Philosophers
Mortimer Adler Rogers Albritton Alexander of Aphrodisias Samuel Alexander William Alston Anaximander G.E.M.Anscombe Anselm Louise Antony Thomas Aquinas Aristotle David Armstrong Harald Atmanspacher Robert Audi Augustine J.L.Austin A.J.Ayer Alexander Bain Mark Balaguer Jeffrey Barrett William Belsham Henri Bergson George Berkeley Isaiah Berlin Richard J. Bernstein Bernard Berofsky Robert Bishop Max Black Susanne Bobzien Emil du BoisReymond Hilary Bok Laurence BonJour George Boole Émile Boutroux F.H.Bradley C.D.Broad Michael Burke Lawrence Cahoone C.A.Campbell Joseph Keim Campbell Rudolf Carnap Carneades Ernst Cassirer David Chalmers Roderick Chisholm Chrysippus Cicero Randolph Clarke Samuel Clarke Anthony Collins Antonella Corradini Diodorus Cronus Jonathan Dancy Donald Davidson Mario De Caro Democritus Daniel Dennett Jacques Derrida René Descartes Richard Double Fred Dretske John Dupré John Earman Laura Waddell Ekstrom Epictetus Epicurus Herbert Feigl Arthur Fine John Martin Fischer Owen Flanagan Luciano Floridi Philippa Foot Alfred Fouilleé Harry Frankfurt Richard L. Franklin Michael Frede Gottlob Frege Peter Geach Edmund Gettier Carl Ginet Alvin Goldman Gorgias Nicholas St. John Green H.Paul Grice Ian Hacking Ishtiyaque Haji Stuart Hampshire W.F.R.Hardie Sam Harris William Hasker R.M.Hare Georg W.F. Hegel Martin Heidegger Heraclitus R.E.Hobart Thomas Hobbes David Hodgson Shadsworth Hodgson Baron d'Holbach Ted Honderich Pamela Huby David Hume Ferenc Huoranszki William James Lord Kames Robert Kane Immanuel Kant Tomis Kapitan Jaegwon Kim William King Hilary Kornblith Christine Korsgaard Saul Kripke Andrea Lavazza Christoph Lehner Keith Lehrer Gottfried Leibniz Jules Lequyer Leucippus Michael Levin George Henry Lewes C.I.Lewis David Lewis Peter Lipton C. Lloyd Morgan John Locke Michael Lockwood E. Jonathan Lowe John R. Lucas Lucretius Alasdair MacIntyre Ruth Barcan Marcus James Martineau Storrs McCall Hugh McCann Colin McGinn Michael McKenna Brian McLaughlin John McTaggart Paul E. Meehl Uwe Meixner Alfred Mele Trenton Merricks John Stuart Mill Dickinson Miller G.E.Moore Thomas Nagel Otto Neurath Friedrich Nietzsche John Norton P.H.NowellSmith Robert Nozick William of Ockham Timothy O'Connor Parmenides David F. 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Jay Wallace W.G.Ward Ted Warfield Roy Weatherford William Whewell Alfred North Whitehead David Widerker David Wiggins Bernard Williams Timothy Williamson Ludwig Wittgenstein Susan Wolf Scientists Michael Arbib Walter Baade Bernard Baars Leslie Ballentine Gregory Bateson John S. Bell Mara Beller Charles Bennett Ludwig von Bertalanffy Susan Blackmore Margaret Boden David Bohm Niels Bohr Ludwig Boltzmann Emile Borel Max Born Satyendra Nath Bose Walther Bothe Hans Briegel Leon Brillouin Stephen Brush Henry Thomas Buckle S. H. Burbury Donald Campbell Anthony Cashmore Eric Chaisson JeanPierre Changeux Arthur Holly Compton John Conway John Cramer E. P. Culverwell Olivier Darrigol Charles Darwin Richard Dawkins Terrence Deacon Lüder Deecke Richard Dedekind Louis de Broglie Max Delbrück Abraham de Moivre Paul Dirac Hans Driesch John Eccles Arthur Stanley Eddington Gerald Edelman Paul Ehrenfest Albert Einstein Hugh Everett, III Franz Exner Richard Feynman R. A. Fisher Joseph Fourier Philipp Frank Lila Gatlin Michael Gazzaniga GianCarlo Ghirardi J. Willard Gibbs Nicolas Gisin Paul Glimcher Thomas Gold A.O.Gomes Brian Goodwin Joshua Greene Jacques Hadamard Mark Hadley Patrick Haggard Stuart Hameroff Augustin Hamon Sam Harris Hyman Hartman JohnDylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Art Hobson Jesper Hoffmeyer E. T. Jaynes William Stanley Jevons Roman Jakobson Pascual Jordan Ruth E. Kastner Stuart Kauffman Martin J. Klein Simon Kochen Hans Kornhuber Stephen Kosslyn Ladislav Kovàč Leopold Kronecker Rolf Landauer Alfred Landé PierreSimon Laplace David Layzer Benjamin Libet Seth Lloyd Hendrik Lorentz Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau James Clerk Maxwell Ernst Mayr John McCarthy Ulrich Mohrhoff Jacques Monod Emmy Noether