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 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 Daniel Boyd F.H.Bradley C.D.Broad Michael Burke Lawrence Cahoone C.A.Campbell Joseph Keim Campbell Rudolf Carnap Carneades Nancy Cartwright Gregg Caruso 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 Austin Farrer Herbert Feigl Arthur Fine John Martin Fischer Frederic Fitch Owen Flanagan Luciano Floridi Philippa Foot Alfred Fouilleé Harry Frankfurt Richard L. Franklin Bas van Fraassen 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 Frank Jackson William James Lord Kames Robert Kane Immanuel Kant Tomis Kapitan Walter Kaufmann Jaegwon Kim William King Hilary Kornblith Christine Korsgaard Saul Kripke Thomas Kuhn Andrea Lavazza Christoph Lehner Keith Lehrer Gottfried Leibniz Jules Lequyer Leucippus Michael Levin Joseph Levine George Henry Lewes C.I.Lewis David Lewis Peter Lipton C. Lloyd Morgan John Locke Michael Lockwood Arthur O. Lovejoy E. Jonathan Lowe John R. Lucas Lucretius Alasdair MacIntyre Ruth Barcan Marcus Tim Maudlin James Martineau Nicholas Maxwell 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. Pears Charles Sanders Peirce Derk Pereboom Steven Pinker Plato Karl Popper Porphyry Huw Price H.A.Prichard Protagoras Hilary Putnam Willard van Orman Quine Frank Ramsey Ayn Rand Michael Rea Thomas Reid Charles Renouvier Nicholas Rescher C.W.Rietdijk Richard Rorty Josiah Royce Bertrand Russell Paul Russell Gilbert Ryle JeanPaul Sartre Kenneth Sayre T.M.Scanlon Moritz Schlick Arthur Schopenhauer John Searle Wilfrid Sellars Alan Sidelle Ted Sider Henry Sidgwick Walter SinnottArmstrong J.J.C.Smart Saul Smilansky Michael Smith Baruch Spinoza L. Susan Stebbing Isabelle Stengers George F. Stout Galen Strawson Peter Strawson Eleonore Stump Francisco Suárez Richard Taylor Kevin Timpe Mark Twain Peter Unger Peter van Inwagen Manuel Vargas John Venn Kadri Vihvelin Voltaire G.H. von Wright David Foster Wallace R. Jay Wallace W.G.Ward Ted Warfield Roy Weatherford C.F. von Weizsäcker William Whewell Alfred North Whitehead David Widerker David Wiggins Bernard Williams Timothy Williamson Ludwig Wittgenstein Susan Wolf Scientists David Albert Michael Arbib Walter Baade Bernard Baars Jeffrey Bada Leslie Ballentine Marcello Barbieri Gregory Bateson Horace Barlow 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 Jean Bricmont Hans Briegel Leon Brillouin Stephen Brush Henry Thomas Buckle S. H. Burbury Melvin Calvin Donald Campbell Sadi Carnot Anthony Cashmore Eric Chaisson Gregory Chaitin JeanPierre Changeux Rudolf Clausius Arthur Holly Compton John Conway Jerry Coyne John Cramer Francis Crick E. P. Culverwell Antonio Damasio Olivier Darrigol Charles Darwin Richard Dawkins Terrence Deacon Lüder Deecke Richard Dedekind Louis de Broglie Stanislas Dehaene Max Delbrück Abraham de Moivre Bernard d'Espagnat Paul Dirac Hans Driesch John Eccles Arthur Stanley Eddington Gerald Edelman Paul Ehrenfest Manfred Eigen Albert Einstein George F. R. Ellis Hugh Everett, III Franz Exner Richard Feynman R. A. Fisher David Foster Joseph Fourier Philipp Frank Steven Frautschi Edward Fredkin Benjamin GalOr Howard Gardner Lila Gatlin Michael Gazzaniga Nicholas GeorgescuRoegen GianCarlo Ghirardi J. Willard Gibbs James J. Gibson Nicolas Gisin Paul Glimcher Thomas Gold A. O. Gomes Brian Goodwin Joshua Greene Dirk ter Haar Jacques Hadamard Mark Hadley Patrick Haggard J. B. S. Haldane Stuart Hameroff Augustin Hamon Sam Harris Ralph Hartley Hyman Hartman Jeff Hawkins JohnDylan Haynes Donald Hebb Martin Heisenberg Werner Heisenberg John Herschel Basil Hiley Art Hobson Jesper Hoffmeyer Don Howard John H. Jackson William Stanley Jevons Roman Jakobson E. T. Jaynes Pascual Jordan Eric Kandel Ruth E. Kastner Stuart Kauffman Martin J. Klein