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Gravitomagnetic horizons and the comprehensive failure of Einstein's 1916 general theory

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A receding horizon-bounded body generates an "effective", gravitomagnetic horizon between the observer and the usual r=2M horizon surface. This purely observer-dependent horizon does not obey SR concepts of causality or the SR shift relationships, and its classical behaviours instead correspond to those of acoustic metrics and of quantum mechanics (including the emission of classical Hawking radiation). Since the horizon position alters with the relative state of motion of the observer, who can be arbitrarily distant, non-SR "acoustic metric" physics then effectively operates across the entire external visible universe. Adjusting the body's gravitational shift equations to match those of its surroundings then also converts the r=2M surface into an observer-dependent "acoustic" horizon, solving a number of long-standing problems in standard theory, including the black hole information paradox. We conclude that the definitions and relationships of special relativity, originally derived for flat spacetime, do not function properly in a gravitational universe, and should not be thought of as valid components of a general theory of relativity.
ResearchGate, 12th February 2021
Gravitomagnetic horizons and the comprehensive
failure of Einstein’s 1916 general theory
Eric Baird
A receding horizon-bounded body generates an “effective”, gravitomagnetic horizon
between the observer and the usual r=2M horizon surface. This purely observer-
dependent horizon does not obey SR concepts of causality or the SR shift
relationships, and its classical behaviours instead correspond to those of acoustic
metrics and of quantum mechanics (including the emission of classical Hawking
radiation). Since the horizon position alters with the relative state of motion of the
observer, who can be arbitrarily distant, non-SR “acoustic metric” physics then
effectively operates across the entire external visible universe. Adjusting the body’s
gravitational shift equations to match those of its surroundings then also converts
the r=2M surface into an observer-dependent “acoustic” horizon, solving a number of
long-standing problems in standard theory, including the black hole information
paradox. We conclude that the definitions and relationships of special relativity,
originally derived for flat spacetime, do not function properly in a gravitational
universe, and should not be thought of as valid components of a general theory of
Table of Contents
1. Introduction………………….3
2. e unavoidability of gravitomagnetic eects………………….4
2.1. Gravitomagnetic effects of moving masses.................................................................................................................4
2.2. Secondary horizons...........................................................................................................................................................4
3. Properties of the secondary horizon……….5
3.1. Overview of the problem.................................................................................................................................................5
3.2. Non-Wheeler behaviour...................................................................................................................................................5
3.3. Gravitomagnetism of a moving black hole:.................................................................................................................5
3.4. Gravitomagnetism of a moving final observer...........................................................................................................6
3.5. Gravitomagnetism of an intermediate observer.........................................................................................................6
4. Experiences of local and distant observers……………………….8
4.1. Observerspace.....................................................................................................................................................................8
4.2. Direct and indirect observation......................................................................................................................................9
5. Compatibility with quantum mechanics…………10
5.1. “Real” and “virtual” particles.........................................................................................................................................10
5.2. Generation of Hawking radiation................................................................................................................................10
5.3. The QM pair-production description, from classical geometry............................................................................11
6. What happened to special relativity?…………12
6.1. Incompatibility of effective horizons with the SR shift equations.......................................................................12
6.2. Replacing the relativistic shift equations to allow Hawking radiation...............................................................12
6.3. Gravitomagnetic shifts are also motion shifts..........................................................................................................13
6.4. All bodies are “strong-gravity” bodies at sufficiently small distances................................................................13
6.5. Goodbye, special relativity............................................................................................................................................14
7. Other notes……………….15
8. Summary……………..16
9. Conclusions…………17
page 1 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
1. Introduction
The subject of gravitationally “cloaked” stars is surprisingly old, and dates at least as far back as
John Michell’s 1983 letter to the Royal Society (published 1784), [1] [2] [3] [4] which explored the
hypothetical behaviour of stars whose gravity was so strong that their escape velocity exceeded
the speed of light. In Michell’s description, the critical surface where vESCAPE=c appeared at a radius
of r=2MG/c2, (often abbreviated asr=2M”). Any light or subluminal matter emitted below this
radius would be turned around by gravity, and could not reach an arbitrarily-distant onlooker
along a “ballistic” or inertial path to us, such stars would appear dark. Particles from below
r=2M could visit the outside region for a limited time, [4] and these “visiting” particles could then
be knocked free from the star’s gravity by random collisions (with passing matter, or each other)
and escape, [5] so these “dark stars” were still able to radiate indirectly, along accelerated paths. i
Einstein’s flat-spacetime special theory of relativity (“SR”, 1905) [6] modified the C19th Newtonian
equations and Doppler relationships, and Einstein’s incorporation of these new relationships into
his larger curved-spacetime general theory of relativity (“GR”, 1916) [7] [8] changed the predicted
behaviour of super-dense gravitational bodies. Under the new system, if a distant observer could
not see light emitted by events occurring below r=2M, then for these observers, the associated
emission events did not take place [9] (or were assigned to the more-than-infinitely-distant future).
With this new, more literal version of perceived causality, where what we can see defines the
physics, [10] the region below r=2M was unable to communicate with the outside world in any
way, there was no longer a mechanism for indirect radiation, and the horizon became an absolute
event horizon. While Einstein argued that GR’s predictions for these dense objects must be
unphysical, [11] John Wheeler championed the concept, [12] and since the new horizons had a
zero temperature and exerted zero outward radiation pressure ... referred to them as black holes.
The 1960s saw a healthy discussion about the legality of absolute horizons, complicated by the fact
that many of our standard coordinate-system tools broke down for regions straddling these
horizons. ii These debates eventually produced a general consensus that, although local physics
appeared unremarkable at the horizon to infalling observers, [13] total collapse and the formation of
absolute event horizons were unavoidable for bodies smaller than r=2M. [14]
In this paper, we instead look outside r=2M, at the gravitomagnetic effect of a retreating GR1916
black hole on its wider environment, and find an external, observer-dependent gravitomagnetic
horizon. Since its position depends on the state of motion of an (arbitrarily distant) observer,
gravitomagnetic behaviour then applies to all moving observer-masses outside r=2M, despite the
SR assumption that small masses can move however they like without affecting the propagation
of light. These arguments tell us that, in effect, the entire outside universe must be operating in
accordance with non-SR physics and non-SR shift equations, after which we lose the original
justification for having a Wheeler horizon. The idea that a general theory can successfully
incorporate SR physics, and the associated idea of an absolute horizon, are self-invalidating.
