The eclipse of causality in 20th Century thought is one of the
leading characteristics of this Dim Age. A revolt against causality
began with influential 18th Century philosophers, notably Hume and
Kant. The revolt grew throughout the 19th Century and, in the late
19th and early 20th Century it reached physics, where it gave rise to
the two central theories of 20th Century physics: relativity and
This may raise some hackles; for while quantum mechanics' disdain
for causality is not the least controversial, relativity is usually
regarded as a causal theory, a haven of sanity compared to quantum
mechanics. Unlike quantum mechanickers, relativists don't crusade
against causality; indeed, they occasionally appeal to it.
Relativity's sins against causality are more subtle, but no less
Causality and Measurement
Relativity's link to the revolt against causality is the movement
called positivism, as exemplified in physics by Ernst Mach (of Mach
number fame). Mach's inspiration was the French philosopher Auguste
Comte, who originated and named positivism. (Comte was also busy in
ethics; he coined the term "altruism.") Mach's influence on physics in
general, and on Einstein in particular, is well known.
Positivism rejects causality. According to positivism, causal
thinking is merely a pre-scientific relic. Modern science is
mathematical; its results are expressed in equations. But these
equations merely report what is observed, namely that certain
quantities are equal; they say nothing about causes. Since equations
are the whole content of modern science, and since they are merely
descriptions, and not causal explanations, modern science need not
be concerned with causes. Science has advanced beyond causality, and
may now discard it.
This positivist argument is a classic example of the fallacy of the
stolen concept. The concepts of "measurement" and "quantity" (not to
mention "equation!") rest on causality. To see this, recall that we
can only identify quantity by means of measurement, that measurement
is a process of counting equal units, and that our only guarantee of
equal units is causality. (For the logical necessity of equal
units, see my essay,
Time, clocks and causality, especially the section "Units,
arithmetic and identity: Experimenting on children.")
The logical requirement of equal units is truly elementary, a
matter of everyday experience. For example, it would be ridiculous to
measure lengths using a bar of Jello because the length of a bar of
Jello would vary with a myriad of causes between measurements; it
would not provide equal units. A steel tape provides a better standard
because its length varies less than the length of a bar of Jello, and
in a more predictable fashion, according to known causes such as
tension and temperature. The speed of light in a vacuum provides an
even better standard, being unaffected by the run of the mill causes
which affect steel tapes and bars of Jello. The less the changes in
one's standard, the more accurate one's measurements.
An absolutely accurate standard would have to be immutable, utterly
immune to causal influences: it would have to be acausal. Since
nothing real is acausal, measurement requires one to discover the
causes which may change one's physical standards, and to correct for
them. Immutable standards are not found lying about in nature; one
constructs an immutable standard by defining a physical standard
according to the best causal knowledge available, and by correcting
for its variations. One can validate one's measurements and identify
quantities only by reference to causality.
Causality is prior to quantity.
This may seem an audacious conclusion, but only in theory. It
reflects the universal practice of all who perform measurements, from
household cooks to Bureaus of Standards. All of them ensure that their
standards are immutable by eliminating as far as possible all the
causes which could change them and, in the last resort, by correcting
for those changes which are unavoidable. It is only this painstaking
care to construct immutable standards which renders measurements
Contrary to the assertions of positivists, causality is essential
to mathematical science. Mathematical science may not dispense with
causality; all of mathematical science--all the equations, laws,
theorems and so on--rests on causality! Only complete and precise
understanding of the causal influences on one's measuring standards
can give meaning to one's measurements. Those measurements in turn
give meaning to the equations based on them.
It is usual these days to regard a physical theory as no more than
the equations it uses, but this is not true. Equations rest on and
summarize a vast body of measurements; those measurements are no more
valid than the standards by which they were made; and the standards
are no more valid than the causal knowledge by which they were
defined. That causal knowledge (or error) is the essence of a physical
theory; wildly different physical theories can have a great many
equations in common.
