The items in this section introduce some of the basic facts about this quantum world. Here we ask some fundamental questions, which arise directly from the bare facts, but as yet we do not look for answers.
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Two simple rules |
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The mathematical formalism of quantum mechanics is (first of all, whatever else it may be) a probability algorithm. It provides us with tools for calculating the probabilities of measurement outcomes. These tools are like machines with an input and an output. Insert the actual outcome of a measurement, and out pop the probabilities of the possible outcomes of other measurements. At the heart of this algorithm are two simple rules.
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A scattering event |
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Suppose that initially there is one particle (N) heading northward and one particle (S) heading southward, and that the next thing we know is that there is one particle (E) heading in a direction we shall call "eastward" and one particle (W) heading westward. What happened in the meantime?
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The most beautiful experiment (without the math) |
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According to a Physics
World poll conducted in 2002, the most beautiful experiment in physics
is the two-slit experiment with electrons. According to Feynman, this
classic gedanken experiment "has in it the heart of quantum
mechanics" and "is impossible, absolutely impossible, to explain in
any classical way."
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The most beautiful experiment (with some math) |
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According to a Physics
World poll conducted in 2002, the most beautiful experiment in physics
is the two-slit experiment with electrons. According to Feynman, this
classic gedanken experiment "has in it the heart of quantum
mechanics" and "is impossible, absolutely impossible, to explain in
any classical way."
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Bell's theorem |
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Here is what we do:
- Pairs of particles are launched in opposite directions.
- Each particle is subjected to one of three possible measurements (1, 2, or 3).
- Each time the two measurements are chosen at random.
- Each measurement has two possible outcomes, indicated by a red or green light.
And here is what we find:
- If both particles are subjected to the same measurement, identical outcomes are never obtained.
- The two sequences of recorded outcomes are completely random. In particular, half of the time both lights are the same color.
If this does not bother you, then please explain how it is that the colors differ whenever identical measurements are performed.
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Prelude to GHZ |
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Let's play a game. Here are the rules:
- There are two opponent teams: the "players" (Andy, Bob, and Charles) versus the "interrogators."
- Each player is asked either "What is the value of X" or "What is the value of Y?"
- Only two answers are allowed: +1 or –1.
- Either all players are asked the first question (about the value of X), or one player is asked the first question and two players are asked the second question (about the value of Y).
- The players win if the product of their answers is –1 in case everyone is asked the first question, and if the product of their answers is +1 in the case that Y-questions are asked. Otherwise they loose.
- The players are not allowed to communicate which each other once the questions have been asked. Before that, they are permitted to work out a strategy.
Is there a failsafe strategy? Can the players make sure that they will win?
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The experiment of Greenberger, Horne, and Zeilinger |
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Please read this first.
Yet there is a failsafe strategy without pre-agreed answers.
Here goes:
- Andy, Bob, and Charles prepare three particles (say, electrons) in a particular quantum state, which defining joint probability distributions over possible measurement outcomes. The probabilities are independent of the distances between the particles.
- Each player takes one of these particles.
- Whoever is asked the X question measures the x component of the spin of his particle (which has two possible values, which we will take to be +1 and –1) and answers with his outcome. Whoever is asked the Y question measures the y component of the spin of his particle and answers likewise.
- Proceeding in this manner, Andy, Bob, and Charles are sure to win every time.
Time for our next million dollar question! Is it possible for the x and y components of the spins of the three particles to be in possession of values even if no values are actually measured?
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The bomb testing experiment of Elitzur and Vaidman |
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The setup consists of two beam splitters BS1 and BS2, two mirrors M1 and M2, two perfect (100% efficient) photodetectors D1 and D2, and (maybe, maybe not) a bomb so sensitive that the detection of a single photon causes it to explode.
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The experiment of Englert, Scully, and Walther |
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Once again there is a plate with two slits, only this time we use atoms instead of electrons. All are of the same type — Cesium-133, say — and all are prepared in the same excited state. In front of each slit there is a microwave resonance cavity. The two cavities are separated by a pair of electro-optically controlled shutters, which are initially closed. Between these shutters there is a photosensor.
The atoms enter the cavities from the left. Quantum mechanics allows us to calculate the probability with which any given atom, upon emerging from the cavities, is found in its ground state — provided that an energy measurement is made. The cavities can be — and are — designed so that this probability is 1. Each atom thus leaves with a lower energy than that with which it entered the cavities. Since energy is conserved, and since there is no way for the "lost" energy ΔE to escape the cavities, this energy is "trapped". It is customary to say that the atom has emitted a photon with this energy, and that this photon remains trapped inside the cavities.
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The bare facts 
