Science > Physics > Smolin's & Rovelli's Three Roads to Quantum Gravity
| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
30 Jan 2004 05:41:59 PM |
| Object: |
Smolin's & Rovelli's Three Roads to Quantum Gravity |
Lecture 5: Rovelli’s History of Quantum Gravity to 1999 pp. 287 – 301
Preamble to Smolin’s and Rovelli’s “Three Royal Roads to Quantum Gravity.”
What does it mean to quantize a theory? This is a top -> down idea. You
start with a classical physics theory. What are the key classical theories?
(i) Newton’s test particle mechanics in Galilean relativity with an
infinite speed of light, Einstein’s 1905 special relativity with a
finite speed of light barrier but without gravity and Einstein’s
geometrodynamic 1915 general relativity with gravity.
(ii) Maxwell’s electromagnetic field theory that cannot be consistently
formulated in Galilean relativity because electromagnetic waves
propagate at the finite speed of light that is the same number for all
observers independent of their speed or motion or their acceleration.
Maxwell’s theory is automatically special relativistic and can be
extended to general relativity with gravity as seen in the cosmological
red shifts of our expanding universe accelerated by repulsive exotic
vacua “dark energy”, and in the gravitational lensing showing clumps
of attractive exotic vacuum “dark matter.”
(iii) Yang-Mills field theories of the weak and strong short-range forces.
(iv) Einstein’s geometrodynamic field theory of gravity as the curving
of a dynamical space-time that is not merely a rigid stage, like in
special relativity where the full action-reaction principle is violated
and on which all the other fields play, but is, rather, itself a player
in “two-way relation” (Bohm and Hiley) obeying the full action-reaction
principle.
The top -> down approach then replaces the real number particle and
field “observables” by square arrays of complex numbers called
“matrices” that are “representations” or faithful images of certain
mathematical groups of transformations of different kinds of “frames of
reference” that represent configurations of macroscopic detectors making
“measurements” of these observables. The measured numbers are real
“eigenvalues” of the square matrix arrays corresponding to columns (or
rows) of complex numbers called “eigenstates”. These matrices are
“quantum computers” or “gates”. The set of eigenstates are strings of a
new kind of non-classical information called “qubits” and they form a
“basis” in which the square matrices are “diagonal” i.e. the real
eigenvalues are on the diagonal positions and all the off-diagonal
positions in the matrix array are zero. A key property is that these
eigenstates can be coherently superposed posed to form a set of
eigenstates that are a basis for a different set of matrices that
represent a different incompatible configuration of detectors. The
“basis” spans a “Hilbert space” or “house” or “container” (the “Bayt” of
Qabala), as it were, where all the quantum strings “live.” This is
where the Heisenberg uncertainty principle comes from -- that not all
observable properties of a system can be measured simultaneously to
arbitrarily high precision, i.e vanishingly small errors. There is also
another important counter-intuitive property called “entanglement”
(technically a “tensor product of Hilbert spaces” – one space for each
part of the entangled whole) in which several quantum systems share a
common pool of quantum information and do not have qubit strings of
their own. Quantum wholes are greater than the simple sum of their
parts. The quantum information comes in two forms called “active” and
“inactive.” This is explained in detail in David Bohm’s and Basil
Hiley’s “The Undivided Universe.” Entanglement is important in quantum
computing applications like “teleportation of qubits” and “untappable
cryptography.” It also is the key idea in “environmental decoherence”,
which is an attempt, only partly successful, that tries to explain the
irreversible thermodynamic flow or “arrow of time” and the “collapse of
the quantum state” or “Von Neumann projection”, i.e. why the large-scale
world of ordinary experience seems “definite” without us being alive and
dead at the same time in the same place as a naïve extrapolation of the
quantum properties of tiny simple objects suggests. Note that while our
inner perceptions of the outer world seem definite without the same
object being in two places at the same time, our pure inner conscious
thought has quantum superposition in which we hold two, or more,
incompatible ideas in our mind’s eye simultaneously as in Hamlet’s
speech “To be, or not to be. That is The Question …” On the other hand
John Archibald Wheeler says “The Question is: What is The Question.”
“Quantum logic” is the study of “quantum binary questions” arranged in a
non-Boolean partially-ordered lattice. This is very different from our
computers whose logic is that of a Boolean lattice. The non-Boolean
lattice, where each question is a node on a graph, has “Isles of
Boolean lattices” corresponding to compatible questions that can be
answered definitely simultaneously with the same configuration of
detectors. There is an approach to quantum gravity called “consistent
histories” which consists of a “story line” of questions (Lee Smolin’s
“The Three Roads to Quantum Gravity”) the problem is that knowing which
questions to ask to tell the story is an insolvable problem, or perhaps
I should say, is an undecidable question in the sense of Godel’s
“incompleteness theorem” of 1931 and it’s corollaries like the “Halting
Problem” of computer theory asking the question “When exactly will the
program stop?” So this is what Wheeler is alluding to in his
cryptographic remark: “The Question is: What is The Question?”
Now first thing we need to understand in looking at Rovelli’s version of
Lee Smolin’s “Three Roads to Quantum Gravity” is that all three roads
are top -> down. But there is a Gurdjieffian “Fourth (bottom -> up)
Way” of “emergence”, ignored completely by Smolin and Rovelli and All
The King’s Men trying to put Humpty Dumpty together again, due to the
great Soviet physicist Andrei Sakharov and also the Princeton physicist
P.W. Anderson. Sakharov called it “metric elasticity”. Anderson called
it “More is different” with an information-rich (low thermodynamic
entropy) giant quantum coherence field that is local without
entanglement with “generalized phase rigidity” making it immune to
“environmental decoherence” that in a special case is Sakharov’s metric
elasticity and also the “tension” of “string theory”. The fact that the
giant quantum coherence field is local automatically explains why the
outer world is definite without the same object being in two places at
the same time and why we are not alive and dead at the same time like
Schrodinger’s Cat out of a story by Lewis Carroll. As Wheeler wrote:
“Physics is simple when it is local.” P.W. Anderson’s “More is
different” explains why large –scale physics is local without needing
Oxford’s David Deutsch’s “excess metaphysical baggage” (Wheeler’s term)
of the quantum “Multiverse” of “shadow objects”. This is not to exclude
“parallel universes”, but one must be vary careful on how “universe" is
defined. It all depends on what you mean by "is". It's the ontology
stupid! J
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