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On Apr 3, 2014, at 2:09 PM, Paul Zelinsky  wrote:

"Also, what do you think the Minkowski fiber bundle represents in modern formulations of GR? It represents a local mapping of the curved base space inner products determine by g_uv onto the Minkowski fibers defined by the globally flat Minkowski metric n_uv."
To which I replied:
 
That’s precisely what I mean by LNIF <—> LIF (both local frames COINCIDENT)
 
frame field for LNIF is eu(LNIF) with curvilinear metric guv(LNIF).
 
One can always find LNIFs where in Taylor series about origin 
 
g^u^v(LNIF) ~ n^u^v(Minkowski) + {Levi-Civita Connection}^u^vw&x^w + {Riemann Curvature Tensor}^u^vwl&x^w&x^l + ….
 
ds^2 = guv(LNIF)e^u(LNIF)e^v(LNIF)
 
frame field for LIF (Cartesian coordinates a must as Einstein stipulates in his papers) eI(LIF)  tangent bundle fiber metric Taylor expansion is
 
n^I^J(LIF) = n^I^J(Minkowsk) + {Riemann Curvature Tensor}^I^JKL&x^K&x^L + ….
 
ds^2 = nIJ(LIF)e^I(LIF)e^J(LIF)
 
Small font indices u,v ... are in the LNIF base space
 
Caps I,J are in the LIF fiber
 
The tetrad transformation is
 
e^u(LNIF) = e^uIe^I(LIF) etc.
 
EEP means that
 
{Levi-Civita Connection}^I^JK = 0
 
though in general
 
{Riemann Curvature Tensor}^I^JK =/= 0
 
ARTIFICAL (FIRST ORDER NON-TIDAL) GRAVITY FIELDS IN SENSE OF EINSTEIN AND NEWTON CORRESPOND TO
 
{Levi-Civita Connection}^u^vw =/= 0
 
Riemann Curvature Tensor}^I^JKL = 0
 
REAL GRAVITY FIELDS IN THE SENSE OF MISNER, THORNE AND WHEELER (SECOND ORDER WEYL TIDAL VACUUM + RICCI MATTER COMPRESSION) CORRESPOND TO
 
Riemann Curvature Tensor}^I^JKL =/= 0
 
Note that e^I(LIF) is a set of 4-vectors with components e^Iu
 
e^u(LNIF) is a set of 4-vectors with components e^uI
 
e^uIe^Iv = kronecker delta uv etc. ORTHOGONAL GROUP O(1,3)
 
ds^2 = nIJ(LIF)e^Ie^J = guv(LNIF)e^ue^v
 
LIF Alice and LNIF Bob are COINCIDENT
 
LIF Alice has zero proper acceleration
 
LNIF Bob has non-zero proper acceleration
 
ds is invariant space interval between 2 neighboring events measured simultaneously by both Alice and Bob.
 
Since we impose COINCIDENCE no problem with simultaneity.
 
Also clock postulate that proper acceleration of clocks in LNIF can be synchronized to clocks in LIF if they are coincident.

 

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)

 

https://www.academia.edu/5154144/Sarfattis_Stargate_Book_Version_of_Nov_19_2013_Work_in_Progress_

 


from my book

Contrary to popular misconceptions, although the local laws of classical physics have the same “tensor” and/or “spinor” form for all motions of detectors measuring all the observable possessed by the “test particles,” nevertheless, there still are privileged geodesic force-free dynamical motions of the test particles in Einstein’s two theories of relativity special 1905 and general 1916.[i]  This was in Einstein’s words “My happiest thought.”

“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.” [ii]

First note the date 1907. Einstein is using Newton's 1686 theory of gravity not his then future 1916 general relativity way of thinking that he has not yet created. Einstein is struggling with the wrong notion of “acceleration.”

"A falling man is accelerated."

Yes, in Newton, but not in Einstein nine years in the future! The falling man's frame is LIF with zero proper acceleration. In fact it's the surface of static LNIF Earth with proper radial acceleration upward rushing toward the falling man.

Proper acceleration of falling man = Relative 1905 SR kinematic acceleration - Proper acceleration of Earth

Proper acceleration of falling man = D2X/ds2

Relative 1905 SR kinematic acceleration = d2X/ds2

Proper acceleration of Earth = {STATIC LNIF EARTH}(dX/ds)(dX/ds)

X = relative separation test particle to detector on Earth.

{  } = Christoffel symbol used in the Levi-Civita connection

v = dX/ds

In fact when v/c << 1, the 3-vector piece of the above 4-vector equation is:

{STATIC LNIF EARTH}(dX/ds)(dX/ds) ~ -GMEarthr/r3

Proper acceleration of falling man = 0 because an accelerometer pinned to the man shows zero on its pointer. Therefore,

Relative kinematic acceleration = Proper acceleration of Earth

Where a Doppler radar measures the relative kinematic acceleration between the falling man and Earth. In contrast, a second accelerometer clamped to the detector at rest on surface of the Earth measures -GMEarthr/ras the weight divided by the mass of the detector.

“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.”

That statement by Einstein in 1907 is how Newton would explain it. Einstein put himself in Newton's shoes for a moment. It's not the way his later 1916 matured GR explains it.

0 = Relative 1905 SR kinematic acceleration - Proper acceleration of Earth

This “cancellation”, the “0” on the above word equation is not a cancellation of two real dynamical fields. Einstein's unfortunate informal language in 1907 has no relevance to his, then, future theory.

"In the accelerated frame of reference, we need a new gravitational field."

That's the LIF, which is not accelerated in the sense of 1916 Einstein GR, but is accelerated in the different sense of 1686 Newton. These subtle oft unnoticed paradigm shifts in the meanings of “acceleration,” “inertia,” “inertial frame” cause many people a great deal of confusion even today,

Einstein was still muddled in 1907 as he struggled to make the great breakthrough. Your understanding is trite and superficial based on semantics and exaggeration of an early remark of Einstein's.

 


[i]  This geodesic premise is Newton’s first law of motion most generally expressed.

 

[ii] On the Relativity Principle and the Conclusions Drawn from It, Albert Einstein,

Jahrbuch der Radioaktivitat und Electronik 4 (1907) – Re-Published in three parts.

Am. J. Phys. 45, Part I - (6), June 1977, pp. 512-517; Part II – (9), September

1977, pp. 811-816, Part III - (Gravitational Part) – (10), October 1977, pp. 899-

902. This paper addresses only Part III – from Peter Brown’s paper.

 

In this EARLY 1907 quote Einstein (who is still under Newton’s magick without magic spell) means Newton's "accelerated frame", that is, dV(test particle)/ds in Newton's first law (geodesic equation) as written in modern POST-1907 GR language. Suppressing indices:

DV(test particle)/ds = dV(test particle)/ds - {LNIF detector}V2(test particle) = 0

The "cancellation" is precisely

 

dV(test particle)/ds - {LNIF detector}V2(test particle) = 0

 

In other words, in the general case that even applies to Newton's 2nd and 3rd laws is:

 

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 

 

Fictitious forces on test particle = Real forces on LNIF detector of test particle's motion

 

In the case of Newton's 3rd law, when Alice and Bob form an isolated closed system

 

DP(Alice + Bob)/ds = DP(Alice)/ds + DP(Bob)/ds = 0

 

Both must be measured in the same frame by Eve, i.e.,

 

DP(Alice or Bob)/ds = dP(Alice or Bob)/ds + {Eve}V(Alice or Bob)P

 

“I continued my thought: A falling man is accelerated. Gravity and inertia are interrelated." Einstein

 

Here is the source of the confusion.

 

Einstein is naturally thinking in Newtonian terms.

 

However, in GR terms that he still had not invented back then in 1907: "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   for the test particle under observation by the local frame detector

 

V = dX/ds

 

X = relative kinematical displacement between test particle and local frame detector as measured by a Doppler radar clamped to the local frame.

 

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, it follows that

 

D2X/ds2 = d2X/ds- {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 the 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.

 

Doppler radars measure the kinematic acceleration.

 

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 = d2X/dsis 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 accelerometer 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 the smallest local radius of curvature A1/2. The curvature is of order A-1

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.

 

“Then what he feels and judges is happening in the accelerated frame of reference.” Einstein

 

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. d2X/ds2

 

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.

 

“There is a new gravitational field, which cancels the gravitational field due to the Earth.”  Einstein

 

This is Einstein's remark that physics cranks pull out of proper context. Yes, Einstein wrote it back around 1907 before he understood the problem the way he eventually would in 1916 and later. 

