| From: Dimi Chakalov <dimi@chakalov.net>
To: Jonathan Halliwell <j.halliwell@ic.ac.uk> Bcc: [snip] Subject: Re: How to answer questions that do no refer to time in any way? Date: Tue, 27 Jan 2004 15:11:06 -0000 Dear Dr. Halliwell, I hope my email of Thu, 08 Aug 2002 10:38:26 +0300, has been safely received. If not, you can read it at http://members.aon.at/chakalov/Halliwell.html I'm curious whether you would be interested in the nature of gravity http://members.aon.at/chakalov/Thiemann.html and the puzzle of 3-D space, http://members.aon.at/chakalov/Halliwell.html#3 http://members.aon.at/chakalov/Zeh.html#note If you are not interested, please don't bother to reply, http://members.aon.at/chakalov/Josephson.html#Bud Yours faithfully, Dimi Chakalov
==== Subject: How
to answer questions that do no refer to time in any way?
Dear Dr. Halliwell, I quoted your gr-qc/0201070 at http://members.aon.at/chakalov/Rovelli.html#Halliwell_Thorwart and I'm reading now your recent Imperial TP/1-02/23, "The Interpretation of Quantum Cosmology and the Problem of Time" [Ref. 1]. Given the empirical fact that we have "points", http://members.aon.at/chakalov/Butterfield.html I'm wondering how one could answer questions that do no refer to time in any way. May I ask three questions. 1. How do you get "points" from Fig 1, (a), (b), and (c) [Ref. 1] to obtain 3-D space? 2. What do you lose by adopting a highly constrained minisuperspace approximation [Ref. 2]? 3. Isn't it true that the problem of time leads to the paradoxical result that there is no space either, due to the full reparametrization invariance of GR [Ref. 3]? Sincerely, Dimiter G. Chakalov
References [Ref. 1] J.J. Halliwell.
The Interpretation of Quantum Cosmology and the Problem of Time. Imperial
TP/1-02/23. Wed, 7 Aug 2002 13:02:39 GMT,
"Now, however, in 2002, far more
is known about the foundations and interpretation of quantum theory. Moreover,
there has also been a considerable amount of activity in the experimental
tests of foundational ideas. As a result of this, the foundations of quantum
theory is now more in the mainstream of physics, when previously it was
regarded as the domain of the philosophers.
"In this contribution to the conference,
I will describe how the decoherent histories approach may be used to provide
a quantization of simple minisuperspace models, perhaps avoiding some of
the serious difficulties outlined above, and agreeing with the heuristic
methods used earlier on.
"The above point turns out to be
quite crucial to what follows in the rest of this paper, so it is worth
saying it in an alternative form. Loosely speaking, the statement is that
only the entire classical path respects the reparametrization invariance
associated with the constraint equation. A section of the classical path
does not.
"In particular, it may be generalized
to the question of interest here, in which the system is in an energy eigenstate
and we would like to answer questions that do no refer to time in any way.
"Central to both the classical and
quantum problems is the notion of an entire trajectory. At the classical
level it appears to be the appropriate reparametrization-invariant notion
for the construction of interesting probabilities. At the quantum level,
the decoherent histories approach appears to handle the problem in a natural
way, perhaps because it readily incorporates the notion of trajectory."
[Ref. 2] A. Peres.
Critique of the Wheeler-DeWitt equation.
[Ref. 3] R. Parentani.
The notions of time and evolution in quantum cosmology.
"Before investigating the problem
of the description of evolution in quantum cosmology, it should be noted
that in classical cosmology, when working with the action in the Hamilton-Jacobi
formalism, one also looses the notion of the (Newtonian) time. As in quantum
cosmology, this results from the invariance of the theory under arbitrary
reparametrizations of time. It should also be noticed that a similar disappearance
applies to space as well, in virtue of the
full reparametrization invariance of general relativity. Surprisingly,
this problem has attracted much less attention that the one associated
with time (...)."
Note: Three comments on a recent paper by Jonathan Halliwell [Ref. 4], which has been aimed at "undergraduates with a basic appreciation of quantum theory", with emphasis on "simple physical ideas and pictures." I'll accentuate certain portions
of the text with bold + red, and will
insert my three comments.
[Ref. 4] Jonathan Halliwell, How the Quantum Universe Became Classical, quant-ph/0501119 v1; Contemporary Physics 46, 93-104 (2005), 24 pages, 11 figures. Abstract: "This is an informal introduction
to the ideas of decoherence and emergent classicality, including a simple
account of the decoherent histories approach to quantum theory. It is aimed
at undergraduates with a basic appreciation of quantum theory. The emphasis
is on simple physical ideas and pictures."
