Complete Lorentz group

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 […]

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Complete Lorentz transformation

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

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The story of nothing

Mathematics is the study of nothing. We make something out of nothing, acting the creator in a world of nothing. Here’s the story: In the beginning is nothing. Not totally nothing because we’re there. But a blank page, a clear slate, a tabula rasa. We draw a distinction, a part of nothing. The indistinct blankness

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Four perspectives on space and time

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

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Change flows

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

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Three arguments for 3D time

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

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Variations on a clock

The U.S. National Debt Clock shows several ‘clocks’ that tick off dollars at a constant rate. The answer to “what time is it?” could be given in dollars. The Census Bureau has a population clock that estimates the present population for the U.S. or the world. The U.S. has a net gain in population of

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Branches of Christianity

Christians accept the four gospels as four different perspectives on the gospel. In fact, each is properly titled, “The Gospel According to …” That is, there is one gospel but four perspectives on it. While it is an interesting exercise to compare the gospels with each other, they are best thought of as parallel accounts

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Conversion of space and time

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

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Time and memory

Is it possible to reverse time? Yes, in a sense. It is possible to reverse thermodynamic time by a local decrease in entropy. Cooling down, metabolism, and memory are examples of decreases in entropy. Memory may be described as an information model: it compresses experience for storage. The information in memory is not all that

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