Abstract

Introduction

The Universe is a Hologram

If the nucleus of a hydrogen atom was the size of the Sun, its electron would be orbiting somewhere in the heliopause, a region of space where the interstellar and solar winds meet, at a distance of 470 astronomical units, or nearly 45 billion miles away. Four times the distance of the Voyager probes.

The nearest electron.

Now take a moment and observe the world around you.

Every atom in the universe — and therefore everything that you are and everything that you see — consists primarily of a vast and unfathomable amount of empty space.

Let that sink in.

And according to the standard model of cosmology, there are just three basic ingredients necessary to constitute this universe: dark energy, cold dark matter, and normal, ordinary matter.

Dark energy is an unknown force that causes space to expand and accounts for 70% of the energy density of the universe. Conversely, dark matter is an unknown force that causes space to contract, consuming another 25% of the budget.

Taken together and permeating the entire universe, these invisible forces constitute at least 95% of its total energetic content.

The remaining 5% of the universe, then, is ordinary matter which encloses volumes of overwhelmingly empty space.

On this precipice of observation are constructed the theories of general relativity and quantum mechanics which form the foundations of the standard models of cosmology and particle physics. These models attempt to describe the universe mathematically as the interaction of matter-energy in space-time mediated by irreducible and fundamental forces. In short, to explain the motions of everything we see.

Though considered state of the art with respect to experimental validation, the theories of general relativity and quantum mechanics nonetheless remain incomplete descriptions of reality due to incompatibilities arising from the intersection of their formulations, particularly at the event horizon of a black hole, where the pillars of science meet.

And the problem is gravity.

We still don’t know how it works.

Fundamental Forces

Accordingly, the study of physics is an effort to explain the behavior of matter and energy in the universe, and to understand the forces impelling its motion. Formulated mathematically as fields, the laws of physics articulate the interactions of matter-energy with the four fundamental forces that are known to exist: gravitational, electromagnetic, strong, and weak.

The gravitational force is the weakest of the forces and is attributed to the curvature of space-time in the presence of matter and energy. This relationship is formulated in Einstein’s general theory of relativity and is expressed in the equations of classical physics. It describes the universe at macroscopic scales where quantum behavior is negligible.

Quantum mechanics accounts for the remaining fundamental forces, particularly at the microscopic scale where gravity is negligible. The strong force describes nuclear binding while the weak force explains radioactive decay. And the electromagnetic force accounts for the propagation of light, electricity, and magnetism, radiation as we know it.

Represented as discrete quantum fields with interactions mediated by elementary wave-particles, the nuclear and electromagnetic forces are expressed in terms of probabilities.

Standard Models

Taken together, general relativity and quantum mechanics describe the structure and evolution of the universe in terms of fundamental forces at nearly all scales and times, from the intergalactic down to the Planckian. With respect to experimental validation, they are considered the state of the art theories of physical reality.

As noted though, the theories of general relativity and quantum mechanics, in present form, are incompatible. More specifically, while the strong, weak, and electromagnetic forces are predicted accurately by quantum field theory, an empirically validated theory of quantum gravity, one that is capable of describing gravity as the quantum behavior of a gravitational field, does not exist.

And as these predictions have increased in precision over the past century, which include the recent discoveries of the Higgs boson and gravity waves, the graviton, nonetheless, remains undiscovered. A graviton is the theoretical force carrying particle of the gravitational field required by the standard model.

In other words, the mechanism by which gravity exerts a force is still unknown.

Theory of Everything

Many attempts have been made to formulate a Theory of Everything that unifies the fundamental forces into a “single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the universe.”

The goal being to explain gravity in a manner consistent with the standard models and find a path that leads to the discovery of the graviton.

To date, all have failed to clear the hurdle of empirical validation. Nonetheless, their explorations have provided a deeper understanding of physics and mathematics, and certainly a broader range of implications concerning the nature of reality should any of them hold true.

In this paper, we will explore one particular thread in the search for quantum gravity, namely, the holographic principle, and examine some of its implications.

But first, a brief review of what we know about reality.

Special Relativity

Near the end of his annus mirabilis in 1905, Albert Einstein published the theory of special relativity which set the stage for our understanding of the universe.

In short, special relativity describes the relationship between space and time, and is based on two postulates:

the laws of physics are invariant in all inertial frames of reference; and the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or observer.

A consequence of these two postulates is that space and time are inseparable, and they cannot be defined independently from one another.

The fabric of reality, therefore, is an interwoven sheet of space-time.

