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New Scientist
October 15, 2005
The riddle of time;
What keeps the cosmic clock surging onwards? The answer is written in
curious elliptical patterns in the sky, says Amanda Gefter
by Amanda Gefter
YOU wake up one morning and head into your kitchen, where you get the
distinct feeling that something strange is going on. A swirl of milk
separates itself from your coffee, which seems to be growing hotter
by the minute. Scrambled eggs are unscrambling and leaping out of the
pan back into their cracked shells, which proceed to reassemble. And
the warm sunlight that had flooded the room seems to be headed
straight for the window. Apparently, you conclude, time is flowing in
reverse.
You can deduce this because it is obvious that time has an arrow,
which, this morning aside, always points in the same direction. We
take the unchanging arrow of time for granted. Yet there is nothing
in the laws of physics as we know them that says it can't point the
other way. So the riddle is: where does time's arrow come from?
Our perception of the direction of time is linked to the fact that
the world's entropy, or disorder, tends to increase. When you pour
milk into your coffee, the concoction, at first, is highly ordered,
with all the milk molecules entering the coffee in a neat stream. But
as time passes, the milk loses its organisation and mixes randomly
with the coffee. Keep watching and you will see it become thoroughly
mixed, but you won't see the milk suddenly regroup. Strange as it may
seem, it's not that such a scenario is impossible. It's just
incredibly unlikely.
That's because there are vastly more ways for the molecules to
arrange themselves in a random, spread out, high-entropy fashion than
in the tight formation in which they began. It's a matter of
probability: as the molecules perpetually rearrange, they almost
always find themselves in high-entropy arrangements. Of course, if
they start off in a high-entropy arrangement, we won't notice any
change. But if entropy is low at the start, it's bound to increase.
Therein lies the origin of the arrow of time as we perceive it. It
has two essential ingredients. The first is a low-entropy beginning,
like the milk starting out in an ordered arrangement. The second is
mixing: the constant rearrangement of the milk and coffee molecules.
Mixing is necessary for the system to evolve and rearrange from a
low-entropy to a higher-entropy state.
And exactly the same must be true on much grander scales. The
cosmological arrow of time - the process that started with the big
bang - requires the universe to have started off with low entropy,
and the contents of the cosmos to have mixed ever since.
First evidence
So can we find these ingredients for time's arrow in our universe?
Cosmologists already have evidence for the first one. They see that
the universe had a low-entropy beginning by looking at the
arrangement of the photons in the cosmic microwave background
radiation that provides a snapshot of the universe near the beginning
of time.
The CMB photons are uniformly spread out, with variations in density
and temperature detectable at a mere 1 part in 100,000. If the spread
of the CMB photons is uniform, we can assume that the other contents
of the nascent universe - such as the atoms - were also spread
uniformly at that time.
At first glance, that seems like the very definition of a disordered,
high-entropy state, but it's not. The universe is governed by
gravity, which always clumps things together, so a spread-out state
is incredibly unlikely. Although no one knows exactly why, it seems
the universe was born in a low-entropy state.
So what provides the second ingredient? What mixes and rearranges the
contents of the universe? According to Vahe Gurzadyan, a physicist at
the Yerevan Physics Institute in Armenia and La Sapienza University
in Rome, the answer is the shape of space itself.
In 1992, Gurzadyan and his student Armen Kocharyan were looking at
what a universe with "negative curvature" would do to the CMB.
Negative curvature - the exact opposite of the curvature of a sphere
- means that every point in space would be curved both up and down,
like the mid-point of a saddle or a Pringle chip. Physicists have
long considered this to be a possible geometry for the universe.
The temperature of the CMB varies slightly from point to point in the
sky, and maps of this variation reveal a multitude of hot and cold
spots. These maps have enabled cosmologists to infer many things
about the universe: its age and composition, for example. In their
theoretical work, Gurzadyan and Kocharyan found that negative
curvature would stretch the CMB spots into ellipses. That's because
the CMB photons we observe today have been travelling through the
universe for nearly 14 billion years. If that journey took them
through negatively curved space, each little patch of light would
appear as if it has been through a distorting lens. Five years later,
Gurzadyan was looking at data from NASA's COBE satellite, one of the
first to map the CMB, and saw exactly what he and Kocharyan had
predicted: all the spots appeared elongated (Astronomy and
Astrophysics , vol 321, p 19).
