## Friday, December 12, 2014

### Quantum Invariance Theory - An Introduction

[Note: If you arrived here from Rick Rosner's twitter link, the post about RR's Informational Cosmology can be found here: Informational Cosmology and the Big Bang ]

An Introduction to Quantum Invariance Theory

Quantum Invariance Theory
Quantum Invariance theory (or "QI") is a theoretical framework in which space and time are quantized together as indivisible hypercubes; and relativistic effects become invariant when viewed from a full 4-dimensional perspective. Quantum Invariance theory aims to reconcile the incompatibility of quantum physics with general relativity and eliminates singularities. No extra dimensions are introduced beyond the ordinary four dimensions of space and time, except for in cases of constructing artificial models for the sake of visualizing topology.

Overview

The starting point for Quantum Invariance theory is the idea that, in accordance with Quantum Mechanics, space and time must be quantized, and in accordance with Relativity theory, space and time must be joined together. Thus, according to QI, space and time are quantized together as inseparable units of 4-dimensional spacetime in the form of hypercubes 1 planck length in extent. Each hyper-voxel of spacetime is called a hyperquantum. In QI a three dimensional object does not exist as a distinct object in space alone, but must exist as a 4-dimensional object with extension through time. Thus a cube of 1 planck length is never just a cube, but instead the cube always exists as a 4-dimensional hypercube. No additional dimension is added, spacetime remains 4-dimensional, with each hypercube building up to form a hyperprism or elongated hypercube.

(A planck cube existing for one planck second appears as a hypercube.)

Dimensional Closure

Quantum Invariance theory is also concerned with the largescale shape of spacetime. Each dimension of space or time are understood to be composed of perfectly straight lines extending in opposite directions for a non-finite distance, eventually meeting back to where they started without curving. These are known as full dimensions which are said to have dimensional closure. (Thus it might be helpful to think of QI as "Full-Dimensional Hyperquantum Invariance Theory). As a whole, each of the four dimensions form a hypercubic lattice which is topologically connected as a flat hypertorus. Because each dimension extends infinitely, eventually meeting back upon itself without curvature, no embedding of the hypertorus in a higher dimensional space is required for it to remain flat.
However, when conceptually modeling the infinite structure of the entire Universe in a finite way as a "map" for the sake of study, the structure can be depicted as a repeated series of 8-dimensional orientable manifolds isomorphic to a Clifford torus. But it is emphasized that this embedding does not reflect the true nature of the actual structure of the Universe, it is merely used as a geometric model for the purpose of visualization. A more simple example of this principle would be to model a single full dimension as a circle in order to study its topology, so long as it is understood that the true dimension has no actual curvature and in reality cannot be shrunken down. In this type of artificial construction the quantum nature of spacetime is lost.

( We can think of this Clifford torus in 4-dimensional space as a representation of 2 ordinary spatial dimensions shrunk down and embedded in hyperspace, but in doing so we sacrifice the quantum nature of spacetime. )

Scale-Recursion

An interesting consequence of this kind of toroidal space is that, given enough time, any path in a straight line eventually returns to where it began. This is true of directional space, time, and even size, known as scale-recursion. Thus, if you were able to zoom in on something infinitely, zooming in on an object, you would eventually see outside of the object to the entirety of the Universe, zooming further you would see the object appearing much larger, and then zooming further, would take you back to where you began. Events in time happen only once, but because the time dimension is a flattened closed loop, all future events will eventually lead back to past events. (This effect can unexpectedly be found in some forms of string theory where the size of a string in relation to the Planck scale is equivalent to the inverse of its size. So that, for example, a string of the size 1/4 is the same as a string of size 4. On enormous scales this effect becomes unnoticeable.)
It is worth pointing out that although space is quantized as a smallest unit in Quantum Invariance theory, it is meaningful to go lower than that size. The wording becomes confusing, but really what is happening is that a smallest size is understood to mean a smallest size before repeating what is equivalent to larger space. Anything below the planck scale is a repetition of larger sizes, accessed from the bottom down rather than from the bottom up. (It sounds strange at first, but it is not much different than distance on a sphere. Traveling a very short distance in one direction will take you to the same point as traveling a very long distance in the opposite direction.)
The nature of time in Quantum Invariance Theory should not be confused with the nature of time in cyclic models. In some cyclic models, identical events recur over and over again, as local time is a finite closed loop in a greater time line. In QI time acts as a closed loop, but there is so much time that there is only enough time for each moment to occur once. So although time is connectedly cyclic, it is not recurring.