Displacement through one is a trade-off in the other. This predicts a universe with time dilation and length contraction, as well as the relativity of simultaneity.

Like in Interstellar, when they went surfing.

Also, there is no absolute universal time.

The experience of time is always dependent on a frame of reference and spatial position. Every point of view, then, is a cosmic light cone. The farther we look into space, the deeper we see into time and the past. And the laws of physics never change. What’s possible here is possible anywhere in the universe.

Following the path of consequences left by special relativity, we find the light cone defining the observable universe, the portion of it with enough time since the Big Bang for light to reach us, is a sphere nearly 100 billion light years across. And within our light cone, we also find that there are at least 2 trillion galaxies, each containing about 100 billion stars.

The extent of the universe outside of our cosmic cone of shame is estimated to be from a thousand to an infinity times larger.

So, according to special relativity and our best guess, there are at least several quadrillion galaxies in the universe that we will never see.

OMG. It’s full of stars.

General Relativity

In 1915, Albert Einstein published the general theory of relativity in which he integrated the theory of special relativity, which describes the structure of space-time, and the theory of mass-energy equivalence, which states that mass is concentrated energy, E = mc^2.

Formulated in the equations of classical physics, general relativity predicts that the curvature of space-time — the force of gravity — is proportional to the energy and momentum of the matter and radiation present.

The more massive-energetic an object, the larger the dent it puts in the universe, proportionally affecting our experience of space and time through its gravitational attraction.

As for space, time, energy, matter … different sides of the same coin. Flipped by the speed of light.

Gravity is what happens when they get mixed up.

That’s the theory.

Cosmological Constant

In order to balance the equations of general relativity for an unchanging and infinite universe, the assumed model of the time, Einstein introduced the cosmological constant, otherwise known as lambda (Λ), to account for the energy density of empty space, or the vacuum energy.

This anti-gravity force was required to push space-time apart and prevent it from collapsing due to the contractions experienced in the presence of matter and energy. Oddly enough, the cosmological constant began as a necessary foundation for keeping the structure of the universe intact.

However, in 1931, Edwin Hubble discovered that the universe was perhaps much larger than anyone imagined, suggesting that nebulae were distant galaxies, well beyond the galactic plane of the Milky Way. He also collected data pointing to a rate of expansion of the universe, the redshifts of light at great distance.

A view at odds with a static universe.

Hubble’s findings were so convincing that Einstein quickly abandoned the idea of the cosmological constant, declaring that it was the biggest mistake of his life.

And despite the evidence suggesting an expanding universe, the scientific community spent the next 60 years mostly assuming the cosmological constant equal to zero, rendering its effects negligible and the universe an infinitely boring place, from a structural point of view.

Dark Energy

And then, in 1998, it was discovered that the universe is, in fact, expanding and which implied a non-zero cosmological constant, and therefore a positive vacuum energy.

This is dark energy in the standard cosmological model and it accounts for 70% of the energy density of the universe.

The energy of empty space pushing itself apart.

Anti-gravity.

Dark Matter

By the end of the 20th century, it was also the consensus of the scientific community that a form of matter exists which does not interact with electromagnetic radiation, but nonetheless deforms the curvature of space-time.

That is, a wave-particle with a gravitational effect that does not emit or reflect light.

To note, it is quite difficult to describe a variety of astrophysical phenomena that we observe without this invisible weakly interacting matter: from gravitational lensing to galaxy structure to the cosmic microwave background radiation.

This theoretical particle is called dark matter and is believed to constitute about 25% of the energy density of the universe, and it “has had a strong influence on its structure and evolution.”

The energy of empty space pulling itself together.

Gravity.

Quantum Mechanics

The remaining forces — electromagnetic, weak, and strong — are described by quantum mechanics, which, more or less, are a statistical interpretation of thermodynamics.

Energy and momentum are formulated as discrete units exhibiting wave-particle duality and they are treated mathematically in terms of probability.

The Standard Model of Particle Physics

As an explanatory model for the standard model of particle physics, quantum mechanics classifies all experimentally observed elementary particles into just two groups: fermions (matter) and bosons (force carriers).

Wave Function

Each particle is modeled as a wave function that provides information about the probability amplitude of its energy, momentum, and other physical properties.

In the Copenhagen interpretation of quantum mechanics, the wave function is the most complete description that can be given of a physical system. Solutions to Schrödinger’s equation describe not only molecular, atomic, and subatomic systems, but also macroscopic systems, possibly even the whole universe.

