The surprise theory of everything
New Scientist 15 October 2012
by Vlatko Vedral
Magazine issue 2886
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 wrote.
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.
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 increase.
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.
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,
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 fulfills
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)
• Entropy increasing
From a tightly defined origin
in the workings of steam engines,
the influence of the second law of thermodynamics
has steadily spread over the past 200 years.
1824
Sadi Carnot (1796-1832)
His Reflections on the Motive Power of Fire
speculates on limits to the efficiency of steam engines.
1851
William Thompson - Lord Kelvin (1824-1907)
Expresses the second law as the impossibility
of an engine converting all its heat to useful work.
1865
Rudolph Clausius (1822-1888)
Recasts the law
"the entropy of the universe
tends to a maximum".
1872
Ludwig Boltzmann ((1844-1906)
Provides an explicit link
between entropy and microscopic disorder.
1900
Max Planck (1858-1947)
Uses Boltzmann's entropy plus
a new "quantum postulate"
to explain a body's heat radiation.
1909
Constantin Carathéodory (1873-1950)
Rewrites the second law in logical terms
of allowed and forbidden processes.
1948
Claude Shannon (1916-2001)
Introduces "information entropy"
as a measure of uncertainty
in an encoded message.
1961
Rolf Landauer (1927-1999)
Shows that any information-destroying process
also increases physical entropy.
1982
Charles Bennett (1943- )
Uses Landauer's principle to show
an intelligent being cannot buck the second law.
1995
Ted Jacobson (1954- )
Suggests that gravity is merely the effect
of bodies increasing their entropy.
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