What I most love of quantum mechanics is that it is nondeterministic, which means that it’s generally doesn’t predict the outcome of any measurement with certainty. Instead, it just provides the probabilities of the outcomes, so that ‘measurements of a certain property done on two apparently identical systems can give different answers’ — to put it simply, the Truth is unfathomable. That’s how I’ve always perceived the universe and therefore life: governed by the uncertain definition inherent in its very core.
Quantum entanglement, also called the quantum non-local connection, is a property of a quantum mechanical state of a system of two or more objects in which their quantum states are linked together so that to describe one object you have to take into account its counterpart — even if they’re spatially separated.
Quantum entanglement creates a paradox since it apparently allows faster-than-the-speed-of-light transmission of information, violating special relativity. But in fact it’s instantaneous conservation of the information of quantumly entangled observable, rather than transmission of information — measurements performed on spatially separated parts of a quantum system can apparently have an instantaneous influence on one another. Why there is an instantaneous conservation probably depends on the interpretation of quantum mechanics.
N. Bohr. "Atomic Physics and the Description of Nature" (1934)
Whatever axis the spins are measured along, they always turn out to be opposite. Such weird behaviour suggests they’re linked in some way: one possible explanation is that they were born with a definite (opposite) spin about every axis, thus giving rise to “hidden variable” theories, another interpretation is that they are so “entangled” that one electron knows what axis its counterpart’s spin is being measured along, and becomes its opposite about that axis just for the fun of it.
I love the idea of hidden variable — extrapolated to everyday life it’s probably some unknown force responsible for “blind chance”, the Unexpected and even Fate.
You can’t possibly trick them, once you’ve measured the electron's spin about the x-axis (and the positron's spin about the x-axis deduced), the positron's spin about the y-axis will no longer be certain (makes me wonder, though, from the positron’s or our point of view?), as if it knows that you’ve messed with its partner. Either that or it has a definite spin already — a spin about a second axis. Too much certainty to quantum mechanics' taste.
Apart from spin many types of physical quantities — what quantum mechanics calls "observables" (a property of the system state determined by some sequence of physical operations) — can be used to produce quantum entanglement (such as momentum). Photon polarization is often used in experiments as polarized photons are easy to prepare and measure.
Looking at the phenomenon from my personal oddball angle, this is what I make of the test (that is, the double-slit experiment) : in order to determine the photon’s polarization direction one photon is split into two new photons that will have the same probability (of polarization direction) as the original photon, because they still share the information of the original one. Therefore, they share the polarization relativity as well, maintaining the original photon’s information before some external power acts on them. If the original polarization relativity is "fulfilled" when we measure the polarization of the first photon, there is no polarization probability “left” for the other one (since the first one has already “used up” their common original unsplit photon’s probability), the other one has to have opposite polarization — just to hammer my point in — because the first one has already used up their common probability.
Additionally, when the electron (or any particle) passes through the double-slit apparatus, it passes through the slits as a wave, but at the moment of hitting the detector (screen), it goes back to its quantum nature without losing its wave nature either (the wave as a whole behaves like a particle). The interference already takes place on the way to the screen.
The paradox feeds the suspicion that quantum mechanics, despite its success in a host of experimental scenarios, is actually an incomplete theory. There must be some unknown mechanism acting on these variables to account for the observed effects. Hidden variable theories pop up as an attempt to address these issues, while scientists claim the more complete theory should contain variables corresponding to all the "elements of reality". But that sounds like a whirl at a working description of God!
The phenomenon of quantum entanglement has some practical applications, or so they say: In quantum cryptography, entangled particles are used to transmit signals that cannot be eavesdropped upon without leaving a trace. In quantum computation, entangled quantum states are used to perform computations in parallel, allowing some calculations to be performed much more quickly than with classical computers.
The most attractive derivative to my eye, though, is so called quantum pseudo-telepathy phenomenon in quantum game theory that relies on the fact that the quantum laws of physics are subtly non-local. This means that to profit from quantum pseudo-telepathy, the players have to share a physical system in an entangled quantum state before the game, and during the game make measurements on this entangled state as part of their game strategy. Games in which the application of such a quantum strategy leads to pseudo-telepathy are also called quantum non-locality games.
To cut the long story short, if the game consists in completing a similar task with your partner being physically unable to communicate with them, for the purpose of mutual win you should share with them an entangled state before the game and make measurements on it during the game that will reveal your partner’s move to you, thus allowing you to act in sync with him.
I wonder if this effect can be used in gambling.
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