Glossary

So likely that the chance of it failing is exactly zero, even though failing is not logically impossible.

For physicists An event of probability measure 1; its complement is a null set but need not be empty (e.g. second Borel–Cantelli lemma for independent events with divergent probability sum).

Used in If the universe is infinite, is there another you?

See also measure problem

A clock that keeps time by counting the extremely regular vibrations of atoms, so precisely that it drifts by only billionths of a second a day.

For physicists A frequency standard locked to an atomic transition: microwave (Cs hyperfine, which defines the SI second; Rb; H maser at 1.42 GHz) or optical (e.g. Al⁺, Sr).

Used in Time runs faster above your head: relativity in GPS

See also gravitational time dilation

Events produced by things we already understand that look just like the new thing we are hunting for.

For physicists Events from known (e.g. Standard Model) processes passing the selection; expected yield $b$ under $H_0$.

Used in What “five sigma” really means — and what it doesn’t

See also null hypothesis

A preferred spacing in how galaxies are clumped, left by pressure waves in the early universe and used as a cosmic measuring stick.

For physicists Imprint of the sound horizon at the drag epoch, $r_d \approx 147$ Mpc, in galaxy clustering; measures $D_M(z)/r_d$ and $D_H(z)/r_d$.

Used in Is the universe infinite?; The neutrino mass mystery: a floor, a ceiling and three suspects

See also cosmic microwave background

A limit on how much information can fit inside a region of a given size and energy.

For physicists $S \le 2\pi k_B R E/(\hbar c)$ for a system of energy $E$ in a sphere of radius $R$ (Bekenstein 1981); saturated by black holes.

Used in If the universe is infinite, is there another you?

A limit on how strongly the results at two distant detectors can agree if each particle carries its own pre-set answers and nothing travels between the detectors; entangled particles break it.

For physicists Any inequality satisfied by all local hidden-variable models, e.g. CHSH: $|E(a,b)-E(a,b')+E(a',b)+E(a',b')|\le2$. Quantum mechanics reaches $2\sqrt2$ (Tsirelson bound). Derived assuming locality and measurement independence.

Used in How entanglement is actually made; Quantum entanglement: what it is (and isn’t)

See also local realism, hidden variables, entanglement, loophole (Bell test)

The property of some crystals that light travels at different speeds depending on the direction it wiggles (its polarization) and the direction it moves.

For physicists Optical anisotropy; in a uniaxial crystal the ordinary wave sees $n_o$ and the extraordinary wave sees $n_e(\theta)$ with $1/n_e(\theta)^2 = \cos^2\theta/n_o^2 + \sin^2\theta/n_e^2$, $\theta$ being the angle between the wavevector and the optic axis. BBO is negative uniaxial ($n_e < n_o$).

Used in How entanglement is actually made

See also polarization, phase matching

The principle that a cause always comes before its effect, for every observer.

For physicists In relativity, causal influences propagate within the future light cone; signals along spacelike curves would permit reversal of time order between frames and closed causal loops.

Used in Why nothing can go faster than light

See also light cone

A faint flash of blue light given off when a charged particle moves through a material, such as water, faster than light itself travels in that material.

For physicists Coherent emission by a charged particle with speed $v > c/n$; the light forms a cone with $\cos\theta_C = 1/(n\beta)$, used by water detectors to reconstruct direction and particle type.

Used in Ghost particles: the neutrinos passing through you right now

See also neutrino

Keeping only the detections that happen together with a detection of a partner particle, so the data can be sorted pair by pair.

For physicists Recording joint detection rates $R_{0j} \propto \langle E_0^{(-)}E_j^{(-)}E_j^{(+)}E_0^{(+)}\rangle$ within a time window; conditional (post-selected) sub-ensembles reveal correlations invisible in single-detector rates.

Used in The quantum eraser: single photons, a double slit, and what “erasing” really means

See also which-path information

How strictly an upper limit is drawn: at 95%, the quoted value is set so that the data would rarely allow anything higher if the assumptions are right.

For physicists Coverage probability of a frequentist interval (e.g. Feldman–Cousins), or posterior probability content of a Bayesian credible interval; the two coincide only in simple cases and can differ near physical boundaries such as $\Sigma m_\nu \ge 0$.

Used in The neutrino mass mystery: a floor, a ceiling and three suspects

See also standard deviation

The distance beyond which anything that happens today can never send us a signal, because the expansion of space will outpace its light forever.

For physicists Proper distance $D_{\mathrm{EH}}(t) = a(t)\,c\int_t^\infty \mathrm{d}t'/a(t')$; about 16.7 Gly today in flat ΛCDM with Planck 2018 parameters, approaching $c/(H_0\sqrt{\Omega_\Lambda})$ at late times.

Used in Is the universe infinite?; Why nothing can go faster than light

See also Hubble sphere, light cone

A proposed burst of extremely fast expansion in the first tiny fraction of a second, which would have smoothed and flattened space.

