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How the Laws of Physics Lie
Nancy Cartwright
, Associate Professor of Philosophy, Stanford University, California
Nancy Cartwright argues for a novel conception of the role of fundamental scientific laws
in modern natural science. If we attend closely to the manner in which theoretical laws
figure in the practice of science, we see that despite their great explanatory power these
laws do not describe reality. Instead, fundamental laws describe highly idealized objects
in models. Thus, the correct account of explanation in science is not the traditional
covering law view, but the ‘simulacrum’ account. On this view, explanation is a matter of
constructing a model that may employ, but need not be consistent with, a theoretical
framework, in which phenomenological laws that are true of the empirical case in
question can be derived. Anti-realism about theoretical laws does not, however, commit
one to anti-realism about theoretical entities. Belief in theoretical entities can be
grounded in well-tested localized causal claims about concrete physical processes,
sometimes now called ‘entity realism’. Such causal claims provide the basis for partial
realism and they are ineliminable from the practice of explanation and intervention in
nature.
Contents
Introduction 1
Essay 1 Causal Laws and Effective Strategies 20
Essay 2 The Truth Doesn't Explain Much 43
Essay 3 Do the Laws of Physics State the Facts? 54
Essay 4 The Reality of Causes In a World of Instrumental Laws 74
Essay 5 When Explanation Leads to Inference 87
Essay 6 For Phenomenological Laws 100
Essay 7 Fitting Facts to Equations 128
Essay 8 The Simulacrum Account of Explanation 143
Essay 9 How the Measurement Problem Is an Artefact of the
Mathematics 163
Introduction
Nancy Cartwright
Philosophers distinguish phenomenological from theoretical laws. Phenomenological
laws are about appearances; theoretical ones are about the reality behind the appearances.
The distinction is rooted in epistemology. Phenomenological laws are about things which
we can at least in principle observe directly, whereas theoretical laws can be known only
by indirect inference. Normally for philosophers ‘phenomenological’ and ‘theoretical’
mark the distinction between the observable and the unobservable.
Physicists also use the terms ‘theoretical’ and ‘phenomenological’. But their usage makes
a different distinction. Physicists contrast ‘phenomenological’ with ‘fundamental’. For
example, Pergamon Press's
Encyclopaedic Dictionary of Physics
says, ‘A
phenomenological theory relates observed phenomena by postulating certain equations
but does not enquire too deeply into their fundamental significance.’
1
The dictionary mentions observed phenomena. But do not be misled. These
phenomenological equations are not about direct observables that contrast with the
theoretical entities of the philosopher. For look where this definition occurs—under the
heading ‘Superconductivity and superfluidity, phenomenological theories of’. Or notice
the theoretical entities and processes mentioned in the contents of a book like
Phenomenology of Particles at High Energies
(proceedings of the 14th Scottish
Universities Summer School in Physics): (1) Introduction to Hadronic Interactions at
High Energies. (2) Topics in Particle Physics with Colliding Proton Beams. (3)
Phenomenology of Inclusive Reactions. (4) Multihadron Production at High Energies:
Phenomenology and Theory.
2
end p.1
Francis Everitt, a distinguished experimental physicist and biographer of James Clerk
Maxwell, picks Airy's law of Faraday's magneto-optical effect as a characteristic
phenomenological law.
3
In a paper with Ian Hacking, he reports, ‘Faraday had no
mathematical theory of the effect, but in 1846 George Biddell Airy (1801–92), the
English Astronomer Royal, pointed out that it could be represented analytically in the
wave theory of light by adding to the wave equations, which contain second derivatives
of the displacement with respect to time, other
ad hoc
terms, either first or third
derivatives of the displacement.’
4
Everitt and Hacking contrast Airy's law with other
levels of theoretical statement—‘physical models based on mechanical hypotheses, . . .
formal analysis within electromagnetic theory based on symmetry arguments’, and
finally, ‘a physical explanation in terms of electron theory’ given by Lorentz, which is
‘essentially the theory we accept today’.
Everitt distinguishes Airy's phenomenological law from the later theoretical treatment of
Lorentz, not because Lorentz employs the unobservable electron, but rather because the
electron theory explains the magneto-optical effect and Airy's does not.