Abraham Pais Howard Pattee Wolfgang Pauli Massimo Pauri Roger Penrose Steven Pinker Colin Pittendrigh Max Planck Susan Pockett Henri Poincaré Daniel Pollen Ilya Prigogine Hans Primas Adolphe Quételet Jürgen Renn/a> Juan Roederer Jerome Rothstein David Ruelle Tilman Sauer Erwin Schrödinger Aaron Schurger Claude Shannon David Shiang Herbert Simon Dean Keith Simonton B. F. Skinner Roger Sperry John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark William Thomson (Kelvin) Giulio Tononi Peter Tse Vlatko Vedral Heinz von Foerster John von Neumann John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss John Wheeler Wilhelm Wien Norbert Wiener Eugene Wigner E. O. Wilson H. Dieter Zeh Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium 
The Measurement Problem
The "Problem of Measurement" in quantum mechanics has been defined in various ways, originally by scientists, and more recently by philosophers of science who question the "foundations of quantum mechanics."
Measurements are described with diverse concepts in quantum physics such as:
The original problem, said to be a consequence of Niels Bohr's "Copenhagen interpretation" of quantum mechanics, was to explain how our measuring instruments, which are usually macroscopic objects and treatable with classical physics, can give us information about the microscopic world of atoms and subatomic particles like electrons and photons. Bohr's idea of "complementarity" insisted that a specific experiment could reveal only partial information  for example, a particle's position. "Exhaustive" information requires complementary experiments, for example to also determine a particle's momentum (within the limits of Werner Heisenberg's indeterminacy principle). Some define the problem of measurement simply as the logical contradiction between two laws describing the motion of quantum systems; the unitary, continuous, and deterministic time evolution of the Schrödinger equation versus the nonunitary, discontinuous, and indeterministic collapse of the wave function. John von Neumann saw a problem with two distinct (indeed, opposing) processes. The mathematical formalism of quantum mechanics provides no way to predict when the wave function stops evolving in a unitary fashion and collapses. Experimentally and practically, however, we can say that this occurs when the microscopic system interacts with a measuring apparatus. Others define the measurement problem as the failure to observe macroscopic superpositions. Decoherence theorists (e.g., H. Dieter Zeh and Wojciech Zurek, who use various nonstandard interpretations of quantum mechanics that deny the projection postulate  quantum jumps  and even the existence of particles), define the measurement problem as the failure to observe macroscopic superpositions such as Schrödinger's Cat. Unitary time evolution of the wave function according to the Schrödinger wave equation should produce such macroscopic superpositions, they claim.
Information physics treats a measuring apparatus quantum mechanically by describing parts of it as in a metastable state like the excited states of an atom, the critically poised electrical potential energy in the discharge tube of a Geiger counter, or the supersaturated water and alcohol molecules of a Wilson cloud chamber. (The pibond orbital rotation from cis to trans in the lightsensitive retinal molecule is an example of a critically poised apparatus). Excited (metastable) states are poised to collapse when an electron (or photon) collides with the sensitive detector elements in the apparatus. This collapse is macroscopic and irreversible, generally a cascade of quantum events that release large amounts of energy, increasing the (Boltzmann) entropy. But in a "measurement" there is also a local decrease in the entropy (negative entropy or information). The global entropy increase is normally orders of magnitude more than the small local decrease in entropy (an increase in stable information or Shannon entropy) that constitutes the "measured" experimental data available to human observers.
