*The
concept of ‘Spacetime’ is not contained in Einstein’s 1905 paper on Special
Relativity. Rather, it was invented
during 1907 – 1908 by Hermann Minkowski (1864-1909), one of Einstein’s mentors
and colleagues. [1]
Spacetime is based solely upon Lorentz’s *ad hoc

**A.
Spacetime is ad hoc, empirically
invalid and physically meaningless on its face.**

Like many scientists of his time, Minkowski viewed Einstein’s Special Theory merely as a generalization or elaboration of Lorentz’s April 1904 theories.[2] (see Goldberg, p. 164; Dingle, 1972, pp. 167 – 169) In September 1908, Minkowski described and explained his geometrical concept of Spacetime to a gathering of German scientists. “It was a literal translation of the rigorous [relativistic] formalism that had been published earlier” by Minkowski in 1907. (Goldberg, p. 163)

Minkowski began his 1908 lecture with the following incorrect and misleading empirical statement:

“The views of
space and time which I wish to lay before you have sprung from the soil of __experimental
physics__, and therein lies their strength.”[3] (Minkowski, 1908 [

On the contrary, and as we shall soon discover, Minkowski’s geometrical
views of space and time actually sprang from (and were completely based upon)
Lorentz’s *ad hoc* physical contraction
of matter hypothesis and his April 1904 treatise; upon Einstein’s *ad hoc* kinematic concepts of relativity,
Length Contraction and Time Dilation; upon the meaningless co-variance of the
empirically invalid Lorentz transformations; and upon Minkowski’s own
imagination and mathematics. Therein lie
their physical and empirical invalidity and their meaninglessness for physics.

In fact, throughout his lecture, Minkowski tells us (in simple and
straightforward language) the fundamental premises upon which his mathematical
concepts of Spacetime are based. First
of all, he asserted that Spacetime is premised upon the null results of
Michelson’s famous interference of light experiments, and upon Lorentz’s
contraction of matter hypotheses which he invented to explain such null
results. (*Id*., p. 81) Minkowski
conjectured that if we have a group of equations (the Lorentz transformation
equations) for the propagation of light in empty space (G* _{c}*) where the velocity of matter is always less than

“it is easy to
see…that we should be able, by employing suitable rigid optical instruments in
the laboratory, to perceive some alteration in the phenomena when the
orientation with respect to the direction of the earth’s motion is changed. But all efforts directed toward this goal, in
particular the famous interference experiment of Michelson, have had a negative
result. To explain this failure, H. A.
Lorentz set up an hypothesis, the success of which lies in this very invariance
in optics for the group G* _{c}*.[4] According to Lorentz any moving body must
have undergone a contraction in the direction of its motion, and in fact with a
velocity

“I will now
show by our figure [see Figures
33.1 and 33.2]
that __the Lorentzian hypothesis is completely equivalent to the new
conception of space and time__, which, indeed, makes the hypothesis much more
intelligible.”[7] (*Id*.

On the contrary, as we have shown in
Chapter 15, any concept of contraction of matter in the direction of motion is
completely *ad hoc*, contrived and
physically impossible. Lorentz’s
physical contraction of matter was also theoretically impossible because it
depends upon the existence of ether, which does not exist. Not only that, but it was totally irrelevant
and unnecessary in order to explain Michelson’s null results.[8] (see Chapters 9, 10, 11 and 12) Thus, when Minkowski based his concepts of Spacetime
on Michelson’s null results and on the false necessity for a contraction of
matter to explain such paradoxical null results, and mathematically constructed
Spacetime geometry so that it would be consistent and ‘completely equivalent’
with respect to Lorentz’s empirically false contraction hypothesis, the result
was that Spacetime was based upon multiple false premises. Such false premises render the invention of
Spacetime and all of its related concepts and mathematical consequences as physically
invalid and empirically meaningless.[9]

