- Apology.
- The light barrier as universal event horizon?
- An Event-horizon universe.
- A holographic principle of an event-horizon universe.
- Modally rotated normal curve as an hour-glass model of the cosmos.
- Relative tachyons and tardyons.
- Necklace multiverse.

Why have I written on an extremely advanced subject, which I am not remotely
qualified to discuss?

I tnink it's because of all the popular science books I have read thru-out my
life, rather like Don Quixote, devouring all the popular romances of his day.
Their contents accumulate higgledy-piggledy in the mind, demanding some
imaginative expression, however unscientific.

Physicists, like Stephen Hawking, suggested that the universe itself might be a black hole (that has evolved from a virtual singularity). A black hole is an object from which not even light can escape, once it has passed a certain critical distance, forming a border called the event horizon. Light has no rest mass but it has mass in its energy of motion, which is therefore subject to gravitational attraction.

In terms of a black hole analogy with the universe, light cannot escape the event horizon but gravity extends beyond the event horizon, pulling objects towards it, until the point of no return. The light speed barrier might be the analog of the event horizon of the universe as black hole. There may be testable consequences that can disprove that assumption. There is the possibility that matter might be drawn into the observable universe. That sounds like a feature of Fred Hoyle's steady state model of the universe. (Hoyle so modified his early ideas that they anticipated later more orthodox thinking.)

Back in 1985, Heinz Pagels (Perfect Symmetry) already anticipates much of
the sophistication of modern cosmology. What follows is only a simplistic
model. That simplicity attracts me, tho it does little justice to the
complexities of reality.

In the context of my notion that the light barrier might be a universal event
horizon, it was thought that nothing could escape a black hole. That is, in a
manner of speaking, until the theory of Hawking radiation (sometimes called
Bekenstein-Hawking radiation). So, according to my way of thinking, Hawking
radiation also escapes the light barrier, as my postulated event-horizon of a
black hole of a universe.

Hawking radiation is supposed to happen like this: on the extremely small sub-atomic scale, the vacuum of space seethes with energy, that is continuously erupting short-lived sub-atomic particles. These are only virtual particles, bound by the restrictions of Heisenberg Uncertainty principle. Quantum theory modifies classical energy conservation law, which would not allow energy to appear out of nothing.

For example, an electron and its anti-particle, a positron, may erupt from
the energy sea. Being positive and negative, there is conservation of energy.
They shoot off in opposite directions, also conserving linear mommentum. In
other words, the books are balanced, despite the vacuum having a zero-sum
energy.

These virtual particles will almost immediately collide with others from the
seething energy sea. And when matter collides with anti-matter, it annihilates.
Again, energy must be conserved and so it radiates in the form of fotons.

Hawking radiation predicts that the event horizon might capture only one of a pair of virtual particles that happens to be created right on its border. The virtual anti-particle gains the extra energy from black hole gravity to become a real particle and escape into space. Fotons are their own anti-particles but are capable of creation in quantum-entangled pairs, for instance as to the compensating effect on each other of changes in their respective polarisations. On the event-horizon, one of these might be captured and the other escape as Hawking radiation.

Since an emitted particle has to have positive energy, the captured particle must have a corresponding negative energy, to an observer in the outside universe. Therefore, the black hole is held to lose mass and eventually (on a cosmic time scale) evaporate, as a result of Hawking radiation.

My unqualified if fevered imagination links this with Feynman
sum-over-histories conception of Quantum Electro-Dynamics. In his popular
lectures, QED, Richard Feynman explains that on the extremely small sub-atomic
scale, light does not travel in a straight line at a constant speed, as it is
familiarly observed to do.

I say to myself, even on the large scale, the classical picture is not true
of the erratic paths of lightning. The leap from the sub-atomic scale of
Feynman's integral paths to the human scale of lightning is as great as the
difference between lightning and, say, some imagined cosmic scaled-up foton, in
the Creation of the universe.

This helps me to believe Feynman sub-atomic description of a foton not merely
moving in a straight line but by all other possible paths and at varying speeds
greater and lesser than observed light speed.

The sum, of all these histories of the foton, averages out to the classical
path of light.

Consider that the constant speed of light is the speed imposed by a universal event-horizon of gravity on light, such that performs the averaging of light speeds, in the sum-over-histories calculation.

