Causality

[Jack Stafurik]

Per our discussion at Friam, here is an article with some radical TOEs. One,
Causal Dynamical Triangulations, give us our four dimensional spacetime if
you make the assumption of causality. I wonder how many people in the world
really understand the concepts and mathematics behind these. Would I require
a PhD plus many postdoc years to understand these?

Jack

Four radical routes to a theory of everything
  a.. 02 May 2008
  b.. From New Scientist Print Edition.
  c.. Amanda Gefter

THESE days it seems like every physicist is an Indiana Jones on the hunt for
the Holy Grail, a theory that can unite the fractured worlds of quantum
mechanics and general relativity - Einstein's theory of gravity - and bring
order to the universe. Some call it a "theory of everything", some call it
"quantum gravity", but for decades nearly everyone has been using the same
old treasure map - the one drawn up by string theory.

String theory is the most widely known candidate in the search for a theory
of everything, and with good reason. It has elegance: the messy array of
particles that make up matter and forces, including gravity, can be pared
down to vibrations of infinitesimal strings. It has mystique: it posits the
existence of six or seven hidden dimensions of space. And it has manpower:
the vast majority of researchers working on a quantum theory of gravity have
wrapped themselves up in strings.

But string theory also has a fundamental problem. Though remarkably
successful at describing the behaviour of particles, so far it fails to
explain the nature of space and time. According to general relativity,
gravity is a manifestation of the curvature of space-time, so to truly unite
quantum mechanics with gravity, physicists need to deduce the quantum
structure of space-time itself. A theory of everything that leaves out space
and time hardly lives up to its name, so over the years physicists have
proposed several alternatives to string theory. The best known is loop
quantum gravity (New Scientist, 12 August 2006, p 28), though this too has
its share of problems.

Now a growing number of physicists are starting to solve these kinds of
problems by developing alternate ways of understanding space-time itself.
Though their approaches are still at an early stage, four groups in
particular have made crucial progress and are beginning to challenge our
most basic notions of cosmology. They represent a significant shift in the
search for a theory of everything: suddenly there are a wide variety of
non-string-theory approaches, any of which might be the starting point of an
ultimate answer (see Table).

Causal dynamical triangulations

The first, and perhaps most advanced, of these is known as causal dynamical
triangulations (CDT). Developed over the last few years by Renate Loll of
Utrecht University in the Netherlands and her colleagues Jan Ambjorn and
Jerzy Jurkiewicz, CDT models space-time as being made up of tiny, identical
building blocks - in this case, higher-dimensional analogues of triangles,
called 4-simplices. Governed by quantum mechanics, the triangles perpetually
rearrange themselves into new configurations, each of which has its own
curvature.

Just as you can glue six equilateral triangles together at a point to make a
piece of flat space, so CDT can produce flat, positively curved or
negatively curved space-time by allowing different numbers of 4-simplices to
meet at a point. The triangles are not physical objects; rather, they are a
mathematical and computational tool - and they lead to compelling results.

The crucial step in deriving space-time on a large scale is to "sum over"
all possible configurations of these triangles. This is in keeping with the
spirit of Richard Feynman's approach to quantum mechanics, in which every
possible path of a particle must be added up to calculate how it gets from A
to B. Back in the late 1970s, a similar approach to space-time was taken by
Stephen Hawking at the University of Cambridge, but it failed as it ended up
producing universes that had either no dimensions or an infinite number of
them.

Loll's insight was to include time in the mix, or more precisely, causality.
She insisted that causal structure - the fixed ordering of cause and
effect - be incorporated in the way the triangles can arrange themselves
from one configuration to the next. Due to some quantum quirks, the sum of
these configurations could yield a space-time with any number of dimensions.
Yet when she performed the calculation, what emerged were three dimensions
of space and one of time - a smooth, expanding universe like the one in
which we live, governed by the laws of general relativity and consistent
with standard cosmology.

This is a notable achievement. Even loop quantum gravity, for instance, has
yet to generate a familiar space-time at large scales. What's more, the
result suggests that quantum-level causality may even explain why we live in
a four-dimensional universe in the first place. "Her models are the furthest
anyone has gotten to show explicitly the geometry of space emerging from
something more fundamental. I take that seriously," says physicist and noted
string-theory critic Lee Smolin of the Perimeter Institute for Theoretical
Physics in Waterloo, Ontario.

According to CDT, though, space-time is four-dimensional only at large
scales. At the tiniest scales, the model comes up with only two dimensions,
and it produces a space-time with a fractal structure - rough, jagged and
self-similar, with increasingly detailed structure at ever-smaller scales.
This could be a clue as to how gravity behaves at extremely small distances,
where general relativity is thought to break down.

