Download A. Is the wave function a description of the physical world?

Physics, Metaphysics, & Other Nonsense
H.S. Hestevold
Handout 15
Spring 2014
Quantum Mechanics: Philosophical Concerns, Part II
VI.
Wave function and wave function collapse
Read: Lawrence Sklar, “The Quantum Picture of the World” in SUP, 164.4-167 and diagram at the
top of p. 168.
A.
What is a wave function? First, some review: the
formula F = ma is a mathematical description of an
object's force. One can determine the force of a
particular automobile by multiplying the automobile's
mass by the automobile's acceleration. Similarly, a
wave function can be thought of as a mathematical
description of an entity in superposition -- a
description that allows us to make use of the bizarre
status of an entity (e.g. an electron or photon) in
superposition… whatever superposition may involve.
B.
LeClair: "What the Wave Function Means to Me:" We will
have a few minutes of Show-And-Tell from LeClair:
exactly, what can a wave function do for you? What
payoff does it allow you to enjoy?
C.
How should one interpret the wave function?
1.
Reminder: The wave function is a mathematical
description that works. That is, using the wave
function allows one to make successful predictions
about the behavior of physical entities, and it
allows one to solve real-world problems.
2.
The task of interpretation. If you show 'F=ma' to
the average middle-school student in Alabama, the
student will have no understanding of what the
letters and equality sign mean. To allow the
student to understand and make use of the formula,
you will need to provide the student with an
interpretation of the formula. You will need to
explain what the 'm' and 'a' represent, what the
mass of an object involves, what the acceleration
of an object involves, what the concept of force
involves, and why the concept of the force of an
object is useful.
3.
Interpreting the wave function. Plugging values
into a wave function works -- it allows physicists
and engineers to make predictions and solve
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problems. But what type of physical world is the
wave function about? What type of physical world
makes the wave function work? What are the photons
and electrons like that behave so bizarrely and
yet are describable by a wave function that is
operationally sound?
D.
a.
Is the wave function a description of nonparticle-like, non-wave-like material
entities that don’t exhibit the standard
intrinsic properties of sub-atomic particles?
b.
Is the wave function a description of the
probabilities that certain measurements will
be made if measurements are made at a
particular place and time?
c.
Is the wave function a description of the way
a particular material entity (e.g. photon or
electron) behaves in different actual worlds
at a given time?
d.
Is the wave function something else
altogether?
Wave function collapse. With respect to the double-slit
experiment, assume that between leaving the electron
gun at t1 and striking the detection screen at t8, an
electron E1 is in superposition -- a state in which it
lacks a definitive location with definitive intrinsic
properties. Suppose that you want to know whether
electron E1 is or isn't in particular spatial location
S92. You put your detector in S92 at t6, and you will
find that the particle is (or isn't0 there. You thereby
cause a wave function collapse: you bring it about that
there is no longer some non-zero and non-one
probability that the E1 is in location S92. Rather, the
detector reveals that the particle is in fact there (or
not, as the case may be).
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VII. The Copenhagen interpretation of QM
Read: Lawrence Sklar, “The Quantum Picture of the World” in SUP, 172.2-.175.2; Fib. 4.6 on p. 184.
A.
Is the wave function a description of the physical
world? As I understand the Bohr/Heisenberg
interpretation, the answer is No. It is a mistake to
believe that the wave function is a mathematical
description of a particle, a wave, or something that
has the property of being in superposition (or in any
other such state). Rather, the wave function is a
description of the probability that certain
measurements will be made at certain places at certain
times. That is, the wave function may tell us that we
have a certain probability of detecting that an
electron E1 passing through the left slit with an upspin if we place a detector by the left slit at a given
time. The wave function, then, is about the probability
that certain measurements will be made, not the
probability that there is a material entity at a
certain spot with certain properties that would cause
us to make certain measurements.
B.
What are detectors and what causal properties do they
have?
1.
According to some interpretations of QM, when one
uses a detector to determine whether a particle is
or isn’t within a particular region of space, the
detector causes a “wave function collapse” -- i.e.
it becomes a fact that the electron is within that
region or it becomes a fact that the electron is
not with that region. If no detector is employed,
there is no fact (known or unknown) as to whether
the electron is or isn’t within that region.
2.
If, however, two electrons undergo a simple
interaction with one another, no detector is
involved and thereby there occurs no wave function
collapse. That is, it would remain false that
either electron has a definitive spatial location.
3.
Detector mystery #1. What is the difference
between a bunch of particles that constitute a
detector and a bunch of particles that constitute
doorknob?
4.
Detector mystery #2. Is there a bizarre causal
connection between consciousness and the state of
the world at any given? (Please don't grow
obsessed with this option.)
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C.
The Schrodinger/Einstein cat objection (Figure 4.6).
VIII. The many-worlds interpretation of QM
Read: Lawrence Sklar, “The Quantum Picture of the World” in SUP, 193.4-195.2.
A.
Hugh Everett’s “many worlds” interpretation.1
1.
Does the many-worlds interpretation allow a wave
function collapse?
2.
What the wave function describes.
3.
Multiple actual worlds.
4.
Reminder: the Deutsch/Lockwood model of time
travel turned on the many-worlds interpretation of
QM.
B.
Schrodinger's cat revisited: What does the many-worlds
interpretation imply about Schrodinger's poor cat?