For physicists A quasi-de Sitter phase driven by a slowly rolling scalar field; predicts $|\Omega_K|$ far below current sensitivity and nearly Gaussian, nearly scale-invariant adiabatic perturbations; often eternal.

Used in If the universe is infinite, is there another you?; Is the universe infinite?

See also spatial curvature

The faint glow of microwaves filling the sky, released when the young universe first became transparent, which is the oldest light we can see.

For physicists Blackbody radiation at $T_0 = 2.7255$ K from the last-scattering surface at $z_* \approx 1090$, comoving distance $\chi_* \approx 13.9$ Gpc; its anisotropies encode the acoustic scale $\theta_*$.

Used in Is the universe infinite?; The neutrino mass mystery: a floor, a ceiling and three suspects

See also observable universe, baryon acoustic oscillations

The simplest kind of dark energy: an energy of empty space that stays exactly the same as the universe expands.

For physicists Vacuum energy with equation of state $w = -1$ and constant density; the Λ of ΛCDM. Evolving alternatives are often written $w(z) = w_0 + w_a z/(1+z)$.

Used in The neutrino mass mystery: a floor, a ceiling and three suspects

See also dark energy

A measure of how likely a collision is, expressed as the size of the target one particle effectively presents to another.

For physicists $\sigma$ such that the interaction probability in a thin target is $n\sigma L$; solar-neutrino–electron elastic scattering has $\sigma \sim 10^{-45}\ \mathrm{cm^2}$.

Used in Ghost particles: the neutrinos passing through you right now

See also mean free path

The unknown something that makes the expansion of the universe speed up rather than slow down.

For physicists Component with equation of state $w \approx -1$ driving late-time acceleration; in base ΛCDM a cosmological constant with $\Omega_\Lambda \approx 0.685$ (Planck 2018).

Used in Is the universe infinite?; The neutrino mass mystery: a floor, a ceiling and three suspects; Why nothing can go faster than light

See also cosmic event horizon

NASA’s set of giant radio dishes around the world that send commands to distant spacecraft, receive their data and measure where they are.

For physicists NASA’s network of 34-m and 70-m antennas providing telemetry, command and radiometric tracking data (two-way Doppler, ranging, ΔDOR) for deep-space missions.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also Doppler tracking, delta-DOR

A way of pinning down where a spacecraft is on the sky by timing its radio signal at two dishes far apart and comparing with a distant quasar.

For physicists Delta-differential one-way ranging: VLBI-style differenced arrival times at two stations, differenced again against an angularly nearby extragalactic radio source; accuracy approaching 1 nrad.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also Deep Space Network, Doppler tracking

How much a spacecraft has to change its speed or direction with its engines; the basic currency of a space mission’s fuel budget.

For physicists The magnitude of an impulsive velocity change, $\Delta v = \lvert \mathbf v_\text{after} - \mathbf v_\text{before}\rvert$; summed over maneuvers it sets propellant mass via the rocket equation.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also Hohmann transfer, newton-second

Working out how fast a spacecraft is moving toward or away from Earth from the tiny shift in the pitch of its radio signal.

For physicists Two-way coherent measurement of topocentric range rate, $\Delta f \approx 2 v_\text{los} f / c$; insensitive to motion perpendicular to the line of sight except through the diurnal signature.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also Deep Space Network, delta-DOR

A mathematical stand-in that copies everything neutrino mass does to the universe but is allowed to go below zero, to show where the data would like to be.

For physicists $\Sigma m_{\nu,\rm eff}$ (Elbers et al. 2025): equals $\Sigma m_\nu$ for positive values and continues all background and perturbation effects to negative energy density; DESI DR2 + CMB give $-0.101^{+0.047}_{-0.056}$ eV (68%) in ΛCDM.

Used in The neutrino mass mystery: a floor, a ceiling and three suspects

See also neutrino, confidence level

A tiny unit of energy, the energy one electron gains when pushed by one volt, handy for measuring the energy of single particles of light.

For physicists $1\,\mathrm{eV} = 1.602\,176\,634\times10^{-19}\,\mathrm{J}$ (exact in the 2019 SI). A photon of vacuum wavelength $\lambda$ has $E = hc/\lambda \approx 1239.84\,\mathrm{eV\,nm}/\lambda$.

Used in What “five sigma” really means — and what it doesn’t; Ghost particles: the neutrinos passing through you right now; How entanglement is actually made; The neutrino mass mystery: a floor, a ceiling and three suspects; Why nothing can go faster than light

See also photon

A link between particles that are described by one shared state, so their measurement results are correlated in ways no pre-arranged plan can explain, however far apart they are.

For physicists A pure state of a composite system is entangled iff it is not a product state, $\ket{\psi}\neq\ket{\psi_A}\otimes\ket{\psi_B}$; a mixed state iff it is not a convex combination of product states. Entanglement is necessary (not sufficient, for mixed states) for violating a Bell inequality, and never permits signaling.

