Information Loss at Event Horizons

Jack Dikian

December 2010

Introduction

In the last 15 years, much has been written about whether information is conserved when approaching and falling into the centre of a black hole. Information loss contradicts principles of the conservation of information and goes against basic underpinnings of quantum theory.

When the event horizon of a black hole is seen as a two-dimensional representation (surface) of the three-dimensional object at its centre - information held by an object falling into a black hole may leave a signature at both the central mass of the black hole as well as the event horizon.

Hawking radiation leaking from the event horizon may therefore be connected back to the object falling into the black hole thus maintaing conservation of information.

This can be extended to a more generalized view where our everyday three-dimensional reality (life) is represented twice. Once in the very things we do, and the other projected (presumably in a scrambled manner) onto a two-dimensional plan at the edges of the universe.

No hair theorem

Stephen Hawking showed that black holes should slowly leak energy, which poses a problem. Black hole solutions of the Einstein-Maxwell equations of gravitation and electromagnetism (general relativity) can be described by 3 observable parameters: mass, electric charge, and angular momentum.

Other information about material falling into it, "disappears" behind the black-hole event horizon and is therefore permanently inaccessible to external observers, viz a viz, the no-hair theorem.

So one would expect the Hawking radiation to be completely independent of the material entering the black hole. However, if the material entering the black hole were a pure quantum state, the transformation of that state into the mixed state of Hawking radiation would destroy information about the original quantum state - thus presenting a physical paradox

Objective

Incomplete

The Cheshire Cat's Grin, Alice in Wonderland, and Information Loss

Jack Dikian

December 2010

Introduction

As I was trying to fall asleep last night – I thought about a thought experiment that I’ve gone back to over and over again. In fact, since I was a boy. Rocketing away in a spaceship and looking back at my house, my street, my suburb and friends.

After a while, they become scarcely distinguishable and not much more than mere inhabitants, faceless beings without person or form. I’ve always felt I’m taking away with me the knowledge of the frequent earth-born misunderstandings, the eagerness of people to kill one another, their hatreds, imagined self-importance, and the delusion that we have some privileged position in the Universe as this tiny pale blue home disappeared in the vastness of the countless stars.

As I got older and learned more about cosmology and exotic phenomena such as black holes, I would wounder how it would be if trapped in a black hole. And overtime, I’d wonder if there was a way to let my friends know what I once knew. Is the knowledge (actually information) I’m carrying destroyed as gravitational forces pull me apart?

Conservation of information in quantum mechanics

Quantum mechanics incorporates a principle that information about a system is encoded in its wave function, and that the evolution of the wave function is determined by a unitary operator implying that information is conserved (in the quantum sense). Here, quantum determinism, and reversibility are at play.

Any deterministic time reversible theory must conserve information and the evolution of the wave function satisfies this. However, whenever an observation is made it would seem that new information is created, and reconciling this, with the absolute conservation of information in the physical universe is not necessarily straight forward.

Causality of information as a subjective human interaction of the mind may be the source of common confusion. A mind act has no information momentum to transfer to the system. A momentum change as a cause of observation was/is always the physical meaning of information. A change in system as an observation then allows the effect of all as information conservation.

Black Holes and Singularities Acting As Sinks

In the 1970s, Stephen Hawking showed that black holes evaporate by quantum processes. He also asserted that information, such as the identity of matter pulled into black holes, is permanently lost thus challenging a fundamental tenet of quantum mechanics - information cannot be lost. Hawking renounced the idea later but unable, as other weren’t able, to show the mechanism for how information might escape a black hole.

More recently, a team of physicists at Penn State, led by Abhay Ashtekar (and his collaborators, Victor Taveras, a graduate student in the Penn State Department of Physics, and Madhavan Varadarajan, a professor at the Raman Research Institute in India) announced they have shown a mechanism by which information can be recovered from black holes. They say their findings expand space-time beyond its assumed size, thus providing room for information to reappear.

To explain the issue, Ashtekar used an analogy from Alice in Wonderland. "When the Cheshire cat disappears, his grin remains," he said. "We used to think it was the same way with black holes. Hawking's analysis suggested that at the end of a black hole's life, even after it has completely evaporated away, a singularity, or a final edge to space-time, is left behind, and this singularity serves as a sink for unrecoverable information."