William R. Klemm Christof Koch Simon Kochen Hans Kornhuber Stephen Kosslyn Daniel Koshland Ladislav Kovàč Leopold Kronecker Rolf Landauer Alfred Landé PierreSimon Laplace Karl Lashley David Layzer Joseph LeDoux Gerald Lettvin Gilbert Lewis Benjamin Libet David Lindley Seth Lloyd Hendrik Lorentz Werner Loewenstein Josef Loschmidt Ernst Mach Donald MacKay Henry Margenau Owen Maroney David Marr Humberto Maturana James Clerk Maxwell Ernst Mayr John McCarthy Warren McCulloch N. David Mermin George Miller Stanley Miller Ulrich Mohrhoff Jacques Monod Vernon Mountcastle Emmy Noether Donald Norman Alexander Oparin Abraham Pais Howard Pattee Wolfgang Pauli Massimo Pauri Wilder Penfield Roger Penrose Steven Pinker Colin Pittendrigh Walter Pitts Max Planck Susan Pockett Henri Poincaré Daniel Pollen Ilya Prigogine Hans Primas Zenon Pylyshyn Henry Quastler Adolphe Quételet Pasco Rakic Nicolas Rashevsky Lord Rayleigh Frederick Reif Jürgen Renn Giacomo Rizzolati Emil Roduner Juan Roederer Jerome Rothstein David Ruelle David Rumelhart Tilman Sauer Ferdinand de Saussure Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Sebastian Seung Thomas Sebeok Franco Selleri Claude Shannon Charles Sherrington David Shiang Abner Shimony Herbert Simon Dean Keith Simonton Edmund Sinnott B. F. Skinner Lee Smolin Ray Solomonoff Roger Sperry John Stachel Henry Stapp Tom Stonier Antoine Suarez Leo Szilard Max Tegmark Teilhard de Chardin Libb Thims William Thomson (Kelvin) Richard Tolman Giulio Tononi Peter Tse Alan Turing Francisco Varela Vlatko Vedral Mikhail Volkenstein Heinz von Foerster Richard von Mises John von Neumann Jakob von Uexküll C. S. Unnikrishnan C. H. Waddington John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss Herman Weyl John Wheeler Wilhelm Wien Norbert Wiener Eugene Wigner E. O. Wilson Günther Witzany Stephen Wolfram H. Dieter Zeh Semir Zeki Ernst Zermelo Wojciech Zurek Konrad Zuse Fritz Zwicky Presentations Biosemiotics Free Will Mental Causation James Symposium 
The Copenhagen Interpretation of Quantum Theory (Annotated)
Heisenberg's "paradox" is that we must use the language and concepts of classical physics to describe the results of quantum physics.
The Copenhagen interpretation of quantum theory starts from a
paradox. Any experiment in physics, whether it refers to the phenomena
of daily life or to atomic events, is to be described in the terms
of classical physics. The concepts of classical physics form the
language by which we describe the arrangements of our experiments
and state the results. We cannot and should not replace these
concepts by any others. Still the application of these concepts
is limited by the relations of uncertainty. We must keep in mind
this limited range of applicability of the classical concepts
while using them, but we cannot and should not try to improve
them.
But Dirac thought new, albeit nonintuitive, concepts might arise from a careful study of quantum physics For a better understanding of this paradox it is useful to compare the procedure for the theoretical interpretation of an experiment in classical physics and in quantum theory. In Newton's mechanics, for instance, we may start by measuring the position and the velocity of the planet whose motion we are going to study. The result of the observation is translated into mathematics by deriving numbers for the coordinates and the momenta of the planet from the observation. Then the equations of motion are used to derive from these values of the coordinates and momenta at a given time the values of these coordinates or any other properties of the system at a later time, and in this way the astronomer can predict the properties of the system at a later time. He can, for instance, predict the exact time for an eclipse of the moon.