If a measuring standard varies who-knows-how, then the quantities
measured by means of it vary who-knows-how, and the equations
connecting those quantities mean who-knows-what. This is precisely the
bog in which relativists have mired themselves; their doctrine of
curved space is symptomatic.
Rigidity and Space
"Curved space" is a staple of 20th Century thought. Space warps are
a cliche of science fiction. Generations of science students have
tried to make sense of curved space, and succeeded only in warping
their minds. Curved space is taken for granted among the learned; if
you protest that curved space is absurd, they roll their eyes and
shake their heads pityingly.
But what the heck does "curved space" mean, and how does it measure
up against the principle of immutable units?
Instruments of geometry
Geometry seeks to measure objects. It deals with such questions as,
"How big is this thing here? How far is this thing here from that
thing yonder? Which is bigger: this thing here, or that thing yonder?"
The answer to them all is straightforward in principle: grab a
measuring stick and go find out.
A gas, a liquid, or a bar of Jello will not make a suitable
measuring stick. If your measurements are to be valid, you will need a
measuring stick which doesn't shrink, expand, shiver, bend or etc. as
you move it from place to place. You need a measuring stick which is
immutable in these respects, one which is rigid.
Measurement requires an immutable standard, and geometrical
immutability is rigidity. Rigidity is prior to geometric quantity.
This is no new thing, as is shown by the traditional instruments of
geometry: the compasses and straight-edge. The distance marked off by
compasses is assumed not to change as the compasses are translated and
rotated; the continued straightness of the straight edge is similarly
assumed. All of classic geometry rests on the assumed rigidity of
compasses and straight edges. These rigid instruments are the
traditional standards of length and straightness.
If any particular compasses and straight-edge are discovered not to
be rigid, that just means they are not adequate to the task we demand
of them, and we must find better ones or apply corrections as needed.
This much is apparent to any beginning student struggling with
slipping compasses and sagging straight-edges. The geometer assumes
rigidity in proving his theorems, but the experimenter must ensure
the rigidity of his standard by reference to causality.
Given rigid standards, the theorems of geometry enable us to
compare near things with far things without actually moving the
things, by defining units, counting them and performing calculations.
We can meaningfully calculate only because our units are
Unfortunately, the classic system of geometry formulated in
Alexandria by Euclid (fl. ca. 300 BC) is silent on the issue of
rigidity. Thereby hangs a tale.
Axiom of parallels
Euclid succeeded in deriving the geometrical knowledge of his day
from five geometrical axioms and five "common notions." (A common
notion is a principle common to all sciences, e.g., "if equals
be added to equals, the results are equal," and "the whole is greater
than a part.") The manifest success of Euclid's system in fields
ranging from carpentry to astronomy testifies that there are no
contradictions among Euclid's axioms, but it has never been clear
whether all the axioms were necessary to the system. Could one of them
be discarded, derived from the other axioms, or replaced with a
Euclid's first four axioms are simple and obvious, so attention
focused on his fifth axiom: the axiom of parallels. There are various
formulations of Euclid's fifth, but one of the simplest states that
precisely one straight line can be drawn parallel to a given straight
line, through any point not on the given line.
There are a number of problems with this axiom. It is messy--its
self-evidence is not obvious. Worse, it is negative; it refers
to what will not be found where you can never
look--i.e., that two lines will not meet at infinity.
Thinkers have long been queasy about Euclid's fifth axiom. There is
clear evidence that issues involved in the axiom of parallels were
discussed in Aristotle's school. (This evidence was collected in a
Scientific American article, published in the 1970s or 80s, on
non-Euclidean geometry in Aristotle. I would
welcome the exact
reference.) Euclid was probably connected with Aristotle's school, and
he himself had qualms about the axiom of parallels, as shown by the
fact that he used it sparingly; he proved his first 28 propositions
without invoking it.
