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.