The Elusive Notion of Motion: The Genius of Kepler, Galileo, Newton, and Einstein

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New Condition: New Soft cover. Save for Later. About this Item Combining science, biography, and history,"The Elusive Notion of Motion" tells the fascinating story of the centuries-long quest of scientific pioneers like Kepler, Galileo, Newton, and Einstein to understand the physics of falling and moving bodies.

This book explains precisely how and why objects move through space, whether they be subject to the force of gravity working alone or to the explosive charge of a bullet working in concert with gravity. The book presents the laws of physics and how they dictate motion, all in an easily digested, yet scientifically rigorous format sure to engage readers at all levels. The colorful personal histories of Kepler, Galileo, Newton, and Einstein along with their key roles in motion physics are presented with refreshing insight. Finally, Einstein's theory of special relativity and its reshaping of Isaac Newton's classical motion physics is clearly explained for the novice, but curious reader!.

Bookseller Inventory Ask Seller a Question. About this title Synopsis: Ever been confused by basic physics and intimidated by the mere thought of Einstein's relativity theories? Store Description We specialize in books covering a wide range of interests. Our offerings embrace meaningful topics with broad appeal which are often difficult to find in today's marketplace. Books on the history of science and technology not textbooks! Biographies and the U. The latter two, translated into Italian by Nicolo Tartaglia, marked a neo-Platonic interest in mathematics, and would strongly influence classical physics.

Kepler and Galileo started their careers as Renaissance scientists, but their most mature work is classical in spirit. They crossed the watershed between ancient and early modern science. Indeed, the Copernican ideology of the moving earth was the motor of the transition from Renaissance to classical physics. Copernicus started it, Kepler, Galileo and Descartes were its chief advocates, and Newton brought it to completion. This period is called Copernican because almost all its heroes considered themselves Copernicans. Their common creed was that the earth moves, and their common aim was to explain this.

The Copernican revolution concerned astronomy and physics, mechanics, magnetism, and optics. Simultaneously it saw a battle between several philosophies. Christianized during the Middle Ages, Aristotelian philosophy dominated the universities, and was mostly defended by conservative professors. It included a realist view of physics and cosmology, in contrast to an instrumentalist view of observational astronomy.

Up till Galileo, most Copernicans were under the spell of this philosophy. It was a reaction to Aristotelian philosophy as well. It saw a revival during the 19th century. Finally, empirism came to life, a new philosophy opposing the rationalistic trends of the preceding ones.

Traces of it can be found in Kepler, Galileo, and Huygens. Francis Bacon was its prophet, and Blaise Pascal, Robert Boyle, and Isaac Newton propagated it under the flag of experimental philosophy. Would it be possible to distinguish theoretical thought from non-theoretical thought? Let me try to answer this question without discussing the far more difficult problem about the nature of thought itself. Natural, non-theoretical thought is spontaneous. It is characterized by an immediate relation between the thinking person, the subject , and the object of their thought. In theoretical thought this direct relation is interrupted, because people put theories between themselves and their object of thought.

A theory is like a medium, mediating between subject and object, it is an instrument.

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I shall elaborate this, without committing myself to instrumentalism. Natural and artificial seeing.

History of Gravity; Theory of Kepler, Galileo, Newton, & Einstein - Part I

In order to clarify the instrumental character of theories, let us compare these with instruments to improve human vision. Seeing is a natural activity of men, and of all animals having eyes. We see objects in our environment — a tree, a tower, a car.

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Occasionally, we also look at a picture of a tree. In an artificial manner, we see a tree, whereas in a natural manner, we see a picture. In a natural way, we cannot see our own face, or the phases of Venus. Using a mirror, we see naturally a picture, but artificially our own face. Using a telescope, we see naturally an image, but artificially the phases of Venus. Artificial seeing is not contrary to natural seeing, but depends on it. Optical instruments are invented in order to see better than would be possible in a natural way.

In Holland, one cannot see the Eiffel tower directly. But one can see a picture of it, a photo, a miniature, or a TV-picture. This kind of artificial seeing seems to be an exclusively human activity. Animals do not see the Eiffel tower, if they see its picture — they only see a piece of paper. Nor do animals invent instruments to improve on their seeing. Contrary to natural seeing, artificial seeing has a history.

Medieval painting, Renaissance and modern art differ widely from each other. Photography was invented in the 19th, television in the 20th century. It is more than a coincidence that the telescope and the microscope were invented during the Copernican revolution.

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The new movement made these discoveries possible, and needed them all the same. Galileo was the first to use the telescope for astronomical observations — it is a historical event. He used these discoveries in his propaganda for the Copernican theory. Natural and artificial thought. There is no need to define seeing — everyone knows what it is. Similarly, natural thinking is familiar. It is a natural activity of men and women, and perhaps of all animals having brains. Natural thought concerns trees, towers, or stars, good or evil deeds, families and churches, colours and paintings.