The researchers suggest that singularities do not exist in the real world and "Information only appears to be lost because we have been looking at a restricted part of the true quantum-mechanical space-time". Once you consider quantum gravity, then space-time becomes much larger and there is room for information to reappear in the distant future on the other side of what was first thought to be the end of space-time."

To conduct their studies, the team used a two-dimensional model of black holes to investigate the quantum nature of real black holes, which exist in four dimensions. That's because two-dimensional systems are simpler to study mathematically. But because of the close similarities between two-dimensional black holes and spherical four-dimensional black holes, the team believes that this approach is a general mechanism that can be applied in four dimensions.

The Lie Group E8 - The Slinky

Jack Dikian

December 2010

While at a clinical behaviour support conference today I was distracted by a close colleague playing with one of the slinkies left on our table amongst other toys and snakes.

The circles of the slinky and the way they were interacting with each reminded me of something I had come across a long time ago - The Lie group E8 with 248 dimensions.

Background

So far, attempts to understand the workings of the forces of nature have been fragmentary. The mathematics describing the very small, i.e, atoms and sub-particles, does not hold for the very large such as that of gravity. The 2 sets of mathematics describing the small and the large do not fit together.

Attempts to develop a single overarching grand unified theory (the theory for everything) that might help explain the forces caused by the movement of sub-particles as well as the force carrying gravitons (for gravity) have proven extremely difficult.

According to some (See Garrett Lisi) the unification of the four fundamental forces may be described by Lie group e8, a mathematical shape that is a collection of circles twisting around each other in a specific pattern 248 times.

To attempt to visualize this is impossible. The simplest Lie group is a circle. Now think about taking a second circle and wrapping it around the first, ensuring it is perpendicular to the first resulting in a Torus, or the surface of a donut.

Now, to end up with the Lie group e8, continue to do this 248 times, producing a shape so complex that computer assisted graphics systems struggle to represent.

The idea of the he Lie group e8 is that each circle represents a particle, so one circle may be an electron, another, a particular force. Interestingly, the theory goes that the way these circles are interacting with each other may be similar to the manner forces interact with each other.

Weird life - A Second Genesis

Jack Dikian

December 2010

Paul Davies in his book the “The Eerie Silence” examines the assumptions that underlie the Search for Extra-Terrestrial Intelligence (SETI) programme, concluding that the lack of a result (hearing from extra-terrestrials) after 5 decades may be due to a number of reasons:

• Life on Earth might be so improbable that our planet is the only one hosting life.
• Life is common but intelligence is so rare that humans are a unique specimen.
• Science itself is unique to Earth.
• Extraterrestrial signs are everywhere but unrecognizable by us.

Davies goes on to say that our human perception may be so Earth-centric, so specific to our evolutionary path that it simply differs in innumerable ways from the perceptions of other civilizations across the void.

Of course when he talks about our evolutionary path, he is referring to the notion of life as we know evolving from a single genesis. Also, life is Carbon based and forms the backbone of biology. Molecules are made up of carbon bonded with other elements, especially oxygen, hydrogen and nitrogen. Often it assumed in astrobiology that if life were to exist elsewhere it will also be carbon based. See Carbon chauvinism.

However, what if there is a second genesis on Earth, and is it living among us undetected?

Which brings us to the announcement by NASA (December 2010) of the discovery of an alien life form. Not on another planet or a star system far away – rather an ‘alien’ bacterium lurking deep in a Californian lake. This excitement is around this “bug’s” (from the GFAJ-1 strain of the Halomonadaceae family) ability to eat and thrive on Arsenic, one of the most toxic chemicals on Earth. It can even incorporate arsenic into its DNA, making it part of its very being.

As every other form of known life uses phosphorus rather than arsenic as a key building block of its DNA, the find suggests that a second form of life is with us, right here on Earth. This supports the conjecture that if one alien life form exists, it is highly likely there are others out there.

• Dr Felisa Wolfe-Simon, from Arizona State University led the US researcher
• Professor Ariel Anbar, an astrobiologist, also from Arizona State University, co-authored the study.

