*Einstein’s
contrived concepts of ‘simultaneity,’ ‘common time’ and ‘proper time’ were
based upon his concept of a ‘synchronous mathematical time for each inertial
system,’ which empirically does not exist.
Thus, Einstein’s ‘common time’ and ‘proper time,’ artificially results
in the same time for all spatially separated events and observers with
synchronized clocks situated at different locations on an inertial system of
coordinates or frame of reference. These
spurious concepts were applied by Einstein to distort measurements throughout
his Special Theory in order to artificially eliminate time intervals, space
intervals and relative motions, all in a failed attempt to achieve his primary
relativistic goal of velocity dependent co-variant magnitudes for all physical
phenomena, including the velocity of light at c.*

During the middle of May 1905, Einstein had a long discussion with his friend and colleague, Michele Besso, about the ‘difficulties’ surrounding the velocity of light.[1] (Folsing, p. 155) The next day Einstein stated to Besso concerning such discussion:

“Thank you. I’ve completely solved the problem. An __analysis of the concept of time__ was
my solution. Time cannot be __absolutely__
defined, and there is an inseparable relation between time and [the] signal
velocity.”[2] (*Id*.

Six weeks after
his meeting with Besso, Einstein finished writing his Special Theory treatise
and it was received by the publisher on June 30, 1905. (*Id*., p. 156)

During such long discussion with Besso, Einstein must
have come to grips with the fact that the real culprit that was causing the
‘difficulties’ of *c* + v and *c* – v was the __relative motion__
between the stationary embankment and the carriage moving linearly away at
v. The evening after such discussion
Einstein must have realized that if he could mathematically negate the __time
interval__ (t') and the __space interval__ (vt) described by the Galilean
transformations, then he could __eliminate the relative motion__ between the
two inertial reference frames and with it the troublesome classical addition of
velocities (*c* ± v) would also be eliminated.
This scenario could provide a solution for Einstein’s mathematical
‘difficulties,’ because then the velocity of light could algebraically remain a
constant magnitude of *c* for all inertial frames and observers on such
frame. It turns out that his Special
Theory, which he wrote during the next six weeks, mathematically accomplished
this artificial solution, as we shall soon see in Chapters 25 through 29.

Section 1 of Einstein’s 1905 Special Theory was
primarily devoted to: 1) his definition
of a synchronous mathematical time on a stationary system of Cartesian
coordinates (frame of reference), and 2)
his description of the constant velocity of light at *c* on such __finite
stationary__ system. In the process,
Einstein defined an absolute ‘common time’ for all spatially separated
observers with synchronous clocks situated on every inertial frame of
reference. By this method, Einstein
artificially did away with __time intervals__ between events and coordinate
measurers (inertial observers) on such frame.
These spurious concepts of time would later distort all of Einstein’s
coordinate measurements, because such distortions (i.e. contractions of
distance and expansions of time) were necessary in order to construct his
relativistic concepts and for his Special Theory as a whole to appear
plausible.

**A.
Time and Simultaneity**

What do we normally mean by the word ‘time?’ According to the writings of Ernst Mach in
the late 19^{th} century, ‘time’ as an independent reality does not
exist. In other words, any concept of
time is only an arbitrary convention or definition of convenience that serves
to relate a sequence of events for an observer.
Poincaré agreed in 1898. (Jammer,
2006, pp. 96, 100, 101)

The normal concept of ‘time’ has at least three distinct meanings: ‘instant,’ ‘interval’ and ‘eternity:’

1. An ‘instant’ can be defined as the __moment__
in the ‘eternity’ of the universe that any light ray is emitted anywhere in the
universe (a ‘light event’), or the moment that such light event is __later__
perceived by a distant human observer.[3]

2. An ‘interval’ of time can then be defined as the duration between two light events or two instants.

3. We define ‘eternity’ as the infinite duration and continuance of existence of things in the universe.

A clock is merely a convenient convention which
humans use to identify an ‘instant,’ or to measure an ‘interval’ of time. The algebraic symbol (t) can either be used
to mean an instant (t) or an interval (such as *c*t or vt), but t_{2}
– t_{1} only algebraically describes an interval. (see Dingle, 1972, pp. 133 – 134) An ‘event’ is mathematically defined as “a
point in __space__ and a point in __time__ together.” [4]
(Rohrlich, p. 5)

As we proceed through this and other chapters, it is
important to distinguish the concepts of ‘simultaneity,’ ‘sequence’ and
‘causality’ (cause and effect) from the above concepts of ‘time.’ ‘Simultaneous’ normally means ‘at the same
time’[5]
(Goldberg, p. 113), or as Poincaré defined it:
when the order of two events may be interchanged.[6] (Poincaré, *Measurement of Time*, 1898
[Miller, p. 174]) “As long as the two
events [occur] at the same place there is no problem.” (Goldberg, p. 110) But when “two physical [events occur] far
from one another,” the simultaneity of their times and the order (‘sequence’)
of their causation or occurrence may not be obvious, and it may require
considerable analysis and explanation.[7] (see Poincaré, 1898 [Miller, p. 174])

It is also very important to realize and remember
that everything we discuss in this chapter (including Einstein’s definitions of
‘simultaneity’ and ‘time’) relates to Einstein’s __contrived__ system of
measurement. He needed his __specific__
system of measurement (with its specific, arbitrary and artificial definitions)
in order to construct his Special Theory, its strange relativistic concepts and
its bizarre mathematical consequences.
All of this for one primary, unnecessary and impossible purpose: to mathematically require that the velocity
of light is *measured* by coordinates to be *c* simultaneously by
every inertial observer in every inertial frame of reference. (Chapters 21E, 21F and 24C)

In 1905, in Section 1 of his Special Theory, Einstein attempted to define ‘time’ in terms of ‘simultaneity.’ However, in the process he defined, illustrated and commingled several very different concepts, including the following:

1. ‘__Actual Observed Distant Simultaneity__’
is the perception that two light events occurred at the same instant by a human
observer who is at the position of the two light events or who is equidistant
from them.[8] (see Figure 25.1A)

2. ‘__Apparent Distant Simultaneity__’ occurs
where two distant light events occur at different instants, but they are
perceived by a local human observer to have occurred simultaneously.[9] (see Figure 25.1B)

3. ‘__Absolute Mathematical Distant
Simultaneity__’ is Einstein’s absolute and generally meaningless definition
for the coordinate measurement of the same instant that two or more light
events occur at different places (usually on a single frame of reference),
where synchronized “clocks at the respective places record the same time for
[such events].”[10] (Resnick, 1968, p. 52; see Figure 25.1C)

In 1898, Poincaré referred to the concept of ‘actual observed distant simultaneity’ as the psychological or ‘conscious’ simultaneity of a human observer. (Jammer, 2006, p. 100) On the other hand, Einstein’s definition of ‘absolute mathematical distant simultaneity’ had nothing to do with conscious or actual perceived simultaneity. It only dealt with light events that abstractly occur at the same instant anywhere in the Cosmos, synchronized clocks at such events, inertial reference frames, coordinates and coordinate measurers (mis-characterized as ‘observers’). (see Figure 25.1C) In other words, Einstein’s coordinate definition of ‘absolute mathematical distant simultaneity’ only deals with the same time or instant in the abstract, rather than the normal concept of the instant of visual perception by a human observer.[11]

Very importantly, it must be realized by the reader at this early juncture that Einstein’s various misleading concepts of simultaneity, of synchronization of clocks, and of time, only served to help him mathematically construct his contrived Special Theory, and to sufficiently confuse the reader into believing that his relativistic concepts might have some empirical merit. However, such concepts have no real meaning for a human observer nor for empirical physics.

Let us now begin to discuss: 1) whether any concept of simultaneity is a reasonable definition of ‘time’ or even a logical or necessary benchmark from which to determine a sequence of events; 2) whether any form of simultaneity has any meaning for a human observer; and 3) why Einstein needed his mathematical or coordinate definition of simultaneity in order to construct his Special Theory.