All thought is characterized by dissociation and association, by logic. Thinking beings are logical subjects , and they think about logical objects. The logical objects of natural thought are concrete, everyday things, events, and their relations. The thinker distinguishes and relates them. A theory, too, is an object. It is certainly not a thinking subject, as it does not think. But it is not a logical object. Except for philosophers, nobody thinks about theories. A theory is an artefact. Theories are used as instruments in human thought. Theoretical thinking is natural thinking, opened up by the use of instruments.

People form concepts of concrete things, of events, and of relations, and they think theoretically about these. Contrary to natural thought, theoretical thought has a history, the history of ideas. It is generally assumed that theoretical thought originated with the Greeks, about BC. The theories of the Greeks differ from the medieval theories, from those of the 17th century, and from the present. Theoretical thought is concerned with statements, and statements concern concrete things, events, and relations. This constitutes a problem, the problem of the relation between artificially conceived theories, statements, and concepts on the one hand, and concrete things, events, and relations on the other hand.

This problem is related to the fact that by using an instrument people enlarge their power of seeing or thinking, but simultaneously diminish their field of vision or attention. Using a microscope one can see much better than without, but at the same time one sees much less. Moreover, the other senses are eliminated.

Looking at a real dog, one does not only see him, but also smell him, and hear him. This continuity of sensory experience is interrupted when looking at a picture of a dog. Therefore, a dog can see another dog, but if shown a picture of a dog, he may not recognize it. In theoretical thought people make abstractions, restricting their conceptual activity, and switching off their other modes of experience — for instance, their feelings.

Often, theoretical thought is at variance with natural thought. An example is the Copernican leading idea of the moving earth, which is counter-intuitive. Whether this is possible and to what extent will be discussed later on. The three worlds of Karl Popper. The correspondence is not perfect, however. Popper seems to think that his classification is complete and exhaustive, that everything belongs to one of his worlds.

My classification is merely logical ; it has merely a logical function. There are more subjects than logical subjects: mathematical subjects like numbers and spatial figures, physical subjects like atoms and stars, biological subjects like plants and animals. Theye have feelings, they act, they love, they believe. Philosophically speaking, something is a subject if it is directly and actively subjected to a given law. An object is passively and indirectly via a subject subjected to a law.

Therefore, whether something is a subject or an object depends on the nomic context. If one wants to discuss individual subjects or objects, one needs typical laws in order to distinguish them from each other. These laws also determine typical relations between subjects and between subjects and objects. However, individual things and events have non-typical relations to each other as well. Next, there are more objects than logical objects. The magnitude of a spatial figure, its length or volume, is a spatial object.

A road is a kinetic object, it does not move, but is indispensable for traffic. Food is a biological object; it does not live, but is a condition for life. A painting is an object of art. There are also far more artefacts than theories and ideas — telescopes, houses, cars, clothing. Hence, distinguishing logical subjects, logical objects, and theories as logical instruments concerns only one of our fundamental modes of experience. The logical aspect of human experience is only one of its segments. Other aspects, like the quantitative, the spatial, the kinetic, and the physical, have played equally important parts in the history of the Copernican revolution, as will be seen in due course chapter 3.

The logical character of a theory. A human mode of experience and relations, logic implies making distinctions and connections. One of the most important logical distinctions to be made is that between the truth and falsity of statements. Hence, the most general logical function of a theory is to prove a statement, to establish its truth content relative to other statements. Omitting statements which are more or less probable, I shall restrict myself to propositions which are hold either false or true. Logical distinctions are made by people.

As a logical subject, a person is actively subjected to logical laws, which they apply in their arguments, and which they have to obey if wishing to argue correctly. The most important logical law is the law of non-contradiction. Within a certain context a statement and its negation cannot both be true. It points out that theoretical reasoning has a relative value.

A statement can be true in one context, false in another one. But a theory is inconsistent if it simultaneously contains a statement and its negation. In addition to the law of non-contradiction several other logical rules or tools of proof are available, such as syllogisms, modus tollens, modus ponens, and argumentum ad absurdum.

Brouwer and other intuitionists accepted a proof only if it is finite. Proof by complete induction is therefore rejected. Brouwer also rejected reductio ad absurdum as proof. The logical definition of a theory. What is a theory? The Greek word theoria means something like contemplation our word theatre is related , but already the earliest Greek philosophers connected theoria with proof, or deductive reasoning. I shall take for granted that a theory invariantly implies logical deduction. It is often assumed that a theory should start from well-known and accepted truths, in order to arrive at new statements or theorems.

Other people maintain that scientific theories start from the unknown, from hypotheses which should explain the observable. In this case, theories are even identified with hypotheses, [15] but I shall consider hypotheses to be statements, not theories. Leaving room for both approaches, from the known to the unknown, or from the unknown to the known, I propose the following provisional definition of a theory, as far as its logical character is concerned. A theory is a deductively ordered collection of statements accepted or proved to be true.