Secondly, if Spacetime was premised
upon Lorentz’s false concept of a contraction of matter depending upon a body’s
velocity, then it must also be based upon and consistent with the empirically
meaningless Lorentz transformations.[10] Minkowski implies that this is the case
because he refers to Lorentz’s 1904 concept of ‘local time’ and to Einstein’s
1905 interpretation of it. (Minkowski,
1908 [Dover, 1952, p. 82]) Minkowski
also used equations with Lorentz’s and Einstein’s Lorentz transformation denominator
(√1 – v^{2}/*c*^{2})
throughout his lecture. (see *Id*._{∞}, but rather with a
group G* _{c}*,” which group G

Thirdly, Minkowski also premised his
concepts of Spacetime upon Einstein’s *ad
hoc* ‘relativity-postulate.’
Minkowski stated that the radically changed mathematical concept of
space which he was inventing might be considered “as another act of audacity on
the part of the higher mathematics.”
(Minkowski, 1908 (

“this further
step is indispensable for the true understanding of the group G* _{c}*, and when it has been
taken, the word

“The validity
without exception of the world-postulate, I like to think, is the true nucleus
of an electromagnetic image of the world, which, discovered by Lorentz, and
further revealed by Einstein, now lies open in the full light of day.” (*Id*.,
p. 91)

Since we now know that any hypothesis
for the contraction of matter in the direction of velocity is completely *ad hoc* and meaningless (Chapter 15),
that the Lorentz transformation equations are completely *ad hoc* and empirically invalid (Chapters 16 and 27), that the
concepts of Length Contraction and Time Dilation are completely *ad hoc* and physically meaningless
(Chapters 26 and 28), and that Einstein’s relativity postulate and his concept
of co-variance are *ad hoc* and
empirically invalid (Chapters 23, 24, 27 and 28), thus so must Spacetime and
its world postulate suffer the same fate (because they are premised upon and
totally consistent with the above relativistic concepts).

**B. A brief description of Minkowski’s Spacetime
geometry.**

Regardless of its empirical invalidity, the remainder of Minkowski’s
lecture was structured “along a purely mathematical line of thought to arrive
at changed ideas of space and time.” (Minkowski,
1908 [Dover, 1952, p. 75]) In Section I
of his lecture, Minkowski began with the mathematical form of *x*,
*y*, *z* be rectangular coordinates for __space__,[11]
and let *t* denote time.” (*Id*.,
p. 76)

“A point of
space at a point of time, that is, a system of values *x*, *y*, *z*, *t*,
I will call a *world-point*.[12] The multiplicity of all thinkable *x*, *y*,
*z*, *t* systems of values we will christen the *world*.” (*Id*.

Minkowski then
described this world point in motion over time from -∞ to +∞; in
other words, over eternity. The changed
coordinate points dx, dy, dz and dt result in a ‘world line.’[13] (*Id*.

Minkowski then asserted “that we may
subject the axes of [spatial coordinates] *x*,
*y*, *z* at *t* = 0 to any __rotation__
we choose about the origin, corresponding to the homogeneous linear
transformations of…*x*^{2}, *y*^{2}, *z*^{2}.” (*Id*., p. 77) This means that the algebraic form of *Id*.,
p. 75) But since “the zero point of time
is given no part to play” in the Galilean transformation equations we have
complete freedom to give “the time axis whatever direction we choose towards
the upper half of the world” for any value of time greater than zero. (*Id*.,
pp. 75, 77)

Minkowski’s connection between the
space axis and the time axis involved a positive parameter *c* and the graphic representation of *c*^{2}*t*^{2}
– *x*^{2} = 1. To understand how Minkowski’s geometry
created a group of transformations (called G* _{c}*)
which “associated the arbitrary displacements of the zero point of space and
time” of any number of world points, see Figure 33.1. Group G

At the end of Section I, Minkowski
stated that we “have in the world no longer space, but an infinite number of
spaces, analogously as there are in three dimensional space an infinite number
of planes [or frames of reference].
Three dimensional geometry becomes a chapter in four dimensional
physics.” (*Id*., pp. 79 – 80)