Euclidean or non-Euclidean?
In the 18th Century, some geometers set out to test the axiom of
parallels by denying it and checking if a contradiction would result.
The axiom of parallels can be denied in two different ways, either by
saying that no parallel to the given line can be drawn, or by saying
that more than one parallel can be drawn. In the 19th century it was
found that both denials led to internally consistent non-Euclidean
systems when combined with the other Euclidean axioms.
It was soon recognized that two-dimensional non-Euclidean systems
applied to curved surfaces rather than planes--provided one was
willing to accept the violence this did to the idea of a straight
line. But what of the three-dimensional case? Could it be that real,
observed, physical space was non-Euclidean, and therefore in some
sense curved? Since the three (kinds of) systems contradicted one
another, they could not all be true. A decision between them was
required, but on what basis?
Mathematicians (under the influence of bad philosophy) had come to
regard coherence, or logical consistency, as the standard of
geometrical truth. But for this problem, coherence was apparently a
non-starter: in terms of the accepted axioms, all the systems were
equally coherent. This was taken to mean that logic could not decide
Furthermore, measurement could not decide between systems. Euclid's
system was obviously consistent with all measurements that had been
made, but to exclude all non-Euclidean geometries would require
infinitely precise measurements, and infinitely precise measurements
are not to be had. With logic and measurement ruled out, a consensus
grew (egged on by philosophical irrationalism) that any decision
between systems would be arbitrary.
There was progress when Gauss (1777-1855) discovered the intrinsic
geometry of surfaces. He found that the shape and curvature of a
surface (in Euclidean space) could be discovered by measurements of
length made entirely in that surface. For example, surveyors on the
Earth can deduce from their surface measurements that the Earth is
approximately spherical. This showed that questions of straightness or
curvature can be settled in some contexts by an appeal to a standard
Riemann (1826-1866) generalized Gauss' result to show that a
"curvature" of higher dimensional spaces could be defined by
measurements made solely within them. He found that these measurements
characterized the many-parallel class of non-Euclidean geometries as
an infinity of spaces of constant negative curvature, the no-parallel
class as an infinity of spaces of constant positive curvature, and
Euclidean geometry as a unique space of constant zero curvature. This
neatly displayed all the contending systems on a continuum of
curvature, but it raised the daunting prospect of yet more infinities
of non-Euclidean spaces of non-constant curvature!
Apparently Riemann had only compounded the muddle by introducing
new infinities of contending geometries. In fact, he had all but
settled the issue; all he lacked was the philosophical principle of
How does Riemann's work enable us to select the correct system of
I cannot resist remarking that when--amid infinities of candidate
geometries with curvatures which range from minus infinity to plus
infinity--and amid further infinities of candidates with curvatures
which vary in more ways than you can imagine--there is precisely one,
single, unique system with a constant curvature of precisely
zero--then it might as well be emblazoned with flashing neon signs and
loudspeakers blaring out, "Pick me! Pick me!" But this is not my
Riemann's measurements are based on "metrics." A metric is a
certain function of position that Riemann was able to define for each
of the candidate systems, and which is that system's standard of
measurement. In the Euclidean case, the metric is independent of
position and yields ordinary length. In non-Euclidean cases, the
metric varies with position. It is precisely this variation which
expresses the "curvature" of the space; a space is "curved" only if
its metric varies with position.
If we now appeal to the principle of rigid units, this settles the
issue of flat vs. curved space! For we have just seen that curved
spaces have standards of length which change with mere change of
position, and the principle of rigid units forbids this! I.e., curved
space diddles the standard of length, and so must be rejected. The
rejection of curved space is neither arbitrary nor dependent on
physical measurement: it is logical.