The observation was exciting but inconclusive because COBE did not
provide sufficiently fine resolution to measure the shape of the
spots precisely. Perhaps, Gurzadyan and Kocharyan reasoned, this
apparent elongation was just an illusion created by the low-quality
images. But when vastly more detailed CMB maps arrived from NASA's
Wilkinson Microwave Anisotropy Probe (WMAP) in 2003, Gurzadyan and
colleagues ran the data through their programs, removing all
irrelevant distortion effects - and there it was (Modern Physics
Letters A , vol 20, p 813). "All the spots have the same constant
elongation, independent of temperature and the size of the spots,"
Gurzadyan says.
Because spots of all sizes are distorted in exactly the same manner,
this effect can't be due to something that happened at the time the
radiation was created. Some of the spots are so big that their
extremities were already out of causal contact at the time of their
creation: light from one side could never reach the other. Just as
there is no way for us to communicate with a region that has slipped
beyond our causal horizon (New Scientist , 20 October 2001, p 36),
there is no way a distortion effect at that point in time could have
produced the symmetry of the ellipse. So it must have happened some
time later, during the photons' journey through the universe.
And if that's the case, Gurzadyan says, we have all the ingredients
we need for the arrow of time. The universe starts out in an
unlikely, low-entropy arrangement, with all of its contents almost
perfectly spread out. But as particles travel through the universe,
their paths follow the curves of space. In a negatively curved space,
any two particles that start off next to one another quickly diverge,
which means all the particles dramatically rearrange: the geometry of
space mixes the cosmos.
Since most particle arrangements correspond to high entropy, the
negative curvature inevitably guides matter into higher-entropy
states. In the case of the universe, that means states with
gravitational clumping: as entropy increases, things like stars and
galaxies form and with them heavy elements and, eventually, us.
Evidence of this process is encoded in the CMB. The elliptical shape
of the CMB spots reveals that the photons' paths diverged in
precisely the way Gurzadyan expected for a negatively curved
universe. If spatial geometry mixed the photons, then it also mixed
everything else. And low-entropy beginnings plus mixing equals the
arrow of time.
Although Gurzadyan has published his ideas and his data in various
places, the work remains controversial: the traditional view is that
the universe is flat, not negatively curved. The usual interpretation
of the WMAP results, which comes not from looking at the shape of the
temperature spots but instead from what's called the power spectrum,
is that the universe is flat. And most cosmologists believe this
flatness supports the cherished theory of inflation, the idea that
the universe underwent a fleeting moment of faster-than-light
expansion shortly after its birth.
The trouble with that objection is that a different aspect of WMAP's
findings goes against inflation's predictions. When astronomers plot
the power spectrum of the data, they see a big problem - hints of
which had also been seen with COBE. The power spectrum compares the
amount of temperature variation at different scales in the sky. When
close regions of the sky are being compared, the temperature
variations of the CMB fit with the predictions of inflation. But on
very large angular scales the variation conflicts with inflation's
prediction. The anomaly, for which there is no accepted explanation,
suggests that there is something strange going on in the large-scale
geometry of the cosmos, perhaps because it is not flat. "This anomaly
is very curious," says Roger Penrose, a mathematical physicist at the
University of Oxford. "It seems to be out of kilter with the
inflation model, and it could be due to negative curvature."
Gurzadyan regards the elongation of the hot and cold spots as
powerful evidence that the universe is negatively curved, and Penrose
agrees. Negative curvature would distort the CMB far more than a flat
universe could, Penrose explains, squashing the light in one
direction and stretching it in another. "If the geometry of space is
negative, then you expect the ellipses to stretch much more than they
would in positively curved or flat space," he says. "And this is
exactly what Gurzadyan sees."
