Noether`s Theorem and Einstein’s “Interval”



Discovering “Noether’s Theorem” and the principle of symmetry conservation was one of the two keys that opened my personal door to the unification theory. The second key was Einstein’s statement that the spacetime “Interval” of light was equal to zero.

Section 9 – Symmetry: Noether`s Theorem and Einstein’s “Interval”
(revised May, 2011)
John A. Gowan
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The Charges of Matter are the Symmetry Debts of Light

Symmetry Principles of the Unified Field Theory (a “Theory of Everything”) – Part I
Symmetry Principles of the Unified Field Theory (a “Theory of Everything”) – Part 2 
Symmetry Principles of the Unified Field Theory (a “Theory of Everything”) – Part 3 (Summary)

Noether’s theorem states that in a multicomponent field, such as the electromagnetic field (or the metric field of spacetime), where one finds a symmetry one also finds an associated conservation law, and vice versa. I soon came to realize that because matter is created from light, this theorem means that any symmetry of light must somehow be conserved in matter, and that (one of) the real world consequences of Noether’s Theorem was the charges of matter are the symmetry debts of light. Charge conservation (including “spin”) = symmetry conservation, in the case of the electromagnetic field; in the case of the metric field of spacetime, the physical consequence of Noether’s theorem is the presence of inertial forces and gravitation. The conservation of “spin” (the quantized spin angular momentum of particles) seems to be a mixture of the charge and inertial force cases. Because the theorem works in two directions, any charge of matter must be associated with a symmetry of light; and further, because charges produce forces, gravity also must be the product of some charge of matter, and therefore gravity presumably represents some symmetry debt of light. In accordance with Noether’s Theorem, charges produce forces which act to return the asymmetric material system to its symmetric origin in light. In the case of gravity, we have the example of our Sun, the stars, quasars, and Hawking’s “quantum radiance” of black holes, returning bound energy to its original symmetric state, light.

But what broken symmetry of light does gravity represent? What is the nature of the gravitational “charge”? For each of the four forces of physics, there must be an associated charge, and these charges are all (presumably) symmetry debts of light. When light is converted to matter, it loses a lot of symmetry – in fact, according to this line of thought, symmetries of at least 4 different kinds, each of which requires a different kind of conserved charge. The action of the force produced by the charge is therefore understood as the attempt to pay the conserved symmetry debt carried (represented) by the charge, returning the system to its original symmetric state (light), in obedience to Noether’s Theorem. The electric charge is prototypical of this effect:

When light creates particle-antiparticle pairs, the particles are produced with opposite and strictly conserved electric charges, whose whole purpose is to produce a long-range attractive force between the particles with sufficient strength to produce an annihilation reaction within the Heisenberg time limit for “virtual reality”, returning the particle pairs to the symmetric state of free energy which created them. Because the photon is the field vector (force carrier) of electric charge, we see light protecting its own symmetry in such annihilations, which occur continuously in the “virtual particle sea”, the Heisenberg realm of virtual reality.

A pathway to the conceptual unification of forces therefore presents itself: identify the symmetries of light which the charges and forces of matter represent; all charges, forces, and particles have their origin in light, which becomes the principle of unification. The question becomes: what are the 4 symmetries of light represented by the 4 charges and forces of physics? This question is pursued (and answered) in the various unification papers, especially: “Symmetry Principles of the Unified Field Theory“.

I like to think of Noether’s theorem (1918) as the “Truth and Beauty” theorem, as it appears to be nothing less than the mathematical expression of Keat’s famous poetic intuition: “Beauty is truth, truth beauty, – that is all ye know on Earth, and all ye need to know” (1819) – where conservation plays the role of truth, and beauty = symmetry. This is an outstanding example of the correspondence between the rational and intuitive powers and sensitivities of the human mind: neither one is to be slighted, much less dismissed.

(See: Emmy Noether: A Tribute to her Life and Work. Brewer, J. W. and M. K. Smith, eds. M. Dekker, New York, 1981

Einstein’s “Interval”
The “Interval” of Light = Zero

The second key in my understanding of the unification pathway was Einstein’s mathematical statement that the spacetime “Interval” of light = zero. Einstein’s “Interval” is an invariant measure of the “quantity” or “interval” of spacetime separating two events. The Interval is so mathematically formulated that it is invariant with regard to the relative motion of observers, and its chief role is to rescue causality from Einstein’s shifting relativistic perspectives of space and time in moving frames of reference. Thus moving observers of two events will not agree, in general, on the space and time measurements separating those events, but they will always agree upon the mathematical product of those measurements when combined in Einstein’s formulation of the “Interval”. The invariance of causality depends upon the invariance of the Interval and the absolute (non-relative) velocity of light.

The zero “interval” of light means light is “non-local”, having no time dimension and no spatial “x” dimension corresponding to length or distance – light’s “clock is stopped” and meter sticks shrink to nothing in the direction of light’s propagation. Light is a 2-dimensional transverse wave. Velocity c, the intrinsic motion of light, is a symmetry condition, drive, or “gauge” for light (free energy) which results in light’s “non-local” character. The zero Interval of light is the formal (mathematical) expression of this fundamental symmetry of light, its “non-local” energy state. Several related symmetries flow from light’s “non-locality”: 1) light has no asymmetric time dimension; 2) light has no asymmetric (local) “rest” mass; 3) light produces no asymmetric gravitational field; 4) being non-local, with an infinite amount of time to go nowhere, in its own reference frame, moving at velocity c, light is everywhere within its conservation domain (spacetime) simultaneously.

The effectively “infinite” velocity of light results in another symmetry – the equitable distribution of light’s energy throughout its conservation domain, everywhere, simultaneously – a symmetry of special significance for gravitation and matter’s “location” charge. “Non-locality” also allows light, or velocity c, to act as the metric gauge of spacetime, including its inertial symmetry, regardless of the size or motion (expansion, contraction) of the domain. Non-locality has the further consequence of producing a condition of complete unity and connectivity between light and space throughout light’s conservation domain of spacetime. It is the (broken) non-local distributional symmetry of light’s energy which is the source of the gravitational “location” charge in matter. “Location”, a charge whose active principle is time, identifies the spacetime location, quantity, and density of bound energy. Matter is an immobile and hence undistributed lump of concentrated mass or bound electromagnetic energy (E = mcc).

The connection between symmetry and entropy enters our theory with “velocity c”, which is the symmetry gauge of free energy, banishing time, distance, mass, charge, and gravitation. “Velocity c” also gauges the entropy drive of free energy (the intrinsic motion of light), causing the expansion and cooling of light’s spatial conservation domain – the Cosmos. This double gauge role of “velocity c” is reflected in the corresponding double conservation role of gravitation: gravitation produces the time dimension of matter, identifying the 4-D spacetime location of mass (light’s distributional symmetry debt); the intrinsic motion of time also serves as the historical entropy drive of matter (light’s “intrinsic motion” entropy debt). Hence gravity: 1) produces the time dimension of matter via the annihilation of space, conserving the spatial entropy drive of light’s intrinsic motion as the historical entropy drive of time’s intrinsic motion; and 2) converts bound to free energy (as in stars, quasars, and Hawking’s “quantum radiance” of black holes) to conserve the distributional symmetry of light’s non-local energy state. Because both light’s entropy drive and non-local distributional symmetry are gauged by “velocity c”, to conserve either function is to conserve the other by default. This has the significant consequence that gravity’s entropy conservation role also falls under the symmetry conservation mantle of Noether’s Theorem. Time is a charge with a symmetry conservation role – as demonstrated by gravity’s conversion of bound to free energy in the stars. (See: “The Double Conservation Role of Gravity“; see also: “The Conversion of Space to Time“.)

The “location” charge of gravitation carries both the entropy debt and the symmetry debt of light’s non-local energy state; it is this double role that has made gravity such a difficult force to understand. The active principle of the gravitational charge is time; the one-way spacetime flow of gravitation is the consequence of time’s intrinsic one-way motion into the historic domain of spacetime. It is the causal function of time that requires its one-way flow. See: Entropy, Gravitation, and Thermodynamics”; also “A Description of Gravitation”.

