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 Bois-Reymond 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 Tom Clark 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.Nowell-Smith Robert Nozick William of Ockham Timothy O'Connor Parmenides David F. Pears Charles Sanders Peirce Derk Pereboom Steven Pinker U.T.Place 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 Jean-Paul Sartre Kenneth Sayre T.M.Scanlon Moritz Schlick John Duns Scotus Arthur Schopenhauer John Searle Wilfrid Sellars David Shiang Alan Sidelle Ted Sider Henry Sidgwick Walter Sinnott-Armstrong Peter Slezak 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 Jean-Pierre 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 Gal-Or Howard Gardner Lila Gatlin Michael Gazzaniga Nicholas Georgescu-Roegen 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 John-Dylan 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 Pierre-Simon Laplace Karl Lashley David Layzer Joseph LeDoux Gerald Lettvin Gilbert Lewis Benjamin Libet David Lindley Seth Lloyd Werner Loewenstein Hendrik Lorentz Josef Loschmidt Alfred Lotka 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 A.A. Roback Emil Roduner Juan Roederer Jerome Rothstein David Ruelle David Rumelhart Robert Sapolsky Tilman Sauer Ferdinand de Saussure Jürgen Schmidhuber Erwin Schrödinger Aaron Schurger Sebastian Seung Thomas Sebeok Franco Selleri Claude Shannon Charles Sherrington 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 C. S. Unnikrishnan Francisco Varela Vlatko Vedral Vladimir Vernadsky Mikhail Volkenstein Heinz von Foerster Richard von Mises John von Neumann Jakob von Uexküll C. H. Waddington John B. Watson Daniel Wegner Steven Weinberg Paul A. Weiss Herman Weyl John Wheeler Jeffrey Wicken 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 |
Albert Einstein - Autobiography (Excerpts)
Comments on Quantum Mechanics
Before I enter upon the question of the completion of the
general theory of relativity, I must take a stand with reference
to the most successful physical theory of our period, viz., the
statistical quantum theory which, about twenty-five years ago,
took on a consistent logical form (Schrödinger, Heisenberg,
Dirac, Born). This is the only theory at present which permits
a unitary grasp of experiences concerning the quantum character
of micro-mechanical events.
Einstein's concern about nonlocality is that it may violate his principle of relativity.
This theory, on the one
hand, and the theory of relativity on the other, are both considered
correct in a certain sense, although their combination
has resisted all efforts up to now. This is probably the reason
why among contemporary theoretical physicists there exist entirely
differing opinions concerning the question as to how the
theoretical foundation of the physics of the future will appear.
Will it be a field theory; will it be in essence a statistical theory?
I shall briefly indicate my own thoughts on this point.
Physics is an attempt conceptually to grasp reality as it is
thought independently of its being observed. In this sense one
speaks of "physical reality." In pre-quantum physics there was
no doubt as to how this was to be understood. In Newton's
theory reality was determined by a material point in space and
time; in Maxwell's theory, by the field in space and time. In
quantum mechanics it is not so easily seen. If one asks: does a
ψ-function of the quantum theory represent a real factual
situation in the same sense in which this is the case of a material
system of points or of an electromagnetic field, one hesitates
to reply with a simple "yes" or "no"} why? What the ψ-function
(at a definite time) asserts, is this: What is the probability
for finding a definite physical magnitude q (or p) in a definitely
given interval, if I measure it at time t? The probability is
here to be viewed as an empirically determinable, and therefore
certainly as a "real" quantity which I may determine if I
create the same ψ-function very often and perform a q measurement
each time.
But what about the single measured
value of q? Did the respective individual system have this
q-value even before the measurement? To this question there
is no definite answer within the framework of the [existing]
theory, since the measurement is a process which implies a
finite disturbance of the system from the outside; it would
therefore be thinkable that the system obtains a definite numerical
value for q (or p), i.e., the measured numerical value,
only through the measurement itself. For the further discussion
I shall assume two physicists, A and B, who represent a different
conception with reference to the real situation as described by
the ψ-function.
According to Einstein's "objective reality," a system variable has a single determinate value between measurements. The only possible measurement is the actual measurement.
A. The individual system (before the measurement) has a
definite value of q (i.e., p) for all variables of the system,
and more specifically, that value which is determined by a
measurement of this variable. Proceeding from this conception,
he will state: The ψ-function is no exhaustive description
of the real situation of the system but an incomplete
description} it expresses only what we know on the
basis of former measurements concerning the system.
The Copenhagen Interpretation asserts that there are at every instant multiple possible values for a system variable. One of these becomes actual in a measurement.
B. The individual system (before the measurement) has no
definite value of q (i.e., p). The value of the measurement
only arises in cooperation with the unique probability which
is given to it in view of the ψ-function only through the
act of measurement itself. Proceeding from this conception,
he will (or, at least, he may) state: the ψ-function is an exhaustive
description of the real situation of the system.
We now present to these two physicists the following instance:
There is to be a system which at the time t of our observation
consists of two partial systems S1 and S2, which at
this time are spatially separated and (in the sense of the classical
physics) are without significant reciprocity. The total system
is to be completely described through a known ψ-function
ψ12 in the sense of quantum mechanics. All quantum theoreticians
now agree upon the following: If I make a complete measurement
of S1, I get from the results of the measurement and
from ψ12 an entirely definite ψ-function ψ2 of the system ψ2.
The character of ψ2 then depends upon what kind of measurement
I undertake on ψ1.
Now it appears to me that one may speak of the real factual
situation of the partial system S2. Of this real factual situation,
we know to begin with, before the measurement of S1, even less
than we know of a system described by the ψ-function. But on
one supposition we should, in my opinion, absolutely hold fast:
the real factual situation of the system S2 is independent of
what is done with the system S1, which is spatially separated
from the former.