Only in Euclidean geometry is there a standard of length which does
not change with position, i.e., which is rigid. Flat, Euclidean space
is the system of geometrical measurements made with rigid
Curved space is simply a system of measurements made with squidgy
units. (E.g., Jello measuring sticks.) That is the trivial secret
behind the gaudy curtain of curved space theories. Despite the mighty
theatrics, there is nothing behind the curtain but a dishonest little
man who refuses to admit that he fudged the units.
Riemann's work serves as a reductio ad absurdum of curved space,
but it is much more useful than that. Once you grasp that curved space
implies variations in your measuring sticks, you can recognize
Euclidean geometry as a logical standard for judging real
If your measurements show space to be "curved," you can validly
deduce that your measuring sticks are not rigid--even if you have
no other evidence of their variations. Then you can ask, "What
causes them to vary?" By adopting the logical standard of
Euclidean space you can discover causes which a curved space theory
would whisk behind the curtain of "space curvature."
Furthermore, there is a mathematical transformation which reduces a
general Riemannian system to a Euclidean one. The transformation to
Euclidean geometry reveals the variations in the measuring sticks, and
the lengths in the Euclidean system are lengths. In other
words, we can extract knowledge of absolute lengths from our
measurements even if our physical measuring sticks are not
This transformation is a precise mathematical form of the common
sense thought that we don't need absolutely rigid sticks, provided we
can figure out how they vary. It tells us that we can figure
out how they vary, so that we can make absolute length
Notice the logical order involved. First, we must demand rigid
units. Then we can select Euclidean geometry as the only system in
which there are rigid units. Then we can identify deviations from
Euclidean geometry as signs of systematic errors in our measurement
standard. Then we can discover and correct for such errors. The
principle of rigid units is the keen sword that slashes the Gordian
knot of curved space.
Just as we can cite contradiction as proof of an error in logic,
and as we can cite dilatory time as proof of an error in time
measurement, so we can cite curved space as proof of an error in
length measurement. (For the case of absolute time, see
Time, Clocks and
We can surmise that variations in other standards will reveal
themselves by similar signs. As we identify such signs for one
standard after another, we will demonstrate the absolute nature of
measurement in field after field--in terms specific to each field. Our
warrant in each case will be the laws of identity and causality, and
the principle of immutable units.
Axiom of rigidity, or a new common
It is now clear that the axiom of parallels can be replaced.
By insisting on a rigid standard of length, we single out precisely
that set of theorems which was derived by means of the axiom of
parallels. In other words, the non-obvious, negative axiom of
parallels can be demoted to a theorem, and replaced by an axiom of
But an axiom of rigidity would simply be an application to geometry
of the principle of immutable standards which is common to all
measurement. Therefore it would be better to make this explicit by
invoking the principle of immutability as a new common notion.
Where does all this leave curved space theories? It leaves them
with neither an epistemological nor a geometrical leg to stand on!
Relativity has encoded (encrypted!) its physical content in terms
of curvaceous space and dilatory time. This procedure is not merely
odd, but flat out wrong--as wrong as constructing a theory out of
contradictions. Freeing modern physics from the 20th century hash of
syncopated clocks, Jello compasses and squirming straight-edges will
be a massive job, but we can leave it to physicists.
The rest of us can heave a sigh of relief as we abandon the
hopeless task of trying to imagine curved space. And the next time
someone tries to sell us an option on curved space, we can roll our
eyes and shake our heads pityingly! We can also use our new
understanding of space to draw some long overdue distinctions.
Space, Void and Vacuum
Space, void and vacuum are usually regarded as synonyms for
emptiness, but this will not be an empty discussion.
Quite the opposite! By drawing distinctions between space, void and
vacuum, we are able to re-affirm that reality is full, that it is a
plenum. This re-affirmation is no mere philosophical nicety, of
concern only to those who take an eccentric interest in obscure issues
of metaphysics. It points to a neglected physical reality of
fathomless importance for human knowledge and action.
