John A. Gowan
The Origin of Space and Time
(revised Oct., 2012)
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Abstract: Why There Are Three
(added Aug., 2013)
Conservation, Causality, Connection: the Dimensions of Spacetime are Entropy Domains Created by Intrinsic Motions c, T, G. The dimensions of spacetime and their metric are the fundamental conservation structures of the Cosmos, necessary for the existence of electromagnetic energy in both its free and bound forms (light and atomic matter).
Fundamentally, the dimensionality of spacetime
is a matter of energy conservation: three dimensions are
sufficient to establish an entropic domain in which the basic
thermodynamic requirements necessary to conserve the energy of
free forms of electromagnetic energy (light, EM radiation, etc.)
are present; likewise, four dimensions are necessary to meet the
conservation requirements of bound forms of electromagnetic
Light is a 2-D transverse wave, with no time dimension and no space dimension in the direction of motion (clocks stop and meter sticks shrink to nothing at velocity c - as per Einstein). Light requires two dimensions to accommodate its alternating electric and magnetic fields, which induce each other at right angles. The energy of light is encoded in its frequency (E = hv) with its implied (but suppressed) time dimension. The intrinsic motion of light ("velocity c") "sweeps out" a third spatial dimension, creating, expanding, and cooling a 3-D spatial volume. The energy component of light is therefore 2-dimensional, while the entropy component corresponds to the 3rd spatial dimension. The entropy "drive" of light (free electromagnetic radiation) is the "intrinsic motion" of light, as gauged by the universal electromagnetic constant "c".
We see that three dimensions are sufficient for
2-D light to establish an entropy domain for its own
conservation needs, and therefore light has no need to explore
additional dimensional possibilities. However, in the case of
3-D bound energy forms of electromagnetic energy (massive atomic
"solids"), one further dimension (time) must be added to
establish the entropy domain for matter (history), in which the
"intrinsic motion" of time produces aging and decay (since atoms
have no spatial form of intrinsic motion they must resort to
time - which also suggests that the 3rd spatial dimension is the
only possible higher-dimensional entropic option for light - if
light is to remain in its free form). Gravity combines these two
electromagnetic entropy domains into our familiar spacetime, the
composite entropy domain of our universe of free and bound forms
of electromagnetic energy. (See: "The
Conversion of Space to Time" .)
(See also the set of four papers, listed below, examining various relationships between the four conservation principles of the Tetrahedron Model of Natural Law) (these short papers are not intended to stand alone):
The central difficulty with the primordial conversion of light to matter is that whereas light is completely connected to its spatial metric and entropic conservation domain by virtue of its intrinsic motion "c", matter lacks any such dimensional connection, as it is intrinsically immobile, "at rest". Indeed, light's intrinsic motion creates space, and also causes its expansion and cooling. "Velocity c" gauges both the spatial entropy drive and the "non-local" metric and distributional symmetry of light. "Velocity c" banishes the asymmetric time dimension (light's "clock is stopped"), maintaining metric symmetry while simultaneously causing the expansion and cooling of space. Matter's energy, however, has no ostensible contact with a spatial metric, entropy drive, or conservation domain, a completely untenable situation from the viewpoint of energy conservation. The solution is found in matter's gravitational field, which forms a physical connection between matter and space, reestablishing contact with light's spatial conservation domain. Through gravity, matter is reconnected to space and light; this connection is not trivial, as it results in the creation of an alternative entropy-carrying dimension (time), entropy gauge ("velocity T"), entropy drive (the intrinsic motion of matter's time dimension) and conservation domain for matter's causal information field (historic spacetime).
This 4th, alternative, entropy-carrying dimension (time) must perform the metric conservation function for bound electromagnetic energy which space performed for free electromagnetic energy. Time is derived from and conjoined to space (by gravity), forming the compound dimensional and entropic conservation domain "historical spacetime", in which both matter and light can interact and find all their conservation needs satisfied.
The spatial/metric connectivity enjoyed by light becomes translated into another type of dimensional/metric connectivity in the case of matter: space becomes converted into time by gravity. The asymmetry of the matter-only particle spectrum invokes a conservation response in a corresponding asymmetry of the dimensional metric: one-way gravitation and time. Material objects are linked by time, gravity, history, and causality, rather than by space and light. The intrinsic motion of our time dimension is metrically and entropically equivalent to light's intrinsic motion in space. Because the Cosmos begins at a single instant of time, every atom in the Universe is of the same age, causally connected, and exists in a universal "now" which is the temporal analog of light's "non-local" habitation of space (see: "A Spacetime Map of the Universe"). We are all connected in time, regardless of our separation in space. (In a black hole, matter apparently falls out of space and into time, to be recycled back into space as light via Hawking's "quantum radiance" of black holes.)
