Allan Goff’s Entanglements

          Quantum tic-tac-toe adds just one rule to the venerable child’s game of classical tic-tac-toe, a rule of superposition. On every move, two marks must be placed in separate squares. These two marks are subscripted with the number of the move so X gets the odd number moves {(X₁, X₁), (X₃, X₃),…} and O gets the even number moves {(O₂, O₂), (O₄, O₄)…}. These pairs of marks are called “spooky” marks in allusion to Einstein’s comment about how the nonlocality of matter in quantum systems implies “spooky action at a distance.” The quantum tic-tac-toe board is drawn with the dividing lines doubled (to reinforce the idea that play requires a pair of spooky marks) and with the squares numbered from 1 to 9. Quantum moves are indicated with hyphens, 1–3, 6–9, … Classical boards are smaller with single lines, unnumbered squares, and utilize only unsubscripted marks.

            Superposition in quantum systems seems to imply that an object can be in two places at once, but only when we are not looking at it! Whenever we do look, that is, whenever a measurement is performed, a particle always ends up in only one place. The act of measurement yields classical values, not quantum ones. To predict the pattern of observations, the formalism of quantum mechanics implies the particle was in two places at once before we looked. 

            Quantum tic-tac-toe provides superposition with an immediate and obvious interpretation. Figure 1 shows the first move of a game where X places his spooky marks in squares 1 and 2. A superposition in quantum tic-tac-toe means that we are really playing two games of classical tic-tac-toe at once. In the first classical game X has moved to square 1, in the second classical game X has moved to square 2. The two classical games are in simultaneous play; they are not independent. Together they are called the classical ensemble and are isomorphic with the state of the game on the quantum board. 

Figure 1.

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            Quantum tic-tac-toe was developed in part to provide both a metaphor and an interactive activity for students to grapple with the weirdness of the quantum world. It requires neither mathematical training nor experimental apparatus of any kind. Although it can be played on paper or on a whiteboard, the most effective medium is a Web-based refereed board.

            Quantum tic-tac-toe is a variation on classical tic-tac-toe that formally adds only one rule, a rule of superposition. The paper consists of three main sections: rules, play, and metaphors. The rules section introduces superposition and the concepts that directly derive from it. Section III elaborates on common aspects and situations that result during the course of play. Section IV explores the features of the quantum world that quantum tic-tac-toe mimics and constitutes the heart of the paper.

            The intent of this paper is to provide an introduction to quantum tic-tac-toe in sufficient depth for classroom use. The teacher can mix and match lectures, play, and challenges as appropriate for the students’ level and coursework. Our expectation is that many students will advance quickly in their understanding of quantum tic-tac-toe and begin contributing observations to the class sometimes ahead of their teacher.

Quantum tic-tac-toe was developed as a metaphor for the counterintuitive nature of superposition exhibited by quantum systems. It offers a way of introducing quantum physics without advanced mathematics, provides a conceptual foundation for understanding the meaning of quantum mechanics, and is fun to play. A single superposition rule is added to the child’s game of classical tic-tac-toe. Each move consists of a pair of marks subscripted by the number of the move (“spooky” marks) that must be placed in different squares. When a measurement occurs, one spooky mark becomes real and the other disappears. Quantum tic-tac-toe illustrates a number of quantum principles including states, superposition, collapse, nonlocality, entanglement, the correspondence principle, interference, and decoherence. The game can be played on paper or on a white board. A Web-based version provides a refereed playing board to facilitate the mechanics of play, making it ideal for classrooms with a computer projector.

We have coined the term, Negative Time Reconnaissance (NTR), to describe the military capability of receiving intel from the future. Currently regarded as strictly science fiction, there are developments in quantum physics that portend this as a serious possibility. We have chosen this term to be consonant with the modern ideal of realtime reconnaissance. Before the invention of satellites, reconnaissance delays were typically days to weeks. Realtime reconnaissance is the holy grail of reducing the delay between when an adversary does something, and when we find out about it, to zero. NTR is simply the idea of continuing this “shortening” past zero, to negative times.

If it ever becomes possible to send information at faster-than-light (FTL) speeds, then NTR becomes conceivable. FTL communications (also called superluminal signaling) requires that physics support spacelike causality.

The conventional wisdom is that quantum nonlocality cannot be used for superluminal communications [REF-Eberhard]. Most impossibility proofs that are eventually overturned are overturned not because of technical flaws, but because of a lack of imagination. To show that Eberard’s objection to quantum based superluminal signaling may suffer from this defect, we will be exploring a game based on quantum principles that show how backwards-in-time causality can be paradox free. That game is Quantum Tic-Tac-Toe.

The April issue of the IEEE Transactions on Information Theory  will publish an article by Jan-Ake Larsson claiming current commercial quantum cryptograph is vulnerable.

Bruce Schneier agrees.  

The Swedes went looking in just the right place for a vulnerability, according to Bruce Schneier, an expert in cryptography and chief technology officer at BT Counterpane, in Santa Clara, Calif. “Authentication has always been a problem with quantum crypto,” he says.

Hat Tip: Quantum City

These are all the quotes that seemed funny enough at the time to make it to the white board. Some have stood the test of time well, others…

This is will be a place to add ones on the spot without filtering. If enough good ones accumulate, we might create a page for the general audience. Enjoy.

In the course of a heated discussion about whether quantum nonlocality permits something like time travel, one member began a presumable clever and relevant line of argument with;

“If you have a classical time machine…” - John Levine c 2007

We can only assume it was clever and relevant since the rest was drowned out by gaffes as the group descended into laughter. Then someone put it up on the white board, and thus the klatuk started.

“Of course you can send stuff back in time.” – Bryan Green c 2007

“Time doesn’t matter.” – Nick Chalko c /shrug

“…that isn’t quit good enough, I just have teleportation.” – Allan Goff c 2007

“Get a friend to provide a lame answer. (How to get expert advice off the web.)” – Duane Gibson c 2008

“Can you make time to discuss your time travel experiments?” – (No one was willing to own up to this one.) c 3008

while(!(success = try())); – C++ language

“Is nature simple, or not?” – Joel Siegel c 2008

Since it is news today, we are reviewing the newly-discovered Memristor in tonight’s meeting of the Philosophickal Salon. We are discussing what, if any, quantum effect itmay have — especially on communications.

Science News notes

NIST physicist Peter Mohr and his colleagues propose engineering so-called hydrogen-like Rydberg atoms–atomic nuclei stripped of all but a single electron in a high-lying energy level far away from the nucleus. In such atoms, the electron is so far away from the nucleus that the latter’s size is negligible, and the electron would accelerate less in its high-flung orbit, reducing the effects of “virtual photons” it emits. These simplifications allow theoretical uncertainties to be as small as tens of parts in a quintillion (one followed by 18 zeros).

Are two electrons in a atom  quantum entangled?  Can we use this big atom in NTR?

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.