 

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 Maxwellian 19th century mechanical aether that acts without being reacted upon that Einstein eliminated in 1905, these two ghostly independently unobservable-in-principle forces are not independently measurable - they are errors of thinking - excess metaphysical informal language baggage. Even the great Einstein got muddled temporarily on this one, though with good reason. Unfortunately many people today who should know better remain muddled. If gravity is not a real force like the electro-weak-strong forces, then what does it mean to unify them?

 
 

The issue before me is how to address them properly in my Stargate book and in my reviews of his book. I will take several weeks pondering this. I will not make Jim's theory a central part of my book as I have plenty of original material myself.


On Oct 20, 2013, at 12:20 AM, "jfwoodward@juno.com" <jfwoodward@juno.com> wrote:

Gentlefolk,

The continuation of last night's comments.  Jack and Paul, by the way, have repaired to a shorter list to continue their mathematical discussions.  As far as I am concerned, this process has been like tapping a kaleidoscope.  I've known about Einstein's predilection for Mach's ideas since reading John David North's history of cosmology back in the '60s.  
 
60's - paleolithic times in cosmology and in general relativity. See Feynman's letter to his wife at Warsaw GR meeting - it's online.

And with every pass, I learn a bit more -- though a bit less with each pass, at least recently.

As I said yesterday, much of the confusion [leaving aside the silliness about "fictitious" forces] in this business seems to be an outgrowth of the now allegedly mainstream view that gravity is only present when non-vanishing spacetime curvature is present -- a view that seems to have its origins in a neo-Newtonian view that large constant potentials can be gauged away as irrelevant.  This comports with the widespread view that the Aharanov-Bohm experiment notwithstanding, potentials in classical situations are not real.  Only the fields derived from them are.
 
Jim's writing about fictitious forces in his book is hardly intelligible to me. 
 
Jim also seems to be confused about "potentials"
 
There are superficial formal analogies between Einstein's geometrodynamics and Maxwell's electrodynamics, but one must be very careful in applying them.
 
Jim cites Bohm-Aharonov. OK first look at Maxwell's electrodynamics. I use Cartan's forms
 
We have a potential 1-form A that is a connection for parallel transport of objects in the U1 circle fiber space.
 
The gauge transformations are
 
A --> A' = A + df
 
f = 0-form scalar
 
d^2 = 0
 
It's line integrals of A around closed loops that give the observable quantum phase shifts in the Bohm-Aharonov effect via Stoke's theorem etc.
 
The EM curvature is the 2-form
 
F = dA which is gauge invariant
 
F' = dA' = dA + d^2f = dA = F
 
Maxwell's field equations concern the 3-forms
 
dF = d^2A = 0  these are two of Maxwell's equations - no magnetic monopoles and Faradays EMF law (motors, generators ....)
 
d*F = *J   these are the last two - Ampere's law with displacement current and Gauss's law
 
* = Hodge dual
 
Finally
 
d*J = d^2*F = 0
 
is local conservation of electric current densities
 
this is a 4-form in 4D spacetime dual to a 0-form.
 
This gauge theory extends to the non-Abelian unitary groups SU2 and SU3 that describe the weak and strong forces (Yang-Mills).
 
Jim's vector theory if done correctly has
 
g00 = 1 + phi/c^2
 
g0i = Ai
 
However, the analogy to EM as a gauge theory breaks down completely, because the F to Jim's A is the Levi-Civita connection.
 
In fact the proper analogy is that the Levi-Civita connection is the analog to the EM A and the curvature tensor is the analog to EM's F.
 
Conservation of currents is the Bianchi identity in GR.
 
However, to make the analogy more transparent. General relativity as a local gauge theory is a non-Abelian Yang-Mills theory based on the Poincare symmetry group of Einstein's special relativity.
 
Einstein's 1905 Special Relativity mathematically is the representation theory of the global 10-parameter Poincare group.
 
General relativity is properly named because it is a limiting case (zero torsion) of the local gauge theory of the Poincare group with the real gravity field as the curvature 2-form from the connection 1-form just as in Maxwell's electrodynamics.
 
However, the connection 1-form corresponding to Maxwell's A is not the Levi-Civita connection from the usual 1916 GR tensor formulation, rather it is the six spin connection 1-forms AIJ  = - AJI with two LIF indices, IJ analogous to the internal indices Aa in Yang-Mills theory of the SU2 and SU3 internal groups and the 4 tetrad connection 1-forms eI.
 