We conclude that Einstein’s decision to use equations derived from flat spacetime in the context
of solving an inherently curved-spacetime problem (gravity) was mistaken. More encouragingly,
the appearance of classical Hawking radiation across the external “effective” horizon appears to
limit our options for a relativistic replacement for the SR relationships to a single solution. [15] The
1916 theory does not just self-invalidate, the nature of the breakdown tells us the identity of the
replacement equations that must appear in a revised and corrected general theory.
 effective
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page 2 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
2. The unavoidability of gravitomagnetic effects
2.1. Gravitomagnetic effects of moving masses
Gravitomagnetism and its analogues exist in almost every area of physics, apart from special
relativity. If the speed of gravitational interactions is finite i then a moving body’s gravitational
field will be slightly “smeared” by its motion, with this smearing effect appearing in a field
description as an additional gravitomagnetic field component (weakening the attraction of the
body’s default “rest field” forwards and strengthening it rearwards), or, in a geometrical
description, as a tilting of the throat of the body’s associated gravity-well, to align with the
moving body’s tilted worldline (weakening the curvature ahead of the moving well, and
increasing it behind). [5] The result is a net pull on nearby objects and light in the direction of a
mass’ motion a gravitomagnetic dragging effect in the rotation plane of a rotating star, the
receding edge should pull more strongly than the approaching edge, and the star will tend to
drag matter and light around with it. Gravitomagnetic effects are compulsory in a general theory
of relativity, with rotational dragging [18] (and therefore a velocity-dependent gravitomagnetic
component) an essential consequence of the relativity of rotation. Carlip’s argument [19] also
makes velocity-dependent gravitomagnetism necessary for the emergence of Newton’s First Law.
The strength of the expected dragging effect can be calculated from the relative velocities of the
bodies involved, and their relative contributions to the total field intensity at the location of a
test body (Wheeler [20]). For the case of a moving black hole event horizon, where external
physics is not allowed to modify the apparent frozen state of the horizon, the dragging effect is
usually treated as absolute (Thorne [21] [22]). “Fossil light”, emitted at r=2M by a body that has
long-ago fallen into a black hole, rotates at the horizon in lockstep with the hole’s rotation.
This same “total dragging” is then also required for the horizon of a black hole moving in a
simple straight line: if outward-aimed light emitted at r=2M is considered to be frozen into the
horizon surface, then, if we subsequently decide to move relative to the hole, the “frozen” light,
still trapped at r=2M, must seem to move with the rest of the hole. Certainly, if the hole recedes
from us at v m/s, the trapped light cannot recede from us at any less than v m/s, or else the
horizon would recede from us faster than the frozen signal, which would then find itself left
behind and exposed outside the absolute horizon, and be free to escape and be seen by us.
Absolute horizons therefore require total light-dragging.
2.2. Secondary horizons
We can also define an effective horizon, as being the critical surface at which light aimed in our
direction neither approaches or recedes. If a black hole moves away from us, then any light
trapped in the surface of its r=2M horizon must also be moving away from us, and is therefore
(by definition) no longer at our effective horizon, but somewhere behind it.
Since light aimed towards us far outside the hole moves towards us, and similarly-aimed light at
or below the horizon moves away from us, a classical gravitational model has to predict an
effective horizon somewhere between these two locations, somewhere outside r=2M. For us, the
standard Wheeler horizon must necessarily be concealed behind an additional secondary,
gravitomagnetic horizon that can be blamed on the receding hole’s increased attraction. ii
We will now briefly look at some of this secondary horizon’s properties.
 '!not
 +!#+
page 3 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
3. Properties of the secondary horizon
3.1. Overview of the problem
We will define O as an arbitrarily-distant observer for whom the hole is receding at v m/s, and X
as the centre of the black hole. On the line O-X, H1 is the intersection point of the absolute
Wheeler horizon at r=2M, and H2 is the corresponding point on the additional, secondary
external horizon. i
O … . . . ……………………… H2 ……. H1 ……… (X)
O' … . . . …………………………….…… H1 ……… (X)
The secondary horizon’s exact position and properties depend on our observer’s circumstances:
if the recession velocity of O was zero (giving O'), H2 would coincide with H1 increasing the
recession velocity moves H2 further away from H1 . ii iii
3.2. Non-Wheeler behaviour
While the region below the H1 surface cannot be seen by O, and the region outside H2 is fully
visible to our distant onlooker, the status and rules of causality of the region between H1 and H2
– which we might refer to as “the twilight zone” – are rather more ambiguous.
Signals created by events generated within this “ambiguous” zone cannot reach our onlooker O
directly, iv but can be seen by the onlooker’s colleagues in a research vessel moving with the
hole, some distance above H2 these observers can see all the way down to H1, and there is
nothing to prevent them communicating what they see back to their distant colleague, O.
The horizon H2 is therefore not an event horizon. It does not exist for all observers, and it does
not mark the location of an absolute causal barrier. While it separates the regions that O can and
cannot see directly, events occurring behind H2 (but outside H1) can still influence O indirectly.
3.3. Gravitomagnetism of a moving black hole:
The receding hole’s increased attraction can also be derived from a range of other arguments: a
redshifted receding body’s apparent slowed timeflow combined with Huygens’ principle results
in light being deflected more towards it; shift equivalence allows the recession redshift to be
interpreted as a gravitational redshift; the apparent field intensity value can be considered as
being timelagged; the body can couple with surrounding bodies via its field, deflecting light and
matter in its direction of motion through indirect collision; momentum exchange; “gravitational
slingshot”-style time domain arguments; classical field effects for a moving “gravitational
charge” analogous those associated with a moving electrical charge; [23] negative virtual particle
pressure; and/or a generalisation of the Fizeau effect. [24]
 O-X!,!!
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page 4 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
3.4. Gravitomagnetism of a moving final observer
If our distant region contains two almost-adjacent observers, O and O', one for whom the hole is
receding and one for whom it is stationary (O'), then although O cannot see all the way down to
the Schwarzschild horizon, their neighbour O' can. O' can tell O what they see, send O a
photograph or video clip, or aim an angled mirror so that O can see things from their viewpoint.
