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The Existence and the Nature|
of Entanglements of Particles
When Erwin Schrödinger formulated the wave mechanics version of quantum physics in 1926 he did not specify what the wave function ψ represented. He thought its squared magnitude would represent something physical such as charge density. Max Born suggested that its squared magnitude represented spatial density of finding the particle near a particular location. Neils Bohr and his group in Copenhagen concurred and the notion that the wave function represents the intrinsic indeterminancy of the particle of the system came to be known as the Copenhagen Interpretation (CI).
Erwin Schrödinger disagreed with this interpretation, as did Albert Einstein. Both constructed gedanken (thought) experiments to discredit the logicality of the CI. Erwin Schrödinger's was one of a cat in a box with a mechanism that might or might not kill the cat. According to the CI until someone looked into box the cat would exist simultaneously in two states; one being alive and the other one being dead.
Einstein constructed more serious challenges to the CI. The most famous was published in an article by himself and two collaborators, Boris Podolsky and Nathan Rosen (EPR). In that article it was envisioned that two particles were created with the same wave function but opposite spins. The two particles were then separated. The spin of one particle was then determined. If, as according to the CI, the particle did not exist other than as wave function then the spin of the particle which was measured had to be communicated to the other particle so it could take the opposite spin. This would involve what the article referred to as "spooky action at a distance." The alternative to the CI was that the particles were material and each had their spins specified at separation.
Subsequently physicists envisioned an experiment in which the spin of one of the two particles was changed. If the particles carried the spins they had at separation then the change in the spin of one would not affect the spin of the other. On the other hand, if the two particles shared the same wave function, as in the CI, then the collapse of the wave function for one particle to a definite value of spin would induce the corresponding definite value of spin for the other particle. Erwin Schrödinger coined the term entanglement to denote what was postulated under the CI.
The issue was unresolved and probably thought by most physicists to be unresolvable for about three decades. Then in 1965 the Irish physicist, John Stewart Bell, formulated a test that in principle would resolve the issue. It was in the form of a theorem. If the alternative to the CI holds then a quantitative measurement would have to satisfy a particular inequality. The Bell test did not sit unimplemented for long. Within just a few years three groups designed experiments to test whether the assumptions of Bell's theorem had relevance for the physical world.
All of the subsequent tests of Bell's theorem utilized photons rather than the electrons in which EPR originally formulated the issue. There has been little or no concern about the possibility that photons differ so radically from electrons in this matter that the results from experiments involving photons have no bearing on the properties of electrons. Consider an application of the Uncertainty Principle to a photon. A photon travels at a precisely defined velocity and those generated by atomic transitions have a frequency also precisely defined. The momentum of a photon is hν/c, where h is Planck's constant, c is the speed of light and ν is the frequency associated with the photon. The uncertainty associated with a photon's momentum would appear to be near zero and thus according to the Uncertainty Principle the uncertainty associated with its location would seem to be extremely large. This situation is often interpreted as the saying the photon's location is spread over the entire universe. This is not really true because the variance of a probability distribution can be infinite without it being uniformly spread over the universe. For a probability distribution to have infinite variance it is only necessary for the probability density to go to zero more slowly than 1/x² where x is the deviation from the mean value for the distribution. But the Uncertainty Principle suggests that photons are more widely spread out than electrons and perhaps all photons could be considered to be entangled.
Using photons not only greatly simplifies the creation of a test apparatus; it simplifies the theoretical analysis. The effect of the alignment of the polarization detectors works out to be proportional to the cosine of the deviation between the angles of alignment of the two detectors.
The graph that shows the comparison of the CI versus the material particle theory is shown below.
It is astounding that the nature of the universe hinges on the relatively small difference between these two displays. The graph below shows the numerical difference between the two.
All but two of the first seven tests carried out found violations of the inequality of Bell's theorem or extensions of it. The astounding thing however is that none of the experimenters chose to validate their results by running independently generated photons through their apparatuses. There was always the possibility that the results for supposedly entangled photons was due to some peculiarity of the apparatuses. If independently generated photons gave the same results there could be two responses from physicists. One response would be that all photons are entangled. The second response would be that the phenomenon being measured is different fro/im what was envisioned.
Here are the published experimental tests and the abstract of their results. In the abstracts there is a bit of jargon that has evolved on the topic. Local means no influence can propagate between two objects faster than the speed of light. Realism, realistic and reality refers to the continual material existence of particles, as opposed to the CI contention that particles do not have material existence except when they are subjected to measurement.
We have measured the linear polarization correlation of the photons emitted in an atomic cascade of calcium. It has been shown by a generalization of Bell's inequality that the existence of local hidden variables imposes restrictions on this correlation in conflict with the predictions of quantum mechanics. Our data, in agreement with quantum mechanics, violate those restrictions to a high statical accuracy, thus providing strong evidence against local hidden-variable theories.
