Entrapped Manifolds

• Introduction
• What is a manifold?
• What is an entrapped manifold?
• The Idea
• Why is the universe flat?
• Why the CMB Dipole?
• Why the CMB Anisotropies?

Introduction

I have an idea. Its a very simple idea. That idea being the fractal geometry of entrapped spacetime manifolds within one another, each a universe to itself.

By exploring this idea we will answer the most pressing questions in physics. Why is the universe flat? What happened to the antimatter at the time of the Big Bang? What caused the dipole and large scale anisotropies of the cosmic microwave background radiation to be formed?

What is a manifold?

To begin, what is a manifold?

Space and time are one. Together they are spacetime acting as a single structure within Einstein’s Theory of General Relativity. This structure as a whole we call a manifold. The number one example of a manifold is our universe as a whole. It is the fabric of spacetime that sets the stage upon which the evolution of our universe unfolds.

In order to measure distances and angles upon a manifold we employ a Lorentzian metric. This metric in turn describes how we go about measuring said distances and angles. Together they set the stage by which the orbits and paths of astrophysical objects in relative motion with respect to each other can be predicted. That predictive power comes from Einstein’s Field Equations of General Relativity.

General Relativity describes how the spacetime fabric of a manifold is curved and warped by the presence of mass-energy density. For example, our sun, composed primarily of hydrogen and helium, has a mass of about \(2*10^{30}\) kilograms with a spherical diameter of around 1.4 million kilometres. This concentration of mass within the sun curves and bends the fabric of spacetime. By how much and to what extent is found by using a solution of Einstein’s Field Equations. We know that the sun warps the fabric of spacetime in observing how the path of light changes as it passes by our sun.

Photons emitted by a distant star travel across the interstellar expanse of the universe’s spacetime manifold. For the greater part, they mostly follow a straight path as the curvature of an empty vacuum is flat as described by Einstein’s Theory of Special Relativity. But if their path comes close to a large object such as another star then that path is curved around the star. The mass of the star causing the manifold to be curved. It was this observation, by Sir Author Eddington in 1919, using a solar eclipse which showed that the path of light from known stars when seen next to the sun was visibly altered by the mass of our sun. It was this experiment that confirmed Einstein’s Theory of General Relativity.

In essence, we can think of a manifold such as our universe as being like a sheet that is curved by the presence of physical objects composed of mass. Even if that mass is invisible, itself entrapped, such as is the case with dark matter. Although completely invisible we see the effects of dark matter where it acts as an intergalactic lens curving the path that light travels along producing these beautiful Einstein Rings. The light emitted from galaxies behind the dark matter lens travels along curved paths whose curvature is formed by the presence of dark matter. Collectively the dark matter acts as a lens magnifying the galaxies behind the lens. As for what exactly dark matter is well in order to understand that we need to talk about entrapment and our idea of entrapped manifolds.

What is an entrapped manifold?

The definition of what an entrapped manifold is given form in considering the extreme logical end point of General Relativity by way of a black hole. There are several types of black holes depending upon the solution to Einstein Field Equations the simplest and most commonly known type is called the Schwarzschild black hole. Named after Karl Schwarzschild who found the first exact solution to Einstein’s field equations in 1916 which describes the gravitational field outside a spherical body with no angular momentum. The idea of a black hole was given form in considering a spherical body with infinite mass in a infinitely small point, the gravitational singularity. Here the gravitational field is so strong that not even light could escape its pull.

A non-rotating black hole has only one physical object inside it and that is the gravitational singularity a point of infinite density. The spherical event horizon that envelops this singularity is defined by the escape velocity being equal to the speed of light. Above the event horizon a photon of light may escape back out into the universe. But below the event horizon the photon becomes entrapped, caught in the gravitational field of the singularity, unable to ever escape. As nothing can travel faster than the speed of light then it becomes impossible for anything trapped inside the event horizon to ever escape it, including light.

In total effect the black hole contained inside the volume of the event horizon can be considered its own entrapped manifold wherein every path travelled leads down and on to the singularity. There is no other path of travel out or away from the singularity once we are inside the event horizon. Once inside the volume of the event horizon there is no escape and we are entrapped.