Nonetheless, most cosmologists are still not ready to abandon the
flat universe or inflation. Although no one has actually shown or
even suggested that there is anything wrong with Gurzadyan's
elliptical spots, they are hesitant to accept its implications. "At
the moment, I don't feel that we have any compelling evidence against
space being flat," says Max Tegmark, a cosmologist at the
Massachusetts Institute of Technology. Princeton University's Lyman
Page, a member of the WMAP team, is similarly reluctant. "Though I'm
a strong believer in alternative analyses of data, it is too early to
put much stock into the interpretation of Gurzadyan's result," Page
says.
Penrose, however, is excited by the result, and says there is much
more to be gained from the CMB than physicists so far seem to
realise. "There's vastly more information in the data than people
look at normally. So far we've seen an infinitesimal amount, and
people tend to look at the same things that everyone else is looking
at. Gurzadyan is only using a tiny bit, but it's a different tiny
bit. I think the analysis has to be taken very seriously."
Elliptical time
Of course, directly linking the ellipses to the flow of time is even
more controversial, but we don't have any other satisfactory
explanation. The flow of time we observe is certainly not compulsory:
it is perfectly possible for the time-symmetry of relativity, quantum
theory and our other descriptions of the universe to produce a
universe where time doesn't flow - or even one where time flows in
the opposite direction to the one we experience. In 1999 Lawrence
Schulman of Clarkson University in Potsdam, New York, showed that in
principle regions of the universe where time flows in the normal
direction can coexist with regions where it flows backwards (New
Scientist , 6 February 2000, p 26).
But in our universe a negative curvature would stop this by imposing
a global condition for the increase of disorder. This may even be
what allows life to exist in the universe, Gurzadyan suggests: a new
kind of anthropic principle .
Of course, if the saddle-shaped universe provides us with a mechanism
for the increasing cosmic disorder, it still doesn't explain the
arrow's ultimate origin: it doesn't explain the first ingredient, why
the universe began with low-entropy conditions. "Of course you need
mixing," explains University of Chicago physicist Sean Carroll, "but
that's the easy part. The hard part is getting the initial entropy to
be low."
That remains a mystery, perhaps only to be resolved by the "theory of
everything" that physicists are avidly searching for. And we do have
hints that this final theory might address the problem. For example,
Rafael Sorkin of Syracuse University in New York state has proposed
"causal set theory", which attempts to unite quantum theory and
relativity. It supposes that the fabric of the universe grows as
effects follow causal events - giving a sense of time's flow (New
Scientist , 4 October 2003, p 36). Although Sorkin and his colleagues
admit it is not yet a complete theory of quantum gravity, it does at
least install a one-way arrow of time and a low-entropy beginning.
Of course, all these attempts to understand the irrepressible passage
of time assume that time's arrow is a "real" phenomenon to do with
the physical universe - and that is not entirely certain. Some think
it might arise from the strange metaphysics of the quantum world;
others see it as a purely psychological phenomenon, an artefact of
our consciousness.
But Gurzadyan is now convinced that the passage of time is a
cosmological process. The hands on the cosmic clock are driven round
by the chaotic movements of photons through the negatively curved
universe, he says. Though that may be a little beyond what most
cosmologists are willing to accept for now, the idea must be worth
exploring: the search for answers to the flow of time goes to the
heart of physics, Penrose believes. "The problem of the arrow of time
is absolutely fundamental," he says. "It's telling us something very
deep about the universe."
Life and time
Amanda Gefter
Vahe Gurzadyan's idea has a startling implication: if the geometry of
space were different, there would be no "arrow" of time. Could life
exist in a universe without an arrow? If not, would that help explain
why the geometry of our universe is as we observe? Gurzadyan has
dubbed this idea the "curvature anthropic principle".
The standard anthropic principle says that certain aspects of the
universe - like the values of physical constants - are the way they
are because otherwise we wouldn't be here to wonder about them. For
instance, if the mass of the electron were different, the universe
would be unable to support human life, so we shouldn't be surprised
by its value, given our very existence. Some scientists consider this
common sense, while others see it as a sorry stand-in for a real
explanation. The curvature anthropic principle applies this logic to
the shape of space: without this negative curvature, we wouldn't have
evolved as we did, Gurzadyan suggests.