From an SR-based point of view, this description is nonsense: when O and O' are adjacent,
a signal that can reach O' must also reach Osignal behaviour is defined by the geometry of the
background space, not by any observer-properties. In our description, however, the different
properties of observers O and O' must be physically altering the behaviour of light in their region
i ii the retreat of O must somehow be contributing to the total curvature between O and X. In
other words, if we (reasonably) assign gravitomagnetic effects to the moving black hole, we also
have to assign them to all other masses that might exchange signals with the hole, and to all
potential observers. iii
Since the motion of hypothetical, or purely mathematical SR-style observers cannot physically
distort spacetime, we must reject this class of observer as “unphysical”, [25] and only accept
“material” observers as valid, possessing both inertial and gravitational mass in accordance with
the principle of equivalence. iv In a valid general theory, “observers” are no longer passive
placeholders in a predetermined spacetime, but active participants in a dynamic geometry. v
3.5. Gravitomagnetism of an intermediate observer
These non-SR behaviours become even more pronounced when we consider the case of
intermediate observers:
If we drop off an “intermediate” observer “OI”, somewhere between O and H2, initially with the
same state of motion as the hole, then since they do not (initially) see the hole to be moving, they
will be able to see all the way down to H1, and since they are outside H2, they can (initially)
relay what they see back to us.
We then have a bizarre situation in which the “twilight zone” H2-H1 region, which is normally
not visible to us, becomes visible though the addition of an intermediate mass (such as a simple
sheet of glass) placed in the signal path we should then be able to see into an initially-
forbidden region by viewing the region through the glass. At this point, the laws of physics are
quite clearly not obeying the rules of Minkowski spacetime: the presence and relative motion of
a mass in the signal path – any mass at all – is modifying the region’s spacetime geometry. vi
 OO'
 !!4#
)* 2holeobserver
#!50relativistic gravitation1
 6any gravitational properties at allOO'+!
)*0 2,1!
 !!!$!!![25]
 3!)+* 2##)*[27]
 2#+!![27][28][29]
page 5 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
Sections 1-3 show that the physics outside a black hole must be non-SR.
Sections 4 onwards explore how this can work, the required modifications to some basic
concepts, and the apparent agreement with quantum theory.
page 6 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
4. Experiences of local and distant observers
4.1. Observerspace
“Observerspace” logic can be characterised as the literal, “no interpretation” interpretation of
data (a “no theory” theory). According to observerspace principles, reality is whatever impinges
on our senses or is experienced by an atom, and there is no such thing as an observational
“artefact”. How a massed particle senses, and how it is sensed, is its physics.
Special relativity is well known for placing great store by “observer” arguments, and as it
assumes flat spacetime and global lightspeed constancy, then, apart from simple signal
timelags as a function of distance ... under SR the universe is exactly as we “observe” it to be, and
observation is reality. Light from events below r=2M never travels outside r=2M, because
according to the distant observer’s projected coordinate system, the emission events never
actually happen. If the light is never emitted, it cannot possibly have indirect consequences. [9]
Special relativity, however, is not quite a pure observerspace theory it applies the
observation principle rather selectively, since Einstein instructs his “SR observers” not to be
“perfect observers” reporting back what they see without interpretation, but to report what they
observe, which to Einstein means correcting the raw data according to the belief that space is flat
and the speed of light is globally fixed. i For Einstein, what an SR entity observes is the result of a
calibrated measurement process, and does not necessarily describe their direct experience. ii iii
Observerspace can be less reliable for more distant observers. If a gravitational-lensing
body moves across our field of view in front of a distant galaxy, we may see that galaxy break up
into multiple smaller copies, which swirl around before magically re-coalescing back into their
original form after the “lens” has passed. We do not treat this view of reality literally and assume
that the lensed galaxy’s component stars really do split and re-merge – we assume that there is a
simpler spatial underlying reality that we would see if only we were close enough.
Similarly with distant causalitywe cannot always assume that what happens lightyears away
can be simply extrapolated directly from what we see, without interpretation. The apparent time-
ordering of events can be “scrambled”, just as our lensed galaxy’s spatial locations appear
scrambled, but we can, again, assume a more rational underlying reality, that applies locally, and
that we would expect to see if only we were close enough to have a proper view.
This conflict between literal (“what we can see defines reality”) and interpreted theory (“reality
decides what we can see”), eventually caused Einstein to change his views on observerspace:
Heisenberg: [10] … And since it is but rational to introduce into a theory only such quantities as can be
directly observed, the concept of electron paths ought not, in fact, to figure in the theory.
To my astonishment, Einstein was not at all satisfied with this argument. He thought that every theory in
fact contains unobservable quantities. The principle of employing only observable quantities simply cannot
be consistently carried out. And when I objected that in this I had merely been applying the type of
philosophy that he, too, had made the basis of his special theory of relativity, he answered simply: ‘Perhaps
I did use such philosophy earlier, and also wrote it, but it is nonsense all the same … it is theory which first
determines what can be observed.
 ) 2*!8!!!non,9!!
!3! 2$,!
 &$)*#)*,,
[18][32][33]):$ 2*
 '&$;!/
<9$) #"*4=40>?)You see, but you do not observe. The distinction is clear*[34]
page 7 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
Acoustic metrics (whose predictions appear to be “dual” to those of quantum mechanics) [27] adopt
this later position, i and are capable of modelling more sophisticated and complex (and sometimes
frustratingly chaotic!) behaviours. It is one of the features of an acoustic metric that, while local
causality is everywhere preserved, a distant onlooker can see things that leave them confused.
Physical reality must generate observed reality in a simple and deterministic way but the
process is under no obligation to work as simply or easily in reverse.
4.2. Direct and indirect observation
The idea that reality must only be defined by what we can directly observe was one of the
defining features of the Copenhagen Interpretation of quantum mechanics. Having decided
that light could only be emitted or absorbed by atoms in discrete quanta, we were not obliged to
assume that the light also moved from emitter to absorber as quanta. Light transmission might still
be wavelike, and perhaps, since any attempt to intercept the light with a detector to measure
whether it really was a wave or particle was doomed to always answer “particle!” because of the
quantised nature of our measuring equipment perhaps the “particle” answer had no deeper
significance. If we chose to decide that light was transmitted as waves, there was no obvious
independent way of showing us that we were wrong.
The Copenhagen Interpretation disagreed. If light was always created and detected as quanta,
then this was reality, and it was philosophically wrong to hypothesise some other underlying
level of reality whose physical existence could only be inferred indirectly. Einstein vehemently
disagreed with the idea that QM statistics represented fundamental reality without a further
underlying explanation [35] (“Quantum mechanics is very worthy of respect. But an inner voice tells
me that this is not the genuine article after all. The theory delivers much, but does not really bring
us any closer to the secrets of the Old One. I am convinced that He is not playing dice[36]), but at
the time, subscribers to “hidden variable” interpretations of QM were in the minority.
