The surprise theory of everything

15 October 2012 by Vlatko Vedral
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Forget quantum physics, forget relativity. Inklings of an ultimate
theory might emerge from an unexpected place

AS REVOLUTIONS go, its origins were haphazard. It was, according to
the ringleader Max Planck, an "act of desperation". In 1900, he
proposed the idea that energy comes in discrete chunks, or quanta,
simply because the smooth delineations of classical physics could not
explain the spectrum of energy re-radiated by an absorbing body.

Yet rarely was a revolution so absolute. Within a decade or so, the
cast-iron laws that had underpinned physics since Newton's day were
swept away. Classical certainty ceded its stewardship of reality to
the probabilistic rule of quantum mechanics, even as the parallel
revolution of Einstein's relativity displaced our cherished, absolute
notions of space and time. This was complete regime change.

Except for one thing. A single relict of the old order remained, one
that neither Planck nor Einstein nor any of their contemporaries had
the will or means to remove. The British astrophysicist Arthur
Eddington summed up the situation in 1915. "If your theory is found to
be against the second law of thermodynamics I can give you no hope;
there is nothing for it but to collapse in deepest humiliation," he

In this essay, I will explore the fascinating question of why, since
their origins in the early 19th century, the laws of thermodynamics
have proved so formidably robust. The journey traces the deep
connections that were discovered in the 20th century between
thermodynamics and information theory - connections that allow us to
trace intimate links between thermodynamics and not only quantum
theory but also, more speculatively, relativity. Ultimately, I will
argue, those links show us how thermodynamics in the 21st century can
guide us towards a theory that will supersede them both.

In its origins, thermodynamics is a theory about heat: how it flows
and what it can be made to do (see diagram). The French engineer Sadi
Carnot formulated the second law in 1824 to characterise the mundane
fact that the steam engines then powering the industrial revolution
could never be perfectly efficient. Some of the heat you pumped into
them always flowed into the cooler environment, rather than staying in
the engine to do useful work. That is an expression of a more general
rule: unless you do something to stop it, heat will naturally flow
from hotter places to cooler places to even up any temperature
differences it finds. The same principle explains why keeping the
refrigerator in your kitchen cold means pumping energy into it; only
that will keep warmth from the surroundings at bay.

A few decades after Carnot, the German physicist Rudolph Clausius
explained such phenomena in terms of a quantity characterising
disorder that he called entropy. In this picture, the universe works
on the back of processes that increase entropy - for example
dissipating heat from places where it is concentrated, and therefore
more ordered, to cooler areas, where it is not.

That predicts a grim fate for the universe itself. Once all heat is
maximally dissipated, no useful process can happen in it any more: it
dies a "heat death". A perplexing question is raised at the other end
of cosmic history, too. If nature always favours states of high
entropy, how and why did the universe start in a state that seems to
have been of comparatively low entropy? At present we have no answer,
and later I will mention an intriguing alternative view.

Perhaps because of such undesirable consequences, the legitimacy of
the second law was for a long time questioned. The charge was
formulated with the most striking clarity by the British physicist
James Clerk Maxwell in 1867. He was satisfied that inanimate matter
presented no difficulty for the second law. In an isolated system,
heat always passes from the hotter to the cooler, and a neat clump of
dye molecules readily dissolves in water and disperses randomly, never
the other way round. Disorder as embodied by entropy does always

Maxwell's problem was with life. Living things have "intentionality":
they deliberately do things to other things to make life easier for
themselves. Conceivably, they might try to reduce the entropy of their
surroundings and thereby violate the second law.

Information is power

Such a possibility is highly disturbing to physicists. Either
something is a universal law or it is merely a cover for something
deeper. Yet it was only in the late 1970s that Maxwell's
entropy-fiddling "demon" was laid to rest. Its slayer was the US
physicist Charles Bennett, who built on work by his colleague at IBM,
Rolf Landauer, using the theory of information developed a few decades
earlier by Claude Shannon. An intelligent being can certainly
rearrange things to lower the entropy of its environment. But to do
this, it must first fill up its memory, gaining information as to how
things are arranged in the first place.

This acquired information must be encoded somewhere, presumably in the
demon's memory. When this memory is finally full, or the being dies or
otherwise expires, it must be reset. Dumping all this stored, ordered
information back into the environment increases entropy - and this
entropy increase, Bennett showed, will ultimately always be at least
as large as the entropy reduction the demon originally achieved. Thus
the status of the second law was assured, albeit anchored in a mantra
of Landauer's that would have been unintelligible to the 19th-century
progenitors of thermodynamics: that "information is physical".

But how does this explain that thermodynamics survived the quantum
revolution? Classical objects behave very differently to quantum ones,
so the same is presumably true of classical and quantum information.
After all, quantum computers are notoriously more powerful than
classical ones (or would be if realised on a large scale).

