Death is not an option

Glah. I don't like the sound of this (via Overcoming Bias)

Hypothetical Apostasy

An interesting proposal.

Quantum Computing and the Church-Turing Thesis

Another interesting article.

The Turing machine model seems to capture the entire concept of computability, according to the following thesis[62]:

Church Turing Thesis: A Turing machine can compute any function computable by a reasonable physical device.

What does “reasonable physical device” mean? This thesis is a physical statement, and as such it cannot be proven. But one knows a physically unreasonable device when one sees it. Up till now there are no candidates for counterexamples to this thesis (but see Ref. [103]). All physical systems, (including quantum systems), seem to have a simulation by a Turing Machine.

Quantum Computing: Introduction

More on the relationship between quantum computing and classical computing. An interesting read.

Another thing which can be expressed in many different ways is information. For example, the two statements ``the quantum computer is very interesting'' and ``l'ordinateur quantique est tres interessant'' have something in common, although they share no words. The thing they have in common is their information content. Essentially the same information could be expressed in many other ways, for example by substituting numbers for letters in a scheme such as a -> 97, b -> 98, c -> 99 and so on, in which case the english version of the above statement becomes 116 104 101 32 113 117 97 110 116 117 109... . It is very significant that information can be expressed in different ways without losing its essential nature, since this leads to the possibility of the automatic manipulation of information: a machine need only be able to manipulate quite simple things like integers in order to do surprisingly powerful information processing, from document preparation to differential calculus, even to translating between human languages. We are familiar with this now, because of the ubiquitous computer, but even fifty years ago such a widespread significance of automated information processing was not forseen.

Quantum Computing vs. Turing Machines

SEP on Quantum Computing:

Although the original Church-Turing thesis involved the abstract mathematical notion of computability, physicists as well as computer scientists often interpret it as saying something about the scope and limitations of physical computing machines. For example, Wolfram (1985) claims that any physical system can be simulated (to any degree of approximation) by a universal Turing machine, and that complexity bounds on Turing machine simulations have physical significance. For example, if the computation of the minimum energy of some system of n particles requires at least an exponentially increasing number of steps in n, then the actual relaxation of this system to its minimum energy state will also take an exponential time. Aharonov (1998) strengthens this thesis (in the context of showing its putative incompatibility with quantum mechanics) when she says that a probabilistic Turing machine can simulate any reasonable physical device at polynomial cost. Further examples for this thesis can be found in Copeland (1996).

AND:

Theoretical as it may seem, the question "what is quantum in quantum computing?" has an enormous practical consequence. One of the embarrassments of quantum computing is the fact that, so far, only one algorithm has been discovered, namely Shor's, for which a quantum computer is significantly faster than any known classical one. It is almost certain that one of the reasons for this scarcity of quantum algorithms is related to the lack of our understanding of what makes a quantum computer quantum (see also Preskill 1998 and Shor 2004). As an ultimate answer to this question one would like to have something similar to Bell's (1964) famous theorem, i.e., a succinct crispy statement of the fundamental difference between quantum and classical systems, encapsulated in the non-commutative character of observables. Quantum computers, unfortunately, do not seem to allow such simple characterization. Observables—in the quantum circuit model there are only two, the preparation of the initial state and the observation of the final state, in the same basis, and of the same variable, at the end of the computation—are not as important here as in Bell's case since any measurement commutes with itself. The non-commutativity in quantum computing lies much deeper, and it is still unclear how to cash it into useful currency. Quantum computing skeptics (Levin 2003) happily capitalize on this puzzle: If no one knows why quantum computers are superior to classical ones, how can we be sure that they are, indeed, superior?

The Illusion of Time

This is a very good article. Reality is not what you think it is.

That Rovelli's approach yields the correct probabilities in quantum mechanics seems to justify his intuition that the dynamics of the universe can be described as a network of correlations, rather than as an evolution in time. "Rovelli's work makes the timeless view more believable and more in line with standard physics," says Dean Rickles, a philosopher of physics at the University of Sydney in Australia.

With quantum mechanics rewritten in time-free form, combining it with general relativity seems less daunting, and a universe in which time is fundamental seems less likely. But if time doesn't exist, why do we experience it so relentlessly? Is it all an illusion?

Yes, says Rovelli, but there is a physical explanation for it. For more than a decade, he has been working with mathematician Alain Connes at the College de France in Paris to understand how a time-free reality could give rise to the appearance of time. Their idea, called the thermal time hypothesis, suggests that time emerges as a statistical effect, in the same way that temperature emerges from averaging the behaviour of large groups of molecules (Classical and Quantum Gravity, vol 11, p 2899).

Imagine gas in a box. In principle we could keep track of the position and momentum of each molecule at every instant and have total knowledge of the microscopic state of our surroundings. In this scenario, no such thing as temperature exists; instead we have an ever-changing arrangement of molecules. Keeping track of all that information is not feasible in practice, but we can average the microscopic behaviour to derive a macroscopic description. We condense all the information about the momenta of the molecules into a single measure, an average that we call temperature.

According to Connes and Rovelli, the same applies to the universe at large. There are many more constituents to keep track of: not only do we have particles of matter to deal with, we also have space itself and therefore gravity. When we average over this vast microscopic arrangement, the macroscopic feature that emerges is not temperature, but time. "It is not reality that has a time flow, it is our very approximate knowledge of reality that has a time flow," says Rovelli. "Time is the effect of our ignorance."

Quark Star

Quark star may hold secret to early universe.

When supernovae explode, they leave behind either a black hole or a dense remnant called a neutron star. However, recent calculations suggest a third possibility: a quark star, which forms when the pressure falls just short of creating a black hole.

Limits of knowledge

A mathematical theory places limits on how much a physical entity can know about the past, present or future

Deep in the deluge of knowledge that poured forth from science in the 20th century were found ironclad limits on what we can know. Werner Heisenberg discovered that improved precision regarding, say, an object’s position inevitably degraded the level of certainty of its momentum. Kurt Gödel showed that within any formal mathematical system advanced enough to be useful, it is impossible to use the system to prove every true statement that it contains. And Alan Turing demonstrated that one cannot, in general, determine if a computer algorithm is going to halt.

A Quantum Threat to Special Relativity

Einstein

This conclusion turns everything upside down. Einstein, Bohr and everyone else had always taken it for granted that any genuine incompatibility between quantum mechanics and the principle of locality would be bad news for quantum mechanics. But Bell had now shown that locality was incompatible not merely with the abstract theoretical apparatus of quantum mechanics but with certain of its empirical predictions as well. Experimenters—in particular work by Alain Aspect of the Institute of Optics in Palaiseau, France, and his co-workers in 1981 and later—have left no doubt that those predictions are indeed correct. The bad news, then, was not for quantum mechanics but for the principle of locality—and thus, presumably, for special relativity, because it at least appears to rely on a presumption of locality.

F-22 Secrets Revealed

Cooooool...

February 12, 2009: The U.S. Air Force has released some performance data on the F-22. The stealthiness factor of the F-22 has turned out to be better than predicted. For radar purposes, the F-22 is about the size of a steel marble. The F-35 comes out as a steel golf ball.