**B.
Apparent Distant Simultaneity and Actual Observed Distant Simultaneity**

By 1905, Einstein and the entire scientific community
knew that there was a distance/time interval delay for the light signal
transmitting at the finite velocity of 300,000 km/s (*c*) from the distant
position of emission of a light ray to the position of a local observer’s
perception of such light ray. This had
been demonstrated by Römer in 1676 and confirmed by Bradley in 1728. [12] (see Figures 6.5, 6.6 and 7.5B) Based upon this fact, Einstein is reputed to
have stated in early 1905: “Time cannot
be absolutely defined, and there is an __inseparable relation between time and
the light signal__.”[13]
(see Einstein,

For example, each morning sunrise is
an empirical light event for every observer on Earth. But it takes a time interval of 8-1/3 minutes
for light emitted by the Sun to propagate the 93 million miles of distance from
the Sun to the Earth at *c* (300,000 km/s).[14] So the Sun __physically__ rises well above
the horizon of the Earth 8-1/3 minutes before the light emitted by the Sun __begins__
to reach our eyes and we on Earth __begin__ to observe the light event of
sunrise. (Figure 25.2A) Thus, no local Earth time can be assigned by
an observer on Earth to such sunrise event, nor to the instant of such distant
emission of light by the Sun, until after this distance/time interval of delay
is factored into such computation.[15]
Not until well after this 8-1/3 minute distance/time interval delay of *c*
transpires, can we fully perceive and understand the sunrise event.[16] (Figure 25.2B)

It is obvious from the above example that the observer on Earth who is
watching the event of a sunrise does not observe the light emitted by the Sun __simultaneously__
with its actual emission 93 million miles away.
Nevertheless, such observer perceives and usually __intuitively assumes__
that such distant light emission and his local observation thereof are
simultaneous events. This is a good
example of ‘apparent distant simultaneity.’
(Figure 25.1B)

Early in Section 1 of his Special Theory, Einstein correctly described
this __universal misperception__ of ‘apparent distant simultaneity,’ with
the following example:

“We have to
take into account that all our __judgments__ in which time plays a part are
always judgments of simultaneous events.[17] If, for instance, I say, ‘That train arrives
here at 7 o’clock,’ I mean something like this:
‘The __pointing of the small hand of my watch to 7__ and the arrival
of the train are simultaneous events.” [18] (Einstein, 1905d [Dover, 1952, p. 39])

Thus where
Einstein and his watch are in the __immediate vicinity__ of a light event
(the arrival of the train) so that the time indicated by the __positions of
the hands of his watch__ and the slightly distant light event (the arrival of
the train) are capable of __almost__ __simultaneous observation__,[19]
and all objects and observers are stationary (relatively at rest), then
Einstein would assert that both events (the positions of the hands on his watch
striking seven and the train’s arrival) are almost actually observed
simultaneous events for the observer with the watch.[20] (see Figures 25.1A and 25.3A) In Special Relativity the above scenario (observing
two events at the same instant) is sometimes referred to as ‘local
simultaneity.’ (see Jammer, 2006, p.
120)

But, actually, the above events only occurred at __approximately__ the
same instant in time as perceived and evaluated by each human observer. In a footnote, Einstein acknowledged that he
chose to ignore the “__inexactitude__ that lurks in the concept of
simultaneity of two events at __approximately__ the same place.” (Einstein, 1905d [Dover, 1952, p. 39,
footnote]) This inexactitude occurs
because of the distance/time interval delay of the light signal with a finite
speed of *c* (300,000 km/s) from the position of the waiting observer
(Einstein) and his clock relative to the position of the __slightly__
distant arriving train.[21]
(see Figure 25.3A) The fact that the clock of the waiting
observer on the platform and the clock of the engineer on the train may be __synchronized__
to exactly the same mathematical time does not make the train’s arrival and the
passenger’s clock pointing to seven empirically or consciously simultaneous
events for either observer.

From the above discussion, one begins to realize that Einstein was going
to co-mingle several very different concepts of simultaneity in his Special
Theory.[22] For example, the ‘mathematical absolute simultaneity’
of any two distant light events only refers to the abstract __instant__ of
their occurrence, regardless of any observation by a human observer. Whereas, the empirical evaluation by a human
observer as to whether two distant light events are actually or absolutely simultaneous
must also consider the __time interval__ from each distant occurrence to
such observer’s eyes. On the other hand,
an observer’s evaluation that a nearby light event and a distant light event
are actually simultaneous events is only an __illusionary misassumption__ of
‘apparent distant simultaneity’ that fails to consider the time interval for
light to propagate from each light event to such observer’s eyes.[23]

Uncountable light events occur every day at the same instant on Earth and throughout the universe. Such absolute simultaneity can have meaning where two human observers are in very close proximity, such as where they simultaneously kiss each other or shake hands. But for the most part there is no meaning for any human observer with respect to such absolute distant simultaneity. In the real world, it is rare for observed distant events to occur simultaneously with any meaning for human observers. It is even more unusual for distant simultaneous events (that could have meaning for humans) to have their actual distant simultaneity measured with precision by any human observer. For example, it is rare indeed for a horse race to end in a dead heat as measured by a judge at the finish line, or for two equidistant supernovae to be observed and measured to have occurred at exactly the same instant.[24] Except for timed events and certain laboratory or technical experiments, the concept of absolute simultaneity (in any form) is hardly a useful concept for physics, or a reliable benchmark from which to judge the local time for the instant of a distant light event or the sequence of any light events.[25]

Why then did Einstein
choose the symmetrical concept of ‘simultaneous events’ as the benchmark for
his definition of ‘time’?[26] Resnick claimed that Einstein was attempting
to create an unambiguous universal time scale, because the illusion of apparent
distant simultaneity resulted in an invalid absolute time scale (t = t') for
the measurement of all events. In other
words: “That the same time scale [t' =
t] applied to all inertial frames of reference was a basic [false] premise of
Newtonian mechanics.”[27] (Resnick, 1968, p. 50) Resnick also inferred that Einstein
synchronized the clocks in a single frame of reference so that he could create
an __unambiguous__ __time scale__ in that frame.[28] (*Id*.*Id*., p. 50), because actual __simultaneity was a relative concept__.[30] (*Id*., pp. 53, 55)

Contrary
to Resnick’s dubious rationalizations and attempted justifications, the real
reasons that Einstein chose simultaneity as the basis for his definition of
time and for his synchronization of clocks on each inertial reference frame had
nothing to do with simultaneity *per se*
and very little to do with any time scale.
In reality, Einstein needed his concept of ‘absolute mathematical
distant simultaneity’ in order to theoretically create an artificial ‘common
time’ or a ‘simultaneous mathematical time’ for all spatially separated coordinate
points or coordinate measurers with synchronized clocks on any inertial frame,
for two basic reasons that were fundamental to his Special Theory. 1) In
order to artificially eliminate __time intervals__ on every inertial
coordinate system (reference frame) moving at v so that he could claim that the
velocity of light had the same temporal coordinate measurement of *c* for
every spatially separated observer on each inertial reference frame (instead of
*c* – v or *c* + v);[31]
and 2) as a stationary benchmark for time
on one inertial reference frame so that observers with differently synchronized
clocks on different inertial reference frames (coordinate systems) with __different
relative velocities__ would have asymmetrical and ‘non-simultaneous’
coordinate measurements for the time of a light event, and out-of-sync and
‘non-simultaneous’ coordinate measurements for the distance (length) of an
object, when measured between such reference frames.

These distorted
coordinate measurements __between__ different reference frames were
necessary for Einstein’s asymmetrical concepts of the ‘Relativity of
Simultaneity’ and the ‘Relativity of Length.’
(see Chapter 26) These two
asymmetrical and distorted concepts would then become the justification for
Einstein’s adoption of the meaningless Lorentz transformation equations, which
were the heart of his Special Theory. (see
Chapter 27) The Lorentz transformations
in turn mathematically eliminated time intervals (t') and space intervals (vt)
of different inertial reference frames, and thus their relative motions, so
that the velocity of light could be simultaneously and algebraically covariant
(a constant *c*) for all inertial observers.

If Einstein had applied
the normal empirical process for determining the local time of a distant light
event for a local human observer, which we have previously described,[32]
there would have been: 1) no need for
Einstein’s concepts of simultaneity, synchronous clocks, or common time, 2) no
coordinate distortions between reference frames, 3) no concepts of the ‘Relativity of Simultaneity’ or the ‘Relativity
of Distance,’ 4) no Lorentz
transformation equations, 5) no absolute
(co-variant) propagation velocity of a light ray at *c* simultaneously for
all inertial observers, and thus 6) no
Special Theory of Relativity.’ It is
just that simple.

It should begin to become obvious to the reader that Einstein’s strategy
for his Special Theory was to assert one dubious concept (absolute mathematical
distant simultaneity), that would rationalize a second artificial concept
(mathematical distant simultaneity of synchronized clocks), that would support
another invalid *ad hoc* concept (the Relativity of Simultaneity), that
would justify another meaningless *ad hoc* concept (Lorentz
transformations), that would mathematically confirm another impossible *ad
hoc* concept (his absolute and simultaneous co-variant propagation velocity
of light at *c* for all inertial observers), that would …well you get the
idea. However, since this relativistic ‘house
of cards’ (see Figure 1.1)
was not only based on many false premises and other illogical false assertions,
but was also *ad hoc* and unnecessary, it was inevitable that it would
ultimately fall.[33]

**C. How did Einstein contrive his artificial and
absolute coordinate definitions of absolute mathematical distant simultaneity, synchronous
or simultaneous mathematical time, and the common time or the proper time of an
inertial reference frame?**

First let us examine how Einstein constructed his mathematical
‘Definition of Simultaneity’ in § 1 of his 1905 Special Theory.[34] Einstein initially referred to an inertial
frame of reference as a “system of coordinates in which the equations of
Newtonian mechanics hold good…to the first approximation.”[35] (Einstein, 1905d [Dover, 1952, p. 38]) Einstein called this reference frame the
‘stationary system’ or the ‘system at rest.’
It was where observers (measurers), their clocks, and the body or point
to be measured by Euclidean geometry, Cartesian coordinates and rigid rods were
all relatively stationary in the same inertial frame of reference.[36] (*Id*.

“If we wish to
describe the *motion* of a material point, we give the __values of its
co-ordinates as functions of the time__.”[37] (*Id*., pp. 38 – 39)

Thereafter Einstein defined “a time exclusively for the place where [a
clock] is located."[38] (*Id*., p. 39) For example, if a light event (such as a
flash of lightening) occurs at exactly the same location as observer A and her
clock, then Einstein asserted that the time of the light event for observer A
was indicated by the observed positions of the hands on her clock. That is to say, the __clock time__
indicated by the hands of her clock and the flash of lightning were __locally
observed__ to be simultaneous events for observer A.[39] (see Figure 25.4A) But, asked Einstein, what if observer A had
“to evaluate the times of events occurring at places remote from [her
clock]?” (*Id*.

When the local observer has “to evaluate the times of events occurring at
places remote from” his or her clock, then the distance/time interval delay of *c*
becomes a factor in relating a local time of observation to the instant that
such distant light event occurred. As
Einstein then pointed out, where lightening strikes at two distant locations (A
and B) on a stationary railway embankment, we can establish an “A time” and a
“B time” by the above method (vis. proximity of each lightning strike to each
observer, the time indicated by the hands of each observer’s clock, and the local
observations of the instant of such light events by observers located at A and
at B). But, cautioned Einstein, “we have
not defined a common ‘time’ for A and B.” [40]
(Einstein,
1905d [Dover, 1952, pp. 39, 40])

Why did Einstein even want to define a common time for A and B? This common or synchronous time for two spatially separated human observers would be the same as the common or synchronous time contained in the Galilean transformation equations (t' = t). It would be meaningless for either human observer as an empirical method to determine the local time for a distant light event on the other frame. It would also result in the same concept as the universal absolute ‘now’ time contained in Newton’s ‘absolute time,’ which Einstein correctly asserted was invalid for precise measurements.

Nevertheless, Einstein then attempted to define a ‘common time’ for
spatially separated observers A and B in such ‘stationary system.’ But first, asserted Einstein, we must
“establish __by definition__ that the ‘time’ required by light to travel
from A to B equals the ‘time’ it requires to travel from B to A.” (*Id.*, p. 40) “By __definition__,” Einstein meant that
he would have to assume: 1) that space
was isotropic and homogeneous (vis., the same in all directions and
everywhere), 2) that the velocity of
light was constant in all directions, and
3) that the geometry of space was Euclidean.[41] (see Miller, pp. 181, 183 – 184)

Einstein then theoretically sent a light ray emitted from A at clock time
t_{A} which propagated towards B and then reflected from B at clock time
t_{B} and propagated back towards A and arrived at A again at clock time
t'_{A}.* * (see Figure 25.5A) In Einstein’s own words:

“Let a ray of
light start at the time ‘A time’ *t _{A}* from A towards B, let it
at the ‘B time’

Einstein then claimed that (in accordance with his definitions) “the two
clocks synchronize if t_{B} – t_{A} = t'_{A} – t_{B}.”[42] (*Id*.*Id*.

According to Resnick, Einstein’s 1905 procedure for synchronizing distant clocks depended upon the following additional requirements:

1. There must be a “measured distance [L] between the clocks…”

2. There
must be an agreed upon procedure between observers “that A will turn on his
light source when his clock reads *t = 0* and observer B will set his
clock to *t = L/c* the instant he receives the signal.” [45] (Resnick, 1968, p. 52)

Neither
Einstein’s synchrony equations nor his equation in § 1 for the to and fro
velocity of light at *c* in a
stationary system (2AB/t'_{A} – t_{A} = *c*) tells us the value of *c*
nor the distance of A to B.[46] (see Figure 25.5A) However, we can now precisely measure these
values, i.e. by laser beams sent from the Earth to the Moon and back, even
without a clock and a man on the Moon to help us.

Why did Einstein define
the synchronization of two spatially separated identical clocks by an __algebraic
equation__, where the clock time t_{B} minus the clock time t_{A}
(one time interval of light propagation) __equals__ the clock time t'_{A}
minus the clock time t_{B} (another time interval of light
propagation)? He had already established
by __definition__ that such two time intervals were equal. Also, why did he define equal time intervals
in terms of a synchronous clock time at each point (light event)? The answer is because Einstein needed to
define time intervals in this __abstract and imprecise__ manner in order to attempt
to demonstrate his concept of the ‘Relativity of Simultaneity’ in Section 2 of his
Special Theory. (see our Chapter 26A)

Toward the end of § 1, Einstein
claimed that each distant light event (at A or at B) was now “simultaneous or
synchronous” for both spatially separated observers (A and B) who shared a __common
synchronous time__ on the same frame of reference. In Einstein’s own words:

“Thus with the
help of certain imaginary physical experiments we have __settled__ what is
to be understood by synchronous stationary clocks __located at different
places__, and have evidently obtained __a definition of ‘simultaneous__,’
or ‘synchronous,’ and of ‘time.’ The
‘time’ of an event is that which is given simultaneously with the event by a
stationary clock located at the place of the event,[47]
this clock being synchronous, and indeed __synchronous for all time
determinations__, with a specified stationary clock.”[48] (Einstein, 1905d [Dover, 1952, p. 40])

But we must ask: How can the ‘time’ of each sequential light
event (emission, reflection and receipt) in Einstein’s above thought experiment
(where t_{B} – t_{A} = t'_{A} – t_{B}) be both
synchronous and/or simultaneous for each observer, A and B? [49]
We only discover the answer to this clever paradox when we read Einstein’s 1916
book, *Relativity*. By a ‘__simultaneous__’
time of two distant sequential events, Einstein meant that the ‘position of the
pointers’ (hands) of each clock (A and B) are simultaneously pointing to the
same number on the face of each spatially separated clock when the instant of
each spatially separated event is determined.[50] (see Einstein, *Relativity*, p. 28) He did
not mean that the instant of occurrence of such spatially separated events was
judged to be simultaneous by a distant observer. Now we begin to understand why Einstein chose
the reading of __clock times__ as his definition or convention for the determination
of the ‘time’ (instant) of an event.[51] Einstein’s rationale for the reading of the
positions of hands of a clock was: “in
this manner a time-value is associated with every event which is essentially __capable
of observation__.” (*Id*.

Jammer further explained the above ambiguous quotation by Einstein concerning a ‘synchronous time’ and a ‘simultaneous time’:

“The notions of
simultaneity and of clock synchronization are intimately related, because
spatially separated events are defined as simultaneous if and only if
synchronized clocks at the locations of these events indicate the same readings
when the events occur. Hence __every
definition of clock synchronization is a definition of simultaneity and vice
versa__.” (Jammer, 2006, p. 120)

What Einstein really defined and settled with his definition of
simultaneous and synchronism is that in his theoretical system of measurement
every spatially separated measurer at every point on a coordinate system
(inertial reference frame) measures with his synchronous clock __the same
mathematical__ ‘synchronous time,’ ‘simultaneous time’ and ‘common time’ for
every spatially separated event on such frame.[52] Einstein made these facts very clear when (at
the end of Section 1) he referred to these times as the “time of the [entire]
stationary system” (frame of reference).
(Einstein, 1905d [Dover, 1952, p. 40])
Einstein also reiterated this concept in 1916:

“It is clear
that this definition [of ‘simultaneity’] can be used to give __an exact
meaning__ not only to two events, but __to as many events as we care to
choose__, and __independently of the positions of the scenes of the events__
with respect to the body of reference (here the railway embankment).[53] We are thus led also to a __definition of
‘time__’ in physics.”[54] (Einstein, *Relativity*, p. 27)

When we strip away all of Einstein’s “imaginary physical experiments,” his arbitrary and misleading definitions, axioms, and conventions, and his dubious analogies and rationalizations, we discover that he has invented at least five more dubious variations of his ‘absolute mathematical distant simultaneity’ concept. Such variations may be described as follows:

1. __Synchronous
clocks__ that simultaneously show the same clock time at spatially separated
coordinate points.[55]

2. The ‘__common
coordinate time__’ or ‘mathematical time’ for all spatially separated points
on a coordinate system (frame of reference).

3. The ‘__common
proper time__’ for all events occurring on an inertial reference frame as
indicated by any observer’s synchronous clock time.

