Philosophia

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by Katie Howard

Quantum mechanics is the theory used to ‘describe’ the processes that take place in the micro-world. From the start quantum mechanics has been a ’strange’ theory, in the sense that it seemed to contradict in various ways the image of a micro-world consisting of ‘objects’ moving around in a three dimensional space, and interacting with each other in this three dimensional space. So from the advent of the theory a lot of disagreement existed as to the ‘physical meaning’ of this quantum theory, and a lot of discussions of a philosophical nature have taken place among the founding fathers. Only however during the last years experiments have been performed that, independently of the strangeness of the quantum theory, confront us directly with the strangeness of the reality of the micro-world. We have in mind the experiments on the EPR problem. In our opinion to be able to ‘understand’ the reality of this micro-world, it will be necessary to introduce new concepts, and become aware of old ‘classical’ prejudices. Certainly in not such a radical way as proposed by what is sometimes called the ‘California interpretation’ of quantum mechanics, but also in not such a vague way as is proposed by what is called the ‘Copenhagen interpretation’ of quantum mechanics. Since we nowadays have very ’specific’ results, on very refined experiments, we should start ‘imagining’ how this ‘micro-reality’ is.  

Quantum Information is an interesting example where purely fundamental andeven philosophical research can lead to a new technology of information andcomputational science. Superposition and entanglement are the essence of a  new quantum information technology era. 

Numerous tests of quantum mechanical nonlocality has been performed over the last 20 years. In such experiments one uses the quantum mechanicalproperty that it is possible to create photon pairs in entangled states that reveal nothing about individual photon properties but still allow strong correlations between the measured quantities. Imagine a pair of subatomic particles (electrons, for example) bound together in a state with zero “spin” (rotational momentum). These particles, as it happens, can’t possess zero spin themselves; they must spin either “up” or “down.” It follows, because of the zero spin of their bound state, that the particles must individually possess different spin states — one must be “up,” the other “down.” We release our bound particles, and they shoot away from one another near the speed of light. They lie 600,000 kilometers apart within a second. If we measure the spin of one, we will instantly, across that vast distance, know the spin of its partner.

Bell compares the correlations found between our particles when we measure their spins in different locations, and shows they must communicate on some level. The separated particles not only know that they’re opposites. They know about the measurements we perform on their distant partners. Physicist Henry Stapp calls this “the greatest discovery of all science.” The story continues, for this entanglement is contagious.  

Quantum teleportation experiments by Anton Zeilinger and others show that particles can exchange their quantum states with others. Artur Ekert, of the Clarendon Laboratory,

Oxford, recently entangled two unrelated photons via an intermediate photon pair. Further, no limit exists on the number of particles that can become entangled. Noah Linden and Sandu Popescu at

Cambridge have studied larger groups; most of the connections they discovered are nonlocal. “Quantum theory isn’t just a tiny bit nonlocal,” says New Scientist. “It’s overwhelmingly nonlocal. Nonlocality is the rule for our universe.”An entangled state of two two-state systems is generally expressed as
,where 0 and 1 label the two possible states of our subsystems. We see that an entangled state is a – possibly nonlocal – common superposition of at least two subsystems. Superpositions of more than two subsystems are usually called Greenberger-Horne-Zeilinger states, e.g.:We will only be concerned with maximally entangled states (where each subsystem is in a completely mixed state), and I will try to demonstrate the various entanglements that can be achieved with photons.There are various ways in which photons can be entangled. We can choose either their momentum (direction), or polarization, or their emission time, and nowadays even entanglement of their orbital angular momentum states was shown. We will analyze the perplexing quantum nonlocality in terms of the realistic picture of quantum motion. Quantum information is physical information that is held in the state of a quantum system. However, unlike classical states, a quantum system can actually use the features of superposition and entanglement. Up to now manyexperiments have been performed to demonstrate enhanced quantum communication and quantum computation by using these quantum phenomena. Since these early achievements, the field of quantum information processing has very much advanced. New schemes and techniques allow the generation and manipulation of entangled photon pairs and even three- and four-photon states. 70 years ago, in 1935, Einstein, Podolsky and Rosen (EPR) argued that quantum theory [8] could not possibly be complete. They showed that one could infer perfectly complementary properties by performing a corresponding measurement on the distant particle that is quantum-mechanically entangled with the first one.Based firmly on plausible assumptions about locality, realism, and theoreticalcompleteness they further argued that quantum states cannot be a complete description of physical reality, but rather give only a statistical one of an ensemble of intrinsically different quantum systems. It was not until almost 30 years later that the EPR program could be formulated in terms of an experimentally-testable prediction referring to the landmark discovery of John Bell [9] that the EPR’s premises of locality and realism put measurable limits on the strength of correlations between outcomes of remote measurements on a pair of systems. These limits are known as

