The complete Lorentz transformation may be written as r′ = γ (r − ct(v/c)), ct′ = γ (ct – rv/c), and γ = (1 – v2/c2)–1/2, which applies only if |v| < |c|, and r′ = γ (r − ct(c/v)), ct′ = γ (ct − r(c/v)), and γ = (1 − c2/v2)–1/2, which applies only […]
This is a continuation of a series of posts that began with Lorentz for space and time. The standard Lorentz transformation applies only if |v| < |c|. The complete transformation for all real values of v is presented here based on both the relative space, absolute time (R-A) Galilean transformation as well as the complementary
There are four perspectives on space and time depending on whether the observer is internal or external to space or time. The four perspectives are internal space with internal time, external space with internal time, internal space with external time, and external space with external time. The internal perspective is that of an observer traveling along
Change happens. In fact, everything in the physical universe is changing. Note that refers to things in the universe, not the universe itself. Whether or not the universe itself changes is another question. There are as many kinds of physical change as there types of energy: kinetic, thermal, chemical, electrical, electrochemical, electromagnetic, sound, and nuclear
There are three main arguments for duration to have three dimensions: (1) The speed of light is a conversion factor between length space (distance) and duration (distime). Transportation conversion factors include the maximum, minimum, or typical speeds associated with different travel modes. Since length space is three dimensional, its conversion into duration space is also
If there exists a constant, characteristic speed, then one may speak of the characteristic conversion of space and time. For example, the speed of light in a vacuum is a defined constant in the SI system of units. So in physical science and its applications one may speak of the characteristic conversion of space into
I have written several times about differences between ancient and modern ways of thinking, for example, this post on Biblical geocentrism. Another way to look at this is whether time or space are primary. What does this mean? We are most familiar with the primacy of space. Things exist within space as mere objects, and
Space and time are complementary aspects of movement. Although space has been associated with stasis and time with change, they both entail movement. Space is the distance side of movement and time is the duration side. There are two ways of looking at movement: one is from the perspective on or within the moving object
A circle or sphere are omnidirectional in two or three dimensions, respectively. This is equivalent to isotropy, uniformity in all directions. A straight line is unidirectional but multiple straight lines may require multiple dimensions. This is equivalent to rectilinear homogeneity. Pure space or average space is homogeneous and isotropic. Then space may be modeled by
In a previous post on Different directions for different vectors I gave this example, for which I’m switching North and East: Suppose someone drives 30 miles North in 50 minutes, then turns East and drives 40 miles in 50 minutes. Overall, they have driven 70 miles in 100 minutes but as the crow flies they