pp. 15-16: "We now have a heuristic
picture of how we can understand the emergence of classical mechanics from
quantum theory. It is time to focus this into something more precise. When
we say that a system is "classical", we mean that it can be described by
variables p, x which have definite values (or at least, probabilities)
and that these variables evolve
"However, it is here that the interesting tension lies, because quantum theory resists the notion of history. This is for two reasons. First, the uncertainty principle limits the precision to within which positions at different times may be specified (since this is equivalent to specifying position and momentum at one time). This means that probabilities for histories cannot be perfectly peaked about a single classical path. However, if we look at positions that are sufficiently coarse-grained compared to the uncertainty principle limits, we might expect the probability to be quite strongly peaked about one path. "Secondly, and more fundamentally,
as we have seen in the double slit experiment interference resists the
assignment of probabilities to histories. However, we know we can get round
this when there is a decoherence mechanism to kill the interferences.
pp. 17-18: "We know from the double slit experiment that that no-interference condition Eq.(24) or Eq.(25) will not be satisfied in general, so probabilities cannot always be assigned to histories. "But it can be satisfied when there
is an environment present to produce decoherence, since satisfaction of
Eq.(24) is very similar to the diagonalization of the density matrix Eq.(20).
When probabilities can be assigned we can talk about the properties of
the system as if they were real, classical
things. Differently put, in the non-Boolean logic of quantum theory, we
look for Boolean subsets."
1. I'm afraid the alleged decoherence mechanism that is supposed to kill the interferences won't kill the "tails", http://www.God-does-not-play-dice.net/Maximilian.html#1
p. 19-20: "Now in quantum theory, conserved quantities have a very interesting property. This is that there can be no interference between different values of a conserved quantity. The reason for this is that to observe the interference effects between, say, states of different charge, one would need a measuring device which violates charge conservation, and this is impossible. Alternatively, if we have a superposition state of conserved quantities (as in Figure 10, for example), the different elements of the superposition can interfere only if they evolve into each other. But conserved quantities don’t evolve anywhere, even in the quantum theory so the different elements of the superposition never meet. So the superposition still “exists” in some sense, but its interference effects are never seen. "In the decoherent histories approach, this means that one can always assign probabilities to histories of conserved quantities. Or in other words, conserved quantities can always be manipulated as if they were classical, even in the quantum theory. Now this is a very important point. It means that in the foggy landscape of quantum theory, the conserved quantities represent the mountain peaks that reach above the clouds, immune to weird quantum behaviour. "Conserved quantities are not the
end of the story. They can be used to define quantities that are not exactly
conserved, but approximately conserved, and so slowly varying. In particular,
we can define the local densities associated with them: if energy, for
example, is conserved, then the energy in a small region of the system
can only change by flowing in or
"Hence the real question is not how to divide up the universe into classical and quantum, or system and environment, but into slowly and rapidly varying, and conservation laws are the fundamental physical principle that guides us in how to do this. "These ideas have been used to give
what is perhaps the most general possible account of emergent classicality
from quantum theory. That is, the approximate conservation of the local
densities has been used to show that they are naturally decoherent, and
to obtain classical equations of motion for them. These equations are hydrodynamics
equations, of
2. It is not clear what is the fate of the imaginary unit in the phase of quantum waves in this "emergent classicality", http://www.God-does-not-play-dice.net/Yang.html#1 Do you get rid of it completely?
If yes, how do you resurrect it, in order to get back to the quantum realm?
3. It is utterly unclear how did the classical world emerge some 13 billion years ago, http://www.God-does-not-play-dice.net/Schwarz.html But since Prof. J.J. Halliwell does not comment on quantum cosmology (no environment present to produce "decoherence"), let's go back to the tail problem above, with an emphasis on "simple physical ideas and pictures." Think of the CPU of your computer, and apply the cat states from the "tails" to all atoms that constitute your CPU. This means that, to a very good approximation, we can expect that the CPU will run properly with only very small errors which will never build up and produce some cascade of errors, say. That's how you can find out whether your quantum CPU can become classical and the logic of computing strictly Boolean by some hypothetical decoherent mechanism. The test of the pudding, you know. Once you have proved that your "decoherent" CPU can indeed work as it does, you may wish to explore the staggering possibility of quantum gravity from quantum computation, after Seth Lloyd ("The Computational Universe: Quantum gravity from quantum computation", quant-ph/0501135 v1). His research work depends crucially on the ideas of Jonathan Halliwell [Ref. 4], and has been supported by various military and academic institutions, such as ARDA/ARO, AFOSR, DARPA, NSF, NEC, RIKEN, and the Cambridge-MIT Initiative. Good luck with 'the proof of the
pudding'.
D. Chakalov
Let's examine the
Pentium
4 processor. It has 42 million transistors implemented on Intel's 0.18u
CMOS process, with six levels of aluminium interconnect. Its 3.2 GB/second
system bus helps provide the high data bandwidths needed to supply data
to today's demanding applications. It adds 144 new 128-bit
Single Instruction Multiple Data (SIMD) instructions called SSE2 (Streaming
SIMD Extension 2) that improve performance for multi-media, content creation,
scientific, and engineering applications. Take a closer look at the so-called
Misprediction
Pipeline.
