Measurement problem
Encyclopedia
The measurement problem in quantum mechanics
is the unresolved problem of how (or if) wavefunction collapse
occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wavefunction
in quantum mechanics
evolves according to the Schrödinger equation
into a linear superposition
of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the process under examination. Whatever that "something" may be does not appear to be explained by the basic theory.
To express matters differently (to paraphrase Steven Weinberg
), the wave function evolves deterministically – knowing the wave function at one moment, the Schrödinger equation determines the wave function at any later time. If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities? As a general question: How can one establish a correspondence between quantum and classical reality?
: a cat is apparently evolving into a linear superposition of basis vectors that can be characterized as an "alive cat" and states that can be described as a "dead cat". Each of these possibilities is associated with a specific nonzero probability amplitude; the cat seems to be in a "mixed" state. However, a single, particular observation of the cat does not measure the probabilities: it always finds either a living cat, or a dead cat. After the measurement the cat is definitively alive or dead. The question is: How are the probabilities converted into an actual, sharply well-defined outcome?
's many-worlds interpretation
attempts to avoid the problem by suggesting there is only one wavefunction, the superposition of the entire universe, and it never collapses—so there is no measurement problem. Instead the act of measurement is actually an interaction between two quantum entities, which entangle to form a single larger entity, for instance living cat/happy scientist. Everett also attempted to demonstrate the way that in measurements the probabilistic nature of quantum mechanics
would appear; work later extended by Bryce DeWitt
.
De Broglie–Bohm theory tries to solve the measurement problem very differently: this interpretation contains not only the wavefunction, but also the information about the position of the particle(s). The role of the wavefunction is to generate the velocity field for the particles. These velocities are such that the probability distribution for the particle remains consistent with the predictions of the orthodox quantum mechanics. According to de Broglie–Bohm theory, interaction with the environment during a measurement procedure separates the wave packets in configuration space which is where apparent wavefunction collapse
comes from even though there is no actual collapse. Decoherence analysis is one way to view this.
Erich Joos and Heinz-Dieter Zeh claim that the latter approach was put on firm ground in the 1980s by the phenomenon of quantum decoherence
. Zeh further claims that decoherence makes it possible to identify the fuzzy boundary between the quantum microworld and the world where the classical intuition is applicable. Quantum decoherence was proposed in the context of the many-worlds interpretation
, but it has also become an important part of some modern updates of the Copenhagen interpretation
based on consistent histories
. Quantum decoherence does not describe the actual process of the wavefunction collapse, but it explains the conversion of the quantum probabilities (that exhibit interference effects) to the ordinary classical probabilities. See, for example, Zurek, Zeh and Schlosshauer.
The present situation is slowly clarifying, as described in a recent paper by Schlosshauer as follows:
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
is the unresolved problem of how (or if) wavefunction collapse
Wavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...
occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
in quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
evolves according to the Schrödinger equation
Schrödinger equation
The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....
into a linear superposition
Quantum superposition
Quantum superposition is a fundamental principle of quantum mechanics. It holds that a physical system exists in all its particular, theoretically possible states simultaneously; but, when measured, it gives a result corresponding to only one of the possible configurations.Mathematically, it...
of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the process under examination. Whatever that "something" may be does not appear to be explained by the basic theory.
To express matters differently (to paraphrase Steven Weinberg
Steven Weinberg
Steven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
), the wave function evolves deterministically – knowing the wave function at one moment, the Schrödinger equation determines the wave function at any later time. If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities? As a general question: How can one establish a correspondence between quantum and classical reality?
Example
The best known is the "paradox" of the Schrödinger's catSchrödinger's cat
Schrödinger's cat is a thought experiment, usually described as a paradox, devised by Austrian physicist Erwin Schrödinger in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The scenario presents a cat that might be...
: a cat is apparently evolving into a linear superposition of basis vectors that can be characterized as an "alive cat" and states that can be described as a "dead cat". Each of these possibilities is associated with a specific nonzero probability amplitude; the cat seems to be in a "mixed" state. However, a single, particular observation of the cat does not measure the probabilities: it always finds either a living cat, or a dead cat. After the measurement the cat is definitively alive or dead. The question is: How are the probabilities converted into an actual, sharply well-defined outcome?
Interpretations
Hugh EverettHugh Everett
Hugh Everett III was an American physicist who first proposed the many-worlds interpretation of quantum physics, which he termed his "relative state" formulation....
's many-worlds interpretation
Many-worlds interpretation
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
attempts to avoid the problem by suggesting there is only one wavefunction, the superposition of the entire universe, and it never collapses—so there is no measurement problem. Instead the act of measurement is actually an interaction between two quantum entities, which entangle to form a single larger entity, for instance living cat/happy scientist. Everett also attempted to demonstrate the way that in measurements the probabilistic nature of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
would appear; work later extended by Bryce DeWitt
Bryce DeWitt
Bryce Seligman DeWitt was a theoretical physicist renowned for advancing gravity and field theories.-Biography:...