The double issue of linkage and entropy drive within a dimensional conservation domain becomes evident when we think about how yesterday is linked to today by the flow of time and the expanding history of our own lives. This is the necessary linkage of causality; we would cease to exist if it were ever broken, as (for example) should the temporal linkage (an extremely extensive matrix) between today and the moment of our birth become severed. A similar linkage exists between points in space - light rays may travel anywhere without "falling off the edge" or "between the cracks" of space.
While temporal linkages begin as points of contact in a linear sequence, they rapidly divaricate into networks of causal relationships that become so extensive and robust there is no simple way in which they can be severed. The prototypical example is the initiating "break" of a rack of pool or billiard balls at a single point of contact. But this happens continuously on the molecular level of our lives, producing what I refer to as "matter's causal matrix". Similarly, on the gravitational and macroscopic scale, my causal interactions with people and my environment have rapidly ramifying consequences which will continuously effect my future experience ("what a complicated web we weave...").
Space is a connecting dimensional and entropic medium which functions as a metric, structural conservation domain for light's free energy. Space does not preexist light, but is actually produced by the intrinsic motion of light itself. The function of space is simply to regulate and ensure the conservation of light's energy, including all other parameters of free energy which require conservation, such as light's entropy and symmetry. Light is the only energy form which can produce its own conservation domain from its own nature (intrinsic motion) - hence its primacy. Time is an asymmetric form of space, (actually produced from space by gravity or the quantum mechanical collapse of an electromagnetic wave), which (via the creation of the historic conservation domain) plays an analogous dimensional conservation role for matter as ordinary space plays for light. (See: "The Conversion of Space to Time".)
In the joint dimensional conservation domain of spacetime created by gravity, light and matter can interact since their entropy drives/gauges c and T are metric equivalents of each other. This compatibility is ensured by the gravitational extraction of time from space itself (from the implicit temporal component of an electromagnetic wave), and is required by energy conservation if free and bound electromagnetic energy are to coexist and interact. ("Velocity T" is also gauged by "c" as the duration required for light to travel a given distance.) (See: "Entropy, Gravity, and Thermodynamics")
It is impossible for massive objets to travel at or exceed velocity c; because velocity T is the metric equivalent of c, the intrinsic motion of time also imposes a similarly impassable barrier. The reason for these dimensional "speed limits" is to protect causality and energy conservation. We cannot move backward in time to tamper with the past, either by means of fast spaceship or time machine; nor can we outrun the limits of our conservation domain - energy cannot escape conservation: the conservation domain of spacetime is seamless and closed. Because we live in a joint dimensional conservation domain, two different but connected "speed limits" exist, one for space and light, and another for time and matter. The consequence of these limits is that once causality and energy conservation is absolutely protected, then below these limits matter can move freely in space and energy can be used and transformed. We can move and work without concern, because no motion or energy transformation that is physically possible can break the linkage of temporal causality or violate energy conservation. Radiant heat and opportunity escape at velocity c and T; neither can be recaptured by any means, insuring the effective operation of entropy, causality, and the conservation of energy. The dimensions of spacetime are entropy domains, established by the intrinsic motions of light, time, and gravitation in which energy can be simultaneously used, transformed, and yet conserved. (See: "A Description of Gravitation".)
The metric fabric can be stretched, curved, and warped, but it will not break; even a "black hole" can only stop time, it cannot make it run backward. The "event horizon" and central singularity of black holes also seal the borders of spacetime against any gravitational loopholes or inertial tampering with causality or energy conservation (as in "wormholes"). The conservation domain of electromagnetic energy is ironclad in its integrity, protected by the infinite velocities of c and T, and at the "event horizon" of a black hole where g = c, the "infinite" strength of gravity replaces the entropic and metric functions of both t and c - stopping clocks and shrinking meter sticks to nothing.
The one-way intrinsic motion of time is required by and protects causality and energy conservation, while simultaneously providing an unbroken dimensional (historical) linkage with the past. The speed limit of "velocity c" has the same effect, but for space rather than time. This complete spatio-temporal connectivity we can actually see in our great telescopes, extending backward to the origin of space and time in the "Big Bang" itself. As we look outward in space, we look backward in time; nothing that we see is actually accessible to us in the state that we see it, for that would be tampering with causality. But the connectivity of the spatio-temporal Universe is complete and actually visible (in part). The only exception is our own past, but that is visible to other observers, and in principle visible to us also (but only partially), through a mirror. See: "A Spacetime Map of the Universe".