Minkowski’s “idea was very simple: since the Lorentz transformation on which the
special theory of relativity is based involves a transformation of space as
well as of time one may treat time just like another dimension of space, a
fourth dimension, as it were.[14] This…idea of a four-dimensional ‘space’,
three dimensions of ordinary space and one time dimension,[15]
became known as *Minkowski space.*”[16] (Rohrlich, p. 75)

Minkowski’s new Spacetime geometry illustrated Cartesian coordinates; it used straight lines and was flat like Euclidean geometry. (D’Abro, 1950, p. 196) However, we shall “see that we are not dealing with ordinary Euclidean geometry.” (Born, p. 305) Spacetime has its own special nomenclature, its own conventions, its own symbols and its own mathematical expressions. (see Dingle, 1972, p. 176)

In Section II of his lecture,
Minkowski described an axiom, *c*^{2}dt^{2}
– dx^{2} – dy^{2} – dz^{2}, which he asserted means
“that any velocity v always proves less than *c*.” This was, of course,
completely consistent with Lorentz’s April 1904 treatise and with Einstein’s
Special Theory.

What did Minkowski mean that the
world would have an infinite number of spaces?
At the beginning of Section III of his lecture, Minkowski __individualized__
space and time for each world point (i.e. each event or observer) by giving it
its own set of four axes. (see Figure 33.3A) The 0 was the zero-point of Spacetime for
each world point. Minkowski illustrated
the velocity of light at *c* as a
straight line (a ‘light line’) beginning at the zero (0) point of Spacetime and
continuing at a 45° angle equidistant between the x (space) axis and the t
(time) axis. (Figure 33.3B) If one passed this light line through a 360°
rotation, the result would be a ‘light cone’ with the vertical time axis in the
center and an infinite number of x and y axes in all possible directions on an
xy plane.[17] (Figure 33.3A) Again, each event (or observer) in Spacetime
has its own lightcones. (Rohrlich, p.
78) Since “three dimensional ordinary
space…is infinite our __symbolic picture__ of it [the xy plane is]…also
infinite. But so is time.” (Minkowski, 1908 [Dover, 1952, pp 83 –
84]) Thus we must also construct a light
cone into the past, and we end up with a double light cone. (*Id*.,
p. 83) Each world point had a past light
cone for all other “world-points which send light to 0,” and a future light
cone for all other “world-points which receive light from 0.”[18] (Minkowski, 1908 [

Because Special Relativity
postulates that no material body can exceed the speed of light, “only light
itself has a world line that is on the cone.”
(Rohrlich, p. 83) All other material
bodies that have a velocity less than c remain inside each light cone and must
angle toward the time line; the closer these world lines are to the time line,
the less is their relative velocity.
These world lines are often called ‘time-like’. The areas outside each light cone are *a
priori* not accessible, and therefore “all accessible future events lie
inside the future light cone, and all…[accessible past events] lie inside the
past light cone.” (*Id*.

In order to graphically illustrate
Einstein’s relativistic concept of relative motion and kinematics (length
contraction and time dilation), Minkowski tilted both axes of the moving frame
equally toward the light line. In other
words, “observers in relative motion have worldlines inclined to each
other.” (Harrison, p. 132; see Figure 33.4A) The algebraic formula which “relates the
intervals of time and space of observers in relative motion at speed v…[is the]
Lorentz transformations.”[19] (*Id*.,
p. 133)

At the beginning of Section IV of his lecture, Minkowski conjectured the following:

“To show that the assumption of group G* _{c}* for the laws of physics
never leads to a contradiction, it is unavoidable to undertake

Thereafter,
Minkowski proceeded to mathematically revise the whole of physics with four
equations (vectors) corresponding to the four axes of Spacetime. [21] Except for Einstein’s and Minkowski’s *ad hoc* assumptions that the empirically
invalid Lorentz transformations should apply to physics, there would be no need
to revise the whole of physics. The
fourth equation turned out to be “the kinetic energy of the mass point

…It
comes out very clearly in this way, how the energy depends on the system of
reference.”[22] (*Id*.,
p. 87)

At the end of Section IV,, Minkowski set forth an equation:

.

