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On Oct 12, 2013, at 4:26 PM, Robert Addinall <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

Z: I think Addinall's remarks and suggestions make sense, with the main exception that Jack is not talking about Einstein's theory, he's talking about Wheeler's theory.

There is nothing wrong with focusing on dynamical acceleration and geodesic structure since these are the features of GR that are physically the most interesting.

However, anyone who wants to understand the Machian interpretation of GR (which doesn't mean that they have to agree with it) needs to recognize the basic
differences between Einstein's version of GR and Wheeler's.


Z,
 
RA: I do understand some of the historical debate, and that at least Einstein's initial interpretation of the equivalence principle is different from the modern one (and that Jim is working from Einstein's original EP).
 
JS: I'm not so sure about that. I think Einstein got it right, but the historians of physics have muddled it. The main problem is keeping clear when Einstein is talking about Newton's artificial gravity force fields - the subject of EEP and when he is talking about his new conception of real gravity force fields as curvature. Sure if you go back to 1907 he is not yet clear on curvature until perhaps 1915. 
 
Newton's artificial gravity force fields exist in real curvature gravity fields (and even in zero curvature). In, e.g., the real static gravity near field of a spherical mass M
 
g00 = 1 - 2GM/c^2r  etc
 
2GM/c^2r < 1
 
with real Einstein gravity field curvature components ~  GM/c^2r^3 ~ Ahorizon^1/2/r^3
 
radii of curvature A(r)^1/2 ~ (c^2r^3/GM)^1/2 ~ square root of thermodynamic entropy
 
(based on local Rindler horizon version of EEP - see Ted Jacobson's papers)
 
Newton's artifical gravity force field per unit mass is the unbalanced quantum electrical force (mostly molecular Van der Waals)
 
Fe/m = +(1 - 2GM/c^2r)^-1/2GMr/r^3
 
needed to keep the test mass m stationary at fixed r in the curved spacetime g00 etc.
 
Note that this static electrical reaction force is classically infinite at the black hole horizon.
 
If you make the horizon Lp thick in sense of r-coordinate thickness not proper thickness, doing Taylor series to first order
 
1 - A^1/2/(A^1/2 + Lp) ~  1 - 1/(1 + Lp/A^1/2) ~ 1 - 1 + Lp/A^1/2 ~ Lp/A^1/2
 
(1 - 2GM/c^2r)^-1/2 ~ A^1/4/Lp^1/2 >> 1
 
(GM/c^2)r/r^3 ~ A^-1/2
 
Therefore
 
(Fe/m)max ~ c^2/(A^1/2Lp)^1/2
 
A = area-entropy of the corresponding black hole horizon with Hawking temperature T
 
kBT ~ hc/(A^1/2Lp)^1/2
 
T ---> infinity in the classical limit Lp = (hG/c^3)^1/2 ---> 0
 
 
RA: Jack has expressed an interest in avoiding the historical debate, so my suggestions to him were based on that.
 
That's why in my second set of points (the first set are numbered 1 to 6, the second 1 to 5) I suggested that Jack describe Einstein's theory in point 3, and move on to focusing the reader on dynamical frames in point 5. I could be missing something, but I didn't find Jack's simplified description of Einstein's GR terribly controversial. It's when Jack moves to dynamical frames and electrical contact forces that he's non-Machian.
 
JS: I am not Machian in the sense that Jim Woodward understand's Mach - yes. Whether Jim, or Sciama properly understood Mach is another story. Perhaps, perhaps not.
 

RA: With regard to the apple falling on Newton's head - well, as far as I can gather it's correct to say that the apple is moving inertially on a timelike geodesic (it is in a LIF) and Newton is accelerating (in a LNIF). Earth's mass determines that the geodesics will be curved.
 
JS: Correct.

RA: Frame dragging doesn't seem important over a relatively short distance.
 
JS: Correct, for Jim to invoke frame dragging as necessary for Newton's third law seems totally off the wall. Jim's handwaving is unintelligible to me when he mentions frame dragging a very tiny effect hard to measure e.g. Gravity B NASA.

RA: My impression is that the Machian question comes into play in determining why the apple immediately goes into a LIF... is the rest of the matter in the universe the origin of the inertia? Or is it just an intrinsic property - something will move along a geodesic until it is forced off it?
 
