My Brain Hurts!

[David Farber <dave () farber net>]

________________________________________
From: Randall Webmail [rvh40 () insightbb com]
Sent: Thursday, June 26, 2008 9:05 AM
To: dewayne () warpspeed com; David Farber; johnmacsgroup () yahoogroups com
Subject: My Brain Hurts!

http://www.sciam.com/article.cfm?id=the-self-organizing-quantum-universe&print=true

Using Causality to Solve the Puzzle of Quantum Spacetime
A new approach to the decades-old problem of quantum gravity goes back to basics
and shows how the building blocks of space and time pull themselves together

By Jerzy Jurkiewicz, Renate Loll and Jan Ambjorn

Editor's Note: Click here for the web animations mentioned in the article

How did space and time come about? How did they form the smooth four-dimensional
emptiness that serves as a backdrop for our physical world? What do they look
like at the very tiniest distances? Questions such as these lie at the outer
boundary of modern science and are driving the search for a theory of quantum
gravity—the long-sought unification of Einstein's general theory of relativity
with quantum theory. Relativity theory describes how spacetime on large scales
can take on countless different shapes, producing what we perceive as the force
of gravity. In contrast, quantum theory describes the laws of physics at atomic
and subatomic scales, ignoring gravitational effects altogether. A theory of
quantum gravity aims to describe the nature of spacetime on the very smallest
scales—the voids in between the smallest known elementary particles—by quantum
laws and possibly explain it in terms of some fundamental constituents.

Superstring theory is often described as the leading candidate to fill this
role, but it has not yet provided an answer to any of these pressing questions.
Instead, following its own inner logic, it has uncovered ever more complex
layers of new, exotic ingredients and relations among them, leading to a
bewildering variety of possible outcomes.

Over the past few years our collaboration has developed a promising alternative
to this much traveled superhighway of theoretical physics. It follows a recipe
that is almost embarrassingly simple: take a few very basic ingredients,
assemble them according to well-known quantum principles (nothing exotic), stir
well, let settle—and you have created quantum spacetime. The process is
straightforward enough to simulate on a laptop.

To put it differently, if we think of empty spacetime as some immaterial
substance, consisting of a very large number of minute, structureless pieces,
and if we then let these microscopic building blocks interact with one another
according to simple rules dictated by gravity and quantum theory, they will
spontaneously arrange themselves into a whole that in many ways looks like the
observed universe. It is similar to the way that molecules assemble themselves
into crystalline or amorphous solids.

Spacetime, then, might be more like a simple stir fry than an elaborate wedding
cake. Moreover, unlike other approaches to quantum gravity our recipe is very
robust. When we vary the details in our simulations, the result hardly changes.
This robustness gives reason to believe we are on the right track. If the
outcome were sensitive to where we put down each piece of this enormous
ensemble, we could generate an enormous number of baroque shapes, each a priori
equally likely to occur—so we would lose all explanatory power for why the
universe turned out as it did.

Similar mechanisms of self-assembly and self-organization occur across physics,
biology and other fields of science. A beautiful example is the behavior of
large flocks of birds, such as European starlings. Individual birds interact
only with a small number of nearby birds; no leader tells them what to do. Yet
the flock still forms and moves as a whole. The flock possesses collective, or
emergent, properties that are not obvious in each bird's behavior.

A Brief History of Quantum Gravity
Past attempts to explain the quantum structure of spacetime as a process of
emergence had only limited success. They were rooted in Euclidean quantum
gravity, a research program initiated at the end of the 1970s and popularized by
physicist Stephen Hawking's best-selling book A Brief History of Time. It is
based on a fundamental principle from quantum mechanics: superposition. Any
object, whether a classical or quantum one, is in a certain state—characterizing
its position and velocity, say. But whereas the state of a classical object can
be described by a unique set of numbers, the state of a quantum object is far
richer. It is the sum, or superposition, of all possible classical states.

For instance, a classical billiard ball moves along a single trajectory with a
precise position and velocity at all times. That would not be a good description
for how the much smaller electron moves. Its motion is described by quantum
laws, which imply that it can exist simultaneously in a wide range of positions
and velocities. When an electron travels from point A to point B in the absence
of any external forces, it does not just take the straight line between A and B
but all available routes simultaneously. This qualitative picture of all
possible electron paths conspiring together translates into the precise
mathematical prescription of a quantum superposition, formulated by Nobel
laureate Richard Feynman, which is a weighted average of all these distinct
possibilities.

With this prescription, one can compute the probability of finding the electron
in any particular range of positions and velocities away from the straight path
that we would expect if the electrons followed the laws of classical mechanics.
What makes the particles' behavior distinctly quantum mechanical are the
deviations from a single sharp trajectory, called quantum fluctuations. The
smaller the size of a physical system one considers, the more important the
quantum fluctuations become.

[SNIP]


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