Relativity posts
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 […]
Part 1 is here. C Measures of motion A motion in RN is a differentiable mapping x: I → RN, where I is an interval on the real axis. The derivative is called the velocity vector at the point r0 ∈ I. The second derivative is called the acceleration vector at the point r0. We
Mathematical methods of classical mechanics, part 2 Read More »
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
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
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
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
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.
Revised 2022-08-23. There are many expositions of the famous Michelson-Morley experiment (for example here) but they all assume the variable in common is time, which is not the case. In fact, distance is the variable in common, and so the experiment is temporo-spatial (1+3). Let us examine the original experiment as it should have been
The relativity of uniform motion was stated by Galileo in the 17th century, though it was known to Buridan in the 14th century. Galileo’s statement of the principle of relativity is in terms of ships in uniform motion: … so long as the motion is uniform and not fluctuating this way and that. You will
This post was inspired by Chandru Iyer’s post here. Consider a light ray sent a certain distance s that is immediately reflected back. According to Newtonian mechanics if a light ray travels at speed c, then for a body moving at speed v relative to the stationary frame, the light ray should travel at the