The reason is subtle, and it lies in a connection between entropy and
probability contained in perhaps the most profound and beautiful
formula in all of science. Engraved on the tomb of the Austrian
physicist Ludwig Boltzmann in Vienna's central cemetery, it reads
simply S = k log W. Here S is entropy - the macroscopic, measurable
entropy of a gas, for example - while k is a constant of nature that
today bears Boltzmann's name. Log W is the mathematical logarithm of a
microscopic, probabilistic quantity W - in a gas, this would be the
number of ways the positions and velocities of its many individual
atoms can be arranged.

On a philosophical level, Boltzmann's formula embodies the spirit of
reductionism: the idea that we can, at least in principle, reduce our
outward knowledge of a system's activities to basic, microscopic
physical laws. On a practical, physical level, it tells us that all we
need to understand disorder and its increase is probabilities. Tot up
the number of configurations the atoms of a system can be in and work
out their probabilities, and what emerges is nothing other than the
entropy that determines its thermodynamical behaviour. The equation
asks no further questions about the nature of the underlying laws; we
need not care if the dynamical processes that create the probabilities
are classical or quantum in origin.

There is an important additional point to be made here. Probabilities
are fundamentally different things in classical and quantum physics.
In classical physics they are "subjective" quantities that constantly
change as our state of knowledge changes. The probability that a coin
toss will result in heads or tails, for instance, jumps from ½ to 1
when we observe the outcome. If there were a being who knew all the
positions and momenta of all the particles in the universe - known as
a "Laplace demon", after the French mathematician Pierre-Simon
Laplace, who first countenanced the possibility - it would be able to
determine the course of all subsequent events in a classical universe,
and would have no need for probabilities to describe them.

In quantum physics, however, probabilities arise from a genuine
uncertainty about how the world works. States of physical systems in
quantum theory are represented in what the quantum pioneer Erwin
Schrödinger called catalogues of information, but they are catalogues
in which adding information on one page blurs or scrubs it out on
another. Knowing the position of a particle more precisely means
knowing less well how it is moving, for example. Quantum probabilities
are "objective", in the sense that they cannot be entirely removed by
gaining more information.

That casts in an intriguing light thermodynamics as originally,
classically formulated. There, the second law is little more than
impotence written down in the form of an equation. It has no deep
physical origin itself, but is an empirical bolt-on to express the
otherwise unaccountable fact that we cannot know, predict or bring
about everything that might happen, as classical dynamical laws
suggest we can. But this changes as soon as you bring quantum physics
into the picture, with its attendant notion that uncertainty is
seemingly hardwired into the fabric of reality. Rooted in
probabilities, entropy and thermodynamics acquire a new, more
fundamental physical anchor.

It is worth pointing out, too, that this deep-rooted connection seems
to be much more general. Recently, together with my colleagues Markus
Müller of the Perimeter Institute for Theoretical Physics in Waterloo,
Ontario, Canada, and Oscar Dahlsten at the Centre for Quantum
Technologies in Singapore, I have looked at what happens to
thermodynamical relations in a generalised class of probabilistic
theories that embrace quantum theory and much more besides. There too,
the crucial relationship between information and disorder, as
quantified by entropy, survives (

One theory to rule them all

As for gravity - the only one of nature's four fundamental forces not
covered by quantum theory - a more speculative body of research
suggests it might be little more than entropy in disguise (see
"Falling into disorder"). If so, that would also bring Einstein's
general theory of relativity, with which we currently describe
gravity, firmly within the purview of thermodynamics.

Take all this together, and we begin to have a hint of what makes
thermodynamics so successful. The principles of thermodynamics are at
their roots all to do with information theory. Information theory is
simply an embodiment of how we interact with the universe - among
other things, to construct theories to further our understanding of
it. Thermodynamics is, in Einstein's term, a "meta-theory": one
constructed from principles over and above the structure of any
dynamical laws we devise to describe reality's workings. In that sense
we can argue that it is more fundamental than either quantum physics
or general relativity.

If we can accept this and, like Eddington and his ilk, put all our
trust in the laws of thermodynamics, I believe it may even afford us a
glimpse beyond the current physical order. It seems unlikely that
quantum physics and relativity represent the last revolutions in
physics. New evidence could at any time foment their overthrow.
Thermodynamics might help us discern what any usurping theory would
look like.

For example, earlier this year, two of my colleagues in Singapore,
Esther Hänggi and Stephanie Wehner, showed that a violation of the
quantum uncertainty principle - that idea that you can never fully get
rid of probabilities in a quantum context - would imply a violation of
the second law of thermodynamics. Beating the uncertainty limit means
extracting extra information about the system, which requires the
system to do more work than thermodynamics allows it to do in the
relevant state of disorder. So if thermodynamics is any guide,
whatever any post-quantum world might look like, we are stuck with a
degree of uncertainty (

My colleague at the University of Oxford, the physicist David Deutsch,
thinks we should take things much further. Not only should any future
physics conform to thermodynamics, but the whole of physics should be
constructed in its image. The idea is to generalise the logic of the
second law as it was stringently formulated by the mathematician
Constantin Carathéodory in 1909: that in the vicinity of any state of
a physical system, there are other states that cannot physically be
reached if we forbid any exchange of heat with the environment.