Hence, a theory is not just a set of statements, but a qualified collection. It only concerns the formal structure of a theory. A theory is a deductively ordered set of statements, meaning that each statement is directly or indirectly connected with each other statement by way of a deductive argument, a deduction.

In a technical sense, a theory is a partially ordered set, because it is never the case that each pair of statements is connected such that one is deduced from the other one. Because of this definition, a theory is called closed with respect to deduction, but it is quite open in other respects, as we shall see presently. Later on, various kinds of statements in a theory will be discussed 1. At present, I observe that in most if not all theories, data are indispensable for the deductive process.

But data are exchangeable. A datum can be replaced by its negation, as long as this does not lead to contradictions. This means that a theory is an open system. With this criterion it can be decided at any moment which statements belong to the theory. Each theory consists of a number of independent axioms and data, and a number of theorems, which are derived from the axioms and data. Hence, in a theory two statements may be directly connected, if one is deduced from the other, or indirectly , either if both are deduced from the same set of axioms and data, or if both are used to deduce a third statement.

The deductive ordering in a theory ought to be non-circular: circular reasoning is a logical fallacy. A theory is a set of statements taken to be true within the context of the theory. This is the most intriguing part of our definition. It is a necessary part, because of the fact that a false statement allows of any conclusion.

Put otherwise, a theory is required to be consistent , i. From a logical point of view, a statement asserted to be false is a contradiction. From a couple of contradictory statements, any statement whatever can be validly inferred. Hence, if one admits both p and its negation, q is always true. Therefore, a statement asserted to be false cannot be used in a logical process.

On the other hand, very often in a theory statements are used which are known to be false in a wider context. Theories of planetary motion now state that the earth is a point, then that it is a perfect sphere, although it is very well known that these statements contradict each other, and are both wrong. The subjunctive method of using counterfactuals is so common, and so fruitful, that it cannot be ignored. Clearly, saying that only true statements in a theory are admitted is not meant to adhere to absolute truth in whatever sense.

It is not even demanded that the statements are believed to be true — nobody believes the earth to be a point. Theories as logical instruments are used by people, by logical subjects, in general not by a single person, but by a group of people, who want to use the theory together. These people must decide which statements they want to consider true, for the sake of the discussion. In other words: statements or propositions are true within a certain context — the context of the theory, and the context of the discussion between the people who use the theory.

Outside this context the same statements may be false, or uncertain. But to make the deductive process possible it has to be assumed that the starting points are true. Then, if no logical mistakes are made, all deduced statements are equally true. This leads to a most important conclusion: A theory is never able to prove a statement conclusively. The truth of any proved statement completely depends on the truth of the axioms and data from which the theory starts. A theory determines the truth of a statement relative to the truth of other statements.

In how far the latter are true must be decided in a different way. A theory is an instrument to propagate truth, to transfer truth, but never to create truth. Three logical relations. Clearly a theory functions in three logical relations:. In the logical subject-object relation , a theory is an instrument between subject and object.

A theory is made and used by people individual or in groups , and is concerned with logical objects, the things or events about which people want to theorize. Each statement has a non-logical content, besides a logical form. A theory has a function in an argument, a discussion, a logical debate between people who want to convince each other of the truth or falsity of statements. The participants in the debate must agree on the initial assumptions and the applied methods of proof, because otherwise a discussion would be impossible.

This intersubjective relation is a logical subject-subject relation. In using a theory, people are bound to logical rules or logical laws. Hence a theory is indirectly subjected to logical laws; it functions in a logical subject-law relation. Strictly speaking, it is not the theory which has to obey these laws, but the people who use the theory. Only they can be responsible for any use or misuse of existing or new theories. In all three relations, logical subjects are involved.

Theories cannot be considered apart from the people who make them and who use them. The functions of a theory. From the above definition it follows that a theory can never be intended to give a mere description of whatever state of affairs. A description can be given with the help of words and sentences, and usually by a setof sentences, like a narrative. But a mere description is not an ordered deduction, and does not constitute a proof.

As a narrative, it has more a lingual than a theoretical structure 1. A theory has other functions than to provide a description of reality. These functions: to predict, to explain, to solve problems, to systematize our knowledge, will be discussed in the next chapters. The distinction between a mere statement or set of statements and a theory as a deductive scheme may be illustrated by comparing Copernicus with his so-called precursor, Aristarchus of Samos, of whom little is known but his assumption that the earth moves around the sun.

Copernicus was aware of this difference, when he wrote:. Before starting the discussion of the functions of a theory, the logical character of a theory will be investigated in relation to the characters of concepts and statements. Logical reasoning is based on meaningful distinctions and connections. Not only theories, but also concepts and statements have an instrumental, an intermediary function in reasoning. Distinctions and connections are made in our subjective thought, and they concern external, objective affairs.

