We are living but on a spec of dust looking out into the darkness

Jack Dikian

September 2011

The more I think about just how much we have been able to infer about the universe we live in the more amazing it all seems. I mean, here we are living on an unassuming rock orbiting a star near the outskirts of a galaxy. Our galaxy is estimated to contain 200 to 400 billion stars. Current estimates guess that there are 100 to 200 billion galaxies in the Universe. The universe is vast and we are living but on a spec of dust looking out into the darkness, looking back in time, and trying to make sense of it all.

The WMAP Explorer mission that launched June 2001 to make fundamental measurements of cosmology is analogies to a trapdoor spider coming out of its silk-lined burrow to examine the perimeter surrounding its burrow before it goes back inside to think about how might other terrains be like, what kind of soils, how small puddles of water be compared to vast oceans, and so on and so forth.

But, that’s exactly what the WMAP has been able to achieve. It has been able to study the properties of our universe as a whole. WMAP has been stunningly successful too, producing our new Standard Model of Cosmology. The 7-year data provide compelling evidence that the large-scale fluctuations are slightly more intense than the small-scale ones, a subtle prediction of many inflation models.

One of the problems the Big Bang theory was not able to explain is the horizon problem. Distant regions of space in opposite directions of the sky are so far apart that, assuming standard Big Bang expansion, they could never have been in causal contact with each other. This light travel time between them exceeds the age of the universe. Yet the uniformity of the cosmic microwave background temperature tells us that these regions must have been in contact with each other in the past.

The Inflation Theory, developed by Alan Guth, Andrei Linde, Paul Steinhardt, and Andy Albrecht, offer a solution to this and several other open questions in cosmology. Inflation supposes a burst of exponential expansion in the early universe, assuming distant regions of the universe were actually much closer together prior to Inflation than they would have been with only standard Big Bang expansion. Thus, such regions could have been in causal contact prior to Inflation and could have attained a uniform temperature.

Other reading

Alan H. Guth & Paul J.Steinhardt, "The Inflationary Universe", Scientific American, May 1984.

Andrei Linde, "The Self-Reproducing Inflationary Universe", Scientific American, November 1994.

Scott Watson, "An Exposition on Inflationary Cosmology", WWWarticle, 2000.

Alan H. Guth, "The Inflationary Universe : The Quest for a New Theory of Cosmic Origins", 1998.

Black Holes Older Than The Universe

Jack Dikian

May 2011

According to the work by Professor Bernard Carr from Queen Mary University in London and Professor Alan Coley from Canada's Dalhousie University published on the pre-press website arXiv.org, some black holes may be primordial. That is some black holes bounce between a contracting and expanding universes.

Coley and Carr speculate that primordial black holes could survive as separate entities and from a previous epoch (assuming of course that a bounce occurs at all and survives singularities).

According to general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity - a point in space-time at which the space-time curvature becomes infinite and much of the physics we know breaks down.

Even with the success of quantum mechanics we don't have a good theory of quantum gravity.

Still, such a speculation, as well as pushing the boundaries of our current theories, bounces in the universe may also allow for differences in the fundamental constants of nature such as (say) the speed of light.

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.