Given that gravity moves at light speed, in the present universe, fotons and gravitons may be deeply related, in the unfolding universe, according to conservation principles.

"The cosmic egg" (to use a Terry Pratchett sort of concept) in a zero-sum energy vacuum of practicly infinite extent (nothing that is potentially something) might consist of, say, a particle-pair that realises an inconceivably small probability of creating a universe within the permitted bounds of the Uncertainty principle. The more energy that goes into a virtual particle-pair creation, the less time it is likely to last.

I dont set much store by this not-so-simple paragraph but I imagined one Creation scenario as a proto-foton, which has no rest mass. It might be one of a pair of quantum-entangled particles, the other becoming massively concentrated to a virtual singularity of a black hole. (Light still has energy of motion, so the universal black hole must have negative kinetic energy, whatever that is.) That is to say they are two parts of a conservative system, where a change in one part must be offset by a balancing change in the other part.

It is assumed such quantum entanglement is possible, because particles and black holes are both basicly similar, being described by the same properties of mass, force charges and spin.

As the proto-foton grows universal, the increasing gravity of the black hole
might relate to the foton, as sum-over histories of different light speeds. The
gravity might capture slow speed light paths and energise them into tardyons,
real particles, moving slower than observed light. Likewise fast light paths
might be energised into tachyons, real particles moving faster than light.

(This is an extension of the idea of Hawking radiation, where a virtual
particle pair on a black hole event-horizon results in one escaping as a real
foton.)

Thus, observed light velocity just happens to be the velocity of light at the event-horizon to a universal black hole.

The speed of light happens to be what it is, possibly because it just happens to be the speed associated with the event-horizon produced by the particular strength of the universal black hole in this particular universe. There may be a random selection of other universes with black holes of differing gravitational pulls and thus different event-horizons with different corresponding light speeds. That is a multiverse of "black holes and baby universes" to name the Hawking title.

Normally, light is not much altered by gravity which is too weak to affect it. The standard model of physics accounts for three forces of nature, because the fourth, gravity is so weak that it can be left out of account. Only on astronomic scales, involving the gravity of a star, does a passing light ray even bend out of its normal straight path.

Suppose, on the universal scale, light moves in a straight line because it is held apparently straight by its huge event-horizon, presumably a three-dimensional horizon that is the volume of space. The observed universe would be three-dimensional event-horizon.

An event horizon is not normally straight, it curves round the black hole,
but on a universal scale, the horizon would be so large as to look straight,
just as the Earth looks flat, to those on it, tho it is a sphere.

The observable universe has an almost flat spatial geometry, in accord with the
large-scale homogenous distribution of mass, not causing any marked curvature
of space.

Finding a curvature of light in inter-stellar space would perhaps measure the circumference of the universe, as an event-horizon.

The early universe was thought to hold just energetic radiation that
gradually underwent a transition to particle masses, like water crystalising,
as it cools.

Taking into account the infered existence of dark matter and dark energy, the
universe appears close to critical density, for its relative stability or
equilibrium. So, after Creation from a Big Bang, it does not collapse or fall
back, under gravity, nor does it so escape from gravity as to rapidly expand to
the point of dissipation.

What is the reason for this happy coincidence?

Suggested answer: because the universe, at critical density, is the poise of an
event-horizon (of a) universe.

This critical density may be like an orbital trajectory, rather than a
falling trajectory or escape trajectory, from the Big Bang. This is analgous to
a planet having orbital velocity round a sun. Likewise, perhaps, the universe
as event-horizon to a black hole.

The universe isn't static but then an event-horizon doesn't have to be static,
either.

Perhaps tardyons would be comparable to centripetal force. Tachyons would compare to centrifugal force. And observed light, as marking a universal event-horizon, would be analgous to orbital velocity of a satellite to the universal black hole.

Ballistics comes from classical physics. Relativist physics would use gravitational mass to curve out spatial paths for attracted bodies. The black hole compares to the maelstrom in the Edgar Allen Poe story. The boat is caught in the curling waters drawn towards the giant whirlpool, which hurls the craft round the whirling rim, which is like the event-horizon.

