## 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.