快猫短视频

Time’s arrow

Australia

GATHER ye rosebuds while ye may, Old Time is still a鈥檉lying.鈥 So wrote Robert
Herrick, the 17th century poet. And who could doubt that time does indeed
fly鈥攐r at least flow? In daily life, the past, present and future have
distinctly different qualities. The past is gone, remembered perhaps, but
unalterable. The future has yet to come into being, and is still open. Only the
present moment is truly real. All this seems like common sense. Yet many
scientists and philosophers are adamant that we have got it all wrong. They
insist that time does not flow at all.

The Cambridge philosopher John McTaggart set the scene for this debate at the
turn of the century, when he put forward two seemingly contradictory images of
time. One view treats time simply as a coordinate to label events, just as
latitude and longitude label places. The other view refers to flowing time,
where events happen and the future comes into being. Which is right?

Philosopher Donald Williams of Harvard University tried to answer this in a
famous essay published in 1951 entitled 鈥淭he Myth of Passage鈥, in which he
argued that only the static, coordinate time is real. It is a point of view
supported by many other philosophers. Jack Smart, a retired philosopher now
living in Canberra, concedes that we certainly feel time passing. But he
believes that this feeling arises out of 鈥渁 metaphysical confusion鈥. After all,
he asks, how fast does time pass? Well, one second per second, of course. But
for us to go beyond tautology and talk meaningfully of the motion or passage of
something, we need a time to gauge it against, as when we say an arrow moves at
ten metres per second. When that something is time itself, what do we use as a
measure?

This may seem like simply playing with words, but there are also sound
physical reasons to doubt the flow of time. The trouble started with Einstein鈥檚
theory of relativity, which demolished the idea that time is universal with a
common present moment for everybody. Einstein showed that two spatially
separated events judged to occur simultaneously by one observer can occur at
different moments for another.

For instance, suppose you want to know what the Pathfinder space probe is
doing on Mars now. According to relativity theory, it depends on how you are
moving when you ask the question. If you are sitting at home, you will get one
answer, if you are flying in an aircraft you will get another. If you could move
close to the speed of light relative to Earth, the difference could amount to
many minutes.

Persistant illness

This strange phenomenon, called the relativity of simultaneity, has been
thoroughly verified by experiment. It dramatically changes the way we must think
about time. If there are many Martian 鈥渘ows鈥 for each Earth now (and vice versa)
it is clearly meaningless to claim that only one moment of
time鈥攏ow鈥攊s real. Einstein himself expressed it succinctly when he
said that 鈥減ast, present and future are only illusions, however persistent鈥.
Physicists prefer to envisage time as all there at once, a timescape stretched
out in its entirety, like a landscape. It is a concept often referred to as
鈥渂lock time鈥.

But if our perception of the flow of time is just some sort of mental quirk,
rather than a property of the physical Universe, what causes it? Explanations
vary. Some attribute it to the structure of our language, others seek
explanations in the workings of the brain. Many scientists, most notably Roger
Penrose of Oxford University, suspect it has something to do with quantum
mechanics and the so-called collapse of the wave function
(鈥淓scape from the quantum whirlpool鈥, 快猫短视频,26 April, p 38).
The link between
quantum physics and consciousness is a deep and contentious one. The basis of
quantum mechanics, which describes the behaviour of matter at the atomic level,
is uncertainty. Given a particular atomic state, you cannot generally predict
how it will change. For example, if you have an excited atom, you cannot know in
advance exactly when it will decay; all you know are the betting odds. A fancy
way to describe this indecision is to say that there are two alternative
universes, one with an excited atom, one with a decayed atom. According to the
weird rules of quantum mechanics, an atomic state will generally involve both
universes coexisting and overlapping each other in a sort of hybrid reality.

Human beings, however, always observe just one universe, so somehow the act
of making an observation provokes nature into making a choice between contending
realities. To use the jargon, the wave function collapses into one possibility.
It is as if the act of inspecting the world projects one of the ghostly
alternative universes into concrete actuality. The nature of this process is not
fully understood, but all investigators accept that it seems to move only one
way in time. Once the choice of reality has been made, it can鈥檛 be unmade. So,
the argument goes, our perception of the flow of time could arise from the ways
that our consciousness resolves ambiguous quantum states.

Even if time doesn鈥檛 literally flow from past to future, it still seems that
the world is strongly lopsided in time. If you take a movie of a typical
everyday scene and run it in reverse, everybody laughs. They have no trouble
spotting the deception. In real life, raindrops don鈥檛 rise into the sky and
broken eggs don鈥檛 mend themselves.

A lopsided world

But this time asymmetry doesn鈥檛 depend on time flowing: you don鈥檛 actually
have to run the movie to find it. A vertical stack of still frames would display
a structural directionality. People grow old, cars rust, eggs break, snowmen
melt, radio waves spread out from transmitters. Physicists often use the term
鈥渢he arrow of time鈥 to denote the asymmetry between past and future directions
of time. It can be misinterpreted though, because arrows also fly, and so the
term could also refer to time flowing. The correct way to picture the arrow of
time is by analogy with a compass needle or weather vane, which point in a
direction but do not move towards it.

