The blackbody spectrum, against what classical physics predicted

At its defaults it draws the blackbody spectrum, against what classical physics predicted. Spectral exitance against wavelength for a blackbody at 3000, 4000, 5000 kelvin, in kilowatts per square metre per nanometre. Each curve peaks at the wavelength Wien's displacement law gives — 966 nm at 3000 K, 724 nm at 4000 K, 580 nm at 5000 K — and falls to nothing at short wavelengths.

planck-spectrum is one function in lib/figures/quantum.js — the quantum of light and the wave of matter. Everything below came out of it during this build, at parameters taken from the essays rather than invented for this page. A figure here is the figure a reader meets in an essay, and if the generator changes, this page changes with it.

Spectral exitance against wavelength for a blackbody at 3000, 4000, 5000 kelvin, in kilowatts per square metre per nanometre. Each curve peaks at the wavelength Wien's displacement law gives — 966 nm at 3000 K, 724 nm at 4000 K, 580 nm at 5000 K — and falls to nothing at short wavelengths.

The retarding force on a perfectly absorbing body moving through isotropic radiation at 2.725 kelvin, against its speed, for three areas. Moving through a bath of radiation is not free: the radiation arriving from ahead is blue-shifted and more intense and the radiation from behind is red-shifted and weaker, so the body absorbs more momentum from the front than from the back and decelerates. A square metre at half the speed of light feels 3.7e-14 newtons. That is the reason a preferred frame exists without relativity being violated: the laws are the same in every frame and the radiation is not — it is a physical system with a state, and its state picks out the frame in which it is isotropic, exactly as a body of water does.

The spectrum of a blackbody at 2.725 kelvin in its own frame, seen by an observer it is moving past at 0.4 of the speed of light, in 3 directions. Each curve is a Planck spectrum exactly — the Planck form survives a Doppler shift, with the temperature multiplied by the shift — and the temperatures run from 1.78 kelvin looking one way to 4.16 looking the other. So the body is a perfect blackbody in each direction and has no single temperature. A thermometer placed in the radiation reads something between, and what it reads depends on where it is put and on how much of the sky it sees — which is the reason a transformation law for temperature was argued about for sixty years without being found.

The time an electron takes to lose most of its energy to a 2.725-kelvin bath of radiation, against its Lorentz factor, both logarithmic. The mechanism is the drag of the previous figure applied to a single electron, which scatters the radiation rather than absorbing it: the cross-section is Thomson's, and the energy it loses per second goes as the square of the Lorentz factor while its own energy goes as the first power — so the cooling time falls as the reciprocal of the factor. An electron at a Lorentz factor of 10 takes 2.3e+11 years and one at 1e+5 takes 2.3e+7. The steep dependence is what makes the process matter: it is negligible for anything slow and it is the dominant loss for the fast electrons in radio galaxies, whose spectra steepen from the top down as the fastest ones go first.

The time an electron takes to lose most of its energy to a 2.725-kelvin bath of radiation, against its Lorentz factor, both logarithmic. The mechanism is the drag of the previous figure applied to a single electron, which scatters the radiation rather than absorbing it: the cross-section is Thomson's, and the energy it loses per second goes as the square of the Lorentz factor while its own energy goes as the first power — so the cooling time falls as the reciprocal of the factor. An electron at a Lorentz factor of 1000 takes 2.3e+9 years and one at 1e+7 takes 2.3e+5. The steep dependence is what makes the process matter: it is negligible for anything slow and it is the dominant loss for the fast electrons in radio galaxies, whose spectra steepen from the top down as the fastest ones go first.

The retarding force on a perfectly absorbing body moving through isotropic radiation at 5772 kelvin, against its speed, for three areas. Moving through a bath of radiation is not free: the radiation arriving from ahead is blue-shifted and more intense and the radiation from behind is red-shifted and weaker, so the body absorbs more momentum from the front than from the back and decelerates. A square metre at half the speed of light feels 7.5e-1 newtons. That is the reason a preferred frame exists without relativity being violated: the laws are the same in every frame and the radiation is not — it is a physical system with a state, and its state picks out the frame in which it is isotropic, exactly as a body of water does.

physicscheck asserts something about planck-spectrum that could fail — it draws it and measures the result against a value reached some other way.

Across the library: 100 interrogated, 2 exercised only, 1 untouched, of 103. Read out of the gate's source by the gate's own two patterns — and the gate's last claim fails the build if that read disagrees with what it was handed while running.