Excerpts. I like Mashoon’s operational “engineer’s” pragmatic approach rather than the more abstract formal
pedagogy of most GR text books.
On Nov 27, 2017, at 12:15 PM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
The destiny advanced future (local retro causation) would then seem to explain repulsive anti-gravity
dark energy. I have other reasons for that conjecture.
"The truth is incontrovertible. Malice may attack it, ignorance may deride it, but in the end, there it is." Winston Churchill
On Nov 27, 2017, at 11:48 AM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
"The accelerated observer is locally (i.e. pointwise) inertial by the postulate of locality; therefore, Einstein's principle of equivalence renders observers pointwise inertial in a gravitational field and opens the path toward a geometric interpretation of gravitation as the Riemannian curvature of the spacetime manifold.”
This is a common misconception by physicists who should know better. Local Non-Inertial Frame Observers Bob feel g-forces (i.e. electrical reaction forces pushing them off timelike geodesics)
In contrast Local Inertial Frame Observers Alice are weightless.
The distinction is physical as shown by local accelerometers attached to the frames. What EEP means is that there is a transformation of coordinates LNIF <—> LIF connecting what Alice and Bob see when observing the same events. They can compute their own invariants from their local data - send messages to each other and confirm that they get the same invariant numbers. This LNIF <—> LIF mathematical transformation is more accurate the closer Alice and Bob are to each other - they need to be closer than the scale of radii of curvature.
"The truth is incontrovertible. Malice may attack it, ignorance may deride it, but in the end, there it is." Winston Churchill
On Nov 27, 2017, at 11:32 AM, JACK SARFATTI <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:
Fyi interesting discussion of fundamental operational meaning of GR
Not sure if I buy his past memory addition explaining dark matter - we now know he would also need to add future signals in sense of Wheeler-Feynman, weak measurements etc.
<(NonllocalGravity)International Series of Monographs on Physics) Bahram Mashhoon-Nonlocal Gravity-Oxford University Press (2017).pdf>
"Einstein's general relativity is a field theory of gravitation patterned after Maxwell's
field theory of electromagnetism. It is interesting to recall that the electrodynamics
of media is inherently nonlocal ; that is, in general, nonlocal constitutive relations
naturally arise in the treatment of electrodynamics of bulk matter (Jackson 1999).
This circumstance directly leads to nonlocal Maxwell's equations for the electrodynamics
of continuous media. Nonlocal characterization of the properties of continua
has a long history (Poisson 1823; Liouville 1837; Hopkinson 1877); indeed, the corresponding
memory-dependent phenomena, such as hysteresis, have been the subject of
many investigations see, for example, Bertotti (1998). Along this line of thought, one
wonders whether a similar constitutive approach can be adopted for gravitation? Can
general relativity be rendered nonlocal in analogy with the electrodynamics of media?
It is possible to arrive at general relativity (GR) from the standpoint of the gauge
theories of gravitation. Indeed, the gauge approach to gravity naturally leads to spacetime
theories with curvature and torsion. There is a spectrum of such theories such that
at one end of the spectrum, one has GR based upon a pseudo-Riemannian spacetime
manifold with only curvature and no torsion, while at the other end of the spectrum
are spacetime theories with torsion and no curvature. Of the latter, there is a unique
one that is essentially equivalent to Einstein's general relativity: this is the teleparallel
equivalent to general relativity (GRjj ), where gravity is described in terms of local
frames in Weitzenbock spacetime. Teleparallelism has a long history; its application to
gravitational physics has been considered by many authors starting with Einstein in
1928. GR is the gauge theory of the Abelian group of spacetime translations. As such,
it bears a certain formal resemblance to electrodynamics, which is the gauge theory
of the Abelian U(1) group. The analogy with electrodynamics led Friedrich W. Hehl
to suggest that one should attempt a nonlocal GR through a nonlocal constitutive
relation as an indirect way of constructing a nonlocal generalization of GR. This fruitful
suggestion was then developed in two papers that Hehl and I published in 2009.
Within our formal framework for a nonlocal theory of gravity, the kernel must satisfy
certain requirements but is otherwise undetermined. It is possible that the kernel could
be derived from a more comprehensive future theory.
In nonlocal gravity, the gravitational field is local but satisfies partial integrodifferential field equations.
Using simple assumptions regarding the constitutive kernel,
our preliminary studies revealed that gravity can be nonlocal even in the Newtonian
limit; that is, in the Newtonian regime, we find an integro-differential equation for
the gravitational potential. This equation can be expressed as the Poisson equation of
Newtonian gravitation, except that the source term now includes, in addition to matter
density, a term induced by nonlocality that is reminiscent of the density of dark matter.
Surprised by this development, we sent a preliminary version of our paper to the
late Jacob Bekenstein for his comments. He kindly pointed out to us that our modied
Poisson equation had already been proposed by Jerey R. Kuhn in the 1980s. From
Bekenstein we learned of the Tohline{Kuhn modified gravity approach to the explanation
of the flat" rotation curves of spiral galaxies. The nonlocally modified Newtonian
gravitation appears to provide a natural explanation for the dark matter problem; that
is, nonlocality appears to mimic dark matter. In the absence of a deeper understanding
of the gravitational interaction, we therefore adopt the view that the kernel of nonlocal
gravity must be determined from observational data regarding dark matter. In other
words, there is no dark matter in nonlocal gravity; therefore, what appears as dark
matter in astrophysics and cosmology must be the nonlocal aspect of the gravitational
interaction.
Among the basic interactions in nature, gravitation has the unique feature of
universality. We assume that it is also history-dependent. That is, the gravitational
interaction has an additional feature of nonlocality in the sense of an influence
memory") from the past that endures.”
Also a back-from-the-future destiny-dependent influence!
"Is there any compelling evidence that
Einstein's theory of gravitation should be modified? The theory is in good agreement
with observational data from submillimeter scales to the scale of the Solar System and
binary star systems. However, on galactic scales and beyond the theory fails unless
one invokes the existence of the hypothetical dark matter. Indeed, on such large scales,
gravity is dominated by the attraction of dark matter.”
Also repulsive dark energy.
"Can nonlocal gravity explain away what appears as dark matter in astronomy?
It is important to note that the persistent negative result of experiments that have
searched for the particles of dark matter naturally leads to the possibility that what
appears as dark matter in astrophysics and cosmology is in fact an aspect of the
gravitational interaction. The nonlocal character of gravity, however, cannot yet replace
dark matter on all physical scales. Indeed, dark matter is currently needed for
explaining: (i) gravitational dynamics of galaxies and clusters of galaxies, (ii) gravitational
lensing observations in general and the Bullet Cluster in particular and
(iii) the formation of structure in cosmology and the large-scale structure of the
universe. We emphasize that nonlocal gravity theory is so far in the early stages of
development and only some of its implications have been confronted with observation,
thanks to the work of Sohrab Rahvar on the rotation curves of a sample of spiral
galaxies as well as on the internal dynamics of a sample of Chandra X-ray clusters of
galaxies. Indeed, the establishment of nonlocal gravity theory on both theoretical and
experimental fronts is certainly work in progress and much remains to be done.
Nonlocal gravity is presented in this book within an extended general relativistic
framework that includes the Weitzenbock connection. This framework is described in
Chapter 5 and the field equation of the nonlocal generalization of Einstein's
theory of gravitation is developed in Chapter 6. I assume throughout that the reader
is familiar with the basic tenets of general relativity; in fact, the required background
material can be found in standard introductory textbooks such as Ryder (2009),
Misner, Thorne and Wheeler (1973), Weinberg (1972) and Landau and Lifshitz (1971).
No exact solution of the field equation of nonlocal gravity beyond Minkowski spacetime
is known. The absence of any exact nontrivial solution of the theory implies that
the nonlinear regime of the theory has yet to be studied. Thus exact cosmological
models or issues involving the formation and evolution of black holes are beyond the
scope of the present work.
