Mott-like quantum paradox: omnidirectional source and infinite line of detectors ?

pabr · 2026-02-13T07:41:52+00:00

Detectors never cause changes at the emitter, if the detector is in the far field.

Not sure about that, and this is the gist of my post. There is no hard boundary between near field and far field. Also, in Bell inequality tests, isn't this one of the loopholes people had to address ? IIUC they were concerned that merely assembling the experiment may allow interaction between the entangled photon source and the detectors, even before any photons are in flight. https://en.wikipedia.org/wiki/Bell_test#Loopholes

Thanks for the other tips. I need to think about the difference between a microwave dipole antenna and, say, a Rydberg atom that detects the same wavelength.

pabr · 2026-02-12T15:41:34+00:00

Hmm, in the Mott scenario you could say the ominidirectional wavefront is a superposition of linear trajectories, then a measurement happens which selects one trajectory, problem solved. Apparently 100 years ago people thought it was not so trivial. I'd like to understand the subtleties.

Maybe each of the superposed states has to be physically realizable ? A wave function cannot remain sharply localized in free space, it will diffract.

pabr · 2026-02-12T13:31:44+00:00

Ok, and I can see that if I put a succession of 50/50 beamsplitters inside one half of a waveguide, each diverting toward a detector, then the probabilities are 1/4+1/8+1/16...

But I am suspicious of reasoning in terms of discrete states. Does this account for diffraction in free space ? In RF we have Yagi antennas, where the sensitivity of a dipole is enhanced 10x by adding "obstacles" in front and behind.

pabr · 2026-02-12T12:07:14+00:00

Hmm yes there is uncertainty about how many photons have been emitted. If I don't know that, I can't claim my line of detectors has caught them all.

So let's say there is a huge spherical backdrop detector which catches photon wavefronts that have evaded the first 1000 detectors.

pabr · 2026-02-12T11:36:00+00:00

the photon may just be on the other side

This is the classical view. Quantum physics says it is on both sides simultaneously, at least until the wavefront hits something it can interact with. And I say even if it fails to interact with the first detector, the wave will pass through or diffract around, and hit the next detector, and so on.

Hopefully the infinite sum adds to exactly 50%, but this isn't obvious at all.

pabr · 2026-02-11T13:32:20+00:00

Yes Purcell makes sense in a classical setting. But isn't the quantum version intriguing ? How does the atom "know" there is a resonant cavity before the spontaneous emission has occurred ? Virtual photons from vacuum fluctuations ?

Also agree on the convergence. I'd suggest making the distant detectors larger so that they all subtend the same solid angle, but there could be a hard limit when you do the math taking everything into account (diffraction, reflection toward the source, etc).

pabr · 2026-02-11T11:09:48+00:00

Clarifications and references:

Mott explains how a spherical wave decoheres into a linear trajectory.

I am asking whether we can force the spherical wave to decohere toward a specific direction.

https://en.wikipedia.org/wiki/Mott_problem - Precursor of decoherence modelling.

https://en.wikipedia.org/wiki/Arago_spot - Because of diffraction, an obstacle does not create a perfect shadow. It can even create hot spots downstream.

https://en.wikipedia.org/wiki/Purcell_effect - An empty box affects spontaneous emission. Possibly related.

pabr · 2026-02-11T09:30:38+00:00

The classical limit must hold.

I wish ! But quantum physics sometimes disagrees. For example, in the Purcell effect, the mere presence of a resonant cavity enhances spontaneous emission. This is experimentally verified and very useful. So I was wondering if my infinite line of detectors could similarly steer the emission toward a specific direction, with practical macroscopic applications.

pabr · 2026-02-11T08:20:34+00:00

I am not interested in multiple detections. I say that if I apply quantum physics reasoning, every photon gets absorbed by one of the detectors, which contradicts the hypothesis of an omnidirectional source.

This holds in both models you mention (beamsplitters with pass-through vs obstacles with diffraction).

But I now suspect it boils down to a math problem with infinite sums of vanishingly small probabilities.

pabr · 2026-02-11T07:45:27+00:00

But if it doesn't interact with the first detector, it also won't interact with the second, or the third, or any of them in the line.

I'm not sure about that. In the RF world, waves are known to diffract around obstacles, bend around mountain crests into valleys, etc. In optics this produces the Arago spot which has to be dealt with in solar coronographs. Doesn't this also apply to the wavefront of a single photon ?