This
equation (in various different algebraic forms) is now called the ‘spacetime
interval.’[23] Sklar asserts that “in Minkowski spacetime we
do not discuss distances between events, but rather the interval between them
[along a curve]. This Spacetime
interval] is a number and which is an __invariant__ property of the
spacetime.”[24] (Sklar, pp. 58 – 59) Thus, very happily for Einstein, the interval
between events in Spacetime is always invariant, and the interval along a light
line in Minkowski’s absolute world is always zero.[25] (see Figures 33.4B and 33.5)

Why did Minkowski invent a ‘fundamental invariant’ for his absolute world? Because Einstein discovered that the classical absolutes of “lengths, durations and simultaneities were all found to…vary in magnitude when we:

“changed the constant magnitude of the relative velocity existing between
ourselves as observers and the events observed.
On the other hand, here at least was an invariant magnitude *ds*^{2},
representing the square of the spatial distance covered by a body in any Galilean
frame, minus *c*^{2} times the square of the duration required
for this performance (the duration being measured, of course, by the standard
of time of the same frame). It mattered not whether we were situated in
this frame or in that one; in every case, if *ds*^{2} had a definite
value when referred to one frame, it still maintained the same value when
referred to any other frame.”
[26]
(D’Abro, 1951, p. 195)

This is nothing more than mathematical gibberish.

The mathematical justification for Minkowski’s __absolute__
Spacetime Interval ds^{2} depended *inter alia* upon Einstein’s
relativistic concepts of kinematics, *inter alia*, the ‘Relativity of
Simultaneity’ and the ‘Relativity of Length,’ and their mathematical
counterparts ‘Time Dilation’ and ‘Length Contraction.’ (see Figure 33.4B) In previous chapters of this book we have
explained why these *ad hoc* concepts are arbitrary, empirically invalid
and meaningless. (Chapters 26 and
28) It also depended upon Einstein’s impossible
second postulate concerning the absolute propagation velocity of light at *c*,
relative to everything, which we have also found to be empirically
invalid. (see Chapter 21) Therefore, there is not even a valid
mathematical justification for the Spacetime Interval ds^{2}.

Empirically, we also know that the
time interval and the space interval for the transmission of light from one
place to another, or from one star to the Earth, is not zero; rather it is *c*t. In the twenty-first century we can measure
these real intervals with EM radiation (vis., radar, radio waves, and lasers),
and we can detect and calculate such measurement data with sensors and computers. Therefore, the invariant Spacetime Interval
(ds^{2}), which has an absolute relativistic value of zero, is
empirically invalid and meaningless in the real empirical world of space and
time.[27]

In Section V of his lecture,
Minkowski described what he called a striking advantage afforded by his world
postulate; it involved “the effects proceeding from a point change __in any
kind of motion__ according to the Maxwell-Lorentz theory.”[28] (Minkowski, 1908 [Dover, 1952, p. 88]) This was, of course, a generalization of
Einstein’s Special Theory which only involved inertial motion. Minkowski then proposed a new four
dimensional law of attraction, which he claimed mathematically resulted in
Kepler’s laws. According to Minkowski,
this new law of attraction, when combined with his new mechanics (reformed in
accordance with the world postulate), was just as capable of explaining
astronomical observations as *Id*.,
p. 90) Finally, Minkowski ended his
lecture with the assertion that he had just pre-established a “harmony between
pure mathematics and physics.” (*Id*., p. 91)

Why did Minkowski feel compelled to
invent Spacetime geometry, with all of its bizarre mathematical concepts, axioms,
conventions and consequences? Because
this was the only way he could describe a multidimensional world that was
governed by the Lorentz transformations, Special Relativity and
mathematics. If we discard the *ad hoc* Lorentz transformations and
Einstein’s empirically invalid Special Theory, as we must, then the only remaining
rationale for Spacetime geometry is a playground for pure mathematicians.