PART II: The Origin of
Space and Time
Everything From Light
The intrinsic motion or entropy drive of time creates an historic conservation domain for information which is joined to space by gravitation (historic spacetime). In addition, because gravity is producing time from space, gravity creates a naturally equilibrated joint dimensional conservation domain of free and bound energy, the continuum of spacetime. How does the formation of this continuum come about? Let us now reexamine this connection from the point of view of time rather than gravity.
As mentioned in part 1, the central conservation problem in the conversion of light to matter is how to duplicate for matter the dimensional connectivity of light with space (that is, how to provide an entropic, dimensional conservation domain for bound energy), since unlike light, matter has no intrinsic spatial motion or connection and cannot move at "velocity c". The solution is the creation (by gravity) of time, a moving dimension in which matter can achieve, in effect, an entropy drive or an intrinsic motion "T" which is metrically equivalent to light's "velocity c" in space. The moving time dimension creates expanding history, the entropic analog of expanding space. In the case of time, however, it is the dimension which moves, not the energy form, conversely to the arrangement between light and space. Matter cannot move at c but it can occupy a unique dimension (time) that itself moves with a velocity which is the metric equivalent of c. (See: "The Time Train".)
Only light itself could establish a moving dimension (time) that was metrically and entropically equivalent to "velocity c". The intrinsic motion of light produces space, and the intrinsic motion of light is also the indirect source of time. This is where time gets its intrinsic motion, and why velocity c and T are exact metric equivalents. Light produces all the dimensions; light is a 2-dimensional transverse wave whose intrinsic motion sweeps out a third spatial dimension. Time is a 4th dimension extracted by gravity from space, 1/2 of the usual spatial dimension in that it is one-way. Each higher dimension is at right angles to those below; time is at right angles to all three spatial dimensions. Matter is one-half of light's particle-antiparticle bound energy form; matter's entropy drive, time, is likewise one-half of light's dimensional or metric form, space.
The spatial dimensions are associated with light's "wavelength", the temporal dimension is associated with light's "frequency". Mathematically, velocity c is the product of light's wavelength and frequency: wavelength x frequency = c. Space ("wavelength") and time ("frequency") are both inherent potentials of light's energetic composition. If light can make space and matter, light can also create matter's time dimension; space and time are but the dimensional conservation domains of electromagnetic energy's free and bound states, light and matter. It should be no surprise that electromagnetic energy can and does produce the dimensional conservation domains required by its two principle energy forms, especially since these can freely transform one into the other (as in the creation and annihilation of particle-antiparticle pairs).
Time is produced by the gravitational annihilation of space, extracting a temporal residue which is the metric equivalent of the annihilated space. Quantum mechanically, time is produced when light collapses to form matter or bound energy (see: "The Gravity Diagram No. 2"). The collapse of the electromagnetic wave to form bound energy also converts light from its wavelength or "space-like" mode to its frequency or "time-like" mode. Both modes have a metrically equivalent intrinsic motion that creates a dimensional conservation domain appropriate for its energy type, space for the free-energy "wave" mode, time and history for the bound-energy "frequency" mode. These intrinsic, dimension-creating motions of light are the primordial entropy drives of free and bound energy, light and matter, creating, cooling, and expanding space on the one hand, creating, aging, and decaying matter, history, and information on the other. (See: "The Conversion of Space to Time".)
Gravity converts space and the drive of spatial entropy (light's intrinsic motion) to time and the drive of historical entropy (time's intrinsic motion). Mechanically, space, light, and time cannot be disentangled; the intrinsic (entropic) motion of time drags space after it, down to the center of mass and the beginning of the one-way linear timeline. Three-dimensional space must collapse to a zero-dimensional point to enter the beginning of the timeline, which is situated at the gravitational center of mass. Space simply self-annihilates as it is squeezed into the zero-dimensional beginning of the one-dimensional timeline, which is at right angles to all three ordinary spatial dimensions. The annihilation of space yields a temporal residue, which in turn moves down the timeline, dragging more space after it, in an endlessly repeating and self-feeding cycle. This time flow establishes the historical temporal conservation domain, which is just as real as the other spatial dimensions (it is created by the "frequency" mode of electromagnetic energy), but due to its intrinsic motion and its orientation (at right angles to space), history is neither visible nor accessible to those who create it - effectively preventing any tampering with causality and energy conservation (because intrinsic motion "T" is the metric equivalent of velocity "c").