If we measure the z-component of S1 electron spin, then the z-component of S2 must be found to be in the opposite direction, to conserve total spin = zero.
According to the type of measurement which
I make of S1, I get, however, a very different ψ2 for the second
partial system ( Ψ2, Ψ21,... ). Now, however, the real situation
of S2 must be independent of what happens to S1. For the
same real situation of S2 it is possible therefore to find, according
to one's choice, different types of ψ-function.
Schrödinger says that ψ12 is a single wave function describing the two particles. A measurement anywhere collapses both particles into single-particle Ψ2 and Ψ2. Both are measured, e.g., in z-direction, conserving all properties for both.
(One can escape
from this conclusion only by either assuming that the measurement
of S1 ((telepathically)) changes the real situation of
S2 or by denying independent real situations as such to things
which are spatially separated from each other. Both alternatives
appear to me entirely unacceptable.)
If now the physicists, A and B, accept this consideration as
valid, then B will have to give up his position that the ψ-function constitutes a complete description of a real factual situation.
For in this case it would be impossible that two different
types of ψ-functions could be co-ordinated with the identical
factual situation of S2.
The statistical character of the present theory would then
have to be a necessary consequence of the incompleteness of the
description of the systems in quantum mechanics, and there
would no longer exist any ground for the supposition that a
future basis of physics must be based upon statistics. - - -
It is my opinion that the contemporary quantum theory by
means of certain definitely laid down basic concepts, which on
the whole have been taken over from classical mechanics, constitutes
an optimum formulation of the connections.
In his final remarks, Einstein said any future theory will probably incorporate quantum theory!
I believe,
however, that this theory offers no useful point of departure for
future development. This is the point at which my expectation
departs most widely from that of contemporary physicists. They
are convinced that it is impossible to account for the essential
aspects of quantum phenomena (apparently discontinuous and
temporally not determined changes of the situation of a system,
and at the same time corpuscular and undulatory qualities
of the elementary bodies of energy) by means of a theory which
describes the real state of things [objects] by continuous functions
of space for which differential equations are valid. They
are also of the opinion that in this way one can not understand
the atomic structure of matter and of radiation. They rather
expect that systems of differential equations, which could come
under consideration for such a theory, in any case would have
no solutions which would be regular (free from singularity)
everywhere in four-dimensional space. Above everything else,
however, they believe that the apparently discontinuous character
of elementary events can be described only by means of an
essentially statistical theory, in which the discontinuous changes
of the systems are taken into account by way of the continuous
changes of the probabilities of the possible states.
All of these remarks seem to me to be quite impressive. However,
the question which is really determinative appears to me
to be as follows: What can be attempted with some hope of
success in view of the present situation of physical theory? At
this point it is the experiences with the theory of gravitation
which determine my expectations. These equations give, from
my point of view, more warrant for the expectation to assert
something precise than all other equations of physics. One
may, for example, call on Maxwell's equations of empty space
by way of comparison. These are formulations which coincide
with the experiences of infinitely weak electro-magnetic fields.
This empirical origin already determines their linear form; it
has, however, already been emphasized above that the true
laws can not be linear. Such linear laws fulfill the super-position-principle for their solutions, but contain no assertions concerning
the interaction of elementary bodies. The true laws
can not be linear nor can they be derived from such. I have
learned something else from the theory of gravitation: No ever
so inclusive collection of empirical facts can ever lead to the
setting up of such complicated equations. A theory can be tested
by experience, but there is no way from experience to the setting
up of a theory. Equations of such complexity as are the
equations of the gravitational field can be found only through
the discovery of a logically simple mathematical condition which
determines the equations completely or [at least] almost completely.
Once one has those sufficiently strong formal conditions,
one requires only little knowledge of facts for the setting
up of a theory; in the case of the equations of gravitation it is
the four-dimensionality and the symmetric tensor as expression
for the structure of space which, together with the invariance
concerning the continuous transformation-group, determine the
equations almost completely.
Our problem is that of finding the field equations for the
total field. The desired structure must be a generalization of
the symmetric tensor. The group must not be any narrower than
that of the continuous transformations of co-ordinates...
A Brief Note on Completeness
Now it would of course be possible to object: If singularities
are permitted at the positions of the material points, what justification
is there for forbidding the occurrence of singularities
in the rest of space? This objection would be justified if the
equations of gravitation were to be considered as equations of
the total field. [Since this is not the case], however, one will
have to say that the field of a material particle may the less be
viewed as a pure gravitational field the closer one comes to
the position of the particle. If one had the field-equation of the
total field, one would be compelled to demand that the particles
themselves would everywhere be describable as singularity-free
solutions of the completed field-equations. Only then
would the general theory of relativity be a complete theory.
[So for Einstein, even his four-dimensional field theory is not yet complete. Completeness would eliminate possibilities in favor of a single determinate actuality; if only one possibility, there are no probabilities. All is certain. No new information is possible in the universe. And there is no irreversibility. All times are present in a deterministic block universe. See Einstein's remarks on Kurt Gödel's ideas on an arrow of time. Note that Einstein's views about quantum mechanics in 1949 were essentially unchanged from his views in 1930. See his explanation of how field theories came to be a part of our description of reality - alongside material particles - as a result of Maxwell's equations in his 1931 article "Maxwell's Influence on the Evolution of the Idea of Physical Reality." And Einstein arguably grew pessimistic about the possibilities for deterministic continuous field theories (by comparison with indeterministic and statistical discontinuous particle theories) in his later years: To Leopold Infeld he wrote in 1941, For Teachers
For Scholars
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