As intermediary artefacts, explicit expressions of human thought, concepts have an objective character, but they are not the primary objects of thought. Hence, theories, statements, and concepts have a logical character as instruments of thought , and a non-logical meaning, referring to non-logical states of affairs. In natural thought explicit concepts and statements are not much in need. In theoretical thought they are indispensable.

Classification and conceptualization belong to the first phase of any field of theoretical thought. Because a concept is not a statement, it cannot be an element of a theory. But a definition is a statement, and can therefore be an element of a theory. A definition is employed in order to introduce explicitly a new concept into a theory.

Usually, however, concepts are tacitly or implicitly introduced. Any theory contains well-defined concepts alongside ill-defined concepts. Each user of a theory can be challenged to clarify his concepts, to distinguish them clearly from other concepts. However, it is impossible to define all concepts, because concepts are needed to define others.

Each theory has a number of primitive concepts, which cannot be defined within the theory. It is sometimes said that a definition is free. This is not entirely true, if one wants to introduce a new concept into an existing theory. Also definitions are subjected to the logical law of excluded contradiction. The definition of a new concept should not contradict the definitions of already accepted concepts in the theory.

Any definition should avoid a contradiction in terms. Concepts may have an individual or a universal character. In the first case they establish an identity, in the second case a species or class. By its identity each thing can be distinguished from every other thing, each event from every other event, or each individual relation from every other individual relation. Since ancient times, Mercury, Venus, Mars, Jupiter, and Saturn were identified as planets, as wandering stars.

This means, for instance, that last night and tonight one recognizes the same planet to be Mars, even though it has moved on meanwhile. A significant result of Greek astronomy, ascribed to Pythagoras, was the identification of the morningstar and the eveningstar as the same planet, Venus. The idea of identity is subjected to the logical law of identity. Each thing is identical with itself. In the course of a logical argument it is not allowed to change the identity of the things about which one argues. A common fallacy of identity is equivocation, to identify what is not identical.

Classes and species may refer to things, like minerals, plants, animals; to events; to human acts, artefacts and associations; and much more. For instance, Aristotle distinguished four classes of change: variation of essence, of quality, of quantity, and of position. Change of position, also called local motion, was further divided into natural and violent motion.

Natural motion was divided into motion towards the centre of the universe, away from the centre, or around the centre. A system of related classes and subclasses is called a taxonomic system. It constitutes the barest kind of theory, for if one states that a certain individual belongs to a certain subclass, it can be deduced that it does not belong to other subclasses, and that it belongs to one or more superclasses.

A class concept points to things or events of the same kind, and are often indicated by a noun , like stars, planets, motions, dogs, lightings, birthdays. Properties, on the other hand, point to quite different things or events, which have something in common. In our language they are often indicated by an adjective , such as red, heavy, light-reflecting. Properties connect and disconnect classes. They are used to define classes.

The property light-reflecting connects planets with houses, and distinguishes planets from stars. Properties serve to mark distinctions and similarities. Aristotle distinguished between essential and accidental properties of an individual thing. Its essential properties indicate its nature, its essence, the species to which it belongs. Uniform circular motion around the centre of the universe is an essential property of a planet. But it is accidental that Mars takes about two years, Jupiter about twelve years to complete one period.

Intension and extension of the concept of a planet. A class concept involves both an intension meaning and an extension the number of things or events belonging to the class. Extensional logic is restricted to the extension of concepts; predicate logic also concerns their intension. Consider, for example, the concept planet as conceived during the Copernican revolution. Before Copernicus, a planet was defined as a wandering star, a celestial body moving with respect to the fixed stars.

Besides Mercury, Venus, Mars, Jupiter, and Saturn, both the sun and the moon were recognized as planets. In his heliocentric theory, a planet is a celestial body primarily moving around the sun. Hence, the earth became a planet, and the sun and the moon ceased to be so. Not only the intension of the concept planet changed accordingly, but also its extension. The number of the planets decreased from seven to six. The Copernicans introduced the new concept of planetary system, namely a central body surrounded by one or more satellites.

Copernicus knew two planetary systems, the solar system and the earth-moon system. It showed that the concept of a planetary system was not an arbitrary and improbable alternative for the geocentric systems of Aristotle and Ptolemy. Any theoretical definition has to take into account the character of planets as wandering stars. Only with respect to the sun, the earth, and the moon the three theories differ. The difference with respect to intension implies a partial shift with respect to the extension.

The extension of a concept can be changed without changing its intension, for example by the discovery of a new planet, like Uranus Such may be predicted with the help of a theory, as was the case with Neptune The recognition of Pluto as a planet was later undone, because it appeared not to fit into the intension of the concept planet as conceived in It has concealed the fact that there is another kind of concepts, namely relations.

