We introduce a new approach in dealing with pattern recognition issue. Recognizing a pattern is definitely not the exploration of a new discovery but rather the search for already known patterns. In reading for example the same text written in a hand writing, letters can appear in different shapes. Still, the text decoding corresponds with interpreting the large variety of hand writings shapes with fonts. Quantum mechanics also offer a kind of interpretation tool. Although, with the superposition principle it is possible to compose an infinite number of states, yet, an observer by conducting a measurement reduces the number of observed states into the predetermined basis states. Not only that any state collapses into one of the basis states, quantum mechanics also possesses a kind of correction mechanism in a sense that if the measured state is “close enough” to one of the basis states, it will collapse with high probability into this predetermined state. Thus, we can consider the collapse mechanism as a reliable way for the observer to interpret reality into his frame of concepts. Both interpretation ideas, pattern recognition and quantum measurement are integrated in this paper to formulate a quantum pattern recognition measuring procedure.
We introduce a new approach in dealing with pattern recognition issue. Recognizing a pattern is definitely not the exploration of a new discovery but rather the search for already known patterns. In reading for example the same text written in a hand writing, letters can appear in different shapes. Still, the text decoding corresponds with interpreting the large variety of hand writings shapes with fonts. Quantum mechanics also offer a kind of interpretation tool. Although, with the superposition principle it is possible to compose an infinite number of states, yet, an observer by conducting a measurement reduces the number of observed states into the predetermined basis states. Not only that any state collapses into one of the basis states, quantum mechanics also possesses a kind of correction mechanism in a sense that if the measured state is “close enough” to one of the basis states, it will collapse with high probability into this predetermined state. Thus, we can consider the collapse mechanism as a reliable way for the observer to interpret reality into his frame of concepts. Both interpretation ideas, pattern recognition and quantum measurement are integrated in this paper to formulate a quantum pattern recognition measuring procedure.
In this paper, we will see that we can reformulate the purely classical probability theory, using similar language to the one used in quantum mechanics. This leads us to reformulate quantum mechanics itself using this different way of understanding probability theory, which in turn will yield a new interpretation of quantum mechanics. In this reformulation, we still prove the existence of none classical phenomena of quantum mechanics, such as quantum superposition, quantum entanglement, the uncertainty principle and the collapse of the wave packet. But, here, we provide a different interpretation of these phenomena of how it is used to be understood in quantum physics. The advantages of this formulation and interpretation are that it induces the same experimental results, solves the measurement problem, and reduces the number of axioms in quantum mechanics. Besides, it suggests that we can use new types of Q-bits which are more easily to manipulate.
In an interesting series of articles published few years ago Afshar and coworkers [1,2] reported an optical experiment in which they claimed to refute the well known N. Bohr principle of complementarity [3, 4]. Obviously this result, if justified, would constitute a serious attack against the orthodox interpretation of quantum mechanics (known as the Copenhagen interpretation). This work stirred much debate in different journals (see for examples references [5–12]). We think however that there are still some important misunderstandings concerning the interpretation of this experiment. In a preprint written originally in 2004 [5] (and following some early discussions with Afshar) we claimed already that the interpretation by Afshar et al. can be easily stated if we stay as close as possible from the texts written by Bohr. The aim of the present article (which was initially written in 2005 to precise a bit the thought developed in [5]) is to comment the interpretation discussed in [1]. We will in the following analyze the meaning of Bohr principle and show that far from disproving its content the experiment [1] is actually a complete confirmation of its general validity. The difficulties associated with the understanding of this principle are not new and actually complementarity created troubles even in Einstein mind [3] so that we are here in good company. To summarize a bit emphatically Bohr’s complementarity we here remind that this principle states that if one of a pair of non commuting observables of a quantum object is known for sure, then information about the second (complementary) is lost [3, 4, 15, 16]. This can be equivalently expressed as a kind of duality between different descriptions of the quantum system associated with different experimental arrangements which mutually exclude each other (read in particular [3,4]). Later in the discussion we will try to precise this definition but for the moment it is enough to illustrate the concepts by examples Consider for instance the well known Young double-pinholes interference experiment made with photons. The discrete nature of light precludes the simultaneous observation of a same photon in the aperture plane and in the interference pattern: the photon cannot be absorbed twice. This is already a trivial manifestation of the principle of Bohr. Here it implies that the two statistical patterns associated with the wave in the aperture plane and its Fourier (i. e., momentum) transform require necessarily different photons for their recording. It is in that sense that each experiment excludes and completes reciprocally the other. In the case considered before the photon is absorbed during the first detection (this clearly precludes any other detection). However even a non-destructive solution for detection implying entanglement with other quantum systems has a radical effect of the same nature: the complementarity principle is still valid. For example, during their debate Bohr and Einstein [3] discussed an ideal which-way experiment in which the recoil of the slits is correlated to the motion of the photon. Momentum conservation added to arguments based on the uncertainty relations are sufficient to explain how such entanglement photon-slits can erase fringes [15–19]. It is also important for the present discussion to remind that the principle of complementarity has a perfidious consequence on the experimental meaning of trajectory and path followed by a particle. Indeed the unavoidable interactions existing between photons and detectors imply that a trajectory existing independently of any measurement process cannot be unambiguously defined. This sounds even like a tragedy when we consider once again the two-holes experiment. Indeed for Bohr this kind of experiments shows definitely the essential element of ambiguity which is involved in ascribing conventional physical attributes to quantum systems. Intuitively (i. e., from the point of view of classical particle dynamic) one would expect that a photon detected in the focal plane of the lens must have crossed only one of the hole 1 or 2 before to reach its final destination. However, if this is true, one can not intuitively understand how the presence of the second hole (through which the photon evidently did not go) forces the photon to participate to an interference pattern (which obviously needs an influence coming from both holes). Explanations to solve this paradox have been proposed by de Broglie, Bohm, and others using concepts such as empty waves or quantum potentials [20, 21]. However all these explanations are in agreement with Bohr principle (since they fully reproduce quantum predictions) and can not be experimentally distinguished. Bohr and Heisenberg proposed for all needed purposes a much more pragmatic and simpler answer: don’t bother, the complementarity principle precludes the simultaneous observation of a photon trajectory and of an interference pattern. For Bohr [3]: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path
In recent years, the notion that information may be the basis for reality, rather than the other way around, has become more popular. Here we consider the issue within the context of a general relation between the role of physical objects against the background in shaping the pattern of distinctions that can then be translated into information. It is found that from this perspective, in classical physics substance is more fundamental than information, while in general relativity they are on an equal footing. Quantum superposition and collapse, on the other hand, introduce new considerations. A foundational principle is introduced to give an explanation for quantum superposition, and from this principle it becomes evident that to the extent that one frames the nature of quantum objects in terms of this dichotomy, in quantum theory information is more fundamental. This implies that the description of quantum objects in a superposition is dependent on features of the background, as these features set boundary conditions on such manifestations. Thus, if this principle really does underlie quantum mechanics, it means that the term ”background independent quantum theory ” has to be considered a contradiction, which has implications for the search for a quantum theory of gravity. 1
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.