Phenomenological laws describe what happens. They describe what happens in
superfluids or meson-nucleon scattering as well as the more readily observed changes in
Faraday's dense borosilicate glass, where magnetic fields rotate the plane of polarization
of light. For the physicist, unlike the philosopher, the distinction between theoretical and
phenomenological has nothing to do with what is observable and what is unobservable.
Instead the terms separate laws which are fundamental and explanatory from those that
merely describe.
The divide between theoretical and phenomenological commonly separates realists from
anti-realists. I argue in these essays for a kind of anti-realism, and typically it is an anti-
realism that accepts the phenomenological and rejects the theoretical. But it is not theory
versus observation that I reject. Rather it is the theoretical as opposed to the
phenomenological.
end p.2
In modern physics, and I think in other exact sciences as well, phenomenological laws are
meant to describe, and they often succeed reasonably well. But fundamental equations are
meant to explain, and paradoxically enough the cost of explanatory power is descriptive
adequacy. Really powerful explanatory laws of the sort found in theoretical physics do
not state the truth.
I begin from the assumption that we have an immense number of very highly confirmed
phenomenological laws. Spectra-physics Incorporated continuously runs a quarter of a
million dollars' worth of lasers to death to test their performance characteristics. Nothing
could be better confirmation than that. But how do the fundamental laws of quantum
mechanics, which are supposed to explain the detailed behaviour of lasers, get their
confirmation? Only indirectly, by their ability to give true accounts of lasers, or of
benzene rings, or of electron diffraction patterns. I will argue that the accounts they give
are generally not true, patently not true by the same practical standards that admit an
indefinite number of commonplace phenomenological laws. We have detailed expertise
for testing the claim of physics about what happens in concrete situations. When we look
to the real implications of our fundamental laws, they do not meet these ordinary
standards. Realists are inclined to believe that if theoretical laws are false and inaccurate,
then phenomenological laws are more so. I urge just the reverse. When it comes to the
test, fundamental laws are far worse off than the phenomenological laws they are
supposed to explain.
The essays collected in this volume may be grouped around three different but
interrelated arguments for this paradoxical conclusion.
(1)
The manifest explanatory power of fundamental laws does not argue for their truth.
(2)
In fact the way they are used in explanation argues for their falsehood. We explain by
ceteris paribus
laws, by composition of causes, and by approximations that improve
on what the fundamental laws dictate. In all of these cases the fundamental laws
patently do not get the facts right.
(3)
The appearance of truth comes from a bad model of
end p.3
explanation, a model that ties laws directly to reality. As an alternative to the
conventional picture I propose a
simulacrum
account of explanation. The route from
theory to reality is from theory to model, and then from model to phenomenological law.
The phenomenological laws are indeed true of the objects in reality—or might be; but
the fundamental laws are true only of objects in the model.
1. Against Inference to Best Explanation
I will argue that the falsehood of fundamental laws is a consequence of their great
explanatory power. This is the exact opposite of what is assumed by a well-known and
widely discussed argument form—inference to the best explanation. The basic idea of
this argument is: if a hypothesis explains a sufficiently wide variety of phenomena well
enough, we can infer that the hypothesis is true. Advocates of this argument form may
disagree about what counts as well enough, or how much variety is necessary. But they
all think that explanatory power, far from being at odds with truth, leads us to it. My first
line of argument in these essays denies that explanation is a guide to truth.
Numerous traditional philosophical positions bar inferences to best explanations.
Scepticism, idealism, and positivism are examples. But the most powerful argument I
know is found in Pierre Duhem's
Aim and Structure of Physical Theory
,
5
reformulated in
a particularly pointed way by Bas van Fraassen in his recent book
The Scientific Image
.
6
Van Fraassen asks, what has explanatory power to do with truth? He offers more a
challenge than an argument: show exactly what about the explanatory relationship tends
to guarantee that if
x
explains
y
and
y
is true, then
x
should be true as well. This challenge
has an answer in the case of
causal
explanation, but
only
in the case of causal
explanation. That is my thesis in ‘When Explanation Leads to Inference’. Suppose we
describe the concrete causal process by which a phenomenon is brought about. That kind
of explanation
end p.4
succeeds only if the process described actually occurs. To the extent that we find the
causal explanation acceptable, we must believe in the causes described.
For example, consider the radiometer, invented by William Crookes in 1853. It is a little
windmill whose vanes, black on one side, white on the other, are enclosed in an
evacuated glass bowl. When light falls on the radiometer, the vanes rotate. At first it was
assumed that light pressure causes the vanes to go round. Soon it was realized that the
pressure of light would not be nearly great enough. It was then agreed that the rotation is
due to the action of the gas molecules left inside the evacuated bowl. Crookes had tried to
produce a vacuum in his radiometer. Obviously if we accept the agreed explanation, we
infer that Crookes's vacuum was imperfect; the explanation demands the presence of
molecules in the jar.
There were two rival hypotheses about what the molecules did. Both ideas are still
defended by different camps today. A first proposal was that the vanes are pushed around
by pressure of the molecules bouncing more energetically from the black side than the
white. But in 1879 James Clerk Maxwell, using the kinetic theory of gases, argued that
the forces in the gas would be the same in all directions, and so could not push the vanes.
Instead differential heating in the gas produces tangential stresses, which cause slippage
of the gas over the surface. As the gas flows around the edge, it pulls the vanes with it. In
his biography of Maxwell, Francis Everitt urges the superiority of Maxwell's account
over the more widely accepted alternative.
7
His confidence in Maxwell's causal story is
reflected in his ontological views. His opponents think the tangential stresses are
negligible. But unlike them, Everitt believes that if he builds a radiometer big enough he
will be able to measure the flow of gas around the edge of the vanes.
The molecules in Crookes's radiometer are invisible, and the tangential stresses are not
the kinds of things one would have expected to see in the first place. Yet, like Everitt, I
believe in both. I believe in them because I accept Maxwell's causal account of why the
vanes move around. In producing this account, Maxwell deploys certain fundamental
laws, such as Boltzmann's equation and the equation of continuity, which I do not believe
in. But one can reject theoretical laws without rejecting theoretical entities. In the case of
Maxwell's molecules and the tangential stresses in the radiometer, there is an answer to
van Fraassen's question: we have a satisfactory causal account, and so we have good
reason to believe in the entities, processes, and properties in question.
Causal reasoning provides good grounds for our beliefs in theoretical entities. Given our
general knowledge about what kinds of conditions and happenings are possible in the
circumstances, we reason backwards from the detailed structure of the effects to exactly
what characteristics the causes must have in order to bring them about. I have sometimes
summarized my view about explanation this way: no inference to best explanation; only
inference to most likely cause. But that is right only if we are very careful about what
makes a cause ‘likely’. We must have reason to think that this cause, and no other, is the
only practical possibility, and it should take a good deal of critical experience to convince
us of this.
We make our best causal inferences in very special situations—situations where our
general view of the world makes us insist that a known phenomenon has a cause; where
the cause we cite is the kind of thing that could bring about the effect and there is an
appropriate process connecting the cause and the effect; and where the likelihood of other
causes is ruled out. This is why controlled experiments are so important in finding out
about entities and processes which we cannot observe. Seldom outside of the controlled
conditions of an experiment are we in a situation where a cause can legitimately be
inferred.
Again the radiometer illustrates. Maxwell is at odds with the standard account. To resolve
the debate, Maxwell's defender, Everitt, proposes not further theoretical analysis, but
rather an experiment. He wants to build an enormous radiometer, where he can control
the partial vacuum and its viscosity, vary the coefficient of friction on the vanes, vary
their widths, take into account winds in the jar, and
end p.6
finally determine whether the tangential stresses are really the major cause of rotation.
The dispute about normal and tangential stresses highlights a nice point about
observation. Philosophical debate has focused on entities. Instrumentalists, who want to
believe only in what they can see, get trapped in footling debates: do we really ‘see’
through a microscope? An electron microscope? A phase-interference light microscope?
Even with the naked eye, do we not in any case see only effects? But many of the things
that are realities for physics are not things to be seen. They are non-visual features—the
spin of the electron, the stress between the gas surface, the rigidity of the rod.
Observation—seeing with the naked eye—is not the test of existence here. Experiment is.
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How the Laws of Physics Lie
Nancy Cartwright
, Associate Professor of Philosophy, Stanford University, California
Nancy Cartwright argues for a novel conception of the role of fundamental scientific laws
in modern natural science. If we attend closely to the manner in which theoretical laws
figure in the practice of science, we see that despite their great explanatory power these
laws do not describe reality. Instead, fundamental laws describe highly idealized objects
in models. Thus, the correct account of explanation in science is not the traditional
covering law view, but the ‘simulacrum’ account. On this view, explanation is a matter of
constructing a model that may employ, but need not be consistent with, a theoretical
framework, in which phenomenological laws that are true of the empirical case in
question can be derived. Anti-realism about theoretical laws does not, however, commit
one to anti-realism about theoretical entities. Belief in theoretical entities can be
grounded in well-tested localized causal claims about concrete physical processes,
sometimes now called ‘entity realism’. Such causal claims provide the basis for partial
realism and they are ineliminable from the practice of explanation and intervention in
nature.
Contents
Introduction 1
Essay 1 Causal Laws and Effective Strategies 20
Essay 2 The Truth Doesn't Explain Much 43
Essay 3 Do the Laws of Physics State the Facts? 54
Essay 4 The Reality of Causes In a World of Instrumental Laws 74
Essay 5 When Explanation Leads to Inference 87
Essay 6 For Phenomenological Laws 100
Essay 7 Fitting Facts to Equations 128
Essay 8 The Simulacrum Account of Explanation 143
Essay 9 How the Measurement Problem Is an Artefact of the
Mathematics 163
Introduction
Nancy Cartwright
Philosophers distinguish phenomenological from theoretical laws. Phenomenological
laws are about appearances; theoretical ones are about the reality behind the appearances.
The distinction is rooted in epistemology. Phenomenological laws are about things which
we can at least in principle observe directly, whereas theoretical laws can be known only
by indirect inference. Normally for philosophers ‘phenomenological’ and ‘theoretical’
mark the distinction between the observable and the unobservable.
Physicists also use the terms ‘theoretical’ and ‘phenomenological’. But their usage makes
a different distinction. Physicists contrast ‘phenomenological’ with ‘fundamental’. For
example, Pergamon Press's
Encyclopaedic Dictionary of Physics
says, ‘A
phenomenological theory relates observed phenomena by postulating certain equations
but does not enquire too deeply into their fundamental significance.’
1
The dictionary mentions observed phenomena. But do not be misled. These
phenomenological equations are not about direct observables that contrast with the
theoretical entities of the philosopher. For look where this definition occurs—under the
heading ‘Superconductivity and superfluidity, phenomenological theories of’. Or notice
the theoretical entities and processes mentioned in the contents of a book like
Phenomenology of Particles at High Energies
(proceedings of the 14th Scottish
Universities Summer School in Physics): (1) Introduction to Hadronic Interactions at
High Energies. (2) Topics in Particle Physics with Colliding Proton Beams. (3)
Phenomenology of Inclusive Reactions. (4) Multihadron Production at High Energies:
Phenomenology and Theory.
2
end p.1
Francis Everitt, a distinguished experimental physicist and biographer of James Clerk
Maxwell, picks Airy's law of Faraday's magneto-optical effect as a characteristic
phenomenological law.
3
In a paper with Ian Hacking, he reports, ‘Faraday had no
mathematical theory of the effect, but in 1846 George Biddell Airy (1801–92), the
English Astronomer Royal, pointed out that it could be represented analytically in the
wave theory of light by adding to the wave equations, which contain second derivatives
of the displacement with respect to time, other
ad hoc
terms, either first or third
derivatives of the displacement.’
4
Everitt and Hacking contrast Airy's law with other
levels of theoretical statement—‘physical models based on mechanical hypotheses, . . .
formal analysis within electromagnetic theory based on symmetry arguments’, and
finally, ‘a physical explanation in terms of electron theory’ given by Lorentz, which is
‘essentially the theory we accept today’.
Everitt distinguishes Airy's phenomenological law from the later theoretical treatment of
Lorentz, not because Lorentz employs the unobservable electron, but rather because the
electron theory explains the magneto-optical effect and Airy's does not.
Phenomenological laws describe what happens. They describe what happens in
superfluids or meson-nucleon scattering as well as the more readily observed changes in
Faraday's dense borosilicate glass, where magnetic fields rotate the plane of polarization
of light. For the physicist, unlike the philosopher, the distinction between theoretical and
phenomenological has nothing to do with what is observable and what is unobservable.
Instead the terms separate laws which are fundamental and explanatory from those that
merely describe.
The divide between theoretical and phenomenological commonly separates realists from
anti-realists. I argue in these essays for a kind of anti-realism, and typically it is an anti-
realism that accepts the phenomenological and rejects the theoretical. But it is not theory
versus observation that I reject. Rather it is the theoretical as opposed to the
phenomenological.
end p.2
In modern physics, and I think in other exact sciences as well, phenomenological laws are
meant to describe, and they often succeed reasonably well. But fundamental equations are
meant to explain, and paradoxically enough the cost of explanatory power is descriptive
adequacy. Really powerful explanatory laws of the sort found in theoretical physics do
not state the truth.
I begin from the assumption that we have an immense number of very highly confirmed
phenomenological laws. Spectra-physics Incorporated continuously runs a quarter of a
million dollars' worth of lasers to death to test their performance characteristics. Nothing
could be better confirmation than that. But how do the fundamental laws of quantum
mechanics, which are supposed to explain the detailed behaviour of lasers, get their
confirmation? Only indirectly, by their ability to give true accounts of lasers, or of
benzene rings, or of electron diffraction patterns. I will argue that the accounts they give
are generally not true, patently not true by the same practical standards that admit an
indefinite number of commonplace phenomenological laws. We have detailed expertise
for testing the claim of physics about what happens in concrete situations. When we look
to the real implications of our fundamental laws, they do not meet these ordinary
standards. Realists are inclined to believe that if theoretical laws are false and inaccurate,
then phenomenological laws are more so. I urge just the reverse. When it comes to the
test, fundamental laws are far worse off than the phenomenological laws they are
supposed to explain.
The essays collected in this volume may be grouped around three different but
interrelated arguments for this paradoxical conclusion.
(1)
The manifest explanatory power of fundamental laws does not argue for their truth.
(2)
In fact the way they are used in explanation argues for their falsehood. We explain by
ceteris paribus
laws, by composition of causes, and by approximations that improve
on what the fundamental laws dictate. In all of these cases the fundamental laws
patently do not get the facts right.
(3)
The appearance of truth comes from a bad model of
end p.3
explanation, a model that ties laws directly to reality. As an alternative to the
conventional picture I propose a
simulacrum
account of explanation. The route from
theory to reality is from theory to model, and then from model to phenomenological law.
The phenomenological laws are indeed true of the objects in reality—or might be; but
the fundamental laws are true only of objects in the model.
1. Against Inference to Best Explanation
I will argue that the falsehood of fundamental laws is a consequence of their great
explanatory power. This is the exact opposite of what is assumed by a well-known and
widely discussed argument form—inference to the best explanation. The basic idea of
this argument is: if a hypothesis explains a sufficiently wide variety of phenomena well
enough, we can infer that the hypothesis is true. Advocates of this argument form may
disagree about what counts as well enough, or how much variety is necessary. But they
all think that explanatory power, far from being at odds with truth, leads us to it. My first
line of argument in these essays denies that explanation is a guide to truth.
Numerous traditional philosophical positions bar inferences to best explanations.
Scepticism, idealism, and positivism are examples. But the most powerful argument I
know is found in Pierre Duhem's
Aim and Structure of Physical Theory
,
5
reformulated in
a particularly pointed way by Bas van Fraassen in his recent book
The Scientific Image
.
6
Van Fraassen asks, what has explanatory power to do with truth? He offers more a
challenge than an argument: show exactly what about the explanatory relationship tends
to guarantee that if
x
explains
y
and
y
is true, then
x
should be true as well. This challenge
has an answer in the case of
causal
explanation, but
only
in the case of causal
explanation. That is my thesis in ‘When Explanation Leads to Inference’. Suppose we
describe the concrete causal process by which a phenomenon is brought about. That kind
of explanation
end p.4
succeeds only if the process described actually occurs. To the extent that we find the
causal explanation acceptable, we must believe in the causes described.