Observer Effect

When the world interacts with a particle, the wave function collapses into a single observable state selected from a superposition of all possible states.

The act of observation invariably changes the behavior of the particle being observed.

Uncertainty Principle

There are also limits to the precision of observation. The uncertainty principle implies that it is impossible to predict the value of a quantity with an arbitrary certainty, even if all initial conditions are specified. The more precisely we know a particle’s momentum, the less precisely we can know its position.

Quantum Entanglement

Another peculiar feature of quantum mechanics is entanglement. When particles interact and entangle, their quantum states cannot be described independently of the other, even when separated by vast distances.

A change in the state of one particle instantaneously affects an identical change in the state of the other particle, faster than the speed of light. This is called non-locality, or actions at a distance. Einstein thought they were “spooky.”

Nonetheless, they are real, and they are spectacular, which is to say, experimentally verified and fundamental to nature.

Big Bang Cosmology

Despite the limitations of general relativity and quantum mechanics, we are still able to construct an accurate model of the universe using their equations at the appropriate scales in order to form a timeline of its evolution. And while many predictions of the standard models continue to be proven with increasing accuracy, there are still some features in need of theoretical explanation.

Planck Epoch

At 10–43 seconds post-bang, a unit of Planck time, it is believed that the universe experienced a phase transition in which the fields of force and their particles began to separate and stabilize at cooler temperatures.

Prior to this moment, there are currently no physics to describe the state of the universe when all matter-energy and the fundamental forces were unified. After this moment, we can start using the equations of general relativity and quantum mechanics to start teasing them apart and making sense of the universe.

Inflationary Epoch

During the first 10–32 seconds, the universe experienced an extraordinary inflation, the equivalent of an object one nanometer — about half the width of a DNA molecule — expanding to 10.6 light years in length, or roughly 62 trillion miles across.

Although light and objects within space-time cannot travel faster than the speed of light, in this case it was the metric governing the size and geometry of space-time itself that changed in scale.

It is not clear why this happened nor why it ended.

Following the inflationary period, the universe continued to expand but at a much slower and predictable rate.

Baryogenesis

Baryons are particles such as protons and neutrons, the precursors to atoms and molecular matter.

At around 10–11 seconds following the big bang, as quarks were coalescing into matter, there should have been an equal amount of anti-baryons created, which in theory, would have resulted in the annihilation of all baryonic matter.

For reasons still not understood, there was a baryon asymmetry in the newborn universe, a necessary condition for the existence of matter, which raises the question:

What happened to all of the anti-matter?

Cosmic Microwave Background

377,000 years after the big bang, the universe had cooled sufficiently enough to begin forming atoms. As electrons settled into stable orbits around protons to form hydrogen and helium atoms, they released photons, and we see this today as the cosmic microwave background radiation.

Prior to this moment, the universe was a hot ionized plasma and photons were unable to escape from the electromagnetic soup. Following it, light and matter were decoupled from each other, providing the first glimpse of a transparent cosmos.

Dark Ages and Galactic Structure

However, from 377,000 to about half a billion years after the Big Bang, the universe, though transparent, was still dark as stars had not yet formed. These are considered the dark ages of the universe when matter coalesced slowly into clouds of atoms and molecules under the influence of gravity, eventually igniting into the stars and galaxies we see today.

Dark Energy Dominated Era

About 9.8 billion years after the Big Bang, coincidentally around the same time our solar system was forming, the universe underwent its third large-scale shift of behavior following the radiation and matter dominated eras. It was at this point that the universe’s decelerating rate of expansion stopped.

The universe began to accelerate its push outward, with dark energy overcoming and then dominating the force of gravity, an acceleration and expansion of space that continues to the present day.

Lambda-CDM Model

Pulling it all together is the Lambda-CDM model which is a parametrization of the Big Bang cosmological model in which the universe contains just three components: dark energy, cold dark matter, and ordinary, normal matter.

And it is a simple model with only six parameters:

the age of the universe the density of atoms the density of matter the amplitude of the initial quantum fluctuations the scale dependence of this amplitude, and the epoch of first star formation

Using this model, we can account for the motions of nearly 5% of the universe, assuming that gravity somehow works.

Beyond the Standard Models

While our understanding of the thin slice of the universe that we can see is extraordinary, perhaps even super-natural, we still have yet to understand gravity and explain the vast amount of the universe that we cannot see.

General relativity seems, at best, to be an approximation of an undiscovered mechanism for the gravitational field.