So where does this directionality come from? Well, most irreversible
processes are examples of the second law of thermodynamics. This says that in an
isolated system heat will flow from hot to cold, never the other way. The end
result is a state called thermodynamic equilibrium, with the heat distributed
evenly at a uniform temperature. Thermodynamic equilibrium is the state of
maximum disorder, and as long ago as the 1850s physicists realised that the
second law meant that the Universe is stuck on a one-way slide towards
degeneration and chaos.

A clear-cut example of the thermodynamic arrow of time is the way that a
bottle of perfume evaporates if the stopper is removed. The process is
irreversible because you would never see all the perfume molecules go back into
the bottle on their own. Once they are mixed up with air molecules, the original
state is irretrievable. The transition is best thought of as a change from an
ordered state (perfume neatly in the bottle) to a disordered state (perfume
spread around the room).

Comparison between perfume evaporating and the universe forming

Back and forth

Mystery sets in, however, when you try to trace the source of this
directionality. The molecular agitation that jumbles up the perfume and air
molecules involves lots of intermolecular collisions. But the collision of two
molecules is a reversible process: run the movie backwards and the molecules
retrace their trajectories. This reflects the symmetry in time of the laws
governing molecular behaviour. Indeed, almost all the laws of physics are
time-reversible. The puzzle is how temporally lopsided processes can emerge
from time-symmetric laws.

A possible answer given in the 1950s by German philosopher Hans Reichenbach
lies with the initial conditions. Imagine unwrapping a new pack of cards
arranged in suits and numerical sequence. This highly ordered state is soon
destroyed with a bit of shuffling. There is nothing intrinsically directional
about the shuffling process. The asymmetry arises only because you started out
with the cards in a very special state, and then randomly disturbed it. So too
with the perfume molecules. Order gives way to disorder not because there is a
directionality in the underlying laws, but simply because there are many more
disordered states than ordered states. Disturbing an ordered state will
therefore very probably produce a less-ordered state.

So to work out the ultimate origin of the arrow of time, we have to ask how
the Universe got itself into an ordered state in the first place. The obvious
place to look is in the big bang. But looking there yields a strange paradox. We
know that the early Universe was in fact highly disordered. The big bang was
accompanied by a flash of heat that filled space with radiation. A remnant of
this primeval heat radiation survives in a background of microwaves that still
bathes the cosmos today. Satellite observations show that the spectrum of the
microwave radiation is precisely the 鈥渂lack body鈥 form associated with uniform
temperature and complete microscopic disorder.

So, while the second law of thermodynamics requires that the arrow of time
point from order to chaos, from disequilibrium to equilibrium, it seems that the
early Universe started at equilibrium and is now far from equilibrium鈥攁ll
of which seems to point the arrow in the wrong direction. How can this be?

This is where gravity comes in. Remember the caveat in the second law: it
applies only to isolated systems. In the Universe, matter and heat radiation are
not isolated, because they are free to engage in large-scale motion. This
activity is subject to gravitational forces, and so we must include the
gravitational field as part of the total system.

In the lab, where gravity is negligible, the equilibrium end state of a gas
is a uniform distribution. But taking gravity into account changes everything.
Gravity is an attractive force that tries to pull matter into clumps. The
ultimate triumph of this process is when material falls together completely to
form a black hole. Applying thermodynamics to gravity, the black hole can be
seen as the equilibrium end state.

Attempting to find the equations that link gravity with thermodynamics is
taxing the best brains in physics. But for a clue to how these two processes
might be related from the standpoint of the arrow of time, it helps to think of
order and disorder not in terms of clumpiness and smoothness, but in terms of
information. A totally disordered state needs only a few bits of information to
describe it. For example, the macroscopic state of a flask of gas in
thermodynamic equilibrium can be completely described simply by giving its
temperature and volume. But a gas with lots of hot spots and swirling eddies
would take a lot more information to describe. As a system approaches
equilibrium, it loses information irreversibly.

When a body collapses into a black hole, it loses information. The escalating
gravitational field of the body traps light, and because information cannot
travel faster than light, it is trapped too. Ultimately, an event horizon forms
around the body, preventing any information from getting out. To an external
observer, the information content of the collapsing body disappears irreversibly
down the hole. Not surprisingly, therefore, black holes obey a set of laws
identical to the normal laws of thermodynamics.

The second law of thermodynamics can be thought of as nature鈥檚 way of driving
systems towards equilibrium. If this law is taken to embrace gravitating
systems, it describes a trend from smooth to clumpy.

The microwave background radiation reveals that the early Universe was in
fact extremely smooth鈥攚ith only the merest hint of clumping showing up in
the satellite observations. While this was very close to equilibrium in terms of
matter and heat energy alone, it is very far from equilibrium in terms of
gravitation. Because of this, the matter and radiation could be driven away
from their own equilibrium without violating the second law. As the Universe
developed, it gained thermal order, but also gained gravitational disorder, so
the second law was satisfied throughout.

