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Classical Mechanics and Gravity From Newton to Einstein


Jack Sarfatti


Excerpted from Stargate

Version 12-19-13


I am taking the contemporary approach, not the historical one. This is a reconstruction of Newton and Einstein’s ideas using modern insights. It’s not exactly how they would have thought of what they did, but what I write does not contradict any essential battle-tested truths of their ideas.


Newton’s dynamics of particles is based on Euclidean geometry for space with absolute time the same for all observers no matter how they move. Newton had no idea that the speed of light was finite. In Newton’s theory the speed of light is infinite.


Newton’s first two laws are basically a single law.

Law 1. Force-free motions of test particles are geodesics independent of the mass and internal constitution of the particle.

A test particle is so small that we can neglect the gravity field it generates.

In Newton’s implicit geometry a geodesic is a straight line in space with a test mass moving at constant speed. There is also a state of absolute rest.

Law 2. A real vector[i] force F causes the test particle with velocity vector and instantaneous position vector  to have a curved motion with varying speed that is not geodesic.

Assume the mass m is constant, that is the calculus[ii] derivative dm/dt = 0.

F = dP/dt = d(mV)/dt = mdV/dt = md2r/dt2 = ma

This equation assumes a global inertial frame. A global inertial frame (GIF) is an imaginary cubic lattice of rigid steel rods across the entire universe with a clock at each vertex. All the clocks are synchronized. There are artificial intelligences with each clock that can communicate with each other by light signals. They all have Doppler radars to track the motions of test particles or UFOs. Jim Woodward, in his book Making Starships[iii], uses a simplistic model of the universe by the late Dennis Sciama that implicitly assumes such a global frame. Of course the equations that Professor Woodward proposes as an engine for spaceships will not work - more on this later.

Now in fact, such structures do not exist. We really only have local frames consisting of a finite network of detectors over a small region of space connected by the internet.

Physics is not mathematics. The crackpots I have dealt with do not understand the difference. Theoretical physics is about what detectors measure. We use mathematical models to do that, but the models have an enormous amount of redundant excess baggage that must be factored out in the sense of equivalence relation classes[iv] and homomorphisms[v] preserving essential relevant structure. It’s the same as a compression algorithm[vi] in computer science. Mathematics is like a high-resolution image. However, what we need to do real physics is a much lower resolution compressed image in which certain non-essential features are erased because only some small subset is needed for the measurements of interest.

Finally we have Law 3.

Newton’s third law of motion[vii] is very limited in its domain of validity and is a specialized case of the more general action-reaction conjecture.[viii] Newton’s third law assumes only central forces, which act instantly at a distance. Therefore, it’s only good really for contact interactions in his original theory. It can be generalized when fields are added to Newton’s particles. Newton did not really have the concept of extended dynamical fields[ix] that have a reality equal to localized hard massy marble-like particles. Today we have Noether’s theorem[x] that relates conservation laws to the symmetries[xi] of dynamical actions[xii] of systems of particles and fields in classical physics. Everything becomes fields in quantum physics, where the real particles are excited out of a very complicated vacuum that is a seething frothy quantum foam of virtual particles[xiii] in an ever turbulent Dirac sea.[xiv] Newton’s third law corresponds to only two systems forming a closed system.  More generally a group of space translation symmetries causes the total linear momentum of closed complex systems of particles and fields to be conserved. Similarly, time translation symmetry causes total angular momentum of closed systems to be conserved and rotational symmetry causes total angular momentum to be conserved. There are also internal symmetries beyond spacetime out of which spring the electromagnetic, weak and strong force fields.[xv] When we go to Einstein’s 1905 special relativity[xvi] where space is fused with time into space-time, then rotations that mix space and time together correspond to the Lorentz boosts[xvii] causing time dilation, length contraction and the equivalence of mass to energy. We can even go beyond that to Roger Penrose’s twistor[xviii] conformal group[xix] that includes uniformly accelerated local frames (LNIFs) with Rindler horizons[xx] as well as a topological stretching dilation symmetry that is badly broken in our world.[xxi]

[viii] Einstein, the reality of space, and the action-reaction principle

Harvey R. BrownDennis Lehmkuhl

(Submitted on 20 Jun 2013)