1.1 Lorentz Invariance
The principle of relativity, namely, the assertion that the laws of microphysics are the
same in all inertial frames of reference, refers to the measurements of ideal inertial
observers. The transition from Galilean invariance of Newtonian physics to Lorentz
invariance marks the beginning of modern relativity theory. Lorentz invariance is the
invariance of the fundamental laws of microphysics under the group of passive inhomogeneous
Lorentz transformations. Lorentz invariance has firm observational support;
therefore, we assume throughout that Lorentz invariance is a fundamental symmetry
of nature. The basic laws of microphysics have been formulated with respect to ideal
inertial observers, since these are conceived to be free of the various limitations associated
with actual observers. Each ideal inertial observer is forever at rest in a global
inertial frame of reference, namely, a Cartesian coordinate system that is homogeneous
and isotropic in space and time and in which Newton's fundamental laws of motion
are valid. …
The global inertial frames of reference are all related to each other by passive
inhomogeneous Lorentz transformations …
The inhomogeneous Lorentz transformations form the Poincare group, which is the
ten-parameter group of isometries of Minkowski spacetime. …
The four-parameter Abelian group of spacetime translations and the six-parameter
Lorentz group, which consists of boosts and rotations, are subgroups of the Poincare
group. …
The determination of temporal and spatial intervals constitutes the most basic
measurements of a physical observer. We assume that each inertial observer has access
to an ideal clock as well as infinitesimal measuring rods, and carries along its world
line an orthonormal tetrad frame (or vierbein), that is, a set of four unit axes that are
orthogonal to each other and characterize the observer's local temporal and spatial
axes. …
Each inertial observer in Minkowski spacetime belongs to a class of fundamental observers. ...
In connection with spacetime measurements, we imagine static inertial observers
in a global inertial frame and assume that their clocks are all synchronized; that is,
adjacent clocks can be synchronized. Moreover, the adiabatic transport of a clock to
another location can be so slow as to have negligible practical impact on synchronization.
In a similar way, lengths can be measured in general by placing infinitesimal rods
together. Furthermore, it is assumed in general that for physical measurements, inertial
observers have access to ideal measuring devices. These are free from the specific
practical limitations of laboratory devices that are usually due to the nature of their
construction and modes of operation. The measurements of moving inertial observers
are related to those at rest via Lorentz invariance, which preserves the causal sequence
of events. …
An equivalent ("radar") approach to spacetime measurements relies on the transmission
and reception of light signals. In this procedure, a static inertial observer O1
sends out a light signal at time t1 to static inertial observer O2 . The signal is immediately
transponded without delay back to O1 and is received at time t2 . If the clocks
at O1 and O2 are synchronized, they would both register time t = (t1 + t2 )/ 2 at the
instant the signal is received at O2 . Moreover, the distance between O1 and O2 is
D12 = c( t2 - t1 )/ 2. Thus t2 - t = t - t1 = D12/c .
The inertial physics that is based on the ideal inertial observers and their tetrad
frames has played a significant role in the development of theoretical physics. Inertial
physics was originally established by Newton (Cohen 1960). …
1.1.1 Inertial observers
Imagine a background global inertial frame in Minkowski spacetime. The ideal inertial
observers in this arena are either at rest with local spatial reference frames that
are related to the global axes by a constant rotation or move with constant speeds
on straight lines from minus infinity to plus infinity and carry constant local reference
frames. The fundamental inertial observers are all at rest and carry orthonormal
tetrad frames with axes that coincide with the global Cartesian spacetime axes of the
background inertial frame of reference.
The translational motion of the observer in spacetime fixes its local temporal axis
as well as its spatial frame but only up to an element of the rotation group. ...
1.1.2 Examples of uniformly accelerated observers
Realistic observers in a global inertial frame in Minkowski spacetime would all be
more or less accelerated. We consider here some examples of uniformly accelerated
observers. …
In connection with the propagation of the tetrad frame along the world line of O,
let us briefly digress here and discuss a more general situation that involves an observer
following a timelike path in an inertial frame in Minkowski spacetime. …
These relations mean that while the magnitude of the parallel component of vector V
remains constant along the path, the perpendicular component cannot change in the
perpendicular direction; otherwise, vector V would rotate. That is, the net variation
of the perpendicular component along the path can only be in the direction parallel
to the path. ...
