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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Michelson-Morley re-examined

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

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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 derivation

The first derivation is similar to here. Lorentz transformations for space with time Let unprimed x and t be from inertial frame K and primed x′ and t′ be from inertial frame K′. Since space is assumed to be homogeneous, the transformation must be linear. The most general linear relationship is obtained with four constant

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Equivalence principle

Inertia is the property of a body that resists changes in its motion. Inertial mass of a body is the ratio of the applied force divided by the body’s acceleration. Gravitational mass is the mass of a body as measured by its gravitational attraction to other bodies. The Equivalence Principle takes several forms. The Newtonian version

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Galilean transformations derived

This derivation of the Galilean transformations is similar to that of the Lorentz transformations here. Since space and time are assumed to be homogeneous, the transformations must be linear. The most general linear relationship is obtained with four constant coefficients: A, B, C, and D: x′ = Ax − Bt t′ = Ct − Dx

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Logic and illogic

This post follows several on logic such as here. Contrary opposites are mutually distinguished terms. One cannot exist without the other. If one is taken away, the other is also. Examples of contraries are up and down, in and out, before and after. More than two possibilities might also be distinguished, such as negative, positive,

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