October 15, 2005
The riddle of time;
What keeps the cosmic clock surging onwards? The answer is written in
curious elliptical patterns in the sky, says Amanda Gefter
by Amanda Gefter
YOU wake up one morning and head into your kitchen, where you get the
distinct feeling that something strange is going on. A swirl of milk
separates itself from your coffee, which seems to be growing hotter
by the minute. Scrambled eggs are unscrambling and leaping out of the
pan back into their cracked shells, which proceed to reassemble. And
the warm sunlight that had flooded the room seems to be headed
straight for the window. Apparently, you conclude, time is flowing in
reverse.
You can deduce this because it is obvious that time has an arrow,
which, this morning aside, always points in the same direction. We
take the unchanging arrow of time for granted. Yet there is nothing
in the laws of physics as we know them that says it can't point the
other way. So the riddle is: where does time's arrow come from?
Our perception of the direction of time is linked to the fact that
the world's entropy, or disorder, tends to increase. When you pour
milk into your coffee, the concoction, at first, is highly ordered,
with all the milk molecules entering the coffee in a neat stream. But
as time passes, the milk loses its organisation and mixes randomly
with the coffee. Keep watching and you will see it become thoroughly
mixed, but you won't see the milk suddenly regroup. Strange as it may
seem, it's not that such a scenario is impossible. It's just
incredibly unlikely.
That's because there are vastly more ways for the molecules to
arrange themselves in a random, spread out, high-entropy fashion than
in the tight formation in which they began. It's a matter of
probability: as the molecules perpetually rearrange, they almost
always find themselves in high-entropy arrangements. Of course, if
they start off in a high-entropy arrangement, we won't notice any
change. But if entropy is low at the start, it's bound to increase.
Therein lies the origin of the arrow of time as we perceive it. It
has two essential ingredients. The first is a low-entropy beginning,
like the milk starting out in an ordered arrangement. The second is
mixing: the constant rearrangement of the milk and coffee molecules.
Mixing is necessary for the system to evolve and rearrange from a
low-entropy to a higher-entropy state.
And exactly the same must be true on much grander scales. The
cosmological arrow of time - the process that started with the big
bang - requires the universe to have started off with low entropy,
and the contents of the cosmos to have mixed ever since.
First evidence
So can we find these ingredients for time's arrow in our universe?
Cosmologists already have evidence for the first one. They see that
the universe had a low-entropy beginning by looking at the
arrangement of the photons in the cosmic microwave background
radiation that provides a snapshot of the universe near the beginning
of time.
The CMB photons are uniformly spread out, with variations in density
and temperature detectable at a mere 1 part in 100,000. If the spread
of the CMB photons is uniform, we can assume that the other contents
of the nascent universe - such as the atoms - were also spread
uniformly at that time.
At first glance, that seems like the very definition of a disordered,
high-entropy state, but it's not. The universe is governed by
gravity, which always clumps things together, so a spread-out state
is incredibly unlikely. Although no one knows exactly why, it seems
the universe was born in a low-entropy state.
So what provides the second ingredient? What mixes and rearranges the
contents of the universe? According to Vahe Gurzadyan, a physicist at
the Yerevan Physics Institute in Armenia and La Sapienza University
in Rome, the answer is the shape of space itself.
In 1992, Gurzadyan and his student Armen Kocharyan were looking at
what a universe with "negative curvature" would do to the CMB.
Negative curvature - the exact opposite of the curvature of a sphere
- means that every point in space would be curved both up and down,
like the mid-point of a saddle or a Pringle chip. Physicists have
long considered this to be a possible geometry for the universe.
The temperature of the CMB varies slightly from point to point in the
sky, and maps of this variation reveal a multitude of hot and cold
spots. These maps have enabled cosmologists to infer many things
about the universe: its age and composition, for example. In their
theoretical work, Gurzadyan and Kocharyan found that negative
curvature would stretch the CMB spots into ellipses. That's because
the CMB photons we observe today have been travelling through the
universe for nearly 14 billion years. If that journey took them
through negatively curved space, each little patch of light would
appear as if it has been through a distorting lens. Five years later,
Gurzadyan was looking at data from NASA's COBE satellite, one of the
first to map the CMB, and saw exactly what he and Kocharyan had
predicted: all the spots appeared elongated (Astronomy and
Astrophysics , vol 321, p 19).
