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THE ELEGANT UNIVERSE, Brian Greene, 1999, 2003
```(annotated and with added bold highlights by Epsilon=One)
```(annotated and with added bold highlights by Epsilon=One)
Chapter 5: Notes
1. Stephen Hawking, A Brief History of Time (New York: Bantam Books, 1988), p. 175. Return to Text
2. Richard Feynman, as quoted in Timothy Ferris, The Whole Shebang (New York: Simon & Schuster, 1997), p. 97. Return to Text
3. In case you are still perplexed about how anything at all can happen within a region of space that is empty, it is important to realize that the uncertainty principle places a limit on how "empty" a region of space can actually be; it modifies what we mean by empty space. For example, when applied to wave disturbances in a field (such as electromagnetic waves traveling in the electromagnetic field) the uncertainty principle shows that the amplitude of a wave and the speed with which its amplitude changes are subject to the same inverse relationship as are the position and speed of a particle: The more precisely the amplitude is specified the less we can possibly know about the speed with which its amplitude changes. Now, when we say that a region of space is empty, we typically mean that, among other things, there are no waves passing through it, and that all fields have value zero. In clumsy but ultimately useful language, we can rephrase this by saying that the amplitudes of all waves that pass through the region are zero, exactly. But if we know the amplitudes exactly, the uncertainty principle implies that the rate of change of the amplitudes is completely uncertain and can take on essentially any value. But if the amplitudes change, this means that in the next moment they will no longer be zero, even though the region of space is still "empty." Again, on average the field will be zero since at some places its value will be positive while at others negative; on average the net energy in the region has not changed. But this is only on average. Quantum uncertainty implies that the energy in the field—even in an empty region of space—fluctuates up and down, with the size of the fluctuations getting larger as the distance and time scales on which the region is examined get smaller. The energy embodied in such momentary field fluctuations can then, through E = mc², be converted into the momentary creation of pairs of particles and their antiparticles, (Epsilon=One: Yes! "Particles" (Resoloids) are created in pairs; such pairs are commonly referred to as a "Neutron." No! Particles and antiparticles are not pairs of one another. A Pulsoid, as it progressively pulses to Pulse 3, morphs from an "antiparticle" through a Bois-Einstein state to a particle. During the first three Pulses of a Pulsoid, the orbital and nuclear ellipsoidal envelopes (force fields) juxtapose. At Pulse 2 (Boise-Einstein state) the envelopes are congruent.) which annihilate each other in great haste, (Epsilon=One: There is no annihilation of "each other" under normal evolutionary progression of the Pulsoid from an antiparticle to "dark" matter. However, when an antiparticle is traumatically created, as in a cyclotron, it will "disintegrate" when merged with a particle. The "disintegration" is somewhat analogous to the cancellation of a wave when a crest and trough of two waves merge.) to keep the energy from changing, on average. (Epsilon=One: "On average"—a term, or condition, often arising from extrapolations—can very often mislead many theoretical physicists.) Return to Text
4. Even though the initial equation that Schrödinger wrote down—the one incorporating special relativity—did not accurately describe the quantum-mechanical properties of electrons in hydrogen atoms, it was soon realized to be a valuable equation when appropriately used in other contexts, and, in fact, is still in use today. However, by the time Schrödinger published his equation he had been scooped by Oskar Klein and Walter Gordon, and hence his relativistic equation is called the "Klein-Gordon equation." Return to Text
5. For the mathematically inclined reader, we note that the symmetry principles used in elementary particle physics are generally based on groups, most notably, Lie groups. Elementary particles are arranged in representations of various groups and the equations governing their time evolution are required to respect the associated symmetry transformations. For the strong force, this symmetry is called SU(3) (the analog of ordinary three-dimensional rotations, but acting on a complex space), and the three colors of a given quark species transform in a three-dimensional representation. The shifting (from red, green, blue to yellow, indigo, violet) mentioned in the text is, more precisely, an SU(3) transformation acting on the "color coordinates" of a quark. (Epsilon=One: If theoretical physicists are able to, it would be very helpful with understanding particles to explain what is physically occurring that differentiates the mythical, fractionally charged quarks. Gell-Mann's imagination has probably set back an understanding of fundamental, quantitative evolution more than any other concept since the advancement resulting from Special Relativity.) A gauge symmetry is one in which the group transformations can have a spacetime dependence: in this case, "rotating" the quark colors differently at different locations in space and moments in time. Return to Text