The reciprocal of this fact is that embedded in Spacetime geometry are the Lorentz transformation equations and the mathematical consequences of Special Relativity. Therefore, any Spacetime diagram is nothing more than a graphic representation of how a phenomenon or an event should look from the distorted perspective of Special Relativity. Spacetime geometry illustrates and demonstrates the mathematical consistency of Special Relativity, and vice-versa.

In other words, they are both
mutually validating mathematical constructs.
This *ad hoc* type of validation
is both circular and meaningless. It is
like demonstrating the validity of the Lorentz transformations with the mathematical
consequences of Special Relativity, and vice-versa. The result is absolutely certain, but also
worthless.

**C. Conclusions Concerning Spacetime**

Minkowski referred to Spacetime as an “independent reality” and implied that it was physically real;[30] whereas Dingle characterized Spacetime as ‘metaphysics.’ (Dingle, 1972, p. 169)

“Einstein was not at first impressed by Minkowski’s mathematical recasting of special relativity theory. He found it ‘banal’ and called it ‘superfluous erudition’. (Cropper, p. 220) Dingle describes the reception of Spacetime similarly:

“The immediate effect…of Minkowski’s paper was mainly one of mystification; Einstein himself is reported to have said that after reading it he felt he did not understand his own theory—which is not surprising, since Minkowski’s ‘time’ was only ‘eternity’ and Einstein’s was only ‘instant’ or ‘duration’. (Dingle, 1972, p. 173)

However, as Einstein got involved with his General Theory
of Relativity, Gaussian geometry and Riemann’s concept of curved space, he
found Spacetime to be indispensable. By
1916, Einstein even devoted the entire Chapter 17 of his book *Relativity*
to Minkowski’s four-dimensional Spacetime, and toward the end he stated:

“Without it the general theory of
relativity…would perhaps have got no farther than its long clothes.” (Einstein, *Relativity*, p. 63)

The reason why Einstein used
Spacetime Euclidean geometry for his unnecessary and empirically invalid General
Theory is because his General Relativity is in large part a theory of
non-Euclidean geometry (if that statement makes any sense). He needed Spacetime, *inter alia*, to
illustrate and explain his mathematical concepts of curved space and curved
Spacetime (gravity), and his later mathematical model of a finite spherical
universe. (Einstein, 1917 [Dover, 1952,
pp. 177 – 188) However, one should remember
that all of these contrived and interdependent relativistic and mathematical
theories had their origin in Einstein’s *ad
hoc* Special Theory, and his failed attempt to justify his invalid and
impossible second postulate: that the
velocity of a light ray was always c for every inertial observer regardless of
such observer’s linear motion toward or away from such light ray.

Most of Einstein’s
followers blindly accepted all of the above esoteric and amorphous mathematical
theories as physically real and empirically true. The result is that Spacetime geometry, along
with Special Relativity and General Relativity, are taught to students as
required courses in many of the world’s universities. These *ad
hoc* mathematical theories have almost universally become accepted as valid
science. They are currently the primary
foundation and justification for uncountable pure mathematical theories
concerning the universe and the quantum world.
(For example, see Wheeler’s 1999 book, *Journey Into Gravity and
Spacetime*) The Big Bang,
singularities, the spherical universe, the expanding universe, the expansion of
space, quantum mechanics, particle physics, quantum field theories, and the Superstring
theories are only some of the most notable examples. They form the top of the current theoretical
and relativistic house of cards. This is
not physics; this is not science; it is not even science fiction…it is
pseudo-science.