James Joule's 19th century experiments with beer can be used to
illustrate this idea. The English brewer, whose name lives on in the
standard unit of energy, sealed beer in a thermally isolated tub
containing a paddle wheel that was connected to weights falling under
gravity outside. The wheel's rotation warmed the beer, increasing the
disorder of its molecules and therefore its entropy. But hard as we
might try, we simply cannot use Joule's set-up to decrease the beer's
temperature, even by a fraction of a millikelvin. Cooler beer is, in
this instance, a state regrettably beyond the reach of physics.

God, the thermodynamicist

The question is whether we can express the whole of physics simply by
enumerating possible and impossible processes in a given situation.
This is very different from how physics is usually phrased, in both
the classical and quantum regimes, in terms of states of systems and
equations that describe how those states change in time. The blind
alleys down which the standard approach can lead are easiest to
understand in classical physics, where the dynamical equations we
derive allow a whole host of processes that patently do not occur -
the ones we have to conjure up the laws of thermodynamics expressly to
forbid, such as dye molecules reclumping spontaneously in water.

By reversing the logic, our observations of the natural world can
again take the lead in deriving our theories. We observe the
prohibitions that nature puts in place, be it on decreasing entropy,
getting energy from nothing, travelling faster than light or whatever.
The ultimately "correct" theory of physics - the logically tightest -
is the one from which the smallest deviation gives us something that
breaks those taboos.

There are other advantages in recasting physics in such terms. Time is
a perennially problematic concept in physical theories. In quantum
theory, for example, it enters as an extraneous parameter of unclear
origin that cannot itself be quantised. In thermodynamics, meanwhile,
the passage of time is entropy increase by any other name. A process
such as dissolved dye molecules forming themselves into a clump
offends our sensibilities because it appears to amount to running time
backwards as much as anything else, although the real objection is
that it decreases entropy.

Apply this logic more generally, and time ceases to exist as an
independent, fundamental entity, but one whose flow is determined
purely in terms of allowed and disallowed processes. With it go
problems such as that I alluded to earlier, of why the universe
started in a state of low entropy. If states and their dynamical
evolution over time cease to be the question, then anything that does
not break any transformational rules becomes a valid answer.

Such an approach would probably please Einstein, who once said: "What
really interests me is whether God had any choice in the creation of
the world." A thermodynamically inspired formulation of physics might
not answer that question directly, but leaves God with no choice but
to be a thermodynamicist. That would be a singular accolade for those
19th-century masters of steam: that they stumbled upon the essence of
the universe, entirely by accident. The triumph of thermodynamics
would then be a revolution by stealth, 200 years in the making.

Falling into disorder
While thermodynamics seems to float above the precise content of the
physical world it describes, whether classical, quantum or
post-quantum (see main story), its connection with the other pillar of
modern physics, general relativity, might be more direct. General
relativity describes the force of gravity. In 1995, Ted Jacobson of
the University of Maryland in College Park claimed that gravity could
be a consequence of disorder as quantified by entropy.

His mathematical argument is surprisingly simple, but rests on two
disputed theoretical relationships. The first was argued by Jacob
Bekenstein in the early 1970s, who was examining the fate of the
information in a body gulped by a black hole. This is a naked
challenge to the universal validity of thermodynamics: any increase in
disorder in the cosmos could be reversed by throwing the affected
system into a black hole.

Bekenstein showed that this would be countered if the black hole
simply grew in area in proportion to the entropy of the body it was
swallowing. Then each tiny part of its surface would correspond to one
bit of information that still counts in the universe's ledger. This
relationship has since been elevated to the status of a principle, the
holographic principle, that is supported by a host of other
theoretical ideas – but not as yet by any experiment.

The second relationship is a suggestion by Paul Davies and William
Unruh, also first made in the 1970s, that an accelerating body
radiates tiny amounts of heat. A thermometer waved around in a perfect
vacuum, where there are no moving atoms that can provide us with a
normal conception of temperature, will record a non-zero temperature.
This is an attractive yet counter-intuitive idea, but accelerations
far beyond what can presently be achieved are required to generate
enough radiation to test it experimentally.

Put these two speculative relations together with standard, undisputed
connections between entropy, temperature, kinetic energy and velocity,
and it is possible to construct a quantity that mathematically looks
like gravity, but is defined in terms of entropy. Others have since
been tempted down the same route, most recently Erik Verlinde of the
University of Amsterdam in the Netherlands.

Such theories, which are by no means universally accepted, suggest
that when bodies fall together it is not the effect of a separate
fundamental force called gravity, but because the heating that results
best fulfils the thermodynamic diktat that entropy in the universe
must always increase.

Vlatko Vedral is a professor of quantum information theory at the
University of Oxford and the Centre for Quantum Technologies,
Singapore. He is the author of Decoding Reality (Oxford University
Press, 2010)

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