Physicists visualise this entrapped manifold by way of a Penrose spacetime diagram showing a Schwarzschild black hole. Here the infinite manifold that is our universe is conformally mapped into the finite diamond with the vertical, blue lines, representing time and the horizontal, red lines, representing space. Next to it the black hole is drawn as a separate manifold which maps to the interior of the black hole. The 45 degree boundary between the universe manifold and the black hole manifold is the event horizon of the black hole. Inside the black hole manifold all paths lead down to the inevitable gravitational singularity.

The important part in considering this Penrose diagram of a Schwarzschild black hole lies in this separation of our manifold the universe from the entrapped manifold that is the interior of the black hole itself. The event horizon being the boundary between the two manifolds. The fate of anyone falling into such a black hole is to fall onto the singularity. The fact that black holes exist inside our universe shows that entrapped manifolds exist inside our universe and are a very real thing.

This very simple description of a black hole does not account for rotation as Karl Schwarzschild’s solution of relativity assumes the angular momentum of the body is zero. It took until 1963, a near fifty more years, to find a solution to Einstein’s field equations where rotation of the astrophysical body is non-zero. Named after its discoverer Roy Kerr the Kerr metric can be used to describe a rotating black hole, as opposed to one with no rotation. With rotation the resultant Penrose diagram of a rotating Kerr black hole transforms into becoming something else, a doorway to another universe.

What happens is that with rotation the point singularity of infinite density is spun out into being a ring of infinite density, a ringularity. The formation of this ringularity fundamentally changes the structure of the black hole as a wormhole opens up inside the ringularity. This changes the fate of someone falling into a black hole from an inevitable end of falling onto a singularity to one where we fall through a wormhole.

Viewing the full Penrose diagram of a Kerr black hole we see that it is separated into a series of manifolds. An object falling past the event horizon of a rotating black hole will fall down and through the wormhole. Travelling through the wormhole we arrive at another entrapped manifold, the white hole, whose direction of travel is away from the wormhole and out into either one of two parallel new universes.

The common depiction, popularised in science fiction, of a wormhole is as being like a bridge across spacetime. Or in this case this the wormhole at the centre of the rotational black hole leads to pair of separate universes whose spatial location are completely removed from our own universe. That is, we think of one universe as being its own bubble manifold of spacetime and the other new pair of universes existing as their own separate manifold bubbles of their own reality.

The Idea

It is at this point we are looking to propose a different interpretation and introduce a wholly new but revolutionary idea. So everything up till now is established physics. It is here we consider just the subtlest of ideas. That idea being that rather than those two new universes being separate manifolds in there own right they actually coexist inside our universe sharing the same volume of space as our universe. In effect these two new universes are located inside our universe.

How? Well rather than this wormhole being a bridge across spacetime it is in fact going nowhere. It is not a bridge across spacetime projected through say a hypothetical higher dimensional bulk but rather this wormhole inside the rotational black hole leads nowhere. Meaning the entrance and exit to the wormhole exists inside the absolute volume of the black hole. The rotational black hole is an entrapped manifold which in turn entraps the wormhole’s manifold. So what makes us assume the wormhole is a bridge to another dimension or reality? Rather we consider the idea that the exit of the wormhole is located within the volume of the rotational black hole. Meaning the associated white hole leading from the wormhole exists within the volume of the rotational black hole.

The two new universes, each the parallel of the other, are themselves entrapped manifolds whose actual spatial location is inflating forth from the polar regions of the rotational black hole. The surrounding parent universe coexists spatially together but are in fact temporally disconnected from one another. Like a pair of balloons the inflation and growth of these two child universes are in to the polar regions of space surrounding the black hole. The inflation of these two child universes is driven by the flow of spacetime in from our parent universe into the rotational black hole through the wormhole and out via the adjoining white hole. Meaning the parent universe coexists spatially, but not temporally, with the pair of child universes.

So if we ask the question “What is the child universe expanding into?”. Then the answer to that question is the spatial volume adjacent to the polar regions of the associated black hole that gave birth to it.

Now if we ask the more specific question “What is our universe expanding into?” well let us consider the answer given by mainstream cosmology. The answer is nothing, or to quote X’s Grok “The universe is expanding, but it’s not expanding into anything in the way we might imagine, like a balloon inflating into a larger room.”. This is completely counter to the idea we are considering. Here we are actually imagining a child universe as being like a balloon being inflated inside a larger room, the parent universe. By considering this, as we are about to see, such an explanation allows us to answer the most basic questions in cosmology in quick and rapid succession.

