Evidence and Theory in Physics
Tim Maudlin, NYU
Evidence in the Natural Sciences, May 30, 2014
Two Features of Physics
¡  Physics displays two interesting features:
¡  1) Programmatically, it aspires to be completely
universal.
¡  2) Predictively, it has produced the most
accurate and highly tested predictions in human
history. It also applies the most stringent standards
for the statistical significance of evidence.
Predictive Power
¡  The best current theoretical calculation of the
anomalous magnetic moment of the electron is
1.00115965218113 (± 86).
¡  The best current theoretical value of the
anomalous magnetic moment of the electron is
1.00115965218073 (± 28).
Standard of Evidence
¡  In order for the evidence of the Higgs boson to
count as strong enough to be considered a
“discovery”, it had to be statistically significant at
the 5σ level.
¡  Roughly, that means that the probability of
getting the result just by chance is one out of 3.5
million.
What Does This Mean?
¡  Clearly, this means that physics is getting something
right. But what, exactly?
¡  At the simplest level, it means that at least certain
parts of physics are, in fact, highly predictively
accurate and we can expect the predictions to
continue to be highly reliable.
¡  In the case of the Higgs, we can confidently expect
that in future experiments, effects of the particle will
continue to appear.
More Ambitiously
¡  It would be nice to be able to say something
stronger that this. In particular, it would be nice to
be able to say that this predictive accuracy and
high level of evidential standard means that the
basic picture of the world given to us by
contemporary physics is true or approximately
true or at least on the right track.
But….
¡  Richard Feynman once wrote:
¡  [W]e always have had (secret,secret, close the
doors!) we always have had a great deal of
difficulty in understanding the world view that
quantum mechanics represents. At least I do,
because I’m an old enough man that I haven’t got
to the point that this stuff is obvious to me. Okay, I
still get nervous with it…I cannot define the real
problem, therefore I suspect there’s no real
problem, but I’m not sure there’s no real
problem.” (Simulating Physics with Computers,1982)
What is the World View of
Quantum Mechanics?
¡  Before we can even ask whether the predictive
success of quantum theory is good grounds to think
it is (approximately) true, we need to have some
account of what quantum theory claims about the
physical world.
¡  At present, there is no agreement at all about this.
¡  Further, there are still fundamental problems
understanding how the theory can make any
predictions at all (in a principled way).
The Scope of Physics
¡  Physics was once characterized as the theory of
matter in motion.
¡  As such, everything that can be correctly
described as matter in motion in principle should
be subject to physical analysis.
¡  This includes all of the systems studied by biology,
chemistry, psychology, economics, meteorology,
astrophysics, cosmology, geology, etc.
The “Measurement
Problem”
¡  Since all experiments involve matter in motion, in
order for physics to be internally coherent it must
not only produce predictions for how experiments
will come out but also be capable of modeling the
experiments themselves as physical processes.
¡  One way of trying to do this leads to the
“Schrödinger cat” problem: if there is no “collapse
of the wavefunction” and the wavefunction is a
complete physical description of a system, then the
cat does not end up either alive or dead.
A Deeper Problem
¡  If we are to describe a physical situation as
matter in motion, then the physics must specify
where there is matter.
¡  In quantum theory, though, there is no agreed
account of exactly what sort of matter there is,
according to the theory, located in space and
time.
For Example
¡  Here are some pictures of “electron orbitals”:
Possibilities
¡  The electron is, at all times, “smeared out” in this shape.
¡  The electron is orbiting the nucleus. This is like a time-lapse
photograph.
¡  The electron “pops in and out of existence”. This is like a timelapse photograph.
¡  The electron is nowhere at all until a “position measurement”
is made. This shows where it might “show up”.
¡  Each electron is at rest. This shows the positions of many,
many electrons, superimposed.
Possibility 4 is Incoherent
¡  If electrons aren’t anywhere until measured, then
the electrons in the “measuring apparatus”
aren’t anywhere until “measured” by something
else.
¡  This will not end well.
The Measurement Problem
¡  Quantum theory provides extremely accurate techniques
for predicting the outcomes of “measurements” of
“observable quantities”.
¡  These techniques require characterizing an experiment as
a “measurement” of the “observable”.
¡  But the programmatic universality of physics requires that
one should also be able to simply treat the experiment as
a physical interaction, without needing to characterize it
as a “measurement” of anything.
Ontology and Beables
¡  The notion of an “observable” is tied to the notion
of a “measurement”. But in order to have
measurements, there must be something that is just
there, independently of its being “measured”.
¡  In philosophical terminology, the things that are
postulated to exist according to a theory constitute
the ontology of the theory.
¡  John Bell, in discussing this problem, invented a new
term for this: the beables of a theory.
Bell on Beables
¡  “In particular we will exclude the notion of
‘observable’ in favor of that of ‘beable’. The
beables of the theory are those elements which
might correspond to elements of reality, to things
which exist. Their existence does not depend on
‘observation’. Indeed observation and observers
must be made out of beables.” (Beables for
Quantum Field Theory)
More Bell on Beables
¡  “The concept of ‘observable’ lends itself to very
precise mathematics when identified with ‘selfadjoint operator’. But physically, it is a rather
wooly concept. It is not easy to identify precisely
which physical processes are to be given the
status ‘observations’ and which are to be
relegated to the limbo between one observation
and another.”
Bell con’t.