Digital Geometry

In Quantum Invariance theory, the fact that spacetime is quantized results in a new form of geometry which does not strictly follow the familiar axioms of Euclidean geometry. In Euclidean geometry, two points are connected with a single unique line. In digital geometry more than one line is possible. In Euclidean geometry the parallel postulate states that one unique line can be drawn on a point which is parallel to another line. In digital geometry more than one line can be drawn through a point which is parallel to another line.
Other Non-Euclidean consequences of QI arise from dimensions being fully extended to closure. For example, Euclid states that only  a single line may be drawn to connect two points, but in QI a line may be drawn in the opposite direction which will meet the point from the other side, as well as many other complicated paths. Similar to spherical geometry, but without curvature. (In other words, in QI, transferring a geodesics into ordinary Euclidean space, it would have no curvature. Transferring a geodesic of a sphere would be curved in Euclidean space.) In Euclidean geometry, any straight line segment can be used as the radius of a constructed circle, in QI this is limited to lines which are half the length of a dimension or smaller. And lastly, Euclid's second  postulate states that any straight line segment can be extended indefinitely in a straight line, while in QI, because of dimensional closure, a straight line segment can be extended only so far before it eventually meets back upon itself.

(Squares that appear distorted are not really distorted.)

Invariance

In Quantum Invariance theory, the relativistic effects predicted by Einstein's theories of Relativity should remain the same, but there is a difference between observing apparent relativistic effects in space and understanding invariance of spacetime. An example is the turning of a cube. When you rotate a cube, the shape of the square faces appear to be distorted even though we know that the actual shapes always remain squares. In a shadow, it is true that the shape truly is distorted, but we understand that the shadow is not the thing. It is the same for invariance. We do experience relativistic effects in 3-dimensional space, but without understanding the full picture, we are confusing the shadow for the thing. An example of something that would appear distorted relativistically but not invariantly, would be time dilation and the relativity of simultaneity. In the grand scheme of 4-dimensional spacetime, there is no absolute space, and there is no absolute time, but there is absolute spacetime.

Testable Predictions

One major prediction of Quantum Invariance theory is that the apparent age of the Universe does not represent the actual age of the Universe. (In QI, the Universe does not have an age at all. Only a non-finite time limit before any given point recurs.) The apparent effects of redshifted galaxies and cosmic-microwave background radiation and the supposed metric expansion of space are believed to be relativistic effects that become invariant in the full 4-dimensional view of spacetime. The apparent acceleration of expansion of space is predicted to appear the same in any region of space or time. If true, the apparent age of the Universe should remain the same in the future and it is predicted to have appeared the same age in the past. As methods of measuring the apparent age of the Universe improve with greater precision this will become increasingly easier to falsify or confirm.
Another testable prediction of Quantum Invariance theory is that events in the future must lead to events in the past. This puts a strict limit on what events are able to occur in the future without closing off the possibility of time returning to the current present state of the Universe. The Universe cannot spread out and freeze, for example, and never warm up again. Also, since time is quantized, assuming dimensional closure, the number of total possible Planck seconds must be a definite specific value. According to this specific value, only certain recurring patterns could occur because the amount of cycles must divide evenly into the amount of possible time intervals. For example, if a certain phenomenon was expected to periodically occur once every 10 planck seconds, but the total amount of Planck seconds in a full dimension of time was a power of 2, we would know that the phenomenon would have to change at some point in the future, or would have been different in the past.
As instruments become more sensitive in future experiments, it may be possible to verify the cubic nature of hyperquanta. If shapes besides hypercubes are allowed, this will manifest as apparent changes in the speed of light, apparent changes in mass as particles travel through a square of space, then and octagon, then a square, etc. If space were triangular, we might expect polarity to shift as orientation of each consecutive triangle in a tiling shifts. In truth though, the only possible shape that will be the same everywhere is a hypercube. Anything that requires the structure of spacetime itself to drastically vary would require an explanation.
Lastly, like all theories that involve the extremely small Planck scale, some aspects of Quantum Invariance theory may be very difficult to test. However, because of scale-recursion, where something incredibly small is also incredibly large, it may be possible to see the effects of the Planck scale by observing largescale structures of the Universe. Clues may lay hidden in the cosmic microwave background radiation, or in the detection of gravitational waves. Similarly, we may be able to obtain data about incredibly large timescales by observing incredibly small time scales, effectively observing the future.