6. During the development of the quantum theories of the three nongravitational forces, physicists also came upon calculations that gave infinite results. In time, though, they gradually realized that these infinities could be done away with through a tool known as renormalization. The infinities arising in attempts to merge general relativity and quantum mechanics are far more severe and are not amenable to the renormalization cure. Even more recently, physicists have realized that infinite answers are a signal that a theory is being used to analyze a realm that is beyond the bounds of its applicability. (Epsilon=One: This is true because the theory is flawed/incomplete.) Since the goal of current research is to find a theory whose range of applicability is, in principle, unbounded—the "ultimate" or "final" theory—physicists want to find a theory in which infinite answers do not crop up, regardless of how extreme the physical system being analyzed might be. (Epsilon=One: An "ultimate" or "final" theory MUST incorporate an understanding of Infinity as a Singularity from which all emerges and to which all dissipates . . . in perpetuity. Emergence is from the infinitesimal and dissipation is to the infinite from the perspective of human beings riding the planet Earth. Also, a note to mathematicians: There is, by definition, only ONE Infinity and/or Singularity; not some 40 plus!) Return to Text
7. The size of the Planck length can be understood based upon simple reasoning rooted in what physicists call dimensional analysis. The idea is this. When a theory is formulated as a collection of equations, the abstract symbols must be tied to physical features of the world if the theory is to make contact with reality. In particular, we must introduce a system of units so that if a symbol, say, is meant to refer to a length, we have a scale by which its value can be interpreted. After all, if equations show that the length in question is 5, we need to know if that means 5 centimeters, 5 kilometers, or 5 light years, etc. In a theory that involves general relativity and quantum mechanics, a choice of units emerges naturally, in the following way. There are two constants of nature upon which general relativity depends: the speed of light, c, and Newton's gravitation constant, G. Quantum mechanics depends on one constant of nature
. By examining the units of these constants (e.g., c is a velocity, so is expressed as distance divided by time, etc.), one can see that the combination VG/e^3 has the units of a length; in fact, it is 1.616 x 10^-33 centimeters. This is the Planck length. Since it involves gravitational and spacetime inputs (G and c) and has a quantum mechanical dependence () as well, it sets the scale for measurements—the natural unit of length—in any theory that attempts to merge general relativity and quantum mechanics. When we use the term "Planck length" in the text, it is often meant in an approximate sense, indicating a length that is within a few orders of magnitude of 10^-33 centimeters. (Epsilon=One: Any engineering 101 student is aware that a force must act directly upon its object. Physicists believe in voodoo attraction-at-a-distance to explain gravity's minimum of six forces between objects (reach, grasp, and pull, bidirectionally) for at least 2 objects. Heaven seems to forbid the calculation of forces for many bodies. The gravitation constant is one of the most inaccurate "constants" of academic, theoretical physics. As for the "speed" of gravity, any observation combined with a bit of thought while observing the clockwork synchronization of the Cosmos should cause concern with Einstein's speed limit established over 100 years ago when little was know of the Nature of the Cosmos . . . or light. The speed of light has a component of acceleration that is too small to be detected from the slowest "known" environment in the Universe. The top limit of the speed of gravity and light are the same.) Return to Text
8. Currently, in addition to string theory, two other approaches for merging general relativity and quantum mechanics are being pursued vigorously. One approach is led by Roger Penrose of Oxford University and is known as twistor theory. The other approach—inspired in part by Penrose's work—is led by Abhay Ashtekar of Pennsylvania State University and is known as the new variables method. Although these other approaches will not be discussed further in this book, there is growing speculation that they may have a deep connection to string theory and that possibly, together with string theory, all three approaches are honing in on the same solution for merging general relativity and quantum mechanics. (Epsilon=One: Special relativity, general relativity, and quantum mechanics are all incomplete, as are the standard models of physics and cosmology. You can not reconcile theories that are internally irreconcilable, irreconcilable with one another; and, above all, irreconcilable with observation and Philogic.