Minkowski began Section I of his
1908 lecture with the statement: “I
should like to show how it might be possible, setting out from the accepted
mechanics of the present day, along a purely mathematical line of thought, to
arrive at changed ideas of space and time.”
(Minkowski, 1908 [

“since G* _{c}* is mathematically more
intelligible than G

Dingle agreed with Minkowski and
asserted: “Reduced to its essence,
Minkowski’s paper is a piece of __pure mathematics__.” (Dingle, 1972, p. 169) Dingle also concluded:

“the process of
allowing __mathematics to direct physics__, which began with Maxwell…had now
reached a point at which it is taken as the proper function of mathematics to
order physics along the path which mathematics points out, and __mathematics
is chided for neglecting this duty and allowing physics to choose its own way__. The __return to medieval scholasticism__,
against which the protest of Bacon and the other pioneers of modern science was
thought to have been finally successful, was now complete. __With Minkowski’s work physics had escaped
from experiment and been captured by mathematician__s.” (*Id*.,
pp. 170 – 171)

“[Spacetime]
contributed perhaps more than any other single factor to the __transformation
of mathematics from the servant into the master of physics__, and __introduced
more false ideas__ into the subject—pre-eminently the totally irrelevant idea
of time (eternity)—than anything else.
It is to Minkowski that we owe the idea of a ‘space-time’ as an __objective
reality__—which is perhaps the chief agent in the transformation of the whole
subject from the ground of intelligible physics into the heaven (or hell) of __metaphysics__,
where it has become, instead of an object for intelligent inquiry, an __idol
to be blindly worshipped__.” (Dingle,
1972, p. 169)

All of Dingle’s conclusions are
euphemistically wrapped up in Minkowski’s final conclusion in his lecture: that his Spacetime geometry creates “a __pre-established__
harmony between pure mathematics and physics.”
Minkowski ended this lecture with the following statement:

“The validity
without exception of the world-postulate, I like to think, is the true nucleus
of an electromagnetic image of the world, which, discovered by Lorentz, and
further revealed by Einstein, now lies open in the full light of day.” (Minkowski, 1908 [

Needless to say, Minkowski’s *ad hoc*
Spacetime geometry is empirically meaningless and must be discarded by everyone
(other than pure mathematicians) before it can cause more mischief for physics.

[1] Actually, Poincaré suggested a similar concept in 1905 when he “combined the three spatial coordinates and time into a ‘quadruple vector’…” (Folsing, p. 163)

[2] “From 1905 until…1919… ‘the theory of relativity’…was regarded merely as a more obscure form of a theory that belonged to Lorentz.” (Dingle, 1972, p. 167) Minkowski’s similar conclusion shows his “lack of understanding of the important distinctions between [the work of] Lorentz and Einstein.” (Goldberg, p. 127)

[3] Later in
his lecture, Minkowski made another empirical statement: “Nobody has ever noticed a __place__
except at a time, or a __time__ except at a place.” (Minkowski, 1908 [*ad hoc* mathematical
Spacetime concepts, and a point in space is not a place.

[4] Such
invariance of the transmission velocity of light at *c*, of course, had nothing to do with Lorentz’s contraction
hypothesis. (see Chapters 6, 10, 12, 15
and 21)

[5]
Michelson’s negative results, in conjunction with Lorentz’s *ad hoc* hypothesis that the longitudinal
arm of Michelson’s apparatus had contracted in the direction of motion, were
misinterpreted to mean that the velocity of light was always the same (or
invariant) in all directions of the Earth’s solar orbital motion.

[6]
Minkowski criticized Lorentz’s contraction hypothesis as being *ad hoc*, illogical, fantastical and a
gift from God. But, he then dismissed
these valid criticisms and proceeded mathematically as if he had never made
them.

[7] This, of
course, is *ad hoc* and mathematical __circular__
reasoning.

[8] No contraction of matter is necessary to explain Michelson’s paradoxical null results. The M & M paradox was caused by invalid theoretical measurements from stationary ether which mathematically resulted in a theoretically greater distance for a light ray to propagate in the direction of the Earth’s solar orbital motion. Because stationary ether does not exist there can be no valid measurements from it, therefore such theoretically greater distance for light to propagate never existed either. It’s just that simple. (See Chapter 12 for a full explanation of the M & M paradox.)

[9] Since
Spacetime geometry is empirically invalid on its face, we could end this
chapter at this point. But that would
leave the reader without a full understanding of just how *ad hoc* and artificial Spacetime really is. So we will continue with a more complete
explanation of this totally meaningless mathematical concept.