## Tuesday, December 9, 2014

### Rick Rosner's theory of Informational Cosmology

Rick Rosner on the Big Bang Theory and Informational Cosmology

Excerpts form In-Sight's interview with Rick G. Rosner
© Scott Douglas Jacobsen, In-Sight, and In-Sight Publishing 2012-2014.

http://in-sightjournal.com/2014/10/08/rick-g-rosner-giga-society-member-mega-society-member-ex-editor-1990-96-and-writer/

"There might be some clues to the universe being older than its apparent age. If the universe undergoes repeated multi-billion-year unfoldings, there should be lots of stuff that’s older than the apparent 14-billion-year age of the universe. That stuff won’t necessarily be in our immediate neighborhood – we’re new – we came into being as part of the current unfolding.
Via repeated cycles (not cycles of the entire universe expanding and contracting – not an oscillating universe – more like a rolling boil) of galaxies lighting up and burning out, the dark matter we’re looking for (to explain gravitational anomalies such as the outer rims of galaxies rotating faster than accounted for by the distribution of visible stars) might be a bunch of neutron stars and near-black holes. If anything could survive repeated cycles without being completely ablated away, it would be near-black holes. (Don’t really believe in fully black holes.) A universe which has gone through a zillion cycles might have generated a bunch of burned-out junk (or, in an informational sense, massive settled or solved (for the moment) equations or clumps of correlations or memories or independent processors whose operations the wider universe doesn’t much participate in/isn’t very conscious of) hanging around on the outskirts of galaxies.
A brand-new universe – one that’s unfolded after a single big bang – doesn’t have much opportunity to form a bunch of collapsed matter. But a universe at a rolling boil – that is, a “continuing series of little bangs” universe – would generate lots of junk. It’s that house with all the trashed cars and plumbing fixtures scattered across the front yard.
Just for fun, we could multiply the 14-billion-year apparent age of the universe by the 5 billion lifetime cycles of the human brain. There’s no reason to assume that the universe goes through 500,000 or 5 googol rolling cycles. But anyhow, 5 billion times the apparent age of the universe gives you 70,000,000,000,000,000,000 years. That’s based on not much. What if the expected duration of a self-contained system of information (in terms of rolling cycles) is proportional to the complexity of the system? What if the complexity, like the average distance from the origin of a random walk, is proportional to duration squared? The universe could be really old.
No way the universe unfolds just once. No way it’s only 14 billion years old."

(43.)

"In a Big Bang universe, we can see across nearly 14 billion light years. (Microwave background radiation has spent nearly the apparent lifetime of the universe reaching us.) But we’re not looking at a sphere 14 billion light years in radius, because the background radiation comes from a very small, young, recently exploded universe. (There’s a maximum radius we can see as we look across greater distances and farther into the past. Beyond that radius, we’re seeing increasingly smeared-out images of our universe when it was younger and smaller. Of course, every image we see is of a younger universe, but it’s usually only younger by a few billionths of a second – the time light takes to cross a room.)
If we could see to infinity, we wouldn’t see Big Bang space as completely filling three-dimensional space. Looking farther and farther, we’d see the universe getting smaller and smaller (because younger and younger), until it’s a point at T = 0. But that’s just because we’re looking back in time. Though we can’t see it because of the finite speed of light, a Big Bang universe can be a fully three-dimensional surface of a hypersphere.
But I don’t think we live in a Big Bang universe. Due to the nature of an information-space universe, it looks quite a bit like a Big Bang universe, and that it started with a Big Bang is a natural first conclusion to reach, based on general relativity and the Hubble redshift. Note that the idea of the Big Bang – space exploding from an initial point – while seeming indisputably established, is less than 100 years old, and has been the predominant theory of universal structure for less than 50 years.
A Big Bang universe is nearly the same everywhere – the result of a uniform outward expansion. But a universe that doesn’t blow up all at once isn’t the same everywhere. It has an active center and burned-out and collapsed outskirts clustered close to what looks like T = 0. This universe may not be perfectly three-dimensional – space is highly curved and riddled with collapsed stuff near the apparent origin, which may mean that space is effectively less than three-dimensional at great distances."