This finding bolsters the ‘weird life' theory coined by Paul Davies, who said it is likely that life on Earth has evolved more than once – and the only reason we haven’t found the imposters among us is that we don’t know what we are looking for.

Sense Perceptions and Reality

Jack Dikian

November 2010

In psychology and cognitive science, perception is the process of attaining awareness or understanding of sensory information. The study of perception gave rise to the Gestalt school of psychology, with its emphasis on holistic approach.

Perception is one of the oldest fields in psychology and represents one of the oldest quantitative laws in psychology quantifying the relationship between the intensity of physical stimuli and their perceptual effects.

But can we really trust our senses?

Descartes did not believe that the information we receive through our senses is necessarily accurate and set out to attack what he considered the very foundation of perception systems: the idea that sense perception conveys accurate information.

In the case of visual perception, some people can actually see the percept shift in their mind's eye. Others, who are not picture thinkers, may not necessarily perceive the 'shape-shifting' as their world changes.

This has been shown by experiment: an ambiguous image has multiple interpretations on the perceptual level. The question, "Is the glass half empty or half full?" serves to demonstrate the way an object can be perceived in different ways.

Incomplete :

See:
The analogy of Plato's Cave was coined to express these ideas

What is time

Jack Dikian

Sep 2012

Again, as so often these days, casual remarks made in late night conversations sets me thinking about those ideas we hold with seemingly little need for scrutiny. These are ideas that involve everyday concepts, that, on the surface, are supposedly well understood, defined, and seem as natural as day and night. I’m talking about time.

How hard can it be to explain the passage of time. After all, we can measure time precisely and we all have an innate ability to gauge the flow of time.

The question, perhaps overly simplified: is time a "real thing" that is "all around us", or is it nothing more than a way of speaking about and measuring events.

Psychologically, time can seem to take forever or be over before we know it. The past only exists as memory. The future is something we can’t remember. So, there is really only the present. In the novel “The Merry-Go-Round in the Sea”, by Randolph Stow, a novel I couldn't put down when I was 12, Rob's life is "jolted" by the impending war comes to the realisation “I am six years and two weeks old. I will never be that old again”.

Time is one of the seven fundamental physical quantities in the International System of Units. An operational definition of time, wherein one says that observing a certain number of repetitions of one or another standard cyclical event (such as the passage of a free-swinging pendulum) constitutes one standard unit such as the second.

There are two distinct views on the meaning of time. One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence. This is the realist view, to which Isaac Newton subscribed, in which time itself is something that can be measured.

A contrasting view is that time is part of the fundamental intellectual structure (together with space and number) within which we sequence events, quantify the duration of events and the intervals between them, and compare the motions of objects. In this view, time does not refer to any kind of entity that "flows", that objects "move through", or that is a "container" for events. This view is in the tradition of Gottfried Leibniz and Immanuel Kant, in which time, rather than being an objective thing to be measured, is part of the mental measuring system.

According to John A. Wheeler, Princeton cosmologist, "Time is the most mysterious of the four usual dimensions of our space-time continuum. It's not so much that there's something strange about time, the thing that's strange is what's going on inside time. He continues, we will first understand how simple the universe is when we recognize how strange time is.

Einstein’s in his Special Theory of Relativity he united space and time into one entity - space-time. Within this new continuum, time slows down as you move faster, the time dilation effect.

So time can be viewed as both a psychological construction which we use to interpret our world and a mathematical kind of time, the most basic estimate of which is reflected on our watches and clocks. Also, the direction that time points to can be delineated by a number of physical and psychological phenomena.

• The Psychological Arrow of Time is our subjective sense of time, the fact that we remember events in one direction of time, the past, but not the other, the future.
• The Electromagnetic Arrow of Time as described by Maxwell's equations providing solutions to the propagation of radio waves, and light.
• The Cosmological Arrow of Time sees the history of the universe moving forward in time in an irreversible manner.
• The Thermodynamic Arrow involving the Law of Entropy, explaining the behavior that all the universe progresses from order to disorder

On Consciousness and Reality

Jack Dikian

November 2010

Background

Anyone who has undertaken a physics course beyond that of secondary school will have no doubt been confronted and perhaps shocked with the strange and schizophrenic nature of atoms. The comfortable Copernican view of the atom had to make room to a much weirder explanation of the atom and, by implication, the very bedrock of reality itself vis-à-vis Quantum Mechanics, Exclusion principle, Uncertainty principle, Schrödinger’s cat…

The Copenhagen interpretation of quantum mechanics described as a key feature of quantum mechanics the state of every particle as a wave-function, which is a mathematical representation used to calculate the probability for it to be found in a location or a state of motion.