Used in How entanglement is actually made; Why nothing can go faster than light; Quantum entanglement: what it is (and isn’t); The quantum eraser: single photons, a double slit, and what “erasing” really means

See also superposition, Bell inequality, local realism, no-communication theorem

Describing a random pattern in which looking at many places in one universe tells you the same thing as looking at many separate random universes.

For physicists A statistically homogeneous random field whose spatial averages equal ensemble averages; holds, e.g., for Gaussian fields whose correlations vanish at infinite separation.

Used in If the universe is infinite, is there another you?

See also Hubble volume

Einstein’s theory that explains gravity as the bending of space and time by mass and energy.

For physicists Metric theory of gravitation in which spacetime curvature obeys the Einstein field equations $G_{\mu\nu} = 8\pi G\,T_{\mu\nu}/c^4$ and freely falling bodies follow geodesics.

Used in Time runs faster above your head: relativity in GPS; Is the universe infinite?; Why nothing can go faster than light

See also special relativity, gravitational time dilation

The idealized shape of Earth’s sea level, extended under the continents, where gravity and Earth’s spin combine to make the surface perfectly level.

For physicists Equipotential surface of the gravity-plus-centrifugal potential $W_0$ in the Earth-fixed frame; ideal clocks at rest on it all run at the same rate, with $W_0/c^2 \approx L_G = 6.969290134\times10^{-10}$ defining Terrestrial Time.

Used in Time runs faster above your head: relativity in GPS

See also gravitational time dilation

The bending of light by the gravity of matter it passes on its way to us.

For physicists Deflection by the integrated Weyl potential along the line of sight; for the CMB it smooths the acoustic peaks and is reconstructed from higher-point statistics (amplitude parameter $A_L$).

Used in Is the universe infinite?

See also general relativity

A clock sitting deeper in a gravity well, such as closer to Earth, ticks more slowly than an identical clock higher up.

For physicists In a static weak field, $\dd\tau/\dd t \approx 1 + U/c^2$ with $U$ the Newtonian potential, so two clocks differ in rate by $\Delta f/f = \Delta U/c^2$ (≈ $g\,\Delta h/c^2 \approx 1.1\times10^{-16}$ per meter near Earth's surface); a consequence of the Einstein equivalence principle.

Used in Time runs faster above your head: relativity in GPS

See also general relativity, time dilation, geoid

Unseen properties that particles might carry, which would decide in advance what every measurement on them will show.

For physicists Additional variables $\lambda$ completing the quantum state so that outcomes are (possibly stochastic) functions of $\lambda$ and the setting. Local ones are excluded by Bell’s theorem; nonlocal ones (Bohmian mechanics) are not.

Used in Quantum entanglement: what it is (and isn’t)

See also local realism, Bell inequality

The half-ellipse that just touches the orbit you start on and the orbit you want to reach: the cheapest two-burn route between them.

For physicists Two tangential impulses between coplanar circular orbits via an ellipse with $a = (r_1+r_2)/2$; minimum total $\Delta v$ among two-impulse transfers (bi-elliptic transfers win only for $r_2/r_1 \gtrsim 11.9$).

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also vis-viva equation, delta-v, launch window

How fast the universe is expanding today: how much faster a galaxy recedes for each extra unit of distance.

For physicists $H_0 = \dot a/a$ at $t_0$; Planck 2018 base ΛCDM gives $67.36 \pm 0.54\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, so $c/H_0 \approx 14.5$ Gly.

Used in Is the universe infinite?

See also Hubble sphere

The distance at which the expansion of space carries galaxies away from us at exactly the speed of light; it is not a limit on what we can see.

For physicists $D_{\mathrm{HS}} = c/H(t)$; today $c/H_0 \approx 14.5$ Gly for $H_0 = 67.36\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$. Comoving objects beyond it have $v_{\mathrm{rec}} = HD > c$; it is not a horizon in ΛCDM.

Used in Is the universe infinite?; Why nothing can go faster than light

See also cosmic event horizon, speed of light

Tegmark’s name for a region of space the size of our observable universe, centered on any point.

For physicists A ball of radius ~ the particle horizon (Tegmark uses $4\times10^{26}$ m); not the sphere of radius $c/H_0$. Garriga and Vilenkin’s ‘O-region’ is the interior of the past light cone since recombination.

Used in If the universe is infinite, is there another you?

See also observable universe, Hubble sphere

The pattern of bright and dark bands made when two overlapping waves add up in some places and cancel in others.

For physicists Modulation of a detection probability by the cross term $2\,\mathrm{Re}(\psi_1^*\psi_2)$ in $\lvert\psi_1+\psi_2\rvert^2$; quantified by the visibility $V = (I_\mathrm{max}-I_\mathrm{min})/(I_\mathrm{max}+I_\mathrm{min})$.