(27.)

"I think the universe isn’t inherently unstable in size, with overall stability being a characteristic of an information-based universe. That is, though parts of it can expand and contract, the universe isn’t going to keep flying apart to some cold, thin oblivion or collapse into an infernal dot. (At least without some outside agency acting upon it. The loss or degradation of the physical structure which supports the universe would result in the loss of the information within the universe. As the universe loses information, it would become less well-defined, which might look like a collapse and heating up of the universe – a big bang in reverse.) The scale and size of the universe should be roughly proportional to the amount of information it contains (with local scale and size depending on the information/matter distribution as viewed from each particular neighborhood)."
(30.)

"In a Big Bang universe, it’s unlikely that there aren’t a bunch of civilizations a million years old and more. Unless something consistently wipes out civilizations, which would be weird. Or civilizations link up or are colonized into super-civilizations extending across swaths of the galaxy. So the question becomes, what does a civilization do for a million years or ten million or a billion? I’d guess that there’s some principle that the number of interesting things to do increases along with the computational power of your brain (or your brain plus your super-computing add-ons). Otherwise, you and your civilization would go nuts from boredom.
In an informational cosmology universe, civilizations could survive for longer than the apparent age of the universe. You could have civilizations tens or hundreds of billions of years old or more. I’m guessing that if this is the case, then such civilizations are very involved in the business of the universe. They have a good idea of the universe’s objectives, and they help with its operations. A big, old, highly organized universe might include highly developed technicians. Kinda doesn’t make sense that it wouldn’t.
I imagine that, among other things, long-lasting civilizations might be able to manipulate quasars to hose down dormant galaxies with neutrinos, awakening those galaxies. (Can also imagine this might be wrong and dumb.) Can’t imagine how a civilization or entity could persist for 100 billion years without going stir-crazy, but it has 100 billion years to figure out fun things to do. (A hundred billion years is the ultimate endless Sunday afternoon.)"
(73.)

"With regard to time, I think the biggest question is, if the universe is vastly, wildly ancient, with its Big Bang age only an apparent age, why does the universe look so precisely as if it had a Big Bang? The answer must have to do with the nature of information. (Or with me being wrong. But I’m not.) The active center of the universe is where new information is being formed. Protons entering the active center are new – either they’ve been created from neutrons in collapsed matter, or they’ve come from a soup of unstructured primordial matter around T = 0. (I picture space around T = 0 consisting of collapsed galaxies, separated by their Hubble/general relativistic vectors along with a large local gravitational constant, all suspended in a dense primordial soup.)
All the protons are new, though most of them are contextualized by the once-collapsed and now uncollapsing galaxies they’re part of. They all enter the active center from close to T = 0. The protons’ (and electrons’) interactions with each other puff up the space they share in what looks like a Big Bang. Galaxies don’t have to all enter the active center at the same time. Since all galaxies enter from close to T = 0, more recently lit-up galaxies look like they’re located in part of the universe that’s distant from us, so we’re seeing them earlier in their existence.
The proton interactions have to start from around T = 0. They have to create the space they’re in – the active center, which, as galaxies light up, expands like a Big Bang universe. The protons and their galaxies create information through a shared history that plays out in what looks like a Big Bang – they enter at the beginning of apparent time, and space expands around them.
Some conceptual trouble comes when galaxies burn out. They recede from the active center, which means they’re moving backwards in apparent time. I guess this is okay. Observers within a burned-out galaxy would see something like a Big Crunch, I suppose.
The apparent age of the universe could stay roughly the same for a very long time, as newly lit-up galaxies enter from near T = 0 and burned-out galaxies recede back towards T = 0. Or the apparent age can change as more or less business is done in the active center. You could have relatively few galaxies in the active center, with the universe kind of being asleep, or you could have a relative multitude."
(78.)

