How, for instance, was the earth's circumference determined by simply pacing out steps on the earth's surface while at the same time thinking about this problem? Or, how was the distance to the sun and other planets determined with only their light coming into the eyes of those wise enough to understand and interpret its significance? Why, anyways, is it so significant to understand the nature of light and its distant travels? And how, by the way, do we literally count time and distances when simply standing on the earth's surface? Simply standing on either the moon or mars does not alter this basic question because their distances to the galaxies are not significantly different from that of the earth to these far off filaments in the universe.

As each of these questions - simple and not so simple - came into the minds of great thinkers past, an arduously built staircase of knowledge of experimental and mathematical latices came to be constructed. And what questions were heretofore never even imagined by the Ancients such as whether we exist in a multi-verse system of bubbling, interacting and competing universes, are now being asked by modern cosmologists possessing newer and more powerful tools of theoretical mathematics and applied experimentation.

Finally, of what importance is all this knowledge and understanding to human existence? This is not a minor question.

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This is not an easy question to answer. We all intuitively "understand time" by the clocks and calendars we invent to "measure it". In a sense, therefore, the "concept of time" is given an "operational definition" by these invented instruments which ultimately relate back to earth's axis of rotation as well as its orbital transit about the solar system's sun.

Perhaps a more elegant definition of time would involve the relative motion of objects [ or event-objects ] such as the statement "this event-object occurred before that event-object" in a volume of human-perceived 3-d space.

And the "units of time" are suggested to the human mind by the regularity of recurring event-objects such as the periodicity of the sun's rising and falling. Other units of time were also suggested to the early Greek astronomer-philosophers as they studied the celestial movements of stars and planets.

Dictionary definition of time according to Webster's College Dictionary, 2001: " 1. the system of those sequential relations that any event has to any other, as past, present, or future; indefinite and continuous duration regarded as that in which events succeed one another."

A more precise yet simpler definition of time given by this author: time is an accounting of the relative motions of bodies. Or, time is a system of accounting for the relative motion of bodies. And how we keep "score" is by means of human - invented clocks and calendars.

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To solve this problem, it was necessary in the History of Science for the following to have occurred:

• Tycho Brahe's planetary data, especially that of Mars

• The mathematics of Parallax utilized by Giovanni Cassini in 1672 at the Royal Observatory, Paris

• Kepler's Equations of Planetary Motion

]]>by Isaac Newton:

§ Absolute, true, and mathematical time, of itself and from its own nature, flows equably without relation to anything external, and by another name is called "duration"; relative, apparent, and common time is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time, such as an hour, a day, a month, a year.

§ Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces, which our senses determine by its position to bodies and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude, but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be continually changed.

§ Absolute motion is the translation of a body from one absolute place into another, and relative motion the translation from one relative place into another.

[ note: translated from the original Latin by Andrew Motte ( 1729 ), as revised by Florian Cajori ( Berkeley, University of California Press, 1934) ]

]]>"The clock, not the steam engine, is central to the industrial revolution. The clock is the crowning achievement that all other machines aspire to."

Louis Mumford ( 1895 - 1990 )

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According to Isaac Newton ( 1642 - 1727 ) in his "Opticks" ( 1704 ) light is transmitted at a finite speed by the "Luminiferous Aether Wind" which is the common or universal medium of propagation. This aether wind was further hypothesized as an absolute and stationary "frame of reference" for the measurement of time, especially as James Clerk Maxwell's ( 1831 - 1879 ) equations for electromagnetic radiation - including light - required it.

The Luminiferous Aether was imagined by physicists since Isaac Newton as the invisible "vapor" or "gas aether" filling the universe and hence as the carrier of heat and light to our eyes, although we now understand by Maxwell's equations that these are both a unified electromagnetic phenomena.

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Remember, at this stage of physics understanding ( 1895 ) the idea of the hypothetical luminiferous aether is still being maintained and that the FitzGerald-Lorentz Contraction Equation is being utilized in an ad-hoc fashion in order to rescue the concept of the aether! That is, the interpretation given by Lorentz for this "contraction effect" was wrong, nevertheless the equation was correct and it would shortly enter into a pantheon of other equations developed by Poincaré and others leading ultimately to the tensor mathematics of Special Relativity.

In truth the FitzGerald-Lorentz Contraction Equation only temporarily postponed the eventual abandonment of the concept of an invisible luminiferous aether. It will be Albert Einstein's publication in 1905 of the tensor mathematics of Special Relativity and Einstein's concept of space-time with the Lorentz Transformation Equations ( as the FitzGerald-Lorentz Contraction Equation came to be known ) at its core foundation to have finally "solved" the Michelson-Morley null result.

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1). The Principle of Relativity - All the laws of physics in their simplest reduced form are transformable and hence invariant as between an infinite number of moving reference

systems ( inertial systems ), each one of which is moving uniformly and rectilinearly with respect to any other system and where no one system

is privileged or preferred over any other reference ( inertial ) system when measurements of length or time are taken.

2). The Principle of the Constancy of the Speed of Light - The speed of light in empty ( vacuo ) space is a universal constant as measured in any reference ( inertial ) system when

measured with rods and clocks of the same kind. This is always true notwithstanding any "relativistic effects" of either the

Lorentz length contraction or time dilation as earlier revealed by the Michelson-Morley Experiment (1887 ).

