Background to Special Relativity:
The Wave Theory of Light ca. 1900
Newton’s “New Theory of Light and Colours” stated that white
light is a mixture of heterogeneous rays, separated by refraction
(e.g. by a prism) according to their degrees of refrangibility, with
the degrees of refrangibility corresponding to the spectral colours.
In the wave theory, a ray of light of a given degree of refrangibility,
corresponding to a given colour, is produced by a wave of a given
wavelength.
Light is just one kind of electromagnetic radiation, corresponding
to one small part of a spectrum of possible wavelengths, which
includes waves shorter than those of "violet" light ("ultraviolet"
light) and longer than those of "red" light ("infrared" light).
Wavelike behavior of light:
Interference: waves of differing wavelengths combining to
produce a wave with different characteristics
Diffraction: Bending of light around edges of objects
The Ether: If light is a wave, it is natural to assume that it is a
wave propagating in some medium; the waves must be the
vibrations of something.
Since electromagnetic radiation appears to be everywhere, and
can even pass through solid bodies, this medium must fill all of
space, including the interstitial spaces of the fundamental parts of
matter.
This medium became known as the "luminiferous" (light-bearing)
ether. Measurements of the velocity of light showed that it travels
at a constant velocity (c), which was assumed to be a velocity
relative to the ether.
The Galilei-Newtonian theory of relativity: The laws of physics
make no distiction between uniform motion and rest. Mechanical
effects depend only on the acceleration, not on the velocity, of
the system. Given a system in which the Newtonian relation
between force, mass, and velocity holds, any system in uniform
motion relative to this system is dynamically indistinguishable
from it.
Maxwell-Lorentz electrodynamics: Electrodynamical effects
depend on the propagation of waves in the ether, and therefore
they depend on the velocity of the system relative to the ether.
The velocity of light relative to the ether is a measureable
constant.
Are these two principles incompatible?
No!
The velocity of light is not an absolute velocity in space, but a
velocity relative to the ether. It is, in principle, no more a
difficulty than the existence of a determinate velocity of sound
relative to air.
The velocity of light as measured by any observer should
depend on that observer’s own velocity relative to the ether.
In other words, the velocity of light should obey the Newtonian
principle of the addition of velocities: Newtonian relativity
implies that any velocity depends on the velocity of the system
in which it is measured.
A sufficiently sensitive measurement should reveal the
dependence of the velocity of light on the motion of the earth
through the ether (the “ether wind”).
A light beam from A goes to a half-silvered
mirror at B: the reflected part goes to D, and
the transmitted part goes to E; the paths BD
and BE have the same length (L). The
parted beams are reflected at D and E and
then rejoin. If the apparatus is at rest, times
of the two trips BE and BD are equal, and
the rejoined waves will be in phase.
If the apparatus is moving through the ether
at velocity v, with the direction BE parallel
to the direction of motion, the times of light
travel along the two arms will not be equal.
The time from B to D and back should be
shorter than the time from B + E and back.
But the result of the experiment is null!
How to interpret this?
To accept that motion relative to the ether really makes no physical difference,
we would have to accept the notion that there is actually a velocity (the
velocity of light) that has the same value for observers in different states of
uniform motion-i.e. a velocity that appears the same to observers with different
velocities. This seems absurd.
The Lorentz contraction: The light did not travel at the same speed in both
directions; rather, the times were the same because the path BE contracted. In
other words, the speed of light appears to be the same because the measuring
apparatus contracted in the direction of motion. All objects moving through the
ether contract in the dimension parallel to their motion through the ether, and
this explains why motion through the ether cannot be detected.
Einstein on simultaneity (1917):
We encounter the same difficulty with all physical statements
in which the conception " simultaneous " plays a part. The
concept does not exist for the physicist until he has the
possibility of discovering whether or not it is fulfilled in an
actual case. We thus require a definition of simultaneity such
that this definition supplies us with the method by means of
which, in the present case, he can decide by experiment
whether or not both the lightning strokes occurred
simultaneously. As long as this requirement is not satisfied, I
allow myself to be deceived as a physicist (and of course the
same applies if I am not a physicist), when I imagine that I am
able to attach a meaning to the statement of simultaneity.
