Cramer Explains How to Mod an XBox with Quantum Mechanics

Quantum mechanics is the study of the relationship between energy and matter. It provides us with accurate descriptions for many previously unexplained phenomena such as black body radiation and stable electron orbits.

But quantum mechanics is a desperately crazy and interesting science that contains several preposterous sounding theories that are surprisingly being proven correct day by day. I’ll touch briefly on some of these.

First, we have Planck’s constant. Planck’s constant is used to describe quantization, a phenomenon occurring in subatomic particles such as electrons and photons in which certain physical properties occur in fixed amounts rather than a continuous range of possible values. This constant shows that there is an inherent graininess to our world. I made a statement in a previous article that I thought that if there were a God, he/she/it was disguised as Plank’s constant. I believe this to be the source of all the randomness, diversity, and uncertainty in the world – but that is the subject of yet another article.

Second, we have the Heisenberg uncertainty principle. The Heisenberg uncertainty principle is the statement that locating a particle in a small region makes the momentum of the particle uncertain, and conversely, measuring the momentum of a particle precisely makes the position uncertain. It explains that there is an inherent uncertainty, an inherent fuzziness to our world. It tells us that there are limits to the measurements that we can make of the world, not because of limits in our technology but because of limits in nature itself. The world, it seams, can only be described through probabilities and not hard numbers. Interestingly enough, the uncertainty of our observations (measured as the standard deviation of the measured value from its expected value) is always in multiples of Planck’s constant. On another side note, our buddy Einstein didn’t like this principle very much and said that he refused to believe that God rolled dice. It now appears that God has quite a gambling habit. Don’t worry big guy, we all have our vises.

Third is the observer effect. The observer effect refers to the fact that the mere observation or measurement of a phenomenon will alter it. Even stranger, if the phenomenon is simply put into a position where observing it is possible, without actual observation taking place, it will still (theoretically) alter it.

Yet another one is wave–particle duality. Wave–particle duality is the concept that all matter exhibits both wave-like and particle-like properties. All particles are supposed to also have a wave nature. This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, according to quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones but we can’t detect wave properties of macroscopic objects due to their very small wavelengths.

Here is the big one: Entanglement. Entanglement is so wacky that Albert Einstein, along with Boris Podolsky and Nathan Rosen formulated the EPR paradox, a quantum-mechanical thought experiment with a highly counterintuitive and apparently non-local outcome to show why quantum mechanics could not be a complete/correct theory. This paper was so well thought out that it is still sited as a reference source in almost all papers written on entanglement. But like Einstein’s cosmological constant, he was wrong for all the right reasons. He assumed that quantum mechanics was bunk because it allowed for non-local effects, or “spukhafte Fernwirkung (spooky action at a distance)” as he called it. But once again the universe has proved itself to be just a little crazier than Einstein wanted to believe.

Quantum entanglement is a phenomenon in which the quantum states of two or more particles have to be described with reference to each other, even though the individual particles may be physically separated. For instance, say we have two entangled electrons with one on one side of the galaxy and one on the other. Before we observe any of their quantum states, say their spin along the Z-axis, they both exist in an indeterminate state. Each electron is said to be in a superposition of states in which it can be thought of as the sum of both possible states: spin up and spin down. We can only characterize it by probability, which in this case is a not so surprising 50/50. The interesting part happens when you observe the electron’s spin. Once you observe one electron and find it to be spin up, the other one instantly collapses out of its indeterminate state and, when observed, will always be spin down – even on the other side of the galaxy. What’s really interesting is that you can entangle more than two particles at a time.

Now for some fun with quantum mechanics. Here is an experiment that will drive home just how odd quantum mechanics can be. I have largely copied this from Wikipedia because I am tired and lazy, but I have tweaked it here and there. It’s sad – I’m an adult now but I still copy from the encyclopedia to do my homework assignments.

In the double-slit experiment, light is shone at a solid thin plate that has two slits cut into it. A photographic plate is set up to record what comes through those slits. One or the other slit may be open, or both may be open.

When only one slit is open, the pattern on the plate is a diffraction pattern, a fairly narrow central band and dimmer bands parallel to it on each side. When both slits are open, the pattern displayed becomes much more detailed and at least four times as wide. This is an interference pattern – something that only happens when waves cross paths.

Now, with both slits still open, if something is added to the experiment to allow a determination that a photon has passed through one or the other slit, then the interference pattern disappears and the experimental apparatus yields two simple patterns, one from each slit. The interference pattern disappears! Just by observation we have forced the light to exhibit its particle nature instead of its wave nature.

The most baffling part of this experiment comes when only one photon at a time is fired at the barrier with both slits open. As the pattern is recorded by the film, one photon at a time, again we see an interference pattern emerge. The clear implication is that something with a wavelike nature passes simultaneously through both slits and interferes with itself — even though there is only one photon present. (The experiment also works with electrons, atoms, and even some molecules too.)

There are other intriguing experiments and applications of quantum mechanics – many of them using entanglement. One of them is quantum teleportation, where the state of a particle can be transmitted from one place to another. Another closely related application is quantum cryptography – sending unbreakable codes by using entangled particles coupled with a “classical channel” of communication. The classical channel information is useless without the entangled particles so eavesdropping is impossible.

Another interesting application is quantum ghost imaging. In ghost imaging, entangled photons head off in opposite directions. A mask is placed in front of the path of the photons heading in one direction, with a bucket detector behind it to count when a photon makes it through the mask. If detectors are also set up in the other path, the image of the mask is surprisingly retrieved by recording the joint detection events of the entangled pairs.

This finally brings us to quantum computing. Using entangled particles it is possible to perform some computations like integer factorization and discrete logarithms in an exponentially faster manor than traditional computer architecture allows. These computers will also be terribly good at “brute force” computations where several guesses must be checked before a final answer can be found. With these uses alone, you can say goodbye to even the most hard-core encryption schemes that exist today.

So what about your Xbox? How can you use quantum mechanics to improve its gaming performance? That is a fantastic question. The answer is for you to put down the controller and start paying attention to the world around you. I guarantee that the universe has far better problems for you to solve than any video game. Maybe start paying a little more attention to your math and science teachers. Do a little research every night when you get home. With some work, you can figure out how to build a quantum Xbox. And when you get your award for extreme cleverness, don’t forget to thank Cramer for the inspiration.


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