C.
Concerns.
1.
The usual concerns about multiple-world views.
2.
Tim Maudlin’s concern:2 to talk of the
probabilities that are essential to QM is to talk
about the probability that a wave function will
collapse in a certain way. If, in fact, both ways
do occur. Then, what are probabilities about after
all? They cannot be about the odds that the world
will be in one state but not another. (The
probability is 1 that the cat is alive (in one
world); and the probability is also 1 that the cat
is not alive (in some other actual world).
1 See Tim Maudlin’s “Metaphysics and Quantum Physics," The Oxford Handbook of
Metaphysics ed. by Loux and Zimmerman (2003), p. 467.
2 “Metaphysics and Quantum Physics," p. 468
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IX.
Determinism
A.
Determinism.
D1
Event p is the sufficient causal condition for event q
=Df It is physically necessary that if p occurs, q
occurs.3
DET For any event e that occurs, there is a sufficient
causal condition for e.
B.
Predictability. Some might be inclined to conclude that
Determinism implies Predictability -- that if DET is
true, then in principle, it is possible to predict at
time t the state of the world at any time after t. This
is what John Hospers wrote about the difference between
Determinism and Predictability:
Determinism... is a metaphysical theory: it has to do
with what is, with what exists in reality; but
predictability is an epistemological matter: it has to do
with our knowledge of what is. To predict accurately we
would require not only that everything have a cause but
that we know in detail what these causes are and what are
the laws connecting causes with effects. Predictability
would be a consequence of determinism plus our knowledge
of the laws, but it is not what determinism consists in.4
Hospers should have added that there could be no
predictability unless it is in principle (physically)
possible to have complete knowledge of the state of the
world at a given time. If one couples such knowledge
with complete knowledge of the laws of nature, then one
could in principle predict future states of the world
if DET were true. The following captures the difference
between DET and predictability:
3 Alternatively, to say that p is the sufficient causal condition for q is to
say that, in every possible world that has the same laws of nature as the
actual world, it is true that if p occurs, q occurs.
4 John Hospers, An Introduction to Philosophical Analysis (2nd. ed.; Englewood
Cliffs, NJ: Prentice-Hall, Inc., 1967), p. 328.
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PRE (i) DET is correct; (ii) it is physically possible to
have exhaustive knowledge of the laws of nature; (iii)
it is physically possible to have exhaustive
knowledge of the state of the world at any given time
t; (iv) from exhaustive knowledge of the laws of
nature and the state of the world at any time t, it is
possible to deduce the state of the word at any time
after t.
Clearly, then, if DET is correct, it does not
necessarily follow that Predictability is correct: for
all we know, the world may be such that, it is in
principle impossible for one to have exhaustive
knowledge of the state of the world at some particular
time t. And, if Predictability is true, there is no
guarantee that one will be able to predict the future:
though it may be physically possible to have exhaustive
knowledge of the laws of nature and the state of the
world at any given time, it may nonetheless be true
that we lack the intelligence or technological means to
have such exhaustive knowledge.
C.
X.
For LeClair: What do the findings of QM imply about DET
and PRE?
Why is it that humans can’t solve these problems?
A.
The Kantian view.
B.
Logical empiricism (aka logical positivism).
C.
Are we simply not smart enough?
D.
The New Mysterianism. In writing about inability to
understand the relation between consciousness and brain
states, Colin McGinn writes:
[T]he limits of our minds are just not the limits of
reality. It is deplorably anthropocentric to insist that
reality be constrained by what the human mind can conceive. We
need to cultivate a vision of reality (a metaphysics) that
makes it truly independent of our given cognitive powers, a
conception that includes these powers as a proper part.5
Peter van Inwagen has also contemplated the question of
why there seems to be no agreement among professional
metaphysicians regarding the nature of space and time,
consciousness, free will, etc.:
5 The Problem of Consciousness (Blackwell, 1991), p. 22.
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One might hold that the human failure to achieve
established metaphysical results is due to some special
quirk of the human mind, a quirk that could be absent from
the minds of Martians or intelligent dolphins.
Evolutionary biology suggests that human beings possess a
very specific set of mental talents and that other
intelligent or rational species might possess a different
but equally specific sets of talents. We, as a species are
very good at physics, and -- all the evidence suggests
this -- very bad a metaphysics. Perhaps we shall one day
discover among the stars a species that is very good at
metaphysics and very bad at physics. [Noam Chomsky has
made this conjecture.] It may be that the best human
metaphysicians are like acrobats. Acrobats are people who
in virtue of long training and arduous discipline, can do
what arboreal apes do much better without any training at
all. Acrobats achieve what they do achieve by taking
capacities of hand, mind, and eye that were “designed” for
purposes quite unrelated to swinging through the air and
pushing these capacities to their limits. Perhaps human
metaphysicians are like that: they work by taking human
intellectual capacities designed for purposes quite
unrelated to questions about ultimate reality and pushing
these capacities to their limits. It may be that a
comparison Samuel Johnson used for a rather different
purpose applies to the human metaphysician: such a person
is like a dog walking on its hind legs. “It is not done
well,” said Dr. Johnson, “but you are surprised to find it
done at all.”6
6 Metaphysics (3rd ed.; Westview, 2009), p. 14.
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