Illustrated Physics
physics, drawn
Generator

Two ports, and one of them dark

One function in the quantum library, called 50 times across 9 essays. Below: what it draws at its defaults, what it draws at every branch an essay asks for, whether the site's own gate puts a claim to it, and everywhere it is called.

At its defaults it draws two ports, and one of them dark. The two outputs of a balanced two-path interferometer against the phase added to one arm, in turns. With the arms equal, every photon leaves by the same port and the other receives nothing at all — not a little, nothing, to 6.7e-16 across the whole sweep. The photon has not chosen a path and then been redirected; the two amplitudes for reaching the second port cancel, and cancellation is only available because both paths were taken. Half a turn moves every photon to the other port. This is the apparatus the interaction-free measurement is built on, and the dark port is the whole of the mechanism: a detector at a place where nothing ever arrives is an instrument of enormous sensitivity, because anything at all that arrives there is news.

interferometer 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.

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 ports, and one of them dark. The two outputs of a balanced two-path interferometer against the phase added to one arm, in turns. With the arms equal, every photon leaves by the same port and the other receives nothing at all — not a little, nothing, to 6.7e-16 across the whole sweep. The photon has not chosen a path and then been redirected; the two amplitudes for reaching the second port cancel, and cancellation is only available because both paths were taken. Half a turn moves every photon to the other port. This is the apparatus the interaction-free measurement is built on, and the dark port is the whole of the mechanism: a detector at a place where nothing ever arrives is an instrument of enormous sensitivity, because anything at all that arrives there is news.

The two outputs of a balanced two-path interferometer against the phase added to one arm, in turns. With the arms equal, every photon leaves by the same port and the other receives nothing at all — not a little, nothing, to 6.7e-16 across the whole sweep. The photon has not chosen a path and then been redirected; the two amplitudes for reaching the second port cancel, and cancellation is only available because both paths were taken. Half a turn moves every photon to the other port. This is the apparatus the interaction-free measurement is built on, and the dark port is the whole of the mechanism: a detector at a place where nothing ever arrives is an instrument of enormous sensitivity, because anything at all that arrives there is news.

The interference pattern arriving one particle at a time

The options are the ones One arrival at a time, and the pattern still appears 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 interference pattern arriving one particle at a time. The same double slit — 100 micrometres apart, slits 40 micrometres wide, lit at 633 nm, screen 1 metre away — recorded after 20, 200, 1000 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 20 there is no pattern to see; after 1000 the fringes are unmistakable, with the dark ones exactly 6.33 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 15.8 millimetres and is set by the width of one slit alone.

The same double slit — 100 micrometres apart, slits 40 micrometres wide, lit at 633 nm, screen 1 metre away — recorded after 20, 200, 1000 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 20 there is no pattern to see; after 1000 the fringes are unmistakable, with the dark ones exactly 6.33 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 15.8 millimetres and is set by the width of one slit alone.

The interference pattern arriving one particle at a time

The options are the ones One arrival at a time, and the pattern still appears 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 interference pattern arriving one particle at a time. The same double slit — 200 micrometres apart, slits 40 micrometres wide, lit at 633 nm, screen 1 metre away — recorded after 200, 1000 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 200 there is no pattern to see; after 1000 the fringes are unmistakable, with the dark ones exactly 3.17 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 15.8 millimetres and is set by the width of one slit alone.

The same double slit — 200 micrometres apart, slits 40 micrometres wide, lit at 633 nm, screen 1 metre away — recorded after 200, 1000 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 200 there is no pattern to see; after 1000 the fringes are unmistakable, with the dark ones exactly 3.17 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 15.8 millimetres and is set by the width of one slit alone.

The interference pattern arriving one particle at a time

The options are the ones One arrival at a time, and the pattern still appears 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 interference pattern arriving one particle at a time. The same double slit — 100 micrometres apart, slits 12 micrometres wide, lit at 633 nm, screen 1 metre away — recorded after 1000 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 1000 there is no pattern to see; after 1000 the fringes are unmistakable, with the dark ones exactly 6.33 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 52.8 millimetres and is set by the width of one slit alone.

The same double slit — 100 micrometres apart, slits 12 micrometres wide, lit at 633 nm, screen 1 metre away — recorded after 1000 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 1000 there is no pattern to see; after 1000 the fringes are unmistakable, with the dark ones exactly 6.33 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 52.8 millimetres and is set by the width of one slit alone.

The interference pattern arriving one particle at a time

The options are the ones One arrival at a time, and the pattern still appears 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 interference pattern arriving one particle at a time. The same double slit — 100 micrometres apart, slits 25 micrometres wide, lit at 500 nm, screen 1.4 metre away — recorded after 50, 500 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 50 there is no pattern to see; after 500 the fringes are unmistakable, with the dark ones exactly 7.00 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 28.0 millimetres and is set by the width of one slit alone.

The same double slit — 100 micrometres apart, slits 25 micrometres wide, lit at 500 nm, screen 1.4 metre away — recorded after 50, 500 arrivals, with the intensity that governs them plotted underneath. Each arrival is a single dot in one place, drawn at a position sampled from that intensity. After 50 there is no pattern to see; after 500 the fringes are unmistakable, with the dark ones exactly 7.00 millimetres apart — the wavelength times the screen distance over the separation. The bright ones are not evenly spaced, because the single-slit envelope pulls each maximum toward the centre; its first zero is at 28.0 millimetres and is set by the width of one slit alone.

Three sources, and the number that separates them

The options are the ones The correlation that survives what the phase does not passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.

Three sources, and the number that separates them. The chance of detecting a second photon a delay τ after a first, divided by the chance if the two were independent, for three kinds of light. At long delay every curve is one, which is what independence means. At zero delay they are 2, 1 and 0, and those three numbers are three different physical situations. Thermal light is bunched: its intensity fluctuates, and a photon is more likely to be found where the intensity happened to be high, so it arrives with company for as long as the fluctuation lasts — 4 nanoseconds here. A laser is flat, because a coherent state has no intensity fluctuation to correlate with. And a single emitter is antibunched: it gives zero, exactly, because after emitting it is in its ground state and cannot emit again until it has been re-excited, which takes 12 nanoseconds. The zero is the important one. Every classical field, of every possible intensity distribution, has g²(0) at least one — the inequality follows from the fact that the mean square of a real positive quantity is at least the square of its mean. A measurement below one is not merely evidence for photons; it is a result no wave theory can produce.

The chance of detecting a second photon a delay τ after a first, divided by the chance if the two were independent, for three kinds of light. At long delay every curve is one, which is what independence means. At zero delay they are 2, 1 and 0, and those three numbers are three different physical situations. Thermal light is *bunched*: its intensity fluctuates, and a photon is more likely to be found where the intensity happened to be high, so it arrives with company for as long as the fluctuation lasts — 4 nanoseconds here. A laser is flat, because a coherent state has no intensity fluctuation to correlate with. And a single emitter is *antibunched*: it gives zero, exactly, because after emitting it is in its ground state and cannot emit again until it has been re-excited, which takes 12 nanoseconds. The zero is the important one. Every classical field, of every possible intensity distribution, has g²(0) at least one — the inequality follows from the fact that the mean square of a real positive quantity is at least the square of its mean. A measurement below one is not merely evidence for photons; it is a result no wave theory can produce.

What checks it

physicscheck asserts something about interferometer 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.

Quantum

One arrival at a time, and the pattern still appears

Send particles through a double slit slowly enough that only one is ever in the apparatus, and each arrives as a single dot in one place. Wait, and the dots assemble into fringes that no dot knew about.

 Optics

The correlation that survives what the phase does not

Two telescopes can measure a star's diameter by interfering the light, which requires holding two paths equal to a fraction of a wavelength through an atmosphere that will not hold still. Or they can throw the phase away entirely and correlate the brightness fluctuations, which needs the paths equal to a few metres and works.

 Quantum

The experiment a wave cannot pass

The photoelectric effect is offered everywhere as the proof that light is quantised, and it is not one — a classical wave falling on quantised matter reproduces every feature of it. The measurement that no wave can pass is a different one: send single photons at a beam splitter and count how often both detectors fire.

 Quantum

The fall that leaves the mass in the phase

Every body falls the same way whatever its mass, and a neutron is no exception. But a neutron is also a wave, and the phase that wave accumulates while falling depends on the mass — as its square, at a fixed wavelength. Tilt a neutron interferometer so that one path runs a centimetre higher than the other and the neutrons swing between its two detectors, which in 1975 was the first measurement in which gravity and quantum mechanics both had to be right at once.

 Optics

The fringe and the spectrum are one measurement

An interferometer with no prism and no grating in it measures a spectrum, because what it records as the path difference is scanned is the Fourier transform of the source's spectrum. Coherence length and linewidth are the same fact stated twice, and the resolution is bought in centimetres of travel.

 Quantum

The measurement that never touched it

A balanced interferometer sends every photon to one output and none at all to the other. Put an object in one arm and the empty port starts clicking — and a click there is caused by a photon that cannot have gone near the object, because a photon that goes near it is absorbed. The object has been found by light that never met it.

 Quantum

The noise pushed below the floor

A perfectly steady laser beam still flickers, by an amount set by the vacuum itself, and for most of the twentieth century that flicker was treated as the floor of any optical measurement. It is a floor only for one shape of noise. Light can be made quieter than the vacuum in one property by being made louder in another — and the price, the fragility and the use of that trade are all visible in how the noise is shaped, which is why the world's gravitational-wave detectors now run on it.

 Quantum

The outcomes identical photons refuse

Two identical photons meeting at a beam splitter always leave together, and that one fact carries three more. No classical light can empty the coincidence dip more than halfway, so the depth is a test of what light is; the depth measures how identical two photons are, however they differ; and with three photons in a three-way splitter whole classes of outcome become impossible — the first case of a sum over paths that no known algorithm can evaluate quickly as the photons multiply.

 Quantum

Where the interference goes

A superposition does not stop being a superposition when something interacts with it. What happens is that the coherence moves — out of the system and into a correlation between the system and its surroundings — and the interference disappears from any measurement made on the system alone. For a dust grain in air the move takes 10⁻²⁸ seconds, which is why nothing large has ever been seen in two places.

The whole library · All essays