Symmetry and entropy are connected in light because light occupies its conservation domain completely (space is actually created by the intrinsic motion of light), and the most symmetric dispersion of light within its domain also has the greatest entropy. However, entropy has a further component, temperature, such that while hot or cold light has the same symmetry, cold light has the greater entropy. Hence entropy rather than symmetry actually drives the expansion of space. None of these considerations apply to bound energy (matter), which does not occupy its conservation domain completely (historic spacetime), and does not participate in the expansion of either spacetime or history. It is because of these differing dimensional characteristics that the entropy drives of free and bound energy (the intrinsic motions of light and time as gauged by “velocity c” and “velocity T”) are so vastly different in their entropic consequences and metric equivalence, a difference which we perceive as the anomalous weakness of gravitation. Bound electromagnetic energy (matter) is only tangentially connected to its historical conservation domain via the ephemeral “present moment”. Gravity produces only enough time to provide the temporal entropy drive for this tangential point of contact between matter and history (actually seen as the area of the “event horizon” of a black hole). (See: “Proton Decay and the ‘Heat’ Death of the Cosmos”.)


General Topics:

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    Bekenstein, J. D. Black Holes and Entropy. Physical Review D1973, 7(8), 2333-46.
    Brewer, J. W. and M. K. Smith, eds. Emmy Noether: A Tribute to her Life and Work. M. Dekker, New York, 1981, 180 + x pp. + 10 plates.
    de Chardin, Pierre Teilhard: The Phenomenon of Man. French: Editions du Seuil, Paris, 1955; English: Harper and Row, New York, 1959.
    Close, Frank: Lucifer’s Legacy. 2000. Oxford Univ Press.
    Cronin, J. W. CP Symmetry Violation: the Search for its Origin. Science 1981, 212, 1221-8 (Nobel lecture).
    Gowan, J. C. (Sr.) 1975“Trance, Art, Creativity”
    Greene, B. The Elegant Universe. W.W. Norton & Co. 1999, 448 + xiii pp.
    Greene, B. The Fabric of the Cosmos. A. A. Knoph, 2004, 569 + xii pp.
    Gross, D. J. and F. Wilczek. 1973. Ultraviolet Behavior of Non-Abelian Gauge Theories. Phys. Rev. Lett. 30: 1343.
    Gross, Politzer, Wilczek: Science: 15 October 2004 vol. 306 page 400: “Laurels to Three Who Tamed Equations of Quark Theory.”
    Hawking, S. W. Particle Creation by Black Holes. Communications in Mathematical Physics 1975, 43 (3), 199-220.
    Lederman, Leon with Dick Teresi: The God Particle. 2006. Mariner Books.
    Lederman, Leon and Christopher Hill: Symmetry. 2008. Promethus Books.
    Lovelock, J. E. Gaia. A New Look at Life on Earth. 1979. Oxford University Press.
    Oerter, Robert: The Theory of Almost Everything. Penguin (Plume) 2006.
    Pais, Abraham 1986. Inward Bound: of Matter and Forces in the Physical World. Oxford University Press, NY
    Politzer, H. D.. 1973. Phys. Rev. Lett. 30: 1346.
    Resnick, Robert: Introduction to Special Relativity. 1968. John Wiley and Sons, Inc.
    Stewart, Ian. “Why Beauty is Truth”. 2007, Basic Books
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    Weinberg, S. The First Three Minutes. Bantam. 1977, 177 + x pp.
    Wilczek, Frank. The Lightness of Being. 2008. Basic Books.