QM applied to curvature horizons has since reintroduced and re-legitimised ( via the concept of
“real” and “virtual” particles) the idea of a level of reality that cannot be directly measured (by a
given observer), but whose existence can be deduced indirectly, and which does have a physical
effect on an observer’s other experiences (see: section 5). Hawking radiation has also prompted a
reassessment of some of our ideas about causality. While some QM researchers had believed that
its “unpredictable” processes were truly random, if this was true, the particle-pair-production
description of Hawking radiation implied that the radiation process was producing new,
“random” information from nowhere, [37] and since quantum-level events can be scaled up to
have macroscopic consequences (as in Schrödinger’s “cat” example), we then also lost
macroscopic causality. The universe would be allowed to do things for no reason.
On the other hand, if there was a persistent classical causality underlying and underpinning
quantum statistics (“microcausality”), then the information encoded in Hawking radiation had
to originate behind the horizon, and QM was doing a suspiciously good job of mimicking the
statistics of a universe in which classical horizons were effective rather than absolute, the motion
of massed particles warped spacetime, and SR-based classical theory was wrong. ii
 3"#! 2,[15]!!
! 2!
 /:2@#!!#0
)Quite obviously indirect radiation happens, and quite obviously the associated information comes from inside the
hole – how could anyone think otherwise?*
page 8 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
5. Compatibility with quantum mechanics
5.1. “Real” and “virtual” particles
The gravitomagnetic behaviours in our section 1-3 descriptions, and the resulting distinction
between “directly-observable” and “only-indirectly-observable” events (which makes no sense
under SR-based conventions), may be recognised by some readers as having direct counterparts
in modern quantum-mechanical descriptions of black hole behaviour – modern QM descriptions
support a distinction between particles that can directly reach the observer along unaccelerated
paths (“real” particles), and those that can only affect the observer indirectly, or via acceleration
(“virtual” particles). [39] i
As in our classical description, QM allows “real” particles to be converted to “virtual” particles by
acceleration; [40] [41] [42] ii iii particles deemed “real” for one observer can be “virtual” for another;
[42] a scoop dragged through a supposedly empty region can emerge full, as the scoop’s acceleration
converts virtual particles into real ones: lowering a fibre-optic cable into a hidden region lets us see
particles via light pulled out of the region by the acceleration forces in the cable; and a spaceship
passing by the horizon can be seen illuminated by light that would otherwise not be described as
existing there, with the collisions turning virtual photons into real photons.
In other words, every counterintuitive non-SR effect that results from our purely classical
arguments in sections 1-3 already seems to have a ready-made counterpart behaviour under
quantum mechanics. It would seem that QM already “makes a fit” to these behaviours (at least
qualitatively) in a way that can’t be achieved in an SR-based system.
5.2. Generation of Hawking radiation
Within an acoustic metric, horizon surfaces can be considered a form of observer-dependent
projective geometry. As a result, if a body behind a horizon undergoes a forced acceleration
towards the observer, the resulting spacetime distortion (Einstein 1921 [18]) may make the
projected horizon surface jump discontinuously from a location in front of the body to behind it,
making that body suddenly visible. If we were to mistakenly take the horizon as a fixed
reference, we might think that the object (and a surrounding region of space) had jumped
acausally into existence outside the horizon, perhaps as a quantum-tunnelling event. [43]
Like Hawking radiation under QM, acoustic horizons fluctuate and radiate and leak information.
[27] This ability to generate classical versions of QM effects that had no counterparts under
SR/GR1916 iv provided a strong motivation for the investigation of acoustic metrics, and the
subject started to be studied intensively from the late 1990s onwards. [27] [28] [29] v
 "#4[39])Virtual particle: In quantum mechanics, a particle that can never be directly detected, but whose existence does
have measurable effects.*'!"#,!,!
 Unruh radiation[41]01!
 B[42])Davies … confirmed Fuller’s conclusion that elementary particles are observer dependent. Roughly
speaking, it can be said that uniformly accelerated observers can see as real those particles which inertial observers claim to be
 :2C@("#4 2,C!#
 <![44])Even in the absence of a quantum theory of gravity, we have one robust prediction of such a theory: the existence
and spectrum of black hole Hawking radiation. … Any theory [of quantum gravity] that fails to reproduce this prediction is
almost surely wrong.*/%/%)
page 9 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
5.3. The QM pair-production description, from classical geometry
As previously mentioned, descriptions of Hawking radiation traditionally involve non-
classical pair-production effects occurring outside the horizon. Although the QM description
seems at first sight to defy classical interpretation, it also turns out to be the result of starting
with the “acoustic” classical description, and then inappropriately projecting SR-style
coordinates and causal conventions onto the final outcome:
If a particle undergoes a continuous acceleration or a series of accelerations that take it
outward through an effective horizon, far and fast enough to completely escape and reach a
distant observer, this observer’s attempt to back-calculate an inappropriate inertial history
for the particle will generate the “naive” 1970s description of Hawking radiation –
When we receive the escaped particle, we will know its final trajectory, but we will not
necessarily know anything about the accelerations and changes in trajectory that are part of
the particle’s history, and that are the reason it was able to escape. Working only from the
information available to us, a back-extrapolation of the particle’s supposed path from its final
state creates a false description in which a supposedly non-accelerated particle would have
needed to initially be travelling at more than lightspeed to escape. Since a particle
approaching at v>c is seen with its sequence of events and chiral characteristics reversed, an
escaped electron generates an artificial projected history in which the first, faster,
supposedly-superluminal part of its path appears to us to belong to a positron, moving away
from us. We then have a composite description of an (entirely fictitious!) escape path in
which the electron originated as one half of a particle-antiparticle pair created somewhere
outside the horizon, with the particle escaping and its antiparticle being swallowed.
A classical, continuous, and entirely causal description of radiation effects associated with
physical accelerations, when we try to explain the end results inertially, generates the
“traditional” 1970s non-classical, discontinuous, QM explanation of Hawking radiation. i
A final objection might be that these two descriptions cannot be dual, because if they were,
every observer stationed alongside the fictitious escape path would have to describe the pair-
production event as happening somewhere lower than their own position: different
observers would then assign the supposed event to different positions along the combined
path, potentially all the way down to a Planck distance above the r=2M horizon. ii This
description appears to be contradictory – however, the observer-dependency of the assumed
particle-creation point is also part of the QM description. iii
It appears that we have no obvious way of distinguishing between between the final
predictions of the non-SR “acoustic” description and those of the QM description. QM-
compatibility requires classical inertial physics to appear to be operating according to non-
SR rules and non-SR Doppler relationships.