The “causal structure” of spacetime
time
The future
The present (“now”)
The past
Events that can still be influenced by what
you do now, but that cannot influence what is
happening now
here and now
Events that can influence what happens now,
but that cannot be influenced by anything you
do now
space
What if you couldn’t travel faster than light?
time
Events that can still be
influenced by what you
do now, but that cannot
influence what is
happening now: the
“future light cone” of p
Causally
inaccessible to p
p
Causally
inaccessible to p
Events that can influence what
happens now, but that cannot be
influenced by anything you do
now: the “past light cone” of p
space
If you can’t travel faster than light, then what’s happening
“now” can only influence you later.
time
“now”
p
space
What is simultaneous for a bat?
The bat in spacetime
time
space
Visual simultaneity
Visual perception in spacetime
time
space
If light propagation is isotropic, then light from the
explosion goes equal distances in equal times, and
reaches equidistant points at the same time.
The same
thing, in
space-time
time
space
Einstein on the train
(Dramatization)
Galilean transformations
x' x  vt
Lorentz transformations
x  vt
x'
2
1 v c
y' y
2
y' y
z ' z
z' z
t' t
t'
t  vx c 2
2
1 v c

2
t +
t2
t1
t-
F1
F2
Two views of the electrodynamics of moving bodies:
Einstein:
• The invariance of the
velocity of light is real.
• Simultaneity is relative:
whether two events occur
at the same time depends
on the frame of reference.
• Therefore the Lorentz
contraction and timedilatation are mere framedependent appearances.
Lorentz:
• The contraction and
dilatation are real.
• Simultaneity is absolute:
it is an objective fact
whether two events occur
at the same time.
• Therefore the invariance
of the velocity of light
must be mere appearance.
Mach’s
Principle
Einstein: Two spheres S1 and S2, rotate relative to one
another, and S2 bulges at its equator; how do we explain
this difference?
No answer can be admitted as epistemologically
satisfactory, unless the reason given is an observable fact of
experience....Newtonian mechanics does not give a
satisfactory answer to this question. It pronounces as
follows: The laws of mechanics apply to the space R1, in
respect to which the body S1 is at rest, but not to the space
R2, in respect to which the body S2 is at rest. But the
privileged space R1... is a merely factitious cause, and not a
thing that can be observed.
Einstein, 1916
What does Nature care about our coordinate systems?
Einstein, 1922
What makes the situation appear particularly unpleasant is the
fact that there should be infinitely many inertial systems, moving
uniformly and without rotation with respect to one another, that
are distinguished from all other rigid systems.
Einstein 1949
Bending of light-rays as they pass the Sun
The gravitational lens effect
space-time
geodesics
pole
geodesics of
the earth’s
surface
equator
F1
F2
Particles p1 and p2 fall in the earth’s gravitational field;
how is this fact to be interpreted?
p1
p2
Newton: The particles would follow space-time geodesics g1
and g2, but are forced into curved space-time trajectories
g2
g1
p1
p2
Einstein: The free-fall trajectories g1 and g2 are geodesics of
space-time, and their convergence measures the curvature of
space-time.
g1
p1
g2
p2
Newton’s equation: The strength of the gravitational field, as
measured by the relative acceleration of falling particles,
depends on the distribution of mass.
Einstein’s equation: The curvature of space-time, as measured
by the relative acceleration of geodesics, depends on the
distribution of mass-energy.
Gab = 8πTab
Coordinates in flat and curved spaces
{x,y}
c2
c1
M
P
p1
p2
Black hole’s effect on the light-cone structure
time
“Laplacian determinism” in the classical world: if you knew the
positions and momenta of all particles at a given time t, you
could deduce their trajectories for the entire future or past.
Space at time t
space
Specific assumptions of the classical viewpoint:
Theoretical magnitudes can take on a continuous range of
values.
Any particle has a definite trajectory in space-time, and a
definite position and momentum at any time.