There are therefore 10 connection 1-forms one for each "charge" generator of the Poincare group (linear-momentum-energy, rotational momentum, Lorentz boosts)
 
The Levi-Civita connection is derivable from the spin connections and the tetrads.
 
The four eI are the base 1-forms for a geodesic LIF dual to the tangent vector fiber space basis.
 
The spin connection allows coupling of gravity to spinors, the Levi-Civita connection does not.
 
Therefore, Einstein's 1916 geometrodynamics reformulated in modern Cartan-forms has the local gauge structure
 
D = d + SIJ/   Cartan exterior covariant derivative
 
summation convention over repeated indices - I am too lazy to put in the ^ for upper indices.
 
TI = DeI = deI + SIJ/eI = dislocation defect torsion field 2-form
 
RIJ = DSIJ = dSIJ + SIK/SKJ = disclination defect curvature field 2-form.
 
Einstein's 1916 theory requires the ad-hoc constraint
 
TI = 0
 
In that limit:
 
Einstein-Hilbert action density is the 0-form scalar without cosmological constant for simplicity
 
*(eI/eJ/RKL)
 
with Euler-Lagrange equation for vacuum is the 1-form equation
 
*(eI/RJL) = 0
 
in ordinary tensor language this is
 
Ruv - (1/2)guv = 0
 
Including the matter-field sources gives
 
*(eI/RJK) = (8piG/c^4)*(TIJK)
 
More details are in Rovelli's lectures http://www.cpt.univ-mrs.fr/~rovelli/book.pdf
 
 
This may be true for all other physical fields.  But it is not true for gravity.  The vector part of the gravitational potential very definitely does depend on the particular value of the scalar potential calculated.  There are some formal technical details that complicate this a bit.  But the idea that you can ignore cosmic scale matter currents when computing local gravitational effects is still just wrong.
 
I find above comment by Jim unintelligible - at least at the present time.

Tonight, what I want to do, however, is talk a bit about a couple of other matters.  The first is the "origin" of inertia.  You may recall that Jack gave a long list of mechanisms -- the Higgs process, QCD calculations, and suchlike -- that allegedly are the origin of mass, and thus inertia.  The fact of the matter is that none of these processes (valid in and of themselves) account for the origin of mass and inertia.  Frank Wilczek, after telling you about these processes in his book The Lightness of Being, allows as much (on pages 200 through 202).
 
I am staring at those pages and I see nothing in Wilzcek's text that justifies Jim's extraordinary claim above. Certainly nothing that needs Mach's principle that simply replaces one mystery with another. Again Jim is confounding two different meanings of "inertia" just as he and other confound two different meanings of "gravity field".
 
Mach's Principle only is concerned with how matter affects disclination geodesic deviation (aka curvature). The real gravity field of Einstein's geometrodynamics is the field of "geodesic deviation" corresponding to inhomogeneities in Newton's "gravity field", which is a fictitious force field.
http://en.wikipedia.org/wiki/Geodesic_deviation
http://en.wikipedia.org/wiki/Fictitious_force
Mach's principle is not concerned with the origin of rest masses of elementary particles. Einstein briefly confounded the two, but it led nowhere.  Wilzcek is concerned in those pages 200 - 202 with the cosmic landscape/Anthropic principle issue. Why these particular numbers and not others. http://www.fourmilab.ch/documents/reading_list/indices/book_487.html
 
A word on history. What Einstein may or may not have said in 1907 in his informal language as he groped toward GR is completely irrelevant to the modern understanding of general relativity. This is a normal evolution of all good physical theories. I have no patience with cranks that try to make a big deal over that. Such discussions are a waste of time for me.

Inertia is a universal property of stuff.  And the only universal interaction that couples stuff is gravity.  It is thus obvious that if gravity produces inertial forces (that is, the relativity of inertia obtains), that gravity should have a lot to do with the origin of inertia.  (The origin of inertia was the title of Sciama's first paper on this I note.  So I'm not making this up.)
 
Jim's remark above is unintelligible to me. This is what I mean by "inertial force."
 
inertial force  (-nûrshl)
An apparent force that appears to affect bodies within a non-inertial frame, but is absent from the point of view of an inertial frame. Centrifugal forces and Coriolis forces, both observed in rotating systems, are inertial forces. Inertial forces are proportional to the body's mass. See also General Relativity.
 
Newton's gravity force per unit test mass -GMr/r^3 is an inertial force in exactly the same way as centrifugal and Coriolis forces are.
 
