML (we'll see how it goes), am somewhat literal minded and have approximate knowledge of random things. I like when statements have truth values, and when things can be described simply (which is not exactly the same as shortly) and yet have interesting properties.
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