The creation of new information in a measurement thus follows the same two core processes of all information creation  quantum cooperative phenomena and thermodynamics. These two are involved in the formation of microscopic objects like atoms and molecules, as well as macroscopic objects like galaxies, stars, and planets. According to the correspondence principle, all the laws of quantum physics asymptotically approach the laws of classical physics in the limit of large quantum numbers and large numbers of particles. Quantum mechanics can be used to describe large macroscopic systems. Does this mean that the positions and momenta of macroscopic objects are uncertain? Yes, it does, although the uncertainty becomes vanishingly small for large objects, it is not zero. Niels Bohr used the uncertainty of macroscopic objects to defeat Albert Einstein's several objections to quantum mechanics at the 1927 Solvay conference. But Bohr and Heisenberg also insisted that a measuring apparatus must be a regarded as a purely classical system. They can't have it both ways. Can the macroscopic apparatus also be treated by quantum physics or not? Can it be described by the Schrödinger equation? Can it be regarded as in a superposition of states? The most famous examples of macroscopic superposition are perhaps Schrödinger's Cat, which is claimed to be in a superposition of live and dead cats, and the EinsteinPodolskyRosen experiment, in which entangled electrons or photons are in a superposition of twoparticle states that collapse over macroscopic distances to exhibit properties "nonlocally" at speeds faster than the speed of light. These treatments of macroscopic systems with quantum mechanics were intended to expose inconsistencies and incompleteness in quantum theory. The critics hoped to restore determinism and "local reality" to physics. They resulted in some strange and extremely popular "mysteries" about "quantum reality," such as the "manyworlds" interpretation, "hidden variables," and signaling faster than the speed of light. We develop a quantummechanical treatment of macroscopic systems, especially a measuring apparatus, to show how it can create new information. If the apparatus were describable only by classical deterministic laws, no new information could come into existence. The apparatus need only be adequately determined, that is to say, "classical" to a sufficient degree of accuracy.
How Classical Is A Macroscopic Measuring Apparatus?
As Landau and Lifshitz described it in their 1958 textbook Quantum Mechanics"
The possibility of a quantitative description of the motion of an electron requires the presence also of physical objects which obey classical mechanics to a sufficient degree of accuracy. If an electron interacts with such a "classical object", the state of the latter is, generally speaking, altered. The nature and magnitude of this change depend on the state of the electron, and therefore may serve to characterise it quantitatively...The measurement problem was analyzed mathematically in 1932 by John von Neumann. Following the work of Niels Bohr and Werner Heisenberg, von Neumann divided the world into a microscopic (atomiclevel) quantum system and a macroscopic (classical) measuring apparatus. Von Neumann explained that two fundamentally different processes are going on in quantum mechanics.
Von Neumann claimed there is another major difference between these two processes. Process 1 is thermodynamically irreversible. Process 2 is reversible. This confirms the fundamental connection between quantum mechanics and thermodynamics that information physics finds at the heart of all information creation. Information physics can show quantum mechanically how process 1 creates information. Indeed, something like process 1 is always involved when any information is created, whether or not the new information is ever "observed" by a human being. Process 2 is deterministic and information preserving. Just as the new information recorded in the measurement apparatus cannot subsist unless a compensating amount of entropy is transferred away from the new information, something similar to Process 1b must happen in the mind of an observer if the new information is to constitute an "observation." It is only in cases where information persists long enough for a human being to observe it that we can properly describe the observation as a "measurement" and the human being as an "observer." So, following von Neumann's "process" terminology, we can complete his theory of the measuring process by adding an anthropomorphic Process 3  a conscious observer recording new information in a mind. This is only possible if there are two local reductions in the entropy (the first in the measurement apparatus, the second in the mind), both balanced by even greater increases in positive entropy that must be transported away from the apparatus and the mind, so the overall increase in entropy can satisfy the second law of thermodynamics. For some physicists, it is the wavefunction collapse that gives rise to the problem of measurement because its randomness prevents us from including it in the mathematical formalism of the deterministic Schrödinger equation in process 2. The randomness that is irreducibly involved in all information creation lies at the heart of human freedom. It is the "free" in "free will." The "will" part is as adequately and statistically determined as any macroscopic object.
Designing a Quantum Measurement Apparatus
The first step is to build an apparatus that allows different components of the wave function to evolve along distinguishable paths into different regions of space, where the different regions correspond to (are correlated with) the physical properties we want to measure. We then can locate a detector in these different regions of space to catch particles travelling a particular path. We do not say that the system is on a particular path in this first step. That would cause the probability amplitude wave function to collapse. This first step is reversible, at least in principle. It is deterministic and an example of von Neumann process 2. Let's consider the separation of a beam of photons into horizontally and vertically polarized photons by a birefringent crystal. We need a beam of photons (and the ability to reduce the intensity to a single photon at a time). Vertically polarized photons pass straight through the crystal. They are called the ordinary ray, shown in red. Horizontally polarized photons, however, are deflected at an angle up through the crystal, then exit the crystal back at the original angle. They are called the extraordinary ray, shown in blue.
Note that this first part of our apparatus accomplishes the separation of our two states into distinct physical regions. We have not actually measured yet, so a single photon passing through our measurement apparatus is described as in a linear combination (a superposition) of horizontal and vertical polarization states,
 ψ > = ( 1/√2)  h > + ( 1/√2)  v > (1) See the Dirac Three Polarizers experiment for more details on polarized photons.
An InformationPreserving, Reversible Example of Process 2
To show that process 2 is reversible, we can add a second birefringent crystal upside down from the first, but inline with the superposition of physically separated states,
Since we have not made a measurement and do not know the path of the photon, the phase information in the (generally complex) coefficients of equation (1) has been preserved, so when they combine in the second crystal, they emerge in a state identical to that before entering the first crystal (black arrow). Note that the two crystals can be treated classically, according to standard optics.
An InformationCreating, Irreversible Example of Process 1
But now suppose we insert something between the two crystals that is capable of a measurement to produce observable information. We need a detector that locates the photon in one of the two rays. We can now create an informationcreating, irreversible example of process 1. Suppose we insert something between the two crystals that is capable of a measurement to produce observable information. We need detectors, for example two chargecoupled devices that locate the photon in one of the two rays. We can write a quantum description of the CCDs, one measuring horizontal photons,  A_{h} > (shown as the blue spot), and the other measuring vertical photons,  A_{v} > (shown as the red spot).
We treat the detection systems quantum mechanically, and say that each detector has two eigenstates, e.g.,  A_{h0} >, corresponding to its initial state and correlated with no photons, and the final state  A_{h1} >, in which it has detected a horizontal photon. When we actually detect the photon, say in a horizontal polarization state with statistical probability 1/2, two "collapses" or "jumps" occur. The first is the jump of the probability amplitude wave function  ψ > of the photon in equation (1) into the horizontally polarized state  h >. The second is the quantum jump of the horizontal detector from  A_{h0} > to  A_{h1} >. These two happen together, as the quantum states have become correlated with the states of the sensitive detectors in the classical apparatus. One can say that the photon has become entangled with the sensitive horizontal detector area, so that the wave function describing their interaction is a superposition of photon and apparatus states that cannot be observed independently.  ψ > +  A_{h0} > =>  ψ, A_{h0} > =>  h, A_{h1} > These jumps destroy (unobservable) phase information, raise the (Boltzmann) entropy of the apparatus, and increase visible information (Shannon entropy) in the form of the visible spot. The entropy increase takes the form of a large chemical energy release when the photographic spot is developed (or a cascade of electrons in a CCD). Note that the birefringent crystal and the parts of the macroscopic apparatus other than the sensitive detectors are treated classically. We can animate these irreversible and reversible processes, We see that our example agrees with Von Neumann. A measurement which finds the photon in a specific state n is thermodynamically irreversible, whereas the deterministic evolution described by Schrödinger's equation is reversible. We thus establish a clear connection between a measurement, which increases the information by some number of bits (Shannon entropy), and the necessary compensating increase in the (Boltzmann) entropy of the macroscopic apparatus, and the cosmic creation process, where new particles form, reducing the entropy locally, and the energy of formation is radiated or conducted away as Boltzmann entropy. Note that the Boltzmann entropy can only be radiated away (ultimately into the night sky to the cosmic microwave background) because the expansion of the universe provides a sink for the entropy, as pointed out by David Layzer. Note also that this cosmic informationcreating process requires no conscious observer. The universe is its own observer.