And quantum mechanics dissolves our view into a sea of probabilities with an entangled uncertainty at the center. The act of looking changes everything. Its formulations are typically in the flat space-time of special relativity, which assumes a static universe.

Both theories make assumptions about the other in order to make the effects negligible from their point of view. Subsequently, one of the deepest problems in theoretical physics is reconciling the theory of general relativity with quantum mechanics.

However, this problem must be put in the proper context. In particular, contrary to the claim that quantum mechanics and general relativity are fundamentally incompatible, it is only at the Planck scale that issues arise. One can also demonstrate that the structure of general relativity inevitably follows from the quantum mechanics of interacting theoretical spin-2 massless particles (i.e. gravitons).

Many notions of quantum gravity assume, and to some degree depend on, the existence of the graviton. Despite the lack of experimental validation, it should exist.

In summary, many of the outstanding problems of the standard models of physics revolve around gravity and the contraction and expansion of space, a list including dark energy, dark matter, baryon asymmetry, neutrino mass and the strong CP problem.

Quantum Gravity

Quantum gravity, then, is a branch of physics that seeks to describe gravity using the principles of quantum mechanics, to find the missing graviton.

When applying quantum field theory to gravity in a manner consistent with the nuclear and electromagnetic forces, it currently predicts infinite values for some of the observable properties of the universe, such as mass. This is a problem.

And one approach to addressing the problem of quantum gravity is string theory.

String Theory

String theory can be seen as a generalization of quantum field theory where instead of point particles, all matter and energy are modeled as one-dimensional string-like objects that propagate and interact in space-time.

The folding of a length of string and its resonant frequency determine its properties — mass, charge, spin, etc — and unique combinations of those properties account for the behavior of all the elementary particles.

On scales larger than a string, strings appear just like particles.

It is also important to note the distinction between open and closed strings with respect to their endpoints. Open strings have two endpoints and can be thought of as a line segment, while closed strings have no endpoint and form a closed loop.

Extra Dimensions

In reality, our normal experience of space-time is a four-dimensional structure composed of width, height, depth, and time.

However, mathematically describing a self consistent universe in four dimensions, in which general relativity and quantum mechanics co-exist, has proven quite difficult.

In the case of string theory though, by modeling space-time with extra dimensions, the math becomes tractable which allows for computation and perhaps even some insight.

In its handful of formulations, string theory requires a minimum of 10 dimensions for strings to propagate in order to achieve mathematical consistency, and they are:

The plane of width The plane of height The plane of depth The plane of time The plane of possibility in this universe The plane of possible universe histories given initial conditions (Big Bang) The plane of possible universes given laws of physics with different initial conditions The plane of possible universe histories given laws of physics with different initial conditions The plane of universes with all possible laws of physics and initial conditions The plane of universe histories with all possible laws of physics and initial conditions

Therefore, reality can be modeled as a wave-function of entangled strings in a hyperspace with hidden dimensions.

But since we normally experience just the first four dimensions, arguably the 5th, and perhaps in some extra-ordinary circumstances the 6th, the question remains: where are all of the hidden dimensions?

If they exist and are real, where are they?

D-Branes

An idea central to string theory is the notion of branes. A brane is a generalization of something to a higher dimension. For example, a point is a zero-dimensional brane; and a string is a one-dimensional brane. D-branes, specifically, are a class of branes in string theory that meet certain conditions which allow strings to attach to them.

Following this characterization, one possible explanation would be that the visible universe is a very large D-brane extending over three spatial dimensions.

Material objects, made of open strings, are bound to the D-brane, and cannot move “at right angles to reality” to explore the universe outside the brane.

In this model, the force of gravity is not due to open strings, those attached to D-branes, as with matter and energy, on other hand, gravitons here are vibrational states of closed strings, unattached to D-branes.

Gravitational effects depend on the extra dimensions orthogonal to the brane.

Perhaps this describes the multiverse of Rick and Morty. The portal gun is just shooting gravitons to create a wormhole orthogonal to its D-brane.

Compactification

Another approach to extra dimensions is to compactify them on an extremely tiny scale, to close them up into loops, and to make their effects negligible. One of the requirements of compactification in string theory is that it must be done on a Calabi-Yau manifold, which when projected in 3 dimensions, looks something like this:

3D Projection of a Calabi-Yau Manifold

All we need to know about this exotic shape is that it is a hidden geometry with hyperbolic dimensions that theoretically encodes the history of all possible universes, where strings propagate, weakly interacting with the dimensions we can see.