The future position and momentum of any particle can be
predicted with certainty from its position and momentum at
any given time.
Electromagnetic radiation is wave propagation in a continuous
field.
Black body radiation:
Assumption: Intensity of black body radiation should take
on a continuous range of values. This will be proportional
to the frequency.
Fact: This assumption only agrees with the phenomena at
very low frequencies.
At higher frequencies, according to the assumption, the
intensity heads toward the “ultraviolet catastrophe”.
Planck: The correct values result when radiation is
assumed to be distributed in multiples of a constant
(“Planck’s constant”).
The photo-electric effect:
Light incident on a thin metal foil causes the release of
electrons. You might expect:
--that the energy of the electrons is proportional to the
intensity of the incident light.
Instead it is proportional to the frequency. “Red” light
doesn’t cause electrons to be released, no matter how
intense it is. Violet light, no matter how weak, will release
electrons of the same kinetic energy.
--that there would be some time-lag between the first
incidence and first ejection.
Instead, it begins when incidence begins.
The photoelectric effect
Einstein’s explanation:
Light is distributed in clumps
with energy E = h,
i.e. energy is proportional to
frequency.
The wave theory of light
Polarization:
Linear polarization
Circular polarization
Elliptic polarization
The wave theory of light: destructive interference
Constructive interference
Interference of waves in two-slit experiment
The atomic nature of electricity: the electron
1897: J.J. Thomson discovers that cathode rays consist of
streams of negatively-charged particles, “electrons”. The
ratio of charge to mass of the particle could be measured by
its deflection in a magnetic field.
The old atomic “theory”: Atoms are small, homogeneous
objects. (cf. Newton: “Solid, massy, impenetrable particles”)
J.J. Thomson’s model:
E. Rutherford, 1911:
Atom consists of a positively-charged nucleus surrounded by
negatively-charged electrons.
But the Rutherford model is inherently unstable:
Bohr’s model:
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Principles of the Bohr model of the atom:
1) Electrons assume only certain orbits around the nucleus.
These orbits are stable and called "stationary" orbits.
2) Each orbit has an energy associated with it. For example
the orbit closest to the nucleus has an energy E1, the next
closest E2 and so on.
3) Light is emitted when an electron jumps from a higher
orbit to a lower orbit and absorbed when it jumps from a
lower to higher orbit.
4) The energy and frequency of light emitted or absorbed
is given by the difference between the two orbit energies:
E(light) = Ef - Ei, n = E(light)/h
h= Planck's constant = 6.627x10-34 Js
"f" and "i” = final and initial orbits.
De Broglie’s wave interpretation of the Bohr atom
The Schroedinger equation:
* t represents time,
* r represents displacement,
* m is the mass of the particle,
* i is the square root of minus one and
* h is Planck's Constant.
What does the Schrödinger
equation mean?
Schrödinger’s view: The
wavelike variation of physical
properties of a system in
space and time.
Quantum-mechanical view: A “probability wave,” i.e. the
probability of finding a particle in a particular state
The Solvay Council, 1927
The more I think about the
physical portion of
Schrödinger's theory, the more
repulsive I find it...What
Schrödinger writes about the
visualizability of his theory 'is
probably not quite right,' in
other words it's crap.
--Werner Heisenberg, writing
to Wolfgang Pauli, 1926
We believe we have gained “anschaulich”
(“intuitive,” or “visualizable”) understanding of a
physical theory, if in all simple cases, we can grasp
the experimental consequences qualitatively and see
that the theory does not lead to any contradictions.
Heisenberg, 1927, On the Intuitive Content
[anschaulich Inhalt] of the Uncertainty Relation )
Heisenberg’s Uncertainty Principle (a.k.a.
“Indeterminacy Principle”): The “wave-particle duality”
reflects a fundamental limitation on the determinateness of
the properties of a physical system.
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….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 -rays with a wave length smaller than the size
of the atom would do.
Heisenberg’s Gamma-Ray Microscope: The apparatus used
to measure a particle inevitably disturbs it.
The position of the electron will be known with an accuracy given
by the wave length of the -ray. The electron may have been
practically at rest before the observation. But in the act of
observation at least one light quantum of the -ray 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.