4. A ‘__coordinate
time interval__’ as indicated by different coordinate clock times of
spatially separated synchronous clocks, and algebraically described as t_{2}
– t_{1}.[56]

5. The __equivalence__
of the terms ‘synchronous’ and ‘simultaneous.’

All of the above concepts and their variations may be meaningful for mathematicians, but they are completely meaningless for human observers and for empirical physics. For example:

A. The absolute mathematical simultaneity of distant light events has no meaning for a human observer, unless he can perceive such distant occurrences and understand the significance of their local times. Remember our examples of the dead heat horse race and the simultaneous supernovae.

B. Synchronous clocks cannot help a human observer to understand the local time of a distant light event, nor the time interval of light propagation involved. Rather they actually confuse and distort such understanding.

C. Just
because clocks located at spatially separated points A and B on an inertial
frame are defined to be simultaneous and are synchronized to show the same clock
time, this does not mean that distant light events on such inertial frame are
perceived to be simultaneous by each spatially separated human observer.[57]
(see Figures 25.1C
and 25.3A) It is important to remember throughout this
remainder of this treatise that whenever Einstein (or any of his followers)
refers to simultaneity or simultaneous events, he may just be referring to
events that are arbitrarily __considered to be simultaneous__ or which are mathematically
simultaneous as measured by synchronous clocks.

D. Einstein’s other mathematical concepts, such as ‘common coordinate time’ and ‘common proper time,’ are equally meaningless for human observers for similar reasons.

By this juncture, the reader must realize how artificial and contrived Einstein’s various definitions and examples of simultaneity, synchrony and common time really were. One minute Einstein would talk about the empirical observations of a human observer, and the next minute he would talk about the coordinate measurements of a mathematical measurer…as if they were the same concepts. This commingling of completely different concepts must also be extremely confusing for any reader.[58]

**D. Why
did Einstein need his definitions and concepts of simultaneity, synchrony and
common time? [59]**

There is one very obvious reason:
coordinates and clocks. Einstein
needed his definitions, concepts and algebraic examples of simultaneity,
synchronous clock time, common time, and velocity c to be ‘properly’ measured
by coordinates and clocks in one inertial reference frame theoretically at rest,
as __benchmarks__ for comparison with different ‘non-proper’ coordinate and
clock measurements of the same phenomena __between__ two relatively moving
inertial reference frames.[60] The primary reason for these comparisons of proper
and non-proper coordinate and clock measurements was to illustrate Einstein’s
twin concepts of the Relativity of Simultaneity (time) and the Relativity of
Distance (length) in the next step of his Special Theory.[61] (see Chapter 26)

What do we mean by ‘proper’ and ‘non-proper’ measurements? In Special Relativity, either reference frame
may be called the ‘rest frame.’ This definition
(rest frame) means that the thing to be measured by coordinates, and by the coordinate
measurer (observer) with her rigid measuring rod and synchronized clock, are all
__relatively stationary__ with one another.
All clock and coordinate measurements made in a rest frame are by relativistic
convention called ‘proper.’ (see French,
pp. 105 – 106) The length of a rigid rod
“as measured [by coordinates] in its rest frame is called its proper length…,”
which is designated by l_{0}.[62] (*Id*., p. 106) Similarly, the time of a clock and an event as
observed and measured in its rest frame is called its ‘proper time,’ and is
designated by t_{0}. (*Id*.

In order to construct his Special Theory, Einstein decreed that the ‘proper
time’ of an event is the ‘clock time of a stationary clock with an observer __at__
the place of the event.’ (Einstein, 1905
[Dover, 1952, p. 40]) Thus, a ‘proper
time’ can only be measured in one frame of reference by one clock. (see Goldberg, pp. 77 – 78, 464, and French,
p. 106) All other measurements of time in
Special Relativity are considered to be ‘non-proper.’[63] Therefore, the measurement of clock time __between__
two reference frames is non-proper because it requires two clocks, and the
measurement of a time interval between two events on the same reference frame
is non-proper if such measurement requires more than one clock. (*Id*.

There are also other proper
quantities or measurements in Special Relativity, such as ‘proper mass.’ (*Id*., p. 117) All of the above ‘proper’ quantities or
measurements “represent __invariant__ quantities in relativity theory.”[64] (*Id*., p. 64) It follows that (in relativity theory) all
non-proper measurements and quantities are not invariant (they do not have the
same magnitude or value in all inertial reference frames). Why?
Because, according to Einstein’s method of measurement, coordinate
measurements between different inertial reference frames are distorted as are
time measurements because relatively moving clocks run slow.[65] (see Chapter 28)

All of the above axioms or
conventions concerning proper and non-proper coordinate measurements of length
and clock times of events were, of course, completely *ad hoc*.[66] There is no physical or empirical reason that
would make their existence necessary. Unfortunately,
it is not until we read Chapters 26 and 28 that we can fully understand why
Einstein needed to invent these arbitrary conventions, why they were __essential__
to his artificial relativistic concepts and his Special Theory in general, and
why such conventions and their measurements were so absurd.

A second reason why Einstein needed
his definition of simultaneity and the same synchronous clock time as shown on
all spatially separated clocks of all observers in an inertial reference frame…is
not so obvious. It was in order to
theoretically and artificially __eliminate all time intervals__ between
coordinate points on every inertial reference frame,[67]
so that Einstein and his followers could claim that the velocity of a light ray
propagating through such frame would always be __covariantly__ and
simultaneously measured with coordinates and clocks to be *c* (rather than
*c* ± v) by all inertial observers on every inertial reference frame in
the Cosmos.[68] (see Chapter 24C) Let us now discuss and describe how Einstein may
have rationalized these contrived and artificial results.

Remember that early in Section 1 of his 1905 treatise, Einstein stated
the way that mathematicians describe the motion of a material point: “We give the __values of its coordinates as
functions of the time__” interval of its motion. (see Einstein, 1905d [__all__
have the same value for time there will be no time interval and thus no motion
of the material point that can be mathematically described. This is what Einstein theoretically
accomplished with his synchronous common time for each coordinate point
(measurer with a synchronous clock) on an inertial reference frame.

This scenario would equally apply to
the propagation of a light ray. If the
coordinates of the light ray __all__ have the same synchronous common time,
then there will be no time interval and thus no motion (propagation) of the
light ray that can be mathematically described.[69] Because every inertial observer on an
inertial reference frame theoretically measures a ray of light passing through
the frame as a function of coordinate time, and all clocks at all coordinate
points on such frame are synchronized to the same coordinate time, therefore
Einstein and his followers could claim that the velocity of light was
simultaneously a constant *c *relative to all inertial observers at all
coordinate points, not *c* ± v.[70] (see Chapter 24C)

For example, if Einstein theoretically sent a light ray at velocity *c*
toward a linearly moving reference frame, the light ray’s velocity relative to
any point on such moving frame, as measured by the same synchronous coordinate
time value for all of its coordinate points, would mathematically be *c*
(not *c* – v or *c* + v) regardless of the linear velocity of the
observer at v relative to such light ray.
Why? Because all of such equal
coordinate time values would not permit the mathematical coordinate description
of any motion or propagation.[71]

Perhaps this scenario is what
prompted Dingle to write: Einstein’s
“theory forbids us to form a picture of *any motion at all*.” (Dingle, 1961, p. 21)

“We must
content ourselves with stating the result of an experimental measure of the
velocity of any beam of light with respect to any body at all. The theory therefore demands that we give up
the attempt to picture, not merely what it is that moves, but __the process of
motion itself__, the passage from point to point as time goes on. That requires us to express in a formula the
velocity of light with respect to two relatively moving bodies in such a way
that __the value c results for both__.”[72] (

Later, Einstein artificially and mathematically accomplished this same
result with his Lorentz transformation equations for time. (see Chapter 27) When the Lorentz transformations __translated__
the velocity *c* of a light ray from one reference frame to another, it
artificially eliminated the relative velocity v in the factors x ± vt and t ±
vx/*c*^{2} so that there was __no relative velocity__ that
could mathematically be described and thus there was no mathematical time
interval between the two reference frames.

The final reason why Einstein needed
his concepts of simultaneity and synchrony was in order to remain consistent
with his absolute, co-variant and impossible law for the constant __propagation__
velocity of light at *c* relative to any inertial reference frame in the
Cosmos at any instant. In this regard,
Einstein stated:

“We suppose
further, that, when three events *A*, *B* and *C* occur in
different places in such a manner that *A* is simultaneous with *B*,
and *B* is simultaneous with *C* (__simultaneous in the sense of the
above definition__),[73]
then the criterion for the simultaneity of the pair of events *A*, *C*
is also satisfied.[74] This __assumption is a physical hypothesis
about the law of propagation of light__; it must certainly be fulfilled if we
are to maintain the law of the constancy of the velocity of light *in vacuo*.” (Einstein, *Relativity*, p. 27, F.N.)