In the story, the boat is spat out again by centrifugal force of the spinning waters that spares it, by great good fortune, from going down the plug-hole. In general relativistic terms, a drawn space-craft might be lucky enough to escape by the Poe path to the spatial curvatures near a spinning black hole.

Feynman toyed with the notion that there is only one electron in the universe. Feynman diagrams of sub-atomic interactions can be re-interpreted involving time-reversals. There is all the time in the world for one electron to be all electrons, which indeed appear to be the same.

(There is something called C-P-T [Charge-Parity-Time reversal] symmetry.
Yang and Lee predicted that Parity or mirror reflection symmetry was not
conserved and Madame Wu confirmed in a certain atomic decay experiment that you
could define the difference between left and right. All physical reactions were
not perfectly mirror-symmetrical in the universe: the so-called "left hand of
God."

Only a combination of all three properties was found enough to maintain
conservation.)

In analogy to Feynman one-electron supposition, the universe of light might
be thought of as a sum-over-histories of all possible light paths. These
consists of paths both slower and faster than the observed light speed, which
they average, over (observable) distance.

Quantum entanglement seems to imply expansion of the universe from quantised units of space and time, around the Planck scale. Because, at that scale space and time are thought to break down and the property of quantum-entanglement is that in a conservative system of, say, a pair of particles, a change in one automaticly produces a balancing effect on the other, over any distance and in no time.

The Big Bang might be the agent of transfering timeless and spaceless
properties of sub-atomic particles from the quantum scale to the cosmic scale.

To sum-up this section:

The light speed barrier, that no massive object can surpass, suggests the
universe has a black hole event-horizon, that no mass can surpass, not even
light kinetic energy.

Ultimately, that means that light only moves in straight lines, in the sense
that the horizon of the sea appears straight.

Consider the Creation from a primitive particle pair, as a quantum-entangled conservative system, in sub-space and sub-time scales, possibly under (Heisenberg Uncertainty) random disturbances, driven into extreme opposites of gravitational singularity and universal light.

A cosmological Inflation of a proto-foton as a Feynman sum-over histories might be gravitationly realised analgously to the equilibrium of satellite ballistics.

If the observed constant light speed is analgous to a satellite orbit round
a more massive star, then slow light or tardyons and fast light or tachyons
respectively compare to perfectly balanced forces of centripetal and
centrifugal force, that vector an event-horizon equilibrium of observed light
velocity.

An event-horizon universe might explain the "critical density" problem.

Many of the other seemingly accidental physical parameters of the universe may
be similarly explained as conservative equilibrium effects.

(18 january 2011).

To topHorizon on BBC2, Leonard Susskind gave a simple explanation of his holographic principle. Usually books inform my viewing, rather than the other way around. I'd heard of the principle and of Susskind; could even spell his name. (Don't laugh, that's an achievement of sorts.) I admit, Susskind rehearsing his insight did bring it home to me. And in general, I feel, this is the way science is done.

He was shocked by Stephen Hawking revelations about black holes, briefly refered above. In particular, the evaporation of black holes seemed to imply that the information or precise properties of matter, drawn into them, was lost. This would break a basic law of the conservation of information.

Susskind got round this problem by suggesting that the two-dimensional surface of a black hole event-horizon might act like a hologram, storing the three-dimensional information of the captured objects passing thru that surface of no-return.

Cosmology, like mathematical physics in general, is a subject I am
hopelessly unqualified to discuss. Astronomy has evolved hugely sophisticated
observations, meeting its aspirations to become as effective as a laboratory
science. Witness the 2009 observations of the Fermi telescope of extremely
unequally energetic fotons moving at the same speed for over 7 billion light
years. (A later experiment of even greater accuracy measured a tiny failing in
the constancy of light speed.)

This section adapts my mathematical technique of a geometric mean derivative to
a crude hour-glass model of the universe.

My page, on Mach principle applied to mathematics and special relativity
with a caldera model, treated the Interval in terms of a circular function but
with an extra circle, twice the radius, from a common origin.

(By the way, Gary, from the Special Relativity e-mail group, kindly read that
page and said he had no problem with it. Its faults are mine, not his, of
course.)

By Mach principle, I really meant a self-consistency principle applied to any
self-contained discipline, mathematics, as much as physics. So, all numbers
might be represented by other numbers, in terms of averages. This also applies
to complex numbers, without which, the number system is incomplete.