Space: a concept of method
Space is often supposed to be a sort of box in which existence is
placed, or a sort of insubstantial stage on which the drama of reality
unfolds. These notions have the fatal flaw of making space into
something prior to existence or apart from existence. But nothing
exists apart from existence, so these notions boil down to the idea
that space is simply emptiness, non-existence.
Men tend to think of space as a box because they think of it as
metaphysical--as something which is intrinsic, which exists
independently of consciousness. We draw a firm distinction between
space and the entities in space, from yon cat to stars and galaxies.
We distinguish space from all the "stuffs" which may "fill" space. But
if space is regarded as metaphysical, these distinctions leave it with
nothing whatever that it can be but a shadowy, unperceived box
The puzzle is instantly resolved by recognizing that space is not
metaphysical, but epistemological. Space is a product of human
method just as numbers and concepts are products of human method. Like
them, space does not exist independently of consciousness; like them
it is neither arbitrary nor intrinsic: it is objective.
Space is a grid of reference lines which we imagine to be
constructed according to geometrical method. We imagine these lines to
run through reality in the same way that we imagine lines of latitude
and longitude to overlay the globe of a planet. We construct them to
help us to visualize geometrical measurements.
One indication that space is a concept of geometrical method is
that it grew up with geometry. In Aristotle's pre-Euclidean time,
geometry was relatively new; and Aristotle is silent on the subject of
space. Instead, he speaks of "place," which he defines in terms of
bodies: "the innermost boundary of the containing body." (Phys., IV,
4) Only after geometry had won men's confidence did they boldly extend
their reference lines through the entire universe. The concept of
universal space was the result, as was our modern ability to define
"place" in terms of our reference lines, and thus explicitly to relate
all parts of the universe to each other.
Another indication that space is a concept of method is the fact
that the controversy between flat and curved space is a controversy
over method; should geometry employ rigid units or squidgy units? If
you employ rigid units, then you construct a flat space. If you use
squidgy units that vary with position, you construct a curved space.
The allegedly unknowable changes in your units are revealed by the
flatness or curvature of the resulting space. (See above.)
Space is an epistemological construction, a product of human
This lets us solve the puzzle that although every fragment, scrap
and particle of the universe is in space as in a box, yet the universe
itself is not in space. The reason is that we draw our boxes
in the universe. The universe is not in space, space is in the
Our reference lines do not affect real things; they are, after all,
imaginary. Lines of latitude and longitude cannot trip you; you cannot
stumble over the equator. Even if you resort to squidgy units and take
pains to draw your lines around rocks, you still cannot stumble over
your lines, but only over the rocks. Space is not a cause because
space is not an entity.
It is idle to debate the infinity of the universe by appealing to
concepts of space. Some curved spaces are indeed finite; but that
depends on your choice of units, and your choice of units cannot
dictate to reality. Indeed, those who employ a finite space must face
the jibe that their space is too small for reality, leaving some parts
Flat space on the other hand cannot be too small for reality. When
you use rigid units, you can extend your grid as far as the universe
extends--and the universe is boundless. Existence exists everywhere,
and flat space enables us to extend our lines everywhere. Everywhere
Employing flat space, you can draw your lines in any directions you
wish, passing through any points you wish, because flat space is based
on rigid bodies, and they are rigid under translation and
Flat space is thoroughly and completely acausal. No space is
a cause, but in addition, flat space is not subject to causes. Nothing
whatever can curve, bend, deflect or tangle our flat space reference
lines, for the simple reason that we exclude causes by employing rigid
units. Flat space is utterly acausal; we know it is, because that's
the way we made it.
Our use of acausal, flat space does not hamper our discovery of
real causes: it makes it possible. Curved space can hide causes
behind the squidginess of its units, but flat space is the incarnation
of a null hypothesis. It embodies an assumption of rigidity, of
acausality. Any discrepancy between geometrical knowledge of rigid
bodies and physical measurements of a real body implies that the real
body is not rigid. That's our cue to ask, "What caused that?"
