robryk @robryk@qoto.org

@_thegeoff

I've found a bit more on how that works and it's amusingly simple (tl;dr with a good timing source one can very precisely integrate frequency over time by just counting): https://spie.org/publications/spie-publication-resources/optipedia-free-optics-information/tt61_541_laser_interferometer

The thing I'm still missing is how one gets two closeby frequencies _at orthogonal polarisations_ out of a laser.

@_thegeoff

Sadly, this transformation changes everything far enough that IMO beats do not map to much of anything interesting in the original configuration.

To see that this mapping changes things very significantly, notice that a base frequency and a few harmonics map to something that has no base frequency, but is rather a mixture of a few unrelated frequencies and their common harmonic. This IMO means that interesting relationships between frequencies are not preserved.

If we talk about beats specifically, then the frequency difference "on the audio side" here is a nonlinear function of the frequency difference "on the light side", so even if we were to consider some hypothetical creatures that have very short averaging timescales in vision (so that they can perceive beats at differences e.g. as small as a few MHz[1]), this map to something weird on the audio side (the minimal frequency difference will not be constant over the range we're considering).

[1] This does not necessitate them having awareness of such short time intervals btw.: a human, with help of an FM radio receiver, can do something equivalent to detecting beats with frequency differences of small hundreds of kHz. A creature could have sense organs that can do something similar without their conscious processing having to run at higher speeds.

(BTW. This sounds like a potential worldbuilding idea for a short story.)

@munin @SwiftOnSecurity

> It doesn't - nor can it.

> The shape that is in my mind is unique to me, and will be different in many respects to the equivalent shape in yours -

I'm confused -- how is this related to how well the model (either the one you have or the one you managed to communicate to someone) matches _reality_?

When someone tries to describe a model they have and I don't fully trust it's correct, I desire more precision in what they're saying so that I can evaluate it better. I could try to understand it fully first and then evaluate it, but that might take a lot more time and effort than us both figuring out the model's wrong in some way by having me choose pieces to ask more precision about.

@munin @SwiftOnSecurity

> Communication isn't about precision of words; it's about describing the shape you have in your mind in a way that allows others to create that shape for themselves -

Why would they believe this shape matches reality without precision (or at least ability to call up precision)?

@_thegeoff wait, but didn't this map frequencies to (some multiple) of their inverses?

@_thegeoff wait, but didn't this map frequencies to (some multiple) of their inverses?

@dougmerritt @johncarlosbaez

I don't think children are likely to start with that worldview based on anecdotal evidence: I don't know anyone who initially considered Zeno's (Xeno's?) paradox to be intuitive (@timorl , did you?). When I first learned of it (sometime in primary school) it seemed contrived to me.

@_thegeoff

IIUC you interfere two frequencies that are closeby and thus you can read out the value by looking for a non-zero-frequency envelope in the output. I haven't read enough to know how that works: do they use nonlinear material to literally create a MHzish signal, or do they sample the output light at a MHzish frequency.

(This gives you better tolerance wrt stray light, but I don't know if this is the only reason.)

@johncarlosbaez

Is instantenous speed a central example here? I'm asking because I'm surprised to find it's not an intuitive notion: I don't remember fellow classmates struggling with it (and I do remember struggles with abstractions such as a function that happens to be linear. I will probably ask my 6~8yr old "nephews" in the coming days; suggestions on concrete questions that show the difficulty are very welcome.)

@bert_hubert @johncarlosbaez

Solid state physics had lots of such, ttbomk basically at any time. (I'm not sure whether y'all would call it fundamental physics though; it's in large part about creating models for situations where we already think we have good, albeit intractable, models.)

@_thegeoff btw I've realized that heterodynic(sp?) interferometry is a thing, but haven't managed to dig up how it works exactly (in particular, what's the nonlinear mixer that can accept light and can emit RF, or how does it work without that).

@sophieschmieg

That would be surprisingly nonxenophobic.

@munin What does shot day mean?

@_thegeoff @drskyskull

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.

@_thegeoff @drskyskull

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.

@_thegeoff @drskyskull

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.

@_thegeoff

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).

@_thegeoff

Ah, this surely also relies on the size of the receiver, because it seems to be a consequence of the diffraction limit.

@_thegeoff

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.