A relation is not a property of a single individual, but a property of at least a pair of individuals, or a pair of classes. Aristotelian philosophy had hardly any place for relations. Something is large or small, heavy or light, warm or cold, moist or dry, moving or resting. Gradually, the Copernicans became aware that these binary contraries had better be replaced by relations, such as larger than, heavier than, warmer than.

He rejected the contrary distinction between heavy and light bodies, by showing all bodies to be more or less heavy. He emphasized that rest is not contrary to motion, but is only a gradation of motion, with zero speed. A falling body, starting from rest, has a continuously increasing speed, varying from zero to the final value.

Aristotle distinguished between quantitative and qualitative properties, and he clearly valued the latter much higher than the former. The Copernican revolution changed this radically. The question of how large something is will sooner be raised in a climate in which the relation larger than is more important than the contrary distinction of large and small. More and more the Copernicans became interested in measurable quantities, developing measuring instruments and standards, for instance, a yardstick, a thermometer scale, a standard weight.

During the Copernican revolution, besides quantitative relations, also spatial, kinetic, and physical relations became increasingly important concepts for the physical sciences, as will be seen. Operational definitions. The shift from qualitative to quantitative concepts is one of the most striking features of the scientific revolution of the 17th century. This shift has been of consequence for definitions. In Aristotelian physics, conceptual definitions concern the essence, the nature of things.

Gravity is the tendency of heavy bodies to move towards the centre of the universe. In their theories, Galileo and Newton attempted to describe gravity with the help of measurable properties like acceleration, mass, and weight. The distinction between heavy and light bodies, so important in Aristotelian physics, disappeared. Following Archimedes, both Giovanni Benedetti and Galileo Galilei stated that bodies only move upward spontaneously if their density is less than that of the surrounding water or air.

Definitions determining how a property can be measured are called operational. By an operational definition one does not define a magnitude, but its metric. Hence, a metric has both an experimental measuring and a theoretical aspect calculating. Because of the theoretical character of a metric the same metric may be connected to various measurement methods. As soon as a metric is established, a measuring instrument can be gauged , such that it satisfies the metric agreed upon. If a metric is generally accepted, it serves as a standard.

A coherent set of metrics forms a metrical system. In the 20th century, Percy Bridgman introduced operationism , saying that operational definitions only are fit to determine the meaning of concepts. He thought that such a definition should unequivocally indicate how the property concerned should be measured. For instance, if several possibilities to measure the length of a thing are available, we should rather speak of different concepts of length, according to this somewhat extravagant view, which he later mitigated. The concepts of volume and density cannot be multiplied with another.

He did not define density at all, apparently assuming this concept to be sufficiently known, contrary to mass. Mass or quantity of matter was a completely new concept, introduced by Newton himself. For Descartes, the essence of matter was its extension 3. Being material meant being extended. Hence, the quantity of matter was its volume. For Newton, matter and space were completely different. Therefore, he needed a new definition of quantity of matter. Keeping silent about its essence, he defined how its quantity could be measured. In the context of his ensuing theory, he argued that mass is a real property of any body, independent of its position.

Density could be measured independently of any operation related to the division of mass and volume. Hence, for Newton it was obvious to define the new concept of mass using the well-known concepts of density and volume. However, his definition may very well have been influenced by the assumption that in denser matter atoms are more densely packed.

Statements and their context. Statements may have various functions in a theory 5. The most simple statements are those connecting concepts via the copula is or equivalents. In modern formal logic, the most important operations are negation, conjunction, disjunction, equivalence, and material implication. Propositions or statements are distinguished from propositional functions, in which variables occur. It is not a statement of which the truth can be established.

It can only be ascribed a truth value if the free variables x , y , and z are bound, for instance by a so-called quantifier. The use of variables, first in mathematics, and soon afterwards in physics, is a fruit of the Copernican revolution. The two quantifiers point to the important logical distinction between universal statements and existential ones. It reflects the ontological difference between the law side and the subject and object side of reality.

Universal statements or law statements refer to lawful states of affairs. Existential statements refer to subjects or objects or their relations, or to data. Only statements occur in a theory, and statements are human inventions. But the law determining the motion of the planets around the sun has been valid long before Newton, even long before human beings inhabited the earth and started theoretical thought. Similarly, the fact the Jupiter has moons was established by Galileo in But Jupiter having moons presumably preceded this statement for ages.

Clearly not every all statement is a law statement. Therefore, the logical distinction between universal and existential statements is not identical with the ontological distinction between laws and what is subjected to laws 8. Theory dependence and autonomy. Taylor, Jr. Graviton: In quantum physics, the theoretical but as yet undetected elementary particle that transmits the force of the gravitational field.

In string theory, the graviton is a " string state " rather than a point - particle. See: String Theory. Gravity: Gravity as distinct from ' gravitation ' is a force of mutual attraction between bodies or objects of matter possessing mass. Gravitation on the other hand as set forth in general relativity is the geometrical curvature of spacetime by which non - inertially moving bodies of mass follow the shortest, non - Euclidean path as they tend to accelerate towards one another.