The uncertainty principle limits the accuracy for the position and velocity of a particle
In quantum theory the procedure is slightly different. We could
for instance be interested in the motion of an electron through
a cloud chamber and could determine by some kind of observation
the initial position and velocity of the electron. But this determination
will not be accurate  it will at least contain the inaccuracies
following from the uncertainty relations and will probably contain
still larger errors due to the difficulty of the experiment. It
is the first of these inaccuracies which allows us to translate
the result of the observation into the mathematical scheme of
quantum theory. A probability function is written down which represents
the experimental situation at the time of the measurement, including
even the possible errors of the measurement.
Even in classical physics there are errors in position and velocity that can be expressed as a probability.
This probability function represents a mixture of two things,
partly a fact and partly our knowledge of a fact. It represents
a fact in so far as it assigns at the initial time the probability
unity (i.e., complete certainty) to the initial situation: the
electron moving with the observed velocity at the observed position;
'observed' means observed within the accuracy of the experiment.
It represents our knowledge in so far as another observer could
perhaps know the position of the electron more accurately. The
error in the experiment does  at least to some extent  not represent
a property of the electron but a deficiency in our knowledge of
the electron. Also this deficiency of knowledge is expressed in
the probability function.
"Observed" means some human observer acquired new knowledge In classical physics one should in a careful investigation also consider the error of the observation. As a result one would get a probability distribution for the initial values of the coordinates and velocities and therefore something very similar to the probability function in quantum mechanics. Only the necessary uncertainty due to the uncertainty relations is lacking in classical physics.
The Schrödinger equation of motion gives the probabilities for position at later times, but it does not give any specific positions  an actual path of the particle  just all the possible positions, with calculable probabilities for each position
When the probability function in quantum theory has been determined
at the initial time from the observation, one can from the laws
of quantum theory calculate the probability function at any later
time and can thereby determine the probability for a measurement
giving a specified value of the measured quantity. We can, for
instance, predict the probability for finding the electron at
a later time at a given point in the cloud chamber. It should
be emphasised, however, that the probability function does not
in itself represent a course of events in the course of time.
It represents a tendency for events and our knowledge of events.
The probability function can be connected with reality only if
one essential condition is fulfilled: if a new measurement is
made to determine a certain property of the system. Only then
does the probability function allow us to calculate the probable
result of the new measurement. The result of the measurement again
will be stated in terms of classical physics.
Therefore, the theoreticalinterpretation of an experiment requires three distinct steps: (I) the translation of the initial experimental situation into a probability function; (2) the following up of this function in the course of time; (3) the statement of a new measurement to be made of the system, the result of which can then be calculated from the probability function. For the first step the fulfilment of the uncertainty relations is a necessary condition. The second step cannot be described in terms of the classical concepts; there is no description of what happens to the system between the initial observation and the next measurement. It is only in the third step that we change over again from the 'possible' to the 'actual'.
The next few paragraphs describe Heisenberg's microscope example, which shows how an observation must disturb the particle
Let us illustrate these three steps in a simple ideal experiment.
It has been said that the atom consists of a nucleus and electrons
moving around the nucleus; it has also been stated that the concept
of an electronic orbit is doubtful. One could argue that it should
at least in principle be possible to observe the electron in its
orbit. One should simply look at the atom through a microscope
of a very high revolving power, then one would see the electron
moving in its orbit. Such a high revolving power could to be sure
not be obtained by a microscope using ordinary light, since the
inaccuracy of the measurement of the position can never be smaller
than the wave length of the light. But a microscope using γrays
with a wave length smaller than the size of the atom would do.
Such a microscope has not yet been constructed but that should
not prevent us from discussing the ideal experiment.