However, Oscillation Theory, as symbolically described by Pulsoid Theory, can point the way toward an understanding of most all the current enigmas, which should reduce the subtle, confused suffering from myth and superstition, of laypersons and others, as theoretical physicists struggle to better understand Nature.
Science—dependent upon arbitrary axioms, without a first postulate—that is regulated/constrained by peer review, grants, and academic sinecure, is seldom concerned with any search for truth that may change the accepted status quo.
Currently, every new theoretical, quantum or astrophysics', enigma that shows promise of any resolution tends to only spawn multiple, additional enigmas. The search for truth by extending incomplete axioms usually progresses, to use an analogy, "out toward the tip of a limb"; and, it is quite difficult to climb a tree from the tip of a limb. It is necessary to retreat toward the trunk of the tree to progress up or down depending upon the direction that truth is being sought. Analogies are never good arguments; though, the point is that academic physics must clearly admit their known fallacies rather than continue to indoctrinate aspiring students to build upon the standard model axioms . . . which are all metaphysical forces.
Academic science must recognize the limits of that which is quantitative, embrace the concepts of Infinity's duality and that the first essence of Reality is complex, harmonic oscillations that resonate as particles. All fundamental understanding must incorporate an explanation of the locus of the Universe. Ask, Why? and Why? . . . and Why? again . . . and again! The most simple is the most complex; and, vice versa.
Logically, a situation that spawns increasing enigmas should indicate much fundamental misunderstanding.) Return to Text
2. Richard Feynman, as quoted in Timothy Ferris, The Whole Shebang (New York: Simon & Schuster, 1997), p. 97. Return to Text
3. In case you are still perplexed about how anything at all can happen within a region of space that is empty, it is important to realize that the uncertainty principle places a limit on how "empty" a region of space can actually be; it modifies what we mean by empty space. For example, when applied to wave disturbances in a field (such as electromagnetic waves traveling in the electromagnetic field) the uncertainty principle shows that the amplitude of a wave and the speed with which its amplitude changes are subject to the same inverse relationship as are the position and speed of a particle: The more precisely the amplitude is specified the less we can possibly know about the speed with which its amplitude changes. Now, when we say that a region of space is empty, we typically mean that, among other things, there are no waves passing through it, and that all fields have value zero. In clumsy but ultimately useful language, we can rephrase this by saying that the amplitudes of all waves that pass through the region are zero, exactly. But if we know the amplitudes exactly, the uncertainty principle implies that the rate of change of the amplitudes is completely uncertain and can take on essentially any value. But if the amplitudes change, this means that in the next moment they will no longer be zero, even though the region of space is still "empty." Again, on average the field will be zero since at some places its value will be positive while at others negative; on average the net energy in the region has not changed. But this is only on average. Quantum uncertainty implies that the energy in the field—even in an empty region of space—fluctuates up and down, with the size of the fluctuations getting larger as the distance and time scales on which the region is examined get smaller. The energy embodied in such momentary field fluctuations can then, through E = mc², be converted into the momentary creation of pairs of particles and their antiparticles, (Epsilon=One: Yes! "Particles" (Resoloids) are created in pairs; such pairs are commonly referred to as a "Neutron." No! Particles and antiparticles are not pairs of one another. A Pulsoid, as it progressively pulses to Pulse 3, morphs from an "antiparticle" through a Bois-Einstein state to a particle. During the first three Pulses of a Pulsoid, the orbital and nuclear ellipsoidal envelopes (force fields) juxtapose. At Pulse 2 (Boise-Einstein state) the envelopes are congruent.) which annihilate each other in great haste, (Epsilon=One: There is no annihilation of "each other" under normal evolutionary progression of the Pulsoid from an antiparticle to "dark" matter. However, when an antiparticle is traumatically created, as in a cyclotron, it will "disintegrate" when merged with a particle. The "disintegration" is somewhat analogous to the cancellation of a wave when a crest and trough of two waves merge.) to keep the energy from changing, on average. (Epsilon=One: "On average"—a term, or condition, often arising from extrapolations—can very often mislead many theoretical physicists.) Return to Text
