2991: Beamsplitters

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Beamsplitters

Title text: Under quantum tax law, photons sent through a beamsplitter don't actually choose which path they took, or incur a tax burden, until their wavefunction collapses when the power is sold.

Explanation

A beamsplitter is a device, usually made from a pair of prisms or a half-silvered mirror, that splits a beam of light into two beams going in different directions. Beamsplitters are used in numerous scientific instruments such as microscopes and (here) telescopes. In a microscope, for example, a beamsplitter may be used to direct the imaging beam to the user's eyes, or to a recording device such as a camera, or to both at once so as to allow visual aiming at specific targets at the same time as conducting scientific measurements upon them. Beam-splitting in order to simultaneously analyse a single 'ray' of light with two or more different types of detectors is also scientifically useful.

In this comic, a beamsplitter is being used in a large-scale telescope to "steal" part of the incident light beam and direct it to a photovoltaic cell. The power generated is then sold on the local grid. The scientists could be pocketing the proceeds, or possibly using them to help pay the telescope operation's bills. This could be dark humor, implying that surreptitious and legally/ethically questionable strategies are needed to fund scientists and their projects. The comic pushes the point by supposing that the practice had become so commonplace that the International Astronomical Union (IAU) got wind of it, and has acted to ban it.

Most optical instruments, even large telescopes, are unlikely to capture enough light during regular operations to make the "banned" strategy feasible. (Far more light would reach the solar cell if it was simply left outdoors, even on a cloudy day.) Moreover, the ban is ham-fisted, as it makes legitimate scientific operation of telescopes profoundly more difficult. For the sake of the joke, both of these issues are ignored.

The telescope shown, without the beam splitter, is a reflecting telescope of the general form of a Gregorian telescope, or a derivative, while the sending of (a fraction of) the light out the side is implemented in the manner of a Nasmyth telescope.

The title text humorously conflates financial tax laws, applicable to the sale of the "stolen" electricity, with the laws of quantum physics, governing the behavior of the photons that are generating the electricity. Under typical capital gains tax laws, certain intangible assets such as stocks are not taxed until they are sold, at which point taxes will be levied on the profits of the sale (relative to the asset's purchase price). This is typically done to simplify tax assessment, as it can be very difficult to assign a concrete value (and thus tax burden) to certain assets until they are sold and the value realized.

The title text imagines a fictional "quantum tax law" in which individual photons are treated as taxable assets. Due to the probabilistic nature of the photon's wave function, the monetary value of any given photon entering the telescope is uncertain up until the point where it strikes the photovoltaic cell, generating an electron which is sold to the power grid. Under the quantum tax law, the "wavefunction" of the photon refers not to its traditional quantum wave function, but to the monetary wavefunction which can only be observed once the photon has generated a tangible profit. This is likely an analogy with capital gains tax which does not accrue until assets are sold at a profit over their purchase price.

Transcript

This transcript is incomplete. Please help editing it! Thanks.

[Cross section of a telescope with some parts of the image darkened to represent the path of light, with portions where the light would be more concentrated being darker]

[Labels with arrows as they appear left to right, top to bottom:]

Incoming Light

Primary Mirror

Secondary Mirror

Beamsplitter

Sensor

Secret Solar Panel

Power Sold To Grid

[Caption below the panel:]

Astronomy News: The International Astronomical Union has finally banned beamsplitters, optical devices used by scientists to embezzle light from their instruments.

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Discussion

Pictures taken by telescope are filtered one colour at the time. If the filtered out colours could be diverted, those photons could be harvested without interfering with the scientific studies. Of course, it would still not be economically efficient. 162.158.127.100 00:33, 28 September 2024 (UTC)

Yes, a classic beam-splitter was the first color TV cameras. Three camera tubes (probably vidicons?) on the three outputs of two filtering beamsplitters. Later they did it all in one bottle; still later three chips on two beamsplitters. Color TV can be whacky. --PRR (talk) 01:35, 28 September 2024 (UTC)

The wavefunction explanation at the time the electron is generated is "wrong". The photovoltaic cell and the electron get entangled. See Wigner's Friend watching Schrödinger's Cat. Sebastian --172.68.110.188 16:19, 30 September 2024 (UTC)

Please edit accordingly, with my thanks! 172.68.22.8 16:31, 30 September 2024 (UTC)

[[1]] 172.68.225.192 (talk) 01:00, 19 November 2024 (please sign your comments with ~~~~) <-- this link seems to be a legit comment on Beamsplitters, but the person who dropped it here really doesn't do themselves too many favours...

A difference of 5 magnitudes corresponds to a factor of 100 in brightness. The sun has magnitude -27, and Vega (by definition) is magnitude 0. This means that at Earth, the sun is 6e10 times brighter than Vega. Therefore a 10m diameter telescope (78.5 m^2) collects as much energy from Vega as a solar panel of size 1.23e-9 m^2, or a square 35 microns on a side. The brightest star, Sirius, is magnitude -1.46, which makes our 10m telescope equivalent to a square solar panel 70 microns on a side. (This calculation is a bit rough. To do it properly, we'd need to know the wavelength band which the solar panel can transform into electricity, and the magnitudes of the sun and star at that specific wavelength band.) 198.41.236.144 03:08, 2 October 2024 (UTC)

Suppose that telescope was aimed towards Vega on a sunny day with a clear sky, with a path that didn't intersect the sun. How much brighter is the sky itself, from scattered sunlight, than Vega? There are a lot of factors that would make a great deal of difference, but suppose we assume that the sun is directly overhead. BunsenH (talk) 19:42, 2 October 2024 (UTC)

At first approximation, similar to a panel of the size of the aperture. Although the difference between the power landing on an 'end cap' panel and reaching down into a reciever down the length of the 'telescope tube' would be that the panel receives light from 2π steradians of sky (albeit only at top efficiency towards the perpendicular), whilst the better analogue might be a panel, the size of the barrel and down the barrel, set back where the primary mirror is so as to receiver (effectively, more or less) collimated light from the top end. Probably equal to a slightly overcast whole-sky (assuming it's a panel with good blue-absorption qualities and decent cross-spectrum sensitivity, rather than heavily reliant upon solar energy bands).

The next question is whether the concentration of this viewport of the sky benefits from being concentrated via the lensing, but I suspect not. If anything, the localised heating might lower the efficiency, etc. 172.69.195.103 21:42, 2 October 2024 (UTC)