Used in The quantum eraser: single photons, a double slit, and what “erasing” really means

See also which-path information, wave–particle duality

The mass worked out from the energies and directions of a particle’s decay products; events from a real particle pile up at its mass.

For physicists $m^2c^4 = (\sum E)^2 - \lvert\sum \vec p\rvert^2 c^2$ of the final-state system, independent of reference frame.

Used in What “five sigma” really means — and what it doesn’t

A large experiment in Karlsruhe, Germany, that weighs the neutrino directly by measuring the energies of electrons from radioactive tritium.

For physicists Tritium β-spectroscopy near the 18.6 keV endpoint; it constrains $m_\beta^2 = \sum_i |U_{ei}|^2 m_i^2$, giving $m_\beta < 0.45$ eV (90% CL) from 259 days of data (Science 388, 180 (2025)).

Used in The neutrino mass mystery: a floor, a ceiling and three suspects

See also neutrino

The stretch of days when the planets are lined up so that a spacecraft can reach its target without needing far more fuel.

For physicists The range of departure dates for which a Lambert (two-point, fixed-time) transfer has an acceptable launch energy $C_3 = v_\infty^2$; for Mars it recurs every synodic period.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also synodic period, Hohmann transfer

The set of all places and times that a flash of light from one event could reach, or could have come from; only events inside it can affect or be affected by that event.

For physicists The null cone $s^2 = 0$ through an event; timelike-separated events (inside) have a frame-independent time order, spacelike-separated events (outside, “elsewhere”) do not.

Used in Why nothing can go faster than light

See also causality, spacetime

The distance light travels in one year, about 9.46 trillion kilometers.

For physicists 1 ly = $c \times$ 1 Julian year = 9.4607 × 10¹⁵ m; 1 Gpc ≈ 3.26 Gly.

Used in Is the universe infinite?

See also observable universe

A score that compares how well two competing explanations predict the very data you got.

For physicists $\lambda(\mu) = L(\mu,\hat{\hat\theta})/L(\hat\mu,\hat\theta)$; for discovery $q_0 = -2\ln\lambda(0)$, with $Z \approx \sqrt{q_0}$ asymptotically (Wald; the boundary at $\mu = 0$ handled as in Cowan et al.).

Used in What “five sigma” really means — and what it doesn’t

See also p-value

The everyday view that objects have their properties before anyone measures them, and that nothing done in one place can affect a distant place faster than light.

For physicists The class of models with $P(A,B|a,b)=\int\dd\lambda\,\rho(\lambda)P(A|a,\lambda)P(B|b,\lambda)$ and $\rho$ independent of the settings; ruled out by loophole-free Bell tests, given measurement independence.

Used in Quantum entanglement: what it is (and isn’t)

See also hidden variables, Bell inequality

The more places you search for a surprise, the more likely you are to find a fake one somewhere just by luck.

For physicists The global p-value (excess at least as significant anywhere in the search range) exceeds the local, fixed-position p-value; the ratio is the trials factor, estimated e.g. with the Gross–Vitells upcrossing method, $p_\mathrm{global} \approx p_\mathrm{local} + \langle N_{u_0}\rangle\,\mathrm{e}^{-(u-u_0)/2}$.

Used in What “five sigma” really means — and what it doesn’t

See also p-value, statistical significance

A weakness in a real experiment that would let a model with pre-set answers fake the quantum result, such as detectors that miss too many particles or stations close enough to signal each other.

For physicists An auxiliary assumption a Bell test relies on: locality (space-like separation), fair sampling (closed for CHSH above $\eta^*=2/(1+\sqrt2)\approx82.8\%$, or $2/3$ with Eberhard states), measurement independence, coincidence-time, memory.

Used in How entanglement is actually made; Quantum entanglement: what it is (and isn’t)

See also Bell inequality, local realism

A number that tells you how much a moving clock slows down and how much harder it is to speed something up; it is 1 at rest and grows without limit near light speed.

For physicists $\gamma = (1 - v^2/c^2)^{-1/2}$; time dilation $\Delta\tau = \Delta t/\gamma$, energy $E = \gamma m c^2$, kinetic energy $(\gamma - 1) m c^2$.

Used in Why nothing can go faster than light

See also special relativity, speed of light

The average distance something travels through a material before it hits something.

For physicists $\lambda = 1/(n\sigma)$ for target number density $n$ and cross section $\sigma$; for photons in a plasma, $\lambda = 1/(\kappa\rho)$ with opacity $\kappa$.

Used in Ghost particles: the neutrinos passing through you right now

See also cross section

The puzzle of how to work out probabilities when there are infinitely many cases, because the answer can depend on the order in which you count them.

For physicists Regulator dependence of ratios of infinite observer counts, $P(A) = \lim N_A/N$, in an infinite (especially eternally inflating) universe; proposals include volume-weighted, causal-patch and scale-factor cutoff measures.

Used in If the universe is infinite, is there another you?

See also cosmic inflation

An electrically neutral, extremely light particle that comes in three types and passes through almost all matter without leaving a trace.

