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THE GREATEST STANDING ERRORS IN MATHEMATICS AND PHYSICS
by Miles Mathis
Painting Experiment with an Air Pump by Joseph Wright of Derby, 1768, Tate Gallery, London
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Chapter List
i. Preface. A broad overview of the current state of physics and math, and an explanation of my intent with this book. 5pp.
ii. The Central Discoveries of this Book. What I believe I have achieved; an overview. 7pp.
iii. Death by Mathematics. The pre-meditated murder of physics. 8pp.
1. A Revaluation of Time. This paper offers a simple operational definition of time, one which is useful in understanding the papers that follow. 6pp.
2. Relativity as a Concept. An introduction to the problem, preparing the reader for the mathematical arguments in later papers. 6pp.
3. The Michelson/Morley Interferometer. Here I explain the flaws in various conceptualizations of the interferometer, showing that no fringe effect should have been expected. It was originally published as Appendix A to the long paper in chapter 7. 12pp.
4. A Final Simplification of the Problem (of Special Relativity). This is a short paper glossing my main corrections to Einstein’s transforms. It was written after the papers in chapters 5, 6 and 7. 6pp.
5. The Discovery of First-Degree Relativity and the Refutation of Gamma. This is the paper I sent to several journals, including Annalen der Physik and Physical Review Letters, from 2001 to 2004. It condenses the information from the longer papers in chapters 6 and 7. 21pp.
6. A Critique of Einstein's Original Paper. Here I attack Einstein line for line, using "On the Electrodynamics of Moving Bodies" (Annalen der Physik, 1905) as my text. This was to answer critics of my first paper [chapter 7] who believed that Einstein’s paper of 1905 still had precedence over math published later in the books Relativity and The Meaning of Relativity. This paper was originally published as Appendix C to the longer paper below. 12pp.
7. An Algebraic Correction to the Transformation Equations (The Lorentz Equations) of Special Relativity. This is my first paper on Special Relativity. It includes new first- and second-degree transforms, as well as new transforms for movement toward an observer and at an angle to an observer. In addition, it explains the interferometer, discusses the Hafele-Keating experiment, and suggests a solution to the Pioneer Anomaly. 48pp.
8. The Light Clock. A close analysis of the light clock, showing the many ways it fails as a visualization of time dilation. 3pp.
9. A Final Argument against x' = x - vt. A short addendum to my proofs against this equation, once again using a text of Feynman as an example. 2pp.
10. The Equation x' = x - vt, Again. One more useful visualization of the problem, focusing this time on the immobility of origins in relative motion. 3pp.
11. Proof that Classical Action is Invariant in a Galilean Transformation. A reply to a paper in American Journal of Physics that claimed that action was not invariant in a Galilean transformation. This transformation is x' = x -vt. 3pp.
12. A Break in the Pioneer Case. An article written for a popular journal showing, in the simplest possible way, the cause of the anomaly. 4pp.
13. How the Loss of Gamma affects Minkowski’s Space-time Equations. In this paper I show how Minkowski’s math must be affected by my corrections to Special Relativity. Also see chapter 19 below. 5pp.
14. How New Transforms in Special Relativity Affect Mass, Momentum and Energy Equations. Here I show that Einstein’s mass and energy transforms are also incorrect, including the famous E=mc2. I also show, for the first time, that the classical equation E=mv2/2 is not an approximation. Finally, I derive the number 108 for the proton. 41pp.
15. New Mass and Energy Transforms—a Gloss. A much shortened argument, compressing the paper in Chapter 14. 11pp.
16. An Overview of my Mass Increase Papers. A 2-page presentation of findings only, with no derivations and no analysis. 2pp.
17. Lorentz Invariance. How my corrections affect so-called Invariance, covariance, and violations. 4pp.
18. A Critique of General Relativity. A refutation of Einstein’s thought problem of the spinning disk and an analysis of the tensor calculus. Also, a solution to the primary problem of GR (the deflection of starlight) without tensors or Riemann. 13pp.
19. Why Hyperbolic Math is not applicable to General Relativity. Here I show the flaw in i and the assumption that time travels orthogonally to x, y, z. Also see #13 above. 2pp.
20. Another Critique of Curved Space, using an analogy to the electrical field. 4pp.
21. The Trouble with Tensors, a critique of the tensor and the tensor field as used by GR. 8pp.
22. The Perihelion Precession of Mercury. A long critique of the historical problem, showing the major errors of Einstein and others. 32pp.