This is the energetic landscape of empty space.

Supersymmetry

In addition to the extra dimensions, string theory has another requirement that helps to structure the resolution of some of the hard problems of physics. It is called supersymmetry and it predicts the existence of of super-partners, or shadow particles, identical to the elementary particles with the exception of their spin.

If the supersymmetry theory is correct, it should be possible to recreate these particles in high-energy particle accelerators. But doing so will not be easy, as these particles have predicted masses nearly three orders of magnitude greater than their corresponding ‘real’ particles.

Dualities & M-Theory

As noted earlier, strings can be open or closed. And depending on how we construct a universe — that is, with all open strings, all closed, or some combination — we can arrive at five consistent versions of string theory that, in the 1990s, were shown to be the limiting cases of a single, hypothetical theory in eleven dimensions known as M-theory.

Complex relationships were discovered between the competing theories and bridges were built in the form of dualities, mathematical transformations that modeled physical systems as equivalent in nontrivial ways.

One of the relationships that emerged was an S-duality where a collection of strongly interacting particles in one theory are viewed as a collection of weakly interacting particles in the other.

Another relationship that developed between competing string theories is a T-duality. Here we consider strings propagating around a circular extra dimension.

In other words, these theories are all mathematically consistent yet different descriptions of the same phenomena.

AdS/CFT Correspondence

In addition to the dualities discovered between the various string theories, others were explored connecting string theories to existing formulations of quantum mechanics called conformal field theories (CFT).

Proposed in 1997 by Juan Maldacena, the AdS/CFT correspondence is just such a bridge. On one side of the bridge is string theory and quantum gravity in an Anti-de Sitter (AdS) space, and on the other side is conformal field theory (CFT) which describes quantum mechanics as we know it.

To date, Maldacena’s paper is the top cited particle physics paper of all time.

And one of the most successful realizations of the AdS/CFT correspondence is the duality between Type IIB string theory on AdS5 × S5 space (a product of 5-dimensional AdS space with a 5-dimensional sphere) and N = 4 super Yang–Mills on the 4-dimensional boundary of AdS5.

Or in other words, there is a duality between a 5-dimensional string theory of quantum gravity and the 4-dimensional theory of quantum mechanics that forms the basis of our current understanding of the standard model of particle physics.

Different descriptions of the same phenomena.

Therefore, it is possible to describe a force in quantum mechanics (like electromagnetism, the weak force or the strong force) with a string theory where the strings exist in an anti-de Sitter space with one additional dimension.

The implication being that the geometry of space-time, i.e. reality, is a 5-dimensional anti-de Sitter space with five hidden dimensions compacted on a sphere.

Anti-de Sitter Spaces

Under normal conditions though, we experience reality as a 4D de Sitter space, a universe with the three dimensions of space plus one of time, and a slight positive curvature due to the cosmological constant, dark energy causing its expansion. In two dimensions, this can be visualized as a grid using Euclidean geometry, each point equidistant from its neighbor.

To create an anti-de Sitter universe, we need only to flip the sign of the cosmological constant from positive to negative.

Imagine turning the universe inside out, by changing the direction of its dark energy.

In an anti-de Sitter universe, the distance between points is no longer linear and the space-time geometry more closely resembles a hyperbolic disc in the case of two dimensions. The following image shows a tessellation of a hyperbolic disc by triangles and squares.

It is possible to define the distance between points of the disc in such a way that all the triangles and squares are the same size and the circular outer boundary is infinitely far from any point in the interior.

Now imagine a stack of hyperbolic discs where each disc represents the state of the universe at a given moment in time.

The resulting geometric object is three-dimensional anti-de Sitter space. It looks like a solid cylinder in which any cross section is a copy of the hyperbolic plane, a slice of time.

The surface of this cylinder plays an important role in the AdS/CFT correspondence. As with the hyperbolic plane, anti-de Sitter space is curved in such a way that any point in the interior is infinitely far away from the boundary surface.

And at this boundary, on the surface of the anti-de Sitter space, is defined a space-time for conformal field theory (CFT), or in other words, quantum mechanics.

Holograms

A useful analogy to consider here is the hologram. A hologram is a two-dimensional film that encodes information about all three dimensions of an object as interference patterns of waves of light. A lower dimensional image of a higher dimensional object.

Employing this analogy, it follows that quantum mechanics are a hologram, waves of interference patterns on the surface of an inverted and hyperbolic space-time geometry that contains additional dimensions and lies an infinite distance away.