JS: This is the confusion apples and oranges.
 
apples = "inertia" as geodesic pattern for the apple's path
 
oranges = "inertia" as rest masses
 
Mach only meant apples.
 
In a vague sense of apples and Wheeler's "voting power", sure the universe as a whole determines inertia. But that's not very useful.
 
RA: This is different than Mach's and Jim's example of standing in place and then spinning around and having your arms pulled out to your sides - that is a more convincing Machian argument. However, the apple falling seems to work in either a Machian or non-Machian interpretation.
 
JS: The whirling dervish - Newton's rotating bucket is also a confusion. In modern GR the rotation is simply and off geodesic motion relative to the local geodesics. There is no mystery.
Rotation is relative to the local geodesic field. Of course the local geodesic field is partly determined by distant matter (at least in its past light cone) via Einstein's field equations, propagators and all that.
 
Please explain the distinctions in greater detail if I'm still confused.
 
Rob
 
On Oct 12, 2013, at 4:20 PM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

 


On Oct 12, 2013, at 3:17 PM, Paul Zielinski <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

I think Addinall's remarks and suggestions make sense,
 
Yes, unlike most of yours! Addinall is a smart fellow.

with the main exception that Jack is not talking about Einstein's theory, he's talking about Wheeler's theory.
 
This is a good example of a trite waste of time quibble. I made it very clear that for my purpose I don't give a damn about the historical ups and downs of Einstein's rocky road to his 1916 final version except for his later clarifications with action-reaction and other issues in the 1920s till his death. The action-reaction idea is key to my work in quantum theory and beyond as well as in geometrodynamics.
 
Wheeler's version is the one most useful for experimental physicists and engineers.


There is nothing wrong with focusing on dynamical acceleration and geodesic structure since these are the features of GR that are physically the most interesting.
 
So why do you waste every one's time with red herrings?

However, anyone who wants to understand the Machian interpretation of GR (which doesn't mean that they have to agree with it) needs to recognize the basic
differences between Einstein's version of GR and Wheeler's.
 
The important points for the proper understanding of Jim's proposal is
 
1) "inertia" means the pattern of zero-g force timelike geodesics for Mach' principle (also light cones). It does not mean computing rest masses of actual elementary particles.
 
2) phi = c^2 is not even wrong in my opinion in the context of modern cosmology.
 
3) Sciama's vector theory is way too simplistic. My bet is that what Jim sees in the lab is a systematic error like the faster than light neutrino at OPERA. I could be wrong, but that is my bet.

On 10/12/2013 2:01 PM, JACK SARFATTI wrote:
This email address is being protected from spambots. You need JavaScript enabled to view it.">
On Oct 12, 2013, at 12:14 AM, Robert Addinall <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

Jack,
 
In terms of audience you seem to have decided to increase your focus on engineers and people from various other fields interested in UFOs or building stargates.
 
right

  This version seems a lot better towards that end – it is a lot simpler/clearer (with the emphasis on avoiding difficult math). 
 
right

My overall comments:
 

1.       There were points that emerged from the e-mail discussion of the last week or two which seemed quite clear to me.  I suggest that you might include versions of these statements at key points:

2.       Z’s description that you want to focus on “dynamical frames, such that all local frame acceleration in GR is defined with reference to the geodesics.”

 
I keep emphasizing that. The geodesics are physically privileged, i.e. zero g-force weightlessness as measured locally by real accelerometers. They are mathematically not privileged i.e. the classical local differential equations for the natural laws can be written in any real set of possible physical frames on timelike worldlines geodesic or not - makes no difference. That is what the tensor calculus does for any theory including Newton's Galilean limit and the limit of special relativity.
 
Mach's Principle is all about zero g-force geodesics - that's what he means by "inertia" not "rest mass." In Wheeler's language, Mach's principle is "100 % voting power" - however Jim's phi = c^2 is not an adequate consequence of that in my opinion.
 
1916 GR -> 1905 SR -> Newton's mechanics

 

3.       Your response that focusing on dynamical frames is “good physics… physics should be about real things – phenomena and how they are measured… real accelerometers etc.”

 
Yes, this is the Cornell 1950's 60's disiderata for good physics - keep the math to a minimum.
If you look at archive today things going in opposite direction. Mathematics is the opiate of the theoretical physicist.
 