23. The Perihelion Precession of Mercury, the short version A gloss of the longer paper. 3pp.
24. How to Solve General Relativity Problems without the Tensor Calculus (in 1/100th the time). The title says it all. 3pp.
25. How General Relativity Solves the Metonic Cycle. A mechanical explanation of the cycle, with all the math. 9pp.
26. A Re-definition of the Derivative (why the calculus works—and why it doesn’t). This paper establishes for the first time the true foundation of the calculus. Rather than pursue a diminishing differential, as has been the quest of history, I have discovered the constant differential underlying the basic equation of the calculus. In doing this, I show that instantaneous values are impossible. 28pp.
27. Calculus Simplified. A compression of my long paper on the calculus. 13pp.
28. Trig "Derivatives" found without the old Calculus. Here I show that my simple exponent table from my calculus paper, and the constant differential, apply just as easily to trig functions. 3pp.
29. Another Fatal Flaw in the Historical Foundation of the Calculus. A further flaw in the current proof of the derivative, specifically in the assumption that the terms in an infinite series can approach a limit. I show that the sum approaches the limit, but the terms do not, nullifying the accepted procedure. 4pp.
30. A Disproof of Newton's Fundamental Lemmae. Newton's first 8 lemmae from the Principia are shown to be false. 6pp.
31. Quantum Mechanics and Idealism. My paper on the calculus is tied to QED here. Also a comparison of the idealisms of Heisenberg and Berkeley. Finally, a disproof of both idealisms, and a simple logical and mathematical refutation of the Copenhagen interpretation. 10pp.
32. Superposition. Both superposition and the wave-particle duality are explained mechanically, with a straightforward visualization. This falsifies the Copenhagen interpretation in the most direct way imaginable. 5pp. Also see #76 below.
32b. The Double Slit Experiment. A simple mechanical explanation of the single photon problem and the detector problem. 7pp.
33. Why Schrodinger's Waves move in Q-space. 5pp.
34. Schrodinger's Waves Mechanics Explained. How can electrons have more than three wave motions
in only three dimensions? 4pp.
35. Bohr's First Big Mistake. A major substitution error in the math of the Bohr radius is shown to infect all of QED. 3pp.
36. Electrical Charge. Defining charge as the mass of the radiation. 9pp.
36b. What is "Charge"? It is a resultant acceleration of two fields. 8pp.
37. The Electromagnetic Field (and the Strong Force). How the E/M field and the strong force have changed due to my new Unified Field. 5pp.
38. A Correction to a=v2/r (and a refutation of Newton's Lemmae VI, VII & VIII). In this paper I expose the errors in the derivation of a=v2/r, one of the bedrock equations of circular motion. In doing so I falsify Newton's famous Lemmae VI, VII & VIII from the Principia. 17pp.
39. Celestial Mechanics. A demonstration of the inadequacies of current theory regarding gravity, orbits, and nebulae. 18pp.
40. The Trouble with Tides. A thorough expose of the holes in current tidal theory. 10pp.
41. The Solution to Tides (Part 1). The solution, replacing gravity with E/M as the main cause. 17pp.
42. The Solution to Tides (Part 2). The mechanical cause of spring and neap tides. 7pp.
43. The Solution to Tides (Postscript). Lunar effects and the E/M field. 2pp.
44. The Universal Gravitational Constant. I follow a hint from Maxwell to give the dimensions of G to the mass. 6pp. Also see #60 below.
45. The Third Wave: a Redefinition of Gravity, Part I. No curved space, no force at a distance, no force-carrying particle. Gravity is explained here simply in terms of straight-line motion. Mass, inertia and gravity are all shown to be equivalent, reducible to the same motions. 9pp.
46. The Third Wave: a Redefinition of Gravity, Part II. An explanation of both atomic and macro orbits using the expansion "field" and the E/M field. 7pp.
47. The Third Wave: a Redefinition of Gravity, Part III. An explanation of the inverse square law using expansion theory. It is also shown that the Standard Model contradicts the law. 6pp.
48. The Third Wave: a Redefinition of Gravity, Part IV. Retrograde orbits, Triton, and the lack of angular momentum in the Sun are explained. 10pp.