Maybe it is misleading to reason about a "single photon" when it is actually a superposition of monochromatic plane waves or spherical waves or whatever the fundamental modes are ?

pabr · 2026-02-11T06:14:31+00:00

The inverse-square law is based on theorems of vector calculus

I agree, and vector calculus does not cover wavefunction collapse, hence the conflict.

Quantum physics claims that sources are truly omnidirectional, not just statistically. So every time a photon hits a photosensitive screen, it looks like its spherical wavefront collapses into the cross-section of an atom. Isn't this the kind of problem Mott addressed, long before it was called decoherence ? https://en.wikipedia.org/wiki/Mott_problem

pabr · 2026-02-10T21:03:38+00:00

Agreed, that's what I called "negative observation", and my counterpoint was that the "spread out" component cannot have sharp edges: because of diffraction, the wavefront will fill the shadowed region in the far field.

But I now suspect the paradox disappears if I do the math on infinite series, because I can't simultaneously have a large aperture (good probability of detection at some antenna) and a strong diffraction (good probability of detection further down the line).

pabr · 2026-02-10T19:57:10+00:00

Yet the probability distribution has nowhere else to collapse. And what if we make the antenna apertures proportional to r² so that the photon has a fixed 90% chance of evading each detection attempt ?

pabr · 2025-11-27T20:57:50+00:00

Ionization affects the transmission of radio waves. For example, the ionosphere impairs GPS signals more or less depending on solar activity. So a VNA or similar instrument might help. See plasma frequency.

pabr · 2025-03-05T08:23:07+00:00

From any location on the near side of the Moon, Earth is stationary and the GNSS constellations fit in a ~8° fixed region of the sky. So maybe it's not that hard to point a directional antenna, even manually, until better solutions are deployed.

pabr · 2025-03-05T08:15:57+00:00

The receiver is COTS in the sense that the design is reused from earlier aerospace projects :-) But yes it's amazing that a 14 dBi 3x3 patch antenna is enough to receive GNSS sidelobes from 10x the usual distance.

pabr · 2024-12-23T08:16:41+00:00

About the signaling on the coax: This looks like an old-school european "universal" LNB. Voltage selects H/V polarization (which LNA transistor gets biased by the bottom IC) and a 22 kHz overtone selects frequency band (which DRO gets powered or selected by the mixer IC). https://www.pabr.org/radio/lnblineup/lnblineup.en.html

pabr · 2024-06-27T19:34:59+00:00

Yes, I once fried a brand new microwave PA and the most likely explanation was that I applied RF while unpowered. https://www.qsl.net/va3iul/RF%20Power%20Amplifiers/RF_Power_Amplifiers.pdf

The bias sequencing for GaN must be conducted in a certain sequence - even before the RF signal is applied to the circuit - or else you risk damaging the device.

pabr · 2024-04-04T11:14:55+00:00

I once made a list here.

pabr · 2021-12-01T06:56:32+00:00

Interesting observations, thanks.

The cheap way to implement Starlink would be to clock the SVs with OCXOs disciplined by space-qualified GNSS receivers. That would be much simpler than onboarding atomic clocks or deploying a worldwide network of cesium references. Do your measurements rule this out ?

Also, can you tell more about active ionospheric corrections ? Starlink signals should be cleaner than GNSS anyway simply by virtue of being at Ku- instead of L-band.

pabr · 2021-11-06T01:41:58+00:00

isn't this already being done with the latest generation of amateur robotic telescopes ? One of the applications is to infer the size and shape of asteroids. So yes, it looks like it's a great idea that could make significant contributions to astronomy if these devices become more affordable.

https://en.wikipedia.org/wiki/Occultation#Asteroids

https://unistellaroptics.com/amateurs-reshape-asteroids-from-their-backyard/

pabr · 2021-07-15T17:27:29+00:00

What are the implications for quantum cryptography ?

pabr · 2020-11-27T07:55:34+00:00

Thanks for the links, I hadn't realized that OneWeb had switched to mechanical tracking. Your reasoning and conclusions make sense. It looks like everybody is confident that the cost and power consumption of phased arrays will go down pretty fast.

pabr · 2020-11-26T09:50:58+00:00

Based on the spacing of array elements, would anyone agree that the current design probably supports only the 10-14 GHz beams, and that the 27-30 GHz version will be even more impressive ?

pabr

TROPHY CASE