Background to Special Relativity:

1
Background to Special Relativity The Wave
Theory of Light ca. 1900 Newtons 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).
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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
3
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.
4
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?
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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
observers 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).
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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.
13
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.
14
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.
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The causal structure of spacetime
time
Events that can still be influenced by what you
do now, but that cannot influence what is
happening now
The future
The present (now)
here and now
The past
Events that can influence what happens now, but
that cannot be influenced by anything you do now
space
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What if you couldnt 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
Causally inaccessible to p
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
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If you cant travel faster than light, then
whats happening now can only influence you
later.
time
now
p
space
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What is simultaneous for a bat?
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The bat in spacetime
time
space
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Visual simultaneity
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Visual perception in spacetime
time
space
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If light propagation is isotropic, then light
from the explosion goes equal distances in equal
times, and reaches equidistant points at the same
time.
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The same thing, in space-time
time
space
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Einstein on the train
(Dramatization)
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Galilean transformations Lorentz transformations
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t?
F2
F1
t2
t1
t-?
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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
  time-dilatation are mere frame-dependent
  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.

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Machs Principle
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Einstein Two spheres S1 and S2, rotate relative
to one another, and S2 bulges at its equator how
do we explain this difference?
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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
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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
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Bending of light-rays as they pass the Sun
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The gravitational lens effect
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space-time geodesics
pole
geodesics of the earths surface
equator
F1
F2
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Particles p1 and p2 fall in the earths
gravitational field how is this fact to be
interpreted?
p1
p2
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Newton The particles would follow space-time
geodesics g1 and g2, but are forced into curved
space-time trajectories
g2
g1
p2
p1
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Einstein The free-fall trajectories g1 and g2
are geodesics of space-time, and their
convergence measures the curvature of space-time.
g1
g2
p2
p1
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Newtons equation The strength of the
gravitational field, as measured by the relative
acceleration of falling particles, depends on the
distribution of mass. Einsteins equation The
curvature of space-time, as measured by the
relative acceleration of geodesics, depends on
the distribution of mass-energy. Gab 8pTab
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Coordinates in flat and curved spaces
x,y
c2
c1
M
P
p2
p1
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Black holes effect on the light-cone structure
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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.
time
Space at time t
space
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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.
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Black body radiation
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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 (Plancks
constant).
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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 doesnt 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.
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The photoelectric effect
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Einsteins explanation Light is distributed in
clumps with energy E h?, i.e. energy is
proportional to frequency.
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The wave theory of light Polarization
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Linear polarization
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Circular polarization
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Elliptic polarization
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The wave theory of light destructive interference
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Constructive interference
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Interference of waves in two-slit experiment
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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.
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The old atomic theory Atoms are small,
homogeneous objects. (cf. Newton Solid, massy,
impenetrable particles) J.J. Thomsons model
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E. Rutherford, 1911 Atom consists of a
positively-charged nucleus surrounded by
negatively-charged electrons.
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But the Rutherford model is inherently unstable
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Bohrs 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.
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De Broglies wave interpretation of the Bohr atom
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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.
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What does the Schrödinger equation
mean? Schrödingers 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
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The Solvay Council, 1927
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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
91
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 )
92
Heisenbergs 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.
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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.
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Heisenbergs Gamma-Ray Microscope The apparatus
used to measure a particle inevitably disturbs
it.
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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.
98
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.
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Photons polarized horizontally or vertically
always keep their polarization when measured by
subsequent HV polarizers.
HV
HV
HV
HV
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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
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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
45º
HV
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Niels Bohr and Werner Heisenberg
103
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)
104
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
105

• The Uncertainty Relation two interpretations
• The disturbance theory the uncertainty relations
  concern the inevitable influence of the
  measurement apparatus on the state of the system
  to be measured.
• 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?
106
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.
107
The EPR argument Given two physical systems I
and II that have interacted, they are described
by a common quantum-mechanical state ?. (Assume
that they are sufficiently separated in space to
make interaction impossible.) In the case of two
particles, ? 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.
108
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 ? does
not assign definite values to P and Q. Therefore
? does not give a complete description of
physical reality.
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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.
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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.
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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.
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It must here be remembered that even in the
indeterminacy relation ?q ?p 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 space-time concepts, on the
one hand, and dynamical conservation laws on the
other hand.
113
Bohrs reply to Einstein From our point of new
we now see that the wording of the
above-mentioned 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.
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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. (Bohrs reply)
115
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. (Bohrs
reply)
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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.
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A schematic EPR experiment
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The quantum mechanical state ? 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.
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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.
120
Space-time diagram of a correlation experiment
with Stern-Gerlach magnets no possibility of
causal signaling
Past light cone of the measurement event
Past light cone of the measurement event
Source
121
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?
122
Bells 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? Bells Inequality the minimal
correlation between pairs of outcomes, given that
the outcomes depend only on the hidden
variables.
123
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 ? between the two
magnet-pair orientations probability
½cos2(?/2) When ? 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.)
124
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.
125
When ??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
?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-up-up 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.
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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.
127
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.
132
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)
133
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.
134
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?
135
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?
136
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
137
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
138
Schrodingers 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.
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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)
141
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.
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The Many Worlds Interpretation
143
Einstein EPR correlations, in conjunction with
special relativity, imply the existence of local
hidden variables not described by quantum
mechanics. Bells theorem Empirical correctness
of quantum mechanics implies the impossibility of
local hidden variables.
David Bohm (1917-1992) The conjunction of Bells
theorem with the empirical success of quantum
mechanics implies that a non-local reality lies
beneath the quantum statistics.
144
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.
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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)
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Pilot waves in the double slit experiment