49. The Third Wave: a Redefinition of Gravity, Part V. The aberration of starlight and gravity at the quantum level are explained. A proposal concerning the strong force is also made, linking it to the expansion of matter. 14pp.
50. The Third Wave: a Redefinition of Gravity, Part VI. The Ideal Gas Law as proof of Expansion Theory. 3pp.
51. The Third Wave: a Redefinition of Gravity, Part VII. The Moon as proof of Expansion Theory. Mass and weight using both the gravitational field and the E/M field. 15pp.
51a. An Update on Weight, in which I falsify F=GMm/R2 using a new thought problem. 19pp.
52. The Third Wave: a Redefinition of Gravity, Part VIII. Genesis. I introduce a new cosmology to contain my mechanics. 7pp.
53. The Third Wave: a Redefinition of Gravity, Part IX. The optical size equivalence (angular diameter) of Sun and Moon as proof of my theory. 13pp.
54. The Cavendish Experiment. I show a compensation of errors in all such experiments. 37pp.
55. The Allais Effect and Majorana. Plus commentary on LeSage, Podkletnov, NASA, Wiki, and others. Showing how my compound field answers anomalies where other fields do not. 32pp.
56. The Moon Gives up a Secret. Numbers from the Moon are analyzed to show that "gravity" is a compound field. 4pp.
57. A Call to Astronomers. A call to astronomers for confirmation of a prediction concerning the bending of starlight by Jupiter. 4pp.
58. Bending of Starlight by the Planets.Experimental proof of my theory of gravity. 7pp.
59. The Unified Field Theory. Newton's gravitational equation is shown to be a compound equation that includes the E/M field. I mathematically separate the two field equations, do transforms on them, and create simple and useful Unified Field Equations. 24pp.
60. What is G? It is the transform from one radius to another, but not the radii you think. 9pp. Also see #44 above.
61. Zero-point Energy and the Casimir Effect Zero-point energy is not infinite and the Casimir Effect is not an outcome of quantization. 18pp.
62. Explaining the Ellipse. Holes in the elliptical theory of orbits are filled at last. 4pp.
63. The Cosmic Mass Deficit. A simple, logical, mechanical explanation of the mass deficit, without dark matter or any other ad hoc postulate. 4pp.
64. Contra Feynman. Some introductory comments on Richard Feynman, including a critique of Dicke's experiment. 13pp.
65. Richard Feynman and the Glorification of Heuristics. A further critique of Feynman and QED. 7pp.
66. Some Introductory Remarks on Cantor. A few observations on point-set topology and infinities. 5pp.
67. Zeno's Paradoxes. A short paper on Zeno's various paradoxes showing, among other things, that I am not opposed to limits or infinities in mathematics or in physics when they are used properly. 6pp.
68. Gödel's Incompleteness Theorems. Commentary in passing on Kurt Gödel, including analysis of Karl Popper, Bertrand Russell, and others. 6pp.
69. Why Noether's Theorem is a Tautology. A short proof of Noether's Theorem by algebraic means, showing that symmetries are equivalent to conservation laws. This contradicts the current interpretation that symmetries are primary. 2pp.
70. Entropy. A refining of the concept of entropy, and a rebuttal to the current conceptions of order. 5pp.
71. What is π? Here I show that π is a centripetal acceleration and that the circumference of any circle has complex dimensions. 6pp.
72. String Theory: the Inelegant Universe. A Critique of String Theory and M-theory using Brian Greene's book The Elegant Universe as my text, including a foundational correction to the 11-dimensional math. 14pp.
73. Does Size Matter? The first entry in a new section answering readers' questions. Here I answer a question about the ratio of volume to surface area changing with size. 3pp.
74. Why do Stars Twinkle? A new answer to this question and some commentary on the old answer. 6pp.
75. Squaring the Circle. Here I show various operational inconsistencies in claiming that the circle cannot be squared "with a straight edge and compass." 12pp.
76. The Collapse of the Wave Function. Written as an introduction to my paper on Superposition. See #32 above. 7pp.
77. Goldbach's Conjecture Proved, the simple way. 5pp.
78. The Born-Einstein Letters, extended commentary on QED, GR, and other subjects. 14pp.
79. The Myth of the Black Hole, commentary on black hole theory. 9pp.
80. The Ether, does the ether exist, and if so, in what form? 8pp.
81. Tesla and Einstein were Both Right, about the ether. 8pp.
857pp. total. 4/23/2008.