Space-Time Glossary

In order to speak with precision about time terms (1 + 3) I’ve had to invent many new terms. I’ve tried to make them parallel to the corresponding space terms (3 + 1) terms and to follow scientific practice of using Greek and Latin roots. These new terms are placed parallel to their corresponding terms in this pdf: Parallel Glossary for Classical Physics.

The terms below are from the Parallel Glossary of Space and Time for Classical Physics presented in this format: term in bold, definition, units, etymology, and in some cases a suggested symbol. Other terms in this glossary are in italics.

acceleration is the change of velocity per unit of time; verb accelerate; negative is decelerate; zero is unaccelerated; instantaneous acceleration is dv/dt; units of m/s²; symbol a.

angular levamentum for a tempicle time point is the punctum of levamentum, Γt × h, the cross product of the tempicle’s chronation vector, t, and its levamentum vector, h = nw.

angular momentum for a particle space point is the moment of momentum, Lr × p, the cross product of the particle’s location vector, r, and its momentum vector, p = mv.

arc duration is the duration along a curve.

arc length is the length along a curve.

body is a physical entity with spatial and temporal position and extent.

carrier is a body with vass that fills a time; a measure of the lethargy content of a body.

Cartesian coordinates of an event in 3 × 3 are: x1ex1 + x2ex2 + x3ex3 and t1et1 + t2et2 + t3et3 = (x1, x2, x3; t1, t2, t3) = (x; t), where xi and ti are rectilinear spatial and temporal coordinates respectively, x is the vector of location, and t is the vector of chronation.

centre of mass (or barycentre) is the normalized moment of mass; M = Σi ri mii mi.

centre of vass (or elaphrocentre) is the normalized punctum of vass; N = Σi ti nii ni.

chronation is temporal position.

chronation is temporal position; the temporal coordinates; symbol t.

circular motion: space circle S = wavelength λ = 1/h = μ/w = v/f; circular arc s; space radius R; (spatial) angle θ = s/R; frequency f = 1/T = v/λ; angular velocity v = S/T = λf; if S = 1, then v = f; if R = 1, then v = ω = 2πf = θ/t.

clock (horologe) is a device that displays the duration to the present chronation from the time origin at a standard rate.

cyclic motion: time period T = wavetime μ = 1/f = λ/v = w/h; rotation time t; time radius Q; turn angle ϕ = t/Q; periodicity h = 1/S = w/μ; angular lenticity w = T/S = μh; if T = 1, then w = h; if Q = 1, then w = κ = 2πh = θ/s.

dependent variables (or functions) are measures dependent on an independent variable.

diachronic events occur through time.

direction is the position toward which a body moves; it applies to vectors of space or time.

dischronment is the vector from one time point to another in duration space.

displacement is the vector from one space point to another in length space.

distance is the magnitude of displacement.

duration is the magnitude of dischronment.

duration frame of an observer or body is a frame in standard motion relative to it.

elapsed distance is the distance covered by a reference motion.

elapsed time (distime) is the time covered by a reference motion.

energy: the capacity for doing work; units, J ≡ N·m = W·s; symbol E; energy is conserved over time.

event is a physical occurrence with location and chronation.

facilia is the nonresistance of a body to a change in its state of motion; Latin for easy.

facilial frame (or system) bodies without external releases move with uniform lenticity.

force is the agency that tends to change the momentum of a body; time rate of change of momentum; units in newtons, N = kg m s−2; symbol F ≡ dp/dt, e.g., ma.

frame of reference (frame) is a method to assign each body a unique spatial or temporal position in a coordinate system of points in 3.

frame of reference system is a method to assign every event a unique location and chronation in a coordinate system of points in ℝ3 × ℝ3.

gravitation is the mutual force that all bodies have, which is directed toward the mutual centre of mass.

hodologe is a device that displays the distance to the present location from the space origin at a standard rate.

impulse is a force F applied over a time dt, or the change in momentum; units N·s; symbol JF·dt = dp.

independent variable is a quantity determined by the experimenter.

inertia is the resistance of a body to any change in its state of motion.

inertial frame (or system) has bodies without external forces move with uniform velocity.

instantaneous event occurs in a single time point.

isochron line shows equiduration events.

isodistance line shows equidistant events.

kinematics is the study of spatial and temporal positions and extents.

kinetic energy KE = ½mv².

kinetic lethargy KL = ½nw².

length is a 3D space interval.

length frame of an observer or body is a frame of reference at rest relative to it.

length scale (or distance sc.) is a ratio of map length vs actual length.

lenticity (len·tic′·i·ty) (or inverse velocity) is the space rate of dischronment, Δtx; punctaneous lenticity is the derivative of dischronment with respect to time, dt/dx; symbol w; from Latin lentus, slow.

lethargy is the capacity for repose; units, 1/J ≡ O·s; symbol D = 1/E; lethargy is conserved over distance.

levage is the release exerted on a body by levity (from French).

levamentum is the inverse momentum, vass times the lenticity; the space rate of change of the vass-time punctum; plural, puncta; Latin, point; units of kg−1 s m−1; symbol q = nw.

levitation is the mutual release that all bodies have, which is directed toward the mutual centre of vass.

location is spatial position.

location is spatial position; the spatial coordinates; symbol x.

mass is a measure of a body’s inertia; the resistance of a body to a change in its condition of motion as a net force is applied; inverse of vass; units of kg; symbol m.

matter is a body with mass that occupies a space; a measure of the energy content of a body.

metre is the SI unit of length, distance, and stance.

moment is the product of a physical quantity such as mass or force and its length from/to a space point/axis.

moment of inertia is the second moment of mass; I ≡ Σi ri2mi.

momentum (linear) is the mass times the velocity; the time rate of change of the mass-length moment; plural, momenta; units in kg m s−1; symbol p = mv.

motion of a body is a continuous change of its location and chronation.

observer is a frame associated with a body.

odometer (or hodometer) is a device that measures the arc length of motion between space points.

pace (or inverse speed) is the space rate of change of chronation without regard to direction, Δtx; punctaneous pace is the magnitude of punctaneous lenticity: dt/dx; pace is from racing (cf ritmo); symbol w; units of s/m, etc.

particle is a material point with mass and temporal extension.

peel is a release G applied over a length dx or change in levamentum; units O·m; symbol KR·dx = dh.

perstancial events occur through stance.

placidity is the space rate of repose effected: Q ≡ dV/dx = R·u; units: 1/J·m = O·s/m.

power is the time rate of work done: P ≡ dW/dt = F ·v; units: Watt, W = J/s = N·m/s.

punctaneous event occurs in a single stance point.

punctum is the product of a physical quantity such as vass or release and its time from/to a time point.

punctum of facilia is the second punctum of vass; J ≡ Σi ti2ni.

reciprocal addition (or harmonic or parallel) is the reciprocal of the addend reciprocals; symbol ⊞.

release is the agency that tends to change the levamentum of a body; space rate of change of levamentum; units in oldtons, O = kg−1 s m−2; symbol R ≡ dq/dx, e,g., nb.

relentment is the change of lenticity per unit of length; verb relent; negative is derelent; zero is unrelented; punctaneous relentment dw/dx; units s/m²; symbol b; from re- + Latin lentus, slow.

repose (inverse of work) is a release R applied over a dischronment t: Z R·t; for a constant release: Y = R dt = Q dx; units O·s.

second is the SI unit of time and duration.

simulstanceous events all occur at the same stance; n. simulstanceity.

simultaneous events all occur at the same time; n. simultaneity.

space frame of an observer or body is a frame at rest relative to it.

space mean pace or lenticity is the arithmetic mean of paces or lenticities with a common length unit.

space mean speed or velocity is the harmonic mean of speeds or velocities with a common length unit.

space origin is the origin of a spatial coordinate system.

space point (point) is a spatial point.

spatial means relative to the space frame.

speed of a body is the time rate of change of location without regard to direction, Δxt; instantaneous speed is the derivative of distance traversed with respect to time, dx/dt; symbol v; units of m/s, km/hr, etc.

stance (scalar space) is a point on a stanceline.

stanceline is a number line of distances to (counting down) and/or away from (counting up) the space origin; symbol s.

stopwatch is a device that measures the arc time of motion between time points.

strophence is the punctum of release; the rate of change of angular levamentum, σ = Iβ = t × R; from Greek strophe, turn + (e)nce.

synchronous events occur at the same times; vb. synchronize, to make synchronous.

synstanceous events occur at the same stances; vb. synstancize, to make synstanceous.

tempicle is a material time point with vass and spatial extension.

temporal means relative to the time frame.

time (scalar time) is a point (instant) on a timeline.

time mean pace or lenticity is the harmonic mean of paces or lenticities with a common time unit.

time mean speed or velocity is the arithmetic mean of speeds or velocities with a common time unit.

time origin is the origin of a temporal coordinate system.

time point (instant) is a temporal point.

time scale (or duration sc.) is a ratio of map time vs actual time intervals.

timeline is a number line of durations before (counting down) and/or after (counting up) the time origin; symbol t.

torque is the moment of force; the rate of change of angular momentum, τ = Iα = r × F; units: N·m.

traversed distance is the distance covered by a motion in length space.

traversed time (distime) is the time covered by a motion in duration space.

vass measures a body’s facilia; nonresistance of a body to a change in its condition of motion as a net release is applied; inverse of mass; from (in)v(erse) (m)ass; units of kg−1; symbol n.

velocity is the time rate of displacement, Δxt; instantaneous velocity is the derivative of displacement with respect to time, dx/dt; symbol v; from Latin velocitas, rapidity.

weight is the force exerted on a body by gravity.

work is a force F applied over a displacement x: W F· x; for a constant force: W = F dx = P dt; units: J = N·m.