  1. Gravity, Entropy, and Thermodynamics: Part 2
  2. Gravity, Entropy, and Thermodynamics: Part I
  3. The Conversion of Space to Time by Gravity
  4. The “Tetrahedron Model” vs the “Standard Model” of Physics: A Comparison
  5. Postscript to: Spiritual and Scientific Principles of the Cosmic Tetrahedron Model
  6. Spiritual and Scientific Principles of the “Tetrahedron Model”
  7. A General Systems Approach to the Unified Field Theory – Part 4 (General Systems Discussion)
  8. Symmetry Principles of the Unified Field Theory: Part 3 of 3
  9. Symmetry Principles of the Unified Field Theory (a “Theory of Everything”) – Part 2
  10. Symmetry Principles of the Unified Field Theory: Part 2 of 3
  11. Symmetry Principles of the Unified Field Theory: Part 2
  12. The Particle Table
  13. Symmetry Principles of the Unified Field Theory (Part 1 of 3)
  14. An Introduction to the Papers (Unified Field Theory)
  15. Proton Decay and the “Heat Death” of the Cosmos
  16. Proton Decay and the “Heat Death” of the Cosmos
  17. The Origin of Matter and Information
  18. Introduction to the Higgs Boson Papers
  19. Higgs Table: Unified Force Eras of the “Big Bang”
  20. The Higgs Boson and the Weak Force IVBs: Parts II -IV
  21. The Higgs Boson vs the Spacetime Metric
  22. The Weak Force: Identity or Number Charge
  23. Introduction to The Weak Force
  24. A Description of Gravitation
  25. Introduction to Gravitation
  26. Introduction to The Weak Force
  27. The Weak Force: Identity or Number Charge
  28. A Spacetime map of the Universe: Implications for Cosmology
  29. Negentropic Information
  30. Synopsis of the ‘Tetrahedron Model’
  31. Time and Entropy
  32. Noether`s Theorem and Einstein’s “Interval”
  33. The Intrinsic Motions of Matter
  34. Light and Matter – a Synopsis
  35. A Short Course in the Unified Field Theory
  36. The Information Pathway
  37. Sect. VI: Introduction to Information
  38. Introduction to Fractals
  39. Introduction to General Systems, Complex Systems
  40. A Rationale for Gravitation
  41. About Gravity
  42. Gravity, Entropy, and Thermodynamics: Part 2
  43. A Description of Gravitation
  44. Spatial vs Temporal Entropy
  45. Introduction to Entropy
  46. The Human Connection
  47. Global-Local Gauge Symmetries and the “Tetrahedron Model” Part I: Postscript
  48. Global and Local Gauge Symmetry in the “Tetrahedron Model”: Part I
  49. Global and Local Gauge Symmetries: Part IV
  50. Global and Local Gauge Symmetries: Part V
  51. Global-Local Gauge Symmetry: Part III: The Weak Force
  52. Global and Local Gauge Symmetries: Part II (Gravitation, Section A)
  53. Global and Local Gauge Symmetry: Part II (Gravitation, Section B)
  54. The Origin of Matter and Information
  55. Gravity, Entropy, and Thermodynamics: Part I
  56. The Conversion of Space to Time
  57. The Short-Range or “Particle” Forces
  58. The Time Train
  59. Extending Einstein’s Equivalence Principle: Symmetry Conservation
  60. Introduction to Gravitation
  61. Symmetry Principles of the Unified Field Theory: Part I
  62. The Higgs Boson vs the Spacetime Metric
  63. de Broglie Matter Waves and the Evolution of Consciousness
  64. Nature’s Fractal Pathway
  65. Teilhard de Chardin – Prophet of the Information Age
  66. The Double Conservation Role of Gravity
  67. The Higgs Boson and the Weak Force IVBs: Parts II -IV
  68. Higgs Table: Unified Force Eras of the “Big Bang”
  69. The Higgs Boson and the Weak Force IVBs
  70. Introduction to the Higgs Boson Papers
  71. The Strong Force: Two Expressions
  72. Table of Forces and Energy States
  73. The Origin of Space and Time
  74. “Inflation” and the “Big Crunch”
  75. The “W” Intermediate Vector Boson and the Weak Force Mechanism
  76. The Weak Force Mechanism and the “W” IVB (Intermediate Vector Boson):
  77. Physical Elements of the “Spacetime Map”
  78. The Traveling Twins Paradox
  79. Currents of Entropy and Symmetry
  80. The Half-Life of Proton Decay
  81. Spiritual and Scientific Principles of the “Tetrahedron Model”
  82. An Introduction to the Papers (Unified Field Theory)
  83. The “Spacetime Map” as a Model of Juan Maldacena’s 5-Dimensional Holographic Universe
  84. The “Tetrahedron Model” in the Context of a Complete Conservation Cycle
  85. Symmetry Principles of the Unified Field Theory: Part 3 (Summary)
  86. Symmetry Principles of the Unified Field Theory: Part 2
  87. General Systems “Hourglass” or “Grail” Diagrams
  89. The “Tetrahedron Model” vs the “Standard Model” of Physics: A Comparison
  90. “Dark Energy”: Does Light Create a Gravitational Field?
  91. Human Life-Span Development and General Systems Models
  92. Man’s Role in Nature
  93. Origin of Life: Newton, Darwin, and the Abundance of Life in the Universe