48 | New Scientist | 6 March 2021
a special state of extraordinarily high order.
That is arbitrarily imposed. One of the most
profound aspects of existence is attributed to a
special condition put in by hand. This has been
called the “past hypothesis” and in my view it
isn’t a resolution to the issue of time, but an
admission of defeat.
In fact, an alternative to the past hypothesis
may have been staring us in the face for more
than two centuries. In 1772, mathematician
Joseph-Louis Lagrange proved something about
the behaviour of a system of three particles
that interact according to Isaac Newton’s law
of gravitation. This says that every particle
attracts every other with a force proportional
to their masses and inversely proportional to
the square of the distances between them.Past forwards
Lagrange’s result, which extends to any number
of particles, showed that if a system’s total
energy (potential plus kinetic) is either zero or
positive then its size, essentially its diameter,
passes through a unique minimum at just one
point on the timeline of its evolution. This
process runs just as well backwards as forwards,
Newton’s gravity being time-symmetric.
And with one fascinating exception to which
I will return, the size of the system grows
to infinity both to the past and future.
Interestingly, the uniformity with which the
particles are distributed is greatest around the
point of minimum size. It has long been
known that a uniform distribution of particles
is gravitationally unstable and breaks up into
clusters. What nobody seems to have realised,
however, is that when you run the evolution
of the particles’ motion backwards from
the clustered state to the minimum, most
uniform state and then take it beyond this
point, it goes on to become clustered again.
In a paper I published in 2014, together with
Tim Koslowski at the National Autonomous
University of Mexico and Flavio Mercati at the
University of Naples, Italy, we showed that this
is the case in a simple proxy of the universe.
A computer simulation of a thousand particles
interacting under Newtonian gravity showed
that pretty much every configuration of
particles would evolve into this minimum
state and then expand outwards, becoming
gradually more structured in both directions.
I call the minimal state the Janus point, afterthe Roman god who looks simultaneously
in opposite directions of time.
What would this mean for us? If we lived in
the model universe I have just described, we
must be on one side or the other of the Janus
point. We find Newton’s time-symmetric law
governs what happens around us, but also a
pervasive arrow of time that defines our future.
In our past direction, we can just make out fog- what we call the big bang – and nothing
beyond it. Not realising the fog is a Janus
point, we invoke a past hypothesis to explain
the inexplicable. But Newton’s laws say the
special point must be there, so there is no
need to invoke the past hypothesis. Instead,
we can mathematically define a quantity
that reflects the evolution of our system
of particles into something that looks like
structure. Let’s call it “complexity”.
Complexity is calculated using all the masses
of the particles and all the ratios of the distances
between any two of them. It has nothing to do
with the statistical likelihood of possible states
and differs from entropy in that its growth
reflects an increase in structure, or variety,
rather than disorder. I argue that it should take
the place of entropy as the basis of time’s arrow.
In my recent book The Janus Point, I take
things further. I propose that, ultimately, our
model suggests that the history of the universe
isn’t a story of order steadily degrading into
disorder, but rather one of the growth of
structure or complexity, as we define it.
The suggestion for this comes in the first
place from Newton’s theory of gravity. It isn’t
yet clear it can be extended to a general
relativistic description of gravity. But in many
cases, Newtonian gravity predicts behaviour
almost identical to relativity, so there is a hint
to look for a similar effect in Einstein’s theory.A hiker on Japan’s
Mount Fuji wouldn’t
be able to see its
mirror image in Lake
Kawaguchi. A similarly
limited view might
explain why we think
time flows only one wayLEEROBINSON^ PHOTOGR
APHY