The Boundary between the Classical and Quantum Worlds
Some scientists (John von Neumann and Eugene Wigner, for example) have argued that in the absence of a conscious observer, or some "cut" between the microscopic and macroscopic world, the evolution of the quantum system and the macroscopic measuring apparatus would be described deterministically by Schrödinger's equation of motion for the wave function  ψ + A > with the Hamiltonian H energy operator,
Our quantum mechanical analysis of the measurement apparatus in the above case allows us to locate the "cut" or "Schnitt" between the microscopic and macroscopic world at those components of the "adequately classical and deterministic" apparatus that put the apparatus in an irreversible stable state providing new information to the observer. John Bell drew a diagram to show the various possible locations for what he called the "shifty split." Information physics shows us that the correct location for the boundary is the first of Bell's possibilities.
The Role of a Conscious Observer
In 1941, Carl von Weizsäcker described the measurement problem as an interaction between a Subject and an Object, a view shared by the philosopher of science Ernst Cassirer.
Fritz London and Edmond Bauer made the strongest case for the critical role of a conscious observer in 1939: So far we have only coupled one apparatus with one object. But a coupling, even with a measuring device, is not yet a measurement. A measurement is achieved only when the position of the pointer has been observed. It is precisely this increase of knowledge, acquired by observation, that gives the observer the right to choose among the different components of the mixture predicted by theory, to reject those which are not observed, and to attribute thenceforth to the object a new wave function, that of the pure case which he has found. In 1961, Eugene Wigner made quantum physics even more subjective, claiming that a quantum measurement requires a conscious observer, without which nothing ever happens in the universe. When the province of physical theory was extended to encompass microscopic phenomena, through the creation of quantum mechanics, the concept of consciousness came to the fore again: it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness All that quantum mechanics purports to provide are probability connections between subsequent impressions (also called "apperceptions") of the consciousness, and even though the dividing line between the observer, whose consciousness is being affected, and the observed physical object can be shifted towards the one or the other to a considerable degree [cf., von Neumann] it cannot be eliminated. It may be premature to believe that the present philosophy of quantum mechanics will remain a permanent feature of future physical theories; it will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the conclusion that the content of the consciousness is an ultimate reality. Other physicists were more circumspect. Niels Bohr contrasted Paul Dirac's view with that of Heisenberg: These problems were instructively commented upon from different sides at the Solvay meeting, in the same session where Einstein raised his general objections. On that occasion an interesting discussion arose also about how to speak of the appearance of phenomena for which only predictions of statistical character can be made. The question was whether, as to the occurrence of individual effects, we should adopt a terminology proposed by Dirac, that we were concerned with a choice on the part of "nature," or, as suggested by Heisenberg, we should say that we have to do with a choice on the part of the "observer" constructing the measuring instruments and reading their recording. Any such terminology would, however, appear dubious since, on the one hand, it is hardly reasonable to endow nature with volition in the ordinary sense, while, on the other hand, it is certainly not possible for the observer to influence the events which may appear under the conditions he has arranged. To my mind, there is no other alternative than to admit that, in this field of experience, we are dealing with individual phenomena and that our possibilities of handling the measuring instruments allow us only to make a choice between the different complementary types of phenomena we want to study.Landau and Lifshitz said clearly that quantum physics was independent of any observer: In this connection the "classical object" is usually called apparatus, and its interaction with the electron is spoken of as measurement. However, it must be most decidedly emphasised that we are here not discussing a process of measurement in which the physicistobserver takes part. By measurement, in quantum mechanics, we understand any process of interaction between classical and quantum objects, occurring apart from and independently of any observer. David Bohm agreed that what is observed is distinct from the observer: If it were necessary to give all parts of the world a completely quantummechanical description, a person trying to apply quantum theory to the process of observation would be faced with an insoluble paradox. This would be so because he would then have to regard himself as something connected inseparably with the rest of the world. On the other hand,the very idea of making an observation implies that what is observed is totally distinct from the person observing it.And John Bell said: It would seem that the [quantum] theory is exclusively concerned about 'results of measurement', and has nothing to say about anything else. What exactly qualifies some physical systems to play the role of 'measurer'? Was the wavefunction of the world waiting to jump for thousands of millions of years until a singlecelled living creature appeared? Or did it have to wait a little longer, for some better qualified system...with a Ph.D.? If the theory is to apply to anything but highly idealised laboratory operations, are we not obliged to admit that more or less 'measurementlike' processes are going on more or less all the time, more or less everywhere? Do we not have jumping then all the time?
