GALILEAN SPECIAL RELATIVITY

(about Schroedinger's traveling twin cats, why the Moon has
no aberration while a star next to it does, and a true
understanding of special relativity)

                       Tom Van Flandern
                        Meta Research

Abstract.  The standard (Einstein) theory of special relativity
has been partially confirmed by a variety of experiments, leading
to great confidence in its central corollaries.  But a review of
the experiments shows that they do not confirm certain aspects of
special relativity, nor do they distinguish standard special
relativity from the Galilean variety.  These two differ in their
definition of remote synchronization.  The experiments are
reviewed with emphasis on distinguishing which version of special
relativity explains nature better.  Especially telling in this
regard are two experiments:  One shows that annual aberration
affects the position of a star next to the Moon, but not the
position of the Moon itself.  The other shows how a
"Schroedinger's Cat"-like paradox can arise.  Both favor the
Galilean variety of relativity over the standard version.  At
stake is the corollary that faster-than-light travel in forward
time is impossible, since no such conclusion arises in Galilean
special relativity.  The physical meaning of the two theories is
compared, and definitive new tests whose results will soon be
known are described.

     1.  Introduction

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SUMMARY: The literature on special relativity is filled with
supposed paradoxes and proposed resolutions.  This paper will
review the essentials of the contention, and attempt to add new
insight into its resolution.  It concludes that the understanding
of standard special relativity is in need of modification, as
supported by logic and experimental evidence.
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     In a companion paper, it is demonstrated that gravity acts
without detectable delay.  This circumstance can be reconciled
with Einstein's general theory of relativity, especially since
instantaneous propagation of gravitation is always used in
practical orbit computations anyway.  However, propagation of
gravity at speeds faster than light is contrary to a well- known
and widely adopted corollary of the standard (Einstein) special
theory of relativity.

     It is apparent that either something is wrong with the
interpretation of the experimental evidence concerning the speed
of propagation of gravitation (not to be confused with gravity
waves), or else something is wrong with the corollary of standard
(Einstein) special relativity (hereafter SSR) to the effect that
nothing can propagate faster than light in forward time.

     Having explored the former possibility in the companion
paper, we explore the latter possibility in this paper.  The
unambiguous conclusions reached here, in the light of the
companion paper, are that faster-than-light propagation in
forward time is allowed; that gravitation is a practical example
of a phenomenon behaving in that manner; and that our
understanding of SSR (specifically, its definition of remote
synchronization) must be modified to keep theory and experiment
in accord and avoid new paradoxes.

     The author is well aware of the extensive writing already
existing on this subject; for example, the debate of the famous
twins paradox between Professors H. Dingle and W.H. McCrea in the
pages of Nature magazine [see "Science at the Crossroads" by H.
Dingle, Martin, Brian & O'Keefe Ltd., London (1972), which also
reprints the following articles:  Nature 216, p. 113, p. 119, and
p. 122 (1967); and Nature 217, p. 19 (1968).], discussions of SSR
and the twins paradox in dozens of the leading textbooks (almost
no two of which resolve the twins paradox in the same way), and a
few dozen dissenting papers on various aspects of special
relativity published in the numerous books and several journals
that now exist as outlets for alternatives to mainstream ideas in
this and related fields of inquiry. [Two recent books include: 
"Einstein Plus Two" by P. Beckmann, Golem Press (1990); and
"Escape From Einstein" by R.R. Hatch, the Kneat Kompany (1992). 
Journals include Physics Essays, Galilean Electrodynamics,
Apeiron, and Meta Research Bulletin.]  The matter has also been
extensively debated on the networks. [Especially newsgroup
sci.physics of USENET on the Internet, where the author's address
is metares@well.sf.ca.us; and Science Forum section 16 of
CompuServe, where the author's address is 71107,2320.]  The
author hopes that the present work will be judged as adding
something new to that voluminous literature.

     2.  The Two Postulates of Special Relativity

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SUMMARY: The two basic postulates underlying special relativity
may be understood in either of two different ways.  In one of
them (SSR), the speed of light will actually be the same for all
observers, because space and time change with frame motion.  In
the other (GSR), the speed of light will always be measured to be
the same by observers using electromagnetic signals because
rulers and clocks are affected by motion.  Both meanings are
consistent with Einstein's early papers.
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     Standard (Einstein) special relativity is a theory which
begins with two postulates.  These are (Kacser 1991):
     (1) The basic laws of physics are identical for two
observers who have a constant relative velocity with respect to
each other.  This is called the relativity postulate.
     (2) The speed of light in vacuum is an absolute constant for
all observers, independent of the velocity of the light source or
the velocity of the observer.  This is called the speed of light
postulate.
The relativity postulate is sometimes stated as "No experiment
can determine which of two relatively moving observers is
actually in motion."

     From these two postulates flow many corollaries, such as the
Lorentz transformations of position and time, length
contractions, and time dilations.  Of particular interest here is
the implied definition of "simultaneous" for remote observers:
two events at different places, A & B, are simultaneous if one
occurs at the mid-time between transmission and reception of a
light signal at A, and the other occurs at the bounce time of
that light signal at B.  From that definition and the other
corollaries it follows that time is observer-dependent, and that
ordinary matter cannot travel faster than light in forward time. 
The reasoning behind these conclusions will be clarified later.

     By contrast, if the second postulate is modified to read
that the speed of light in vacuum will be measured to be an
absolute constant by all observers, but time and space retain
their classical, frame-independent meanings, this defines what we
call here "Galilean special relativity" (GSR).  Then length
contraction and time dilation are simply effects on meter sticks
and clocks, not on space and time.  This is analogous to
temperature affecting the length and rate of a pendulum clock --
no one suggests that temperature affects space and time
themselves.

     But if the effect of motion is on clocks and rulers instead
of on time and space, it follows that if motion slows the clocks
in frame B as viewed by frame A, then frame B must view frame A's
clocks as running fast.  In SSR, each frame must apply direct
Lorentz transformations to predict the behavior of clocks in the
other frame; so each sees clocks in the other frame's clocks
running slower.  But in GSR, one frame uses direct Lorentz
transformations, and the other must use inverse transformations. 
The local gravitational field determines which frame is which.

     The important difference is that the speed of light will not
then be an absolute limit to communication or propagation speeds
in GSR as it is in SSR.  It is certainly relevant to point out
that Einstein's own wording of the second postulate may easily be
interpreted as being at least as consistent with GSR as with SSR,
since (translation by Rosser 1964) Einstein's wording of the
second postulate is:  "Any ray of light moves in the 'stationary'
system of coordinates with the determined velocity c, whether the
ray be emitted by a stationary body or by a moving body."

     This difference between SSR and GSR seems pretty basic, not
to mention important.  So our first step will be to examine the
experiments cited as tests of SSR to determine if one of them
already distinguishes between the SSR and GSR interpretations of
the phenomena of nature.

     3.  The Experiments

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SUMMARY: Ten basic experiments provide partial confirmation of
special relativity.  None of these tests the reciprocity of space
contractions and time dilations between relatively moving frames,
and none of them tests the relativistic definition of remote
simultaneity, at the heart of the difference between SSR and GSR.
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     The experimental confirmation of SSR rests upon the
following ten experiments, each of which tests some new aspect of
the theory; and a few others that are essentially repetitions of
these with greater precision.  Following the usual convention, c
= speed of light in vacuum.

  *  Bradley 1728: the apparent source direction for starlight is
displaced by the velocity vector of the observer.  This is called
"aberration".  Bradley showed that light appears to emanate from
the direction of the vector difference between the true light
velocity vector in space and the observer's velocity vector.  If
the direction of a light source follows the vector addition law
for velocities, it was logical to expect that the magnitude of
the speed of light would follow this vector addition law as well. 
It therefore came as a complete surprise when Michelson and
Morley found that to be untrue in 1881.

  *  Fresnel 1817: c is affected by a moving medium ("Fresnel
drag").  Light not only travels at speeds slower than c through
any transparent medium, but is also slightly dragged along by the
medium if the medium is itself moving with respect to the
observer.  This is fully as predicted by classical concepts that
include an "aether" as a medium for lightwaves to propagate
through.  Later, it was shown how relativity might also explain
it.

  *  Airy 1871: aberration is independent of the index of
refraction.  Although the speed of light is slower through air or
water than through vacuum, this slowing does not change the
apparent direction from which the light emanates.  A telescope
tube filled with water sees starlight emanating from the same
place as one filled with air.  This was the first hint that the
simple velocity vector addition law was not the whole story for
explaining light propagation.

  *  Michelson-Morley 1881: c is independent of observer motion. 
The round-trip speed of light was the same in each of two
perpendicular arms of the measuring apparatus, although each arm
should have been affected differently by the Earth's motion
through space.  This was devastating to classical theories of
light propagation, and led to suggestions that the aether through
which light propagated must be entrained by the Earth.

  *  De Sitter 1913: c is independent of source motion.  Light
from one member of a double star doesn't bypass light from the
other en route to us.  Light from the component traveling toward
us does not travel any faster through space than light from the
component heading away from us.  This argued against the
ballistic (particle) nature of light, since particle velocities
are affected by the velocity of their source, and light is not.

  *  Sagnac 1913: rotational motion around a path enclosing an
area does affect measured values of c.  This was the first
apparent experimental contradiction of SSR, but was later
explained as a time-dilation asymmetry caused by the rotational
motion of the light source.  The fact that it technically
violated the spirit of the speed of light postulate was ignored. 
This experiment was reinforced by the Michelson-Gale 1925
experiment, which showed that the same asymmetry in measured
values of c occurs around a path enclosing an area on the surface
of the rotating Earth.

  *  Kennedy-Thorndike 1932: a Fitzgerald-Lorentz contraction of
length alone in the direction of motion is not sufficient to
explain the Michelson-Morley null result.  Time dilation is also
required.  This was demonstrated with a Michelson-Morley-type
apparatus whose two perpendicular arms were of quite different
lengths.

  *  Ives-Stilwell 1941: time dilation occurs between approaching
and receding sources reflected to the same diffraction grating to
measure their relative spectral shift.  This experiment shows
that moving ions radiate at frequencies that depend on their
motion, which is interpreted as evidence that time is dilated for
those ions.

  *  Frisch-Smith 1963: radioactive decay lifetimes of mesons are
also time-dilated.  This was direct evidence that decaying atomic
particles live longer when traveling at high speed.

  *  Hafele-Keating 1982: atomic clocks traveling around the
world are time- dilated.  This experiment showed that the rates
of real clocks depended on their motions relative to the rotating
Earth.  Two clocks traveling around the world in opposite
directions experienced quite different time dilations compared to
a stay-at-home clock.  This was explained as caused by the
eastbound clock moving fastest in inertial space, since the
motion of the aircraft carrying it added to the Earth's rotation;
whereas the westbound clock moved slowest because its aircraft's
motion opposed the Earth's rotational motion.

     Many other experiments might be mentioned here.  But often
their interpretation is ambiguous or unilluminating, or
repetitious of earlier results but with improved precision.  For
example, Champeney 1963 essentially duplicated the
Michelson-Morley experiment using the Mossbauer effect.  The
interpretation of this experiment, often misquoted, is
illuminated by Hayden (1992).  A more complete list of other
recent experiments and their findings is given by Hatch (1992). 
But it is important to note that no existing experiment verifies
that two relatively moving frames each see the other's clocks
running slower; and none of these experiments verifies the
Einstein definition of simultaneity.

     In GSR, the local gravitational field either serves as the
"aether", the medium through which light propagates, or else it
entrains the aether.  The author has developed the latter
possibility as part of a complete cosmology (Van Flandern 1993). 
Starlight then travels mainly through the galactic gravitational
field until it enters the Sun's sphere of influence, then travels
through that medium until it reaches the boundary where the
Earth's field dominates the Sun's.  Stellar aberration would
occur at the Earth-Sun sphere-of-influence boundary, not in the
telescope.  The local aether would be unmoving with respect to
the telescope, so the Airy and Michelson-Morley results are as
expected.

     The Earth clearly rotates with respect to its own gravity
field, so most variants of GSR predict that the Earth's
rotational velocity will show up in tests of special relativity,
even though its orbital velocity does not.  However, if the
Earth's gravity merely entrains the aether, it may be that the
aether acquires some rotational angular momentum as well.  The
original Sagnac experiment using a rotating platform in the
laboratory did show an effect on the speed of light, as GSR
predicts.  The Michelson-Gale and Hafele-Keating result suggests
that the aether does not rotate with the Earth, because then the
east-traveling and west- traveling planes would have experienced
the same clock slowing, which they did not.  The experiments
confirming time dilation all show it in the frame moving with
respect to the local aether only.

     4.  Aberration

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SUMMARY: Two aspects of stellar aberration are inconsistent with
SSR.  Both components of close double stars are displaced by the
same aberration angle despite having different velocities,
showing that the relative velocity between source and observer is
not what determines aberration.  And starlight at the Moon's limb
is displaced by stellar aberration, while the Moon itself is not,
showing that aberration originates at a distance beyond the Moon.
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     If a photon of light were a pure particle, then a telescope
on a moving platform such as the Earth would have to tilt in the
direction ahead of the photon source for the photon to travel
straight down the telescope tube.  If it did not, the motion of
the telescope during the travel of the photon down the tube might
cause the photon to collide with the side of the tube instead of
traveling along the telescope axis.  Only the motion of the
telescope relative to the motion of the photon source would
affect the angle of tilt needed to keep the photon on-axis.

     If light were a pure wave propagating through a medium (the
aether), then the angle of tilt required to keep the wavefronts
perpendicular to the telescope axis would depend on the relative
velocity between the telescope and the local aether, but not on
the velocity of the photon source.

     The angle of tilt of the telescope when observing stars or
other distant objects in the universe is called "stellar
aberration".  The angle actually observed from Earth reaches its
maximum of 20.5 arcseconds in the directions toward and away from
the Sun, and is easily detected with transit telescopes, whose
absolute pointing accuracy is about 0.1 arcsecond.  Astronomers
offer two different ways to describe and compute the angle of
stellar aberration.  If the light source is regarded as fixed
relative to the Sun, then the Earth moves relative to the Sun and
light source at a speed of about 10^-4 c.  As a consequence,
stellar aberration is an angle of 10^-4 radians or 20 arcseconds
in one direction when the light source is at opposition to the
Sun, the same angle in the opposite direction when the light
source is in conjunction with the Sun, and smaller amounts in
between.

     Alternatively, it may be convenient to adopt the Earth as a
fixed platform.  Then the light source must be taken as moving at
10^-4 c in the opposite direction relative to the fixed Earth, in
addition to any velocity of its own relative to the Sun.  Then
because of the finite speed of light, we must look in the
direction where the light source was when its light was emitted,
rather than in the direction the source is now.  For example, the
Sun is seen in a location 20 arcseconds west of its true position
because its light requires 8.3 minutes to reach the Earth, during
which interval the Sun's apparent motion relative to the star
background is 20 arcseconds.

     In the case of the Sun, there is no motion to consider other
than the Earth's orbital velocity.  So the Sun's stellar
aberration and the change in its position due to lighttime delay
are manifestations of a single phenomenon as viewed from the
Sun-fixed or the Earth-fixed frames, respectively.  Planets have
their own orbital motions, so their observed positions can be
correctly computed from either their lighttime delay relative to
a fixed Earth, or from what is called "planetary aberration" in a
Sun-fixed frame.

     With this much background, we will now consider cases of
special interest to an understanding of special relativity.  De
Sitter noted in 1913 that the orbital motion of double stars does
not alter the speed of light from either component.  But what
about aberration?  Hayden (1993) has noted that the displacement
of stars due to stellar aberration is independent of the motion
of the star itself, as demonstrated by components of close double
stars which move rapidly in opposite directions but have the same
aberration.  If only the relative velocity between source and
observer mattered, the two components would be seen at widely
separated positions on the sky because of these large relative
velocities in opposite directions.  Since that is not the case,
it seems clear that stellar aberration is independent of the
motion of the source body for all bodies outside our solar
system.  As Hayden remarks, this is inconsistent with the
relativity postulate, since we can detect the Earth's motion
through the solar system by observing distant objects.  The
relative velocity between source and observer is irrelevant to
aberration, as may most clearly be seen by hypothesizing a double
star in which one component revolves with a period of one year
and a velocity of 10^-4 c, in phase with the Earth's similar
motion around the Sun. [This example was first suggested by H.
Hayden.]  Then Earth and hypothetical star have zero relative
velocity, yet the star is still displaced back and forth by
stellar aberration due to the Earth's motion through the solar
system.  Note that this argument applies regardless of the amount
of lighttime delay between source and observer.

     Does every light source suffer displacement due to the
Earth's orbital velocity?  The answer is apparently "no", since
lights on radio towers are not so displaced.  We can observe the
radio tower lights in summer and winter, just as transit
telescopes observe ground markers.  These observations confirm
that terrestrial light sources retain a fixed direction relative
to the observer, even though stars move back and forth with the
seasons.  Curiously, it is possible to describe the radio tower
lights as shifted by stellar aberration and shifted back by
lighttime delay if they are considered as moving sources in a
Sun-centered solar system.  In such a frame, both Earth and radio
tower lights are moving at 10^-4 c.  The lights may be thought of
as displaced forward by stellar aberration, and then seen in
their delayed positions relative to the Sun because of lighttime
delays from the rapidly moving tower-light frame back to the
observer on Earth.  Thus the two effects cancel exactly,
independent of the distance of the radio tower, yielding no
aberrational displacement, as we would expect by considering only
an observer-fixed frame to start with.

     However, is this construction consistent with SSR? 
Observations show us that artificial Earth satellites, like radio
tower lights, display no stellar aberration, although satellites
are displaced by a smaller amount due to their own orbital motion
about the Earth.  The same is true of our own Moon. ["Explanatory
Supplement to the Astronomical Ephemeris", H.M. Stationery
Office, London (1961).]  That creates the following dilemma:  If
a star is occulted by the Moon as it slowly orbits the Earth, the
last rays of the star's light are displaced on the sky by 20
arcseconds, whereas the Moon's position is not so displaced. 
Such a displacement is readily verified, since it makes a
difference of about 40 seconds of time in the moment when the
star will be seen to disappear from view.  Let us consider the
last rays of starlight before the Moon blocks them.  As the final
ray passes the edge of the Moon, it will proceed in parallel with
a ray from the edge of the Moon.  Both rays will proceed at the
same speed in the same direction, and will suffer identical
delays and bending and changes of apparent direction all the way
to the bottom of the telescope tube on Earth.  So whatever
happens to the star's last ray must happen to the nearby ray from
the Moon's edge, and vice versa.  Yet the star's ray appears
displaced on the sky by 20 arcseconds, and the Moon's ray does
not.

     This is quite contrary to the expectation of SSR, and indeed
seems to tell us that the displacement of the star's apparent
direction on the sky must have occurred before the starlight
passed the Moon.  This odd set of facts seems to make sense only
if one deduces that stellar aberration, the actual displacement
of the apparent direction of starlight, takes place as the
starlight enters the Earth's gravitational sphere of influence. 
If the starlight's immediately preceding condition was determined
by its travel through the Sun's gravitational sphere of
influence, then all the characteristics of stellar aberration may
be fully understood.  But this description is consistent with
GSR, not SSR.

     5.  The General Twins Paradox

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SUMMARY: In a symmetric version of the classical twins paradox in
special relativity, the traveling twin is already younger than
his Earth-frame counterparts in the first half of his journey,
before and accelerations or turn around or frame changes.  This
is because all clocks in a relatively moving frame appear to run
slow, yet time in the relatively moving frame always advances
faster than in one's own frame.  The difference between time on
individual clocks and frame time is due to synchronization
slippage.  The existence or non- existence of such time slippage
is the major difference between SSR and GSR.  The Quasar Paradox
shows how SSR would permit relatively moving frames to be older
than the big bang universe.
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SETUP:  Edward stays on Earth.  Sam passes by Earth on his
spacecraft on his way to Alpha Centauri (AC), exactly 4
lightyears away.  Edward and Sam are born at the instant Sam's
spacecraft passes Earth.  The relative speed between Edward and
Sam is 99% of the speed of light (c).  Alice lives on Alpha
Centauri, and was born simultaneously with Edward as judged by
all observers in the Earth-AC frame.  Clocks positioned beside
Edward, Sam, and Alice are all set to zero at the "Sam passes
Edward" event.

DEFINITIONS:  "Lorentz factor" = gamma = 1 / sqrt(1 - v^2/c^2) =
factor by which moving clocks are slowed and distances are
contracted, where v is the relative velocity of the clock.  "Turn
around" -- a special acceleration in which a traveler nearly
instantly changes direction by 180 degrees, but does not change
his speed, relative to some inertial frame of reference.  (Most
commonly in our examples, turn arounds will be with respect to
the Earth-AC frame.)  "Inertial frame" -- any set of clocks,
rulers, and observers moving with a uniform speed in a fixed
direction.

CONSEQUENCES OF STANDARD (EINSTEIN) SPECIAL RELATIVITY (SSR): 
Gamma is about 7 for a speed v = 0.99 c.  When Sam reaches AC,
Sam will be about 7 months old, while Alice will be about 4 years
old.  If Sam turns around at AC and returns to Earth at the same
speed, he would be 14 months old upon his return, while Edward
would be 8 years old.  If Sam elected instead to continue his
original journey past AC, he would be 14 months old upon his
arrival at Beta Centauri (BC), taken as exactly 8 lightyears
(measured in the Earth-AC frame) from Earth and in the same
direction as AC, while Earth-synchronized clocks on BC would
register 8 years elapsed time.

POSTULATE #1:  Uniform accelerations in general (of which turn
arounds are a special case) can always be done in so short a time
and distance that they have negligible effect on the
instantaneous readings of clocks changing inertial frames. 
Although accelerations don't affect clock readings immediately,
they do produce a lasting change, the amount being a function of
the total speed change only.  This is manifested as a change in
the clock's rate, as judged by the clock's original frame; or as
a slippage of clock synchronization, as judged by the clock's new
frame.

     Justification:  Any uniform acceleration, A, is equivalent
to a gravitational field, GM/r^2, according to Einstein's
equivalence principle.  A velocity change of a clock from 0 to v
may therefore be accomplished by applying a steady acceleration
of A = GM/r^2 (where M is a nearby mass at distance r and G is
the
gravitational constant) for a short time t.  So v = A t. 
Moreover, general relativity tells us that the change a
gravitational field (and therefore an equivalent acceleration)
produces in a clock is given by the expression GM t/(r c^2),
where
GM/r is the potential of the nearby mass.  Therefore the clock
change is rv/c^2.  So one can always choose a distance r small
enough and a time t short enough to make the clock change
negligible.  This remains true no matter how many independent
acceleration steps are applied.  The net rate change of an
accelerated clock is given by its original rate divided by 
gamma, as judged by observers in the original frame.

POSTULATE #2:  When considering any two inertial frames of
reference, only the relative speed of the frames, but not the
direction of that speed, completely determines the relative clock
readings seen by each inertial frame for the other.

     Justification:  Speed v, but not direction, is contained in
the Lorentz factor.  By postulate #1, if a clock changes
direction but not speed through an acceleration, its rate as seen
by the other reference frame will be unchanged.  However, its
rate as viewed from its own original frame before the
acceleration will be changed because it changed speed with
respect to that frame.

POSTULATE #3:  A clock undergoing a continuing change of
direction at a uniform speed, such as would occur with circular
motion, can be thought of as undergoing a great many discrete
accelerations interspersed between short segments of uniform
linear motion.

     Justification:  In the limit as the number of linear
segments and discrete accelerations approaches infinity, the
accelerated clock may approach circular motion indefinitely
closely.

SSR COROLLARY #1:  As long as Sam stays at a fixed speed (e.g.,
0.99 c) relative to the Earth-AC frame at all times, then no
matter what path Sam takes (including changes of direction) or
for how long, and no matter where or when he compares his clock
with a local clock in the Earth-AC frame, the local Earth-AC
clock will read gamma (e.g., 7) times more elapsed time since Sam
passed Earth than Sam's clock will read.

     Justification:  When Sam reaches AC, he is 7 months old,
while Alice is 4 years old.  At any other point along the same
linear path, the ratio of comparative ages between a local
Earth-AC-frame observer and Sam would likewise be 7-to-1.  Using
Postulate #1, if at any point Sam performs a turn around (see
definition), when he gets back to Earth Edward's age will be 7
times Sam's age.  At any other point along the same linear return
path, the ratio of comparative ages between a local
Earth-AC-frame observer and Sam would likewise be 7-to-1.  In
general, for any path Sam takes in any direction with any number
of direction changes for any length of time, as long as his speed
relative to the Earth-AC frame remains fixed throughout, the
ratio of a local (to Sam) Earth-AC-frame observer's age to Sam's
age will be  .

SSR COROLLARY #2:  Sam could perform his entire 4-light-year
journey in a cyclotron on Earth right next to Edward, so that Sam
and Edward are continually within view of one another.  Using
Postulates #2 and #3 and SSR Corollary #1, both Sam and Edward
agree that Edward is always seven times older than Sam.  Sam
expects Edward's frame to age faster than his own.  Edward sees
Sam's frame aging faster, but sees Sam himself slipping
synchronization with respect to Sam's frame as he accelerates in
the cyclotron, with the net result that Sam appears to age
slower.

SSR COROLLARY #3:  Accelerations, turn arounds, and frame changes
are not necessarily a part of the explanation of why the
stay-at-home twin is older than the traveling twin in the
classical twins paradox problem.  Pointing to them may just
confuse the issue.

     Justification:  Using the types of accelerations described
in Postulate #1, and the definition of "turn around", and
considering frame changes that change the direction but not the
speed of the traveling twin, SSR Corollary #1 shows that none of
these actions directly affect the outcome of the comparison of
ages of co-located twins, either immediately before or after the
acceleration event occurs, or at any later time.  The relative
ages of the "moving" twin and a momentarily co-located
"non-moving" twin will differ by the factor gamma whether such
accelerations occur or not.

SSR COROLLARY #4:  Symmetrically, if Sam drags a long train of
clocks behind him, and if the Earth clock and all clocks in Sam's
frame are set to zero in Sam's frame when Sam first passes Earth,
then the particular clock in Sam's frame passing Earth at each
moment will always read gamma times as much elapsed time as the
Earth
clock.

     Justification:  Since Edward and Sam are equivalent
observers differing only by the frame they are in, the same
statements about clocks must be true of both.  Just as Sam always
sees a co-located clock in the Earth-AC frame read gamma times
higher
than his own, likewise Edward must always see a co-located clock
in Sam's frame read gamma times higher than his own clock. 
Indeed,
there is no need to confine this result to a train of clocks
behind Sam.  If Edward accelerates in such a way that his speed
remains 0.99 c with respect to Sam, and travels over any path for
any length of time at that relative speed, whenever and wherever
he checks a co-located clock in Sam's frame, that clock will read 
 times more elapsed time than his own clock since Sam first
passed Earth.

SSR COROLLARY #5:  If all the clocks in the train of clocks
behind Sam (as in #4) were synchronized while still in the
Earth-AC frame, then at a common time reading they are
identically accelerated into Sam's frame (along with Sam), then
those clocks will no longer be synchronized when they reach Sam's
frame.  If they are not then re-synchronized, the elapsed-time
readings of those clocks as they pass Earth will be a factor of  
less than the Earth clock's elapsed time readings.  Note that
observers accompanying those clocks have no option to
re-synchronize their ages.

     Justification:  Clocks in Sam's frame that were synchronized
in Sam's frame when Sam passed Earth will read gamma times higher
than Earth clocks as they pass Earth (SSR Corollary #4).  Clocks
in Sam's frame synchronized in the Earth frame when Sam passes
Earth will read gamma times lower than Earth clocks as they pass
Earth because the acceleration does not change their
instantaneous readings (Postulate #1), and their rate is made  
times slower than that of Earth clocks by the change of frame. 
(This is similar to Edward waiting 4 years, then jumping into
Sam's frame.  His age is unchanged in either frame at the moment
of that jump.)

SSR COROLLARY #6:  If Sam's frame chooses to re-synchronize its
clocks, symmetry is restored between Sam and Earth frames, and
each frame views single clocks in the other as slowed, and time
on the sequence of passing clocks in the other as "sped up" (due
to desynchronization).  If Sam's frame does not re-synchronize
its clocks, then Sam's frame will have slowed clocks (both remote
and local) compared to the Earth frame.

     Commentary:  The choice to resynchronize clocks or not
resynchronize clocks in a relatively moving frame is not
compelled.  If all clocks are synchronized, we arrive at the SSR
interpretation of spacetime.  Two clocks are synchronized in SSR
if a light beam making a round trip from one clock to the other
yields the same readings at the midpoint of the round trip for
one clock as at the instant of reflection at the other.

     Using the SSR definition for remote synchronization implies
that time in every relatively moving frame advances faster than
local time, even though clocks in that frame run slower.  That
leads directly to:

THE QUASAR PARADOX:  Suppose a quasar in a distant part of the
universe is formed shortly after the big bang with a true space
velocity of 0.99 c toward the Sun.  The expansion of space keeps
the quasar and the Sun apart over most of the life of the
universe, but the quasar will finally reach us and will fly by
the Sun this year.  Throughout the 14 Gy lifetime of the universe
(as measured in our frame), time in the quasar's frame will have
been advancing at a rate seven times faster than time in our
frame, and the quasar will have aged seven times slower than
aging in our frame.  So when the quasar flies by, its age will be
2 Gy in a frame nearly 100 Gy old, or seven times older than the
universe.  Both the quasar frame as observed by us, and the Earth
frame as observed from the quasar, will appear to be older than
the universe.

     GSR has no such conceptual difficulties.

     Note that the Einstein definition of synchronization is
impossible to perform if clocks separate at speeds faster than
light.  (This may happen, for example, in the big bang theory
because of the expansion of space, which may exceed the speed of
light in the early universe.)  Separation faster than light means
increasing distance at a rate of more than one astronomical unit
per 8.3 minutes in a chosen inertial frame -- something that is
well-defined, whether achievable or not.  The SSR definition of
synchronization becomes undefined for clocks moving apart faster
than light.

     Consider Sam's clocks as viewed from the Earth frame.  The
synchronizing light beam spends more than 99% of its round trip
time trying to overtake the lead clock, then less than 1% of its
time bouncing back.  So the Einstein definition of
synchronization is not only not compelled, it is also
anti-intuitive and leads directly to the SSR properties that seem
so unphysical despite their mathematical simplicity.

     If we assume that faster-than-light motion in forward time
is possible, we could instead adopt the viewpoint of a "meta
clock": one capable of communication with all other clocks at
nearly infinite velocity.  Then the clocks accelerated into Sam's
frame that appear unsynchronized to Sam really are still
synchronized, because they started out synchronized in the
(non-moving with respect to the meta clock) Earth frame.

     If the two postulates of SSR are worded so as to apply only
to communication with light or electromagnetic phenomena, but not
to gravity, then this alternate definition of synchronization
allows all of SSR to remain intact in an electromagnetic context
only.  This is identical to the "sound analogy" (Van Flandern
1993), in which observers in a sound universe derive all SSR
postulates and experimental results in a sound context only.

     6.  Distant simultaneity

 *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *  
*   *   *   *   *   *   *   *   *   *
SUMMARY: One of the major differences between the two variants of
special relativity is the slippage of clock synchronization that
must occur in SSR, but not in GSR.  Two possible tests for this
are described.  If SSR is taken too literally, then other
paradoxes arise, such as the Schroedinger Twin Cats Paradox.  One
of the twins orbiting a distant planet can apparently cause his
distant twin to die and be resurrected repeatedly.  The standard
twins paradox also points out that all relatively moving frames
in SSR are continually aging faster than one's own frame, even
though their clocks run slower.  In GSR, moving clocks are slowed
compared to non-moving ones, but this can be fully compensated by
a rate change.
 *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *  
*   *   *   *   *   *   *   *   *   *

     Let us assume for the sake of discussion that
faster-than-light motion in forward time is possible, and that
gravity propagates nearly instantaneously for all practical
purposes.  Then all clocks communicating by means of gravity
signals can synchronize, so all are equivalent.  We will refer to
any one such clock as a "gravity clock".  A practical example
might be measures of the maxima and minima in the gravitational
potential emanating from a binary pulsar.

GSR POSTULATE #1:  A gravity clock, by virtue of its
near-infinite propagation speed, can determine a preferred frame
of reference for the synchronization of all clocks.

GSR COROLLARY #1:  If two synchronized clocks are slowly
separated in a frame, and are then found to be no longer
synchronized according to light signals, the amount of that
desynchronization determines the speed of the frame relative to
the preferred frame.

     Note that entrained aether in the Earth's gravitational
field would make the non- rotating Earth a preferred frame for
purposes of laboratory experiments.  But that frame would be
found to be moving with respect to the Sun's frame, or the
galactic frame, if measures using light signals extended into
either of those frames.

     Two experiments that would clearly distinguish these two
possible definitions of synchronization, SSR's and GSR's, are now
possible:

  *  A spacecraft carrying an atomic clock that left the Earth's
gravitational sphere of influence would immediately begin showing
a "Sagnac effect" due to the Earth's orbital motion, according to
GSR.  SSR predicts no difference in the clock before and after it
leaves the Earth's gravity field after allowance is made for the
gravitational redshift effect predicted by general relativity.
  *  A one-way speed-of-light measurement on the rotating Earth
will have a shorter travel time moving east to west than vice
versa according to the most likely version of GSR; but should be
the same both ways according to SSR.

     By contrast, the SSR definition of remote simultaneity
implies that time itself is changed for a moving frame.  Using
the setup for Edward and Sam of the previous section, it scarcely
seems reasonable for Sam to regard inferences about the ages of
distant observers to be "real", even in his own frame.  If he
did, then assume that one of a set of twin Siamese cats
accompanies Sam from Earth to AC, and the other remains on Earth
with Edward.  Assume Edward's cat dies at age 2 years old.  This
would lead to:

THE SCHROEDINGER TWIN CATS PARADOX:  When Sam and his cat arrive
at AC, they could orbit the star at a speed of 0.99 c.  Then for
a while, each time they headed away from Earth in their orbit,
Edward and his cat back on Earth would be 1 month old in Sam's
frame.  And each time Sam and his cat headed toward Earth in
their orbit, Edward would again be 8 years old in Sam's frame,
with his cat long since buried.  Apparently, during each orbit of
Sam at AC, Edward's cat dies and is resurrected again.

     In like manner, Edward's cat would be simultaneously dead
for Alice on AC and alive for Sam passing AC, so that it's state
of health at the event of Sam passing AC would be indeterminate. 
This is similar to the famous Schroedinger's cat problem in
quantum mechanics.  Of course, the images from Earth confirming
the inferred life history of Edward's cat will not arrive until
some later time.

     I conclude that only local ages have physical meaning in
SSR, and inferences about distant ages and times must be
illusions of measurement.  This is similar to the expectation in
GSR, where the slowing of clocks is an effect on the clocks, not
on time.  In GSR, the clock in the moving frame could have its
rate adjusted, allowing it to remain consistent with its
non-moving counterparts.  A similar adjustment is routinely made
to atomic clocks prior to launch aboard Global Positioning System
(GPS) satellites, so that when in orbit, the clocks will run at
the same average rate as ground clocks.

     In SSR, if all frames are synchronized at one point in space
and time, then with or without reference frame changes, Edward
and Sam find themselves younger than the other-framers they meet
anywhere at any time.  This relative aging difference is partly
due to a difference in clock rates, and partly due to the
slippage in clock synchronization that accompanies motion through
space.  We cannot distinguish in a unique way how much of the
difference is due to clock rate and how much to cumulative
synchronization difference, since that is a frame-dependent
judgment.

     Nothing Edward or Sam can do to themselves can cause them to
become older than, or even to stay the same age as, the
other-framers they meet.  But if either accelerates, his clocks
will immediately change rates, and he will immediately begin
slipping synchronization at a different rate.  He will become
relatively younger or older than the other-framers he then meets
compared to what he would have been if he had not accelerated. 
If he returns to his original frame by means of an equal
acceleration in the opposite direction, he resumes aging at the
same rate as his original companions, but locks in a clock (and
aging) slippage between himself and them.  He must always return
younger than his former companions.

     The amounts of clock slippage, and hence the relative rates
of aging between any two frames, are functions of the relative
velocity and the time over which that velocity is maintained.  If
someone accelerates to change frames, he begins slipping
synchronization at the new rate appropriate for his new frame.

     I conclude that frame changes *as such* have nothing to do
with determining who will be younger and who older, since all
frames age at different relative rates, and everyone is always
getting younger compared to those in other frames.  Aging
differences are purely a function of how much time is spent in
each frame, not whether or how often a frame was changed.

     To any observer in an inertial frame (e.g., Edward on
Earth), all observers in all other frames age more slowly.  But
it is also true that Edward sees local time in all other frames
advances more rapidly than his own time, so that Edward also
appears to age more slowly from the perspective of other frames. 
When Sam returns to Earth, he expects to find himself younger
than anyone he encounters in Edward's frame.  Symmetrically,
Edward finds himself younger than passing clocks in Sam's
original frame.  Since Sam is no longer in his original frame,
but has slipped synchronization with it, Edward is not surprised
that Sam is now younger upon his return.

     7.  Conclusions

 *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *  
*   *   *   *   *   *   *   *   *   *
SUMMARY: Meta clocks using variations of gravitational force, for
example from a binary pulsar, would provide a nearly
instantaneous time scale available to all observers, unaffected
by their state of motion.  An analogy with a universe of sound
can explain why the universe behaves as it does.  For example,
clocks using electromagnetic signals slow because their electrons
take longer to complete cycles in a moving medium than in a
stationary one.  Normal Lorentz transformations would describe
the behavior of clocks and rulers in a moving frame, and inverse
Lorentz transformations would describe the non-moving frame as
seen from the moving one.  This change lifts the prohibition on
faster-than-light communication in forward time, leading to a new
understanding of relativity that promises considerable new
insight into how the universe operates.
 *   *   *   *   *   *   *   *   *   *   *   *   *   *   *   *  
*   *   *   *   *   *   *   *   *   *

     Why does the universe behave as it does?  One possible
comprehensive model, derived from first principles, is the Meta
Model (Van Flandern 1993).  It deduces the existence of a "meta
time" against which all observers can synchronize regardless of
their motion.  Regular variations in gravitational fields, as
from a binary pulsar, could be used to set up clocks and a time
scale independent of any frame of reference or the motion of
observers.  We call this "meta time" as measured by "meta
clocks."

     Using such meta clocks, any observer could determine his
state of motion with respect to the medium (whether "spacetime"
or aether) in which light propagates.  This is not as
unrelativistic as it first appears.  Astronomers are already
accustomed to the idea that any observer can determine his
"absolute" motion with respect to the microwave radiation of the
universe.  But that is still a relative velocity of one frame
with respect to another.  By the same token, velocities
determined with respect to local spacetime or aether remain
relative velocities in the same sense.

