A dimension in which events occur sequentially from past to future.Time is a fundamental dimension in which events occur sequentially, from the past through the present to the future. It is not just a backdrop for events but an active participant in the laws of physics, intertwined with space in the fabric of spacetime. The nature of time—whether it flows, whether it has a beginning, and why it appears to have a preferred direction—remains one of the deepest questions in physics, touching on relativity, quantum mechanics, and cosmology.
The modern understanding of time began with Isaac Newton's absolute time, but was revolutionized by Albert Einstein's special and general relativity in the early 20th century, which showed that time is flexible and linked to space. The thermodynamic arrow of time was formalized by Ludwig Boltzmann in the late 19th century.
In Einstein's theory of relativity, time is not absolute but relative: it ticks at different rates for observers in different gravitational fields or moving at different speeds, a phenomenon known as time dilation. The 'arrow of time'—the fact that we remember the past but not the future—is linked to the second law of thermodynamics, which states that entropy (disorder) tends to increase in a closed system. This statistical tendency gives rise to the perceived flow of time, even though the fundamental laws of physics are time-symmetric.
Time dilation is a real effect that must be accounted for in GPS satellites, which experience slightly slower time due to their orbital speed and higher altitude, requiring corrections to maintain accurate positioning.
At the event horizon of a black hole, time as measured by a distant observer appears to come to a standstill, a consequence of extreme gravitational time dilation.
| ρ | variable | density matrix of the open quantum system — density matrix |
| t | variable | time — time second |
| H | variable | Hamiltonian of the system — hamiltonian joule |
| L_n | variable | Lindblad operators (jump operators) for each dissipation channel — lindblad operator |
| i | constant | imaginary unit, square root of -1 — imaginary unit = 1 |
| ħ | constant | Planck constant divided by 2π — reduced planck constant = 1.054571817e-34 joule second |
| d/dt | operator | derivative with respect to time — time derivative |
| [H, ρ] | operator | commutator of H and ρ — commutator |
| {L_n† L_n, ρ} | operator | anticommutator of L_n† L_n and ρ — anticommutator |
| ∑_n | operator | sum over all dissipation channels — sum over channels |
| P | variable | probability of survival or decay — probability |
| t | variable | time — time second |
| α | variable | power-law exponent — exponent |
| P(t) | variable | Survival probability at time t — probability |
| t | variable | Time — time second |
| Γ | variable | Decay rate (inverse lifetime) — decay rate per second |
| t_ff | variable | free-fall time — time second |
| G | variable | gravitational constant — gravitational constant cubic metre per kilogram per second squared |
| ρ | variable | mass density — mass density kilogram per cubic metre |
| t | variable | Measurement time — time second |
| N | variable | Number of particles or events — particle number |
| \propto | operator | Indicates proportional relationship — proportionality |
