Allan Goff’s Entanglements

The core hypothesis of Quantum Temporal Paradox (QTP) is that quantum systems self-collapse when their constituents become cyclically entangled. In this post, we’re going to lay part of the mathematical foundations for exploring this hypothesis.

We’ll start with the idea, already well established in current quantum theory, that the state of a particle is represented by a complex vector. The dimension of this vector is equal to the number of possible states provided by the quantum system and can be infinite. As a special case, we’ll typically consider only four dimensions. In quantum theory, the magnitude of the vector is considered irrelevant, only the direction it points has physical meaning. It is a mathematically convenient way to indicate a “ray.” For this reason, quantum physicists are typically sloppy about normalization, for it can always be corrected for after the fact. While this is convenient mathematically, it is possible that this short cut is masking real physics. Therefore, we shall be anal about normalization.

Given a normalized vector to represent the state of a quantum particle, we will use a taxonomy to characterize the extent of an object’s superposition. This taxonomy will be called the superposition continuum, even though superposition is non denumerable. On one end will be a particle in a classical state, no superposition at all, and on the other end, a full equally weighted superposition amongst all the possible states. The first case will be called “classical” the second “flat.” In between will be the state where the particle is equally weighted between only two possibilities, we’ll call this one “spooky.”  States in between classical and spooky, will be called “localized” and between spooky and flat, “diffuse.” Summarizing, the taxonomy is: classical, localized, spooky, diffuse, and flat. This is a loose and not entirely consistent taxonomy, but it serves a useful purpose; it allows us to concentrate on the essentials by suppressing some of the mathematical noise. A quantum object in a classical state in basis A will be in a flat state in any basis conjugate to A. If QTP is correct, any quantum object entangled with a cyclic entanglement will be in a spooky state in the collapse basis. In general, localized or diffused states indicate an uninteresting basis.

If we want to use the power of a spreadsheet to help explore the QTP hypothesis, we’ll need to be able to represent vectors in either rectilinear or polar coordinates, and then use cells to determine if the vector is normalized and if so, where it lies on the superposition continuum.

the physics arXiv blog writes Why our time dimension is about to become space-like

Now Marc ‘Bars’ Mars and a few pals in Spain say that the Universe’s signature might be about to flip from Lorentzian to Euclidean. In other words, our dimension of time is about turn space-like. Gulp!”

I am ready to take a stroll down memory lane.

I was reading Seth Godin’s blog recently, and his article Write like a blogger resonated strongly. The entire article is excellent, but point number three describes it best:

Drip, drip, drip. Bloggers don’t have to say everything at once. We can add a new idea every day, piling on a thesis over time.

Writing for a blog is different than writing for a scientific journal. This has taken some time for the members of Allan’s Philosophickal Salon to absorb, but I know we will master it soon.

The more I learn about generic programming the more it looks to have the potential to increase programmer productivity by as much as the transition from assembler to procedural languages achieved. My experience with it is limited to C++, and I still understand too little to solve complete problems, but in this post I’ll present an example of the kind of problem that generic programming can in principle solve.

Consider the problem of scientific software, programs that need to work with floating point numbers with physical significance. The major code quality problem is that all these different quantities are not dimensionless. It is a mistake to add an acceleration to a mass but not a mistake to add two masses, two lengths, etc. More challenging, there are composite quantities, products of more basic quantities, such as force. The whole process of insuring that the quantities in a physical equation relate appropriately is called dimensional analysis. There are well known runtime solutions to this problem, but they affect efficiency, typically of major concern to scientific modeling, and furthermore, any problems are not found until the program is running. One would like to have a compile time solution.

In particular, we would like the compiler to pass expressions of the following form (need monospace font, Bryan?),

quantity<mass>           m = 5.0;
quantity<acceleration> a = 9.81;
quantity<force>            f = m*a;
m = m + m;
a = a - a;

and not pass expressions like these,

f = m*m;    // Compiler should reject.
a = v/(t*t); // Ditto.

The challenge is to create a set of classes, functions, macros, typically templates, that enforce these restrictions and do so without any runtime efficiency penalties, as if the quantities were simple floating point types. Let’s consider this problem at the next meeting of the Philosophical Salon.