     So any two observers might come together and synchronize
their clocks, then separate slowly.  Their synchronization will
be maintained with respect to meta clocks.  But if light signals
show that the two are no longer synchronized when separated, they
may safely conclude that they are moving with respect to local
spacetime or aether.

     Why do clocks slow and lengths contract?  The Meta Model
answers with the "sound analogy".  Consider an alternate universe
containing "atoms" each consisting of a "nucleus" and "electrons"
in orbit.  Now let a region of this universe be filled with air,
and let the electrons of our hypothetical atoms propagate around
their nuclei in the manner of waves, just as sound propagates
through air.

     Suppose that an airplane composed of these alternate "sound"
atoms flies through the air by means of propellers.  Since
propellers push against the air, the speed of the airplane is
limited to the speed of sound.  As ever more energy is applied to
make the propellers spin faster, the airplane's speed will
approach the speed of sound ever closer; but it can never quite
reach it.  To a physicist in this alternate universe, it appears
as if the airplane's inertial mass is increasing as its velocity
increases.

     As the airplane's velocity approaches the speed of sound,
the sound waves emanating from it in the direction of motion get
bunched up closer and closer, because their velocity relative to
the airplane gets less and less.  For precisely the same reason,
the orbits of the electrons in the airplane get compressed in the
direction of motion, because they, too, propagate like sound
waves in this special universe.  A physicist in this universe
observing the airplane from a stationary vantage point would
conclude that distances contract in the direction of motion as
the plane's velocity approaches the speed of sound, because all
rulers on the plane are made of atoms with electron orbits
compressed in the direction of motion.

     Moreover, if the matter is judged by a stationary observer,
the electrons will take more time to complete their orbits,
because the round trip time for any particle moving upstream and
downstream in a moving current is greater than the round trip
time in a stationary medium.  A physicist in this universe would
conclude that time measured by clocks consisting of such slowed
electrons had "dilated".  Even biological systems consisting of
slowed atoms would appear to age more slowly.

     The contractions of the units of length and time are exactly
analogous in the alternate universe with respect to the speed of
sound, to what they are in the real universe with respect to the
speed of light.  So it follows that all observers in the
alternate universe performing any of the ten experiments on which
special relativity rests, or trying to measure the speed of
sound, will get the same constant answer regardless of their
state of motion with respect to the air medium, just as that
happens with light in the real universe.  In fact, all
experiments performed in the two universes would be analogous. 
The situation is, of course, reciprocal for "moving" and
"stationary" observers:  Each "sees" the clocks of the other slow
down and distances contract as long as each uses only waves
traveling at the speed of sound to measure such effects.  If
physicists in the universe of sound waves were to discover light,
their problems with synchronization of remote clocks and events
would be solved, because they could define clocks apparently
unaffected by motion at ordinary speeds through the air medium.

     This point is important, so let me state it differently. 
From our perspective, being able to see the two different frames
with "insta-vision", their situation does not appear to be
reciprocal.  But if we were limited to using propagating sound
waves to measure lengths, time, positions, and speeds, all wave
velocities would appear to be the speed of sound.  And all
lengths in relatively-moving frames would appear contracted, and
time would appear slowed, no matter which of the two frames we
were in.

     In our real universe, the Meta Model tells us that gravity
propagates much faster than light, and is therefore suitable for
performing remote synchronization.  Real electrons would take
longer and longer to complete their cycles as bodies containing
them approached the speed of light.  At the speed of light,
electrons could never complete a single cycle because they would
spend all their time keeping up with the nucleus, but could never
get around it.  At faster-than-light (ftl) speeds, electrons
would be forced to reverse the sense of their orbital motions. 
But from the perspective of a meta-physicist with meta clocks,
electromagnetic clocks moving ftl would appear to run backwards
while the rest of the universe continued on in forward "meta
time".  So the relativistic prohibition against ftl communication
can be seen to apply to communication by means of electromagnetic
signals only.

     In the twins paradox, neither twin can tell which one is
moving and which is at rest using electromagnetic signals alone. 
But by using faster-than-light gravitational signals, they can
tell which is which.  They will conclude that the twin moving
faster through the local medium in which electromagnetic waves
propagate will age less.  Time and position in the moving frame
is related to the stationary frame by the Lorentz
transformations.  When using meta clocks, the moving frame would
need to apply an inverse Lorentz transformation to derive time
interval and length in the stationary frame.

     We conclude with the words of Roger Penrose (1989):  "The
construction of a fully objective theory of state-vector
reduction which is consistent with the spirit of relativity is a
profound challenge, since `simultaneity' is a concept which is
foreign to relativity, being dependent upon the motion of some
observer.  It is my opinion that our present picture of physical
reality, particularly in relation to the nature of 'time,' is due
for a grand shakeup -- even greater, perhaps, than that which has
already been provided by present-day relativity and quantum
mechanics."  [Thanks to Paul Kramarchyk for pointng out this
quote.]

     References

Hatch, R.R. (1992), "Escape from Einstein", Kneat Kompany,
Wilmington, CA.

Hayden, H.C. (1992), "Rotating Mossbauer experiments and the
speed of light", Galilean Electrodynamics 3, 114-117.

Hayden, H.C. (1993), "Stellar aberration", Galilean
Electrodynamics 4, 89-92.

Kacser, C. (1991), "Relativity, Special Theory", In "Encyclopedia
of Physics", R.G. Lerner and G.L. Trigg, VCH Publishers, New
York, pp. 1052-1058.

Penrose, R. (1989), "The Emperor's New Mind", Oxford University
Press, New York, p. 371.

Rosser, W.G.V. (1964), "An Introduction to the Theory of
Relativity", Butterworth's, London.

Van Flandern, T. (1993), "Dark Matter, Missing Planets and New
Comets", North Atlantic Books, Berkeley.