Any modern scientific theory has at least one instrumental explanation, which links the mathematical formal system with the prediction of experimental practice. In quantum mechanics, the most common instrumentalism description is the assertion of the statistical law between the state preparation process and the measurement process. That is to say, if a real number is measured many times, starting from the same initial state every time, then the measurement result is a well-defined probability distribution in the real number domain. In addition, quantum mechanics provides a calculation tool to calculate the statistical characteristics of distribution, such as expected value.
The measurement of computing system S needs Hilbert space H in complex number field. When the system S is prepared as a pure state, it is represented as a vector in H, and the measurable quantity is represented as self-adjoint operator on H: they are called observable quantities.
When s is in ψ state, repeated measurements of the observable value A produce a distribution of values. The expected value of this distribution is given by the following expression
As long as we know how to represent the initial state with Hilbert space vector and the measured value with observable value (self-adjoint operator), this mathematical formula provides a simple and direct method for calculating the statistical properties of experimental results.
For example, find that the system is in a given state? The probability of is obtained by calculating the expected values of the following (first-order) projection operators.
The probability obtained is a non-negative real number given by the following formula
Instrumental description can also be regarded as explanation, but it is an abuse of language. Moreover, this usage is somewhat misleading, because instrumentalism directly avoids any explanation; In other words, it did not try to answer the question of why.
2. Classification adopted by Einstein [Edit]
An explanation can be described by several features proposed by Einstein, such as:
reality
Categorization
Local reality
decisive
In order to explain these attributes, it is necessary to further explain the provided images. Interpretation is considered as the correspondence between the elements in the mathematical formal system M and the elements in the interpretation structure I, where
The mathematical formal system M consists of these elements: ket vector mechanism in Hilbert space, self-adjoint operator acting on ket vector space, unitary time correlation of ket vector, and measure operation. In this system, the measurement operation is the transformation from ket vector to probability distribution (see quantum operator for the formal expression of this concept).
Interpretation structure I consists of these elements: states, transitions between states, measurement operations and possible information about the spatial existence of these elements. A measurement operation represents an operation to obtain a value, which may change the state of the system. Spatial information is represented by states, which are represented by functions in the configuration space. Transitions may be non-deterministic, probabilistic, or may have an infinite number of states.
The key to interpretation is whether the elements of I should be physically true. Therefore, the purely instrumental perspective of quantum mechanics explained earlier is not an explanation, because it does not explain the physically real elements.
Realism and completeness originated from Einstein and two other people discussing EPR paradox. In that article, the author put forward the concepts of real elements and the completeness of physical theory. These three people describe real elements as quantities whose values can be accurately predicted before being measured or otherwise influenced, and define a complete physical theory as a theory that gives an explanation to each physical element. From the semantic point of view, if every element in the explanatory structure appears in the mathematical system, then the explanation is complete. Reality is also the attribute of every element in the mathematical system. An element is real if it has corresponding explanatory structural elements. For example, in some explanations of quantum mechanics (such as the multi-world explanation), the ket vector representing the state of the system corresponds to the elements of physical reality, but not in other explanations.
Decisiveness is to describe the nature of the state changing with time. That is to say, the state at a certain time in the future is a function of the current state (see time evolution). It is not obvious whether an explanation is decisive, because the choice of time parameters is uncertain. Furthermore, any theory may have two explanations, decisive and inconclusive.
The local reality includes two aspects:
The measured value is the function value in the state space. In other words, values are real elements.
The propagation speed of measurement results does not exceed some general limit (such as the speed of light). To this end, the measurement operations in the interpretation structure must be localized.
John bell put forward a kind of local reality expressed by the theory of local hidden variables.
Bell theorem combined with experimental test limits the properties that quantum theory can have. The main conclusion is that quantum mechanics cannot satisfy both the principle of locality and the principle of counterfactual certainty.
3, Copenhagen interpretation [edit]
Main project: Copenhagen interpretation
Copenhagen interpretation is the "standard" interpretation of quantum mechanics expressed by niels bohr and Werner Heisenberg when they cooperated in Copenhagen around 1927. Bohr and Heisenberg extended the probability explanation of wave function originally proposed by Max Bonn. Copenhagen's explanation will be "where was it before I measured its position?" There is no point in excluding this kind of problem. The measurement process randomly selects one from various possibilities in a manner consistent with the well-defined probability assigned to each state. According to this explanation, the observer or device outside the quantum system is the cause of the wave function collapse. As paul davis said, "Reality exists in observation, not in electrons".