So the arrow of time ultimately stems from the gravitational arrangement of
the Universe at the beginning. This still begs the question of why the Universe
began in such a gravitationally ordered state. Why didn鈥檛 the big bang cough out
black holes鈥攚hich, gravitationally, represent a much more natural state
than smooth gas?

In recent years, cosmologists have sought an explanation for the primordial
state of the Universe by investigating high-energy particle physics, and the
quantum processes that occurred during the first fraction of a second. Although
these investigations are highly speculative, a common feature is
inflation鈥攁n abrupt and enormous jump in the size of the Universe about
one trillion-trillion-trillionth of a second after the big bang. This could have
created the very smooth state reflected in the cosmic microwave background
radiation.

However, as it turns out, inflation solves only part of the problem. To see
why, consider the situation that would arise if, as some theories suggest, the
Universe eventually ceases expanding, and starts to collapse towards a big
crunch, rather like the big bang in reverse. If the Universe did this, its gross
motion would be symmetric in time鈥攕tarting and ending in similar dense
states. Where鈥檚 the thermodynamic arrow in that?

This large-scale symmetry reflects the underlying time-symmetry of the laws
of gravitation and it prompts the question of why one temporal extremity should
differ from the other. If the big bang was followed by a period of inflation,
couldn鈥檛 the big crunch be preceded by a period of 鈥渄eflation鈥, making the
Universe symmetric in time, not just in its gross motion but in its fine details
too?

Such a theory was suggested by Thomas Gold in the 1960s. He proposed that if
the Universe contracted, the arrow of time would be reversed. Heat would flow
from cold to hot, raindrops would rise and people would grow younger. In short,
the movie would be played backwards. Any inhabitants of this contracting phase
would have their mental processes reversed too, and would not notice anything
unusual.

However, if the arrow of time reversed like this, I believe that it would
produce conspicuous physical effects鈥攚hich nobody has ever seen. For
instance, radiation from the Sun escapes from the Galaxy and heads off into the
void of intergalactic space. In 1995, Jason Twamley, then at the University of
Adelaide, and I calculated that much of this radiation would remain undisturbed
until long after the Universe began recontracting. When the radiation eventually
encountered matter, it would find that all thermodynamic processes had been
reversed. Likewise, radiation emitted in the contracting phase should travel
back in time and reach our region of the Universe now, all of which would play
havoc with causality. What鈥檚 more, the presence of a large amount of 鈥渞adiation
from the future鈥 would almost certainly show up in cosmological observations,
and yet nobody has detected it.

Quantum universes

A more promising explanation, proposed a few years ago by Murray Gell-Mann
from Caltech and James Hartle from the University of California at Santa
Barbara, accepts that the observed Universe is asymmetric, and appeals to
quantum theory to explain it. Quantum physics implies that a given quantum state
of the Universe could evolve in many different ways. Some of these possibilities
correspond to a Universe that starts out smooth and grows clumpy, while others
correspond to the reverse process. Yet others are universes which remain clumpy
and chaotic throughout. A few quantum alternatives involve a universe that
starts out smooth, grows clumpy, and then reverses, ending up smooth again.
Although individual possible universes are generally lopsided, the collection as
a whole does not favour one direction of time over the other, thus maintaining
the underlying time symmetry of nature.

But only a few of these many quantum alternatives could actually be perceived
by living creatures. Life depends on a thermodynamic disequilibrium, so it is no
surprise that we observe a universe with one smooth temporal extremity, which we
term 鈥渢he beginning鈥. However, we are much less likely to observe a
time-symmetric universe. Only a tiny fraction of the possible universes have
both smooth initial and final states, and the overwhelming majority of possible
universes are lopsided in time. So living creatures are most likely to witness a
universe that begins smooth and ends clumpy. And if the Universe does reverse
its expansion, this implies the big bang would be smooth, but the big crunch
would be a messy collapse of clumpy material and black holes.

If these ideas are correct鈥攁nd they are admittedly based on some very
shaky calculations鈥攖hen the arrow of time has a simple spatial analogue.
Just as the laws of physics do not favour a direction of time, neither do they
favour a direction of space. Nevertheless, many physical systems have a definite
orientation in space. For example, the Milky Way galaxy has a rotation axis that
points to a particular part of the Universe. However, the rotation axes of other
galaxies point in different directions, and overall there is no preferred
alignment. So laws can have symmetries that are broken by actual physical
systems. If our Universe didn鈥檛 break the time symmetry of the laws and so
produce an arrow of time, we wouldn鈥檛 be here to notice.

Galaxies point in many directions
  • Further reading:
    The Arrow of Time by P. Coveney and R. Highfield (W. H. Allen, 1990).
  • About Time by Paul Davies (Penguin, 1995).
  • Time鈥檚 Arrow and Archimedes鈥 Point by Huw Price (OUP, 1996).

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