relativity

Relativity posts

General Galilean invariance

The following is generalized from the explanation of Galilean invariance here. Chorocosm (inertial frames) Among the axioms from Newton’s theory are: (1) There exists an original inertial frame in which Newton’s laws are true. An inertial frame is a reference frame in uniform motion relative to the original inertial frame. (2) All inertial frames share …

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Time transformation

The length part of the Galilean transformation is: with the relative velocity v. The time part of the Galilean transformation is: so that time is the same for all observers. Einstein made time relative and symmetric with length (at least in one dimension) by assuming an absolute speed of light, c. With β = v/c …

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Lorentz with round-trip light

This builds on the post Lorentz transformation derivations but given the round-trip light postulate (RTLP) here which states: The mean round-trip speed of light in vacant space is a constant, c, which is independent of the motion of the emitting body. From this empirical principle the round-trip Lorentz transformations may be derived, which are of the …

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Opposite velocities and lenticities

Two opposite velocities — or lenticities — are invariant over time and space. The standard Galileian transformation in the space-time domain is Velocity u transforms as Velocity is not invariant relative to a single inertial observation, but it is relative to observations with opposite relative velocities: That is Harmonic velocities are opposites and so are …

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Galilean invariance of the wave equation

This post follows James Rohlf’s Modern Physics from α to Z0 (p.104-105). See also the slides here. The Galilean transformations are applied here to 3D space and 3D time in this case because both space and time are independent arguments. Start with the standard configuration for relativity in which motion is parallel to the x-t axis. The …

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Independent and dependent variables

There are two kinds of independent variables: (1) functional independent variables, and (2) physical independent variables. To avoid confusion an independent variable it is standard that a variable be of both kinds, since being of one kind does not imply being of the other kind. A physical independent in an experiment remains the independent variable …

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Wave equation with space and time duality

The following is based on section 3.3.2 of Electricity and Magnetism for Mathematicians by Thomas A. Garrity (Cambridge UP, 2015). See also blog post Relative Motion and Waves by Conrad Schiff. The classical wave equation is consistent with the Galilean transformation in the context of space and time duality. Reflected electromagnetic waves are also consistent with …

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Michelson-Morley experiment

This post relates to a previous post here. The Michelson-Morley experiment is a famous “null” result that has been understood as leading to the Lorentz transformation. However, an elementary error has persisted so that the null result is fully consistent with classical physics. The Michelson-Morley paper of 1887 [Amer. Jour. Sci.-Third Series, Vol. XXXIV, No. …

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Light clock with time-space

This post builds on the post about the Michelson-Morley experiment here. One “Derivation of time dilation” (e.g., here) uses a light clock, pictured below: The illustration on the left shows a light clock at rest, with a light beam reflecting back and forth between two mirrors. The distance of travel is set at the beginning …

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