[10] Many relativists agree with this conclusion. For example, see Feynman, 1963, pp. 17-1 through 17-8, and Dingle, 1972, p. 170.

[11] Never
before did coordinates refer to __space__.
Einstein only used them to refer to a material __place__. This abstract statement was as if Minkowski
was referring to

[12] Each world point represented an event or an observer.

[13]
Minkowski conjectured: “in my opinion
physical laws might find their most perfect expression as reciprocal relations
between these world-lines.” (*Id*., p. 76)

[14] In effect, Minkowski “suggested a geometric representation for relativity so that many of [Einstein’s] strange relations between space and time can be pictured and much can be understood without the use of algebra.” (Rohrlich, p. 75) However, “we cannot speak of anything changing or moving in a space and time diagram because time has already been used [as a dimension] and cannot be used twice.” (Harrison, p. 131)

[15] “Time has only one dimension.” (Harrison, p. 130) Its line from the past to the present to the future forms the continuum of eternity. (Figure 33.3A)

[16] The
idea of four dimensions had long been used for depicting sets of connected
events, of which time is a coordinate.”
(Goldberg, p. 163) “Space and
time diagrams, with their events and worldlines, were used by the Medievalists,
and there is nothing particularly difficult or novel about them. Until the beginning of [the 20^{th}]
century they were regarded as a convenient graphic way of illustrating the way
things change. Then came special
relativity and pictures of this kind acquired a new __physical__
meaning.” (

[17] A spherical light wavefront emitted at the zero point of any frame would expand up the surface of the light cone each second in an ever-widening sphere.

[18] Figure 33.1 is situated above the 0 point.

[19] The
author does not expect the reader to fully understand Minkowski’s Spacetime
geometry from the above axiomatic descriptions.
But such descriptions should give the reader an idea of just how
abstract and *ad hoc* Spacetime
geometry really is. See Sklar, pp. 56 –
61, for a short explanation of Minkowki’s Spacetime.

[20] With regard to the theoretical unassailability of the Lorentz transformations, max Born stated as follows: “The simple fact that all relations between space co-ordinates and time expressed by the Lorentz transformation can be represented geometrically by Minkowski diagrams should suffice to show that there can be no logical contradiction in the theory.” For Dingle’s response, see Dingle, 1972, pp. 231 – 232.

[21] For a description of Spacetime, the relativistic ‘four vectors’ and four-vector algebra, see Feynman, 1963, pp. 17-1 – 17-8.

[22] However, we ask the question: How can a system of reference determine a distant magnitude of energy?

[23]
Minkowski stated that such equation ‘becomes perfectly symmetrical in x, y, z,
s [where s = √-1t,
√-1 secs = 3.105 km, and *c*
= 1]; and this symmetry is communicated to any law which does not contradict
the world postulate.” (Minkowski, 1908 [

[24] If the number is positive it is called a ‘space like separation’’ if it is negative it is called a ‘time like separation;’ and if it is zero it is called a ‘light like separation.’ (Sklar, p. 59)

[25] *Id*., p. 134) More circular
reasoning.

[26] For more information about Minkowski’s so-called ‘fundamental invariant,’ see Goldberg, p. 166; Cropper, p. 219; Harrison, pp. 131 – 135; Feynman, 1963, pp. 17-2 – 17-4; Einstein, EB 1969, Vol. 20, pp. 1071 – 1073.

[27]
Nevertheless, in the tiny world of quantum mechanics, it might be __interpreted__
to have an __approximate__ validity and meaning.

[28]
Minkowski thereafter claimed that: “the
fundamental equations for electromagnetic processes in ponderable bodies also
fit in completely with the world postulate.”
(*Id*., p. 90)

[29] What
effect did those *ad hoc* claims by
Minkowski have on Einstein and his quest for a new General Theory of gravity?

[30] Many
other relativists also characterize Spacetime as physically real. For example:
“Space…in
conjunction with time,…possesses __physical__ structure.” (__physical__ reality.”
(*Id*.