4. Even though the initial equation that Schrödinger wrote down—the one incorporating special relativity—did not accurately describe the quantum-mechanical properties of electrons in hydrogen atoms, it was soon realized to be a valuable equation when appropriately used in other contexts, and, in fact, is still in use today. However, by the time Schrödinger published his equation he had been scooped by Oskar Klein and Walter Gordon, and hence his relativistic equation is called the "Klein-Gordon equation." Return to Text
5. For the mathematically inclined reader, we note that the symmetry principles used in elementary particle physics are generally based on groups, most notably, Lie groups. Elementary particles are arranged in representations of various groups and the equations governing their time evolution are required to respect the associated symmetry transformations. For the strong force, this symmetry is called SU(3) (the analog of ordinary three-dimensional rotations, but acting on a complex space), and the three colors of a given quark species transform in a three-dimensional representation. The shifting (from red, green, blue to yellow, indigo, violet) mentioned in the text is, more precisely, an SU(3) transformation acting on the "color coordinates" of a quark. (Epsilon=One: If theoretical physicists are able to, it would be very helpful with understanding particles to explain what is physically occurring that differentiates the mythical, fractionally charged quarks. Gell-Mann's imagination has probably set back an understanding of fundamental, quantitative evolution more than any other concept since the advancement resulting from Special Relativity.) A gauge symmetry is one in which the group transformations can have a spacetime dependence: in this case, "rotating" the quark colors differently at different locations in space and moments in time. Return to Text
6. During the development of the quantum theories of the three nongravitational forces, physicists also came upon calculations that gave infinite results. In time, though, they gradually realized that these infinities could be done away with through a tool known as renormalization. The infinities arising in attempts to merge general relativity and quantum mechanics are far more severe and are not amenable to the renormalization cure. Even more recently, physicists have realized that infinite answers are a signal that a theory is being used to analyze a realm that is beyond the bounds of its applicability. (Epsilon=One: This is true because the theory is flawed/incomplete.) Since the goal of current research is to find a theory whose range of applicability is, in principle, unbounded—the "ultimate" or "final" theory—physicists want to find a theory in which infinite answers do not crop up, regardless of how extreme the physical system being analyzed might be. (Epsilon=One: An "ultimate" or "final" theory MUST incorporate an understanding of Infinity as a Singularity from which all emerges and to which all dissipates . . . in perpetuity. Emergence is from the infinitesimal and dissipation is to the infinite from the perspective of human beings riding the planet Earth. Also, a note to mathematicians: There is, by definition, only ONE Infinity and/or Singularity; not some 40 plus!) Return to Text
7. The size of the Planck length can be understood based upon simple reasoning rooted in what physicists call dimensional analysis. The idea is this. When a theory is formulated as a collection of equations, the abstract symbols must be tied to physical features of the world if the theory is to make contact with reality. In particular, we must introduce a system of units so that if a symbol, say, is meant to refer to a length, we have a scale by which its value can be interpreted. After all, if equations show that the length in question is 5, we need to know if that means 5 centimeters, 5 kilometers, or 5 light years, etc. In a theory that involves general relativity and quantum mechanics, a choice of units emerges naturally, in the following way. There are two constants of nature upon which general relativity depends: the speed of light, c, and Newton's gravitation constant, G. Quantum mechanics depends on one constant of nature