Three Essential Steps in a "Measurement" and "Observation"
We can distinguish three required elements in a measurement that can clarify the ongoing debate about the role of a conscious observer.
When we have only the first two, we can say metaphorically that the "universe is measuring itself," creating an information record of quantum collapse events. For example, every hydrogen atom formed in the early recombination era is a record of the time period when macroscopic bodies could begin to form. A certain pattern of photons records the explosion of a supernova billions of light years away. When detected by the CCD in a telescope, it becomes a potential observation. Craters on the back side of the moon recorded collisions with solar system debris that could become observations only when the first NASA mission circled the moon. For Teachers
For Scholars
John Bell on Measurement
It would seem that the [quantum] theory is exclusively concerned about 'results of measurement', and has nothing to say about anything else. What exactly qualifies some physical systems to play the role of 'measurer'? Was the wavefunction of the world waiting to jump for thousands of millions of years until a singlecelled living creature appeared? Or did it have to wait a little longer, for some better qualified system...with a Ph.D.? If the theory is to apply to anything but highly idealised laboratory operations, are we not obliged to admit that more or less 'measurementlike' processes are going on more or less all the time, more or less everywhere? Do we not have jumping then all the time?
Does [the 'collapse of the wavefunction'] happen sometimes outside laboratories? Or only in some authorized 'measuring apparatus'? And whereabouts in that apparatus? In the Einstein—PodolskyRosen—Bohm experiment, does 'measurement' occur already in the polarizers, or only in the counters? Or does it occur still later, in the computer collecting the data, or only in the eye, or even perhaps only in the brain, or at the brain—mind interface of the experimenter?
David Bohm on Measurement
In his 1950 textbook Quantum Theory, Bohm discusses measurement in chapter 22, section 12.
John von Neumann on Measurement
In his 1932 Mathematical Foundations of Quantum Mechanics (in German, English edition 1955) John von Neumann explained that two fundamentally different processes are going on in quantum mechanics.
Von Neumann claimed there is another major difference between these two processes. Process 1 is thermodynamically irreversible. Process 2 is reversible. This confirms the fundamental connection between quantum mechanics and thermodynamics that is explainable by information physics. Information physics establishes that process 1 may create information. It is always involved when information is created. Process 2 is deterministic and information preserving. The first of these processes has come to be called the collapse of the wave function. It gave rise to the socalled problem of measurement because its randomness prevents it from being a part of the deterministic mathematics of process 2.
Information physics has solved the problem of measurement by identifying the moment and place of the collapse of the wave function with the creation of an observable information structure. The presence of a conscious observer is not necessary. It is enough that the new information created is observable, should a human observer try to look at it in the future. Information physics is thus subtly involved in the question of what humans can know (epistemology).
The Schnitt
von Neumann described the collapse of the wave function as requiring a "cut" (Schnitt in German) between the microscopic quantum system and the observer. He said it did not matter where this cut was placed, because the mathematics would produce the same experimental results. There has been a lot of controversy and confusion about this cut. Some have placed it outside a room which includes the measuring apparatus and an observer A, and just before observer B makes a measurement of the physical state of the room, which is imagined to evolve deterministically according to process 2 and the Schrödinger equation. The case of Schrödinger's Cat is thought to present a similar paradoxical problem. von Neumann contributed a lot to this confusion in his discussion of subjective perceptions and "psychophysical parallelism, which was encouraged by Neils Bohr. Bohr interpreted his "complementarity principle" as explaining the difference between subjectivity and objectivity (as well as several other dualisms). von Neumann wrote: The difference between these two processes is a very fundamental one: aside from the different behaviors in regard to the principle of causality, they are also different in that the former is (thermodynamically) reversible, while the latter is not.