Suppose this Pentium 4 processor is a "decoherent" quantum system, and all quantum fuzziness in the timing of its operations are, to a very good approximation and with only very small errors, completely eliminated [Ref. 4]. They certainly are eliminated, but can you apply the theory of decoherence [Ref. 4] to check out if its predictions match the actual result delivered by Mother Nature? That's 'the proof of the pudding'. Once you prove that the timing of all operations in your Pentium 4 processor are indeed perfectly determined, you may easily expand your 'proof of the pudding' to any supercomputer, such as The Earth Simulator build by NEC, which is capable of performing 35.86 Tflop/s (teraflops or trillions of calculations per second), and the current leader IBM's Blue Gene/L delivering 135.3 Tflop/s with 131,072 processors (expected in July 2005), all of which being "decoherent" quantum systems. To begin with, think of the timing of operations in your Pentium 4 as the pistons of your car: there is an instant at which an operation must stop, in order to initiate the next operation. Denote this stop-instant with tn , and calculate its theoretical quantum fussiness from both the "tales" (there will be always a "part" of the system that is not "here", [Ref. 5]) and the time-of-arrival [Refs. 6 and 7]. To be precise about the stop-instant tn , read Jonathan Halliwell's article "The Decoherence Functional in the Caldeira-Leggett Model" [Ref. 8, pp. 235-236; see footnote on p. 236]: the stop-instant tn is the crucial instant at which we define probabilities for the complete set of alternative histories. We need a fine grained history in which (i) projections are specified at all times, and (ii) each projection is one-dimensional. Once you get all this straight, write down your decoherence functional at the stop-instant tn . Read more about this crucial instant from A. Ashtekar here. If the quantum fuzziness at the stop-instant, tn , is "sufficiently small" and does not lead to cascade of errors, your Pentium 4 (as well as all supercomputers) will indeed work as some "decoherent quantum systems". However, if you want to do better than Jonathan Halliwell, you'll need to address some tough issues in quantum cosmology, particularly the entropy of the gravitational field [Ref. 9, p. 128] and the Reichenbach global system [Ref. 10]. Can you deliver the proof? The stop-instant, tn , is "a unique stable pointer state at the end of a measurement" [Ref. 11]. Try it. [Ref. 12]. If you fail, there are, broadly speaking, two extreme possibilities. One is to commit suicide, like Ludwig Boltzmann did. The other is to follow the attitude of Professor Jonathan Halliwell and feed your students with ... well, let's say "simple physical ideas and pictures" [Ref. 4]. Like Wojciech Zurek, the other editor of Physical Origins of Time Asymmetry [Ref. 8]. Or like Paul Davies. Or Abby Ashtekar. It's a free world, and if you are Professor in Theoretical Physics, you live in a total socialism and are entitled to do anything you want. Not that I didn't want to say what
I didn't actually say,... or did I?
D. Chakalov
[Ref. 5] Rob Clifton, Bradley Monton, Losing Your Marbles in Wavefunction Collapse Theories, quant-ph/9905065. p. 3: "Now if a system’s wavefunction
cannot be made arbitrarily narrow by a collapse, and if it can never
be
completely concentrated in a bounded region -- i.e., if a system’s
wavefunction must virtually always possess ‘tails’ going off to infinity
-- then the standard semantics will block the attribution of a determinate
location to each particle in the system, as well as to the position of
the system as a whole."
[Ref. 6] J. Oppenheim,
B. Reznik, W. G. Unruh, When does a Measurement or Event Occur, Found.
Phys. Lett. 13 (2000) 107-118;
quant-ph/9805064.
[Ref. 7] J. Oppenheim,
B. Reznik, W.G. Unruh, Time-of-Arrival States, Phys. Rev. A59 (1999) 1804;
quant-ph/9807043.
[Ref. 8] H.F. Dowker
and J.J. Halliwell, The Decoherence Functional in the Caldeira-Leggett
Model, in: Physical Origins of Time Asymmetry, ed by J.J.
Halliwell, J. Perez-Mercader, and W.H. Zurek,
Cambridge University Press, Cambridge, 1994, pp. 234-245.
[Ref. 9]
P.C.W.
Davies, Stirring up Trouble, in [Ref. 8], pp. 119-130.
[10] Mario A. Castagnino, The Global Nature of the Arrow of Time and the Bohm-Reichenbach diagram, quant-ph/0005077 v1, Sec. III. "Then through this hierarchical chain,
that begins in the cosmological instability and contains all the irreversible
processes, where each process begins where the corresponding creation device
has finished its task, the irreversible nature of the universe and the
origin of any irreversible process in it can be explained. Therefore Gibbs
ink drop only exists because there was a primordial cosmological instability
and Irreversible Statistical Mechanics can not be explained without
Irreversible
Cosmology. The global system can be symbolized as in fig. 1, which
has a clear time symmetry: the branch arrow of time (BAT), which points
in opposite direction to the unique initial cosmological instability and
follows the evolution of the hierarchical chain towards equilibrium. Reichenbach
global system is clearly a realistic model of the set of irreversible processes
within the universe." [11] Tulsi Dass, Measurements and decoherence, quant-ph/0505070 v1, Sec. 5.
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