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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.

Comments:

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

Subjects:

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)

 

Common misunderstanding of Einstein's "Happiest Thought" corrected & bogus-bad pseudo-physics critiques of Einstein's Equivalence Principle.
1Like ·  · Share
  • Rata Vuloira likes this.
  • Jack Sarfatti Einstein wrote in ~ 1907: "The breakthrough came suddenly one day. I was sitting on a chair in my patent office in Bern. Suddenly the thought struck me: If a man falls freely, he would not feel his own weight. I was taken aback. This simple thought experiment made a deep impression on me. This led me to the theory of gravity. I continued my thought: A falling man is accelerated. Then what he feels and judges is happening in the accelerated frame of reference. I decided to extend the theory of relativity to the reference frame with acceleration. I felt that in doing so I could solve the problem of gravity at the same time. A falling man does not feel his weight because in his reference frame there is a new gravitational field, which cancels the gravitational field due to the Earth. In the accelerated frame of reference, we need a new gravitational field.”
    4 minutes ago · Like · 1
  • Jack Sarfatti Those quotes are from early Einstein around 1907 and Jim Woodward repeats what I said repeatedly that Einstein himself was still unclear in his own mind on how to use words like "accelerated frame" back then. He was in middle of breaking away from Newton's GRIP on the mind of how to think about gravity.
    3 minutes ago · Like · 1
  • Jack Sarfatti Here is the source of the confusion.

    Einstein is naturally thinking in Newtonian terms.

    In GR terms still not invented then

    "acceleration" above means relative kinematical acceleration between test particle and local frame.

    It does not mean real (proper) acceleration (off-geodesic) as measured by an accelerometer.

    The general law is"

    real acceleration on test particle = relative kinematical acceleration between test particle and local frame - real acceleration of local frame.

    DP(test particle)/ds = dP(test particle-frame)/ds - DP'(local frame)/ds

    P = mV test particle

    V = dX/ds

    X = relative kinematical displacement between test particle and local frame detector.

    D/ds = d/ds - {LC frame connection}dX/ds

    DP(test particle)/ds 

    = dP(test particle)/ds - {LC frame connection}(dX/ds)P(test particle)

    when dm/ds = 0

    D^2X/ds^2 = d^2X/ds^2 - {LC frame connection}(dX/ds)^2

    {LC frame connection}(dX/ds)^2 = M^-1DP(frame)/ds

    M = mass of frame/detector

    {LC frame connection} has dimension 1/Length

    ds is PROPER TIME element along world line of object.

    Each term has an independent measurement technique.

    Real accelerations are measured by accelerometers attached to the objects.

    http://en.wikipedia.org/wiki/Accelerometer

    Accelerometers measure off-geodesic "pushes" by real forces.
    en.wikipedia.org
    An accelerometer is a device that measures proper acceleration. The proper accel...See More
  • Jack Sarfatti In contrast, the kinematic acceleration is measured by Doppler radars

    http://en.wikipedia.org/wiki/Doppler_radar

    Therefore

    DV/ds is measured directly locally by an accelerometer clamped to the test particle - real measurement 1

    dV/ds = d^2X/ds^2 is measured indirectly by the Doppler radar clamped to the local frame detector - real measurement 2

    M^-1DP(frame)/ds is measured directly by a second acclerometer clamped to the frame-Doppler radar - measurement 3

    The BASIC LAW is

    measurement 1 = measurement 2 - measurement 3

    provided that test particle and frame Doppler radar are not far away from each other relative to A^1/2 where A^-1 is smallest local radius of curvature.

    The geodesic equation is simply Newton's first law when

    measurement 1 = 0

    Newton's second law is simply when

    measurement 1 =/= 0

    there is never any cancellation of real forces on any one object in this context

    the LNIF ---> LIF in measurement 3 simply means removing a real unbalanced force on the frame detector according to Newton's 1st law.
    en.wikipedia.org
    A Doppler radar is a specialized radar that makes use of the Doppler effect to p...See More
  • Jack Sarfatti Einstein's use of "accelerated" here is in Newton's sense - the rest frame of the freely falling man is kinematically accelerated relative to the Earth

    i.e. d^2X/ds^2

    the freely falling man's local frame is LIF - though Einstein did not yet discover that in 1907 and his informal language is still Newtonian because the modern GR informal language of 1916 and after is not yet emerged.
  • Jack Sarfatti “there is a new gravitational field,
    which cancels the gravitational field
    due to the Earth.”

    This is Einstein's remark that Z and other muddled philosophers and Laputa Scholastics pulls out of proper context. Yes, Einstein wrote it back around 1907 before he understood the problem the way he eventually would in 1916. 

    In fact there is only one gravity field not two.

    The point is that there was never a real gravity force field on the test particle to begin with.

    Therefore, you don't need a second gravity force field to cancel what was never there!

    Indeed, there is no way to measure either of these alleged two real gravity forces to begin with. You can never separate them. Accelerometers on test particles always show zero.

    Therefore, like the mechanical aether these two forces are not independently measurable - they are errors of thinking - excess metaphysical informal language baggage.