Why is the universe flat?

Given that the overall shape of the child universe is determined by the local spacetime curvature of the parent universe then the shape of the child universe is determined by the spacetime curvature in the region surrounding the black hole back out in the parent universe. Meaning if the spacetime fabric of the parent universe in which the child universe as a whole becomes warped then the shape of the child universe is warped by its parent's curvature.

Using our analogy of a balloon being inflated inside a room let us imagine a gravitational wave passing through said balloon. With a gravitational wave the fabric of spacetime contracts, expands, contracts and expands. A metre length contracts and then again expands as a single gravitational wave passes through it. So to does the shape of the balloon contract and expand as the gravitational wave passes through it. The child universe, being like a balloon, as a whole will contract and expand as a gravitational wave of the parent universe passes through it.

Now the vast majority of space is vacuum with nothing in it. So it is a reasonable assumption that the child universe is expanding into the vacuum of the surrounding parent universe. Special Relativity specifically tells us that the local curvature of a vacuum is that it is flat. Meaning the surrounding parent universe into which the child universes are expanding are themselves also flat. Thus the overall shape of the child universe as a whole is going to be flat.

For the greater part of the 20th century the question “What shape is our universe?” has been of prime importance to cosmology. The question of shape arises from considering parallel lines. On a flat surface parallel lines never cross or diverge the distance between the lines is always the same. Alternatively on a surface with positive curvature, such as a sphere, parallel lines converge and cross over each other. Then on a surface with negative curvature, such as a saddle, parallel lines diverge away from one another. In asking the question “What shape is our universe?” cosmologists were looking to answer the question wither parallel lines would remain parallel or not.

After much debate and observations the question to “What shape is our universe?” was given answer. That answer being that the universe is flat. From examination of the cosmic microwave background radiation; to surveys measuring the total energy density of the universe; through to cosmic surveys of large scale structures the evidence clearly shows a universe whose overall shape is of one that is flat. [1] [2] [3]

So in considering the idea of a child universe expanding into the vacuum space of its parent universe we immediately have an answer as to why we live in a universe that is flat. Our universe is flat because it is expanding into the vacuum space of the parent universe that gave birth to us. How simple is that?

The alternative explanation, in asking Grok again, is that “The universe is flat because cosmic inflation smoothed out any curvature in its infancy, stretching space to appear Euclidean on large scales. Its expansion "into nothing" simply means space itself is growing, not that it’s filling some external void.” meaning the standing explanation as to why our universe is flat is because of cosmic inflation given that our universe is not actually expanding into anything. Cosmic inflation itself is driven by a hypothetical scalar field for which no experimental evidence has been found. For example, no particle representation of the inflation field has ever been seen.

So given that our universe is expanding into nothing there is also the mainstream idea that our universe came from nothing. I mean the first law of thermodynamics, the conservation of energy, states energy can neither be created or destroyed. But yet our mainstream explanation for the Big Bang says our universe came from nothing and is expanding into nothing while inventing hypothetical quantum fields in order to explain the observational evidence that our universe is flat.

Occam’s Razor says the simpler explanation tends to be the one that is true.

On the one hand we can imagine our universe, like a balloon being inflated, is expanding into the vacuum space of our surrounding parent universe which I hear in call the Superverse. This is a whole lot more intuitive than trying to imagine what nothingness actually is. As a note, our universe occupies a subset of the volume of the Superverse. So using set theory nomenclature I call it the Superverse as it is the superset to our own universe.

This Superverse has its own law of General Relativity. Same mathematics but operating at a much larger scale. A Planck length in the Superverse could be a metre, it could be parsec, the point being that it operates at its given scale and its given scale compared to ours is truly titanic. The key philosophy of fractal geometry is that self-similar patterns repeat irrespective of scale and this gives us mathematical permission to imagine such a Superverse. Exactly like our own, a fractal mirror, but for one of scale. Then just like our universe the concentration of mass-energy density causes the curvature of the Superverse’s spacetime fabric to be curved and warped.