 

4.       You could also use the version of the statement in #3 from another email: “good physics                   is about real phenomena measured with real instruments… keep it simple stupid… but not simpler than possible.”

Key theme in my philosophy of physics - from Mach, Einstein, Dirac, Wheeler, Feynman ...

 

5.       Your statement that: “Einstein’s proper tensor acceleration = Newton’s apparent acceleration – fictitious LNIF inertial pseudo fictitious forces per unit test particle rest mass = real applied force to the test particle per unit test particle mass.”

 
This is in words what in Einstein's math is (sans tensor indices)
 
DP/ds = dP/ds - {Levi-Civita connection}VP = F(electro-weak-strong)
 
P = mV (test particle)
 
{Levi-Civita connection} describes the detector not the test particle
 
it is zero for a LIF detector - that is EEP.
 
 

 

6.       Your observation that: “What is lacking – except in the Wheeler-Thorne books is a clear description of GR measurement theory – how the symbols connect to real lab procedures” is also good – you seem to have started to include this in the latest version of the chapter.  I suggest finding more detailed examples to use to round out the chapter as you progress.

 
Of course. 

 

An observation of my own: I find that, apart from when theory absolutely demands otherwise, it’s easiest to explain things by simply following the historical sequence of events.  My phd is interdisciplinary in military history and political science.  When I’m writing as a historian this is usually pretty easy.  When I’m writing as a political scientist it gets more difficult.  Nonetheless, taking the above six points into account, I suggest that you organize things as follows:
 

1.       Explain Newton’s theory.

2.       Explain how Einstein’s theory is different.

3.       Explain, in very basic terms, as you have done below, the question that Einstein’s theory answers as well as how it answers it.

4.       Explain the difficulty of the math and how it causes even experienced physicists to have difficulties.

5.       Focus on getting the reader to understand: (a) dynamical frames; (b) how to connect GR theory to real lab procedures.

6.       Provide detailed examples of lab procedures.

I made a few comments in red and blue as I read over the chapter, based on where I had to stop and re-read something a couple of times.  These were either minor stylistic grammar points, or places where as a non-expert in physics I didn’t quite follow the argument.  If you find my comments useful let me know and I’ll comment in the future when I have time.  If you don’t like my style and don’t find anything useful tell me and I won’t comment again.  I’m trying not to interfere with your stream of consciousness “beat” point of view, but simply to provide input on how to organize your comments enough that you can keep the engineers reading.
 
Like some of the engineers, my interest is in ideas that could be experimentally tested within a feasible budget in order to build starships and stargates.  That’s why I find Jim’s work interesting.  If your book inspires people to test the Bose-Einstein condensate and Einstein-Cartan curvature + torsion with anti-gravitating dark energy term ideas, I’ll be happy.
 
That actually reminds me: in the overall introduction to the book, in addition to the section “what is a stargate?”, you might want to state the BEC and Einstein-Cartan ideas as your two main proposed solutions to the task of figuring out how stargates work.  This will get the attention of experimental physicists and engineers who will then keep reading because there is something they might actually get to build and play around with.
 
Right - I have not gotten yet to the actual stargate stuff these are just the preliminaries.
 
 
Rob
 

updated V2 Oct 12, 2013

Chapter 1 Einstein’s Theory of Relativity in a Nutshell

“I was dissatisfied with the special theory of relativity, since the theory was restricted to frames of reference moving with constant velocity relative to each other and could not be applied to the general motion of a reference frame. I struggled to remove this restriction and wanted to formulate the problem in the general case.”  Albert Einstein[i]

 

“Nowhere has a precise definition of the term ‘gravitational field’ been given --- nor will one be given. Many different mathematical entities are associated with gravitation; the metric, the Riemann curvature tensor, the curvature scalar … Each of these plays an important role in gravitation theory, and none is so much more central than the others that it deserves the name ‘gravitational field.’[ii]

 

The physical meaning of Einstein’s relativity, both special (1905) and general (1916) is quite simple in contrast to the mathematics, which quickly gets very difficult. Except for the books by John Archibald Wheeler and his students like Kip Thorne, most books on the general theory get too mathematical leaving the physical meaning obscure.