We have thus far discussed the measurements of inertial observers. We are also
interested in the measurements of accelerated observers. What do accelerated observers
measure? What are the laws of physics according to accelerated observers? What is
the generalization of Lorentz invariance that applies to accelerated observers? We now
turn to a discussion of these issues.
1.1.3 Nonexistence of ideal inertial observers
The special theory of relativity is about the standard relativistic physics of Minkowski
spacetime, where gravity has been turned off. Physical phenomena in each global inertial
frame of reference involve ideal inertial observers as well as accelerated observers.
Indeed, all actual observers are accelerated; that is, inertial observers, though of deep
theoretical signicance, do not in fact exist."
They do in space when rocket engines shut down. JS
"There is a basic dichotomy here involving
theory and experiment that is noteworthy: The basic laws of non-gravitational
physics have all been formulated with respect to ideal inertial observers, yet the
experimental basis of these laws, namely, the foundation of physical science, has
been established via actual observers that are all accelerated. To set the foundation of
physical science on a firm basis, a connection must be established between inertial and
accelerated observers. Simply stated, the fundamental microphysical laws, such as the
principles of quantum mechanics, have been formulated for nonexistent ideal inertial
observers, while all actual observers are accelerated. The resolution of this dichotomy
requires an a priori axiom that relates inertial and accelerated observers. The observational
consequences of such an axiom should then be compared with experimental
results.
Ideal inertial observers are supposed to move on straight lines with constant speeds
from minus infinity to plus infinity in a global inertial frame and carry constant local
reference frames. It is important to note that these theoretical assumptions regarding
ideal inertial observers cannot be directly verified by experiment. For instance,
distant past and future states of the universe are not directly accessible to experimentation.”
Maybe they are (e.g. Yakir Aharonov’s locally retrocausal weak quantum measurements). JS
"Furthermore, repeated observational attempts to determine that an object is
indeed at rest or moves uniformly on a rectilinear path will produce disturbances that
cause deviations from the state of rest or uniform rectilinear motion. The ideal inertial
observers are thus hypothetical and have been introduced to embody the principle of
inertia perfectly. Real observers in this global inertial frame are all accelerated and
we need to determine what accelerated observers actually measure. In this treatment,
observers can be sentient beings or measuring devices. In either case, observers are
classical macrophysical systems that are extended in space. Any real measuring device
is subject to various limitations; for example, it may not operate properly under certain
conditions. Moreover, an accelerated device is under the influence of various internal
inertial effects that could, over time, affect its constitution and mode of operation.
In practice, all such issues require careful consideration; however, for the purposes of
this theoretical discussion, we generally follow the standard practice in the theory of
relativity and represent an observer by a single timelike world line for the sake of simplicity.
This is not considered to be a fundamental limitation; rather, it helps simplify
the analysis. In fact, this notion of an elementary observer can then be extended to
a reference system by considering a congruence of elementary observers that occupy
a finite spacetime domain in a global inertial frame in Minkowski spacetime. That
this construction is indeed possible has been demonstrated in various ways by explicit
examples for simple accelerated systems (see Mashhoon 2008 and the references cited
therein). A general method based on fiber bundles for the construction of such reference
systems involving nonintegrable anholonomic observers has been discussed by
Auchmann and Kurz (2014).
By employing pointlike observers in our theoretical treatment, we avoid the problem
of determination of the integrated influence of inertial effects on measuring devices
that are employed during the measurement process. All observers under consideration
are thus essentially ideal pointlike systems subject to the laws of classical (i.e. nonquantum)
physics. We can therefore concentrate on the theoretical distinction between
pointlike inertial and accelerated observers.
Observational data, collected over time by actual observers that are all more or less
accelerated, have helped establish microphysical laws and have indicated that Lorentz
invariance is a fundamental symmetry of nature. Therefore, a connection must exist
between inertial and accelerated observers. What is this connection?”
To be continued.
"The truth is incontrovertible. Malice may attack it, ignorance may deride it, but in the end, there it is." Winston Churchill