Noise
The Floor Under Every Measurement
The Hiss That Would Not Go Away
In 1964 Arno Penzias and Robert Wilson pointed a horn antenna in Holmdel, New Jersey, at an empty patch of sky and found a hiss they could not remove. It was faint: the equivalent of a body about three and a half degrees above absolute zero, glowing into the horn from every direction at once. They checked the electronics. They pointed away from the Milky Way, and away from New York. They evicted a pair of pigeons and scrubbed out what Penzias later called a white dielectric material. The hiss stayed.
It was the afterglow of the Big Bang, and one of the most important measurements in the history of cosmology arrived labelled as a fault. That is the right place to start a page about noise. Noise is not a mistake. It is the part of what an instrument reports that has not yet been accounted for, and it comes in two kinds. One kind is a signal nobody expected, and Penzias and Wilson got a Nobel Prize for taking it seriously. The other kind cannot be accounted for by anyone, because physics sets it rather than carelessness. It is a floor. This page is about the floor: where it comes from, how low it goes, and the three constants of nature that decide it.
What Noise Is
Every measurement reports a number, and every number wobbles. Read a voltmeter to enough digits and the last ones flicker. Count the photons from a steady star and the count differs from one second to the next. The wobble is noise, and the first thing to know about it is that it is not lawless. It has statistics, and the statistics are as exact as any signal. A noise you understand tells you how many digits to trust, how long to measure, and when to stop trying.
Three floors matter, and each carries a constant of nature. Counting noise comes from the fact that light and charge arrive in whole units, the photon and the electron’s charge, and it scales with the square root of the count. Thermal noise comes from the jostling of anything warm, and it scales with temperature through Boltzmann’s constant, the same constant that prices an erased bit on The Top of Reality. Quantum noise comes from the uncertainty principle and is set by Planck’s constant. Almost everything below is one of the three, or an experimenter’s fight against one of them. The one exception has never been explained, and it gets a section of its own.
Counting Noise
Light does not arrive as a smooth flow. It arrives as photons, one at a time, at random moments, like rain on a roof. Count the drops on one tile for a second and you get a number; count again and you get a different one. In 1918 Walter Schottky worked out how different, for electrons trickling through a vacuum tube, and the rule is the same for photons, raindrops and radioactive decays. If the average count is N, the typical wobble is the square root of N. A hundred photons wobble by ten. A million wobble by a thousand.
So the noise grows as you collect more, but the signal grows faster. Ten out of a hundred is ten percent; a thousand out of a million is a tenth of a percent. Every extra digit of precision costs a hundred times more light. That is why a photograph in dim light is grainy, why astronomers speak of hours of exposure rather than minutes, and why a camera’s smallest pixels are its noisiest: each one catches fewer photons, and the wobble is a larger share of a smaller count.
Schottky’s rule is also an instrument. If you know the current and can measure the wobble, the ratio hands you the size of the units, and within a few years the hiss of a vacuum tube had been used to weigh the charge of the electron. The noise knows what the current is made of.
Heat Noise
The second floor is warmth. In 1928 John Johnson, at Bell Labs, measured a faint voltage across a plain resistor with nothing connected to it, and found that it grew with temperature, with resistance and with the width of the band he listened in, and with nothing else. Harry Nyquist explained it the same year. The electrons in any conductor above absolute zero are in thermal motion, and their random shuffle is a random voltage. The power of that hiss, per unit of bandwidth, is Boltzmann’s constant times the temperature, full stop. It does not care what the resistor is made of.
The numbers are small and not small enough. A one-kilohm resistor at room temperature, listened to across a megahertz of bandwidth, hisses at about four microvolts. A radio telescope’s first amplifier is rated by the temperature of a resistor that would make the same noise, and the best of them are cooled with liquid helium to bring that figure down to a few kelvin. The three and a half kelvin that Penzias and Wilson could not remove was exactly this kind of number: a noise temperature, and the sky’s own.
Johnson noise has a twin in mechanics. The jitter of a pollen grain in water that Robert Brown saw in 1827 and Einstein explained in 1905 is the same thermal shuffle, delivered by molecules instead of electrons; the Statistical Mechanics page tells that story. In 1951 Herbert Callen and Theodore Welton proved the general law behind both. Anything that can drain energy from a system, whether as electrical resistance or as friction, must also feed random energy back into it, in an exact proportion set by the temperature. Damping and noise are one phenomenon seen from two sides. A pendulum that loses energy to the air must also be kicked by the air. There is no such thing as a quiet brake.
