epistemology, science, kinds of knowledge, methodology
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 …
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 …
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 …
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 …
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 …
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 …
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, …
Independent variables are measured first, independent of other variables. They may be either set to a fixed value or allowed to change at a fixed rate. An example of the former is a race in which the distance is the independent variable set for the race, and of the latter is a time variable, which …
The extent of a motion is measured in two ways: by its time (duration) and by its space (length). The relation between these two measures is the subject here. Although a definition of uniform motion was given by Archimedes, Galileo was the first to give a complete definition: Equal or uniform motion I understand to …