According to this interpretation, the act of measurement causes the calculated set of probabilities to "collapse" to the value defined by the measurement. To put this simply, the notion that an unmeasured atom is, in some sense, not real, and its attributes are created or realized through the act of measurement.

This interpretation places observers in a special position - the founders of quantum mechanics debating the role of the observer, and believing that it is the observer that produces collapse. Incidentally, this view was rejected by Einstein calling it anti-scientific. Pauli described quantum mechanics as lucid mysticism.

Hugh Everett in the 1950’s postulated the idea of the many-worlds interpretation which asserts the objective reality of the wave-function, but denies the reality of wave-function collapse, which implies that all possible alternative histories and futures are real. Here, the memories of the observer split at every measurement, leading to the subjective appearance of collapse.

Eugene Wigner made quantum physics even more subjective when in the 1960’s, in his "Remarks on the mind-body question", an assay in his collection of assays Symmetries and Reflections, claimed that a quantum measurement requires a conscious observer, without which nothing ever happens in the universe. The key idea has become known as the consciousness causes collapse interpretation.

Where are we know

Thomas J. McFarlane in an article “Consciousness and Quantum Mechanics” provides a summary of what the quantum realm has revealed to be beneath the illusion of Newton's classical universe. The points below are paraphrased;

• Atomic matter dissolves into waves of potential existence.
• Rigid determinism falls apart, giving us a world with spontaneity.
• The objective world, existing "out there" independent of observers, vanishes, leaving a world in which the observer and the observed are interdependent.
• That the manifold world of separate independent objects interacting locally within space and time is transcended, revealing a realm where all things are nonlocally united in an indivisible whole.

It is the last two points that seem to suggest that consciousness is linked at a deep level with physical reality. Many theories, including interdisciplinary approaches such as that of Saul-Paul Sirag have been developed.

I would like to concentrate on Sirag’s approach in the remaining of this piece.

Sirag's strategy is to look to mathematics for an appropriate structure to describe the relationship between consciousness and the physical world. He finds that unified field theories of the physical forces depend fundamentally on mathematical structures called reflection spaces, which are heierarchically organized in such a way that an infinite spectrum of realities is naturally suggested.

Sirag studied the works of Sir Arthur Eddington and was impressed by Eddington’s use of group theory in developing his unified field theory. Eddington's unification was based upon the 4-element group called the Klein group K4. Eddington thought of this group as describing the structure of the most elemental measurement: seeing whether or not two rigid rods are the same length.

Eddington had declared K4 to be the primary group structure of the acquisition of physical knowledge. Sirag recognized a connection between Eddington’s use of the K4 and Piaget's work on the structure of the acquisition of knowledge by children. Piaget found, by testing children in precisely contrived situations, that K4 was also the basic structure of children's acquisition of physical knowledge. Piaget's names for the four elements of K4 are identify, negation, collaterality and reciprocity.

It is generally believed by physicists working on unified field theory that space-time is hyper-dimensional, with all but four of the dimensions being invisible. Beside space-time dimensions, there are also other internal dimensions called gauge dimensions. In Sirag's view both the extra space-time dimensions and the gauge dimensions are real. This provides scope for considering ordinary reality a substructure within a hyper-dimensional reality.

Sirag's approach is that his version of unified field theory embeds both spacetime and gauge space in an algebra whose basis is a finite group. This is a symmetry group of one of the Platonic solids -- the Octahedron. Thus it is a mathematical entity contained in the reflection space hierarchy. In fact the reflection space corresponding to the Octahedron is 7-Dimensional and is also a superstring-type reflection space, so that a link with the most popular version of unified field theory is provided.