4, multi-world interpretation [edit]
Subject: Multi-world Interpretation
In the multi-world interpretation, the universal wave function satisfies the same decisive invertibility law at every moment. In particular, there is no (deterministic and irreversible) wave function collapse. The phenomena related to measurement are explained by decoherence. Decoherence occurs when the state interacts with the environment, and entanglement occurs at this time. This process repeatedly splits the universe into mutually invisible and spaced histories-different universes in a larger multiverse.
5, consistent historical interpretation [edit]
Subject: Historical Interpretation of Consistency
The consistent historical explanation extends the traditional Copenhagen explanation and tries to provide a natural explanation for quantum cosmology. This theory is based on a consistency standard, which allows a certain description of the system, so that the probabilities of various histories conform to the sum of classical probabilities. This explanation claims to conform to the Schrodinger equation.
According to this explanation, the purpose of quantum mechanics theory is to predict the relative probability between different histories.
6, ensemble interpretation, or statistical interpretation [edit]
Main projects: ensemble interpretation
Ensemble interpretation, also called statistical interpretation, is a minimalist interpretation. In other words, it only makes the least assumptions about the standard mathematical system. It adopts the statistical interpretation of Bonn to the maximum extent. This explanation holds that the wave function cannot be applied to a single system, such as a single particle. It is only an abstract statistic, which can only be applied to the ensemble of similar systems (or particles) (that is, a large number of groups). Perhaps the most famous supporter of this explanation is Einstein:
Trying to imagine the description of quantum theory as a complete description of individual system will lead to abnormal theoretical explanation. As long as we agree that the description of quantum theory is made for an ensemble of systems rather than a single system, we don't need to think so.
-Einstein In Albert Einstein: Philosopher-Scientist, ed. P.A. Hill (Harper & new york Row)
At present, the most famous advocate of ensemble interpretation is Leslie E. Valentin, a professor at Simon Fraser University and the author of the master's textbook Quantum Mechanics, a Modern Development. Video clip of Akira Nomura 1 There are experiments to illustrate ensemble interpretation. [2] It can also be seen from the double-slit experiment of multi-electron ensemble that the ensemble must be described because the wave function of quantum mechanics describes a complete interference image.
7, de Broglie-Bohm theory [edit]
Main Project: De Broglie-Bohm Theory
De Broglie-Bohm theory was put forward by Louis de Broglie and then extended to measurement theory by David Bohm. Particles always have positions and are guided by wave functions. The wave function evolves according to Schrodinger wave equation and never collapses. The theory adopts a single space-time and is nonlocal and inconclusive. At the same time, determining the position and velocity of particles conforms to the limitation of general uncertainty principle. This theory is generally regarded as a hidden variable theory, which satisfies Bell inequality by adopting nonlocality. Because the particle has a definite position at any time, the measurement problem is solved. [3] Collapse is interpreted as an external phenomenon. [4]
8, relational quantum mechanics [edit]
Main Project: Relational Quantum Mechanics
The basic idea of relational quantum mechanics follows the special theory of relativity, which holds that different observers may give different explanations for the same group of events. For example, for an observer at a certain moment, the system may be in a unique "collapse" characteristic state; However, for another observer at the same time, the system may be in the superposition of two or more states. Therefore, relational quantum mechanics holds that to make quantum mechanics a complete theory, "state" not only describes the observed system itself, but also describes the relationship or correlation between the system and the observer. The state vector of quantum mechanics becomes the observer's dependence on some internal degrees of freedom of the observed system. Moreover, relational quantum mechanics holds that this applies to all physical objects-whether they are macroscopic or not. Any "measurement event" is simply regarded as a general physical interaction, that is, the establishment of that kind of correlation. Therefore, the physical content of the theory involves not only the objects themselves, but also the relationship between them. [5][6]
There is also a relationship treatment of quantum mechanics, which is an interpretation that imitates David Bohm's special theory of relativity [7]. It regards the measurement event as establishing a relationship between the quantum field and the measuring instrument. In this way, the ambiguity inherent in the application of Heisenberg uncertainty principle is avoided. [8]
9, the basic ring [edit]
The basic idea of this explanation is the following empirical fact that Louis de Broglie noticed about wave-particle duality: elementary particles appear repeatedly in time and space because their energy and momentum are determined by Planck constant. This means that any natural system can be described by the basic space-time ring. This repetition is applied as a semi-classical quantization condition, which is similar to the quantization of infinite deep potential wells. The obtained ring mechanics is formally equivalent to the standard formal system of quantum mechanics and Feynman's formal system [9]. See [10] for comments. It is an improvement of Bohr-Sommerfeld quantization (or vibration). As Hooft put forward decisively [1 1], quantum mechanics is regarded as a statistical approximation of extremely fast periodic motion. This concept has applications in modern physics, such as the geometric description of metric invariants [12] and the explanation of Maldacena duality [13].