However, Einstein’s above contrived example was a non sequitur. A light ray may take the same time interval
to propagate to and fro between events A and B, and the same time interval to
propagate to and fro between events B and C, but this does not mean that all of
such events occur simultaneously at the same instant. The reason why such example was (for
Einstein) “a physical hypotheses about the law of propagation of light” *en
vacuo* was so that such velocity of light could theoretically and
mathematically always be a constant and co-variant magnitude of *c*
simultaneously (in the above __non__sense) with respect to A, B and C, and
regardless of their linear velocities (or empirical time intervals) relative to
the light ray. [75]

In 1914, Einstein asserted that his concept of simultaneity was “the most
important, and also __the most controversial theorem__ of the new theory of
relativity.” (Einstein, 1914 [Collected
Papers, Vol. 6, p. 4]) And for good
reason!

Where did Einstein’s concept of the ‘common time of an entire inertial frame’ really come from? In Lorentz’s April 1904 treatise, he asserted that each inertial reference frame in his contraction theory had its own unique “local-time.” (Lorentz, 1904 [Dover, 1952, pp. 15, 17, 19, 25, 26, 28]; also see Miller, p. 177) In 1905, Einstein copied Lorentz’s April 1904 concept of ‘local time’[76] and ultimately changed its name to the ‘common time’ or ‘proper time’ of an inertial reference frame. How do we know this? Because, as Einstein explained in his 1907 Jahrbuch article:

“One had only to realize
that an auxiliary quantity introduced by H. A. Lorentz and named by him ‘local
time’ could be defined as ‘__time’ in general__. If one adheres to this definition of time,
the basic equations of Lorentz’s theory correspond to the principle of
relativity, provided that the [Galilean] transformation equations are __replaced__
by ones [vis. the Lorentz transformations] that correspond to the new
conception of time.”[77]
(Einstein, 1907 [Collected Papers, Vol.
2, p. 253])

Pais paraphrased
the above quotation[78]
and also pointed out that in Special Relativity “there are as many times as
there are __inertial frames__.”
(Pais, p. 141) Born also confirmed
these facts, as follows:

Einstein’s mathematical
concepts of a ‘synchronous common time’ and a ‘proper time of the system’
implies that there is a ‘common local time of perception’ for all human
observers situated at different locations on an inertial system. (Figure 25.6A) But, on the contrary, since each human observer
in the Cosmos occupies a unique position, and since there is a unique
distance/time interval delay of *c* from a distant light event to each
observer’s unique position, it follows that there is a unique ‘local time’ of
perception of any distant light event for each human __observer__ in the Cosmos. (Figure 25.6B) The state of motion (common, inertial,
accelerated, or otherwise) of the observer and his frame, and the
synchronization of his clock (or not), is irrelevant to such unique local time
of perception by each human observer.

Of course, Einstein
should have defined ‘local time’ and ‘proper time’ in terms of the unique
position of each human __observer__ at the instant of his perception of a
distant light event and the unique distance/time interval delay of *c*
from such distant light event to such observer’s unique position…regardless of
any common motion or synchronized clocks on an inertial system (frame of
reference). But that would not have
furthered Einstein’s relativistic agenda, for the reasons previously set forth
in this chapter.

Einstein’s synchronized ‘common
time’ for each observer, and his arbitrary ‘proper time’ for an entire inertial
system, are only rough __approximations__ of the local time of a distant
event for each human observer located at a different position on an inertial
system.[80] Such concepts might have some semblance or
reasonable approximation of validity in Einstein’s above example, where a man
in a railway station looking at the small hand of his watch pointing to seven
and the arrival of the train at the same station, are located in the same
general vicinity. But even with this
example of an inertial observer in close proximity to two different light
events (sometimes mischaracterized as ‘local simultaneity’), Einstein
acknowledged “the __inexactitude__ which lurks in the concept of
simultaneity of two events at __approximately__ the same place…” [81]

However, not considered nor acknowledged by Einstein in his Special
Theory was the __scale__ of the inertial system: the larger the dimensions of the inertial
system being considered, the greater is this ‘inexactitude.’ For example, the Earth is an inertial
system. All of the people on it experience
its common inertial motion through space, and the clocks of all such people are
sequentially synchronized by time zones.
Does this mean that a woman in

Now imagine, on a much greater scale, an inertial system one thousand
times the size of the Sun, where two observers at opposite ends of a 300,000 km
railway carriage simultaneously create light events. Each observer would not perceive the
simultaneous light event at the other end of the carriage for a time interval
of one second. Thus, even if their
clocks were synchronized to the same ‘common local time’ or common ‘proper
time’ of the giant railway carriage, the two distantly separated observers
would not empirically perceive the two simultaneous light events to be
simultaneous because of the distance/time interval delay of *c* between them. Empirically, there is no ‘common local time’
of perception for these observers with synchronized clocks, located on the same
inertial frame and sharing the same common inertial motion. Likewise, there is no common ‘proper time’ or
‘common local synchronous time’ for perceptions by any spatially separated human
observers on any inertial system.

From the above examples, it becomes
obvious that empirically there are as many unique ‘local times of perception’
of a distant light event, as there are __observers located at unique positions__
in the Cosmos. This is true, regardless
of the state of motion of such observers or the state of synchronization of
their clocks. (Figure 25.6B) Once this fact is realized, the __common
relative motion__ of inertial frames, inertial observers and the
synchronization of their relatively stationary clocks become __irrelevant__
to the determination of the time of occurrence of distant events by each human observer. The only thing that remains relevant to the
concept of ‘local time’ is the distance/time interval delay of *c*, from
the unique __position__ of the distant light event at the instant of light
emission…to the unique __position__ of the eye of each human observer at the
instant of perception of such light event.

Since Einstein knew that the local
time of perception of a distant light event was unique to each individual human
observer’s position,[82]
why then did he adopt the synchronized ‘common local time’ of an entire
inertial system as his definition of ‘time’ for all observers and all events on
such inertial system, regardless of their different positions? Why did Einstein define and apply ‘proper
time’ and ‘simultaneity’ as between __inertial systems__ (frames of reference),
and not as between the __position__ of emission of light and the position of
an observer’s perception thereof?

We have already answered these
questions in the previous Section 25D of this chapter, and in other prior
chapters. The most obvious answer
is: because Einstein’s Special Theory
was constructed upon the concepts of Cartesian coordinates, Galileo’s
Relativity of inertial motions, the uniform velocities of Lange’s __inertial
reference frames__ (systems), and the Galilean transformation equations from
one inertial system (frame of reference) to another. The contrived differences in the perceptions
of times, time intervals and distances which Einstein needed in order to
demonstrate his concepts of the Relativity of Simultaneity and the Relativity
of Distance (Chapter 26), so as to justify substituting the Lorentz
transformations for the Galilean transformations (Chapter 27), could only be
claimed as viewed and measured between two different __inertial reference frames__
or systems (each with a different relative velocity and a different
synchronous, common and proper time); not between the positions of a distant
event and a local human observer. In
other words, Einstein needed the ‘inexactitudes’ inherent in ‘apparent distant
simultaneity’ and in the ‘common time’ and ‘proper time’ of different inertial
reference frames in order to demonstrate and justify such twin concepts. (see Chapter 26)

In addition, transformation equations, and especially the Lorentz
transformations, which constituted the mathematical foundation for his Special
Theory, could only theoretically apply __between__ inertial reference frames
or (coordinate) systems in Lange’s abstract version of Galileo’s Relativity,
not between the positions of individual human observers. (see Chapters 13, 14 and 16) In effect, Einstein’s Special Theory would
not work if all that was considered was the unique position of each individual
observer relative to the position of a distant light event, regardless of the
state of their relative motion or the synchronization of their clocks.

There is yet another reason why Einstein’s ‘proper time of an inertial system’ or ‘modified local time’ is mathematically flawed and empirically meaningless. Lorentz’s April 1904 transformation equation for ‘modified local time’ (t'),

t'_{ }= __t – vx/ c^{2}__

√1 – v^{2}/*c*^{2},

was theoretically measured from the ‘true time’ (t) of clocks absolutely at rest in the ether. Since neither ether nor absolute rest exists, there is no way to determine such ‘modified local time’ from universal ‘true time’ (t), which was pure fiction. (Bohm, pp. 40, 41) Since Einstein’s factor for ‘common time’ in his Lorentz transformation for time (t') is admittedly nothing more than Lorentz’s April 1904 transformation factor for ‘modified local time’ by the different name of ‘common time’ or ‘proper time’ (Pais, p. 141; Born, p. 250; Einstein, 1907 [Collected Papers, Vol. 2, p. 253]), there is no way to mathematically determine the value of such ‘common time’ or ‘proper time’ from such fictional true time (t). The above algebraic symbols are empirically meaningless in both theories?

Apparent distant simultaneity (Figure 25.1B) is an
illusion; it is not actual or empirical simultaneity, where two events occur at
the same instant. It may even be
described as __relative simultaneity__; that is, simultaneity relative to
the distance/time interval delay of *c* between the distant occurring
event and the eyes of the local human observer.
No one needs to prove these empirical conclusions; they are
obvious. Does Einstein’s reference to a
distant light event and a local observer as being on different inertial
reference frames __change__ the above scenario? No.
Does Einstein’s synchronization of clocks on each different inertial
frame __change__ the above scenario?
No, but it does create an absolute and meaningless form of mathematical
distant simultaneity which theoretically and mathematically makes “events
occurring at two different places in that frame…simultaneous.” (see Resnick, 1968, p. 52; Figure 25.1C) Has Einstein’s synchronization of clocks in
each co-moving frame resulted in a universal time scale that is used by humans?[83] No…only chaotic confusion for mathematicians between
reference frames. (see Chapters 26 and
28) Was this Einstein’s intent when he
invented his Special Theory? Possibly.

Rohrlich suggested a light
experiment to test the simultaneity of events between two relatively stationary
locations and clocks: the light
location/clock A on Earth and the mirror location/clock B on the relatively
stationary Moon, as measured on coordinates by an Earth observer and an
observer on a rocket R' moving at v.
(see Figure 25.7A) Rohrlich concluded from the scenario
described on Figure
25.7A that __simultaneity__ between A and B had been established.[84] (*Id*., pp. 63 – 64)

Of course, the time of clock/event A
and the time of clock/event B were not __empirically__ simultaneous, nor was
the time of event C. They did not occur
at the same instant. The time of the
clocks at positions A and B were only __synchronized__ by light rays and __mathematically__
simultaneous according to Einstein’s system of measurement, as were the events
of emission (event A), reflection (event B) and receipt again at A (event
C). Because this scenario was described
as an inertial reference frame, the clocks of A and B showed the same
synchronous common time, and for this reason Einstein would say that their time
was simultaneous. (Einstein, 1905d
[Dover, 1952, p. 40]) Similarly, the
stationary observer at position A measured event A and event C with the same
clock and within the same frame of reference, so both of such measurements
could be considered by Einstein to be ‘proper times;’ and of course a ‘proper
time’ is equivalent to ‘common synchronous time.’ Does any of this make any logical or
empirical sense? No.

Rohrlich then stated that the above
procedure could “be depicted graphically” by coordinates on a ‘space-time
diagram.’ (Rohrlich, p. 64) Rohrlich’s space-time diagram is illustrated
on Figure 25.7B. Based on such space-time diagram Rohrlich concluded
that: “__The point B _{1} is
simultaneous with A_{1} because at the instant t_{0} + t/2 both
are halfway in time__ between sending and receiving at A.” (

Rohrlich also graphically demonstrated Einstein’s mathematical and coordinate concept of Relative Simultaneity. (Figure 25.7C) The fact that the relatively moving rocket pilot might mark down different coordinates for the same events because of his relative translatory motion v and his resulting physical delay in plotting such coordinates has absolutely nothing to do with the actual simultaneity or non-simultaneity of such events. (see Chapter 28) It is like comparing fire with water.

This abstract ‘space-time’ type of
geometric simultaneity was invented in 1908 by Einstein’s colleague Hermann
Minkowski *inter alia* for the specific purpose of illustrating Einstein’s
concepts of Special Relativity. (see
Chapter 30) Such a geometric abstraction
may be mathematically meaningful to a pure mathematician, but it is certainly
not the same concept as __empirical__ simultaneity which even Einstein
originally defined as: the ‘same instant
that the hands of his watch point to seven and the train arrives at the
station.’ Mathematical analogies and
consequences may assist the mathematical physicist in his thinking process as
long as he doesn’t take them too seriously, literally or confuse them with empirical
reality. In the end, whatever concept or
theory he comes up with must pass the empirical test of observation, experiment
and physical reality. (Chapter 1)

For all of the above reasons, it becomes apparent that Einstein’s
mathematical (coordinate, inertial frame, and synchronous time) concept of
‘simultaneity,’ which is fraught with artificial definitions, inexactitudes and
illusionary misassumptions, is not the proper method with which to analyze and
describe the concept of the ‘time’ (instant or interval) of a distant light
event for a local observer. The correct
empirical procedure is to determine (by contemporary technological methods) the
distance/time interval between the distant light event (at the instant of its
emission) and the local observer (at the instant of his observation), and then
apply the distance/time interval delay of *c* (300,000 km/s) to such
determination.

We have also demonstrated that
Einstein’s related concepts of a synchronous ‘common time’ for various
spatially separated observers, and the ‘proper time’ for an inertial system as
a whole with respect to an event, with which Einstein attempted to create an
illusionary assumption of simultaneity, are in fact merely rough __approximations__
of time intervals and actual observed distant simultaneity which were invented
by him in order to attempt to make his Special Theory work. These abstract, *ad hoc* and contrived
concepts are replete with ‘inexactitudes’ and inaccuracies which produce all
kinds of distorted measurements of time, space and distance, and other bizarre
consequences when used to plot the positions, distances, and time intervals of
different events on different sets of inertial coordinates relative to one
another.[85]
(see Guilini, pp. 51 – 58; Hoffmann, pp. 96 – 105) Such antiquated, invalid, meaningless, and
distorting concepts must be discarded.

In the next Chapter 26, we will
discover how Einstein used his arbitrary and artificial concepts of
‘simultaneity,’ ‘common time’ and ‘proper time’ to create his twin illusions of
the ‘Relativity of Simultaneity’ and the ‘Relativity of Distance.’ These twin concepts then constituted his
rationalizations and justifications for scrapping the Galilean transformation
(translation) equations and replacing them with his radical Lorentz
transformation equations. (Chapter 27)

[1]
Seventeen years later, Einstein recalled that:
“we discussed every aspect of the problem.” (Folsing, p. 155) Of course, we now know from Chapters 21 and
22 that there were no __real__ empirical difficulties concerning the
velocity of light.

[2] Here
Einstein meant that __distant simultaneity__ cannot be absolutely defined by
a human observer, because “there is an inseparable relation between time and
[light] signal velocity.” And he was
right. However, later he contradicted
himself and asserted that there was an ‘absolute mathematical distant
simultaneity’ for all observers with synchronized clocks on an inertial
reference frame. We will explain what
all of this means later in this chapter.

[3] It
follows that any __moment__ in the eternity of the universe is simultaneous
for every observer located anywhere in the infinite universe. But these simultaneous events that occur at
such moment and at different places throughout the infinite universe are not
perceived by spatially separated human observers to be simultaneous, because of
the distance/time interval delay of each light signal that propagates from such
distant light event through empty space at the __finite__ velocity of *c*
to the eye of the local human observer.

[4] “The eruption
of a volcano is specified as an event when not only the __location__ of the
volcano is given but also the exact __time__ of the eruption.” (Rohrlich, p. 65)

[5] This definition of course begs the question: what do we mean by ‘time’? For example: is it an empirically observed time or a mathematical time in the abstract?

[6] As we shall soon see, Einstein would give many different, strange, and non-intuitive meanings to the word ‘simultaneous,’ in order to construct his Special Theory.

[7] In the “analysis of two widely separated physical facts, the notion of causality, simultaneity and time [can sometimes become] intermingled.” (Miller, p. 174)

[8] Any form of ‘actual simultaneity’ could also be characterized as ‘absolute simultaneity.’

[9] This
concept has also been mischaracterized as ‘relative simultaneity,’ because the
perceived actual simultaneity of such events is __relative__ to the
distance/time interval delay of *c* between the distant position of light
emission and the local position of its perception by a local observer.

[10] This
concept has also been characterized as ‘coordinate time.’ (see Jammer, 2006, p. 111) Resnick concluded that: “Events occurring at two different places in
that frame must be called *simultaneous*.”
(Resnick, 1968, p.52) Later in
this chapter we will demonstrate why this mathematical conclusion by Resnick is
empirically invalid and generally meaningless for a human observer.

[11] Even though three distant light events in Figure 25.1C are actually simultaneous or mathematically simultaneous, they could not be perceived by a distant human observer to be simultaneous, and such actual ‘apparent distant non-simultaneity’ would have no meaning for a human observer.

[12] This
distance/time interval delay of *c* for a distant light event in the Solar
System*,* and the instant of its perception by an observer on Earth, was
implicit in Römer’s 1676 deductions concerning the __finite__ velocity of
light, and his delayed perceptions on Earth of the eclipses of Jupiter’s moon,
Io. (Figure 6.5)

[13] This
statement and others like it are often asserted as Einstein’s challenge to the
validity of *Principia* because Bradley did not empirically
confirm it until 1728 (the year after __no universal ‘now’__ as there was
with

[14] We
shall refer to this delay phenomenon of the light signal as the “distance/time
interval delay of *c*.”