Einstein regarded as one of the triumphs of his 1915 theory of gravity --- the general theory of relativity --- that it vindicated the action--reaction principle, while Newtonian mechanics as well as his 1905 special theory of relativity supposedly violated it. In this paper we examine why Einstein came to emphasize this position several years after the development of general relativity. Several key considerations are relevant to the story: the connection Einstein originally saw between Mach's analysis of inertia and both the equivalence principle and the principle of general covariance, the waning of Mach's influence owing to de Sitter's 1917 results, and Einstein's detailed correspondence with Moritz Schlick in 1920.


To appear in "The Nature of Reality", P. Ghose (ed.), Oxford University Press


History and Philosophy of Physics (physics.hist-ph); General Relativity and Quantum Cosmology (gr-qc)

Cite as:

arXiv:1306.4902 [physics.hist-ph]


(or arXiv:1306.4902v1 [physics.hist-ph] for this version)



New opening of my book Stargate
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  • Jack Sarfatti Stargate

    Making Star Trek Real

    Jack Sarfatti

    Internet Science Education Project


    I'm very well acquainted, too, with matters mathematical,

    I understand equations, both the simple and quadratical,

    About binomial theorem I'm teeming with a lot o' news,

    (Bothered for a rhyme)

    With many cheerful facts about the square of the hypotenuse.

    I'm very good at integral and differential calculus;

    I know the scientific names of beings animalculous:

    In short, in matters vegetable, animal, and mineral,

    I am the very model of a modern Major General.

    Pirates of Penzance, Gilbert and Sullivan

    Sing Heav'nly Muse, that on the secret topOf Oreb, or of Sinai, didst inspireThat Shepherd, who first taught the chosen Seed,In the Beginning how the Heav'ns and EarthRose out of Chaos: Or if Sion Hill [ 10 ]Delight thee more, and Siloa's Brook that flow'dFast by the Oracle of God; I thenceInvoke thy aid to my adventrous Song,That with no middle flight intends to soarAbove th' Aonian Mount, while it pursues [ 15 ]Things unattempted yet in Prose or Rhime.And chiefly Thou O Spirit, that dost preferBefore all Temples th' upright heart and pure,Instruct me, for Thou know'st; Thou from the firstWast present, and with mighty wings outspread [ 20 ]Dove-like satst brooding on the vast AbyssAnd mad'st it pregnant: What in me is darkIllumin, what is low raise and support;That to the highth of this great ArgumentI may assert Eternal Providence, [ 25 ]And justifie the wayes of God to men. John Milton, Paradise Lost

    In another moment Alice was through the glass, and had jumped lightly down into the Looking-glass room. Lewis Carroll

    All our space-time verifications invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meeting of two or more of these points. Moreover, the results of our measuring are nothing but verifications of such meetings of the material points of our measuring instruments with other material points, coincidences between the hands of a clock and points on the clock dial, and observed point-events happening at the same place at the same time. The introduction of a system of reference serves no other purpose than to facilitate the description of the totality of such coincidences. Albert Einstein, “Grundlage der allgemeinen Relativitätstheorie”, Annalen der Physik, 49 (1916)[1]

    “That with no middle flight intends to soar …”

    “A wormhole is a hypothetical shortcut for travel between distant points in the universe. The wormhole has two entrances called ‘mouths,’ one (for example) near Earth, and the other (for example) in orbit around Vega, 26 light years away. The mouths are connected to each other by a tunnel through hyperspace (the wormhole) that might be only a kilometer long. If we enter the near-Earth mouth, we find ourselves in the tunnel. By traveling just one kilometer down the tunnel we reach the other mouth and emerge near Vega, 26 light-years away as measured in the external universe.” Kip Thorne[i]