Is the first step, the translation of the result of the observation into a probability function, possible? It is possible only if the uncertainty relation is fulfilled after the observation. The position of the electron will be known with an accuracy given by the wave length of the γray. The electron may have been practically at rest before the observation. But in the act of observation at least one light quantum of the γray must have passed the microscope and must first have been deflected by the electron. Therefore, the electron has been pushed by the light quantum, it has changed its momentum and its velocity, and one can show that the uncertainty of this change is just big enough to guarantee the validity of the uncertainty relations. Therefore, there is no difficulty with the first step. At the same time one can easily see that there is no way of observing the orbit of the electron around the nucleus. The second step shows a wave pocket moving not around the nucleus but away from the atom, because the first light quantum will have knocked the electron out from the atom. The momentum of light quantum of the γray is much bigger than the original momentum of the electron if the wave length of the γray is much smaller than the size of the atom. Therefore, the first light quantum is sufficient to knock the electron out of the atom and one can never observe more than one point in the orbit of the electron; therefore, there is no orbit in the ordinary sense. The next observation  the third step  will show the electron on its path from the atom.
We cannot say the particle has a classical path. Is this an epistemological problem or an ontological problem?
Quite generally there is no way of describing what happens between
two consecutive observations. It is of course tempting to say
that the electron must have been somewhere between the two observations
and that therefore the electron must have described some kind
of path or orbit even if it may be impossible to know which path.
This would be a reasonable argument in classical physics. But
in quantum theory it would be a misuse of the language which,
as we will see later, cannot be justified. We can leave it open
for the moment, whether this warning is a statement about the
way in which we should talk about atomic events or a statement
about the events themselves, whether it refers to epistemology
or to ontology. In any case we have to be very cautious about
the wording of any statement concerning the behaviour of atomic
particles.
Actually we need not speak of particles at all. For many experiments it is more convenient to speak of matter waves; for instance, of stationary matter waves around the atomic nucleus. Such a description would directly contradict the other description if one does not pay attention to the limitations given by the uncertainty relations. Through the limitations the contradiction is avoided. The use of 'matter waves' is convenient, for example, when dealing with the radiation emitted by the atom. By means of its frequencies and intensities the radiation gives information about the oscillating charge distribution in the atom, and there the wave picture comes much nearer to the truth than the particle picture.
Bohr says the wave picture and particle picture are complementary. He uses complementarity frequently in describing the proper interpretation of the new quantum theory. Therefore,
Bohr advocated the use of both pictures, which he called 'complementary'
to each other. The two pictures are of course mutually exclusive,
because a certain thing cannot at the same time be a particle
(i.e., substance confined to a very small volume) and a wave (i.e.,
a field spread out over a large space), but the two complement
each other. By playing with both pictures, by going from the one
picture to the other and back again, we finally get the right
impression of the strange kind of reality behind our atomic experiments.
Bohr uses the concept of 'complementarity' at several places in
the interpretation of quantum theory. The knowledge of the position
of a particle is complementary to the knowledge of its velocity
or momentum. If we know the one with high accuracy we cannot know
the other with high accuracy; still we must know both for determining
the behaviour of the system. The spacetime description of the
atomic events is complementary to their deterministic description.
The probability function obeys an equation of motion as the coordinates
did in Newtonian mechanics; its change in the course of time is
completely determined by the quantum mechanical equation, but
it does not allow a description in space and time. The observation,
on the other hand, enforces the description in space and time
but breaks the determined continuity of the probability function
by changing our knowledge of the system.
Position and momentum are complementary. Spacetime descriptions (usually waves with positions in time) are complementary to deterministic (i.e., causal) descriptions (usually particles with momentum and energy) The deterministic and continuous evolution of the probability is complementary to the discontinuous observation of an actual position
Waves vs. particles were a new philosophical dualism, the origin of Bohr complementarity?
Generally the dualism between two different descriptions of the
same reality is no longer a difficulty since we know from the
mathematical formulation of the theory that contradictions cannot
arise. The dualism between the two complementary pictures  waves
and particles  is also clearly brought out in the flexibility
of the mathematical scheme. The formalism is normally written
to resemble Newtonian mechanics, with equations of motion for
the coordinates and the momenta of the particles.