The central theme of Sirag's theory is that this 7-Dimensional reflection space is a universal consciousness, and that individual consciousnesses tap into this universal consciousness. This implies that the high level of consciousness enjoyed by humans is due to the complex network of connections to the underlying reflection space afforded by a highly evolved brain.

Is our brain hard-wired to believe in God

Jack Dikian

August 2003

Are human beings hard-wired to believe in God. That is, it possible that brain-structure is designed such that the belief in God is to serve as an anxiety reducing function.

The connection between the temporal lobes of the brain and religious feeling has led a Canadian neuroscientist, Dr Michael Persinger, from Laurentian University to attempt and answer if there is a biological and brain basis to some of the concepts that are called the God belief and the God experience.

If the brain basis for the sense of self is tied to language and left hemispheric processes then the right hemispheric equivalent, Persinger believes is a second sense which when experienced is the sense presence or the prototype of the God experience.

One hypotheses is that as we developed an ability to forecast our own self disillusion, and our own death, which generates a great deal of anxiety, the efforts of our brain’s

right temporal lobe is to relieve the anxiety of death - what we sense when we think we are sensing God.

What's Real - Grand Design

Jack Dikian

Thoughts and Comments

The Grand Design

Bantam books 2010

According to one internet based dictionary, “Real” is being or occurring in fact or actuality; having verified existence; not illusory; "real objects"; "real people -not ghosts" etc…

When philosophy is leaned-upon, things become, expectedly a little more murky. Despite the seeming straightforwardness of the realist position, in the history of philosophy there has been continuous debate about what is real. In addition, there has been significant evolution in what is meant by the term "real".

Contemporary philosophical realism is the belief that our reality is completely ontologically independent of our conceptual schemes, linguistic practices, beliefs, etc. Philosophers who profess realism, therefore, also typically believe that truth consists in a belief's correspondence to reality.

Model-dependent realism as discussed by Stephen Hawking and Leonard Mlodinow in their 2010 book The Grand Design is a scientific method of exploration based on how well a model does at describing the physical reality of the situation. Among scientists, this is not, necessarily a controversial approach. This, however, implies that it is somewhat meaningless to discuss the reality of the situation and, rather, the only meaningful thing you can talk about is the usefulness of the given model. One quote from this book…

"There is no picture- or theory-independent concept of reality. Instead we will adopt a view that we will call model-dependent realism: the idea that a physical theory or world picture is a model (generally of a mathematical nature) and a set of rules that connect the elements of the model to observations. This provides a framework with which to interpret modern science."

The authors seem to have developed a theory familiar to philosophers since the 1980s, namely 'perspectivalism'. Perspectivism is the view developed by Friedrich Nietzsche that all ideations take place from particular perspectives.

So according to Hawking and Mlodinow, not only does science fail to provide a single description of reality, they say, there is no theory-independent reality at all. Here, we are told not to expect a unifying theory of everything, rather a set of theories (such as M-theory) that overlap at their boundaries. They argue that the scientific obsession with formulating a single new model may be misplaced, and that by synthesising existing theories we may better provide a picture of unification (my words).

Also, according to the authors, enough is known about M-theory to see that God is not required to answer for the existence of all, instead the existence of a multiverse, à la string theory will suffice.

The authors point out that the laws of nature seem to be tuned incredibly precisely to allow life to exist. Tweak them every so slightly, and there might not even be suns and planets, let alone living things. So the vast majority of those different universes would be uninhabitable.

The author’s argument against divine creation is based on string theory and one associated interpretation, multiverse – however, both strings and multiverse are ideas lacking, obviously, empirical evidence and consistent interpretation.

A thoroughly lucid and accessible book, nicely illustrated and thought provoking.

Atoms In The Known Universe

Jack Dikian

March 2010

The universe as we know it is made up of 91 naturally occurring elements. As of October 2006, we know of 117 elements in total. Some, like silver, gold, and iron have been known for thousands of years. Others, such as darmstadtium and ununquadium have only recently been created synthetically.

Also, we can know approximate the number of atoms in the known universe. This number is:

1,

000,000,000,000,

000,000,000,000,

000,000,000,000,

000,000,000,000,

000,000,000,000,

000,000,000,000

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