[15]
Likewise, each individual observer cannot determine, relate and assign a __local
Earth time__ to the instant that light was emitted by a distant light event
vis., an exploding star: i) until the
light signal from such event, transmitting at the constant finite speed of
300,000 km/s, reaches such observer’s eye so that she can perceive it; and ii) __unless__ and until the distance
interval and/or the time interval from such observer to such distant light
event is determined and factored into the computation.

[16] Rocket scientists, astronomers and mathematicians must consider these delayed perceptions when they compute a trajectory to a distant planet.

[17] This is
not really a correct statement. In
reality, our judgments normally concern __apparently simultaneous__ distant
events, such as an automobile passing us on the other side of the freeway or a
distant jetliner entering a cloud.

[18] The ‘stationary system’ on the Earth (the
train station) in Einstein’s example was, of course, an inertial system in
uniform rectilinear motion through space, where the observers, clocks and
events all share the __common motion__ of the Earth and are in somewhat
close proximity to one another. In
effect, Einstein was describing the motions and the __approximate__ common
times of an observer and two events on an inertial reference frame (the Earth)
in Galileo’s Relativity.

[19] Later
Einstein would assert that the __simultaneous observation__ by two distant
observers of the hands of two different synchronous clocks pointing to the same
clock number is what he meant by a ‘simultaneous time’ and ‘simultaneous
events;’ not that one observer would judge such distant events to occur at the
same instant. (see Einstein, *Relativity*, pp. 27 – 28) Mathematically Einstein was correct, but
empirically he was not correct. (see Figure 25.1)

[20] “[I]n
the remainder of the relativity paper Einstein used the term __event__ to
mean an occurrence at a particular position, measured relative to an inertial
reference system by a rigid measuring rod, and whose time [proper time] was
registered by a clock at that point.”
(Miller, p. 182) This may be a
‘mathematical event,’ but it is not an empirical event.

[21] Of course,
such events are not rigorously or exactly simultaneous; they are only __perceived__
to be simultaneous by the observer. Even
where two observers are standing one behind the other near to the arriving
train, their perceptions of the time of arrival of the train are not __exactly__
simultaneous, because of the slight difference in distance from each observer’s
eyes to the train, and because of the slight difference in the distance/time
interval delay of *c* relative to each pair of eyes. On the other hand, such __perception__
would be empirically simultaneous if such two observers were exactly __equidistant__
from the train.

[22] Some of these concepts of simultaneity would be empirical with a human observer, some of these concepts would be mathematical with coordinates and/or a theoretical measurer, and some of these concepts would be totally false.

[23] Even
where two observers are equidistant from a light event, they still may not
evaluate such light event to be simultaneous.
This difference in evaluation can result from the __relative linear
motion__ of either the light event or the observer during the propagation of
the light. (see Figure 25.3B) Our contrived example is similar to the
contrived example that Einstein used to demonstrate his Relativity of
Simultaneity concept. (see Figure 26.3)

[24] Most
likely such a simultaneous supernovae event has never been witnessed, nor may
it ever be. The only way that an
observer could ever know whether such supernovae were actually simultaneous
would be to empirically determine the exact distance/time interval delay of *c*
from each distant supernova to his eye.

[25] If one
uses the concept of the distance/time interval delay of *c* for the determination of the local instant of perception of
distant light events and current technology to measure the distance, then any
concept of simultaneity becomes superfluous even as a benchmark for such
determination of time or sequence.

[26] One reason, of course, was simply because it was symmetrical. (see Jammer, 2006, pp. 115, 120, 125, 139, 201 – 219)

[27] Therefore, asserted Resnick, the time measurements for events in Newtonian mechanics were inaccurate, and “we certainly shall not have a universal time scale if different inertial observers disagree as to whether two events are simultaneous.” (Resnick, 1968, p. 50)

[28] “We
certainly cannot have observers in the same reference frame disagree on whether
clocks are synchronized or not.” (Resnick,
1968, p. 51) “Then we can set up time
scales in exactly the same way in all inertial frames and compare what
different observers have to say about the __sequence__ of two events, A and
B.” (*Id*., p. 51)

[29] This __velocity
dependent__ universal time scale was the Lorentz transformation equation for
‘local time:’

t' = t – v/*c*^{2}.x
/ √1 – v^{2}/*c*^{2}. (see Einstein, *Relativity*, p. 37)

[30] Neffe
in effect refuted all of the above dubious characterizations and
rationalizations by Resnick by asserting that such ambiguities and differences
in time and time scales “had been __standard knowledge__ in physics for a
long time prior to Einstein.” (Neffe, p.
129) Miller went even further and stated
that such known differences in the time of distant events were __intentionally
ignored__ by Poincaré and other mathematicians so that the definition of
physical time in physics could “be expressed in a convenient and simple form,”
i.e. the equation t' = t contained in the Galilean transformations. (Miller, p. 176) Thus, Einstein’s criticism of the
inexactitude of distant times contained in the Galilean transformation equation
for time (t' = t) was not the great __revelation__ for physics that Einstein
and his followers claim it to be.

[31] Without time intervals between coordinate points, the results of these artificial measurements would be the same as if time was t' = t and the velocity of light was instantaneous rather than finite. (see Chapter 21.E) We will explain these distorted time measurements for the velocity of light in detail later in this chapter.

[32] This
normal process involves the empirical determination of the distance/time
interval delay of velocity *c* from the position and instant of a distant
light emission (event) to the eyes of the local human observer at the instant
of his perception.

[33] Despite the many attempted rationalizations, misanalyses, conjectures, false confirmations, etc., of Einstein’s followers.

[34] In 1916, Einstein also contrived a somewhat different mathematical ‘definition of simultaneity,’ which we shall discuss later in this chapter and in detail in Chapter 26.

[35] It was
“a coordinate system in which *Id*.,
p. 141) The footnote (“to the first
approximation”) was added in 1923, because in Special Relativity the Galilean
transformations are only considered to be a first approximation of the
relativistic Lorentz transformations at low velocities. (*Id*., pp. 141, 142)

[36] Resnick illustrated a framework of measuring rods and clocks that an observer (such as Einstein) might have used to determine the space-time coordinates of an event. (see Figure 25.5B)

[37]
Einstein did the same thing when he wished to mathematically describe the __propagation
of a light ray__.

[38]
Remember that Einstein’s example of this ‘proper time’ concept was where the
hands of his watch pointing to 7 o’clock and the arrival of the train in the
station were __observed to be simultaneous events__.

[39] This concept is what Einstein and his followers would later call a ‘proper time.’

[40] In
1898, Poincaré had already anticipated and discussed in detail the problems of
determining ‘simultaneity’ and a ‘common time’ for distant observers. In 1898, Poincaré pointed out in his treatise
on the *Measurement of Time*: “Not
only do we have no direct experience of the equality of two times, but we do
not even have one for the __simultaneity__ of two events occurring in
different places.” (Folsing, p. 175;
Jammer, 2006, p. 100) It is obvious that
Einstein got the idea to define ‘time’ in terms of ‘simultaneity’ from
Poincaré’s earlier writings.

[41] These
were substantially the same assumptions or __conventions__ that Poincaré
used for the same reasons in 1898.
(Miller, pp. 175 – 176, 181)
Poincaré had adopted such conventions in order to avoid the vicious circle
of defining the ‘velocity of light’ with ‘time,’ and defining ‘time’ with the
‘velocity of light.’ (Jammer, 2006, pp.
101, 102) It turns out that such
time/space assumptions were also consequences of Einstein’s two fundamental
postulates for Special Relativity.
(Miller, pp. 183 - 184) What a
coincidence?

[42]
Einstein was correct, where the distance to and fro is the same __finite
distance in a stationary system__. In
this context, ‘time’ means reading the ‘instant’ of a light event (such as
emission) as shown by the hands of __both__ synchronized clocks, the clock
at A and the clock at B. (Jammer, 2006,
p. 111) Einstein’s method of
synchronizing clocks by light signals had also been previously anticipated,
devised and published by Poincaré.
(Folsing, p. 175; see Jammer, 2006, pp. 104, 108)

[43]
Einstein’s ‘synchrony equation’ was necessary for his Special Theory as a
stationary algebraic benchmark for one reference frame, from which to compare
two different algebraic time intervals for a relatively stationary inertial
reference frame and a __relatively moving__ inertial reference frame in his
concept of the Relativity of Simultaneity.
(see Chapter 26A)

[44] Einstein then described how his definition of synchronism could be “possible for any number of points.” “1. If the clock at B synchronizes with the clock at A, the clock at A synchronizes with the clock at B. 2. If the clock at A synchronizes with the clock at B and also with the clock at C, the clocks at B and C also synchronize with each other.” (Einstein, 1905d [Dover, 1952, p. 40]) In effect, Einstein’s definition and examples of synchronism were nothing more than spatially separated clock times in his concept of ‘absolute mathematical distant simultaneity.’ (see Figure 25.1C) They are meaningless for a human observer.