CDT still has its work cut out - for instance, it needs to show how matter
arises, and how the 2D fractal geometry at small scales affects the physics
of elementary particles. Loll and her colleagues need to make specific
testable predictions. For now, though, the fact that they have derived
something resembling our universe from quantum interactions is unique. "They
are the one research programme that makes quantum gravity look reasonable,"
says physicist Olaf Dreyer at the Massachusetts Institute of Technology.

Quantum Einstein gravity
Martin Reuter, a physicist at the University of Mainz in Germany, has other
ideas. He has been developing a different theory he calls "quantum Einstein
gravity", which begins where the earliest approaches to quantum gravity left
off.

After physicists successfully merged the classical theory of
electromagnetism with quantum theory to create quantum electrodynamics in
the 1940s, and later extended their methods to work with the strong and weak
nuclear forces, they had hoped that they could likewise "quantise" gravity.
The idea failed miserably, because of the way gravity behaves at small
scales. As you zoom in on smaller distances, the strength of gravity
increases, but gravity also acts on itself, creating a feedback loop that
sends the gravitational force skyrocketing. Eventually the ability of
general relativity to describe the fabric of the universe breaks down.

So most physicists went off in other directions, mainly towards string
theory. Reuter, however, feels they were too quick to abandon the methods
that had worked when applied to every other force in nature. He had been
thinking about an idea proposed by physicist Steven Weinberg in the 1970s:
that at extremely small scales, there might be a "fixed point" at which the
strength of gravity no longer increases, no matter how much you zoom in.
There is reason to think this might work. Quantum chromodynamics, the theory
of how the strong nuclear force acts on quarks and gluons, says that the
strong force decreases at smaller scales until it reaches a fixed point,
where it goes to zero. If a similar point exists for gravity, it would mean
that physics would be able to describe gravity down to the quantum realm.

When Weinberg proposed the idea, physicists didn't have the mathematical
tools to calculate this fixed point in the four-dimensional space-time of
general relativity. Then in the late 1990s Reuter developed such a method.
His calculations were approximate, but they suggested that a fixed point for
gravity might indeed lurk in the equations. "Personally, I am completely
convinced that it exists," he says.

Intriguingly, in quantum Einstein gravity, space-time at the smallest scales
is fractal and the number of dimensions shrinks from the familiar four to
two. This is reminiscent of CDT, which leads some to wonder if they are two
descriptions of the same theory. "Ultimately the two approaches could turn
out to be equivalent," Reuter says.

Quantum graphity
While CDT and quantum Einstein gravity start with space-time and apply
quantum mechanics to it, other physicists are taking a more radical
approach: doing away with space-time altogether. Their idea is to show that
space-time, and gravity, emerge from what they call a "pre-geometric" state.

Fotini Markopoulou of the Perimeter Institute and her colleagues are
developing one such model, which they have whimsically named "quantum
graphity". It starts with the idea that at extremely small scales and
extremely high energies - conditions that would have applied at the birth of
the universe - there is no such thing as space. All that exists is an
abstract network, a graph made of nodes connected by edges governed by
quantum mechanics. In this state, every node is connected to every other
node. It's a highly counter-intuitive picture, as if every atom in the
universe were next to every other atom. "When everything is on top of
everything else, there's no notion of space," she says.

The idea of a pre-geometric phase of the universe originated in the 1950s
with the late John Wheeler, the physicist who pioneered the field of quantum
gravity. "My intention was to be a bit more radical about what it means,"
says Markopoulou. "People talk about pre-geometry and quantum geometry, but
they seem to mean something more like really bumpy geometry. It turns out
it's actually much stranger than people thought."

According to quantum graphity, this pre-geometric phase didn't last long.
When the early universe cooled, it went through a phase transition akin to
ice crystals forming when water freezes. During this phase transition, many
of the nodes became unlinked; everything was no longer connected. Some nodes
became far away from others, so distance, and hence space, emerged and the
collection of nodes "crystallised" into a regular lattice-like structure.
This structure represents space on the quantum scale and gives rise to
smooth space at large scales.

Markopoulou thinks this transition might explain a long-standing puzzle in
cosmology: the fact that there are distant regions of the universe that are
at precisely the same temperature. This would require these regions to have
been near enough to each other in the past to be able to exchange radiation
and even out their temperatures. But if we extrapolate their earlier
positions based on the speeds at which they have been moving apart, we find
they would never have been sufficiently close. To get round this difficulty,
the well-known inflationary model of cosmology proposes that the early
universe went through a brief period of faster-than-light expansion.