For physicists Neutral lepton of the Standard Model in three flavors ($\nu_e, \nu_\mu, \nu_\tau$), interacting only through the weak interaction and gravity; flavor states are superpositions of mass states $\nu_{1,2,3}$ with $\sum m_i \gtrsim 0.059$ eV.

Used in What “five sigma” really means — and what it doesn’t; Ghost particles: the neutrinos passing through you right now; The neutrino mass mystery: a floor, a ceiling and three suspects

See also neutrino oscillation, neutrino mass ordering

Whether the odd one out among the three neutrino masses is the heaviest (normal ordering) or the lightest (inverted ordering).

For physicists The sign of $\Delta m^2_{31}$: normal ordering $m_1 < m_2 < m_3$, inverted $m_3 < m_1 < m_2$. Minimum sums for a massless lightest state: 0.0588 eV (NO) and 0.0989 eV (IO) with NuFIT 6.0.

Used in The neutrino mass mystery: a floor, a ceiling and three suspects

See also neutrino, neutrino oscillation

The way a neutrino created as one type can later be caught as a different type, which only happens if neutrinos have mass.

For physicists Flavor conversion from the interference of mass eigenstates; in vacuum the two-flavor probability is $P = \sin^2 2\theta\,\sin^2(1.27\,\Delta m^2[\mathrm{eV^2}]\,L[\mathrm{km}]/E[\mathrm{GeV}])$, so oscillations measure $\Delta m^2_{ij}$ and mixing angles, not absolute masses.

Used in Ghost particles: the neutrinos passing through you right now; The neutrino mass mystery: a floor, a ceiling and three suspects

See also neutrino, neutrino mass ordering

The metric unit for the size of a push: a force in newtons multiplied by how many seconds it lasts.

For physicists SI unit of impulse $J = \int F\,\dd t$ (equivalently momentum, kg·m/s); 1 lbf·s = 4.448 221 615 260 5 N·s exactly.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also delta-v

The rule that entanglement cannot be used to send a message: what one side does never changes the odds of the other side’s own results.

For physicists For any bipartite state and local operations, the reduced state of B (hence all of B’s marginal statistics) is independent of A’s choice: $\sum_A P(A,B|a,b)=\sum_A P(A,B|a',b)$.

Used in Why nothing can go faster than light; Quantum entanglement: what it is (and isn’t)

See also entanglement, causality

A transparent crystal whose atoms respond to light in a lopsided way, which lets it mix, double or split the colors of light passing through it.

For physicists A non-centrosymmetric medium with a non-zero second-order susceptibility $\chi^{(2)}$, so the polarization contains a term $P_i^{\mathrm{NL}} = \varepsilon_0 \sum_{jk}\chi^{(2)}_{ijk}E_jE_k$ (e.g. β-BaB$_2$O$_4$, KTiOPO$_4$).

Used in How entanglement is actually made

See also spontaneous parametric down-conversion, birefringence

Light atomic nuclei joining to make a heavier nucleus, releasing energy; it is what makes the Sun shine.

For physicists Exothermic nuclear reactions between light nuclei; in the Sun, net $4p \to {}^4\mathrm{He} + 2e^+ + 2\nu_e$ releasing 26.73 MeV, via the pp chain (about 99%) and the CNO cycle (about 1%).

Used in Ghost particles: the neutrinos passing through you right now

See also standard solar model

The boring explanation you try to rule out, such as “there is no new particle, only things we already know about.”

For physicists The hypothesis $H_0$ under test; in a discovery search, the background-only model ($\mu = 0$), including its nuisance parameters.

Used in What “five sigma” really means — and what it doesn’t

See also p-value, statistical significance

The ball of space around us from which any signal could in principle have reached us since the Big Bang, about 46 billion light-years in radius; the oldest light we see comes from just inside it, about 45 billion light-years away.

For physicists Interior of the particle horizon, comoving radius $D_p = c\int_0^{t_0}\mathrm{d}t/a = c\int_0^1 \mathrm{d}a/(a^2H)$ ≈ 46.1 Gly (14.1 Gpc) for Planck 2018 base ΛCDM.

Used in If the universe is infinite, is there another you?; Is the universe infinite?; Why nothing can go faster than light

See also Hubble sphere, cosmic event horizon, cosmic microwave background

How much of the cosmic microwave background light was scattered by free electrons after the young universe’s gas was ionized again.

For physicists Thomson optical depth $\tau = \sigma_T \int n_e\, c\,\dd t$ to reionization; constrained by large-scale E-mode polarization, Planck $\tau = 0.054 \pm 0.007$; degenerate with $A_s$ through $A_s e^{-2\tau}$.

Used in The neutrino mass mystery: a floor, a ceiling and three suspects

See also cosmic microwave background

The curved path an object follows around a much heavier body, falling toward it but always moving sideways fast enough to keep missing it.