At the same time one can easily see that there is no way of
observing the orbit of the electron around the nucleus. … the
first light quantum will have knocked the electron out from the
atom. The momentum of light quantum of the -ray is much
bigger than the original momentum of the electron if the wave
length of the -ray 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.
Photons polarized horizontally or vertically always keep their
polarization when measured by subsequent HV polarizers.
HV
HV
HV
HV
But if a polarization measurement is followed by a
measurement in a different orientation, the initial polarization
is lost.
45º polarized photons, after passing through an HV polarizer,
subsequently emerge at random through a second ±45º filter.
45º
±45º
HV
±45º
On the wave model, it is easy to see how polarized waves
can be recombined to the original polarization state. But
how does this happen with polarized photons?
45º
45º
45º
HV
45º
HV
±45º
Niels Bohr and Werner Heisenberg
It would in particular not be out of place in this connection to
warn against a misunderstanding likely to arise when one tries
to express the content of Heisenberg's well-known
indeterminacy relation by such a statement as ‘the position
and momentum of a particle cannot simultaneously be
measured with arbitrary accuracy’. According to such a
formulation it would appear as though we had to do with some
arbitrary renunciation of the measurement of either the one or
the other of two well-defined attributes of the object, which
would not preclude the possibility of a future theory taking
both attributes into account on the lines of the classical
physics. (Bohr 1937, p. 292)
“According to relativity theory, the word “simultaneous” admits
of a definition in no other way than through experiments in which
the velocity of light propagation enters essentially. If there were a
“sharper” definition of simultaneity, for example by signals that
propagate infinitely fast, relativity theory would be
impossible….The case is similar with the definition of the
concepts, “position of the electron,” “velocity,” in quantum
theory. All the experiments that we can perform toward the
definition of these words necessarily contain an uncertainty…. If
there were experiments that made possible a sharper
determination of p and q than that corresponding to [the
uncertainty relations], quantum mechanics would be impossible.”
Heisenberg, 1927
The Uncertainty Relation: two interpretations
1. The disturbance theory: the uncertainty relations
concern the inevitable influence of the measurement
apparatus on the state of the system to be measured.
2. The “Copenhagen interpretation”: The state of a
(quantum) physical system cannot be meaningfully
specified independently of its interaction with particular
(classical) measuring devices. The definitions of concepts
such as “position” and “momentum” must make
reference to the means of measuring them.
Is it possible to decide between these views on the basis of
experiment?
“Can the Quantum-Mechanical Description of Physical
Reality Be Considered Complete?” (Einstein, Podolsky, and
Rosen, 1935)
Criterion of Completeness: “Whatever the meaning assigned to
the term complete, the following requirement for a complete
theory seems to be a necessary one: every element of the physical
reality must have a counterpart in the physical theory.”
Criterion of Reality: “If, without in any way disturbing a system,
we can predict with certainty the value of a physical quantity,
then there exists an element of reality corresponding to this
quantity.”
The EPR argument:
Given two physical systems I and II that have interacted, they are
described by a common quantum-mechanical state ψ.
(Assume that they are sufficiently separated in space to make
interaction impossible.)
In the case of two particles, ψ assigns to their positions a negligible
probability of being found within some large (macroscopic) area.
By measuring an observable A on system I, we can predict with
certainty the result of a measurement of observable P on system II.
By measuring some different observable B on system I, we can
predict with certainty the result of a measurement of observable Q
on system II.
But observables P and Q are non-commuting, i.e. they cannot have
definite values, according to the Uncertainty Principle. (E.g. P is
position, Q is momentum.)
Since the measurements on I are made without disturbing II (recall
that the two are two far apart to interact), we can conclude that the
values of P and Q are both elements of reality.
But the quantum mechanical state ψ does not assign definite values
to P and Q.
Therefore ψ does not give a complete description of physical
reality.
“One could object to this conclusion on the grounds that our
criterion of reality is not sufficiently restrictive. Indeed, one
would not arrive at our conclusion if one insisted that two or
more physical quantities can be regarded as simultaneous
elements of reality only when they can be simultaneously
measured or predicted.