Quantum graphity, however, can potentially solve this thermal equilibrium
puzzle without the need for inflation. If everything was in contact with
everything else during the pre-geometric phase, then we should expect to see
striking similarities between distant regions of the universe. Markopoulou
says that she has a lot more work to do before her model can compete with
inflation, but she is excited about the prospect of finding evidence for it
in the vastness of space. "I like the fact that it should have large-scale
signatures, because in quantum gravity you're often stuck in really
small-scale physics," she says. "Here, cosmology would be the place to
look."

Internal relativity
At MIT, Dreyer is developing a similar model called "internal relativity",
in which space-time emerges from a pre-geometric state - and he is betting
the laws of general relativity will too. This is perhaps the most ambitious
model of all. Dreyer's starting point is a simple quantum system of spins,
each of which can be either up or down, in a random distribution. At a
critical temperature, the system undergoes a phase transition in which the
spins align to form an ordered pattern.

The trick, he says, is to consider what observers inside the system see
after the phase transition. They will never see the underlying spins that
act as a backdrop; all they see are the excitations of the system which, it
turns out, they perceive as space-time and matter. Taking this "internal"
perspective seriously, Dreyer says, he has shown that the effects of special
relativity, such as time dilation and length contraction, arise naturally.
What's more, he has been able to derive Newtonian gravity by showing that
two nearby particles in his model will mutually attract, as this lowers the
overall energy of the system.

It is more difficult to show that general relativity also arises in Dreyer's
model, but he is confident he can do it. According to general relativity,
space-time and matter influence one another but remain distinct. Dreyer's
confidence is inspired by the fact that in his model space-time and matter
are no longer considered separate, but emerge together from the same
pre-geometric state. Markopoulou is supportive of his approach to deriving
the equations of general relativity. "It's the only thing I've heard in
years that gives us a chance to actually explain the Einstein equations,"
she says.

For now, Dreyer's claim that general relativity will emerge remains
conjecture. If it does, though, he thinks his model can help solve another
vexing problem, that of Einstein's cosmological constant. Representing the
energy of space-time itself, the constant is predicted from quantum theory
to be enormous, but experiments reveal it is extremely small. "This problem
is a result of making a split between space-time and matter. That gets you
into a lot of trouble," Dreyer says. In internal relativity, on the other
hand, there is no space-time without matter, so the energy of space-time
would have to be calculated differently. He predicts it would be tiny, as is
observed.

Dreyer has come up with a way to test his model. If the early universe went
through a period of inflation, we should be able to detect relic
gravitational waves rippling through the cosmic microwave background. If,
however, the universe emerged from a pre-geometric state, no such waves
should be found. The Planck satellite, expected to be launched by the
European Space Agency later this year, should be sensitive enough to detect
these gravity waves if they exist, and either corroborate or rule out
Dreyer's model.

It's anyone's guess which quantum gravity treasure map, if any, will lead
physicists to a theory of everything. For now they've got plenty of clues
and no shortage of paths to follow. They might converge on the answer, or
they might be heading down blind alleys.

"For most of my time in quantum gravity, it was hard enough just to have one
theory," Dreyer says. "Now we have so many different approaches and a lot of
them are making progress. We have to ask nature which one is the right one.
This gets me really excited. It's the way physics is supposed to work."

Cosmology - Keep up with the latest ideas in our special report.

Quantum World - Learn more about a weird world in our comprehensive special
report.

Related Articles
  a.. The theory of everything: Are we nearly there yet?
  b.. http://www.newscientist.com/article.ns?id=mg18624971.500
  c.. 30 April 2005
  d.. String theory: The fightback
  e.. http://www.newscientist.com/article.ns?id=mg19526121.200
  f.. 11 July 2007
  g.. Is mathematical attern the theory of everything?
  h.. http://www.newscientist.com/article.ns?id=mg19626303.900
  i.. 17 November 2007
  j.. The second quantum revolution
  k.. http://www.newscientist.com/article.ns?id=mg19426091.600
  l.. 20 June 2007
Weblinks
  a.. Renate Loll, University of Utrecht
  b.. http://www.phys.uu.nl/~loll/Web/title/title.html
  c.. Martin Reuter, University of Mainz
  d.. http://wwwthep.physik.uni-mainz.de/~reuter/
  e.. Fotini Markopoulou, Perimeter Institute
  f..
http://www.perimeterinstitute.ca/index.php?amp;option=com_content&task=view&id=30&Itemid=72?=Fotini_Markopoulou
  g.. Olaf Dreyer's paper on internal relativity
  h.. http://arxiv.org/abs/gr-qc/0604075
>From issue 2654 of New Scientist magazine, 02 May 2008, page 29-31


