Relativity posts
Although there are many experimental methods available to measure the speed of light, the underlying principle behind all methods [is] the simple kinematic relationship between constant velocity, distance and time given below: c = D / t (1) In all forms of the experiment, the objective is to measure the time required for the light […]
Speed of a motion is the time rate of length change, that is, the length interval with respect to a timeline interval without regard to direction. Pace of a motion is the space rate of time change, that is, the time interval with respect to a baseline interval without regard to direction. The symbol for
Two transformations of inertial reference frames are well-known: the Galilean and the Lorentz transformations. There is a third transformation as well, which will be called the dual Galilean transformation. Below is a derivation of all three transformations, closely following the paper Getting the Lorentz transformations without requiring an invariant speed by Andrea Pelissetto and Massimo
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
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
Since one may associate either the arclength (travel length) or the arctime (travel time) with direction, one might think that the full coordinates for every event are of the form (s, t, ê), with arclength s, arctime t, and unit vector ê. Since the direction is a function of either the arclength or the arctime,
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
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 –
Since the development of relativity theory, space and time have been combined in a four-dimensional continuum. Because the speed of light is an absolute value in relativity theory, it acts as a conversion factor between space and time. Accordingly, the four dimensions may be understood as any combination of space and time: 4 + 0:
This blog has described how as the distances between places cover three dimensions of space, so the durations between events cover three dimensions of time. One way of looking at this is as a map with the distance and duration given between places, such as this from the Interstate Drive Times and Distances: There are