For physicists A Keplerian conic (ellipse, parabola or hyperbola) solving the two-body problem $\ddot{\mathbf r} = -GM\,\mathbf r/r^3$; bound orbits have specific energy $E = -GM/2a < 0$.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also vis-viva equation, periapsis

A number that says how stretched an orbit is: 0 is a perfect circle, and values closer to 1 are longer, thinner ovals.

For physicists For a Keplerian ellipse with semi-major axis $a$, $r = a(1 - e\cos E)$; perigee and apogee radii are $a(1\mp e)$.

Used in Time runs faster above your head: relativity in GPS

See also satellite navigation (GNSS)

If the boring explanation were true, the chance of seeing a result at least as extreme as the one you actually got.

For physicists $p = \int_{t_\mathrm{obs}}^{\infty} f(t\,|\,H_0)\,\mathrm{d}t$ for a test statistic $t$ whose larger values mean worse agreement with $H_0$; it is not the probability that $H_0$ is true.

Used in What “five sigma” really means — and what it doesn’t

See also null hypothesis, statistical significance

The lowest point of an orbit, where a spacecraft passes closest to the planet it is going around or flying past.

For physicists The point of minimum radius on a conic, $r_p = a(1-e)$; for a hyperbolic approach $r_p = (-\mu + \sqrt{\mu^2 + B^2 v_\infty^4})/v_\infty^2$ for impact parameter $B$.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also orbit

The condition that the two new particles of light carry, between them, exactly the push (momentum) of the original one, so that light made in different parts of the crystal adds up instead of cancelling.

For physicists $\Delta\mathbf{k} = \mathbf{k}_p - \mathbf{k}_s - \mathbf{k}_i = 0$ with $|\mathbf{k}| = n(\lambda,\theta)\,2\pi/\lambda$; for a crystal of length $L$ the generated intensity scales as $\mathrm{sinc}^2(\Delta k L/2)$. Achieved in birefringent crystals by angle tuning, or by quasi-phase matching in periodically poled crystals.

Used in How entanglement is actually made

See also birefringence, spontaneous parametric down-conversion

The smallest possible packet of light of a given color; detectors register light as a series of these individual clicks.

For physicists A single excitation of a mode of the quantized electromagnetic field: massless, spin 1 with two helicity (polarization) states, energy $E=h\nu$.

Used in What “five sigma” really means — and what it doesn’t; How entanglement is actually made; Why nothing can go faster than light; Quantum entanglement: what it is (and isn’t); The quantum eraser: single photons, a double slit, and what “erasing” really means

See also polarization

The direction, across its path, in which a light wave’s electric field swings; a polarizing filter lets through light swinging along its own direction and blocks light swinging across it.

For physicists The state of the transverse field vector, a two-level system (e.g. basis $\ket{H},\ket{V}$). A single photon polarized at angle $\theta$ to a polarizer passes with probability $\cos^2\theta$ (Malus’s law for single quanta).

Used in How entanglement is actually made; Quantum entanglement: what it is (and isn’t); The quantum eraser: single photons, a double slit, and what “erasing” really means

See also photon, entanglement

A chemical or physical clue that might have been made by living things but still needs more study before anyone can say whether life was involved.

For physicists NASA’s usage: a substance or structure that might have a biological origin but requires more data or further study before a conclusion about the presence or absence of life.

Used in If the universe is infinite, is there another you?

How plausible an idea seemed before you looked at the new data; the updated value afterwards is called the posterior.

For physicists $\pi(H)$ in Bayes’ theorem, $P(H\,|\,x) \propto P(x\,|\,H)\,\pi(H)$; posterior odds = likelihood ratio × prior odds.

Used in What “five sigma” really means — and what it doesn’t

See also likelihood ratio

A way for two people to build a shared secret key using quantum measurements, so that any eavesdropping leaves detectable traces.

For physicists Protocols such as BB84 (prepare-and-measure) and E91 (entanglement-based, security checked by a Bell test); device-independent QKD bounds the eavesdropper’s information from the observed CHSH value alone.

Used in How entanglement is actually made; Quantum entanglement: what it is (and isn’t)

See also entanglement, Bell inequality

Transferring the exact quantum state of one particle onto a distant particle, using a shared entangled pair plus an ordinary message; the original state is destroyed in the process.

For physicists Bell-state measurement on the input and one half of a shared Bell pair, two classical bits sent to the receiver, then a local Pauli correction (Bennett et al. 1993); no-cloning and no-signaling are respected.

Used in Quantum entanglement: what it is (and isn’t)

See also entanglement, no-communication theorem

A spinning wheel inside a spacecraft that turns the craft by speeding up or slowing down; when it spins too fast, small thrusters fire to unload it.

For physicists Momentum-exchange actuator; external torques (e.g. solar radiation pressure) accumulate wheel momentum, which is dumped by thruster firings (momentum desaturation) that also impart a small net $\Delta v$.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also delta-v

Because Earth spins, a light signal sent around it eastward takes longer than one sent westward, which must be allowed for when synchronizing clocks.