Different descriptions of the same phenomena.

Gravity emerges from this model in a holographic way, that is, when observed. Yet the light of observation, for some reason, reveals a universe that seems to be pretty square and good at hiding things, including gravitons.

A stereogram

Nonetheless, and despite the discrepancies with experience, the AdS/CFT correspondence is perhaps the most successful realization of the holographic principle, an idea about quantum gravity first proposed by Gerard ‘t Hooft and later expanded on in the context of string theory by Leonard Susskind.

The Holographic Principle

The holographic principle states that the description of a volume of space can be encoded on a lower-dimensional boundary of that region.

The holographic principle was inspired by the study of black hole thermodynamics, that is, what happens at the event horizon of a black hole where general relativity and quantum mechanics meet.

Black Holes

A few months after Einstein published his general theory of relativity in 1915, Karl Schwarzschild found a solution to its field equations, predicting some rather strange behavior for the gravitational effects of massive objects.

At a distance now known as the Schwarzschild radius, the equations of general relativity predicted that, given sufficient mass, the curvature of space-time would be so extreme that not even light could escape.

A singularity in the form of a black hole.

However, it wasn’t until the 1960’s and 70's that the implications of the Schwarzschild radius and other discoveries started to coalesce into the idea of a black hole that we imagine today. This is when the notion began taking on a gravity of its own,resulting in the golden age of black hole thermodynamics research.

Black Hole Entropy

Preceding this golden age, we assumed that black holes were zero entropy objects, with all of the matter-energy compacted into a highly ordered singularity of no size and a temperature of absolute zero.

However, in 1972, Jacob Bekenstein discovered that black holes have entropy, which in the case of a black hole, is essentially hidden information.

He also discovered that the entropy in the interior of black hole is proportional to the surface area of its event horizon, and not its volume, as might be expected.

In other words, the arrangement of hidden information within a black hole is directly related to its surface .

And with the Bekenstein bound, he demonstrated that there is a maximum amount of entropy that can be stored in a finite region of space. And that a black hole was just such a maximal information storage mechanism.

This was a key observation leading to the holographic principle.

Hawking Radiation

Building on Bekenstein’s discoveries of black hole entropy, Stephen Hawking predicted that black holes radiate energy as heat due to quantum effects near the event horizon. And over long enough periods of time, black holes will completely evaporate due to these effects.

The discovery of Hawking radiation gave rise to the black hole information paradox, which is a result of asking the question: what happens to information when it falls into a black hole?

General relativity predicts an infinitely long journey to the singularity while quantum mechanics predicts that all of the information radiates away slowly over time. Quantum mechanics also requires that information, like energy, is conserved.

Thus the paradox.

Black Hole Information Paradox

According to the second law of thermodynamics, energy can neither be created nor destroyed, only transformed.

When energy falls into a black hole, according to Hawking’s discovery, information can be destroyed in the process if the Hawking radiation is completely independent, quantum mechanically, from the in-falling radiation. There would be no way to recover the in-falling matter from the outgoing Hawking radiation. Information would be destroyed.

This is the essence of the black hole information paradox.

The breakthrough to resolve this paradox came from the insight that the informational content of objects falling into a black hole can be contained in the surface fluctuations of the event horizon.

The holographic principle resolves the black hole information paradox within the framework of string theory.

This idea was made more precise by Leonard Susskind, who had also been developing holography, largely independently. Susskind argued that the oscillation of the horizon of a black hole is a complete description of both the in-falling and outgoing matter. The space-time in quantum gravity would emerge as an effective description of the theory of oscillations of a lower-dimensional black-hole horizon

Matter-Energy-Information Equivalence

Another useful concept in black hole thermodynamics is the idea of Shannon entropy, a concept borrowed from information theory.

In physics, thermodynamic entropy is relatively straightfoward. The temperature of a gas in a balloon is a measure of its thermodynamic entropy. The higher the temperature, the greater the entropy. Entropy, then, is a counting of the number of possible arrangements of the atoms in a balloon.

Shannon entropy is the same idea applied to information theory and signal communication. A counting of the degrees of freedom for information.

In an article in the August 2003 issue of Scientific American titled “Information in the Holographic Universe”, Bekenstein summarized:

“Thermodynamic entropy and Shannon entropy are conceptually equivalent: the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information one would need to implement any particular arrangement” of matter and energy.

The only difference between thermodynamic entropy and Shannon entropy, then, are the units of measure. In the former, units of energy divided by temperature; and the latter, dimensionless “bits” of information.