For example, consider the radiometer, invented by William Crookes in 1853. It is a little
windmill whose vanes, black on one side, white on the other, are enclosed in an
evacuated glass bowl. When light falls on the radiometer, the vanes rotate. At first it was
assumed that light pressure causes the vanes to go round. Soon it was realized that the
pressure of light would not be nearly great enough. It was then agreed that the rotation is
due to the action of the gas molecules left inside the evacuated bowl. Crookes had tried to
produce a vacuum in his radiometer. Obviously if we accept the agreed explanation, we
infer that Crookes's vacuum was imperfect; the explanation demands the presence of
molecules in the jar.
There were two rival hypotheses about what the molecules did. Both ideas are still
defended by different camps today. A first proposal was that the vanes are pushed around
by pressure of the molecules bouncing more energetically from the black side than the
white. But in 1879 James Clerk Maxwell, using the kinetic theory of gases, argued that
the forces in the gas would be the same in all directions, and so could not push the vanes.
Instead differential heating in the gas produces tangential stresses, which cause slippage
of the gas over the surface. As the gas flows around the edge, it pulls the vanes with it. In
his biography of Maxwell, Francis Everitt urges the superiority of Maxwell's account
over the more widely accepted alternative.
7
His confidence in Maxwell's causal story is
reflected in his ontological views. His opponents think the tangential stresses are
negligible. But unlike them, Everitt believes that if he builds a radiometer big enough he
will be able to measure the flow of gas around the edge of the vanes.
The molecules in Crookes's radiometer are invisible, and the tangential stresses are not
the kinds of things one would have expected to see in the first place. Yet, like Everitt, I
believe in both. I believe in them because I accept Maxwell's causal account of why the
vanes move around. In producing this account, Maxwell deploys certain fundamental
laws, such as Boltzmann's equation and the equation of continuity, which I do not believe
in. But one can reject theoretical laws without rejecting theoretical entities. In the case of
Maxwell's molecules and the tangential stresses in the radiometer, there is an answer to
van Fraassen's question: we have a satisfactory causal account, and so we have good
reason to believe in the entities, processes, and properties in question.
Causal reasoning provides good grounds for our beliefs in theoretical entities. Given our
general knowledge about what kinds of conditions and happenings are possible in the
circumstances, we reason backwards from the detailed structure of the effects to exactly
what characteristics the causes must have in order to bring them about. I have sometimes
summarized my view about explanation this way: no inference to best explanation; only
inference to most likely cause. But that is right only if we are very careful about what
makes a cause ‘likely’. We must have reason to think that this cause, and no other, is the
only practical possibility, and it should take a good deal of critical experience to convince
us of this.
We make our best causal inferences in very special situations—situations where our
general view of the world makes us insist that a known phenomenon has a cause; where
the cause we cite is the kind of thing that could bring about the effect and there is an
appropriate process connecting the cause and the effect; and where the likelihood of other
causes is ruled out. This is why controlled experiments are so important in finding out
about entities and processes which we cannot observe. Seldom outside of the controlled
conditions of an experiment are we in a situation where a cause can legitimately be
inferred.
Again the radiometer illustrates. Maxwell is at odds with the standard account. To resolve
the debate, Maxwell's defender, Everitt, proposes not further theoretical analysis, but
rather an experiment. He wants to build an enormous radiometer, where he can control
the partial vacuum and its viscosity, vary the coefficient of friction on the vanes, vary
their widths, take into account winds in the jar, and
end p.6
finally determine whether the tangential stresses are really the major cause of rotation.
The dispute about normal and tangential stresses highlights a nice point about
observation. Philosophical debate has focused on entities. Instrumentalists, who want to
believe only in what they can see, get trapped in footling debates: do we really ‘see’
through a microscope? An electron microscope? A phase-interference light microscope?
Even with the naked eye, do we not in any case see only effects? But many of the things
that are realities for physics are not things to be seen. They are non-visual features—the
spin of the electron, the stress between the gas surface, the rigidity of the rod.
Observation—seeing with the naked eye—is not the test of existence here. Experiment is.
[ Pobierz całość w formacie PDF ]