The Noise Nobody Has Explained
Johnson found something else in his vacuum tubes in 1925, three years before the thermal hiss, and it has never been fully explained. At low frequencies the noise did not flatten out. It kept growing as the frequency fell, roughly in proportion to one over the frequency: slow wobbles were louder than fast ones, without limit. It was called flicker noise, and then one-over-f noise once it turned up in resistors, transistors, and nearly everything else.
The list of everything else is the strange part. The same law describes the year-to-year fluctuation of the Nile’s floods, the beat-to-beat variation of a healthy heart, the loudness of music across a whole piece, the brightness of quasars, and the timing of neurons. In 1975 Richard Voss and John Clarke showed that music from Bach to the Beatles has one-over-f statistics in its loudness and pitch, and three years later that melodies generated from one-over-f noise sound more like music than melodies generated from white noise do. No single mechanism produces all of these; several separate ones produce some of them. Whether anything deep unites them is open.
For measurement, one-over-f noise has one brutal property. Averaging does not defeat it. Counting noise falls as you measure longer; flicker noise does not fall at all, because the slow drifts a longer measurement lets in are as loud as the fast wobbles it has averaged away, and anything slower than one-over-f grows. Every precision experiment has a time beyond which measuring longer stops helping, and the trick is to switch the signal on and off faster than the drift and look only at the difference. This is why the finest measurements chop, modulate and compare, rather than stare.
The Quantum Floor
Cool the electronics to a thousandth of a kelvin, gather photons for a year, and one floor remains. To measure where a mirror is, you bounce light off it. More light means less counting noise on the reflected beam. But every photon that bounces gives the mirror a tiny kick, and more light means more random kicks, which move the mirror you were trying to locate. Somewhere in between is a best power, and the noise at that best power is the standard quantum limit. Vladimir Braginsky saw it in 1968 and Carlton Caves gave it its modern form in 1981. It is the uncertainty principle in a laboratory coat.
Caves also saw the way past it, and it is the same loophole the Uncertainty page describes. The principle constrains a product of two uncertainties, not either one. Light can be prepared in a squeezed state, with less noise in the property you read and more in the one you do not. Where counting noise dominates, that is a straight gain; where the kicks dominate, you squeeze the other way. LIGO began injecting squeezed light in 2019, and by 2023 it was squeezing differently at different frequencies, so that each band gets the side it needs and the two noises partly cancel. It now runs below the plain floor across a band, the equivalent of a larger detector without laying another metre of vacuum pipe. The floor did not move. The measurement stepped around it.
Noise as Messenger
Every floor above is also a window. Brownian jitter gave Jean Perrin the number of molecules in a mole. Johnson’s hiss is now a thermometer: because its power depends only on temperature and a resistance you can measure, noise thermometry is one of the ways the kelvin itself is realized in standards laboratories. Shot noise weighed the electron. The three-and-a-half-kelvin hiss that would not go away turned out to be a photograph of universe at three hundred and eighty thousand years old. And the noise curve of a gravitational wave detector, drawn against frequency, is a map of where each floor bites: ground motion and the thermal jitter of the suspensions at the low end, counting noise at the high end, and a handful of narrow spikes where the suspension fibres ring like violin strings.
The lesson is one physics keeps relearning. Noise is what the world sounds like when you listen closer than the signal. It is where the constants of nature are loudest, because it is made of them.
Where the Floor Is Not the Floor
Each floor is exact and each is conditional. Thermal noise falls with temperature, and detectors go to a thousandth of a kelvin to lower it. Counting noise falls with the square root of time, and telescopes stare for weeks. The quantum floor stands only for a fixed way of asking the question, and squeezing changes the question. What no trick removes is the product that Planck’s constant guards: gain on one side and you pay on the other, and the payment can be pushed somewhere you do not care about but never to nothing.
So the honest statement is not that measurement has a floor. It is that every measurement has a floor, set by how it is asked, and moving the floor is most of what experimental physics is. The one limit at the bottom of them all is the same one the Limits of Knowledge page files under quantum: not a wall in front of a fact, but the absence of a fact to find.