They are all part of the Levi-Civita connection which vanishes at the origin of a Local Inertial Frame (LIF).
 
 
The "force of gravity" you feel as weight on Earth is the unbalanced electrical force pushing you off a timelike geodesic of the local curvature real gravity field mostly due to the mass of Earth. You need that unbalanced force on you to keep you still (with respect to Earth) in the curved spacetime we live in. Earth pushes up on you and you push down on Earth etc. - action-reaction Newton's 3rd law.
Therefore, I find Jim's discussion of inertial forces here and in his book unintelligible and not mainstream.

This is more obvious still when you discover that phi = c^2 is the condition that must be satisfied for inertial forces to be due to gravity.  You don't even have to fudge with dimensions to get this to work.  
 
I also find "phi = c^2" unintelligible and not mainstream physics.
 

The dimension of phi is velocity squared.  You may not like this result.  Jack it seems doesn't.  But it is a simple consequence of GRT.  You might think that this means that should the rest of the matter in the universe be made to disappear (or should you screen an object from the gravity of all that matter) the mass of an object would go to zero -- as is assumed in a number of discussions of Mach's principle and the origin of inertia.  But that's not what happens.  Read chapters 7 and 8.
 
Unintelligible to me still as of this date.

The last thing I want to comment on is, how the devil did all this get so bolixed up?  Recent kaleidoscope tapping suggests that there were two crucial mistakes that are largely responsible for all the confusion.  The first mistake was made by Einstein in 1921.  By that time, he had been worked over by Willem deSitter and disabused of his naive Machianism (which is why he started talking about spacetime as an "ether" about this time).  So the claims he put into his Princeton lectures on Mach's principle were more tentative than they had been previously.  One of the things he calculated that he took to be in accord with Mach's ideas was the effect of "spectator" matter (that is, nearby stuff) on the mass of an object.  He claimed that piling up spectator matter would cause the mass of the object in question to increase (because of its changed gravitational potential energy).  A very small amount.  But if the origin of mass is the gravitational influence of cosmic matter, this is just the sort of effect you might expect to see.
 
OK

It turns out that Einstein was wrong about this.  That's what Carl Brans showed in 1962 (as part of his doctoral work at Princeton with Bob Dicke).  The EP simply forbids the localization of gravitational potential energy.  So, the inference that GRT is explicitly non-Machian regarding inertia and its origin is perfectly reasonable.  It's the inference that Brans and Dicke -- and everyone else for that matter -- took away.  Brans and Dicke, to remedy this presumed defect of GRT, resuscitated Pasqual Jordan's scalar-tensor version of gravity, hoping the scalar field part could bring in Machian ideas.
 
OK

The second crucial mistake is the inference everyone made that Brans' EP argument meant that Mach's principle isn't contained in GRT.  Indeed, exactly the opposite is the case.  Brans' conclusion from the EP is absolutely necessary for Mach's principle to be contained in GRT.  It is the conclusion that must be true if inertial reaction forces are always to satisfy Newton's third law, for it guarantees that phi = c^2 ALWAYS when measured locally.  But everyone had adopted the false inference that GRT is non-Machian.  It's no wonder that issues of Mach's principle in GRT has been so confused.  It's no wonder that C+W (really Wheeler I'd guess, for he witnessed the Mach wars of the '50s and '60s) tried to use Lynden-Bell's initial data and constraint equations approach to implement Einstein's parting shot at Mach's principle in the '20s.  The origin of inertia is just too important to let go with the sort of "explanations" now floating around.
 
Unintelligible. EEP follows trivially once one understands that Newton's gravity force is simply the fictitious force on the weightless geodesic test particle as seen visually in a static LNIF from real electrical forces pushing the static LNIF off a local timelike geodesic.
 

On a personal note, I've known that phi = c^2 (locally) is the condition to get all of the Mach stuff to work since around 1992.  But I was focused on inertial forces and how they might be transiently manipulated.  And doing experiments.  I won't tell you how long it took for the other aspect of the origin of inertia to sink in -- even though it was staring me in the face. . . .
 
Unintelligible.

Keep the faith,
 
Sorry Jim but the faith required here is not scientific in my opinion.

Jim
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Common misunderstanding of Einstein's "Happiest Thought" corrected & bogus-bad pseudo-physics critiques of Einstein's Equivalence Principle.
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  • 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.