The observation was exciting but inconclusive because COBE did not
provide sufficiently fine resolution to measure the shape of the
spots precisely. Perhaps, Gurzadyan and Kocharyan reasoned, this
apparent elongation was just an illusion created by the low-quality
images. But when vastly more detailed CMB maps arrived from NASA's
Wilkinson Microwave Anisotropy Probe (WMAP) in 2003, Gurzadyan and
colleagues ran the data through their programs, removing all
irrelevant distortion effects - and there it was (Modern Physics
Letters A , vol 20, p 813). "All the spots have the same constant
elongation, independent of temperature and the size of the spots,"
Gurzadyan says.
Because spots of all sizes are distorted in exactly the same manner,
this effect can't be due to something that happened at the time the
radiation was created. Some of the spots are so big that their
extremities were already out of causal contact at the time of their
creation: light from one side could never reach the other. Just as
there is no way for us to communicate with a region that has slipped
beyond our causal horizon (New Scientist , 20 October 2001, p 36),
there is no way a distortion effect at that point in time could have
produced the symmetry of the ellipse. So it must have happened some
time later, during the photons' journey through the universe.
And if that's the case, Gurzadyan says, we have all the ingredients
we need for the arrow of time. The universe starts out in an
unlikely, low-entropy arrangement, with all of its contents almost
perfectly spread out. But as particles travel through the universe,
their paths follow the curves of space. In a negatively curved space,
any two particles that start off next to one another quickly diverge,
which means all the particles dramatically rearrange: the geometry of
space mixes the cosmos.
Since most particle arrangements correspond to high entropy, the
negative curvature inevitably guides matter into higher-entropy
states. In the case of the universe, that means states with
gravitational clumping: as entropy increases, things like stars and
galaxies form and with them heavy elements and, eventually, us.
Evidence of this process is encoded in the CMB. The elliptical shape
of the CMB spots reveals that the photons' paths diverged in
precisely the way Gurzadyan expected for a negatively curved
universe. If spatial geometry mixed the photons, then it also mixed
everything else. And low-entropy beginnings plus mixing equals the
arrow of time.
Although Gurzadyan has published his ideas and his data in various
places, the work remains controversial: the traditional view is that
the universe is flat, not negatively curved. The usual interpretation
of the WMAP results, which comes not from looking at the shape of the
temperature spots but instead from what's called the power spectrum,
is that the universe is flat. And most cosmologists believe this
flatness supports the cherished theory of inflation, the idea that
the universe underwent a fleeting moment of faster-than-light
expansion shortly after its birth.
The trouble with that objection is that a different aspect of WMAP's
findings goes against inflation's predictions. When astronomers plot
the power spectrum of the data, they see a big problem - hints of
which had also been seen with COBE. The power spectrum compares the
amount of temperature variation at different scales in the sky. When
close regions of the sky are being compared, the temperature
variations of the CMB fit with the predictions of inflation. But on
very large angular scales the variation conflicts with inflation's
prediction. The anomaly, for which there is no accepted explanation,
suggests that there is something strange going on in the large-scale
geometry of the cosmos, perhaps because it is not flat. "This anomaly
is very curious," says Roger Penrose, a mathematical physicist at the
University of Oxford. "It seems to be out of kilter with the
inflation model, and it could be due to negative curvature."
Gurzadyan regards the elongation of the hot and cold spots as
powerful evidence that the universe is negatively curved, and Penrose
agrees. Negative curvature would distort the CMB far more than a flat
universe could, Penrose explains, squashing the light in one
direction and stretching it in another. "If the geometry of space is
negative, then you expect the ellipses to stretch much more than they
would in positively curved or flat space," he says. "And this is
exactly what Gurzadyan sees."
Nonetheless, most cosmologists are still not ready to abandon the
flat universe or inflation. Although no one has actually shown or
even suggested that there is anything wrong with Gurzadyan's
elliptical spots, they are hesitant to accept its implications. "At
the moment, I don't feel that we have any compelling evidence against
space being flat," says Max Tegmark, a cosmologist at the
Massachusetts Institute of Technology. Princeton University's Lyman
Page, a member of the WMAP team, is similarly reluctant. "Though I'm
a strong believer in alternative analyses of data, it is too early to
put much stock into the interpretation of Gurzadyan's result," Page
says.
Penrose, however, is excited by the result, and says there is much
more to be gained from the CMB than physicists so far seem to
realise. "There's vastly more information in the data than people
look at normally. So far we've seen an infinitesimal amount, and
people tend to look at the same things that everyone else is looking
at. Gurzadyan is only using a tiny bit, but it's a different tiny
bit. I think the analysis has to be taken very seriously."
Elliptical time
Of course, directly linking the ellipses to the flow of time is even
more controversial, but we don't have any other satisfactory
explanation. The flow of time we observe is certainly not compulsory:
it is perfectly possible for the time-symmetry of relativity, quantum
theory and our other descriptions of the universe to produce a
universe where time doesn't flow - or even one where time flows in
the opposite direction to the one we experience. In 1999 Lawrence
Schulman of Clarkson University in Potsdam, New York, showed that in
principle regions of the universe where time flows in the normal
direction can coexist with regions where it flows backwards (New
Scientist , 6 February 2000, p 26).
But in our universe a negative curvature would stop this by imposing
a global condition for the increase of disorder. This may even be
what allows life to exist in the universe, Gurzadyan suggests: a new
kind of anthropic principle .
Of course, if the saddle-shaped universe provides us with a mechanism
for the increasing cosmic disorder, it still doesn't explain the
arrow's ultimate origin: it doesn't explain the first ingredient, why
the universe began with low-entropy conditions. "Of course you need
mixing," explains University of Chicago physicist Sean Carroll, "but
that's the easy part. The hard part is getting the initial entropy to
be low."
That remains a mystery, perhaps only to be resolved by the "theory of
everything" that physicists are avidly searching for. And we do have
hints that this final theory might address the problem. For example,
Rafael Sorkin of Syracuse University in New York state has proposed
"causal set theory", which attempts to unite quantum theory and
relativity. It supposes that the fabric of the universe grows as
effects follow causal events - giving a sense of time's flow (New
Scientist , 4 October 2003, p 36). Although Sorkin and his colleagues
admit it is not yet a complete theory of quantum gravity, it does at
least install a one-way arrow of time and a low-entropy beginning.
Of course, all these attempts to understand the irrepressible passage
of time assume that time's arrow is a "real" phenomenon to do with
the physical universe - and that is not entirely certain. Some think
it might arise from the strange metaphysics of the quantum world;
others see it as a purely psychological phenomenon, an artefact of
our consciousness.
But Gurzadyan is now convinced that the passage of time is a
cosmological process. The hands on the cosmic clock are driven round
by the chaotic movements of photons through the negatively curved
universe, he says. Though that may be a little beyond what most
cosmologists are willing to accept for now, the idea must be worth
exploring: the search for answers to the flow of time goes to the
heart of physics, Penrose believes. "The problem of the arrow of time
is absolutely fundamental," he says. "It's telling us something very
deep about the universe."
Life and time
Amanda Gefter
Vahe Gurzadyan's idea has a startling implication: if the geometry of
space were different, there would be no "arrow" of time. Could life
exist in a universe without an arrow? If not, would that help explain
why the geometry of our universe is as we observe? Gurzadyan has
dubbed this idea the "curvature anthropic principle".
The standard anthropic principle says that certain aspects of the
universe - like the values of physical constants - are the way they
are because otherwise we wouldn't be here to wonder about them. For
instance, if the mass of the electron were different, the universe
would be unable to support human life, so we shouldn't be surprised
by its value, given our very existence. Some scientists consider this
common sense, while others see it as a sorry stand-in for a real
explanation. The curvature anthropic principle applies this logic to
the shape of space: without this negative curvature, we wouldn't have
evolved as we did, Gurzadyan suggests.