To this end, geometric mean calculations on complex numbers produced a second
circle, twice the radius of the first.

The inner circle radius was not quite the conventional Interval measure (every observers common space-time measure) itself. Instead, the Interval equation was simply transformed so that light speed was the length of the inner circle radius. Light speed was on the inner circle circumference. Every speed less than that radius was sub-light speed (or tardyonic speed). Every speed correspondingly above light speed was super-luminal (or tachyonic speed).

The caldera model meant that faster-than-light particles or tachyons were
confined to an outer caldera slope of our tardyonic universe. However, the
outer and inner slopes are of infinite height and never quite meet.

Tho, "quantum tunneling" might display tachyonic symptoms of the near presence
of the outer universe to our inner universe.

On the cosmic scale, my web page about a caldera model of the cosmos perhaps
left out half the picture. Suppose the normal distribution is rotated about its
norm, as being at the middle of an hour-glass. It may be that the derivation of
the Interval in terms of the normal curve can be better adapted to the caldera
model. The caldera model may itself be refined, actually into an "hour-glass."
Why an hour-glass?

A volcanic explosion producing a caldera does not explain where the explosion came from. But a back-to-back caldera, like an hour-glass, can explode both ways into a universe and an anti-universe. This is a bit like two people pulling a party cracker. One can just imagine George Gamov using such a picture, in his Mr Tompkins book.

The point of such a both-ways explosion is that it is in keeping with the
law of conservation of energy and conservation of momentum. For instance, even
the vacuum of space is thought a seething sea of virtual energy. Virtual
particles and their anti-particles can spontaneously emerge, from each other,
shooting off in opposite directions, to balance the energy books, within the
probabilities estimated by the Uncertainty principle.

They are annihilated in collisions with other oppositely charged particles,
likewise created and annihilated.

It has been suggested (for instance, in Black Holes And Baby Universes, by Stephen Hawking or Physics Of The Impossible, by Michio Kaku) that whole matter and anti-matter universes might be created on such lines. The hour-glass model follows this idea. One half of the hour-glass is a universe of matter. The other half is a universe made of anti-matter. When matter and anti-matter meet, they annihilate and their energy goes into the resulting explosion of radiation.

Figure 1 is not to scale, of course, and the hour-glass shape is not meant
to be taken too literally. The normal curve in the hour-glass shape is itself
just a mathematical illustration of some sort of exponential function to
describe a process like the Big Bang.

Current measurements show universe present space-time expansion to be
accelerating. The figure for that would be a flaring, not a vertically-ended,
hour-glass.

Figure 1 is a crude model of the Big Bang. The usual example, for popular reading, shows the universe expanding from virtually nothing, like a balloon. The surface is imagined as a two-dimensional simplification of a stretching "fabric" of space-time.

Thus figure 1, the horizontal axis thru origin, 0, shows velocity. It is greatest at the origin, decreasing to either left or right (or indeed radially considered like a three-dimensional hour-glass). The shape of the hour-glass from its origin or middle, traveling verticly with time, governs the acceleration, or rate of change of velocity. Starting from the middle, it is at its narrowest stage, meaning that velocity remains very high over time; velocity then reduces rapidly over time, as the hour-glass billows out; until the walls become nearly vertical, meaning relatively less change in velocity over time.

The hour-glass can most simply be treated by reducing it to the normal curve, that created it, by a symmetrical rotation about the norm, as origin. The symmetry means that everything that applies to one planar section of rotation, the normal curve in two dimensions, applies all the way round the radius of the hour-glass. The normal curve is actually external to the matter and anti-matter universes. Looking at figure 1 sideways, the velocity is a function of the time.

The Minkowski Interval is the mathematical space-time form of Special Relativity which deals with observers in velocity frames of reference.

General Relativity starts from Einstein's Principle of Equivalence of observers acceleration frames of reference to gravitational rest frames of reference. The early universe is a balance of forces of accelerating expansion and gravitational attraction. So, the Big Bang is modeled on General Relativity.

A normal distribution is an exponential function, which can be turned into an hour-glass model for cosmology. To see it this way, the normal curved hour-glass would have to be placed on its side, instead of figure 1's upright position. The normal curve conventional x-axis is thus the time axis and the y-axis is the velocity axis.