    Prior to the development of digital computers in the 20th century, the only systems on Earth, which incorporated bulk, reliable digital storage, were living organisms. DNA, neural networks and brains, and the adaptive immune system all have the ability to robustly store large quantities of information and retrieve it when needed. But storage is tough—each of these biological systems is enormously more complicated than any existing computer, and it took biology billions of years to evolve its second and third kinds of digital storage. The intertwined complexity of DNA and protein synthesis in even the simplest living cells is such that how it came to be remains one of the central mysteries of biological science, a conundrum so profound that one of the two discoverers of the structure of DNA, Nobel Prize winner Francis Crick, believes the first living cells were placed on Earth by intelligent aliens from elsewhere in the Galaxy. (But then how did the aliens get started?) John Walker, Computation, Memory, Nature, and Life

    Is digital storage the secret of life? [ii]

    My “great Argument” in this book, “things unattempted yet in” theoretical physics “And justifie the wayes of God to men,” is that Hawking’s chronology protection conjecture[iii] is wrong and that Crick’s “aliens” are actually future humans who have mastered time travel to the past through stargates and have found at least one that was created in the very early universe, which allows them to get to Earth and create us and obviously themselves in a physical globally self-consistent[iv] Godelian strange loop[v] in time. In other words the time travel bootstrap paradox[vi] is not a paradox at all, but is the way reality works including our own consciousness.

    “Das aus sich rollende” (self-rolling wheel)

    Art thou a new strength and a new authority? A first motion? A self-rolling wheel? Canst thou also compel stars to revolve around thee?

    Friedrich Nietzsche: Thus Spake Zarathustra

  • Jack Sarfatti The University of California Berkeley announced in November, 2013 that statistical analysis of the NASA Kepler Space Craft data[viii] shows that about one fifth of the exoplanets[ix] of Sun type stars are in the habitable zone on which carbon-based life like our own might evolve. The nearest star system with such an exoplanet is twelve light years away from us. Therefore, the probability of contact with an advanced civilization with warp drive [x]stargate technology is much higher than previously thought. This puts the UFO evidence into a new more immediate international security perspective.

    This book is meant for curious intelligent well-educated people who want to understand the universe. To get the most value, the reader while reading should have immediate access to the Web at their fingertips to look up unfamiliar words and to click on the hyperlinks mostly in the extensive endnotes – in the e-book version. This book is not meant for people who have no familiarity whatsoever with high school mathematics including vector analysis, matrix algebra, partial differential and integral calculus, or who have never had at least a high school physics course from a competent teacher and are unfamiliar with basic symbols like c for the speed of light in vacuum, or G for Newton’s gravity constant, or h for Planck’s quantum of action, or kB for Boltzmann’s constant of entropy etc. Engineers and computer programmers should be able to understand most of this book easily. This is not a traditional orthodox boring textbook teaching basic physics, nor is it a watered down pop physics book. Rather it is a supplement for physics textbooks and hopefully a useful guide to online sources of mainstream information organized according to my original eclectic nonlinear stream of consciousness “beat” point of view connecting many different branches of physics in a way not familiar to the average physicist.[xi] 

    [1] My original writing is in 14 fonts Times New Roman double line spaces. Writings by others are in 12 fonts Times New Roman single line spaces.

    [i] “Black Holes and Time Warps”, P. 484 (1994) W.W. Norton, New Yorkkip

    [ii] http://www.fourmilab.ch/documents/comp_mem_nat_life/

    [iii] http://en.wikipedia.org/.../Chronology_protection_conjecture

    [iv] http://www.princeton.edu/.../Novikov_self-consistency...

    [v] http://en.wikipedia.org/wiki/I_Am_a_Strange_Loop

    [vi] http://en.wikipedia.org/wiki/Bootstrap_paradox

    [vii] https://www.youtube.com/watch?v=ypEaGQb6dJk opening of Kubrick’s film Space Odyssey

    [viii] http://kepler.nasa.gov


    [ix] http://en.wikipedia.org/wiki/Extrasolar_planet

    [x] http://en.wikipedia.org/wiki/Alcubierre_drive

    [xi] David Kaiser, MIT “How the Hippies Saved Physics” – I would have preferred “Beats” or “Poets” in the sense of Jack Kerouac instead of “Hippies”. On this see “Bohemia” by Herbert Gold for another description of me. Nick Herbert, part of the motley crew, has some talent for rhyme.
    Computation, Memory, Nature, and Life
  • Jack Sarfatti