 D!!!!)!*!
"#014[39])One can regard the member of the virtual pair that fell into the black hole (say, the antiparticle) as a
particle travelling backward in time out of the hole.*
 '"#+!!!,!!,!
 F.E0!GGE1$#[4]
page 10 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
6. What happened to special relativity?
6.1. Incompatibility of effective horizons with the SR shift equations
The mechanism for indirect escape though a horizon does not work with SR-based systems.
Under special relativity, the Doppler equation for a body receding at v is: [6]
E'/E =
Swapping the sign of the velocity inverts the equation, so in SR-based systems, the gravitational
blueshift, E'/E, is the inverse of the corresponding gravitational redshift. For a hypothetical
stationary emitter-observer at the Schwarzschild horizon, the outward redshift on signals
exchanged with a distant observer would be E'/E=zero, and the inward blueshift, E'/E=infinity.
Such a body would be instantaneously vaporised by the infinitely-blueshifted infalling radiation,
and unable to resist the infinite associated inward radiation pressure. Not only can a massed
particle at r=2M not move outwards, it cannot even remain stationary. The r=2M horizon is then
an absolute barrier, analogous to the SR lightspeed barrier in standard C20th inertial physics.
If the gravitomagnetic H2 horizon obeyed the SR shift relationships and the associated shift was a
function of velocity as predicted by SR, then since the H2 horizon for O has a shift of E'/E=0, O
should presumably again expect the blueshift seen by a body at H2 to be infinite. H2 would need
to be another absolute horizon, and it should be impossible for O to accept that a body could
hover legally there. But in reality, a spaceship at H2 is quite capable of firing its engines and
hovering or passing outward through H2 into the visible zone.
We therefore have to conclude that the H2 horizon’s defining Doppler equation, as judged by O,
with v as the recession velocity of the hole, cannot be the one supplied by special relativity.
6.2. Replacing the relativistic shift equations to allow Hawking radiation
The fact that bodies must be allowed to move outward through H2 then puts severe limits on the
possible Doppler law candidates.
Assuming that the principle of relativity still holds, any departure from the SR shift equations
must be “Lorentzlike”, of the form E'/E = [1 v2/c2]x . If we plot a graph of the inward blueshift
seen at the horizon as a function of x, only one solution is both non-infinite and non-zero [15]a
“cliff-edge” solution, that only appears when the predicted shifts are exactly one full Lorentz
factor redder than SR’s. i
We therefore conclude that in order for a relativistic theory to allow classical Hawking radiation
(and agree with our gravitomagnetic description), the Doppler equations that apply in the
horizon region must be redder than those of SR by an additional gamma factor, representing the
additional effect of geometry-change due to gravitomagnetism. ii
This, coincidentally, turns out to be the same modification already required to bring Einstein’s
GR (which was originally designed around a static universe [45]) into line with modern
expanding-universe cosmology, [46] and to function consistently with gravitomagnetism.
 "#black hole information paradox[37][38]!!!
 /,#&,<did!!
&HI&-0c,v1Ic 2!8<J
0!1!@&$) *
page 11 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
6.3. Gravitomagnetic shifts are also motion shifts
Gravitomagnetic shifts, like conventional motion shifts, are red for recession and blue for
approach. For a black hole, they have the same sign and magnitude as a conventional Doppler
shift, and take the same form as a conventional (non-SR) Doppler shift. If the gravitomagnetic
shift acts in addition to the SR motion shift, then the total motion shift must be non-SR and
around twice as strong as expected. A more credible option is that the gravitomagnetic shift is
the motion shift, calculated outside the time domain from the curvature associated with relative
motion. i In this case, the motion shift on a black hole is still non-SR. If a signal moving between
two gravitational bodies with relative velocity v also changes velocity en route by v, ii then light
has already adjusted to the speed of the receiver as it arrives the gravitomagnetic effect
extinguishes and replaces the conventional motion shift.
We then also have gravitomagnetically-regulated local lightspeed constancy for all observer-
masses and no further need for special relativity.
6.4. All bodies are “strong-gravity” bodies at sufficiently small distances
At this point we might be tempted to create separate “domains” for the strong-gravity physics of
our moving black hole, and the negligible-gravity, effectively-flat physics of special relativity.
This is not possible (see page 5, footnote iii). Metric theories require the signals from a cluster of
objects with different macroscopic field strengths to shift with velocity by precisely the same
amount. The principle of relativity agrees if weak-gravity bodies obeyed the SR Doppler
relationships, and strong-gravity bodies obeyed a different relationship, observers would be able
to tell who was “really” moving, and how fast, by exchanging and comparing signals. The
principle of relativity rejects the possibility of any difference between the Doppler shifts of
strong-gravity bodies and those of other masses if the gravitomagnetic motion-shift of a
moving black hole is forced to obey a different equation to SR’s, then so must that of every other
mass, and we must live in a wholly non-SR universe. iii
The same geometrical tyranny that says that SR must be correct in a relativistic universe
supporting global c says that SR must not be correct in a relativistic universe with gravitation. We
may or may not like these results: the geometry does not care.
 'J6+!,
5!,+! 
!!!,! 2
 ,!gravitomagnetic differentialv
c2&<&'B&2 !9!!
 F80.=14[49])… apparently no true test particles exist, hence the question is, how do we know how
“small” a particle should be in order to be considered a test particle (i.e., its gravitational field can be neglected)?*
there are no true test particlesthere are no massed particles even approximating “ideal” test particles
,!!+ 2%3+
2arbitrarily close)*8
page 12 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
6.5. Goodbye, special relativity
Special relativity is, of course, the provably-correct solution to restricted relativity in flat
spacetime. What is more challenging is establishing that the same flat equations should still hold
when we move on to a more advanced, general theory, in which all observer-masses have
associated curvature (via the principle of equivalence of inertia and gravitation), and in which
the motion of observer-masses must be accompanied by complicating gravitomagnetic effects
that the special theory does not attempt to model. Once we have multiple masses with relative
motion, all associated with their own velocity-dependent curvatures, we have a geometrically
dynamic system instead of the fixed flat geometry of Minkowski spacetime.
As pointed out by Moreau (1994 [50]), Minkowski spacetime and special relativity can be derived
from just the relativistic aberration formula and the SR Doppler predictions for wavelength-
change (which assume flat spacetime). Since all relativistic models share the same aberration
formula, any deviation from Minkowski geometry that still obeys the principle of relativity can
must be expressible as a Lorentzlike deviation from the SR Doppler relationships, after which, we
are no longer doing “special” relativity. i ii
A general theory of relativity must also be a theory of gravitomagnetism, and gravitomagnetism
is fundamentally incompatible with SR. As a matter of geometrical principle, the SR-style
simplifications and the resulting “flat” SR equations do not “carry over” into a gravitomagnetic
theory, in which any relative motion of matter must be associated with curvature side-effects. iii
GR and SR are two distinct solutions for two different scenarios, existing within two different
and logically-separate universes. It is therefore quite legitimate to defend the validity of SR in flat
spacetime, while rejecting its inclusion in a more advanced general theory. iv
 &4)… the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are
able to disregard the influences of gravitational fields on the phenomena (e.g. of light).*[52]6!!
 A:2C!!r-.!
)the greatest crisis in physics of all time*[53]!
&$!!)No inconsistency of principle has ever been found in Einstein’s
geometric theory of gravity*[53]5C
indirectaccelerated!% 240
!!total absence!
J! 2!
)The greatest crisis in physics of all time*&$ 2
'!:2@ 2J
 /)+ 2*!$!!
+,[53][54]prove geometrically!
!gravitomagnetic!0&.4[18] 1
' 2$!,!must%
not0+1 2$[25]
 /)*#!!
!3!! 2D):2!*,
 2![51]F,
!! 2!!0
!!be described in terms ofà la<[59]1,!!!
page 13 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
7. Other notes
i ii iii iv v vi
 6++09!!1[15]
 :2#!!+6(
##! 2!+0, 219!!!
)!*!!+ 2,+!
 !!!!#
, 2%0.15&$C
 '!%/)%*!%
:2C)*C%Hawking radiation"#
 <!!!)shut up and calculate*[60]!!!
!1!!are0e.g.)In spite of the fact that the Fulling-
Davies-Unruh (FDU) effect can be rigorously derived and extended to nonlinear quantum fields from the general Bisognano
and Wichmann’s theorem, the technicalities involved and probably its ‘paradoxical appearance’ has kept part of the community
quite skeptical up to now … Many physicists, thus, have decided to ‘leave the case to the experiments’.*[42]1
 '#!!%!!
 2!+89!!
page 14 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
8. Summary
Sections 1-3 of this paper show that Einstein’s 1916 general theory is, in its current
configuration, essentially unworkable.
Once we realise that distant observers can see different depths into a gravity-well depending on
their states of motion, the principle of relativity requires the relative motion of all masses to be
associated with strong gravitomagnetic curvature; once we accept the existence of velocity-
dependent curvature, we have a nonlinear, gravitomagnetic, “acoustic” metric rather than the
Minkowski metric, and a different set of equations to SR; once we realise that inertial physics is
not a flat-spacetime problem and is not correctly described under GR by flat-spacetime SR, then it
becomes clear that current “textbook” general relativity has been partly founded on inappropriate
geometry and principles, and also has the wrong gravitational shift equations.
Sections 4 onwards exist to reassure the reader that there is a way forwards: that the scary
“new” behaviours described are not new, i are not irrational or inexplicable, can be described
geometrically with the help of an acoustic metric, and are already predicted by quantum
mechanics. However, even if the reader does not accept the suggested solution, or acoustic
metrics, or Hawking radiation, or quantum mechanics, sections 1-3 alone are enough to put an
end to Einstein’s 1916 general theory. A researcher finding a problem in a current theory is not
obliged to offer a solution: if one is offered (as here), and the reader does not like it, then they are
cordially invited to try to construct their own but regardless of whether or not “acceptable”
alternatives are available, the existing theory is still wrong. ii
It should be stressed that the non-SR behaviours described in sections 1-3 are not some tentative
proposed “hypothesis” or “theory” based on any personal convictions or beliefs as to how physics
might or ought to behave, and are not a matter of personal judgement or opinion: they are pure
geometry. Once we accept the existence of the secondary horizon in the case of a receding black
hole, all these non-SR physical behaviours are already in play.
While it was quite understandable that Einstein would want his initial theory of relativity to live
on as part of his general theory, [52] geometrical considerations make this impossible, leaving the
1916 theory dead in the water. At best we can consider it a transitional theory, with one foot in the
past and one foot in the future, a temporary “bridge” attempting to include aspects of two different
and incompatible systems, that might prepare the way for a “proper” general theory at some later
date. Unfortunately, a more appropriately-designed general theory then failed to materialise. iii iv
 &<$=E#
 M/!#%#/!!
 &!,!
 &$;;#!%) 2*C
!)beyond a shadow of a doubt*[58]8#!!:2C$![49]
0$!1:2 2!empirically
page 15 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
9. Conclusions
It is a damning measure of the degree of failure of the 1916 theory that it cannot consistently
describe the external appearance of the simplest possible gravitational object, moving in a straight
line at constant velocity, as seen by a distant massed observer in otherwise-flat spacetime.
While the Mach-Einstein concept of a general theory was visionary, Einstein’s attempted
implementation of a general theory, as proposed in 1916, [8] does not work either as a physics or as
a geometry. This is due to the 1916 theory’s inappropriate adoption of relationships and
conventions derived from the 1905 theory’s assumption of flat spacetime, which fail in a curved-
spacetime context, and make the theory internally inconsistent and incompatible with modern
cosmology, [46] gravitomagnetism, and quantum mechanics.
A general theory of relativity is also a theory of relativistic gravitation and a theory of
gravitomagnetism, and relativistic gravitomagnetism turns out to require a very specific Doppler
relationship that is not the one given by special relativity. Constructing a valid general theory to
Einstein’s specifications, in which gravitational theory reduces to SR physics over small regions
for small bodies, is therefore a geometrical impossibility. A genuine general theory is an entirely
separate class of theory, and has to reject the 1905 theory’s “flat” philosophy, definitions and
relationships, and re-invent relativity theory from first principles, in the new context of metric-
distorting observers, gravitomagnetic lightspeed regulation, QM-style observer-dependency, and
curved spacetime. It must be designed as an iteration of relativity theory, not as an incremental
upgrade that tries to retain all the features of the previous system. What Einstein delivered in
1915/1916 was in many ways still an evolutionary step, when what was required was something
much more revolutionary.
While these problems can all be fixed this paper mentions the necessary additional Lorentz
modification that needs to be made to the SR/GR1916 Doppler relationships, and existing peer-
reviewed work on acoustic metrics provides an analytical and definitional framework for an
“acoustic” relativistic replacement to Minkowski spacetime [27] the biggest problem preventing
further scientific advance is not technical, but psychological and social:
It requires us to understand and appreciate, in the face of a century’sworth of teaching to the
contrary, that special relativity is not to be thought of as a proper or credible foundation theory
for gravitational physics.
page 16 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
 M)On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of
the diminution of the velocity of their light …*Philosophical Transactions of the Royal Society of London
vol. 740=G1!E;,;4=I=G=
.  )John Michell and black holes*Journal for the History of Astronomyvol. 1001
!G.,GE4 I.=.=CG 
E ::NThe man who invented black holes [his work emerges out of the dark after two centuries]N
New Scientist0.=M1!
G O! Black Holes and Time Warps: Einstein’s outrageous legacy0K!G1)<!E4
!GGE' DJEEECECE
; &DRelativity in Curved Spacetime0<.1)§11: Dark Stars and Black Holes*
!,GGP)§9.12: The Tilted Gravity-well, §9.13: Zeno revisited: The ‘impossibility’ of motion*!
;,' DJ;;C=
C /&)Zur Elektrodynamik bewegter Körper*Annalen der Physikvol. 322Q0;1
translated and reprinted as:
/&)On the Electrodynamics of Moving Bodies*The Principle of Relativity0.E1
!E;,C;' DJG=CC=;
 /&)9:2R*/K#G0C1
translated and reprinted as:
/&)The Foundation of the General Theory of Relativity*The Principle of Relativity0
.E1!,CG' DJG=CC=;
= &The Times!!0810J.=1
 !"#)Classical Theory*!<!6The Nature of Space and Time
0KAKC1' DJCEG
 "Encounters with Einstein : And Other Essays on People, Places, and Particles
0KAK=1!E,G' DJC.GEE.
 /&)On a stationary system with spherical symmetry consisting of many gravitating masses*The
Annals of Mathematics, Second Seriesvol. 40no. 406E1!..,E
. M/OFGeons, black holes, and quantum foam: A life in physics
0J=1' DJEEGCG.
E !"#2K)The singularities of gravitational collapse and cosmology*
Proceedings of the Royal Society, London: Avol. 3140.M1!;.,;G= 
G 2K)Structure of Spacetime Singularities*!<!The Nature of Space and
Time0KAKC1' DJCEG
; &D)The Doppler equations of Newtonian optics as a unique solution to quantum gravity*
C "#)Black hole explosions?*J248!E5E0G1 
4 E=I.G=E 
 "#)Particle creation by black holes*Communications in Mathematical Physicsvol.43
E0;1!,..4 IDF.EG;.
= /&May 1921 “Stafford Little” Princeton lectures!
The Meaning of Relativity0..1)The General Theory of Relativity (continued)*
' DJG;.=;==
) A body must experience an accelerating force when neighbouring masses are accelerated, and, in fact, the force
must be in the same direction as that acceleration. … There is an inductive action of accelerated masses, of the
same sign, upon the test body. *
 <!)Aberration and the Speed of Gravity*Physics Letters A 267.5E0.1
!=,=!4IIICI E;,C01,=
page 17 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
. M/A Journey into Gravity and Spacetime 0 /81
)7: The Boundary of a Boundary*!=,.P)Gravity’s Next Prize: Gravitomagnetism*!.E.,.EE
' DJCCEG
. O! Black holes and time warps: Einstein’s outrageous legacy0G1F
=!.,..' DJEEECECE
)At the horizon, space is locked tightly onto the horizon: It rotates at precisely the same rate as the horizon spins*
.. 2"KO! )The Membrane Paradigm for Black Holes*Scientific Americanvol. 258
)An observer just outside the hole circles the hole in step with its rotation; more distant observers orbit more slowly. Each
observer is at rest in ‘absolute space,’ but space itself is dragged along by the rotation of the hole.*
.E 6")Electromagnetic waves, the propagation of potential, and the electromagnetic effects of a
moving charge*The Electrician0===,==1and in
Electrical Papers vol. 20=G1
.G 2BM)‘Fresnel Aether Drag’ in a Transversely Moving Medium*Proceedings of the Royal
Society of London. A. Mathematical and Physical Sciencesvol. 328;G0EM.1!
.; &D)Problems with the frame approach under general relativity*ResearchGate0E9..1
)3.1. Accelerated frames do not adequately describe the relativistic physics of accelerated observers*
)3.2. General relativity and the covariance paradox: Geometrical laws vs. physical laws* 
)3.3. Physical vs. unphysical observers*)7.1. Weak-field solutions*4 EGI2:..GC.;EGG= 
.C &D)Ten proofs of special relativity*ResearchGate0.EM..1 
)37. SR Argument 37: ‘Special relativity deals with weak gravity, GR deals with strong gravity’ * 
4 EGI2:..E;GG 
. <DS 8B)Analogue Gravity*Living Reviews in Relativityvol.14
.= B)Acoustic Black Holes: Horizons, Ergospheres, and Hawking Radiation*Classical and Quantum
Gravityvol. 15C0M=1!C, 
. B<DS 8)Analogue Models of and for Gravity*General Relativity
and Gravitationvol. 3406..1!,EG4.EI/4.=G.G
E ::2KMr Tompkins in Paperback0<AKE1'2K
!+' DJ;.GG.
E M)Invisibility of the Lorentz Contraction*Physical Reviewvol. 1160;J;1
E. & )The twists and turns of the Terrell effect*American Journal of Physicsvol. 56E0==1
EE &DRelativity in Curved Spacetime0<.1)§7: Apparent Length-Changes in
Moving Objects*!,C' DJ;;C=
EG /<9)A Scandal in Bohemia*The Strand Magazine0M=1
E; /&DK#J2)Can quantum-mechanical description of physical reality be
considered complete?*Physical Reviewvol. 470E;1!,= 
EC /&The Einstein Papers: Volume 15: The Berlin Years: Writings & Correspondence
)426: To Max Born, 4 December 1926*!GE!4II!!!!I;,IGE
E 8 #)Black Holes and the Information Paradox*Scientific American/! 
