Two waves 180° out of step, and their sum
At its defaults it draws two waves 180° out of step, and their sum. Two sine waves differing in phase by 180 degrees, drawn faintly, with their sum drawn solid. The sum is computed point by point.
superposition is one function in lib/figures/waves.js —
travelling, standing, adding and shifting. 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.
At its defaults
Drawn even though every essay passes options, because a default nothing exercises is a trap for the next essay to call this with none — which has happened here twice.
Two sine waves differing in phase by 180 degrees, drawn faintly, with their sum drawn solid. The sum is computed point by point.
A travelling wave, caught at one instant
The options are the ones A wave is a shape that travels, and nothing else does passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats. The ghosted curve is the same wave a moment later.
A travelling wave, caught at one instant
The options are the ones A wave is a shape that travels, and nothing else does passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats. The ghosted curve is the same wave a moment later.
A travelling wave, caught at one instant
The options are the ones A wave is a shape that travels, and nothing else does passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats.
A travelling wave, caught at one instant
The options are the ones A wave is a shape that travels, and nothing else does passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
A sine wave plotted against position at a fixed moment. The wavelength is the distance between repeats. The ghosted curve is the same wave a moment later.
How far the vacuum is from being a nonlinear medium
The options are the ones The one medium that was supposed to add exactly passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
The size of the vacuum's departure from linearity, as a fraction, against the electric field it is subjected to — thirteen decades of field and twenty-eight of correction, both logarithmic. The scale is the Schwinger field, computed here from the electron's mass and the fundamental constants as 1.32e+18 volts per metre: the field at which a pair gains its own rest energy over a Compton wavelength, and therefore the field at which the vacuum stops being a passive backdrop. The marks are the strongest fields that exist. a laboratory magnet, 10 T is 2.3e-9 of it; a hydrogen atom's own field is 3.9e-7 of it; a 10²² W/cm² laser focus is 2.1e-4 of it; the Schwinger field is 1.0e+0 of it; a magnetar, 10¹¹ T is 2.3e+1 of it. So a laboratory is twenty-eight decades from making the effect large, and a magnetar's field is above the critical one — which is why the only places the vacuum's nonlinearity has been seen are the two where the fields are not human: the ultraperipheral collision of two heavy nuclei, and the surface of a neutron star.
What checks it
physicscheck asserts something about superposition 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.
Where it is called
Changing this generator changes every figure on this list. That is what makes the list worth publishing rather than keeping in a check script.
A wave is a shape that travels, and nothing else does
In a wave on water, no water goes anywhere. What moves is the shape — and separating the two motions is the whole of wave physics.
WavesThe one medium that was supposed to add exactly
Superposition holds because an equation is linear, and every material stops being linear at some amplitude. Empty space was the exception: Maxwell's equations are linear exactly, and two beams cross with no interaction of any kind. Quantum electrodynamics says otherwise — light scatters light, and a strong field makes the vacuum birefringent — at a field of 1.3 × 10¹⁸ volts per metre, which no laboratory has come within four decades of.
ElectromagnetismThe term that made light
Ampère's law contradicts itself the moment a current stops being steady, and the contradiction is visible in one picture: two surfaces on the same loop, with a current through one of them and nothing through the other. The term that repairs it turns four equations into a wave, whose speed is two constants measured in a room with the lamps off.
WavesWhat adding does to the energy
Waves add their amplitudes and detectors read squares, so two waves together do not deliver the sum of what each delivers. Where the two get dimmer, the natural question is where the energy went — and the answer depends entirely on whether the sources can feel each other.
WavesWhen two waves meet, they simply add
Waves pass through each other unchanged and their displacements add point by point. From that one impoverished-sounding rule comes interference, beats, and the evidence that light is a wave at all.