.
De Broglie–Bohm theory tries to solve the measurement problem very differently: this interpretation contains not only the wavefunction, but also the information about the position of the particle(s). The role of the wavefunction is to generate the velocity field for the particles. These velocities are such that the probability distribution for the particle remains consistent with the predictions of the orthodox quantum mechanics. According to de Broglie–Bohm theory, interaction with the environment during a measurement procedure separates the wave packets in configuration space which is where apparent wavefunction collapse
Wavefunction collapse
In quantum mechanics, wave function collapse is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer...
comes from even though there is no actual collapse. Decoherence analysis is one way to view this.
Erich Joos and Heinz-Dieter Zeh claim that the latter approach was put on firm ground in the 1980s by the phenomenon of quantum decoherence
Quantum decoherence
In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
. Zeh further claims that decoherence makes it possible to identify the fuzzy boundary between the quantum microworld and the world where the classical intuition is applicable. Quantum decoherence was proposed in the context of the many-worlds interpretation
Many-worlds interpretation
The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction, but denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternative histories and futures are real, each representing an...
, but it has also become an important part of some modern updates of the Copenhagen interpretation
Copenhagen interpretation
The Copenhagen interpretation is one of the earliest and most commonly taught interpretations of quantum mechanics. It holds that quantum mechanics does not yield a description of an objective reality but deals only with probabilities of observing, or measuring, various aspects of energy quanta,...
based on consistent histories
Consistent histories
In quantum mechanics, the consistent histories approach is intended to give a modern interpretation of quantum mechanics, generalising the conventional Copenhagen interpretation and providing a natural interpretation of quantum cosmology...
. Quantum decoherence does not describe the actual process of the wavefunction collapse, but it explains the conversion of the quantum probabilities (that exhibit interference effects) to the ordinary classical probabilities. See, for example, Zurek, Zeh and Schlosshauer.
The present situation is slowly clarifying, as described in a recent paper by Schlosshauer as follows:
- Several decoherence-unrelated proposals have been put forward in the past to elucidate the meaning of probabilities and arrive at the Born rule … It is fair to say that no decisive conclusion appears to have been reached as to the success of these derivations. …
- As it is well known, [many papers by Bohr insist upon] the fundamental role of classical concepts. The experimental evidence for superpositions of macroscopically distinct states on increasingly large length scales counters such a dictum. Only the physical interactions between systems then determine a particular decomposition into classical states from the view of each particular system. Thus classical concepts are to be understood as locally emergent in a relative-state sense and should no longer claim a fundamental role in the physical theory.
Further reading
See also
- Measurement in quantum mechanicsMeasurement in quantum mechanicsThe framework of quantum mechanics requires a careful definition of measurement. The issue of measurement lies at the heart of the problem of the interpretation of quantum mechanics, for which there is currently no consensus....
- Philosophy of physicsPhilosophy of physicsIn philosophy, the philosophy of physics studies the fundamental philosophical questions underlying modern physics, the study of matter and energy and how they interact. The philosophy of physics begins by reflecting on the basic metaphysical and epistemological questions posed by physics:...
- Quantum Zeno effectQuantum Zeno effectThe quantum Zeno effect is a name coined by George Sudarshan and Baidyanath Misra of the University of Texas in 1977 in their analysis of the situation in which an unstable particle, if observed continuously, will never decay. One can nearly "freeze" the evolution of the system by measuring it...
- Objective collapse theoryObjective collapse theoryObjective collapse theories are an approach to the interpretational problems of quantum mechanics. They are realistic, indeterministic and reject hidden variables...
- Wave function collapse
- Ghirardi-Rimini-Weber theoryGhirardi-Rimini-Weber theoryThe Ghirardi–Rimini–Weber theory, or GRW, is a collapse theory in quantum mechanics. GRW differs from other collapse theories by proposing that wave function collapse happens spontaneously. GRW is an attempt to avoid the measurement problem in quantum mechanics...
- Quantum decoherenceQuantum decoherenceIn quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. A consequence of this dephasing leads to classical or probabilistically additive behavior...
- EPR paradoxEPR paradoxThe EPR paradox is a topic in quantum physics and the philosophy of science concerning the measurement and description of microscopic systems by the methods of quantum physics...
- Quantum pseudo-telepathyQuantum pseudo-telepathyQuantum pseudo-telepathy is a phenomenon in quantum game theory resulting in anomalously high success rates in coordination games between separated players. These high success rates would require communication between the players in a purely classical world; however, the game is set up such that...
- Absolute time and spaceAbsolute time and spaceOriginally introduced by Sir Isaac Newton in the Philosophiæ Naturalis Principia Mathematica, the concepts of absolute time and space provided a theoretical foundation that facilitated Newtonian mechanics...
External links
- The Quantum Measurement Problem Two presentations: a non-technical and a more technical presentation.