Void: an epistemological error
"Very well," you may ask, "if space is our visualization of
geometry, what are we to call a place from which everything has
been removed?" The name for this notion is "void," but like the
unicorn, there ain't no such animal!
If everything were to be removed, what would be left would
be nothing. As Parmenides pointed out about 2500 years ago, and
as Ayn Rand reminded us more recently, there is no nothing. To say
that a void exists is to say that there is a place where non-existence
nevertheless exists. Void is absurd--an epistemological error, a
figment. There is something everywhere; reality is full. It has no
"gaps." This conclusion has puzzled thinkers since ancient times, and
their struggles are instructive.
If reality is full, how can we see gaps all over the place?
To perceive a number of entities is to perceive that they are
separate; to see this cat and yon dog is to see a gap between
Faced with this, Parmenides himself lapsed into collectivism and
rationalism: he declared that there are no separate entities, that our
senses deceive us; there is only a mystic unity: The One.
Ancient atomists sought to preserve individuality and the evidence
of perception by ditching Parmenides' axiom: they declared that
everything is made up of atoms and the void, and that
void--non-existence--exists every bit as much as the atoms! Their
desperate expedient was doomed from the start, for a trivial exercise
in logic will extract from it the same rationalistic, collectivist
conclusion: "Void is nothing, and void separates the atoms; so nothing
separates the atoms. So all is One, and individuality is mere sensory
illusion." Atomists raised the specter of a real void, and it has
haunted the outer reaches of science ever since.
Parmenides and the atomists share the error that perceptual gaps
are voids. They differ only in the way they use the error.
Parmenides says, contrary to perception, that gaps do not exist;
because voids do not exist, and gaps are voids. The atomists insist,
contrary to the axiom of existence, that void exists; because gaps
exist, and gaps are voids.
The solution is to admit--on the warrant of perception--that
perceptual gaps exist, and--on the warrant of the axiom of
existence--that gaps are not nothing: something exists between
What is it? Void is not an option, and space is no answer. Space is
merely our system of reference lines. Our new question is "What is the
stuff through which we draw those lines between entities?" This
stuff is prior to our lines, prior to space. What's the stuff?
Rationalists may as well leave right now, for this question
cannot be answered by deduction; we have no premises from which
the deduction could proceed. The only positive fact we know about our
"stuff" is that it exists, and you cannot deduce what a thing is from
the premise that it is something. To learn more, you must observe
Bricks, to air, to vacuum, to ...?
Suppose we observe a cat and a dog on opposite sides of a brick
fence. What is between them? Obviously there are bricks between them.
That's no problem for anyone: we all know that bricks exist.
But if we remove the bricks from between our critters, they don't
merge into the mystic unity of The One. They are still apart; they are
still distinct entities. Now what's between them?
You might hazard the suggestion that there is air between them.
Congratulations! That recognition marks a great and difficult advance
of science. The existence of air was not always obvious; as late as
Alexandrian times, experiments demonstrating the reality of air were
thought to be necessary. After all, air is shapeless, colorless,
invisible, non-dog, non-cat, non-etc. If you focused on these
negatives, you would be led to think that air is mere void. But you
would be wrong; there is air between our cat and dog; air
Gradually, by further observation and experiment, man learned that
air is not a fundamental, elemental constituent of reality. Rather,
air is made of entities: air is a mixture of molecules, which are made
up of atoms, which are made up of subatomic particles. But those
particles aren't merged into mystic unity; there is something
between them. What is it?
In the context of knowledge sketched above, the answer is
vacuum, or if you prefer, ether. The description of vacuum
involves even more negatives than the description of air; but no list
of negatives, however long, can justify the conclusion that
vacuum is void: void is a mere figment. To the contrary, we have
positive evidence for the existence of vacuum, namely, the
separateness of particles.
There is vacuum between particles: vacuum exists.
