Watches didn’t always exist. Neither did clocks that were transportable or manufactured in large quantities. I mention this because one way to determine the simultaneity of events is to have synchronized clocks transported to multiple locations – even an endless number of locations in theory. How can an observer determine the simultaneous events from their […]
Rates of motion are almost always expressed as a ratio with respect to time (duration space). For example, the average speed of a body is the travel distance of the body divided by the travel time. This makes the independent variable time and distance the dependent variable. However, there is no physical dependency of motion
Rest means no motion, or at least no motion detected by an observer. We know what rest for space means: staying in the same place. That is, rest means no change of position, no travel distance, no length of motion. So at rest the numerator of the speed is zero. Yet clocks tick on. The
In a paper titled Nothing but Relativity (Eur. J. Phys. 24 (2003) 315-319) Palash B. Pal derived a formula for transformations between observers that is based on the relativity postulate but not a speed of light postulate. In a paper titled Nothing but Relativity, Redux (Eur. J. Phys. 28 (2007) 1145-1150) Joel W. Gannett presented
*** Revised from June 2017 *** With circular motion there is a radius and circumference that may be measured as distance or duration. Call the length space circumference S, and the duration space circumference T, which is known as the period. Distinguish the length and duration versions of the radius: R, for base, and Q,
The Galilean transformation is typically presented for motion in direction of the x-axis, with the other axes unchanged: x´ = x – vt, y´ = y, z´ = z, and t´ = t, where v is the relative velocity of the observers. This is incompatible with the Lorentz transformation, but more than that, it is
This post continues the parallelism between length and time, and includes some new terms. Length and time both have base units in SI metric: the meter (or better: metre to distinguish it from a device) and the second. They can both be associated with direction. Length in a direction is from or toward an event
Observers detect objects and events with objects. These objects are essentially passive; they must be made to do things by force and work. Participants are subjects among subjects, actively engaging in events and making them happen. Subjects participate and participants are subjects. The perspectives of an observer and a participant are inverses of each other.
The first edition of New Foundations for Classical Mechanics (1986) by David Hestenes included “Foundations of Mechanics” as Chapter 9. This was removed for lack of room in the second edition, but is available online as a pdf here. This space-time foundation may serve as a guide for the foundation of mechanics for either space-time
Foundations of mechanics for length space or duration space Read More »
There is a symmetry between length space and duration space (time). As one can transform an observation by rectilinear motion (translation), or by rotation, or by a time line change, so one can transform 3D length into an equivalent 3D duration. This is not a continuous change so don’t expect a simple equation. There are