In either case, Newton's Law of Universal Gravitation still provides an excellent approximation to this natural phenomenon of attracting bodies but only at speeds considerably less than that of the speed of light, , or other electromagnetic radiation phenomena. Hadron: Any sub - atomic strongly interacting " heavy " composite particle divided into two classes:. Baryons - strongly interacting composite fermions usually related with matter such as protons and neutrons made up of combinations of three quarks. Mesons - strongly interacting, force - carrying boson particles usually related with radiation such as the at rest, massless photon made up of combinations of two quarks with integral.

Higgs Boson [ The God Particle; since discovered by the Large Hadron Collider - ]: The Large Hadron Collider LHC , located at CERN - European Organization for Nuclear Research - northwest of Geneva on the border between France and Switzerland, began its operation in May and one of its first tasks will be to empirically verify the existence of the hypothetical, yet elusive, Higgs Boson, the massive elementary scalar particle predicted to explain mass that all other elementary particles possess, especially between the massless at rest photon, carrier of electromagnetism, and the relatively heavy and bosons seemingly responsible for radioactive decay.

Isotropy - spacetime is uniform and symmetric in all directions. Homogeneity - spacetime possesses the quality of uniformity in structure and composition in all directions. That is, the geometry metric of spacetime is the same from any point to any other point in the universe. The observer is the red dot in the rotating, non - inertial accelerating frame of reference [ lower picture ] observing the constant speed and straight - line movement of the body or particle as it transits its inertial non - accelerating frame of reference [ upper picture ], whereupon the observer will view the material body or particle as following a curved, accelerated path.

The apparent acceleration of the material body or particle seen by the observer without any other external force present is defined as inertial acceleration. The best example of inertial apparent acceleration is Coriolis acceleration, also commonly known as Coriolis Effect. Inertial Mass: The measure of resistance of a body or object to changes in its velocity acceleration can be expressed as the ratio of an externally applied force to a body or object and the resulting acceleration is inertial mass:.

Inertial masses are those masses for which Newton's 1st and 2nd Laws of Motion are valid. Inertial Frame of Reference [ inertial reference frame, Lorentz frame of reference ]: A frame of reference in which Newton's 1st and 2nd Laws of Motion are valid. That is, those frames of reference in which bodies or particles are not subject to external forces and hence are moving in straight - line directions at uniform rates of speed without any rotational motion, are defined as inertial frames of reference.

Furthermore, given one inertial frame of reference, any other reference frame s moving likewise in straight - line direction s at uniform rate s of speed without any rotational motion relative to the first inertial frame of reference, will also equivalently be considered as an inertial frame s of reference. This latter statement expresses the principle of equivalence of inertial reference frames. Interference [ wave interference ]: The interaction of two or more light waves and thereby producing a distinctly different light wave pattern. Inverse Compton Effect: Occurs whenever a photon gains energy from an incoming high velocity, high energy electron and thereby achieves a higher energy level as well as a shorter decreased wavelength and a higher frequency of radiation.

See: Compton Effect. Isotropy: Spacetime is uniform and symmetric in all directions exhibiting constant values - viz. That is, there is no one preferred reference point or direction in spacetime.

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While examining the cosmic microwave background CMB for the large - scale universe, the cosmos appears nearly isotropic although not perfectly. Law of Continuity: Whenever the differences between any two causes are infinitesimally reduced, the difference as between their respective effects are concomitantly reduced since the principle of the identity of indiscernibles is invoked. See: Continuum. Law of Newton's Universal Gravitation: According to Newton's derivation in his " Philosophiae Naturalis Principia Mathematica " published July 5, , the mutually attractive force existing between any two bodies in the universe is given as.

Lepton: The electron, muon, tau and their associated neutrinos are all members of the elementary lepton particle family. Light Cone: For an observer of an event at time , all those sets of directions of light traveling away from the event future light cone together with all those sets of directions of light traveling towards the event past light cone constitutes the light cone associated with the given event. All other events are in Elsewhere and will never affect, or be known to, the observer at time.

Local Frame of Reference [ local reference frame ]: Normally the coordinate systems of a frame of reference extends indefinitely into unlimited spacetime of the celestial sphere. A local frame of reference is one where the coordinate system is defined only in the immediate or restricted vicinity of some spacetime region containing a specified point or trajectory of a massive body or particle. If a local frame of reference is defined within a larger frame of reference such that an object within its definition appears unaccelerated while the overall local frame of reference relative to the larger reference frame is engaged in accelerated motion, the object will have the experience of being in a free - falling frame of reference - i.

Furthermore, this restricted local frame of reference special case of the larger frame of reference is also known as a " Galilean region ". The free - falling frame of reference cannot, however, itself be extended indefinitely over spacetime since the non - Euclidean metric curvature of unlimited and infinite spacetime becomes obvious as larger gravitational fields exert themselves. Therefore, in order, to maintain a universal constant speed of light in any light sphere in any direction by Einstein's special relativity proposition, longitudinal length contraction must be invoked.