http://en.wikipedia.org/wiki/Richard_G._Rosner

# The Largest Blueshifts of [O III] emission line in Two Narrow-Line Quasars

### http://arxiv.org/abs/astro-ph/0409546

The Narrow-Line Region of Narrow-Line Seyfert 1 Galaxies
http://arxiv.org/abs/1106.4898

### http://arxiv.org/abs/astro-ph/0007437

There are faraway active galaxies that show a blueshift in their [O III] emission lines. One of the largest blueshifts is found in the narrow-line quasar, PG 1543+489, which has a relative velocity of -1150 km/s.[2] These types of galaxies are called "blue outliers".[2]

http://en.wikipedia.org/wiki/Blueshift

Aoki, Kentaro; Toshihiro Kawaguchi; Kouji Ohta (January 2005). "The Largest Blueshifts of the [O III] Emission Line in Two Narrow-Line Quasars". Astrophysical Journal 618 (2): 601–608. arXiv:astro-ph/0409546. Bibcode:2005ApJ...618..601A. doi:10.1086/426075

### Non-Euclidean Axioms for Digital Geometry

In digital geometry many of Euclid's axioms do not hold up.

Some other interesting consequences of digital geometry:

Intersections can contain more than one unit, and in some cases an intersection can contain multiple units that are not connected.

In digital geometry, Euclid's 5th axiom, the parallel postulate, does not hold up:

above, the blue and purple lines are parallel to the black line and both go through the red point, yet the two lines are not the same.

### 3-dimensional Corrugated Fractal torus discovered (2012)

When constructing a "flat" torus in 3-dimensional space there is significant distortion of distance along one axis. By "flat", mathematicians mean it has no Gaussian curvature, the way a cylinder is considered "flat", but not a sphere (which has positive curvature) or hyperbolic paraboloid (which has negative curvature).

The distortion of distances can be avoided by folding the torus in 4-dimensional space instead, as a Clifford Torus. (Or, equivalently, in a 2-dimensional complex space.)

It has recently been discovered (2012) that there is an alternate way to construct a flat torus in 3-dimensioal space, which will not distort distances. The construction involves a weird corrugated fractal surface.

http://math.univ-lyon1.fr/~borrelli/Hevea/Presse/index-en.html
http://www2.cnrs.fr/en/2027.htm
http://www.science4all.org/le-nguyen-hoang/flat-torus/

## Monday, May 5, 2014

http://en.wikipedia.org/wiki/Infinity

http://en.wikipedia.org/wiki/Apeirogon

http://en.wikipedia.org/wiki/Point_at_infinity

http://en.wikipedia.org/wiki/Line_at_infinity

http://en.wikipedia.org/wiki/Plane_at_infinity

http://en.wikipedia.org/wiki/Hyperplane_at_infinity

http://en.wikipedia.org/wiki/Extended_real_number_line

http://en.wikipedia.org/wiki/Extended_real_number_line

http://en.wikipedia.org/wiki/Controversy_over_Cantor%27s_theory

http://en.wikipedia.org/wiki/Georg_cantor

http://en.wikipedia.org/wiki/Transfinite_number

http://en.wikipedia.org/wiki/Aleph_number

http://en.wikipedia.org/wiki/Beth_number

http://en.wikipedia.org/wiki/Ordinal_number

http://en.wikipedia.org/wiki/Even_and_odd_ordinals

http://en.wikipedia.org/wiki/Limit_ordinal

http://en.wikipedia.org/wiki/Continuum_hypothesis

http://en.wikipedia.org/wiki/Cardinality_of_the_continuum

http://en.wikipedia.org/wiki/Surreal_number

http://en.wikipedia.org/wiki/Monogon

http://en.wikipedia.org/wiki/Digon

http://en.wikipedia.org/wiki/Countable_set

http://en.wikipedia.org/wiki/Transfinite_induction

http://en.wikipedia.org/wiki/Abraham_Robinson

http://en.wikipedia.org/wiki/Non-standard_analysis

OTHER:

