Shot noise is fluctuation associated with discrete transfer events. For an electric current, individual charge carriers contribute finite amounts of electric charge, even when a meter displays a smooth mean. The simplest model is a stream of equal, independently arriving charges with constant rate: its Poisson process predicts both the mean electric current and the variance around it. Discreteness alone does not imply a Poisson distribution; the timing and correlations matter.

The useful surprise is that noise can reveal something a mean hides. Two devices can carry the same mean electric current yet have different fluctuations because one transfers charges independently and the other groups or regulates them. A calibrated shot noise photocurrent measurement can connect a macroscopic voltage variance to the elementary charge. Thermal electrical noise instead exists in an unbiased resistor at thermal equilibrium; a measured background can contain both mechanisms.

Walter Schottky's 1918 paper Über spontane Stromschwankungen in verschiedenen Elektrizitätsleitern treated amplifier sensitivity limits. Part II considered independent discrete transfers, including thermionic emission through a vacuum. On p. 563 he proposed amplifying fluctuations from a separate discharge tube to determine the elementary charge; those experiments were prospective, not reported results.^[ref]

Fluctuations associated with nonzero temperature, including mechanical Brownian motion and electrical noise.

Low-frequency noise with an approximately inverse-frequency power spectral density over a specified range. It can dominate the flat spectrum of a weakly confined mechanical coordinate or an electronic readout at low frequencies. A $1/f$ law cannot hold with finite total variance over unlimited frequency range, so its measured bandwidth and low-frequency cutoff matter. An observed excess alone does not uniquely identify the microscopic source.

Improve a circuit's signal-to-noise ratio by reducing unwanted coupling and physical noise sources while retaining the signal bandwidth. Important methods include lowering appropriate resistances or temperature to reduce thermal electrical noise, controlling leakage and bias currents relevant to shot noise, minimizing pickup with shielding and small loop area, and selecting an operational amplifier for the source electrical impedance. Filtering limits integrated noise only if it preserves the information-bearing spectrum; a lock-in amplifier can move detection above a flicker noise region and select a narrow band. Uncorrelated noise variances add, whereas coherent pickup requires its phases and correlations to be considered. Repeated averaging reduces independent random error, but does not remove an arbitrary systematic error or slow drift.

Radon is the chemical element with atomic number 86 and symbol $\mathrm{Rn}$. It is a noble gas. All its isotopes are radioactive. Radon-222 is formed in the uranium decay series and can leave the mineral containing its solid parent because it is a gas, linking nuclear decay with transport through pores and buildings.^[ref]

Krypton is the chemical element with atomic number 36 and symbol $\mathrm{Kr}$. It is a noble gas. It is a monatomic gas under ordinary conditions and occurs as a minor component of air. Electrical excitation produces characteristic emission lines, connecting its atomic levels with lighting and spectroscopy.^[ref]

The nitrogen isotope with seven protons and seven neutrons.

NAD+ is the oxidized form of nicotinamide adenine dinucleotide; NADH is its reduced form.

A magnetic horn uses a pulsed magnetic field around a high-current conductor to focus charged secondary pions and kaons of a selected sign. Their decays then create a directed neutrino beam. The field acts on the charged parents, not on the neutral neutrinos.

A decay tunnel provides a low-density flight region where selected unstable particles decay before remaining charged particles are removed or absorbed. For a pion-produced neutrino beam, its length balances pion decay probability against backgrounds from longer-lived daughters.

Neptunium-239 is a radioactive isotope with ninety-three protons and one hundred forty-six neutrons. It beta-decays to plutonium-239.

It occurs in the sequence following neutron capture by uranium-238 and beta decay of uranium-239. This is an example of transmutation changing the chemical element through a nuclear process, unlike an ordinary chemical reaction that rearranges electrons and bonds.

Outside a Schwarzschild metric horizon $r_s$, write $r-r_s={\rho }^2/(4r_s)$. To leading order the radial metric isIt has Rindler coordinates with $\alpha =c/(2r_s)$. The proper-distance-like coordinate $\rho$ has null paths exponential in $\pm ct/(2r_s)$; the Schwarzschild coordinate difference $r-r_s\propto {\rho }^2$ is exponential in $\pm ct/r_s$.

Inside, writing $r_s-r={\rho }^2/(4r_s)$ instead gives $d{s}^2\simeq d{\rho }^2-[c\rho /(2r_s){]}^{2}d{t}^2$, where the radial coordinate is timelike. The negative-$x$ Rindler wedge is therefore not the black-hole interior: its time coordinate retains the same causal type as in the positive-$x$ wedge. The flat radial limit does not remove the genuine curvature of the full Schwarzschild spacetime.