Measurement problem
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The measurement problem is the key set of questions that every interpretation of quantum mechanics must address. The wavefunction in quantum mechanics evolves according to the Schrödinger equation into a linear superposition of different states, but the 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.
The best known example is the "paradox" of the Schrödinger's cat: 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 an alive cat, or a dead cat. After that measurement the cat stays alive or dead. The question is: how are the probabilities converted to an actual, sharply well-defined outcome?
Different interpretations of quantum mechanics propose different solutions of the measurement problem.
- The Copenhagen interpretation is rooted in the philosophical positivism. It claims that quantum mechanics deals only with the probabilities of observable quantities; all other questions are considered "unscientific" (meta-physical). Copenhagen regards the wavefunction as a mathematical tool used in the calculation of probabilities with no physical existence (not an element of reality). Waveform collapse is therefore a meaningless concept; the waveform only describes a specific experiment.
- Consciousness causes collapse proposes that the presence of a conscious being causes the wavefunction to collapse. However, this interpretation depends on a definition of "consciousness". This interpretation, however, is seen as unscientific by critics due to its inability to be falsified.
- The measurement apparatus is a macroscopic object. Perhaps, it is the macroscopic character of the apparata that allows us to replace the logic of quantum mechanics with the classical intuition where the positions are well-defined quantities.
Some interpretations claim that the latter approach was put on firm ground in the 1980s by the phenomenon of quantum decoherence. It is claimed that decoherence allows physicists 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 ("Copenhagen done right"). Quantum decoherence does not describe the actual process of the wavefunction collapse, but it explains the conversion of the quantum probabilities (that are able to interfere) to the ordinary classical probabilities.
Hugh Everett's relative state interpretation, also referred to as the many-worlds interpretation, attempts to avoid the problem by suggesting it is an illusion. Under this system 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 and others and renamed the many-worlds interpretation. Everett/DeWitt's interpretation posits a single universal wavefunction, but with the added proviso that "reality" from the point of view of any single observer, "you", is defined as a single path in time through the superpositions. That is, "you" have a history that is made of the outcomes of measurements you made in the past, but there are many other "yous" with slight variations in history. Under this system our reality is one of many similar ones.
The Bohm interpretation 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 create a "quantum potential" that influences the motion of the "real" particle in such a way that the probability distribution for the particle remains consistent with the predictions of the orthodox quantum mechanics. According to the Bohm interpretation combined with the von Neumann theory of measurement in quantum mechanics, once the particle is observed, other wave-function channels remain empty and thus ineffective, but there is no true wavefunction collapse. Decoherence provides that this ineffectiveness is stable and irreversible, which explains the apparent wavefunction collapse.
[edit] References
- Schlosshauer, Maximilian (2004). "Decoherence, the Measurement Problem, and Interpretations of Quantum Mechanics". Rev. Mod. Phys. 76: 1267. arXiv:quant-ph/0312059, doi:10.1103/RevModPhys.76.1267.
[edit] See also
[edit] External links
- This Quantum World What is quantum mechanics trying to tell us about the nature of Nature?
- The Quantum Measurement Problem Two presentations: a non-technical and a more technical presentation.
