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Showing 61–90 of 1709 reference entries

Physics · MeasurementElectric current

Current measures charge crossing a chosen surface per unit time.

DefinitionPhysicsElectric field and force

An electric field assigns force per unit test charge.

DefinitionPhysicsMagnetic force on a moving charge

Magnetic force depends on charge motion relative to the field.

ModelPhysicsOhm's law and its domain

A linear current-voltage relation requires suitable conditions.

Empirical findingPhysicsFirst law of thermodynamics

Keep the heat and work sign convention explicit in an energy balance.

ModelPhysicsSecond law: isolated-system entropy

Apply entropy increase to the whole isolated system.

ModelPhysics · ChemistryIdeal-gas equation of state

A simple gas model relates pressure, amount, volume and temperature.

ModelPhysicsPhoton energy and frequency

One photon's energy is proportional to its frequency.

ModelPhysics · Mathematics & logicInvariant spacetime interval

Lorentz transformations preserve a combined space-time separation.

ModelPhysicsNewton's third law

Interaction forces act on different bodies in equal and opposite pairs.

ModelPhysicsAngular momentum and torque

Torque changes angular momentum about a specified origin.

ModelPhysicsHydrostatic pressure

Static fluid pressure rises with depth under gravity.

ModelPhysicsArchimedes' buoyancy principle

The hydrostatic upward force equals displaced-fluid weight.

ModelPhysicsMaxwell equations in free space

Four field equations connect electric and magnetic fields with charge and current.

ModelPhysicsSchrödinger time evolution

A quantum wavefunction evolves according to its Hamiltonian.

ModelPhysicsBorn position probability

A normalized wavefunction assigns probabilities to position intervals.

ModelPhysics · MeasurementElementary charge

The elementary charge has an exact SI numerical value.

DefinitionPhysics · MeasurementBoltzmann constant

The Boltzmann constant has an exact SI numerical value.

DefinitionMeasurement · Chemistry · PhysicsAvogadro constant

The mole is linked to a specified number of entities.

DefinitionMeasurement · PhysicsSI defining luminous efficacy

A specified frequency fixes the photometric SI reference.

DefinitionChemistryAtoms and elemental identity

The proton count of an atomic nucleus identifies its chemical element.

DefinitionChemistryIsotopes and mass number

Isotopes share a proton count but have different neutron counts.

DefinitionChemistryPeriodic organization of the elements

Atomic-number order reveals recurring patterns in electron structure and chemical properties.

ModelChemistryChemical bonds

Bonding describes interactions that bind atoms into molecules or extended structures.

DefinitionChemistry · MeasurementMole and amount of substance

The mole counts specified entities using the exact Avogadro constant.

DefinitionChemistryReaction stoichiometry

Balanced coefficients relate the amounts consumed and produced by a reaction.

MethodChemistryBalancing atoms and electric charge

A chemical equation must preserve each element's atom count and the total charge.

MethodChemistryDynamic chemical equilibrium

At equilibrium, opposing reactions continue without net composition change.

ModelChemistryBrønsted acids and bases

In the Brønsted description, an acid donates a proton and a base accepts it.

DefinitionChemistryGibbs energy and thermodynamic direction

Gibbs-energy change distinguishes thermodynamic favourability from reaction speed.

Model
ModelSource checked

Invariant spacetime interval

PhysicsMathematics & logic

Lorentz transformations preserve a combined space-time separation.

Key knowledge

Between two events in flat spacetime, Δs² = Δx² + Δy² + Δz² − c²Δt² is invariant under Lorentz transformations between inertial frames, using the spatial-positive sign convention.

Values and equations

Δs² = Δx² + Δy² + Δz² − c²Δt²

Δs²
Squared spacetime interval in the stated sign convention m²
Δx, Δy, Δz
Spatial coordinate differences between the same two events m
Δt
Time coordinate difference between those events s
c
Speed of light in vacuum m s⁻¹

Conditions and scope

  • Coordinates are inertial Cartesian coordinates in special relativity.
  • The opposite overall sign is also a common convention; remain consistent.
  • Curved-spacetime geometry is outside this formula's global scope.
Sources · 2

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. University Physics, volume 3: The Lorentz TransformationSamuel J. Ling, Jeff Sanny and William Moebs / OpenStax, Rice UniversityTextbook chapteropenstax.orgRead source
  2. Relativity · invariant quantitiesAndrew Steane · University of OxfordCourse notes · PDFusers.physics.ox.ac.ukRead source

Evidence and review

OpenStax 5.5, spacetime interval and Lorentz invariance.

2026-10-10 · Flat-spacetime interval with explicit sign convention and units only; no general-relativistic metric is supplied.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Agreement within this scope

The flat-space interval with spatial-positive metric is invariant under Lorentz transformations.

Multiplying the metric by an overall minus sign is an alternative convention.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–3 of 3 relationships

Scientific relationships · 3 / 3

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 1

    The flat-spacetime interval uses the vacuum speed c; its sign convention is explicit.

  2. Related to
    Relationship sources · 1

    Linked statements

    • In general relativity, an ideal force-free test particle follows a metric geodesic: d²x^μ/dλ² + Γ^μ_αβ(dx^α/dλ)(dx^β/dλ) = 0 for an affine parameter λ.

    Metric geometry extends flat-spacetime interval reasoning; affine geodesics use the curved metric connection.

  3. Related to
    Relationship sources · 1

    Linked statements

    • For inertial frames in standard configuration with S′ moving at v along S's x axis, x′=γ_v(x−vt), t′=γ_v(t−vx/c²), y′=y and z′=z, where γ_v=(1−v²/c²)⁻¹ᐟ². Events simultaneous in one frame need not be simultaneous in another.

    The standard collinear inertial boost preserves the flat-spacetime interval with the chosen coordinates.

Entry detailsPermanent link to this entry ↗
Record identity
physics-spacetime-interval
Revision
core.1
Structured reference record
Essential core · first collection · University core expansion