On this point of view, since either one or the other, but not both
simultaneously, of the quantities P and Q can be predicted, they
are not simultaneously real. This makes the reality of P and Q
depend upon the process of measurement carried out on the first
system in any way. No reasonable definition of reality could be
expected to permit this.”
Niels Bohr, 1935: “Can the Quantum-Mechanical Description of
Physical Reality Be Considered Complete?”
EPR argument does not affect the soundness of quantum
mechanics, “which is based on a coherent mathematical formalism
covering automatically any procedure of measurement like that
indicated. The apparent contradiction in fact only discloses an
essential inadequacy of the customary viewpoint of natural
philosophy for a rational account of physical phenomena of the
type with which we are concerned in quantum mechanics.”
“A criterion like that proposed by EPR contains...an essential
ambiguity when it is applied to the actual problems with which
we are here concerned. The ambiguity regards the meaning of
the expression, ‘without in any way disturbing the system.’”
The question is not the mechanical disturbance of one system
by the measurement of the other. It is, instead, “an influence on
the very conditions which define the possible types of
predictions regarding the future behaviour of the system.”
It must here be remembered that even in the indeterminacy
relation [Δq Δp ≈ h] we are dealing with an implication of the
formalism which defies unambiguous expression in words
suited to describe classical pictures. Thus a sentence like "we
cannot know both the momentum and the position of an atomic
object" raises at once questions as to the physical reality of two
such attributes of the object, which can be answered only by
referring to the conditions for an unambiguous use of spacetime concepts, on the one hand, and dynamical conservation
laws on the other hand.
Bohr’s reply to Einstein:
From our point of new we now see that the wording of the abovementioned criterion of physical reality proposed by Einstein,
Podolsky, and Rosen contains an ambiguity as regards the
meaning of the expression ' without in any way disturbing a
system.' Of course there is in a case like that just considered no
question of a mechanical disturbance of the system under
investigation during the last critical stage of the measuring
procedure. But even at this stage there is essentially the question
of an influence on the very conditions which define the possible
types of predictions regarding the future behaviour of the system.
Since these conditions constitute an inherent element of the
description of any phenomenon to which the term "physical
reality" can be properly attached, we see that the argumentation
of the mentioned authors does not justify their conclusion that
quantum-mechanical description is essentially incomplete. On
the contrary, this description, as appears from the preceding
discussion, may be characterised as a rational utilisation of all
possibilities of unambiguous interpretation of measurements,
compatible with the finite and uncontrollable interaction between
the objects and the measuring instruments in the field of
quantum theory.
(Bohr’s reply)
In fact, it is only the mutual exclusion of any two experimental
procedures, permitting the unambiguous definition of
complementary physical quantities, which provides room for new
physical laws, the coexistence of which might at first sight appear
irreconcilable with the basic principles of science. It is just this
entirely new situation as regards the description of physical
phenomena that the notion of complementarity aims at
characterising.
(Bohr’s reply)
The spin of a particle: for a given spatial axis, the particle has an
“intrinsic angular momentum,” its tendency to be deflected up or
down.
A schematic “EPR” experiment:
The quantum mechanical state ψ for a system of two particles,
created at a single source and therefore initially in causal
interaction, implies certain correlations between their respective
behaviors afterwards.
In a symmetrical Stern-Gerlach experiment, there is a statistical
correlation between spins of particles on each side.
But the correlation, apparently does not depend on characteristics
of the particular particles, or the orientation of the pair of magnets
through which any particle passes.
Rather, it depends on the relative orientation of the two pairs of
magnets.
How does each particle know what to do when it reaches its
magnet? How does it know how its magnet is oriented with
respect to the other one?
By signals?
The correlation is, in principle, completely independent of the
distance between the two pairs of magnets. The experiment can
be arranged to rule out any possibility of communication at the
speed of light or less.
