relativity

Changing coordinates for the wave equation

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. Reflected electromagnetic waves are also consistent with classical physics using the dual Galilean transformation, in …

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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. Let us look at it in detail: The Michelson-Morley paper of 1887 …

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Temporo-spatial light clock

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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Michelson-Morley re-examined

There are many expositions of the famous Michelson-Morley experiment (for example here) but they all assume the independent variable is time, which is not the case. As we shall see, distance is the independent variable, and so the experiment is temporo-spatial (1+3). Let us examine the original experiment as it should have been done: The configuration …

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Principle of relativity

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 …

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Reflected motion

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 …

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Space and time reciprocity

This post is related to others, such as here. Consider an analogue clock: The movement of the hand clockwise relative to the dial is equivalent to the movement of the dial couter-clockwise relative to the hand. That is, the motion of the hand relative to the dial corresponds to the opposite motion of the dial …

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Inverse units, inverse algebra

The use of space (stance) as an independent variable and time as a dependent variable leads to inverse ratios. There is pace instead of speed, that is, change in time per unit of length instead of change in length per unit of time. But a faster pace is a smaller number, which is counterintuitive and …

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Lorentz transformation derivations

What follows are four derivations of the Lorentz transformation from the complete Galilei (Galilean) transformations for space with time (3+1) and time with space (1+3). Their intersection is linear space and time (1+1), which is the focus of the derivations. The other dimensions may be reached by rotations for space or time. I. Space with …

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Light clocks with multidimensional time

A previous post on this subject is here. One reference for this post is V. A. Ugarov’s Special Theory of Relativity (Mir, 1979). A light clock is a device with an emission-reflection-reception cycle of light that registers the current timeline point and placeline point in units of cycle length and duration. Consider two identical light …

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