The linear-polarization correlation of pairs of photons emitted in a radiative cascade of calcium has been measured. The new experimental scheme, using two-channel polarizers(i.e., optical analogues of Stern-Gerlach filters), is a straightforward transposition of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment. The present results, in excellent agreement with the quantum mechanical predictions, lead to the greatest violation of generalized Bell's inequalities ever achieved.
Correlations of linear polarizations of pairs of photons have been measured with time-varying analyzers. The analyzer in each leg of the apparatus is an acousto-optical switch followed by two linear polarizers. The switches operate at incommensurate frequencies near 50 MHz. Each analyzer amounts to a polarizer which jumps between two orientations in a time short compared with the photon transit time. The results are in good agreement with quantum mechanical predictions but violate Bell's inequalities by 5 standard deviations.
It is suggested, that due to a numerical coincidence between the photon flight time and switching frequency, the time-dependent experiment of Aspect et al. is not conclusive. Improved experiments are proposed.
We report on a high-intensity source of polarization-entangled photon pairs with high momentum definition. Type-II noncolinear phase matching in parametric down conversion produces true entanglement. No part of the wave function must be discarded, in contrast to previous schemes. With two-photon fringe visibilities in excess of 97%, we demonstrated a violation of Bell's inequality by over 100 standard deviations in less than 5 min. The new source allowed ready preparation of all four of the EPR-Bell states.
In 1973 Holt and Pipkin using photons generated by atomic transitions in mercury got results in agreement with Bell's inequalities. This paper was distributed as a preprint, but apparently did not appear in a journal.
Holt, R.A. , “Atomic Cascade Experiments,” Ph.D. Thesis, Physics Department, Harvard University.
In this paper we show that, in every atomic-cascade experiment performed up to now for testing Bell's inequality, the second photon of the atomic cascade undergoes rescattering with considerable probability. The only experiment of this type in which rescattering is negligible is the Holt and Pipkin's one, but this is also the only experiment whose results grossly violate quantum-mechanical predictions.
In 1974 Kasaday, Ullman and Wu used the pairs of gamma ray photons produced by electron-positron annihilations to test Bell's inequalities and found results in agreement with quantum mechanics and in violation of Bell's inequalities.
The inequality of Bell has been tested by the measurement of the spin correlation in proton-proton scattering. Measurements were made at Ep = 13.2 and 13.7 MeV using carbon analyzers of 18.6 and 29 mg/cm², respectively, accumulating a total of 104 coincidences. The experimental analyzing power, geometric correlation coefficients, and energy spectra are compared to the results of a Monte Carlo simulation of the apparatus. the results are in good agreement with quantum mechanics and in disagreement with the inequality of Bell if the same additional assumptions are made. The conditions for comparing the results of the experiments to the inequality of Bell are discussed.
In 1976 using pairs of protons generated by focusing an accelerator's beam of protons on a target of protons, Lamehi-Rachti and Mittig obtained the data displayed below
In 1976 Fry and Thompson using pairs of photons generated by a mercury isotope got results in agreement with quantum mechanics and in violation Bell's inequalities.
We have measured the linear polarization correlation between the two photons from the 73S1→63P1→S0 cascade from Hg200. The results were used to evaluate Freedman's version of the Bell inequality, δ<~0. Our result is δexp=+0.046±0.014, in clear violation of the inequality and in excellent agreement with the quantum mechanical prediction, δQM=+0.044±0.007.
Although no actual experimental tests using independently generated photons appear in the literature there are a couple of articles by the same two physicists considering a theoretical analysis.
In the usual Bell's-inequality experiments two particles carrying spin or polarization are prepared in an entangled state generated from the decay of an unstable quantum-mechanical system. These particles are then delivered to spin or polarization analyzers. The statistics of the measurements reported by analyzers are incompatible with our notions of local realism. Here we show that Bell's-inequality violations occur even when the initial state is a direct product state. ln fact, the two particles can come from two independent widely separated sources.
In conventional Einstein-Podolsky-Rosen (EPR) experiments an unstable system decays into an entangled state of two or more particles. When appropriate measurements are made on this entangled state, phenomena are exhibitted that run counter to our classical notions of local realism. Using a variant of a gedanken experiment proposed by Greenberger, Horn, and Zeilinger, it is shown that EPR effects can arise even when the particles come from independent widely separated sources.
Some of the articles which question the entanglement theory and experimental results are:
We obtain a local realistic model, involving just one angular hidden variable, giving predictions, for the coincidence counts in atomic cascade experiments, which come extremely close to those of the quantum mechanical model, and which fit the experimental data as closely as do the predictions of that model.
A straightforward derivation of the coefficient of correlation of polarization present in Bell's inequalities is given, where appeal to an action-at-a-distance interaction is explicitly made. This demonstrates that nonlocal hidden variables theories may be compatible with quantum mechanics, and the relevance of Bell's inequalities to the problem of nonlocality in such theories. It follows that, despite some recent criticism, the assumption plays an essential role in the derivation of Bell's inequalities.
The idea of entanglement seems to be generally confirmed. The missing piece is experimental results for independently generated particles. Pending that information one can only conclude that it is likely but not certain that entanglements of photons exists.
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