Two ports, and one of them dark
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.
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 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 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 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 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.
Lamp noise that a decay does not notice
The options are the ones The absorption measured with a stopwatch passes. A branch drawn at its own defaults instead would be a picture no essay asked for and no assertion has been run against.
400 simulated measurements of an absorption of 1 × 10⁻⁷ per metre, with a source whose brightness jumps by 5 per cent between shots and a detector with 0.1 per cent noise. Read directly, as transmission through a metre of gas, each measurement scatters by 7 × 10⁻² per metre and the true value is five orders of magnitude below that. Read as a fitted decay from a cavity with 99.99 per cent mirrors, it scatters by 5 × 10⁻⁸, about a million times less. The slope of a logarithm has no information about how bright the pulse started, so a source's noise simply is not in the answer. Most of the method's sensitivity comes from this and only some from the long path.
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.
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.
OpticsThe absorption measured with a stopwatch
The usual way to measure how much light a gas absorbs is to compare a beam before and after, and a very weak absorption vanishes in the flicker of the lamp. Trap a pulse between two excellent mirrors, and it bounces for ten kilometres inside a tube a metre long, leaking out a little at each bounce. How fast that leak dies measures the gas, and how bright the pulse began does not matter at all. A brightness measurement has become a measurement of time.
OpticsThe 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.
OpticsThe depth a broad spectrum can see
Interference is usually spoiled by a broad spectrum: many colours drift out of step, and fringes wash out a few wavelengths from where two paths are equal. Turned round, that failure is a ruler. Light whose colours stay in step only when two paths match to within a few micrometres can report the depth of every reflecting layer inside something translucent — a retina, a skin, a coat of paint — to that precision, without cutting it open. Optical coherence tomography reads depth off the width of a spectrum, and it has become one of the most used imaging methods in medicine; its resolution is set by how many colours the light contains, and the finest instruments use sources whose spectra span hundreds of nanometres.
QuantumThe 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.
OpticsThe faint light a bright one makes measurable
A photodetector does not respond to a light wave's field; it responds to the square of it. Shine a strong beam onto the detector together with a weak one at a slightly different frequency, and the square contains a term that is the weak field multiplied by the strong one — oscillating at the difference frequency, carrying the weak light's phase, and as large as the strong beam cares to make it. That product lifts a picowatt out of an amplifier's noise to the limit set by counting photons, turns an optical frequency shift into a radio one, and carries with it a quantum price that decides why radio telescopes and optical telescopes are built so differently.
QuantumThe 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.
OpticsThe 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.
QuantumThe grating made of light
A diffraction grating is ordinarily made of matter and diffracts light. In 1933 Pyotr Kapitza and Paul Dirac proposed the opposite: a standing wave of light, whose bright and dark bands repeat every half wavelength, should diffract a beam of electrons. It took fifty-three years to see the effect with atoms and sixty-eight to see it with electrons, because a free electron barely notices light. The grating works by momentum: it can only change a particle's motion in whole pairs of photon kicks. A brief flash scatters particles into a spread of orders in proportions fixed by Bessel functions; a slow, gentle one sends every particle one way, which is how laser light became the mirrors and beam splitters of atom interferometers.
OpticsThe hooks that weigh an absorption line
A strong absorption line is black at its centre, and how black it is says almost nothing about how many atoms made it — double them and the line hardly darkens. The atoms are still there, and they still bend light: on either side of the line, where the vapour is transparent, its refractive index rises and falls by an amount proportional to their number. In 1912 Dmitry Rozhdestvensky found a way to read that index straight off a photograph. Interference fringes passed through a spectrograph curl into hooks beside the line, and the distance between the hooks, squared, counts the atoms — whatever the line's shape and however saturated its core.
QuantumThe 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.
QuantumThe molecule that interferes until it glows
A molecule of seventy carbon atoms, sent through a matter-wave interferometer, travels both arms at once and lands in fringes, as an electron or a neutron does. Heat it, and the fringes fade. Nothing has touched it from outside: a hot molecule glows, and each photon it gives off is a messenger that may carry away the information of which arm it was in. Whether it does depends on one comparison — the photon's wavelength against the separation of the arms. Long photons leave the fringes alone; short ones erase them. The loss of interference that is usually described as the onset of the classical world is here a measurement made by the molecule's own light, and its threshold can be computed.
QuantumThe 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.
QuantumThe 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.
OpticsThe width a perfect laser still has
A laser's light is the nearest thing to a single pure frequency that anything makes, and it is still not one. Every photon spontaneously emitted into the lasing mode adds a kick of random phase, and because nothing in a laser cares what its phase is, nothing pulls the phase back: it wanders, and a wandering phase is a line of finite width. Schawlow and Townes worked out how wide in 1958, before any laser had been built. For a milliwatt helium–neon laser the answer is a few thousandths of a hertz, a coherence length a quarter of the way to the Sun — and no real laser of that kind has ever come close, because mirrors move. For a semiconductor laser the answer is megahertz, and the measured lines were wider still, by a factor nobody expected.
QuantumWhere 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.