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[Carl Tollander]

I've been urging more people to read Stephenson's "Quicksilver",  for
some sense of how new theories are embedded in historical context.   The
first of many fine pithy quotes from the book,

   "Those who assume hypotheses as first principles
      of their specualtions...may indeed form an
      ingenious romance, but a romance it will still be."
                               --Roger Cotes,
                                  Preface to Sir Isaac Newton's  
Principia Mathematica
                                  Second edition, 1713

That said, I like theory anyhow, but in order to approach any of these
TOE's, I've found that it helps to seek some understanding of their
historical context (such as from the math and physics community blogs
we've referred to elsewhere).  I found some of Lee Smolin's popular
books (Three Roads to Quantum Gravity, The Trouble with Physics, etc.)
to be useful - one wants to understand what problems all these different
TOE folks are trying to answer, and where did those problems come from?  
Personally I think the Markopoulou stuff  may be more accessible for
this reason, but nobody should take that as a recommendation.  The CDT
stuff has been too hard for me to situate thus far  (again, not a
recommendation either way, I may simply be too dim).

So, to answer your last question, no, I don't think that would be
enough.  The accessibility of the ideas comes through an understanding
of their history.  Otherwise, well, one is left with an "ingenious
romance".  Which can be fun too for awhile, but ultimately frustrating,
since one is then forced to take on a bunch of assumptions without
knowing where they came from -- the whole corpus starts to feel way too
intimidating.

I do believe that a TOE should live up to its name; it should inform all
our models, including, e.g., biology and economics.  One would hope that
it would inform our thinking about complexity.  However, we keep
assuming the unification of the physics of the itty-bitty and the
mighty-big will lead to some fundamental set of building blocks that
will inform our daily modeling practice.   Maybe that's one reason why
background-independent theories in physics and mathematics are still
regarded as 'radical'.

Carl

Jack Stafurik wrote:
> Per our discussion at Friam, here is an article with some radical TOEs. One,
> Causal Dynamical Triangulations, give us our four dimensional spacetime if
> you make the assumption of causality. I wonder how many people in the world
> really understand the concepts and mathematics behind these. Would I require
> a PhD plus many postdoc years to understand these?
>
> Jack
>
>  

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[Günther Greindl]

Carl, Jack,

Carl Tollander wrote:
> That said, I like theory anyhow, but in order to approach any of these
> TOE's, I've found that it helps to seek some understanding of their
> historical context (such as from the math and physics community blogs
> we've referred to elsewhere).  I found some of Lee Smolin's popular
> books (Three Roads to Quantum Gravity, The Trouble with Physics, etc.)
> to be useful - one wants to understand what problems all these different
> TOE folks are trying to answer, and where did those problems come from?  

I think there are two aspects involved: first, of course there is a
history to research - people build on what's already there, nobody
starts from scratch. In such a way, early accidents (=theory choice) can
channel scientific research directions for quite some time; and I agree,
only by looking at the history of research can one understand current
problems.

But in the long run, science is successful because avenues that show
promise are followed and blind alleys are abandoned. So radical new
theories get their chance when old ones do not advance anymore.

And then, in hindsight, one will usually see why this or that TOE
approach did not work, and where conceptual shifts where necessary; and,
on the other hand, seemingly highly disparate theories will suddenly be
seen as the same thing, when deep connections are revealed.

So, in this sense, one should not be too troubled by "historicity" -
many paths may lead to a TOE, and it does not matter which one one
takes, as long as one starts to walk.


> Personally I think the Markopoulou stuff  may be more accessible for
> this reason, but nobody should take that as a recommendation.  The CDT
> stuff has been too hard for me to situate thus far  (again, not a

I agree that the Markopoulou and (even more so the Dreyer) approach look
very interesting. I'll have a look at their papers, thanks for the New
Scientist article.

>> really understand the concepts and mathematics behind these. Would I require
>> a PhD plus many postdoc years to understand these?

A lot of math is certainly necessary - but not only the "mechanical"
rules (as it is often taught, even at university nowadays) but the
concepts which lie behind them. Math is essentially the science of
"precise ideas", if you like :-))

Apart from that, I think a lot of earnest thinking by oneself is
necessary - you have to have a genuine interest in these things.
Knowledge and insight come from "diu noctuque incubando" (by brooding
day and night), a saying Nietzsche ascribed to Newton in "The Gay
Science" (a wonderful book by the way).

Cheers,
Günther


--
Günther Greindl
Department of Philosophy of Science
University of Vienna
[hidden email]

Blog: http://www.complexitystudies.org/
Thesis: http://www.complexitystudies.org/proposal/


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