Space-time diagram of a correlation experiment with SternGerlach magnets: no possibility of causal signaling
Past light cone of the
measurement event
Past light cone of the
measurement event
Source
Hidden variables: the “reality” of which quantum
mechanics gives an “incomplete” picture?
Is it possible that the particles “know what to do” by
“previous arrangement”?
Does their behavior when measured depend on their
own internal states, as determined in their common
causal past?
Could there be “instruction sets” laid down at the
source, that result in the correlations observed at the
magnets?
“Bell’s theorem” (John S. Bell)
Is it possible to express these questions mathematically,
and thereby to answer them by experiment?
Is it possible to set minimal conditions on correlations that
may result from previously established “hidden states”?
That is, is it possible to “instruct” pairs of particles in
advance so that when they are measured-- later-- the
outcomes are correlated as required by quantum
mechanics?
Bell’s Inequality: the minimal correlation between pairs of
outcomes, given that the outcomes depend only on the
“hidden variables.”
According to quantum mechanics, the experiment described
yields anti-correlations for spin values.
The probability that the two particles will have opposite values
of spin (up vs. down) depends on the angle θ between the two
magnet-pair orientations:
probability = ½cos2(θ/2)
When θ= 0 (when both pairs have the same orientation), the
particles will have opposite spin values with probability =1.
When the angle between the orientations =+120º,
probability of opposite spins = 1/4
(Recall that the detectors can be sufficiently separated to
preclude any causal influence.)
How could we prepare the particles to produce these results?
Consider three possible orientations: vertical, + 120o from vertical,
and -120o. In the case of the constant anticorrelation (when both
detectors have the same orientation), the initial states of the particles
could contain instructions that produce opposite spins:
Particle L: “spin up when the detector is vertical, down if +120o,
and down if -120o”.
Particle R: “down if vertical, up if +120o, up if -120o”
But these instructions work only on the assumption of identical
orientations.
When θ0, however, there are six possible pairs of orientations:
12, 21, 13, 31, 23, 32
If the particles have the instructions described above, which were
rigged to yield opposite spins when θ=0 i.e. up-down-down and
down-up-up -then clearly in two of the six possible orientation
pairs, namely 23 and 32, the two particles will have opposite spins.
Moreover, since there could also be pairs with instructions: up-upup and down-down-down, which would always show opposite
spins, two out of six is only the minimum value for the probability
of opposite spin values.
Bell's theorem: if the eventual spin measurements of particle
pairs are determined by hidden initial states, then in all cases
where the detectors have different orientations, spin values will
be opposite with a probability of at least 1/3.
Prediction of quantum mechanics: 1/4.
Which is wrong?
1.Locality: Systems that are spacelike separated do not
influence on another. Causal influence is transmitted through
space at the speed of light, or slower.
2.Separability: The complete description of the state of any
system does not include any information about systems that
are spacelike separated from it.
3.The predictions of quantum mechanics.
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Which of our classical assumptions does quantum
mechanics compel us to abandon?
Pierre Duhem (1861-1916)
W.V.O. Quine (1908-2000)
The Duhem-Quine thesis: No scientific principle can be
tested in isolation.
The totality of our so-called knowledge or beliefs, from the most
casual matters of geography and history to the profoundest laws
of atomic physics or even of pure mathematics and logic, is a
man-made fabric which impinges on experience only along the
edges. Or, to change the figure, total science is like a field of
force whose boundary conditions are experience. A conflict with
experience at the periphery occasions readjustments in the
interior of the field. Truth values have to be redistributed over
some of our statements. Re-evaluation of some statements entails
re-evaluation of others, because of their logical interconnections
-- the logical laws being in turn simply certain further statements
of the system, certain further elements of the field. (W.V.O.
Quine, 1951)
If this view is right, it is misleading to speak of the empirical
content of an individual statement -- especially if it be a
statement at all remote from the experiential periphery of the
field. Furthermore it becomes folly to seek a boundary
between synthetic statements, which hold contingently on
experience, and analytic statements which hold come what
may. Any statement can be held true come what may, if we
make drastic enough adjustments elsewhere in the system.
Even a statement very close to the periphery can be held true in the
face of recalcitrant experience by pleading hallucination or by
amending certain statements of the kind called logical laws.