E= MK#)Do Black Holes Destroy Information?*Black Holes, Membranes, Wormholes and
Superstrings: Proceedings of the International Symposium0 G1' DJ==G;;G=G
E !"#A Brief History of Time: From the Big Bang to Black Holes0D==1
' DJ;E;=;
G K<9)Scalar production in Schwarzschild and Rindler metrics*Journal of Physics A:
Mathematical and Generalvol. 8G0;1!C, 4==IE;,GGI=IGI..
G :A)Notes on black-hole evaporation*Physical Review Dvol. 140C1!=, 
page 18 of 19
Gravitomagnetic horizons vs. Einstein’s GR, Eric Baird, February 2021
G. :&/9/B)The Fulling–Davies–Unruh effect is mandatory: The proton's
testimony*International Journal of Modern Physics Dvol. 110..1!;E,;4
IG.I .=.=..=
GE #OK#F##)Hawking radiation as tunneling*Physical Review Lettersvol. 85
GG <!)Quantum Gravity: A Progress Report*Reports on Progress in Physicsvol. 64=
G; "J)Einstein’s Conversion from His Static to an Expanding Universe*The European
Physical JournalHvol. 390F.G1!E,C.4GI!(I.E,GE,C
GC &D)Cosmological redshifts vs. gravitational redshifts*ResearchGate0.;M.=1 
G !"#)Information Preservation and Weather Forecasting for Black Holes*
G= T)Stephen Hawking: 'There are no black holes'*NatureJ0.GM.G1 
G K  8BF)Theory of gravitation theories: A no-progress report*
International Journal of Modern Physics Dvol. 17EG!E,G.E0.=1 
4G.I .=.==.
; )Wave Front Relativity*American Journal of Physicsvol. 62;0G1
; &D)Reduction to special relativity may be unphysical*ResearchGate0E/.=1 
;. /&Relativity: The Special and the General Theory0.1..
)… it has often been contended by opponents of the theory of relativity that the special theory of relativity is
overthrown by the general theory of relativity … Not in the least … There could be no fairer destiny for any
physical theory than that it should point the way to a more comprehensive theory in which it lives on as a
limiting case.*
;E <O! M/0)*1Gravitation0FE1)§6.1:
Accelerated observers can be analysed using special relativity*)§44.1: Gravitational collapse as the greatest
crisis in physics of all time*)44.2: Assessment of the theory that predicts collapse*' DJCEGG
;G &FM/Spacetime Physics: Introduction to special relativity: Second
edition0"F.1)Box 4.1:Do we need general relativity? No!*!E.' DJC.E.
;; OJ)Space-Time Structure near Particles and Its Influence on Particle Behavior*
International Journal of Theoretical Physicsvol. 230J=G1!E,G
;C /&)On the Generalized Theory of Gravitation*Scientific Americanvol. 182G0/!;1
; B)General Relativity at 100: Einstein’s Unfinished Masterpiece*New ScientistEG. 
;= <Was Einstein Right? Putting General Relativity to the Test0DD#=C1
/!!+)Special Relativity: Beyond a Shadow of a Doubt*' DJGC;==;
; O<)On the Space-eory of Maer” (lecture abstract, 21 February 1870), Proceedings of the
Cambridge Philosophical Society (1864-1876)vol. 2!;,;=
C J9)What's Wrong with this Pillow?*Physics Todayvol.420/!=1!
page 19 of 19
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Although SR-style "frame" arguments work well in flat spacetime, the mass-dependent curvatures inherent in a general theory of relativity prevent a physical observer's local properties from being extrapolated cleanly across the surrounding region. We question the geometrical sense of using frame arguments in a general theory, list some of the resulting difficulties, and conclude that special and general theories of relativistic physics must be regarded as alternative and distinctly-different logical frameworks. The "frame" problem shows that, within a GR environment, the SR solution can only apply exactly to unphysical observers, and not to real masses with relative motion-a valid general theory cannot reduce to SR physics.
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The paper analyses (in some cases, apparently for the first time) a number of common proofs and supporting arguments for the correctness and unavoidability of special relativity. It finds a pattern of bad fact-checking, bad analysis (or no analysis!), bad logic, math and geometry, and a tendency for the community to repeat impressive-sounding statements favouring SR, which, on investigation, turn out to be untrue. Some of the wider theory-space of potential alternative relativistic systems is explored, along with some of the required properties for a curved-spacetime replacement for special relativity.
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According to the Einstein Equivalence Principle (EEP), any classical curved-spacetime geometrical theory of gravity must reduce to the physics of special relativity over small regions. However, the existence of null solutions means that a flat-spacetime geometry does not always equate to a flat-spacetime physics-in the "Cliffordian" acoustic-metric counterexample, particles and particle interactions have associated curvatures, the resulting equations are inherently non-SR, and the "flat limit" instead represents the disappearance of any physical objects and observers with which to attempt physics. Any thorough review of relativity theory therefore needs to also consider non-SR solutions.
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Under current theory, Einstein's 1916 general theory of relativity applies the Doppler equations of special relativity to motion shifts and gravitational shifts, while cosmological shifts are thought to obey a different shift law. However, geometrical considerations require these arguments and equations to be interchangeable. If this geometrical argument is correct, either the cosmological shift law and/or the core relationships of general relativity will need to be modified.
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One of the greatest challenges of quantum gravity is the resolution of the black hole information paradox, a disagreement between classical and quantum theory as to whether and how massenergy and information can escape a gravitational horizon. The disagreement appears when a classical physics based on Minkowski spacetime is compared to the predictions of quantum mechanics, but does not arise with the Newtonian Doppler relationships, or with acoustic metrics. Examining the range of other potential relativistic solutions that might allow classical information-escape across a gravitational horizon, we find that the Newtonian solution appears unique.
During the last 30 years Kip Thorne has had the joy of participating in a great quest. The quest to understand Einstein's general theory of relativity and its predictions about the universe, and the quest to discern where and how Einstein's theory fails and what then replaces it. This quest has lead him through the labyrinths of exotic objects: black holes, white dwarfs, neutron stars, singularities, gravitational waves, worm-holes and yes, even time machines. The quest, with its hundreds of participants scattered over the globe has led him to appreciate the international character of science, the different ways that scientific enterprise is organized in different societies, and the inexorable manner in which science bas been intertwined with political currents, especially the Soviet/American conflict. This book is the author's attempts to share these insights with lay readers, and the scientists who work in fields other than his. A book of many interlocking themes held together by a thread of history; the history of the development of our times about curved space and warped time, and most especially black holes.