That is, length contraction is imputed in order to maintain a universal constant speed of light when determining time dilation in both Einstein's Special and General Relativity equations as the following definitional velocity equation shows:. Lorentz Factor [ Lorentz term ]: Owing to its ubiquity in special relativity for time dilation, length contraction and relativistic mass, the Lorentz factor is given as. Lorentz Frame of Reference [ Lorentz Coordinate System in Minkowski geometry ]: The spacial coordinates in a Lorentz frame of reference for units of time in Minkowski four - dimensional spacetime geometry are chosen so that the speed of light in empty space in vacuo is invariant in all directions, at all locations and at all times.

At small values of , where velocities are within the normal range of human experience excluding of course experiences of Quantum particle physicists, ha! Maxwell's Theory of the Electromagnetic Field: According to Maxwell's equations, electromagnetic radiation EM is a self - propagating transverse wave with electric and magnetic components where the oscillating electric and magnetic field components induce their respective opposites and vice versa. These electric and magnetic components oscillate at right angles to each other where the entire electromagnetic " envelop " or field propagates perpendicularly to these oscillating electromagnetic wave - components in the direction in which they indefinitely travel unless absorbed by intervening matter.

That is, each kind of field - electric and magnetic - generates the other in order to propagate the entire composite structure moving forward through empty space at the finite speed of light,. In order of increasing frequency, the types of electromagnetic waves include radio and television waves; microwaves; infrared radiation; visible light; ultraviolet light; - rays; gamma rays; and finally, cosmic rays. See: " Action at a Distance ". Hence, pointing one arm of the Michelson - Morley Interferometer in the direction of Earth's transit orbit should produce an interference fringe pattern amounting to 0.

And in this way, it should be able to detect either the Earth's velocity thru the stationary aether or from the perspective of the laboratory, the velocity of the aether wind itself should be detected across a stationary Michelson - Morley Interferometer. Minkowski Space [ Minkowski spacetime, Minkowski spacetime geometry, flat spacetime ]: A four - dimensional, non - Euclidean geometry which best and most elegantly represents special relativity theory was published in by Jewish - German mathematician Hermann Minkowski Russian born - , three years after Einstein's special relativity mathematics came into being.

They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality " , by Hermann Minkowski, Neutrino: Elementary particle traveling close to the speed of light, , without electric charge and almost massless whose exact mass is still too small to be presently measured at this time.

Neutrinos are therefore extremely difficult to detect where, for example, emanating from the Sun's solar wind more than 50 trillion solar electron neutrinos pass through the human body every second! Neutron Star: An extremely dense collapsed remnant of certain massive stars consisting almost entirely of neutrons having densities in general of less than 1. Emmy Amalie Noether's Theorem: All physical laws of conservation are based upon the proposition that they are invariant with respect to time.

Parallax [ stellar parallax ]: Against a very distant seemingly " fixed star " background, any relatively nearby star will display an apparent movement as Earth makes its yearly orbital transit about the Sun. This apparent movement produces an angle of perception called " angle of parallax " which is used to measure the distance to the star from Earth. This phenomenon is similar as to when an object is held at arm's length and seems to move against a more distant background as each eye is opened and closed.

However at extreme distances the angle of parallax becomes infinitesimally small and hence unusable. See: Parsec; also Aberration of starlight which is a totally different phenomenon. Parallel Transport: Gyroscopic motion. Gyroscopes moving in an affinely smoothly connected field of gravity. See: Geodesic; Geodesic Equation. Parsec: Angle of parallax in seconds of arc which is used to measure distances to stars from Earth. See: Parallax. Photoelectric Effect: A quantum physics phenomenon whereby electrons are ejected from metal matter after bombardment by electromagnetic photons in the range of either visible light or - rays whose mathematical explanation by Albert Einstein extended the quanta work of Max Planck.

Einstein won the Nobel Prize in Physics precisely " Ironically, however, Einstein never won any Nobel Physics Prize for special relativity theory as this was deemed theoretical mathematics, actually belonging to the realm of philosophy, and hence not eligible for any Nobel prize.

About the Book

The quantum energy content of the photon Lichtquant is given as:. Planck's Constant: Nature's fundamental constant, designated as. Without Planck's Constant there would no understanding of sub - atomic processes as it is used to set the basic sizes of quantization for all other sub - atomic phenomena such as the electron and photon and the like. Principle of Equivalence: Since gravity is indistinguishable from the effects of acceleration, we may state this fact as a general relativity foundational proposition or principle:.