If we look ahead to a hypothetical future, it may turn out that
vacuum, too, is made up of some kind of entities. Then the axiom of
existence will oblige future scientists to ask what exists between
those entities. Or, if future scientists find they can remove even
vacuum from a vessel, then the axiom of existence will oblige them to
ask what exists between the walls of the vessel. Or, perhaps, vacuum
will turn out to be elemental, a primary constituent of reality. Only
further evidence can decide the issue.
What can we say about vacuum? Not much, but some. Vacuum transmits
electrical and magnetic forces with a time delay which depends on
distance. Vacuum transmits gravitational force. If one assumes that
gravitational force travels through vacuum at the speed of light and
is aberrated like light, one arrives at the correct orbit for the
fast-moving planet Mercury. (Paul Gerber published this calculation in
1898. See Petr Beckmann's
"Einstein Plus Two," Sec. 3.1) Vacuum transmits light and, near
massive bodies, it deflects light. Certain kinds of clocks run more
slowly as they move faster through vacuum. Particle masses increase
with their speed through vacuum.
These facts are all certified by uncontroversial experiment. They
are conventionally "explained" in terms of relativistic space-time
curvature, but such explanations are worthless. Curvaceous space and
dilatory time are means to delude yourself by using squidgy measuring
sticks and inconstant clocks. What delusion might one seek by means of
variable units? Relativists choose their variable units to maintain
the delusion that vacuum does not exist.
I'm not guessing about this; it is implicit in their procedure.
They begin by denying a real vacuum--in their jargon, an "ether" or
"preferred reference frame"--and they derive units which vary
precisely as required by that dogma. Their fudged units obediently
conceal much of the evidence for vacuum. (The evidence that they
have fudged the units--namely, their curved space and inconstant
time--remain manifest to all who look.) Relativists' denial of vacuum
revives the irrational metaphysics of the ancient atomists, for it
amounts to the assertion that non-existence exists between
We can now understand why relativists must postulate the
speed of light in vacuum to be a universal constant. They equate
vacuum with void; and if vacuum were nothing, there would indeed be
nothing which could change the speed of light in vacuum! Relativists
have no grounds to be smug about this fragment of consistency, for it
comes at a terrible price: it banishes reason and causality from
Just as a void would be unable to cause any change in the speed of
light, it could not cause light to have a speed, and certainly
could not cause it to have one particular speed rather than another.
Instead of regarding the motion of light in vacuum as an experimental
fact to be explained by its causes, relativists must regard it as a
metaphysical miracle, forever and in principle inexplicable:
absolutely causeless. Indeed, light itself and all forces
between particles become miraculous; for they would have to propagate
through a void, i.e., through nothing at all! To equate vacuum
with void is to spawn an endless torrent of contradictions, for void
is itself a contradiction.
Back in reality, variations in the speed of light in material media
are commonplace; they cause the everyday effect of refraction.
Refraction between air and glass or plastic makes eyeglasses work, and
refraction between air and water makes a stick which is partially
immersed in water appear sharply bent at the water surface. Refraction
between warmer and cooler air causes the "heat waves" that you can see
over a paved road on a sunny day.
There is positive evidence that vacuum (or ether) is pretty much
like any other medium, being affected in specific ways by specific
causes. For example, starlight passing near the sun is deflected from
its usual course. The straightforward conclusion is that vacuum is a
refracting medium, i.e., that the speed of light in vacuum is reduced
near massive bodies.
It's high time for physicists to expel the void from their minds,
and to admit that vacuum exists. They will then be free to standardize
their measuring sticks, to steady their clocks, and to use these tools
to study vacuum.
There's no telling what they'll find! The potential of vacuum
studies for human progress and prosperity is boundless. Vacuum
occupies most of the volume of the universe, and even most of the
volume of every atom of ordinary matter. If men can devise methods to
make this ubiquitous stuff (or stuffs!) serve human purposes, what
might they achieve!