Our universe’s shape as a whole is warped and shaped by the curvature of the Superverse within the volume it has expanded into. Close to the black hole the curvature will be great but the further the universe expands away from it and out into the vacuum of the Superverse the curvature flattens out. As the curvature of the vacuum in the surrounding Superverse is itself flat implies that the shape of our universe as a whole is flat.

In comparison the alternative mainstream explanation sees ourselves making up hypothetical fields while violating the first and most basic law of thermodynamics by creating the entire universe from nothing.

Honestly, these days I don’t know wither to laugh or cry about the state of modern theoretical cosmology. For example, cosmic inflation says that tiny quantum fluctuations in the very early universe expanded to very large scales during its period of very rapid inflation. The evidence of which, it claims, is to be found in the cosmic microwave background radiation. But when it actually comes to the observed and measured comic microwave background the actual main results are ignored and argued away as not being part of the microwave sky.

What am I talk about? The CMB Dipole and the large scale anisotropies seen in both WMAP and Planck to name but a few. Starting with the CMB Dipole which has the greatest temperature gradient of all the features identified in the microwave sky. Ever since its discovery in the late 80s the CMB Dipole has been explained away as a doppler shift that arises because of Earth’s movement through the universe relative to the rest frame of the microwave sky. But numerous studies of quasar groups have shown that this kinematic interpretation of the CMB Dipole is actually invalid. [4] [5] [6] [7] [8] [9]

Why the CMB Dipole?

So what caused the CMB Dipole?

Returning back to picturing our universe as expanding forth from a black hole and expanding out into the expanse of a much larger parent universe, the Superverse, I noted that there are two expanding child universes. One expands from the north pole and the other expands from the south pole. We consider two universes because firstly in the conformal solution of the Kerr metric the white hole exits into one of two universes. Secondly, following CPT-Symmetry a fundamental law of quantum mechanics a universe of antimatter would be a manifold travelling in the polar opposite direction to our own. In this way we are able to not only account for “What happened to the anti-matter at the time of the Big Bang?” question but also in doing so we see why our parallel universe of antimatter is exactly that. It is a universe of antimatter because the expansion of that universe is in the exact polar opposite direction to the expansion of our own universe.

Specifically there are two poles to a rotational body, such as our black hole. One north pole and one south pole. The expansion of each universe is from each of the two poles. One universe expands into the region above the north pole and the other universe expands into the region below the south pole. Given this interpretation we can see that the expansion of each universe is unidirectional. Given this unidirectional expansion of our universe we would expect to see one half of the microwave sky to be very much significantly hotter than the other. Or rather, in asking the question “What caused the CMB Dipole?” then our answer is that it arises from the unidirectional arrow of travel away from the black holes polar region.

That’s three major questions answered. Why is our universe flat? What caused the CMB Dipole? and What happened to all the antimatter at the time of the Big Bang?

Ok let’s keep going.

Why the CMB Anisotropies?

Now about those large scale anisotropies seen in both WMAP and Planck. Here we can see in the southern hemisphere two large spiral arms, one hot and one cold. I would love to present you with an alternative explanation from mainstream cosmology but in truth this reproduced result is barely even given the time of day by theorists. Why? Because theoretical cosmologists have no explanation except to dismiss it. Unfortunately, for them a new study using Planck CMB data has confirmed that the universe is a significantly more “clumpier” in the areas of these large scale anisotropies. Meaning they are physically real structures within our not so perfectly homogenous universe. [10]

In developing my Big Bang Kilonova Hypothesis I propose that these twin spiral anisotropies are caused by the gravitational waves within the parent Superverse. These gravitational waves of the Superverse are generated by the inward death spiral of two neutron stars in said parent universe. Just like in our universe a pair of neutron stars spiralling into towards each other generates spiralling gravitational waves. The Superverse operating by its own form of General Relativity generates twin spiral gravitational waves. We say this because the mathematical law of fractal geometry is that self-similar patterns repeat irrespective of scale. Even if the size of that scale is larger than the entire universe as a whole. After all instead of trying to make stuff up about how the Big Bang singularity was born from nothing we study how a singularity is actually born inside our universe in order to build a Big Bang theory that can explain the observed microwave sky.

Following the spacetime curvature of our parent Superverse one spiral wave creates a spiral trough into our very early universe. This trough fills up with the primordial plasma of the early universe. Vice versa, the other spiral wave creates an indentation into our universe pushing aside the primordial plasma. As the gravitational waves recede the shape of our early universe then flattens out but the spiral waves have left their mark.