Space collapses symmetrically from all directions because time is equivalently connected to all spatial dimensions. Similarly, the constantly applied force or intrinsic motion of time causes the accelerated motion of the spatial collapse. Gravity is the convergent, accelerated motion or collapse of spacetime itself, explaining why all things, including light, "fall" at the same rate - everything is a "co-mover" with spacetime. (Einstein's "Equivalence Principle" allows either a static or dynamic interpretation of the gravitational field; here I find the dynamic view more meaningful.) (See: "Extending Einstein's Equivalence Principle".)
As space collapses and self-annihilates gravitationally at the center of mass, it yields a temporal residue, just as the quantum mechanical collapse of the wave function of light produced a temporal residue (swapping "frequency" for "wavelength") when it first created bound energy. The temporal residue moves on down the time line, dragging more space after it, which produces another temporal residue, etc. Time is the active agent of gravitational motion - it is the intrinsic motion of time dragging space after it which produces the gravitational flow of space; in turn, this flow of space provides fuel to continue the cycle in the form of temporal residues - much as the intrinsic motion of light in ordinary space is propagated by the reciprocal induction of electric and magnetic fields. Time is consuming space gravitationally to fuel and maintain its own intrinsic motion. A gravitational field is the spatial consequence of the intrinsic motion of time.
The time dimension of matter is thus "funded" by the gravitational deceleration of spacetime: the positive spatial entropy-energy lost to the cosmic expansion is compensated in metrically equivalent units by the positive temporal entropy-energy gained by the aging historic dimension. The amount of the entropy-energy, the energetic cost of creating matter's asymmetric time dimension from the symmetric spatial dimensions is -Gm. The conversion from a spatially symmetric entropy drive to a historically asymmetric entropy drive is "uphill" - it requires energy to convert space to time, which is the energetic reason why gravitational entropy-energy is "negative" energy, and why the temporal mode of light collapses space: it must use space for entropy-fuel. The implicit temporal entropy drive of space ("frequency") becomes the explicit entropy drive of history (time). Gravity simply converts implicit time to explicit time at an energetic cost of -Gm. (See: "Spatial vs Temporal Entropy".)
The magnitude of G is determined by the small energy difference between the symmetric spatial entropy drive (S) of free energy as gauged by the intrinsic motion of light ("velocity c"), and the asymmetric temporal entropy drive (T) of bound energy, as gauged by the intrinsic motion of time ("velocity T"): S - T = -G. This is just equivalent to the energetic difference between implicit (S) vs explicit (T) time. Using the same symbols, the gravitational conversion of the drive of spatial entropy to a metrically equivalent drive of temporal entropy may be represented by a "concept equation":
-Gm(S) = (T)m
-Gm(S) - (T)m = 0
If we accept the import of this "concept equation", then we are forced to conclude that the "warpage" or "curvature" of spacetime in Einstein's General Relativity describes (quantitatively) the gravitational conversion of space to time (or allows such an interpretation).
Seamless dimensional continuity, protection of causality and energy conservation, entropic compatibility, and an entropy drive plus entropy conservation, are all provided in the joint dimensional conservation domain of free and bound electromagnetic energy (spacetime) by the intrinsic motions of light and time, by their metric equivalence, and by their inter-convertibility. All this is possible only because time is derived directly from light (light's frequency aspect, exposed by the quantum-mechanical collapse of light's wave function) and from light's conservation domain, space (the temporal residues of gravitationally collapsed space). And though we experience the physical effect of spacetime every day, we are hardly aware of its dual nature (and typically unaware of the metric or dimensional function of gravity), it is so natural and commonplace; this is of course the way things have to be if the Cosmos is to function properly.
PART III: The Creation of Space
As for the intrinsic motion of light and the creation of space, curiously, as in the case of gravity, we can also attribute this to the intrinsic motion of time. Electric and magnetic fields induce each other to produce the propagation of light; so also do the frequency and wavelength of light induce each other to produce velocity c.
The essential meaning of the electromagnetic constant "c" is that it is the entropy/symmetry gauge of the spacetime metric, which functions specifically to prevent the explicit formation of the asymmetric, one-way time dimension, and the conversion of symmetric light to asymmetric matter (witness the continuous annihilation of "virtual" particle-antiparticle pairs in the "vacuum" of spacetime). The dimensional and energetic parameters of this system are thoroughly linked such that the wavelength of light (its spatial expression) multiplied by the frequency of light (its temporal expression) always equals the electromagnetic constant "c".