 

“The Question is: What is The Question?” John Archibald Wheeler

 

The question that Einstein’s relativity is the answer to is this: Alice and Bob have measuring instruments and they decide as voyeurs to watch Eve’s dance. How do they compare their data?  Relativity is an algorithm, a set of rules, which takes the raw measurement data input and processes it to give a set of “invariant” output real numbers. If Alice and Bob get the same set of invariants, then they can be quite confident, in the sense of Bayesean probability estimates, that they measured the same set of events and that their measurements were good within the accuracy and precision limits of the technology of their measuring instruments. This is basically classical because Heisenberg’s quantum uncertainty principle will provide a barrier when Alice and Bob attempt to measure the same individual quantum events.

Einstein’s 1905 special theory of relativity at first only considered inertial frames of reference. What is a frame of reference? Basically it is a local set of detectors. What kind of detector? It’s necessary that an accelerometer, like the scales we weigh ourselves with, be included along with other devices like telescopes, Doppler radars etc. The test for an inertial frame is simple, the pointer of the accelerometer reads zero. Every object in the inertial frame is weightless in free-float like the astronauts in the International Space Station shown in the movie “Gravity.”  In this case of free-float zero g-force, we say that the center of mass of the local inertial frame (LIF) moves on a timelike geodesic world line in Einstein’s four-dimensional spacetime continuum. Therefore, we here on Earth are not in inertial frames. We are in non-inertial frames. Unfortunately, Newton defined the word “inertial frame” differently from Einstein and this continues to lead to much confusion when physicists attempt to communicate with each other because Newton’s theory is in closer accord with our common sense. Einstein’s relativity is counter-intuitive.  In Newton’s theory, points on the surface of Earth are approximate inertial frames if we ignore its rotation about the poles. However, in Einstein’s theory, any point on Earth, approximated as an ideal non-rotating spherical surface has a real local objective tensor proper acceleration pointing radially outward from the center of the sphere. Of course, we are not moving relative to the center of the idealized spherical Earth yet we are accelerating and this is counter-intuitive violating common sense. It only makes sense in the curved space non-Euclidean differential geometries of Karl Friedrich Gauss and Bernard Riemann. Proper dynamical acceleration is what accelerometers measure. There is also the apparent kinematical acceleration that Doppler radars measure. Therefore, these two quantities can be measured independently by different kinds of detectors. Ideally in principle must be accelerometers on both the test particle and the detector.  In addition, the detector is equipped with Doppler radar to measure both the kinematic velocity and kinematic acceleration of the test particle relative to the detector. The general rule is:

 

Proper dynamical local acceleration of a test particle = Kinematical nonlocal acceleration of a test particle – Proper local dynamical acceleration of the detector.

With the additional rule:

Proper dynamical acceleration of the detector = Fictitious pseudo-acceleration on the test particle = Levi-Civita connection terms

= Real force on detector per detector mass

 

Let us consider all four physically interesting possibilities.

1)   Accelerometer on test particle shows zero, accelerometer on detector shows zero. This is then a geodesic test particle whose motion is measured by an on-geodesic LIF detector. Of course, these are two different geodesics in general.

2)   Accelerometer on test particle shows zero, accelerometer on detector shows not-zero. This is then a geodesic test particle whose motion is measured by an off-geodesic LNIF detector. The LNIF observer looking at his Doppler radar tracks mistakenly thinks that there is some kind of universal force on the test particle proportional to its mass causing it to move in a curve at different speeds along it. Indeed, Newton called this “gravitational force” when he looked at the parabolic orbits of apples falling off trees and cannon balls, especially the latter to see a good parabola. Similarly for the elliptical orbits of the planets about the Sun. The Coriolis and centrifugal motions are essentially the same as Newton’s gravity force field because they too are universal proportional to the mass of the test particle. Newton could not have conceived that his apple was on a timelike geodesic straightest possible world line in Einstein’s future idea of the curved four-dimensional spacetime continuum. Newton could not have conceived that it was him who was really accelerating to the apple, which was not really accelerating at all!  Indeed, many engineers and ordinary people – and even some physicists still cannot properly and consistently conceive of it so stuck are they in the persistent illusions of common sense.

 

Both 1) and 2) correspond to Newton’s first timelike geodesic law of test particle motion:

Proper dynamical local acceleration of a test particle = Kinematical nonlocal acceleration of a test particle – Proper local dynamical acceleration of the detector = 0

We are only interested in the center of mass of the test particle and ignore rotations about some axis through its center of mass.