But by a simple transformation it can be rewritten to resemble a wave equation for an ordinary threedimensional matter wave. Therefore, this possibility of playing with different complementary pictures has its analogy in the different transformations of the mathematical scheme; it does not lead to any difficulties in the Copenhagen interpretation of quantum theory. A real difficulty in the understanding of this interpretation arises, however, when one asks the famous question: But what happens 'really' in an atomic event? It has been said before that the mechanism and the results of an observation can always be stated in terms of the classical concepts. But what one deduces from an observation is a probability function, a mathematical expression that combines statements about possibilities or tendencies with statements about our knowledge of facts So we cannot completely objectify the result of an observation, we cannot describe what 'happens' between this observation and the next. This looks as if we had introduced an element of subjectivism into the theory, as if we meant to say: what happens depends on our way of observing it or on the fact that we observe it. Before discussing this problem of subjectivism it is necessary to explain quite clearly why one would get into hopeless difficulties if one tried to describe what happens between two consecutive observations. For this purpose it is convenient to discuss the following ideal experiment: We assume that a small source of monochromatic light radiates toward a black screen with two small holes in it. The diameter of the holes may be not much bigger than the wave length of the light, but their distance will be very much bigger. At some distance behind the screen a photographic plate registers the incident light. If one describes this experiment in terms of the wave picture, one says that the primary wave penetrates through the two holes, there will be secondary spherical waves starting from the holes that interfere with one another, and the interference will produce a pattern of varying intensity on the photographic plate.
The blackening of the photographic plate is a quantum process, a chemical reaction produced by single light quanta. Therefore, it must also be possible to describe the experiment in terms of light quanta. If it would be permissible to say what happens to the single light quantum between its emission from the light source and its absorption in the photographic plate, one could argue as follows: The single light quantum can come through the first hole or through the second one. If it goes through the first hole and is scattered there, its probability for being absorbed at a certain point of the photographic plate cannot depend upon whether the second hole is closed or open. The probability distribution on the plate will be the same as if only the first hole was open. If the experiment is repeated many times and one takes together all cases in which the light quantum has gone through the first hole, the blackening of the plate due to these cases will correspond to this probability distribution. If one considers only those light quanta that go through the second hole, the blackening should correspond to a probability distribution derived from the assumption that only the second hole is open. The total blackening, therefore, should just be the sum of the blackenings in the two cases; in other words, there should be no interference pattern. But we know this is not correct, and the experiment will show the interference pattern. Therefore, the statement that any light quantum must have gone either through the first or through the second hole is problematic and leads to contradictions. This example shows clearly that the concept of the probability function does not allow a description of what happens between two observations. Any attempt to find such a description would lead to contradictions; this must mean that the term 'happens' is restricted to the observation.
Here begins some confusion about the role of the observer. Does "reality" depend on whether we observe it?
Now, this is a very strange result, since it seems to indicate
that the observation plays a decisive role in the event and that
the reality varies, depending upon whether we observe it or not.
To make this point clearer we have to analyse the process of observation
more closely.
To begin with, it is important to remember that in natural science we are not interested in the universe as a whole, including ourselves, but we direct our attention to some part of the universe and make that the object of our studies. In atomic physics this part is usually a very small object, an atomic particle or a group of such particles, sometimes much larger  the size does not matter; but it is important that a large part of the universe, including ourselves, does not belong to the object. Now, the theoretical interpretation of an experiment starts with the two steps that have been discussed. In the first step we have to describe the arrangement of the experiment, eventually combined with a first observation, in terms of classical physics and translate this description into a probability function. This probability function follows the laws of quantum theory, and its change in the course of time, which is continuous, can be calculated from the initial conditions; this is the second step.
"Possibilities" are perfectly understandable for the lay person. "Tendencies" and Aristotle's "potentia" are unnecessary. For each possibility, quantum mechanics lets us
The probability
function combines objective and subjective elements. It contains
statements about possibilities or better tendencies ('potentia'
in Aristotelian philosophy), and these statements are completely
objective, they do not depend on any observer; and it contains
statements about our knowledge of the system, which of course
are subjective in so far as they may be different for different
observers. In ideal cases the subjective element in the probability
function may be practically negligible as compared with the objective
one. The physicists then speak of a 'pure case'.
calculate the probability. When we now come to the next observation. the result of which should be predicted from the theory, it is very important to realize that our object has to be in contact with the other part of the world, namely, the experimental arrangement, the measuring rod, etc., before or at least at the moment of observation. This means that the equation of motion for the probability function does now contain the influence of the interaction with the measuring device.