http://www.math.rutgers.edu/~zeilberg/Opinion108.html

http://en.wikipedia.org/wiki/Ultrafinitism

http://en.wikipedia.org/wiki/Doron_Zeilberger

http://mathworld.wolfram.com/ComplexInfinity.html

## Monday, April 21, 2014

### An infinite circle is a straight line

This is how the Universe works.

A circle with infinite radius is a line

The edge of a circle with infinite radius is straight

http://en.wikipedia.org/wiki/Inversive_geometry

"In geometry, inversive geometry is the study of those properties of figures that are preserved by a generalization of a type of transformation of the Euclidean plane, called inversion. These transformations preserve angles and map generalized circles into generalized circles, where a generalized circle means either a circle or a line (loosely speaking, a circle with infinite radius). Many difficult problems in geometry become much more tractable when an inversion is applied. "

Apeirogons
http://en.wikipedia.org/wiki/Apeirogon#Regular_apeirogons

"A regular apeirogon has equal-length sides and equal corner angles, just like any regular polygon. Its Schläfli symbol is {∞}.

If the corner angles are 180°, the overall form of the apeirogon resembles a straight line, This line may be considered as a circle of infinite radius, by analogy with regular polygons with great number of edges, which resemble a circle."

Numberphile video "Epic Circles"

### Hawking - It is wrong to take the Big Bang literally

Stephen Hawking
The Grand Design (2010)
pages 128-129

Stephen Hawking
The Grand Design (2010)
pg. 128-129

Measurements of helium abundance and the CMBR [Cosmic Microwave Background Radiation] provided convincing evidence in favor of the Big Bang picture of the very early Universe, but although one can think of the Big Bang picture as a valid description of early times, it is wrong to take the big bang literally, that is, to think of Einstein's theory as providing a true picture of the origin of the Universe. That is because General Relativity predicts there to be a point in time at which the temperature, density, and curvature of the Universe are all infinite, a situation mathematicians call a singularity. To a physicist this means that Einstein's theory breaks down at that point and therefore cannot be used to predict how the Universe began, only how it evolved afterwards. So although we can employ the equations of general relativity and our observations of the heavens to learn about the Universe at a very young age, it is not correct to carry the Big Bang picture all the way back to the beginning.

### Singularities "cured" by String Theory

Briane Greene
The Hidden Reality
pg. 111

### Absolute Spacetime and "Invariance Theory"

Brian Greene,
The Fabric of the Cosmos (2004)
pg. 51

### Singularities - When theories break down

Stephen Hawking
A Brief History of Time
page. 49

page 63

The predictions of the theory
"break down at the big bang singularity"

"Classical general relativity,  by predicting points of infinite density, predicts its own downfall, just as classical mechanics predicted its downfall by suggesting that atoms should collapse to infinite density"

Paul Steinhardt, Neil Turok
Endless Universe
pages 37, 38

page  126

pages 184, 185

"In practice, when you’re calculating something in physics and you find a singularity in your calculation (this happens all the time), which usually looks like “1/x”, then that means that there’s a mistake somewhere, or you’re looking at something that never happens, or there are physical laws or effects that haven’t been taken into account."

# (new scientist)

"An imprint left on ancient cosmic light that was attributed to ripples in spacetime – and hailed by some as the discovery of the century – may have been caused by ashes from an exploding star.
In the most extreme scenario, the finding could suggest that what looked like a groundbreaking result was only a false alarm. Another possibility is that the stellar ashes could help bring the result in line with other cosmic observations. We should know which it is later this year, when researchers report new results from the European Space Agency's Planck satellite."