And with another duality we again have different descriptions of the same phenomena.

Matter, energy, information.

All the same thing.

And from an entropy perspective, black holes contain nearly all of the information content of the universe. That is, nearly all of the possible arrangements of matter and energy.

The holographic principle states that the entropy of ordinary mass (not just black holes) is proportional to surface area and not volume.

That volume itself is illusory and the universe is really a hologram which is isomorphic to the information “inscribed” on the surface of its boundary.

Beyond the Event Horizon

According to general relativity, the inward gravitational collapse of a black hole never stops. The interior volume continues to grow larger over time as space stretches towards the center. The rabbit hole keeps getting deeper, and the in-falling energy never reaches the singularity. From the outside, the black hole remains the same size, expanding only when new energy falls in.

As for the energy trapped inside, imagine a ball of entangled strings in a state of agitated motion on an infinitely stretching hyperbolic landscape.

Like a boiling pot of hyper-dimensional nuclear pasta.

The Flying Spaghetti Monster

The hidden micro-states of the strings can be expressed as degrees of freedom on the event horizon, which is a scrambled hologram of the interior, a rippling surface of bits evolving over time.

Quantum Computing

With Bekenstein’s insights, we can now look at a black hole as a sort of quantum computer.

A black hole’s entropy counts the number of possible arrangements of its bits, and the Bekenstein bound sets a fundamental limit to the number of bits for any region of space. The number of hidden bits in the interior is equal to the surface area of the event horizon in Planck units.

This is the information storage limit of a black hole, its memory capacity.

Computational Complexity

Concerning the expansion of a black hole’s interior over time, Susskind and his collaborators proposed there is a corresponding increase in the entanglement entropy of the strings contained within, representing a measure of its complexity, or degrees of freedom.

Building on the idea that the quantum state of a black hole is encoded in the geometry of its interior, Susskind et al found that the action of the interior of a black hole plays the role of complexity in quantum gravity. And that black holes produce complexity at the fastest possible rate.

Consequently, there is a speed limit on the evolution of a black hole’s degrees of freedom. As fast as physically possible, at a rate of 2E∕πℏ.

This is a black hole’s clock speed.

Entanglement Entropy

If complexity does underlie spatial volume in black holes, Susskind envisions consequences for our understanding of cosmology in general.

“It’s not only black hole interiors that grow with time. The space of cosmology grows with time, I think it’s a very, very interesting question whether the cosmological growth of space is connected to the growth of some kind of complexity. And whether the cosmic clock, the evolution of the universe, is connected with the evolution of complexity. There, I don’t know the answer.”

Quantum Entanglement and Tensor Networks

“Entanglement is the fabric of space-time,” said Swingle, who is now a researcher at Stanford University. “It’s the thread that binds the system together, that makes the collective properties different from the individual properties. But to really see the interesting collective behavior, you need to understand how that entanglement is distributed.”

Tensor networks enable physicists to compress all the information contained within the wave function and focus on just those properties physicists can measure in experiments: how much a given material bends light, for example, or how much it absorbs sound, or how well it conducts electricity. The key to achieving this simplification is a principle called “locality.” Any given electron only interacts with its nearest neighboring electrons. Entangling each of many electrons with its neighbors produces a series of “nodes” in the network. Those nodes are the tensors, and entanglement links them together. All those interconnected nodes make up the network. A complex calculation thus becomes easier to visualize. Sometimes it even reduces to a much simpler counting problem.

Combine those insights with Swingle’s work connecting the entangled structure of space-time and the holographic principle to tensor networks, and another crucial piece of the puzzle snaps into place. Curved space-times emerge quite naturally from entanglement in tensor networks via holography. “Space-time is a geometrical representation of this quantum information,” said Van Raamsdonk.

Quantum Error Correction

Physicists have discovered in the last few years that the AdS/CFT correspondence works exactly like a “quantum error-correcting code” — a scheme for securely encoding information in a jittery quantum system, be it a quantum computer or a CFT. Quantum error correction may be how the emergent fabric of space-time achieves its robustness, despite being woven out of fragile quantum particles. Calculations suggest that to reconstruct information about a black hole’s interior from qubits on the boundary, you need access to entangled qubits throughout roughly three-quarters of the boundary.

Curvature of the Universe

The Lambda-CDM model of the universe predicts a uniformly flat space-time extending infinitely, with a cosmological constant slightly above zero, a tiny amount of dark energy. However, measuring dark energy precisely has proven difficult and there are still discrepancies concerning its value.