Obviously, time is implicit in the frequency of light, but at c, time is prevented from becoming explicit. Light has no time dimension: light's "clock is stopped". The seed is present, but its growth is suppressed; indeed, time would be required in its explicit aspect should light assume its particle form and produce matter. In fact, we need to discover the origin of the time dimension in light if we are to build a truly unified theory of energy and its dimensional conservation domain, a theory which traces the origin of all forces to light.
It is the ever-present threat of time, implicit in the very nature of light ("frequency"), which propels the electromagnetic wave forward in space to protect its metric symmetry. The flight of space ("wavelength") from time ("frequency") produces the intrinsic ("self-motivated") motion of light, a symmetric dimensional state of energy fleeing an asymmetric dimensional expression which is, however, an internal potential of its own nature (the original "bur under the saddle"). Since this flight also produces the (positive) march of spatial entropy, we see again that energy conservation, symmetry, and entropy are all related and share a common factor, "c". At the level of principle or natural law, we can say the intrinsic motion of light is produced by a hidden entropy drive (implicit time), which simultaneously maintains metric symmetry in the service of energy conservation. This is the self-same temporal component that becomes explicit when space is collapsed either gravitationally or quantum mechanically.
Hence we see that while explicit time is the entropic driver of the world of bound energy (atonic matter), implicit time is the entropic driver of the realm of free energy (light). Time is the "metabolic agent" of the Cosmos, the entropic driver of all change, whether in space, history, light, or matter. (See: "The Conversion of Space to Time" and "Gravity Diagram No. 2".)
(For more on this topic, see: "Entropy, Gravitation, and Thermodynamics" and "A Description of Gravitation".)
In the "black hole", the electromagnetic metric
of light and space (as gauged by the universal electromagnetic
constant "c") is completely overwhelmed and replaced by the
gravitational metric of matter and time (as gauged by the
universal gravitational constant "G"). The energy of the black
hole is encoded in its mass (hv = mcc), while the entropy
is encoded in the two-dimensional "event horizon" (as per
Bekenstein and Hawking - see: Scientific American Aug.
2003 pp. 58 - 65.) The entropy drive of matter and the black
hole is the "intrinsic motion" of matter's time dimension, which
creates the spatial flow of matter's gravitational field. A
gravitational field is the spatial consequence of the
intrinsic motion of time. The expansion of the black
hole's "event horizon" is required (when energy is added to the
hole) since the gravitational intensity and material density of
the hole is already at a maximum (g = c); therefore the only way
to increase the gravitational flow (which is necessary to
increase the temporal entropy encoding for the added energy) is
to increase the size of the gravitating mass, in other
words, increase the boundary or surface area of the event
horizon, which is the only part of the hole in active/actual
contact with the outside spatial universe. If the black hole has
a 3-dimensional "volume" at all, it is permanently hidden behind
the event horizon, which is in fact a temporal entropy surface
Description of Gravity"). Hence the extreme
temporal/gravitational/material metric suppresses space just as
the extreme spatial/electromagnetic/light metric suppresses
Information is encoded in our ordinary universe in all four dimensions. Information requires the one-way 4th dimension (time) for its entropy drive and for its historical conservation domain, due to the causal characteristic of information. Because the black hole either destroys, suppresses, or hides both the third and 4th dimensions, (time stands still at the event horizon and meter sticks shrink to nothing), the black hole contains almost no information, or as John Wheeler says: "A black hole has no hair". Information may live forever in the historical domain, but not in the black hole. Hawking should have stuck to his guns. (See: Leonard Susskind: "The Black Hole War"; Back Bay Books, Little, Brown and Co., 2008.)
The energy and entropy of information are encoded
in the black hole's mass and the surface area of its event
horizon. The causal component of information ceases to form new
linkages upon entering the black hole and inside the event
horizon distinguishable atoms are converted to "anonymous"
photons. Causal linkages created by information outside the
black hole, however, continue to propagate forever in historic
spacetime. Entangled elements swallowed by the black hole are
moot, since they remain hidden forever, suspended or "frozen" in
time at the event horizon.
Gravity is one-way and (hence) asymmetric;
Time is one-way and asymmetric;
Entropy is one-way and asymmetric;
Matter (bound energy) is asymmetric - due to its time dimension, gravitational field, lack of intrinsic motion, mass, lack of an antimatter complement, and due to its specific position in spacetime (unlike all-symmetric light (free energy), which is everywhere simultaneously). A black hole is therefore the most asymmetric object (physical state of energy) in our universe.