[45] But, practically, how would the distance between clocks be precisely measured in 1905, especially in empty space? Realistically, how long would it take for A to react, then for B to react and then for A to react? Unless such reactions were instantaneous the results would be distorted or merely approximations.

[46]
Einstein’s equation (2AB/t'_{A} – t_{A} = *c*) was also necessary as a benchmark from which to compare two
different theoretical algebraic velocities for light in Einstein’s so-called
proof of the Relativity of Simultaneity.
(see Chapter 26A)

[47] This axiom is the basis for Einstein’s concept of ‘proper time,’ which we will discuss in detail in Chapter 25D.

[48] This axiom is the original basis for Einstein’s concept of the ‘common proper time of all events on an inertial system.’

[49] The concepts of ‘synchrony’ and ‘simultaneity’ may both be symmetric, but they are certainly not identical. (see Jammer, 2006, p. 115)

[50] In other words, all that Einstein was really claiming was that such spatially separated clocks showed a synchronous time. Was not this clever and misleading definition also devious?

[51] In *Relativity*, we also discover another
artificial meaning for simultaneous time:
two light rays that require “the same time [interval] to traverse” equal
distances may be considered to do so in simultaneous times. (see Einstein, *Relativity*, p. 27) Here ‘simultaneous’ means ‘equal.’ In this regard, Einstein stated: “There is only one demand to be made of the
definition of simultaneity, namely, that in every real case it must supply us
with an empirical decision as to whether or not the conception that has to be
defined is fulfilled.” (*Id*.

[52] Any of
these times are substantially identical to the impossible __absolute time__
(t' = t) described by the Galilean transformations where the light signal must
have an instantaneous or infinite speed.

[53] This is
Einstein’s 1916 restatement of his axiom for the ‘__common proper time__ of
events on an inertial system.’ This
concept means that the clock time for one event is also the clock time for all
events that occur on the same frame at the same instant, even if such events
are spatially distant from a synchronized clock. But if the clocks of all spatially separated
observers are synchronized to show exactly the same clock time, how can any one
human observer know or understand from such synchronized clocks the instant that
any distant event empirically occurred?
She cannot.

[54] For all of the reasons set forth in this chapter, Einstein’s ‘definition of time in physics’ is meaningless for a human observer and also probably for physics.

[55] This concept is basically the same as the 24 ‘time zones’ that the Earth is currently divided into, where each time zone has the same synchronous time for all observers and events.

[56]
Einstein needed a coordinate time interval to be described __imprecisely__
by algebraic clock times (i.e. t_{2} – t_{1}) rather than
precisely by empirically elapsed time intervals, in order to confuse and
mislead his readers and to construct his other relativistic concepts. (for example, see Chapter 26)

[57] The
clocks of an observer in

[58] Section 1 of Einstein’s 1905 treatise is perhaps the most misleading, confusing and contrived section of his entire Special Theory.

[59] Many writers suggest various reasons, but everyone seems to be confused. For example, Miller suggests that Einstein “declared the definition of simultaneity to be identical with clock synchronization.” (Miller, p. 183) Einstein did, but that is not an answer for why. (also see Jammer, 2006, p. 110; Resnick, 1968, p. 52)

[60] For
this reason, at the end of Section 1 of his 1905 Special Theory, Einstein
stated: “It is __essential__ to have
time defined by means of stationary clocks in the stationary system…” (Einstein, 1905d [Dover, 1952, p. 40])

[61]
Unfortunately, the reader cannot fully understand why such ‘proper’
measurements made __in__ a rest frame and ‘non-proper’ measurements made __between__
relatively moving frames were so critical to Einstein’s Special Theory, until
we discuss such artificial measurements in detail in Chapters 26 and 28. Suffice it to say at this point that if
Einstein had not invented ‘proper’ measurements and used __coordinates__ and
clock times to make his measurements, there would be no Special Theory. Modern technological methods of measurements
would not have worked for Einstein’s Special Theory.

[62] “Any
other measurement of length is called non-proper, and…yields a value less than
l_{0} by a factor corresponding to the Lorentz transformation.” (French, p. 106) The reason for this will become apparent in
Chapters 27and 28.

[63]
Non-proper time measurements are considered to be slower than t_{0} by
a factor corresponding to the Lorentz transformation. The reason for this will become apparent in
Chapters 27and 28.

[64] In other words, they have the same value in all inertial reference frames.

[65] Do any of Einstein’s contrived methods of measurement make any empirical sense? Of course not.

[66] They
are all very similar to the *ad hoc* conventions that Lorentz invented for
his April 1904 transformation treatise.
(see Chapter 16; Goldberg, pp. 98 – 102)

[67] This is a result that Einstein would later accomplish mathematically with his Lorentz transformations. (see Chapter 27)

[68] Why do
we come to these conclusions? Because *c*
+ v and *c* – v basically describe a relative velocity, a relative
velocity cannot exist between reference frames without a time interval, and
there is no time interval between reference frames for a __covariant__
algebraic magnitude, __no matter now it is accomplished__. (see Einstein, *Relativity*, pp. 47 –
48)

[69] In other words, it would be as if t' = t; a light ray would theoretically and mathematically propagate instantaneously from one point to another without any time interval for such propagation.

[70]
Restated in different words: if Einstein
stipulated that the tip of a ray of light always propagates through empty space
with the absolute constant velocity *c*, and that clocks at all coordinate
points in an inertial frame are synchronized to show the same coordinate time,
and if the velocity of a light ray passing through an inertial frame is
measured as a function of coordinate time, then he could assert that a light
ray measured with the same coordinate time at all points has the same velocity *c*
for all inertial observers, rather than *c* + v or *c* - v.

[71] Imagine
that a light ray was propagating from * c* relative to every linearly moving observer
along the way (instead of *c* – v or *c* + v).

[72] This is also what Einstein mathematically accomplished with his relativistic formula for the composition of velocities. (see Chapter 29)

[73] Very
importantly, here the __non__sense of Einstein’s definition of simultaneity
was that light takes the same __time interval__ to travel a certain distance
in two opposite directions.

[74]
Einstein’s criteria for the simultaneity of events A and C is that light takes
the same __time interval__ to propagate between A – B and then between B –
C; not that events A and C occurred simultaneously __at the same instant__
as perceived by a human observer.

[75] It becomes obvious that for Einstein ‘simultaneity’ and ‘synchronous clocks’ were a form of symmetry.

[76] As we
pointed out in Chapters 16 and 24, Lorentz’s ‘local time’ in April 1904 was not
the same as his much more limited concept of ‘local time’ in his 1895
treatise. Lorentz’s 1895 local time (t'
= t + vx/*c*^{2}) was merely an
arbitrary measurement from true time that was invented to algebraically remove
the factor v from the results of first order light experiments. However Lorentz’s ‘modified local time’ of
April 1904, which added √1 – v^{2}/*c*^{2} as a denominator, theoretically resulted in an
entirely different and unique time for each inertial reference system. (see Goldberg, pp. 94 – 100) It was Lorentz’s April 1904 ‘modified local
time’ that Einstein adopted for his Special Theory.

[77] Poincaré also based his synchronization procedure for clocks on Lorentz’s April 1904 ‘modified local time’ before Einstein did. (see Jammer, 2006, p. 104)

[78] “All that was needed was the insight that an auxiliary quantity introduced by H.A. Lorentz and denoted by him as ‘local time’ can be defined as ‘time’ pure and simple.” (Pais, p. 141) But since Lorentz’s April 1904 modified concept of ‘local time’ was based on the ‘true time’ of ether, it is meaningless. Therefore, Einstein’s ‘common time,’ ‘proper time’ and time (pure and simple) based on such modified ‘local time’ is also meaningless.

[79] In
Special Relativity, every inertial system has a unique common local time,
regardless of its __size__.

[80] These arbitrary times can also create a false or illusionary assumption of simultaneity.

[81] Again, this inexactitude is caused by the somewhat greater distance/time interval delay of the light signal from the headlight of the somewhat more distant train to the eye of the observer with his watch in the train station. The linear motion of the train only varies the inexactitude.

[82] This
knowledge was demonstrated by Einstein’s acknowledgement of the __inexactitude__
of approximate simultaneity in his railway station example.

[83] Is it ever even referred to by astronomers or astrophysicists? Probably not.

[84] It
turns out that the __simultaneity__ between A and B was established __only
in the sense__ that the clocks on A and B were __synchronous__.

[85] Einstein’s algebraic and coordinate approximations may have been state of the art in 1905, but they are certainly archaic now.