Explorations of multidimensional space and time with linear and angular motion.
Space and time are dual concepts. They are complementary to one another as an inverse binary symmetry. They go together as space with time in classical physics or time with space or spacetime as in relativistic physics. Parallel terms: Space Time 3D space +reference time 3D time + reference length vector space + scalar time […]
In 3D space the distance between points is the magnitude of the displacement vector, which is a path length. In 3D time the duration between instants (time points) is the magnitude of the dischronment vector, which is a path time. Radial space is space with radial coordinates, 2D polar or 3D spherical, in which the
An odologe (o′∙do∙loje) is a constant-rate length-measuring device synstancialized with a common waypoint. It is a new coinage from odo(s), path + (horo)loge, clock. In short, it is a clock that shows length instead of time. The simplest odologe takes time from a clock and multiplies it by a conversion speed to produce a length.
Many differences are proposed between space and time. This post briefly indicates how all of them are a matter of convention, and so not real. For details, consult posts on this blog. (1) There are three space dimensions but only one time dimension. Directionality can be associated with either length or time (duration). 3D time
Carlo Rovelli’s “Analysis of the Distinct Meanings of the Notion of “Time” in Different Physical Theories” (Il Nuovo Cimento B, Jan 1995, Vol 110, No 1, pp 81–93) describes ten distinct versions of the concept of time, which he arranges hierarchically. Here are excerpts from his article: We find ten distinct versions of the concept
J. C. C. McKinsey, A. C. Sugar and P. Suppes (hereafter MSS) wrote “Axiomatic foundations of classical particle mechanics”, (Journal of Rational Mechanics and Analysis, v.2 (1953) p.253-272), which is also described in Suppes’ Introduction to Logic (Van Nostrand, New York, 1957), pp.291-322 (see here). It is only a partial axiomatization of Newtonian mechanics but is
Bodies with space-time orbit by gravitation around their barycenter, the center of mass. The word barycenter is from the Greek βαρύς, heavy + κέντρον, center. The barycenter is one of the foci of the elliptical orbit of each body. For the two-body case let m and M be the two masses, and let r and
For some background, see here and here. Velocity is defined as: “The time rate of change of position of a body; it is a vector quantity having direction as well as magnitude.” Speed is defined as: “The time rate of change of position of a body without regard to direction; in other words, the magnitude
A dimension is informally regarded as the number of coordinates needed to specify the location of a body or point. That may suffice for a mathematical dimension, but a physical dimension is a dimension of something, that is, some unit. In that sense, the dimensions of force are different from the dimensions of velocity. However,
Relativity may be derived as an algebraic relation among differentials. Consider motion in the x spatial dimension, with a differential displacement, dx, differential velocity displacement, dv, and arc (elapsed) time t: dx² = (dx/dt)²dt² = dv²dt² = d(vt)². Let there be a constant, c: dx² = d(vt)² = d(cvt)²/c² = d(ct)² (v/c)² = d(ct)² (1 –