A recent paper published in November 2019 in the journal Nature Astronomy argues that the universe may, in fact, be closed. It is curved around and closed in on itself like a sphere.

The authors re-analyzed a major data set of the cosmic microwave background (CMB) radiation and concluded that it predicts a cosmological constant more than 3 standard deviations away from zero.

The analysis predicts a closed universe with 99% certainty — even as other evidence suggests the universe is flat. The alternate explanation is a statistical fluke in the data, similar to flipping a coin heads 11 times in a row.

Axions

The axion “is kind of the best dark matter candidate that we have at the moment,” he said, given that others have failed to turn up in experiments. One theory of axions relevant to cosmology predicted that they would have no electric charge, a very small mass, and very low interaction cross-sections for the nuclear forces. Because of their properties, axions would interact only minimally with ordinary matter and would change to and from photons in magnetic fields. Inflation suggests that axions were created abundantly during the Big Bang. Because of a unique coupling to the instanton field of the primordial universe (the “misalignment mechanism”), an effective dynamical friction is created during the acquisition of mass following cosmic inflation. An instanton field represents the transition probability of a particle quantum tunneling through a potential barrier This coupling robs all such primordial axions of their kinetic energy. If axions have low mass, thus preventing other decay modes, this predicts that the universe would be filled with a very cold Bose–Einstein condensate of primordial axions. And hence, axions could plausibly explain the dark matter problem of physical cosmology. Additionally, the axion represents the leading solution to the strong CP problem. Axions would also have stopped interaction with normal matter at a different moment than other more massive dark particles. We show that both the baryon asymmetry of the universe and dark matter (DM) can be accounted for by the dynamics of a single axion-like field. In this scenario, the observed baryon asymmetry is produced through spontaneous baryogenesis — driven by the early evolution of the axion — while its late-time coherent oscillations explain the observed DM abundance. Like photons, axions are very wavelike, falling on the wavy end of the wave-particle duality. Their minuscule mass makes them extremely low-energy waves, with wavelengths somewhere between a building and a football field in length. A discovery would permanently rewrite the laws of particle physics and cosmology, but today axions remain entirely hypothetical.

Theoretical Implications

Either the universe has the properties of a hologram.

Or the hologram has the properties of a universe.

What is the Universe?

The universe is a black hole. And every black hole is a universe. The big bang is the collapse of our black hole into a singularity, creating a universe in its interior. The universe is a black hole contained in a parent universe with the same laws of physics and other black holes. The 7th dimension of string theory is the plane of possible universes with the same laws of physics but different initial conditions.

What are Black Holes?

A black hole is a quantum computer. Entanglement creates a tensor network of strings. Entanglement entropy is a measure of the complexity of the string configuration, its degrees of freedom. In a black hole, complexity evolves as fast as possible. This is its algorithm and its clock rate. The number of hidden bits in the interior is equal to the surface area of the event horizon in Planck units. This is its memory capacity. The AdS/CFT correspondence works exactly like a quantum error-correcting code. The surface fluctuations of the event horizon are a hologram of the interior. Quantum interference patterns on the event horizon are computations in a higher number of dimensions an infinite distance away.

What about the Hard Problems?

Dark energy is the growth rate of entanglement entropy within the interior of our black hole. Dark matter is a very cold Bose-Einstein condensate of primordial axions with no kinetic energy — a field of entangled superfluid quantum vortices leftover from the Big Bang, if you will. Axions form an entangled background grid of wave-particles that permeate the universe, weakly interacting with matter, occasionally turning into photons. Axions are a universal data-bus. The axion also provides a solution to baryon asymmetry and the strong CP problem. Neutrino mass is explained by the graviton. The graviton explains gravity, and like the axion, it’s just another wave-particle we can’t see.

What is Reality?

From an entropy perspective, black holes contain nearly all of the information in the universe, the possible arrangements of matter and energy Dark matter is a hyper-dimensional quantum entangled super-fluid network described by a single wave function, permeating the universe, shaping the space-time within it, and weakly interacting with the matter-energy around it. Reality can be described mathematically with a wave-function formulating the evolution of hyper-dimensional strings entangled in a tensor network The geometry of reality is a 5-dimensional anti-de Sitter space with five additional dimensions compacted on a sphere The perception of reality is a 4-dimensional de Sitter space And remember, the observer effect collapses the wave-function and changes everything.

It’s not turtles all the way down, it’s hyper-dimensional spaghetti monsters.