Special and General Relativity. Proper Time: The time - invariant companion associated with the spacetime distance invariant interval. More simply, proper time is the time measured by a stationary clock at rest between two events occurring coincident with the clock itself. It is analogous to arc length in Euclidean three - dimensional space. See: Spacetime Interval. Quanta: Discrete and indivisible " packets " of energy such as for the massless at rest photon:. Quark: A fundamental particle that is one of the two of basic constituents of matter, the other being the lepton.

The quark is the building block for protons, neutrons as well as all other hadrons and mesons. This particle is the only fundamental particle which interacts with all four fundamental forces of nature. The anti - particle of the quark is the anti - quark. Quintessence: A theoretical form of dark energy which possesses an equation of state for scalar energy density fields that varies through time and space, in contrast to a static cosmological constant for fixed scalar energy densities in the universe. See: Dark Energy; Equation of State. Relativistically Invariant: That which remains constant under some transformation in all frames of reference - viz.

Relativity Principle: 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.

See: Absolute motion, time and space by Isaac Newton. Rest Energy: The amount of energy that a body or particle possesses as observed in a frame of reference to which it is at rest. According to Special Relativity rest energy is equivalent to rest mass:. Rest Mass [ invariant mass, intrinsic mass, proper mass ]: The amount of mass that a body or particle possesses as observed in a frame of reference to which it is at rest.


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This essentially states that the magnitude of the energy - momentum vector is equal to the mass rest energy where in particle physics rest mass,. See: Special Theory of Relativity. Spacetime [ space - time ]: Einstein's mathematical model of 4 - dimensions combining space with time into a geometric construct called spacetime spacetime continuum whose warping metric distortion in the presence of mass is interpreted as gravitational attraction.

Spacetime Curvature [ space - time curvature ]: The non - Euclidean geometry whose metric curvature provides the shortest " straightest " possible path for mutually attracting massive bodies in curved warped spacetime fabric. That is, the gravitational inertial effect of acceleration derived from massive bodies of matter upon relativistic beams of light, is what produces the geometry of spacetime curvature. See: General Theory of Relativity. Spacetime Interval [ space - time interval ]: A four - dimensional " distance - invariant " between any two spacetime events for all observers across all frames of reference provided that a Lorentz coordinate system is used - i.

This " distance - invariant " is unlike other intervals of time or distance for observers in relative motion which can vary according to relative velocities assigned to the respective reference frames; thus the ' spacetime interval ' is the distance concept used in the geodesics of general relativity. The values of a spacetime interval may be zero, real or even imaginary, but for those spacetime intervals which are real and positive, invariant proper time is counted at a clock from an arbitrarily chosen point between the two events by a co - moving observer traveling between them where relativistic time different from proper time!

The trajectory of a particle or massive body forms a spacetime curve whose four - dimensional event - points are time - wise separated by invariant proper time intervals, and any clock carried alongside the particle or massive body will generally indicate proper time if not otherwise effected by gravitational masses, accelerations, or other external forces. Scalars: Quantities having only magnitude such as distance, speed, energy, time, and mass. See: Vectors. In fact, it is vitally important for human perception of the external world that light slows down upon entering Earth's prismatic atmosphere and thence into the glass lenses of telescopes as well as the intraocular lenses of human eyes as this allows for a time delay for human eyes and brains to process images.

Otherwise, human eyes would perceive only distortions of the external world such as what Star Aberration produces. See: Star Starlight Aberration. Also the splitting and recombination of strings appear to produce analogous situations in quantum theory for known interactions of particles emitting and absorbing other particles. The ultimate goal of string theory is to produce a higher mathematics of physics uniting all four forces of nature by combining general relativity and quantum field theory physics into a comprehensive DNA - like " Theory of Everything " where one such result would therefore be " quantum gravity ".

Presently all string theories have not yet produced falsifiable hypotheses which could be submitted to verifiable empirical testing, however with the Large Hadron Collider LHC in CERN coming on line in May it may yet be possible to devise a series of testable string hypotheses within our lifetimes. Superluminal Velocity FTL, faster than speed of light : The apparent velocity of an object at speeds greater than the speed of light. This illusory appearance of velocity greater than is caused by a " projection effect " by the object's acute angle of motion towards almost perpendicular to the line - of - sight of an observer on Earth.

See: Speed of Light. Tachyon: Originally inspired by early string theorists, these hypothetical particles were characterized as having superluminal velocity FTL or faster than speed of light, but according to modern quantum physics field theory these particles are non - existent due to the theoretical instabilities that they would bring into all other quantum systems. Greek etymology: tachys ; " tachy " meaning fast, accelerated, rapid. Tensors: A mathematical object usually represented as a matrix having components equal in number to the dimensionality of the geometry of the spacetime in which it is being defined.

The mechanics of tensor manipulation are an extension, or actually a generalization, of linear matrix algebra into a multi - linear matrix algebra. Trajectory: The curved path along which a massive body or other particle travels through spacetime. In special relativity, the trajectory is described by Minkowski's four - dimensional spacetime coordinates.


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