For physicists In a frame rotating at $\omega$, light (or slow clock transport) around a closed path picks up $\Delta t = 2\omega A/c^2$, with $A$ the area projected on the equatorial plane: 207.4 ns for one eastward circuit of the equator.

Used in Time runs faster above your head: relativity in GPS

See also satellite navigation (GNSS), special relativity

A system of satellites carrying precise clocks whose timed radio signals let a receiver work out where it is and what time it is.

For physicists Global navigation satellite systems (GPS, GLONASS, Galileo, BeiDou): a receiver measures pseudoranges $\rho_j = c(t_R - t_j)$ to ≥ 4 satellites and solves for its position and clock bias, with relativistic corrections for clock rates, orbit eccentricity and the Sagnac effect.

Used in Time runs faster above your head: relativity in GPS

See also atomic clock, Sagnac effect

The decades-long puzzle that detectors caught only about a third to a half of the neutrinos the Sun was predicted to make.

For physicists Deficit of measured $\nu_e$ rates (Homestake about 30% of prediction, Kamiokande about 46%) relative to standard-solar-model predictions, resolved by SNO’s 2002 neutral-current measurement showing flavor conversion of solar $\nu_e$.

Used in Ghost particles: the neutrinos passing through you right now

See also neutrino oscillation, standard solar model

Space and time treated as a single four-dimensional stage, where each event has a place and a moment.

For physicists A 4-dimensional Lorentzian manifold; in special relativity, Minkowski space with invariant interval $\mathrm{d}s^2 = -c^2\mathrm{d}t^2 + \mathrm{d}x^2 + \mathrm{d}y^2 + \mathrm{d}z^2$ (signature −+++).

Used in Why nothing can go faster than light

See also light cone, special relativity

How space itself is bent: whether the angles of a huge triangle add up to exactly, more than, or less than 180 degrees; the gentler the bend, the bigger the curvature radius.

For physicists Curvature $K = k/a^2$ of the FLRW spatial sections, parametrized by $\Omega_K = -kc^2/(a_0H_0)^2 = 1-\Omega_{\rm tot}$; curvature radius $R = (c/H_0)/\sqrt{|\Omega_K|}$. $\Omega_K<0$ closed, $\Omega_K>0$ open.

Used in Is the universe infinite?

See also three-sphere, topology (of space)

Einstein’s 1905 theory of how space and time look to observers moving steadily relative to each other, built on the idea that light’s speed is the same for all of them.

For physicists The theory of physics in flat spacetime whose symmetry group is the Poincaré group; inertial frames are related by Lorentz transformations, and $c$ is invariant. Gravity requires the extension to general relativity.

Used in Time runs faster above your head: relativity in GPS; Why nothing can go faster than light

See also speed of light, spacetime, Lorentz factor

The one speed that every observer measures to be the same, about 300,000 kilometers per second, which nothing carrying energy or information can exceed.

For physicists The invariant speed $c$ of Minkowski spacetime, fixed in the SI (since 2019) as a defining constant, $c = 299\,792\,458\ \mathrm{m\,s^{-1}}$ exactly; massless fields propagate at $c$, and the metre is derived from it and the caesium frequency.

Used in Time runs faster above your head: relativity in GPS; Why nothing can go faster than light

See also special relativity, Lorentz factor, light cone

A rare event inside certain crystals in which one particle of light splits into two particles of light that share its energy.

For physicists A $\chi^{(2)}$ three-wave-mixing process, $\omega_p \to \omega_s + \omega_i$ with $\mathbf{k}_p = \mathbf{k}_s + \mathbf{k}_i$, seeded by vacuum fluctuations of the signal and idler modes. To lowest order the output is $|0\rangle + \kappa|1_s 1_i\rangle$ with $|\kappa|^2 \propto$ pump power.

Used in How entanglement is actually made; The quantum eraser: single photons, a double slit, and what “erasing” really means

See also nonlinear crystal, phase matching, entanglement

The typical size of the random scatter of measurements around their average.

For physicists $\sigma = \sqrt{\operatorname{Var}(X)}$; for a Poisson count with mean $b$, $\sigma = \sqrt{b}$.

Used in What “five sigma” really means — and what it doesn’t; How entanglement is actually made; The neutrino mass mystery: a floor, a ceiling and three suspects

See also statistical significance

Physicists’ best computer model of the inside of the Sun, used to predict how many neutrinos it makes.

For physicists One-dimensional evolutionary model of the Sun calibrated to its present radius, luminosity, surface composition and age; predicts neutrino fluxes (e.g. B16) and helioseismic observables.

Used in Ghost particles: the neutrinos passing through you right now

See also nuclear fusion, solar neutrino problem

A p-value restated as “how many standard deviations out on a bell curve,” so that bigger numbers mean more surprising.