Conversely, by the same token, no statement is immune to revision.
Revision even of the logical law of the excluded middle has been
proposed as a means of simplifying quantum mechanics; and what
difference is there in principle between such a shift and the shift
whereby Kepler superseded Ptolemy, or Einstein Newton, or
Darwin Aristotle?
Even a statement very close to the periphery can be held true in the
face of recalcitrant experience by pleading hallucination or by
amending certain statements of the kind called logical laws.
Conversely, by the same token, no statement is immune to revision.
Revision even of the logical law of the excluded middle has been
proposed as a means of simplifying quantum mechanics; and what
difference is there in principle between such a shift and the shift
whereby Kepler superseded Ptolemy, or Einstein Newton, or
Darwin Aristotle?
Hilary Putnam: “Is logic empirical?” (1968)
Quantum mechanical experiments can be reconciled with realism
if we accept a revision in our logic.
Distributive law:
A and (B or C) (A and B) or (A and C)
e.g. “The electron reached the screen and
(passed through slit B or passed through slit C)” implies:
“The electron reached the screen and passed through slit B”
OR,
“The electron reached the screen and passed through slit C”
The measurement problem:
How does a superposition of different possibilities resolve
itself into some particular observation?
John Von Neumann (1903-1957)
Process 1: Determination of the state
of a system by a measurement
process
Process 2: Deterministic evolution
according to the Schrodinger
equation
Schrodinger’s “Cat paradox”
One can even set up quite ridiculous cases. A cat is penned up
in a steel chamber, along with the following diabolical device
(which must be secured against direct interference by the cat):
in a Geiger counter there is a tiny bit of radioactive substance,
so small that perhaps in the course of one hour one of the atoms
decays, but also, with equal probability, perhaps none; if it
happens, the counter tube discharges and through a relay
releases a hammer which shatters a small flask of hydrocyanic
acid. If one has left this entire system to itself for an hour, one
would say that the cat still lives if meanwhile no atom has
decayed. The first atomic decay would have poisoned it. The
Psi function for the entire system would express this by having
in it the living and the dead cat (pardon the expression) mixed
or smeared out in equal parts.
It is typical of these cases that an indeterminacy originally
restricted to the atomic domain becomes transformed into
macroscopic indeterminacy, which can then be resolved by
direct observation. That prevents us from so naively accepting
as valid a “blurred model” for representing reality. In itself it
would not embody anything unclear or contradictory. There is a
difference between a shaky or out-of-focus photograph and a
snapshot of clouds and fog banks.
(Schrodinger, 1935)
The “ensemble interpretation”:
Quantum mechanics has nothing to say about the
properties of individual particles or systems.
Its essential subject matter is the statistical correlations
exhibited by large collections, or “ensembles,” of objects.
The “Many Worlds” Interpretation
Einstein: EPR correlations, in conjunction with special
relativity, imply the existence of local hidden variables not
described by quantum mechanics.
Bell’s theorem: Empirical correctness of quantum mechanics
implies the impossibility of local hidden variables.
David Bohm (1917-1992): The
conjunction of Bell’s theorem
with the empirical success of
quantum mechanics implies
that a non-local reality lies
beneath the quantum statistics.
Bohmian mechanics: Particles move deterministically in a
Galilean-- pre-relativistic-- background spacetime. Their
motions are guided by “pilot waves,” which are responsible
for their wave-like behavior.
“Is it not clear from the smallness of the scintillation on the
screen that we have to do with a particle? And is it not clear,
from the diffraction and interference patterns, that the motion of
the particle is directed by a wave? De Broglie showed in detail
how the motion of a particle, passing through just one of two
holes in screen, could be influenced by waves propagating
through both holes. And so influenced that the particle does not
go where the waves cancel out, but is attracted to where they
cooperate. This idea seems to me so natural and simple, to
resolve the wave-particle dilemma in such a clear and ordinary
way, that it is a great mystery to me that it was so generally
ignored.” (Bell 1986)
Pilot waves in the double slit experiment