. By examining the units of these constants (e.g., c is a velocity, so is expressed as distance divided by time, etc.), one can see that the combination VG/e^3 has the units of a length; in fact, it is 1.616 x 10^-33 centimeters. This is the Planck length. Since it involves gravitational and spacetime inputs (G and c) and has a quantum mechanical dependence () as well, it sets the scale for measurements—the natural unit of length—in any theory that attempts to merge general relativity and quantum mechanics. When we use the term "Planck length" in the text, it is often meant in an approximate sense, indicating a length that is within a few orders of magnitude of 10^-33 centimeters. (Epsilon=One: Any engineering 101 student is aware that a force must act directly upon its object. Physicists believe in voodoo attraction-at-a-distance to explain gravity's minimum of six forces between objects (reach, grasp, and pull, bidirectionally) for at least 2 objects. Heaven seems to forbid the calculation of forces for many bodies. The gravitation constant is one of the most inaccurate "constants" of academic, theoretical physics. As for the "speed" of gravity, any observation combined with a bit of thought while observing the clockwork synchronization of the Cosmos should cause concern with Einstein's speed limit established over 100 years ago when little was know of the Nature of the Cosmos . . . or light. The speed of light has a component of acceleration that is too small to be detected from the slowest "known" environment in the Universe. The top limit of the speed of gravity and light are the same.) Return to Text8. Currently, in addition to string theory, two other approaches for merging general relativity and quantum mechanics are being pursued vigorously. One approach is led by Roger Penrose of Oxford University and is known as twistor theory. The other approach—inspired in part by Penrose's work—is led by Abhay Ashtekar of Pennsylvania State University and is known as the new variables method. Although these other approaches will not be discussed further in this book, there is growing speculation that they may have a deep connection to string theory and that possibly, together with string theory, all three approaches are honing in on the same solution for merging general relativity and quantum mechanics. (Epsilon=One: Special relativity, general relativity, and quantum mechanics are all incomplete, as are the standard models of physics and cosmology. You can not reconcile theories that are internally irreconcilable, irreconcilable with one another; and, above all, irreconcilable with observation and Philogic.
However, Oscillation Theory, as symbolically described by Pulsoid Theory, can point the way toward an understanding of most all the current enigmas, which should reduce the subtle, confused suffering from myth and superstition, of laypersons and others, as theoretical physicists struggle to better understand Nature.
Science—dependent upon arbitrary axioms, without a first postulate—that is regulated/constrained by peer review, grants, and academic sinecure, is seldom concerned with any search for truth that may change the accepted status quo.
Currently, every new theoretical, quantum or astrophysics', enigma that shows promise of any resolution tends to only spawn multiple, additional enigmas. The search for truth by extending incomplete axioms usually progresses, to use an analogy, "out toward the tip of a limb"; and, it is quite difficult to climb a tree from the tip of a limb. It is necessary to retreat toward the trunk of the tree to progress up or down depending upon the direction that truth is being sought. Analogies are never good arguments; though, the point is that academic physics must clearly admit their known fallacies rather than continue to indoctrinate aspiring students to build upon the standard model axioms . . . which are all metaphysical forces.
Academic science must recognize the limits of that which is quantitative, embrace the concepts of Infinity's duality and that the first essence of Reality is complex, harmonic oscillations that resonate as particles. All fundamental understanding must incorporate an explanation of the locus of the Universe. Ask, Why? and Why? . . . and Why? again . . . and again! The most simple is the most complex; and, vice versa.
Logically, a situation that spawns increasing enigmas should indicate much fundamental misunderstanding.) Return to Text