Let me know what you come up with.

The Pauli Spin Matrices are an example of a conjugate basis set (CBS). Each matrix is a projector, its square is the identity matrix. Recall that when multiplying matrices in a complex space one must be converted to the the complex conjugate, rows and columns swap and all imaginary components change sign. In a conjugate basis set, every basis is conjugate to every other. By conjugate we mean the property that any classical state in one basis is in an equally weighted superposition in all the states in any basis conjugate to it.

We have been investigating conjugate bases in a 4D Hilbert space, and have our first breakthrough. We can now identify families of bases pairs conjugate to each other and to the lab bases. We can also smoothly rotate the pair maintaining the mutual conjugate relationship between all three bases. It is clear from this rotation that there is at least one more degree of freedom to identify.

The reason this advance is significant, is that the theory of Quantum Temporal Paradox (QTP) postulates the hypothesis that a cyclic entanglement will be self-referential in only one basis and it is in this basis that the system self-collapses. Self-reference leads to a natural nonlinearity. Combined with the symmetry breaking of a unique basis, this hypothesis frees quantum physics from the problematical need for an “observer” to cause collapse of the wave function. It is a promising solution to the measurement problem.

With the mathematical foundation, we are step closer to testing this hypothesis.

Hey, someone has noticed QT3 and is thinking about it! Check this out:

http://pwnedbyagrue.blogspot.com/2008/03/forcing-draw-in-qt3-or-propping.html

A dogmatist, an atheist, and a scientist are out and about when they stumble across an exquisite watch. They are all mesmerized by its intricacy, elegance, and features. Many a happy hour is spent teasing it apart to learn how it works, and for this effort, their curiosity is well rewarded. However, although they have access to all the same data, they reach rather different conclusions. The Dogmatist asserts that there must be a watchmaker, and because he believes in God, claims that the watchmaker is God. The atheist, who does not believe in God, claims there must be a watch factory. The scientist doesn’t think there is enough evidence for either conclusion, but after a little thought reasons that the “God hypothesis” lacks predictive power, while the existence of a watch factory would offer all kinds of new wonders to explore. He therefore agrees to accompany the atheist on his search for a watch factory.

After a long time, to the scientist’s amazement, and the atheist’s relief, they do indeed find a watch factory. It is a huge complex, dauntingly intricate, and produces far more than just watches. Many a happy year is spent exploring it and like they did with the watch, teasing apart how it works. In due time, they publish their results for all to enjoy. As before, the three, even with the same data, reach rather different conclusions. The dogmatist is most upset, and loudly denies the existence of the watch factory, calling it a fraud, a lie, and an evil deception. The atheist, refusing to consider that there might be a factory maker, loudly retorts that no Maker exists. The more they argue, the more they seem merely to cement each other’s position. To the scientist, who reaches yet a third conclusion, their debate seems to completely miss the point. From his perspective, the scientific evidence for a Creator is neutral, but it is most definitely not neutral on the character of such a Creator.

If the dogmatist is right, that a watchmaker would be worthy of worship, then by that much more must a factory maker be worthy of worship. While science is silent on the existence issue it is not silent on the grandeur issue. With each new discovery science increases the grandeur we must accord to the Creator, should He exist. Perhaps the existence question is better pursued by other vehicles than science. But on the grandeur question, science is eloquent. If this place is a “creation,” then we should stand in humble awe of the Creator.

…or at least a leap in quantum communications!

Fascinating stuff.

Found this interesting site on mathematics. I am sure my friends at the Philosophical Salon will enjoy!

the physics arXiv blog writes A new class of photon gun

Here’s the breakthrough: Andrew Shields, at Toshiba’s research labs in Cambridge, UK, plus a few pals from a nearby university, say they can create the photons using a quantum dot that they zap with two precisely timed voltage pulses. The first pulse injects charge carriers into the diode while the second suddenly shifts the quantum dot’s emission characteristics so that it can emit light. When that happens, the dot emits a photon of a specific energy

Another piece in the puzzle.

(Via Slashdot.)

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