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Ia. Corollary - space-time:

II. Result 2 - "The Failure of Simultaneity at great distances":

III. Result 3 - Length Contraction:

IV. Result 4 - Time Dilation ( Time Contraction ):

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At velocities approaching the speed of light, mass-particles and other object bodies contract in the direction of motion as well as the measurement of time dilates ( contracts ) as seen by an outside ( relatively ) stationary observer. In fact, the speed of light itself determines the very upper limit of velocity at which any object body or mass-particle can attain because otherwise the frame of reference of such an object body ( or mass-particle ) would "outrun" any light propagation from itself and would thus violate the Lorentz Transformation Equations upon which all has been derived up to this point in our discussion of Special Relativity by giving imaginary number results as can be viewed directly from the Lorentz equations themselves.

However for velocities simply approaching the speed of light, nevertheless no simple Galilean addition of velocities of two or more frames of references of bodies will suffice because of physical body distance contraction and time dilation effects.

How to solve this problem of Addition of Relativistic Velocities will now form the following text.

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Conservation of Mass: The total amount of mass contained in any aggregate of object bodies [ or mass-particles ] before any change(s) in motion will be equal to the total amount of aggregate mass after any change(s) in motion of this aggregation of object bodies [ or mass-particles ].

Conservation of Momentum:

According to Newton's 3rd Law ( Principle of Equality of Action and Reaction ) for every action there is an equal and opposite reaction.

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different for different observers residing in different systems.

However ...

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Dearest Bethie!

It's just Algebra.

And diagrams.

But truthfully it does defy ordinary common sense.

Think of it this way ...

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• Because these localized packets of energy are comprised of a variety of wavelengths of different waves, therefore a wave-particle also possesses a variety of momenta since ...

• We can now plainly see that in order to maintain constancy in the above equation, that as the composite variety of wave lengths for a mass-particle becomes overall shorter, the overall composite magnitude of the variety of momenta must become greater.

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There is probably no physicist living today whose name has become so widely known as that of Albert Einstein. Most discussion centres on his theory of relativity. This pertains essentially to epistemology and has therefore been the subject of lively debate in philosophical circles. It will be no secret that the famous philosopher Bergson in Paris has challenged this theory, while other philosophers have acclaimed it wholeheartedly. The theory in question also has astrophysical implications which are being rigorously examined at the present time.

... Similarly, when a quantum of light falls on a metal plate it can at most yield the whole of its energy to an electron there. A part of this energy is consumed in carrying the electron out into the air, the remainder stays with the electron as kinetic energy. This applies to an electron in the surface layer of the metal. From this can be calculated the positive potential to which the metal can be charged by irradiation. Only if the quantum contains sufficient energy for the electron to perform the work of detaching itself from the metal does the electron move out into the air. Consequently, only light having a frequency greater than a certain limit is capable of inducing a photo-electric effect, however high the intensity of the irradiating light. If this limit is exceeded the effect is proportional to the light intensity at constant frequency. Similar behaviour occurs in the ionisation of gas molecules and the so-called ionisation potential may be calculated, provided that the frequency of the light capable of ionising the gas is known.

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But a century ago, pieces of a strange mechanism with bronze gears and dials were recovered from an ancient shipwreck off the coast of Greece. Historians of science concluded that this was an instrument that calculated and illustrated astronomical information, particularly phases of the Moon and planetary motions, in the second century B.C.

The instrument, the Antikythera Mechanism, sometimes called the world’s first computer, has now been examined with the latest in high-resolution imaging systems and three-dimensional X-ray tomography. A team of British, Greek and American researchers deciphered inscriptions and reconstructed the gear functions, revealing “an unexpected degree of technical sophistication for the period,” it said.

The researchers, led by the mathematician and filmmaker Tony Freeth and the astronomer Mike G. Edmunds, both of the University of Cardiff, Wales, are reporting their results today in the journal Nature.

They said their findings showed that the inscriptions related to lunar-solar motions, and the gears were a representation of the irregularities of the Moon’s orbital course, as theorized by the astronomer Hipparchos. They established the date of the mechanism at 150-100 B.C.]]>

Historians and economists have long struggled to understand how this transition occurred and why it took place only in some countries. A scholar who has spent the last 20 years scanning medieval English archives has now emerged with startling answers for both questions.

Gregory Clark, an economic historian at the University of California, Davis, believes that the Industrial Revolution — the surge in economic growth that occurred first in England around 1800 — occurred because of a change in the nature of the human population. The change was one in which people gradually developed the strange new behaviors required to make a modern economy work. The middle-class values of nonviolence, literacy, long working hours and a willingness to save emerged only recently in human history, Dr. Clark argues.

]]>BUT ESPECIALLY PHILOSOPHER AND ASTRONOMERS

BEING SUCH AS HAVE BEEN OBSERVED BY

GALILEO GALILEI

A GENTLEMAN OF FLORENCE

PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF PADUA,

WITH THE AID OF A

TELESCOPE

lately invented by him ... ]]>