In this cosmological case, it is convenient to re-set the y-axis from infinite velocity to zero velocity, by making the height of the norm as infinity minus infinity. The walls of the hour-glass become straighter as acceleration decreases to its present measured rate. Then, the height of the normal curve, getting closer to the x-axis, would be re-set to infinite speed minus current speed.

The question arises whether this re-setting of values is just a mathematical convenience or whether the area under the normal curve, which is outside the matter and anti-matter universe expansions, actually represents the properties of that external area.

A recent physical theory replaces an Inflationary preliminary to the Big Bang, with an explosion of light, at infinite speed, gradually slowing down, as the universe expands to its present size, by which time, light has assumed its familiar constant speed, at least within current limits of experimental accuracy. This Deformed (or Doubly) Special Relativity theory, or its second version, known as DSR2, is described in Lee Smolin book: the trouble with physics.

Inflation is a rather ad hoc explanation, which just had to be brought-in to straighten-out the scenario, without naturally arising from it. Inflation may be dubious but that doesnt necessarily mean it is wrong. And most physicists seem to think that Inflation right, tho there are many competing models of it.

The declined light-speed model conforms to an implicit mutability principle of a temporal universe, where nothing lasts forever, without under-going transformation, possibly not even the universe itself. Even the proton is assumed to decay, tho the decay rate has not been determined, at the time of writing.

It is always possible to argue the point, that is why science requires evidence. However, it could be argued that, since time comes to a stop at light speed, it has the property of immortality. Another possibility is that light-speed varies with chance from universe to universe, while remaining constant within each universe. This assumption does away with the need for some sophisticated theory to derive the light speed constant, not to mention the other physical constants, that are just measured and plugged-in, without being logicly derivable from a theory like the Standard Model (of three of the four known forces of nature).

Suppose a Big Bang of light in equal and opposite directions of infinite speed, thus balancing the energy books, at any rate with regard to momentum. Suppose this two-ways imparting of light, at infinite speed, comes out of a sea of zero-speed light energy, located around the origin or middle of the hour-glass in figure 1.

A Creation infinite light speed event, balanced in positive and negative directions, leaves the logical possibility of an external residue of light at zero speed. Suppose, as the infinitely speeding light slowed down to its presently observed constant speed, the corresponding energy seas light, outside the hour-glass, would be infinite speed minus current light speed. That is to say, external energy-sea light speed would have become greater than observed light speed, or tachyonic.

In special relativity, no masses can ever reach the speed of light. They are always observed to be slower than light speed. But the mathematics also allows for a sort of mirror-image process to normal reality, an Alice-in-Wonderland world of tachyons or faster-than-light particles that can never become slow enough to reach down to observed light speed.

A virtue of a varying external light speed, converse to a varying internal light speed, is that external light starts off from zero speed, so it is evident that external particles could not be less than zero light speed. (Quantum uncertainty might further explain why they could not be exactly zero speed either.) As external light speed increased, this tachyonic property of particles, not being able to go under light speed, might be conserved, conversely to the observed universe, which would also have its relative tardyons approaching a speed of light faster than that currently observed.

I guess the extra-universal (or extra-hour-glass) energy sea, forming the
area of the normal curve, might be of tachyonic matter, in a relative sense
that extra-universal matter could never go below the extra-universal light
speed.

Even if the universe had no declining light speed, tachyons and tardyons could
still be relative, if not within the universe, across universes, in a
multiverse, consisting of a statistical array of different constant light
speeds in each universe.

At present, physicists' measurements suggest an accelerating universe.
According to Victor S Stenger, author of The Comprehensible Cosmos, this
finding is not at all adverse to the possibility of a closing universe.

In terms of an hour-glass model, the hour-glass would join to the base of other
hour-glasses like a string of beads. To carry the analogy further, the string
might even be in a loop, like a necklace. Given that the beads are "strung" in
the time dimension, then time itself would be in a loop, being re-born every
time the universe re-opened.

More-over, the row of hour-glass beads could be nested in multiple rows of beads. This would be a multiverse of parallel universes. In terms of figure 1, they could be imagined as side by side.

*Richard Lung.
4; 11 september; 13 december 2010; 18 january 2011.
Edited november 2016 but needs further revision.*