Bell inequalities and quantum mechanics does not satisfy them.Probably the best known Bell-type inequality is the Clauer-Horne-Shimony-Holt  (CHSH) [10] inequality. The two receivers, Alice and Bob, choose randomly between two measurement settings, A1 or A2 and B1 or B2, where each of these measurements has only two possible outcomes, +1 and -1. If the particles behave according to any local hidden variable model, the correlations have a maximum limit.We have to mention another train of happenings that lead to even more obscurification of the real meaning of the EPR reasoning. Somebody could say: “All right, I follow your argument, coming to the conclusion that the nature of the incompleteness of quantum mechanics already touched by a reasoning ex absurdum in the original EPR paper is the impossibility for quantum mechanics to describe separated quantum entities. But, did the EPR experiments, culminating the experiment of Alain Aspect in 1982, not show, that exactly the situation considered by Einstein, Podolsky and Rosen in their paper, and later reformulated by David Bohm for entangled spins, prove that quantum mechanics ‘does’ deliver a good description of the two quantum entities flying apart after having interacted? Was this not all what is was about? Namely that, since

Bell inequalities still got violated by the far apart coupled spin entities, it is true that quantum mechanics delivers a good model for this situation?” The answer is ‘yes’ and ‘no’ and hence needs some explanation. At the time that Einstein proposed the example of quantum entities having interacted and then flying apart, one would have guessed that being sufficiently apart, the entities would start to behave as separated quantum entities. This was still the case when Bohm proposed the spin model and

Bell derived his inequalities. The experiments have shown that in this typical situation of quantum entities having interacted and then flying apart it is ‘possible’, making a big effort, to have the quantum entities flying apart while still remaining non separated entities. This quantum effect has meanwhile been called nonlocality. So the experiments prove that quantum nonlocality (or entanglement) can be retained for quantum entities being distances apart that are of a macroscopic nature, and were ‘at first sight’ one would not expect this to happen. This is a very interesting and intriguing possibility offered by quantum entities, and we analyse it in great length in the section “Nonlocality, entanglement and the role of space”. But it has very little to do with the EPR reasoning. Einstein, Podolsky and Rosen, to be able to make their reasoning, need the situation of quantum entities that fly apart, and do get separated after a while. Only on such separated entities the reasoning can be made. The reasoning can not be made on entities that fly apart and remain nonseparated or entangled. This does not mean that I underestimate the findings of the experiments (as can be seen in the space I give to them in section “Nonlocality, entanglement and the role of space”), the nonlocality effect is one of the most important ones identified for quantum entities in the last decades. But of course, also experiments could be made where the quantum entities that fly apart do get separated and the entanglement gets broken. They have never been made consciously, because the experimentators involved did not understand that these would be the situations leading to the Einstein Podolsky Rosen paradox. But obviously most of the badly performed EPR experiments will separate the flying apart quantum entities. Hence, the EPR reasoning needs these experimental situation where entanglement gets broken, and the flying apart entities get separated, and that is the physical situation that reveals the incompleteness of quantum mechanics. The incompleteness of quantum mechanics is not revealed in the physical situation of quantum entities flying apart and remaining nonseparated, which means that if these situations are well described by quantum mechanics, as the violation of

Bell inequalities proves, these is no contradiction. The incompleteness of standard quantum mechanics of not being able to deliver a model for the joint entity consisting of two separated quantum entities is not revealed on the level of the states, but on the level of the properties (represented by orthogonal projections in standard quantum mechanics), and the dynamics.