Einstein's Biggest Blunder

Jack Dikian

May 2011

A team of planetary scientists using the Anglo-Australian Telescope contributed to the mapping of galaxies over a volume of the Universe and has shown that dark energy responsible for expanding the universe is real and not a mistake by Einstein viz a viz the cosmological constant.

When George Gamow was discussing cosmological problems with Einstein, he (Einstein) had remarked that the introduction of the cosmological term was the biggest blunder of his life.

Einstein introduced his cosmological constant it into his general theory of relativity almost as a last resort wanting to force his theory to yield a static universe as he had thought the universe to be.

We know now the universe is not static and is expanding at an accelerating rate, just as his original field equations were predicting. Einstein was never comfortable with the [constant] and a clue is in his 1917 paper which ends with

“It is to be emphasized, however, that a positive curvature of space is given by our results, even if the supplementary term [cosmological constant] is not introduced. That term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocities of the stars”.

The survey of 200,000 galaxies by an international team, led by Chris Blake of Swinburne University, took four years to complete, aimed to measure the properties of "dark energy" — the concept of which was revived in the late 1990s when astronomers began to realize the universe was expanding at an accelerating rate.

The acceleration was a shocking discovery, indicating the universe is filled with a new kind of energy that is causing it to expand at an increasing speed.

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.

I Am Convinced God Does Not Play Dice

Jack Dikian

March 2011

Introduction

The Copenhagen interpretation of quantum mechanics proposes, generally, that the outcome of any measurement cannot be measured with certainty. This leads to the situation where measurements of a property performed on two identical systems can give different answers.

However, can a deeper reality, hidden beneath quantum mechanics, described by a more fundamental theory predict the outcome of measurement with certainty. Einstein, a proponent of a deeper reality (hidden variables) hidden famously insisted that, "I am convinced God does not play dice”.

Quantum mechanics puzzle

Quantum mechanics creates the puzzling situation in which a measurement of one system can "poison" the measurement of the other system, no matter what the distance between them. One could imagine the two measurements were so far apart in space that special relativity would prohibit any influence of one measurement over the other.

For example, say, in a neutral-Pion decay, where two photons travel some light years apart – if the spin of one photon is measured, quantum mechanic suggests that that measurement instantaneously forces the second photon into a state of well-defined spin - even though it is light years away from the first.

Einstein, Podolsky, and Rosen (EPR) argued that elements of reality must be added to quantum mechanics and postulated that the existence of unknown properties should account for the discrepancy – that there is a deeper reality.

A conundrum

How do we reconcile the fact that the second photon "knows" that the spin of the first photo has been measured, even though they are separated by light years of space and far too little time has passed for information to have traveled to it according to special relativity?

We can accept the postulates of quantum mechanics its seemingly uncomfortable coexistence with special relativity, or we may believe that quantum mechanics is not complete:

Are we smart enough

Jack Dikian

February 2011

Last night I was invited to dinner at my close friends and neighbors – towards the end of the night we got onto a conversation topic that’s always near to my heart; the lofty subject concerning the universe. Its size, structure, complexity, age, origin and not least what seems like the insignificance of our lives in the vastness of even the known universe.

Not only is the universe vast, there are billions and billions of stars and planets with the almost infinite of mysteries that may lie within each star system waiting to be uncovered. Our knowledge, of course, is still in its primordial stages. In an infinite universe, there are infinite possibilities and the idea of god might not be so unlikely.

We may be seeing the universe as it is because otherwise we wouldn't be here to see it, we wouldn't exist. Some claim there are many universes and because their sub-atomic particles are slightly different than ours they do not support life.

Some theories propose that the universe is best explained in 11 dimensions, and there could be another entire universe less than a millimeter away from us….and us being oblivious to it. But it may be more than that, it’s entirely possible that we, living in the restricted dimensions of space and time are beyond understanding the workings of the universe.

In the same way fish may be barely be aware of the medium in which they live and swim, so the microstructure of empty space could be far too complex for our unaided human brains." It's as if a fish is swimming in one pond, completely unaware that thousands of other ponds exist mere meters away from it.

Understanding that those ponds even exist, let alone understanding their connection to the original pond, is understandably beyond the comprehension of a single fish.

We similarly, attempt to make meaning and develop constructs such a unifying theory to describe how the universe works, idea of multiple parallel universes, human consciousness and the very idea of reality – we as fish may well find that the universe be simply beyond our understanding.

A second universe

Jack Dikian

January 2011

Paul Adrien Maurice Dirac (whilst not a household name) is considered by many to be the greatest British theorist since Sir Isaac Newton. All the great minds that pioneered atomic physics were left trailing by Dirac. When Einstein read a paper by the young Dirac, he said, I have trouble with Dirac – "this balancing on the dizzying path between genius and madness is awful..".

In 1925, for reasons only known to himself, he set out to unite the two most difficult and counter-initiative ideas in history – Quantum Mechanics and Special Relativity (where as a fall out, objects behave differently as they travel at speeds approaching the speed of light). It must be remembered that by the late 1920’s quantum mechanics was consistently producing erroneous results for calculations describing electrons as they traveled at high speed.

As well as this, Dirac had an additional aim. Dirac had a much more esoteric motivation. He was once quoted of saying “a physical theory must have mathematical beauty”. For him, the fact that quantum mechanics and relativity weren’t reconciled was more that just an inconvenience – it was ugly.

Around 1925 he put his extra ordinary mind on the problem of bringing together the two new ideas of twentieth century physics. It is said that he worked on this problem alone for some three years before in 1928 he honed in on one mathematical formulation – an entirely new description of what goes on within the atom. Dirac knew it was right partly because it had mathematical beauty (see equation above).

As far as human achievements go it up there with Shakespeare's greatest works (something which by the way a very dear friend constantly reminds me of) and the Origin of the Species. Dirac’s equation describes how reality works at the fundamental level.

But, incredibly when Dirac looked at his own equation he noticed something that can only be said to be shocking. He later said, his equation [knew] more than he did.

In essence his equation was telling him that there is another universe that we had never noticed before. That’s because instead of his equation having one answer, it has two. The first describes the universe we know…the second describes a kind of mirror image to our universe made of atoms whose properties are reversed. As well as matter, Dirac’s equation predicts the existence of antimatter.

Dirac seems to be saying that for every piece of matter in our known universe, there can exist a corresponding piece of antimatter. Just like a world in a mirror a universe made of antimatter would look and work just like ours.

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.