Describing the measuring apparatus in classical terms does not mean it is not a quantum object. Heisenberg thinks classical terms are necessary for us to communicate knowledge
This influence introduces a new element of uncertainty,
since the measuring device is necessarily described in the terms
of classical physics; such a description contains all the uncertainties
concerning the microscopic structure of the device which we know
from thermodynamics, and since the device is connected with the
rest of the world, it contains in fact the uncertainties of the
microscopic structure of the whole world. These uncertainties
may be called objective in so far as they are simply a consequence
of the description in the terms of classical physics and do not
depend on any observer. They may be called subjective in so far
as they refer to our incomplete knowledge of the world.
After this interaction has taken place, the probability function contains the objective element of tendency and the subjective element of incomplete knowledge, even if it has been a 'pure case' before. It is for this reason that the result of the observation cannot generally be predicted with certainty; what can be predicted is the probability of a certain result of the observation, and this statement about the probability can be checked by repeating the experiment many times. The probability function does  unlike the common procedure in Newtonian mechanics  not describe a certain event but, at least during the process of observation, a whole ensemble of possible events.
Quantum mechanical systems evolve in two ways
The observation itself changes the probability function discontinuously;
it selects of all possible events the actual one that has taken
place. Since through the observation our knowledge of the system
has changed discontinuously, its mathematical representation also
has undergone the discontinuous change and we speak of a 'quantum
jump'. When the old adage 'Natura non facit saltus' is
used as a basis for criticism of quantum theory, we can reply
that certainly our knowledge can change suddenly and that this
fact justifies the use of the term 'quantum jump'.
the first is the wave function deterministically exploring all the possibilities for interaction, the second is the particle randomly choosing one of those possibilities to become actual. The discontinuous transition form "possible" to "actual" should not be confused with the Heisenberg "cut" or with the transition from quantum to classical This discontinuity (or "collapse" of probabilities) registers new information first at the quantum level. Quantum information is subsequently amplified in the macroscopic apparatus and only later recorded as new knowledge in the Therefore, the transition from the 'possible' to the 'actual' takes place during the act of observation. If we want to describe what happens in an atomic event, we have to realize that the word 'happens' can apply only to the observation, not to the state of affairs between two observations. It applies to the physical, not the psychical act of observation, and we may say that the transition from the 'possible' to the 'actual' takes place as soon as the interaction of the object with the measuring device, and thereby with the rest of the world, has come into play; it is not connected with the act of registration of the result by the mind of the observer. The discontinuous change in the probability function, however, takes place with the act of registration, because it is the discontinuous change of our knowledge in the instant of registration that has its image in the discontinuous change of the probability function. To what extent, then, have we finally come to an objective description of the world, especially of the atomic world? In classical physics science started from the belief  or should one say from the illusion?  that we could describe the world or at least parts of the world without any reference to ourselves. This is actually possible to a large extent. We know that the city of London exists whether we see it or not. It may be said that classical physics is just that idealisation in which we can speak about parts of the world without any reference to ourselves. Its success has led to the general ideal of an objective description of the world. Objectivity has become the first criterion for the value of any scientific result. Does the Copenhagen interpretation of quantum theory still comply with this ideal? One may perhaps say that quantum theory corresponds to this ideal as far as possible.
John von Neumann's and Eugene Wigner's claims that a "conscious observer" is needed for a quantum process to become actual seems to be no part of the original Copenhagen Interpretation of Heisenberg?
Certainly quantum
theory does not contain genuine subjective features, it does not
introduce the mind of the physicist as a part of the atomic event.
But it starts from the division of the world into the 'object'
and the rest of the world, and from the fact that at least for
the rest of the world we use the classical concepts in our description.