For physicists $Z = \Phi^{-1}(1-p)$ for a one-sided p-value (the particle-physics discovery convention); $Z = \Phi^{-1}(1-p/2)$ if both directions count.

Used in What “five sigma” really means — and what it doesn’t; Ghost particles: the neutrinos passing through you right now

See also p-value, standard deviation

A situation in which a quantum system is in a combination of possible states at once, with the outcome of a measurement not decided until it is made.

For physicists A state written as a linear combination $\ket{\psi}=\sum_i c_i\ket{i}$ of basis states, with measurement probabilities $|c_i|^2$ (Born rule); “superposition” is basis-relative.

Used in How entanglement is actually made; Quantum entanglement: what it is (and isn’t); The quantum eraser: single photons, a double slit, and what “erasing” really means

See also entanglement

How long it takes for two planets to come back to the same position relative to each other; for Earth and Mars about 26 months.

For physicists $1/S = \lvert 1/P_1 - 1/P_2 \rvert$ for sidereal periods $P_1, P_2$; Earth–Mars $S \approx 779.9$ d.

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also launch window

A mistake or doubt in how the measuring itself is done, such as a mis-calibrated clock, that often does not shrink just by collecting more data.

For physicists A bias or uncertainty common to all events (calibration, modelling, background shape), typically included as constrained nuisance parameters in a profile likelihood; unlike statistical error it does not scale as $1/\sqrt{N}$.

Used in What “five sigma” really means — and what it doesn’t

See also standard deviation

The three-dimensional version of the surface of a ball: a finite space with no edge, where a straight path eventually brings you home.

For physicists $S^3 = \{x\in\mathbb{R}^4 : |x| = R\}$, constant positive curvature $1/R^2$, volume $2\pi^2R^3$; the spatial section of a closed ($k=+1$) FLRW model.

Used in Is the universe infinite?

See also spatial curvature, topology (of space)

A finite space with no edge, like a box in which leaving through any wall brings you back in through the opposite wall.

For physicists The compact Euclidean manifold $E_1 = \mathbb{E}^3/\mathbb{Z}^3$ obtained by identifying opposite faces of a parallelepiped by translations.

Used in If the universe is infinite, is there another you?; Is the universe infinite?

See also topology (of space)

A clock that is moving relative to you ticks more slowly than an identical clock at rest beside you.

For physicists Proper time along a worldline moving at speed $v$ in an inertial frame: $\dd\tau = \dd t\,\sqrt{1 - v^2/c^2} \approx \dd t\,(1 - v^2/2c^2)$ for $v \ll c$; in GNSS literature also called the second-order Doppler shift.

Used in Time runs faster above your head: relativity in GPS; Why nothing can go faster than light

See also special relativity, gravitational time dilation

How space is connected overall, for example whether traveling far enough in a straight line could bring you back to where you started.

For physicists Global structure of the spatial manifold, e.g. a quotient $\mathbb{E}^3/\Gamma$ of the covering space by a discrete group of isometries; general relativity fixes local curvature but not topology.

Used in Is the universe infinite?

See also three-torus, three-sphere, spatial curvature

A rule that tells you how fast something on an orbit moves at any distance from the Sun, given only the size of its orbit.

For physicists $v^2 = GM\,(2/r - 1/a)$, the energy integral of the two-body problem, with $a$ the semimajor axis ($a<0$ for hyperbolae).

Used in One wrong unit: how we navigate to Mars, and how we once lost a spacecraft

See also orbit, Hohmann transfer

The way quantum objects spread out and interfere like waves while traveling, yet are always detected as single, whole lumps.

For physicists Bohr complementarity in interferometers: path predictability or distinguishability and fringe visibility are mutually exclusive, quantified by $P^2+V^2\le1$ (single particle) and $D^2+V^2\le1$ (with a which-way marker).

Used in The quantum eraser: single photons, a double slit, and what “erasing” really means

See also interference, which-path information

One of nature’s four basic forces: the only one that can turn one kind of particle into another, and the only way neutrinos can affect ordinary matter.

For physicists The SU(2)$_L$ part of the electroweak theory, mediated by $W^\pm$ (charged current) and $Z^0$ (neutral current); at low energy its strength is set by $G_F = 1.1663788\times10^{-5}\ \mathrm{GeV^{-2}}$.

Used in Ghost particles: the neutrinos passing through you right now

See also neutrino

Any physical record, even one nobody ever reads, that could in principle reveal which of two routes a particle took.

For physicists Path-correlated marker states in $(\lvert\psi_1\rangle\lvert M_1\rangle + \lvert\psi_2\rangle\lvert M_2\rangle)/\sqrt2$; for equal path weights the fringe visibility equals $\lvert\langle M_1\vert M_2\rangle\rvert$ and obeys $D^2+V^2\le1$ with the distinguishability $D$.

Used in The quantum eraser: single photons, a double slit, and what “erasing” really means

See also interference, coincidence counting