 

3)   Accelerometer on test particle shows not-zero, accelerometer on detector shows zero. This is then an off-geodesic test particle whose motion is measured by an on-geodesic LIF detector.

4)   Accelerometer on test particle shows not-zero, accelerometer on detector shows not-zero. This is then an off-geodesic test particle whose motion is measured by an off-geodesic LNIF detector.

Both 3) and 4) correspond to Newton’s second off-geodesic law of test particle motion whose equation in words is

Proper dynamical local acceleration of a test particle = Kinematical nonlocal acceleration of a test particle – Proper local dynamical acceleration of the detector =

Real local force on test particle per mass of test particle.

 

The proper tensor acceleration of any object is described by the “covariant derivative of the velocity tensor of the object with respect to proper time along the world line of the object in four-dimensional spacetime.

 

Einstein’s 1905 special relativity showed that if Alice and Bob were each on different zero g-force timelike geodesics, then they would measure the same invariant speed of light c ~ 3 x 108 meters per second in vacuum. However, Alice looking at Bob’s clock would see it running slow (time dilation) and vice versa. A moving meter stick shrinks along its direction of motion relative to the observer for simultaneous measurements of the edges of the meter stick by the observer. However, a more careful analysis of light rays coming from a fast moving object by Richard Terrell in the 1950’s revealed that the object looks rotated rather than contracted.

 

We all know about E = mc2 and I will not dwell on the details of special relativity here. What is not well known however, even by physicists is that one can use special relativity to deal with properly accelerating frames of reference. However, to do so, one must use the full tensor language of Einstein’s 1916 general relativity. The only difference is that the curvature tensor computed from the “covariant curl” of the Levi-Civita connection with itself vanishes everywhere. Special relativity still works for artificial Newtonian gravity fields without curvature that appear in a rotating space station for example where the normally fictitious centrifugal pseudo force balances a real quantum electrical force in a rigid constraint connecting the test object to its detector.

 

Alice and Bob working together do the actual measurement of the local spacetime curvature tensor field. It’s important that they are both on timelike geodesics and what they measure is their relative kinetic acceleration from each other (aka “geodesic deviation”) in different spatial orientations to get all ten components of the Weyl tensor in space. The Weyl tensor causes stretch-squeeze elliptical distortions in a set of geodesic test particles initially configured in a circle.  There are also ten other components of the Ricci tensor coincident with mass-energy sources, but that is harder for Alice and Bob to directly measure.  The Ricci tensor causes the radius of the circle of geodesic test particles to contract for positive mass-energy sources and to expand for the negative mass-energy exotic sources needed for warp-wormhole advanced super-technology. The full Riemann curvature tensor in four-dimensional spacetime is the sum of the Weyl vacuum and the Ricci matter tensors.

 

Curvature introduces a severe restriction on measurements not found in Minkowski spacetime empty of real gravity fields. When the curvature is not zero Alice and Bob, both watching Eve’s activities, must be “physically coincident” in order to compare their data by calculating invariants. This means that the actual physical separations between Alice and Bob must be less than the smallest radius of curvature in the components of the Riemann curvature tensor. Eve, however, can be arbitrarily far away with Alice and and Bob getting light signals and/or cosmic rays from her.  The mathematics of tensor general coordinate transformations only connects physically coincident local frames of reference. In fact there are three groups of these reversible coincident frame transformations.

1)   LNIF  à LNIF’ general coordinate transformations corresponding to the local translation group T4(x).

2)   LIF  à LIF’ local Lorentz transformations corresponding to the local Lorentz group SO(1,3)

3)   LIF à LNIF tetrad transformations corresponding to Einstein’s equivalence principle (EEP) for cancellation of Newton’s artificial gravity force field. Of course there is no cancellation of Einstein’s real gravity curvature field.



[i] How I created the theory of relativity, Albert Einstein, Translated by

Yoshimasa A. Ono, Physics Today, pp. 45-47 (August 1982) cited by Peter Brown in http://arxiv.org/pdf/physics/0204044v2.pdf

 

[ii] Gravitation, Misner, Thorne and Wheeler, (W.H. Freeman and Company, 1973)

 
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