Having previously stated that the overall shape of our universe is determined by the local spacetime curvature in the parent Superverse then the presence of these twin spiral gravitational waves would warp our very early universe leaving their imprint. Off course, it is very important to note that immediately following the collision and birth of a new black hole the generation of gravitational waves ceases and the surrounding region flattens back out.

The spiral wave that created the trough filled with primordial plasma would then go on to become the hot spiral arm. The surrounding regions in turn being filled with more plasma would have a far greater than average density with respect to the rest of the universe. This feature we see in the newly identified and named Hemispherical Power Asymmetry in the CMB. Vice versa, the cold spiral arm comes about because the plasma has been pushed aside implying that when the wave recedes and the universe flattens back out what remains is empty void.

From this we are able to make the prediction that one side of our universe should contain much more mass with respect to the other side. Namely, I would expect the area where the hot arm is located to be filled with the additional matter that accumulated in the trough created by one of the kilonova’s gravitational waves. Off course, as the wave recedes the trough flattens out flinging this matter into the surrounding regions. Coupled to this I would predict that region where the cold spiral arm is located would contain much less matter a spiral void having been created when the other gravitational wave in the kilonova receded. And this is exactly what a new study has found backing up confirmation that these spiral arm anisotropies are in fact part of the cosmic microwave background radiation. [10]

So with one explanation that being that our universe is shaped by the local spacetime curvature of our parent Superverse we have been able to explain the large scale anisotropies and the fact that we see the shape of our universe as being flat. Then in considering the expansion of two universes we are also able to give answer to the mystery of antimatter at the time of the Big Bang as well as explain the CMB Dipole.

All this from the simple consideration of one idea. That idea being that our universe is an entrapped manifold that was born from and is expanding inside a pre-existent parent universe. In doing so we have given simple answer to some of the most fundamental and pressing questions in all of modern physics. And some of those questions have not been answered by anyone else in the field of physics apart from us here in. And this is only the beginning.

Until next time.

References:

• [1] A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation : P. de Bernardis, P.A.R.Ade, J.J.Bock, J.R.Bond, J.Borrill, A.Boscaleri, K.Coble, B.P.Crill, G.De Gasperis, P.C.Farese, P.G.Ferreira1, K.Ganga, M.Giacometti, E.Hivon, V.V.Hristov, A.Iacoangeli, A.H.Jaffe, A.E.Lange, L.Martinis, S.Masi, P.Mason, P.D.Mauskopf, A.Melchiorri, L.Miglio, T.Montroy, C.B.Netterfield, E.Pascale, F.Piacentini, D.Pogosyan, S.Prunet, S.Rao, G.Romeo, J.E.Ruhl, F.Scaramuzzi, D.Sforna, N.Vittorio
• [2] What is the Universe Made Of? : NASA
• [3] Large-Scale Surveys and Cosmic Structure - J.A. Peacock (University of Edinburgh)
• [4] The CMB Dipole - Eppur Si Muove
• [5] - Planck enhanced anomalies - ESA
• [6] Evidence of vorticity and shear at large angular scales in the WMAP data: a violation of cosmological isotropy? - T. R. Jaffe, A. J. Banday, H. K. Eriksen, K. M. Gorski, F. K. Hansen
• [7] Bayesian analysis of anisotropic cosmologies: Bianchi VIIh and WMAP - J. D. McEwen1, T. Josset et al (2018)
• [8] A Test of the Cosmological Principle with Quasars - Nathan J. Secrest, Sebastian von Hausegger, Mohamed Rameez, Roya Mohayaee, Subir Sarkar, and Jacques Colin
• [9] Testing the Cosmological Principle with CatWISE Quasars: A Bayesian Analysis of the Number-Count Dipole - Lawrence Dam, Geraint F. Lewis1y & Brendon J. Brewer
• [10] A Reassessment of Hemispherical Power Asymmetry in CMB Temperature Data from Planck PR4 using LVE method - Sanjeev Sanyal, Sanjeet K. Patel, Pavan K. Aluri, Arman Shafieloo
• [11] Cosmic Microwave Background Dipole - Swinburne University of Technology