10, transaction interpretation [edit]
Main item: transaction explanation
The transactional interpretation of quantum mechanics, also known as TIQM, was put forward by john kramer, who was inspired by Le Feynman's absorber theory. [14] He described the interaction of quantum mechanics with the standing wave formed by delayed wave (propagating along time) and advanced wave (propagating against time). The proposer claims that this avoids the philosophical obstacle of Copenhagen interpretation, avoids introducing observers and solves other paradoxes of quantum mechanics.
1 1, random interpretation [edit]
Subject: random interpretation
1966, Edward Nelson, a professor at Princeton University, proposed a completely classical derivation and explanation of the Schrodinger equation based on Brownian motion. [15] Previously, R Felt (1933), I F é Nyes (1952) and Walter Weizel( 1953) made similar views, and Nelson also quoted them in the article. Recently, Pa Wen has done some work on random interpretation. [16] Rumen Cekov proposed another random interpretation. [ 17]
12, objective collapse theory [edit]
Subject: objective collapse theory
The objective collapse theory regards wave function and collapse process as ontological objectivity, which is different from Copenhagen explanation. In this theory, crashes occur randomly ("spontaneous localization") or when a certain physical threshold is reached. Observers do not play a special role. Therefore, this is a real, uncertain and non-hidden variable theory. The standard quantum theory does not specify the mechanism of collapse. If the objective collapse is correct, it needs to be expanded, that is to say, the objective collapse is more a theory than an explanation. Examples of this explanation include GRW theory [18] and Penrose explanation. [ 19]
13, von Neumann/Wigner Interpretation: Consciousness leads to collapse [Editor]
Main project: quantum physical and mental problems
John von neumann deeply analyzed the so-called measurement problem in his book Mathematical Basis of Quantum Mechanics. He believes that the whole physical universe follows the Schrodinger equation (cosmic wave function). He also explained how the measurement caused the wave function to collapse. [20] eugene wigner expanded this view. He believed that the consciousness of human experimenters (even the consciousness of dogs) played a key role in the collapse, but he later gave up this explanation. [2 1][22]
The variant explained by von Neumann is:
Subjective collapse research
The principle of collapse caused by consciousness is the intersection of quantum mechanics and physical and mental problems; Researchers try to detect conscious events related to physical events-according to quantum theory, conscious events should lead to the collapse of wave functions. But so far, the research has not reached a clear conclusion. [23][24]
Participatory selection principle
Main project: anthropic principle
John wheeler's Participatory Anthropic Principle holds that consciousness plays the role of turning the universe into reality. [25]
Other physicists explained their own variations on von Neumann's interpretation, including:
Henry P. Stapp (The Universe with Mind: Quantum Mechanics and Participating Observers)
Bruce Rosenbloom and Fred kutner (Quantum Mystery: Physics Encounters Consciousness)
Amit Goswami (self-conscious universe)
14, multi-heart interpretation [edit]
Main Project: Interpretation of Multiple Spirits
The polycentric interpretation of quantum mechanics is an extension of the multi-world interpretation. This explanation shows that the differences between multiple worlds should be placed on the spiritual level of individual observers.
15, quantum logic [edit]
Main project: quantum logic
Quantum logic can be regarded as propositional logic, which is suitable for understanding the anomalies related to quantum measurement, especially the combination of measurement operations of complementary variables. This research and its name were put forward by Garrett boekhoff and john von neumann in 1936. Their starting point is to combine classical Boolean logic with the obvious inconsistency between quantum mechanics measurement and observation facts.
16, quantum information theory [edit]
Quantum information theory is an interdisciplinary subject of information science and quantum theory. It applies quantum mechanics to information science and technology, and provides a brand-new principle, method and approach for the development of information science. In the process of quantum information processing, the carrier of information is quantum state, so logical operation can be completed by directly regulating the quantum state of microsystem. The basis of quantum information theory is the principle of quantum mechanics. Transistors and integrated circuits are of course based on quantum mechanics, but in quantum information theory, its algorithm introduces the principles and methods of quantum mechanics, which is essentially different from classical theory. That is to say, the classical bits composed of binary 0 and 1 are extended to quantum bits containing complex numbers by using the superposition property of wave functions in quantum mechanics.
17, modal interpretation of quantum theory [edit]
18, spatio-temporal bifurcation theory [edit]
19, other notes [edit]
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