This is a correct description of the situation. I'll add a bit more. The possible polarizations of light (or of a photon) form a 3-ball, known as the Poincaré sphere. The pure states lie on the surface, a 2-sphere, while mixtures of pure states lie within the volume, unpolarized light at the center. Left and right circularly polarized light are at the poles, linearly polarized light at the equator, elliptically polarized light in-between. Rotating the plane of polarization by θ corresponds to moving around the equator by 2θ, so going around by 360º means rotating the polarization plane by 180º, which restores the starting point. Opposite states of polarization are diametrically opposite on the Poincaré sphere. If a polarizer transmits photons in state P, and an analyzer accepts photons in state A, then the probability that a photon is accepted is cos(ϕ/2)^2, where ϕ is the angle between P and A subtended from the center of the Poincaré sphere. This generalizes the simple case of a pair of sheet polarizers oriented at angle θ, where the transmitted irradiance varies as cos(θ)^2. The usual entangled photon source emits a pair of photons with opposite, but otherwise random, polarizations. Suppose Alice sets her analyzer to A, and Bob sets his analyzer to B. Each, separately, will observe unpolarized light, always half of the photons go into the "accept" channel, the other half into the "reject" channel and the pattern is random. (Note that this assumes the use of a polarizing beam splitter that transmits both polarizations into separate beams. A lossless beamsplitter necessarily has eigenstates that are opposite in the sense used here.) But if they record their results and compare records, they will find that they agree (both accept or both reject) a fraction sin(ϕ/2)^2 of the time, and they disagree (one accepts, the other rejects) a fraction cos(ϕ/2)^2 of the time, where ϕ is the angle between A and B. The fact that the photons are always randomly accepted or rejected for Alice and Bob individually means that this scenario cannot be used to communicate information. Nothing that Alice does can influence Bob's data. This is the quantum theoretical prediction, and all experimental measurements to date are consistent with it. But some people like to go beyond the observable, and ask "what is really happening?" Einstein, Podolski, and Rosen (EPR), in their famous paper on the incompleteness of quantum mechanics, proposed that if the result of a measurment on a physical system can predicted with certainty, then that physical situation has "an element of physical reality". Now, suppose Alice and Bob agree to set their analyzers to the same orientation, A=B. Then every time that Alice receives a photon in the accept channel, she knows for certain that Bob will receive his corresponding photon in the reject channel. So it seems that the polarization states of Bob's photons have "an element of physical reality". Thus, in the sense of these "elements of physical reality", it appears that Alice's measurement has acted at a distance on Bob's photon. Since the time and distance between Alice's and Bob's measurements may require the action to propagate faster than light, it is "spooky". Suppose the polarization of the photons is determined at the source at the time of emission, i.e. the photons are given random but opposite polarizations at emission. This is untenable. Suppose Alice and Bob both accept horizontally polarized light and reject vertically polarized light. But some of the time, the source will emit photons that have polarizations that are neither horizontal nor vertical; it might be at 45º, or it might be circular or elliptical. These photons will be accepted or rejected with cos^2 probabilities, and independently for Alice and Bob, so the perfect correlation will be destroyed. When quantified, this becomes one of the many possible Bell inequalites that must be satisfied by any causal theory that ascribes reality to the polarizations of the individual photons prior to measurement. But there is yet a (rather silly) loophole. Suppose the source can sense the analyser orientations and emit just the right sort of photons. This is where John Wheeler's delayed choice enters. The analyzer orientation typically uses an electro-optic modulator, which can respond in nanoseconds, while the photons can propagate through kilometers of optical fiber with negligible degradation. So Alice and Bob can choose A[n] = B[n] from a prearranged script of random numbers, and can easily delay the commands to their electro-optic modulators until after the entangled photons have left the source. This delayed choice experiment has been done, and the results are again consistent with quantum theory. In summary, the EPR notion of physical reality is inconsistent with causality (i.e. that physical influence cannot propagate faster than light or backward in time). Nevertheless, the spooky EPR action at a distance cannot be used to sent information acausally. EPR made use of the quantum theoretical predictions to argue that quantum theory, as formulated by Niels Bohr, is incomplete, but they agreed with Bohr as to what these predictions are. Bohr's reply was to reject the notion of "elements of physical reality". As Wheeler would phrase it, the polarizations of the individual photons do not come into being until the measurement is made. A note for historical accuracy: The EPR paper used position, momentum, and the Heisenberg uncertaintainty principle. Later David Bohm suggested spin or polarization as conceptually cleaner and more amenable to experiment. Finally,a request for some feedback: It takes a considerable amount of time for me to compose, edit, and proofread these little physics essays. Are they appreciated? -- Gene ________________________________ From: Dave Dyer <ddyer@real-me.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, August 13, 2009 12:27:41 PM Subject: Re: [math-fun] Plenty of Room at the Bottom, Part II My layman's understanding is this: Suppose you have a supply of entangled particles and manage to ship half of each pair to New York and London. You know that if you observe one and find it in "up" state, the other would instantaneously be observable in "down" state. You can verify this later (after light speed delay) by comparing notes. The problem is that you can't use this to communicate, (1) You can't set the state of the particle, only observe (so you can't set the New York particles to "up" or "down" so London can see the effect. (2) You also can't tell if a particle has already been observed, so you can't signal by selectively not observing. In the math used to describe these processes, there is no state until you make an observation, so there is no loophole by which you can tease more information out of the system. It remains to be seen if the math, which has withstood 100 years of practical tests, is absolutely correct. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun