The
Comprehensible Cosmos: Where Do the
Laws of Physics Come from?
Victor
Stenger
Prometheus
Books, New York, 2006, ISBN 1-59102-424-2.
After
the backlash comes the return to orthodoxy. In A Brief History of Time,
Stephen Hawking suggested that physics was on the verge of solving the final
puzzles of creation: the marriage of quantum physics and gravity and the origin
of the universe. Since then, there has been a general sense of
disappointment at the progress made by pretenders such as string theory.
A number of works have suggested that mankind is still scrabbling around in the
foothills of understanding, and that the universe may not even be ultimately
explicable by our scientific and mathematical tools. Now, in a new
magisterial account of the state of modern physics, Stenger reasserts the
original optimistic outlook: physics has explained almost all that is and has
been, and the few remaining pockets of resistance must soon fall.
He
argues that the measure of the success of physics is that it can be
encapsulated in a set of succinct equations which account for almost all
human experience. In the first half of the book, he guides the reader
through the historical development of physics, passing through special and
general relativity and then dealing with particle physics, embarking
on a brief excursion through statistical thermodynamics, before reaching the
standard model and finally cosmology. He shows that this historical
development can be seen as the expression of two principles: the
principle of objectivity - that the laws of physics should be
independent of our formulation of them and of our position in the universe -
and the principle of symmetry. He shows that, in many cases, our theories
are the simplest that can result from “point of view invariance” and
symmetry. Thus, the universe is comprehensible.
Given
the centrality of invariance to the thesis of the book, and the enormous power
of his approach, it is unfortunate that Stenger does not spend more time
introducing it to the reader, as he does, for instance, with the concept of
symmetry later in the book. He explains that “point of view invariance”
means that the laws of physics must look the same wherever you are – an experiment
will have the same result whether it is carried out in England or France, say,
and can be explained using the same theories in either place. In mathematical terms, this means that
vectors must be unchanged by a co-ordinate transformation. This is
accompanied by an obscure diagram (p47). But he does not say, in simple
terms, that it is not the expression of the vector in the transformed
co-ordinate system that is unchanged. In fact, the expression of that
vector will be changed. It is the vector itself, as a point in space,
that does not actually move when the co-ordinate system is changed. It is
still the same point, although its expression in the new co-ordinate system is
different. A little more time explaining and demonstrating co-ordinate
transformations would remove the risk that an uninformed reader might be led
astray, and would make the deductions that follow from invariance even more
breathtaking.
The
first half of the book almost entirely eschews equations (even E=mc2
is avoided by referring to Einstein’s "familiar formula"
(p49)). Stenger calls on his own profound understanding to digest
relativity and quantum physics in language accessible to the lay reader,
communicating some of the beauty and logic of these theories with the passion
of the practitioner. The second half of the book contains all the
equations that were excised from the first half. It is not a tutorial in
the mathematics of relativity and quantum physics, nor is it a reference work
for those already familiar with these areas. Rather, it is like a guided
tour through a mathematical museum displaying the most beautiful and important
exhibits. You can tour a natural history museum and admire all the
skeletons of dinosaurs without already having or aspiring to have a deep understanding
of paleontology. In the same way, the second half of The
Comprehensible Cosmos will show you the mathematical landmarks of modern
physics and make you gasp with their simplicity and beauty, even if you only
grasp a tiny proportion of their meaning. It is no criticism to say that
the second half of the book fails to identify a target readership, because that
is effectively impossible given the task it has set itself. It is perhaps
suitable for a student familiar with differential geometry, including covariant
derivatives and the curvature tensor, but not relativity and who is familiar
with functional analysis, including operators on Hilbert spaces, but not
quantum physics. Towards the end, Stenger can only refer the interested
reader to relevant "textbooks" (pp305, 306) to fill in the yawning
chasms of logic that he spans in a few lines. The second half of the book
is, nevertheless, a valiant attempt to introduce the reader to some of
the beauty of the underlying mathematics and makes an intriguing guided
tour.
The
optimism of Stenger’s judgment on physics follows from his philosophy of
science, which he sets out at the start of the book. He takes an
operational view of measurement - the definition of a particular measure is the
set of operations that are used to make it. He sets out, by way of
example, the various ways in which the “metre” has been defined by a particular
canonical measurement - as the length of a particular metal bar at a particular
temperature, a certain percentage of the wavelength of a part of the cadmium
spectrum and most recently as the distance light travels in a certain
time. This raises an obvious question: if the “metre” is defined purely
operationally, then these different operational definitions must refer to
different measures. Why are they all called the “metre”, unless there is
some additional concept underlying the operations which unifies them all and
justifies using the same name? Leaving this difficulty to one side,
Stenger builds his scientific theories on top of operationally defined
measurements. He eschews the culturally laden word “theory”, preferring
to use the word “model”. His models take these empirical measurements and
provide a description of them. Models are useful if and to the extent
that they are consistent with the measurements - the larger the number of
measurements that are explained by a theory, the better it is.
This
approach provides a clear empirical basis to physics and allows models to be
easily compared. If two different models explain the same facts, then
they are equal in value and either can be used (although an appeal to parsimony
may be used to choose between them in this case). It serves well as a
philosophical background to the historical narrative in The Comprehensible
Cosmos, showing how each model builds on its predecessors by explaining
slightly more of the sum of human experience and measurement. Above all,
it is to be preferred to the complete absence of any philosophical background
found in many similar popular physics books.
However,
there is a problem with this approach. To begin with, there is an
ambiguity in the use of the word “model”. A model can be a description of
a set of facts, such as a description of the position and velocity of the Earth
at points in its orbit. This description might consist of a large
number of different measurements at different times, but a more parsimonious
model would consist of a few measurements together with rules to calculate new
positions and velocities at times other than those explicitly set out. We
might describe this as a “model of the Earth’s orbit”. But a model, in
the sense of a scientific theory adopted by Stenger, also means a set of laws
that can be used to develop a model, in the narrower sense. For instance,
we might create a “model of gravity” (to employ the rather infelicitous phrase
used by Stenger at p26) that embodies an inverse square rule, which could then
be used to create a model of the Earth’s orbit. Stenger wants to elide
these two meanings, because he does not want to deal with the metaphysical
questions raised by the existence of laws within scientific models - he just
wants to concentrate on the empirical facts. This accords with his
narrative view of a progression of scientific theories each having a slightly
better empirical basis than the previous one.
Unfortunately,
this elision misses out something essential to scientific theories. It
eliminates the laws that stand behind the physical models. Stenger
rightly points out that so-called “laws” do not themselves force material
objects to obey them, and in that sense are different from the laws that apply
to humans. However, jurisprudential laws do not “force” human action
either. Jurisprudential laws are normative statements: they say that a
human should do something at some point in the future. They do not
predict that the person will actually do that thing - humans break human laws
all the time. But, whether obeyed or not, the law of jurisprudence does
correctly assert that a normative obligation will apply to a person in certain
circumstances. A scientific law is not a jurisprudential law. It
does not say that a particle will be “obliged” to move at some point, it simply
predicts that it will move in certain circumstances. The common element is
prediction. By downgrading scientific laws, Stenger downgrades the
importance of prediction in science.
Laws
are not necessary for models that describe what has already happened. A
set of measurements can be a correct model in these circumstances - although
not particularly interesting - and it need not contain any laws. But laws
are essential when making predictions. A law predicts what will happen in
certain sets of circumstances. It cannot simply be a descriptive
list. An essential difference between scientific theories is in the
qualities of the predictions that they make and the sets of circumstances that
their predictions cover. This is why Einstein’s theory of
relativity cannot simply be characterized as Newton’s theory plus a minor
tweak to correct some observed wobbles in the orbit of Mercury. It
imposes a new paradigm consisting of a new, enhanced set of predictions that
follow from a new set of laws.
Stenger’s
comparison of scientific theories on the basis of quantity of correct descriptions,
minimizing the role of laws and prediction, need not stop at downgrading
Einstein. What are Newton’s laws but a minor refinement of the law that
planets move in ellipses, which fit the data well to a lesser
approximation? And why stop there? Let’s just agree that the
planets move in circles - a far more parsimonious theory that still fits a good
proportion of the data. This reductio ad absurdum is only possible
because Stenger’s philosophy of science fails to capture something central to
physical theories - that they contain laws that make statements about the
future - and it is exactly this failure that provides the temptation to
subscribe to an excessively optimistic view of physics.
Nevertheless,
Stenger’s optimistic view based on the high proportion of data fit by modern
scientific theories serves to propel the reader through Newton, Einstein and
into quantum physics and cosmology. The extraordinary depth of theory
that follows from an axiomatic reliance on “point of view invariance” and symmetry
do convince the reader that the cosmos is comprehensible, and why. It
must be admitted that there is a slight letdown when it is revealed
that current theories only explain about 3.5% of the matter and energy in
the universe, and for the rest we rely on some dubious appeals to “dark
matter”, “dark energy” and, even worse, “quintessence”. Similarly, the
upper reaches of particle physics become less satisfying when the symmetries
start to break down and the number of observed parameters starts to multiply.
But these are minor quibbles compared to the total breadth of explanation.
The Comprehensible Cosmos is an
entertaining and stimulating tour of the upper reaches of modern physics,
driven by the unifying themes of “point of view invariance” and symmetry.
It demonstrates how much of the universe is comprehensible as a result of a few
basic principles. It is a welcome reminder how far physics has come,
whatever your opinion on how much further physics still has to go.
Adam
Sanitt