Quantum Mechanics, by Albert Messiah, on Measurement
Messiah says a detailed study of the mechanism of measurement will not be made in his book, but he does say this.
The dynamical state of such a system is represented at a given instant of time by its wave function at that instant. The causal relationship between the wave function γ(t_{o}) at an initial time t_{o}, and the wave function γ(t) at any later time, is expressed through the Schrödinger equation. However, as soon as it is subjected to observation, the system experiences some reaction from the observing instrument. Moreover, the above reaction is to some extent unpredictable and uncontrollable since there is no sharp separation between the observed system and the observing instrument. They must be treated as an indivisible quantum system whose wave function Ψ(t) depends upon the coordinates of the measuring device as well as upon those of the observed system. During the process of observation, the measured system can no longer be considered separately and the very notion of a dynamical state defined by the simpler wave function γ(t) loses its meaning. Thus the intervention of the observing instrument destroys all causal connection between the state of the system before and after the measurement; this explains why one cannot in general predict with certainty in what state the system will be found after the measurement; one can only make predictions of a statistical nature^{1}.1) The statistical predictions concerning the results of measurement are derived very naturally from the study of the mechanism of the measuring operation itself, a study in which the measuring instrument is treated as a quantized object and the complex (system + measuring instrument) evolves in causal fashion in accordance with the Schrödinger equation. A very concise and simple presentation of the measuring process in Quantum Mechanics is given. in F. London and E. Bauer, La Théorie de l'Observation en Mécanique Quantique (Paris, Hermann, 1939). More detailed discussions of this problem may be found in J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton, Princeton University Press, 1955), and in D. Bohm, (Quantum Theory New York, PrenticeHall, 1951).
Decoherence Theorists on Measurement
In general, decoherence theorists see the problem of measurement as why do we not see macroscopic superpositions of states. Why do measurements always show a system and its measuring apparatus to be in a particular state  a "pointer state," and not in a superposition? Our answer is that we never see microscopic systems in a superposition of states either. Dirac's principle of superposition says only that the probability (amplitudes) of finding a system in different states has nonzero values for different states. Measurements always reveal a system to be in one state. Which state is found is a matter of chance. [Decoherence theorists do not like this indeterminism.] The statistics from large numbers of measurements of identically prepared systems verify the predicted probabilities for the different states. The accuracy of these quantum mechanical predictions (1 part in 10^{15}) shows quantum mechanics to be the most accurate theory ever known. Guido Bacciagaluppi summarized the view of decoherence theorists in an article for the Stanford Encyclopedia of Philosophy. He defines the measurement problem as the lack of macroscopic superpositions: The measurement problem, in a nutshell, runs as follows. Quantum mechanical systems are described by wavelike mathematical objects (vectors) of which sums (superpositions) can be formed (see the entry on quantum mechanics). Time evolution (the Schrödinger equation) preserves such sums. Thus, if a quantum mechanical system (say, an electron) is described by a superposition of two given states, say, spin in xdirection equal +1/2 and spin in xdirection equal 1/2, and we let it interact with a measuring apparatus that couples to these states, the final quantum state of the composite will be a sum of two components [that is to say, a macroscopic superposition, which is of course never seen!], one in which the apparatus has coupled to (has registered) xspin = +1/2, and one in which the apparatus has coupled to (has registered) xspin = 1/2...Maximilian Schlosshauer situates the problem of measurement in the context of the socalled "quantumtoclassical transition," namely the question of exactly how deterministic classical behavior emerges from the indeterministic microscopic quantum world. In this section, we shall describe the (in)famous measurement problem of quantum mechanics that we have already referred to in several places in the text. The choice of the term "measurement problem" has purely historical reasons: Certain foundational issues associated with the measurement problem were first illustrated in the context of a quantummechanical description of a measuring apparatus interacting with a system. The main concern of the decoherence theorists then is to recover a deterministic picture of quantum mechanics that would allow them to predict the outcome of a particular experiment. They have what William James called an "antipathy to chance." Max Tegmark and John Wheeler made this clear in a 2001 article in Scientific American:
The discovery of decoherence, combined with the ever more elaborate experimental demonstrations of quantum weirdness, has caused a noticeable shift in the views of physicists. The main motivation for introducing the notion of wavefunction collapse had been to explain why experiments produced specific outcomes and not strange superpositions of outcomes. Now much of that motivation is gone. Moreover, it is embarrassing that nobody has provided a testable deterministic equation specifying precisely when the mysterious collapse is supposed to occur. H. Dieter Zeh, the founder of the "decoherence program," defines the measurement problem as a macroscopic entangled superposition of all possible measurement outcomes: Because of the dynamical superposition principle, an initial superposition Σ c_{n}  n > does not lead to definite pointer positions (with their empirically observed frequencies). If decoherence is neglected, one obtains their entangled superposition Σ c_{n}  n >  Ψ _{n} >, that is, a state that is different from all potential measurement outcomes  n >  Ψ _{n} >. This dilemma represents the "quantum measurement problem" to be discussed in Sect. 2.3. Von Neumann's interaction is nonetheless regarded as the first step of a measurement (a "premeasurement"). Yet, a collapse seems still to be required  now in the measurement device rather than in the microscopic system. Because of the entanglement between system and apparatus, it would then affect the total system.Zeh continues: It's not clear why the standard ensemble interpretation is "ruled out," but Zeh offers a solution, which is to deny the projection postulate of standard quantum mechanics and use an unconventional interpretation that makes wavefunction collapses only "apparent": A way out of this dilemma within quantum mechanical concepts requires one of two possibilities: a modification of the Schrodinger equation that explicitly describes a collapse (also called "spontaneous localization"  see Chap. 8), or an Everett type interpretation, in which all measurement outcomes are assumed to exist in one formal superposition, but to be perceived separately as a consequence of their dynamical autonomy resulting from decoherence. While this latter suggestion has been called "extravagant" (as it requires myriads of coexisting quasiclassical "worlds"), it is similar in principle to the conventional (though nontrivial) assumption, made tacitly in all classical descriptions of observation, that consciousness is localized in certain semistable and sufficiently complex subsystems (such as human brains or parts thereof) of a much larger external world.Jeffrey Bub worked with David Bohm to develop Bohm's theory of "hidden variables." They hoped their theory might provide a deterministic basis for quantum theory and support Albert Einstein's view of a physical world independent of observations of the world. The standard theory of quantum mechanics is irreducibly statistical and indeterministic, a consequence of the collapse of the wave function when many possibilities for physical outcomes of an experiment reduce to a single actual outcome.
This is a book about the interpretation of quantum mechanics, and about the measurement problem. The conceptual entanglements of the measurement problem have their source in the orthodox interpretation of 'entangled' states that arise in quantum mechanical measurement processes... References
Bacciagaluppi, Guido, The Role of Decoherence in Quantum Mechanics, first published Mon Nov 3, 2003; substantive revision Mon Apr 16, 2012 Jeffrey Bub, Interpreting the Quantum World. Cambridge University, 1997, p.2. Adriana Daneri, A. Loinger, and G. M. Prosperi, Nuclear Physics, 33 (1962) pp.297319. (W&Z, p.657) Erich Joos, H. Dieter Zeh, et al., Decoherence and the Appearance of a Classical World in Quantum Theory. Springer, 2010, Gunter Ludwig, Zeitschrift für Physik, 135 (1953) p.483 Maximilian Schlosshauer, Decoherence and the QuantumtoClassical Transition. Springer, 2007, pp.4950 Leo Szilard, Behavioral Science, 9 (1964) pp.30110. (W&Z, p.539) Max Tegmark and John Wheeler, Scientific American, February (2001) pp.6875. John von Neumann, The Mathematical Foundations of Quantum Mechanics, (Princeton, NJ, Princeton U. Press, 1955), pp.347445. (W&Z, p.549) John Wheeler and Wojciech Zurek, Quantum Theory and Measurement (Princeton, NJ, Princeton U. Press, 1983) (= W&Z) Eugene Wigner, "The Problem of Measurement," Symmetries and Reflections (Bloomington, IN, Indiana U. Press, 1967) pp.15370. (W&Z, p.324)