This division is arbitrary and historically a direct consequence
of our scientific method; the use of the classical concepts is
finally a consequence of the general human way of thinking. But
this is already a reference to ourselves and in so far our description
is not completely objective.
It has been stated in the beginning that the Copenhagen interpretation of quantum theory starts with a paradox. It starts from the fact that we describe our experiments in the terms of classical physics and at the same time from the knowledge that these concepts do not fit nature accurately. The tension between these two starting points is the root of the statistical character of quantum theory. Therefore, it has sometimes been suggested that one should depart from the classical concepts altogether and that a radical change in the concepts used for describing the experiments might possibly lead back to a nonstatistical, completely objective description of nature. This suggestion, however, rests upon a misunderstanding. The concepts of classical physics are just a refinement of the concepts of daily life and are an essential part of the language which forms the basis of all natural science. Our actual situation in science is such that we do use the classical concepts for the description of the experiments, and it was the problem of quantum theory to find theoretical interpretation of the experiments on this basis. There is no use in discussing what could be done if we were other beings than we are. At this point we have to realize, as von Weizsäcker has put it, that 'Nature is earlier than man, but man is earlier than natural science.' The first part of the sentence justifies classical physics, with its ideal of complete objectivity. The second part tells us why we cannot escape the paradox of quantum theory, namely, the necessity of using the classical concepts. We have to add some comments on the actual procedure in the quantumtheoretical interpretation of atomic events. It has been said that we always start with a division of the world into an object, which we are going to study, and the rest of the world, and that this division is to some extent arbitrary.
The measuring apparatus could be treated quantum mechanically. It is a quantum object. But the location of the Heisenberg "cut" is arbitrary. We still must use classical concepts (the "paradox").
It should indeed not make any difference
in the final result if we, e.g., add some part of the measuring
device or the whole device to the object and apply the laws of
quantum theory to this more complicated object. It can be shown
that such an alteration of the theoretical treatment would not
alter the predictions concerning a given experiment. This follows
mathematically from the fact that the laws of quantum theory are
for the phenomena in which Planck's constant can be considered
as a very small quantity, approximately identical with the classical
laws. But it would be a mistake to believe that this application
of the quantumtheoretical laws to the measuring device could
help to avoid the fundamental paradox of quantum theory.
The measuring device deserves this name only if it is in close contact with the rest of the world, if there is an interaction between the device and the observer. Therefore, the uncertainty with respect to the microscopic behaviour of the world will enter into the quantumtheoretical system here just as well as in the first interpretation. If the measuring device would be isolated from the rest of the world, it would be neither a measuring device nor could it be described in the terms of classical physics at all.
It is not arbitrary that we somewhere separate the "object" of study from the "subjective" physicist and the tools made by experimenters.
With regard to this situation Bohr has emphasised that it is more
realistic to state that the division into the object and the
rest of the world is not arbitrary. Our actual situation in research
work in atomic physics is usually this: we wish to understand
a certain phenomenon, we wish to recognise how this phenomenon
follows from the general laws of nature. Therefore that part of
matter or radiation which takes part in the phenomenon is the
natural 'object' in the theoretical treatment and should be separated
in this respect from the tools used to study the phenomenon. This
again emphasises a subjective element in the description of atomic
events, since the measuring device has been constructed by the
observer, and we have to remember that what we observe is not
nature in itself but nature exposed to our method of questioning.
Our scientific work in physics consists in asking questions about
nature in the language that we possess and trying to get an answer
from experiment by the means that are at our disposal. In this
way quantum theory reminds us, as Bohr has put it, of the old
wisdom that when searching for harmony in life one must never
forget that in the drama of existence we are ourselves both players
and spectators. It is understandable that in our scientific relation
to nature our own activity becomes very important when we have
to deal with parts of nature into which we can penetrate only
by using the most elaborate tools.
The Copenhagen Interpretation of Quantum Theory" was the third of the GiffordLectures given by Heisenberg in winter 1955/56 at St. Andrews University, Scotland. The lectures have been published in the book Werner Heisenberg: Physics and Philosophy (Harper & Brothers, New York, USA, 1958).
Summary
