Measurements are described with diverse quantum physics and concepts such as:

• wave functions evolving deterministically according to the linear Schrödinger equation,
• superposition of states, i.e., linear combinations of wave functions with complex coefficients that carry phase information and produce interference effects(the principle of superposition)
• quantum jumps between states accompanied by the "collapse" of the wave function (the projection postulate)
• probabilities of collapses and jumps given by the square of the absolute value of the wave function for a given state (the axiom of measurement)
• the Heisenberg indeterminacy principle.

The original problem, said to be a consequence of Neils Bohr's "Copenhagen interpretation" of quantum mechanics, is 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 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 non-unitary, discontinuous, and indeterministic collapse of the wave function. John von Neumann saw a problem with two distinct (indeed, opposite) processes.

Others define the measurement problem as the failure to observe macroscopic superpositions.

Decoherence theorists (e.g., H. Dieter Zeh), who use various non-standard 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 superpositions such as Schrödinger's Cat. Unitary time evolution of the wave function according to the Schrödinger wave equation should produce such macroscopic superpositions.

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 pi-bond orbital rotation from cis- to trans- in the light-sensitive retinal molecule is the opposite example of exciting the 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. This entropy increase is normally orders of magnitude more than the small increase in stable information (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. This means that 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. Niels Bohr used the uncertainty of macroscopic objects to defeat Albert Einstein's several objections to quantum mechanics at the 1927 Solvay conferences.

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 Einstein-Podolsky-Rosen experiment, in which entangled electrons or photons are in a superposition of two-particle 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 "many-worlds" interpretation, "hidden variables," and signaling faster than the speed of light.

We develop a quantum-mechanical 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.

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...

We have defined "apparatus" as a physical object which is governed, with sufficient accuracy, by classical mechanics. Such, for instance, is a body of large enough mass. However, it must not be supposed that apparatus is necessarily macroscopic. Under certain conditions, the part of apparatus may also be taken by an object which is microscopic, since the idea of "with sufficient accuracy" depends on the actual problem proposed.

Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case [correspondence principle], yet at the same time it requires this limiting case for its own formulation.

(Quantum Mechanics, Lev Landau and Evgeny Lifshitz, pp.2-3

Von Neumann explained that two fundamentally different processes are going on in quantum mechanics.

1. A non-causal process, in which the measured electron winds up randomly in one of the possible physical states (eigenstates) of the measuring apparatus plus electron.

   This process came to be called the collapse of the wave function or the reduction of the wave packet.

   The probability for finding the electron in a specific eigenstate is given by the square of the coefficients c_n of the expansion of the original system state (wave function ψ) in an infinite set of wave functions φ that represent the eigenfunctions of the measuring apparatus plus electron.

   This is as close as we get to a description of the motion of the particle aspect of a quantum system. According to von Neumann, the particle simply shows up somewhere as a result of a measurement.

   Information physics says that the particle shows up whenever a new stable information structure is created, information that can be observed.

2. A causal process, in which the electron wave function ψ evolves deterministically according to Schrödinger's equation of motion for the wavelike aspect.
   (ih/2π) ∂ψ/∂t = Hψ.

   This evolution describes the motion of the probability amplitude wave ψ between measurements. The wave function exhibits interference effects. But interference is destroyed if the particle has a definite position or momentum.

   The particle path can not be observed.

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.

Process 2 is deterministic and information preserving.

The wave-function collapse gave rise to the so-called problem of measurement because its randomness prevents us from including it in the deterministic mathematics of the Schrödinger equation in process 2. GianCarlo Ghirardi (with his principal colleagues, Alberto Rimini and Tomaso Weber) looks to explain the collapse that accompanies measurement as a consequence of additional non-linear random terms which they add to the linear Schrödinger equation.

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 determined as any macroscopic object.

The first step is to build an apparatus that separates the quantum system physically into distinguishable paths or regions of space, where the different regions correspond to (are correlated with) the physical properties we want to measure.

We do not actually distinguish the paths at 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 one 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 though 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.

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.

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.

Let's consider an ideal photographic plate capable of precipitating visible silver grains upon the receipt of a single photon (and subsequent development). Today photography cannot detect single photons, but detectors using charge coupled devices (CCDs) are approaching this sensitivity.

We can write a quantum description of the plate as containing two sensitive collection areas, the part of the apparatus measuring horizontal photons, | A_h > (shown as the blue spot), and the part of the apparatus 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 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 information-creating process requires no conscious observer. The universe is its own observer.

(ih/2π) ∂/∂t | ψ + A > = H | ψ + A >.

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.

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.

We note the essential role played by the consciousness of the observer in this transition from the mixture to the pure case. Without his effective intervention, one would never obtain a new function.

(The Theory of Observation in Quantum Mechanics, Fritz London and Edmond Bauer, in Wheeler and Zurek, p.251)

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.

(Remarks on the Mind-Body Question, Eugene Wigner, in Wheeler and Zurek, p.169)

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.

(Atomic Physics and Human Knowledge, Niels Bohr, p.51)

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 physicist-observer 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.

(Quantum Mechanics, Lev Landau and Evgeny Lifshitz, p.2)

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 quantum-mechanical 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.

(Quantum Theory, David Bohm, p.584)

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 single-celled 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 'measurement-like' processes are going on more or less all the time, more or less everywhere? Do we not have jumping then all the time?

(Speakable and Unspeakable in Quantum Mechanics, "Against Measurement," p. 216)

1. In standard quantum theory, the first required element is the collapse of the wave-function. This is the projection postulate1. Wolfgang Pauli called it a measurement of the first kind.

   However, the collapse might not leave a determinate record. If nothing in the environment is macroscopically affected so as to leave an indelible record of the collapse, we can say that no information about the collapse is created. The overwhelming fraction of collapses are of this kind. Moreover, information might actually be destroyed. For example, collisions between atoms or molecules in a gas that erase past information about their paths.

2. If the collapse occurs when the quantum system is entangled with a macroscopic measurement apparatus, a well-designed apparatus will also "collapse" into a correlated "pointer" state.

   As we showed above for photons, the detector in the upper half of a Stern-Gerlach apparatus will fire, indicating detection of an electron with spin up. As with photons, if the probability amplitude | ↑ > in the upper half does not collapse as the electron is detected, it can still be recombined with the probability amplitude | ↓ > in the lower half to reconstruct the unseparated beam.

   When the apparatus detects a particle, the second required element is that it produce a determinate record of the event. But this is impossible without an irreversible thermodynamic process that involves: a) the creation of at least one bit of new information (negative entropy) and b) the transfer away from the measuring apparatus of an amount of positive entropy (generally much, much) greater than teh information created.

   Notice that no conscious observer need be involved. We can generalize this second step to an event in the physical world that was not designed as a measurement apparatus by a physical scientist, but nevertheless leaves an indelible record of the collapse of a quantum state. This might be a highly specific single event, or the macroscopic consequence of billions of atomic-molecular level of events.

3. Finally, the third required element is an indelible determinate record that can be looked at by an observer (presumably conscious, although the consciousness itself has nothing to do with the measurement).

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.