¡  “So it could be hoped that some increase in
precision might be possible by concentration on the
beables, which can be described in ‘classical
terms’, because they are there. The beables must
include the setting of switches and knobs on
experimental equipment, the currents in coils, and
the readings of instruments. ‘Observables’ must be
made, somehow, out of beables. The theory of
local beables should contain, and give precise
physical meaning to, the algebra of local
observables.” (The Theory of Local Beables)
Local Beables
¡  Among the beables of a theory, Bell particularly
emphasized the local beables, that is, local in
space and time. It is only local beables that can be
attributed motions through space-time by the
theory. A theory with no local beables cannot be a
theory of matter in motion, and hence not physics
as we understand it.
¡  But there is no accepted account of what the local
beables in quantum theory are! That is why “the
world view the quantum mechanics represents” is
so obscure.
Local Beables and the
Measurement Problem
¡  Suppose a physical theory postulates
¡  1) That there are some local beables.
¡  2) That everyday matter (protons, neutrons and
electrons) are composed of these beables.
¡  3) A dynamics (deterministic or stochastic) for the
these beables.
¡  4) Whatever else is needed to complete the
dynamics (which may include non-local beables).
Results
¡  Such a theory, in principle, should make predictions
(deterministic or probabilistic) about how everyday
matter will behave given a complete physical
specification of a situation.
¡  Therefore, such a theory will make predictions
about what the “empirical data” produced by an
experiment will be, if the experiment is described in
sufficient physical detail.
¡  It is irrelevant whether the experiment is described
as the “measurement” of any “observable”.
Bell again
¡  “Not all ‘observables’ can be given beable
status, for they do not all have simultaneous
eigenvalues, i.e. do not all commute. It is
important to realize therefore that most of these
‘observables’ are entirely redundant. What is
essential is to be able to define the positions of
things, including the positions of pointers or (the
modern equivalent) of ink on computer
output.” (Beables for Quantum Field Theory)
How has Physics Managed
Without Local Beables?
¡  The original approach to understanding
quantum theory was pioneered by Bohr, in the
so-called “Copenhagen interpretation”.
¡  Bohr described his approach this way in 1949:
Bohr on Evidence
¡  “For this purpose, it is decisive to recognize that,
however far the phenomena transcend the scope
of classical physical explanation, the account of all
evidence must be expressed in classical terms. The
argument is simply that by the word “experiment”
we refer to a situation where we can tell others
what we have done and what we have learned,
and that, therefore, the account of the
experimental arrangement and of the results of the
observations must be expressed in unambiguous
language with suitable application of the
terminology of classical physics.”
Copenhagen
¡  Bohr tried to insist on two points:
¡  1) The evidence for a theory must be expressed in
‘classical’ terms, by which he just means in terms of
the positions and motions of macroscopic objects in
space and time.
¡  2) “Quantum systems” cannot be described in
‘classical’ terms: electrons and protons and
neutrons do not have any location or follow any
definite trajectory through space-time.
Ergo…
¡  If one tries to hold both of Bohr’s principles at the
same time, the only conclusion is that
macroscopic objects cannot be described by
quantum theory, or even that macroscopic
objects cannot be composed of quantum
objects, and hence macroscopic objects are not
just collections of electrons, protons and
neutrons.
¡  Bell called this Bohr’s “dual kinematics”.
Bell on Copenhagen
¡  “The kinematics of the world, in this orthodox
picture, is given by a wavefunction (maybe more
than one?) for the quantum part, and classical
variables—variables which have values—for the
classical part: (Ψ(t,q…),X(t)…). The Xs are somehow
macroscopic. This is not spelled out very explicitly.
The dynamics is not very precisely formulated either.
It includes a Schrödinger equation for the quantum
part, and some sort of classical dynamics for the
classical part, and ‘collapse’ recipes for their
interaction.” (Against ‘Measurement’)
Note
¡  The evidence for the theory is determined
entirely by the behavior of the ‘classical’ part: it is
only through this that we have any reason to
accept the quantum theory.
¡  But on Bohr’s picture, the ‘classical’ part is not
given by a quantum-mechanical description at
all. The observable motion of matter is not
derived from the quantum state.
Bell’s Solution
¡  “It seems to me that the only hope of precision with
the dual (Ψ,x) kinematics is to omit completely the
shifty split [between classical and quantum], and let
both Ψ and x refer to the world as a whole. Then
the xs must not be confined to some vague
macroscopic scale, but must extend to all scales. In
the picture of de Broglie and Bohm, every particle is
attributed a position x(t). Then instrument pointers—
assemblies of particles—have positions, and
experiments have results.”
Bell con’t.
¡  “The dynamics is given by the world Schrödinger
equation plus precise ‘guiding’ equations
prescribing how the x(t)s move under the
influence of Ψ. Particles are not attributed
angular momenta, energies, etc., but only
positions as functions of time. Peculiar
‘measurement’ results for angular momenta,
energies, and so on, emerge as pointer positions
in appropriate experimental setups.”
Recapitulation
¡  Ultimately, the evidence for a physical theory is
the motion—the location and shape through
time—of macroscopic objects.
¡  Due to the programmatic universality of physics,
predictions for those motions should be derivable
from the physical description of an experiment.
¡  In its present state, this cannot be done in
quantum theory.
Solution
¡  Bell’s solution is to postulate the existence of
some local beables at microscopic scale,
beables that are just there independently of
being “observed” or “measured”.
¡  The locations and motions of macroscopic
objects is then determined by the locations and
motions of their microscopic parts.
Possible Local Beables
¡  1) Particles (that always have definition locations)
¡  2) Matter density (that has a definite value at
each space-time point)
¡  3) Strings (with definite trajectories)
¡  4) Flashes (point events)
Reprise
¡  Here are some pictures of “electron orbitals”: