| Subject: Brief comments on C. Rovelli's
writings Date: Tue, 21 Aug 2007 19:30:55 +0300 From: Dimi Chakalov <dimi@chakalov.net> To: Chris Isham <c.isham@imperial.ac.uk> Cc: <Thomas.Thiemann@aei.mpg.de>, <bdittrich@perimeterinstitute.ca>, <lsmolin@perimeterinstitute.ca>, <fmarkopoulou@perimeterinstitute.ca>, <bombelli@olemiss.edu>, <rovelli@cpt.univ-mrs.fr> Dear Chris, I posted some brief comments on the ideas of your former student at http://www.god-does-not-play-dice.net/Trautman.html#Rovelli If you or someone else happen to endorse those "partial observables", please drop me a line. Best regards, Dimi =============== Subject: Scrupulous intellectual honesty: The nature
of time
Dear Dr. Rovelli, In MATTERS OF GRAVITY, gr-qc/0109034, you've said the following: Carlo Rovelli: "But success, I think, can only be granted by scrupulous intellectual honesty. (...) The hardest part to digest is not the relational nature of space; it is the relational nature of time." I believe the puzzle of "relational nature" of time, as explained by John Baez five years ago, http://members.aon.at/chakalov/right.html#Baez_April97 is an extremely subtle issue, and we all should approach it with scrupulous intellectual honesty. You define 'partial observables' in gr-qc/0110035 as "a physical quantity to which we can associate a (measuring) procedure leading to a number" [Ref. 1]. Philosophically, this is nothing but a 'shadow on Plato's cave', as explained with John's jackets parable, http://members.aon.at/chakalov/right.html Regrettably, you chose not to reply to my email notes sent in the past two years. In your completely revised version of gr-qc/0111037 from 22 February 2002 [Ref. 2] and in its follow-up gr-qc/0202079 [Ref. 3], you declared that will start "from scratch". Regrettably, you didn't acknowledge the Ithaca Interpretation of QM [Ref. 4] and the work by many researches advocating the 'relational reality' interpretation of QM [Ref. 5 and Ref. 6]. In my email from Wed, 07 Nov 2001 12:44:17 +0100, subject: gr-qc/0111016, I asked a simple question: "Can you compute something related to QFT and gravity that other people can't?" Regrettably, you chose again to keep silent. Please bear in mind that the whole idea of 'relational reality' or 'correlations, not correlata' [Ref. 4] means one simple thing: the quantum reality does NOT exist in the physical time, as read with a clock, http://members.aon.at/chakalov/Stachel.html#PS http://members.aon.at/chakalov/Shimony.html Hence the nature of time boils down to the challenge of the *geometrical* presentation of the infinitesimal, http://members.aon.at/chakalov/Wagh.html Do you believe that those bubbles in loop quantum gravity might do the job, provided we get "a much better understanding of the theory of (intersecting) knots in 3 dimensions" http://members.aon.at/chakalov/Ashtekar.html ? I will be happy to hear from you. I'm sure you will reply with scrupulous intellectual honesty. You can read this email at http://members.aon.at/chakalov/Rovelli.html
Sincerely yours, Dimiter G. Chakalov
References [Ref. 1] Carlo Rovelli. Partial observables.
Sat, 6 Oct 2001 10:50:25 GMT,
"The distinction between partial and complete observables was discussed in [C. Rovelli, "Is there incompatibility between the ways time is treated in general relativity and in quantum mechanics?", in "Conceptual problems of quantum gravity", A. Ashtekar and J. Stachel, eds., Birkhauser, New York, 1991]. The distinction is often implicitly used, but we are not aware of any other detailed discussion on it in the literature. "Partial observables and complete observables "Let us start from the following two definitions. "Partial observable: a physical quantity to which we can associate a (measuring) procedure leading to a number. "Complete observable: a quantity whose value can be predicted
by the theory (in classical theory); or whose probability distribution
can be predicted by the theory (in quantum theory).
[Ref. 2] Carlo Rovelli. A note on the
foundation of relativistic mechanics. I: Relativistic observables and relativistic
states. Date (revised v2): Thu, 21 Feb 2002 16:11:49 GMT,
Abstract: "Is there a version of the notions of "state" and "observable" wide enough to apply naturally and in a covariant manner to relativistic systems? I discuss here a tentative answer." [Sec. III B] "The usual nonrelativistic definition of
state refers to the properties of a system at a certain moment of time.
Denote this conventional notion of state as the "instantaneous state".
The space of the instantaneous states is the usual nonrelativistic phase
space.
[Sec. IV] "The fundamental ingredient is once more the
extended configuation space of the partial observables C .
Quantum theory gives probabilities of observing a certain correlation given
that a certain other correlation was (has? - D.C.) been observed.
[Sec. V] "Mechanics can be seen as the theory of the evolution
of the physical variables in time only in the nonrelativistic limit. In
a fully relativistic context, mechanics is a theory of correlations between
partial observables, or the theory of the relative evolution of partial
observables with respect to each other."
[Ref. 3] Carlo Rovelli. A note on the
foundation of relativistic mechanics. II: Covariant hamiltonian general
relativity. Thu, 21 Feb 2002 16:20:22 GMT,
"In particular: what are "states" and "observables" in
a theory without background spacetime, without external time and without
an asymptotic region?
"The very foundation of general covariant physics is the
idea that the notion of a simultaneity surface all over the universe is
devoid of physical meaning.
"A generally covariant notion of instantaneous state,
or evolution of states and observables in time, make little physical sense.
In a general gravitational field we cannot assume that there exists a suitable
asymptotic region, and therefore we do not have a notion of scattering
amplitude and S matrix. In this context, it is not clear what we can take
as states and observables of the theory, and what is the meaning of dynamics.
(...) I have argued that mechanics can be seen as the theory of the evolution
in time only in the nonrelativistic limit. In general, mechanics is a theory
of relative evolution of partial observables with respect to each other.
More precisely, it is a theory of correlations between partial observables.
Given a state, classical mechanics determines which correlations are observable
and quantum mechanics gives the probability amplitude (or probability density)
for each correlation.
"It simply means that the general relativistic spacetime
coordinates are not directly related to observations. The theory does not
describe the dependence of the field components on x^m, but only the relative
dependence of the partial observables of C on each other."
[Ref. 4] N. David Mermin. The Ithaca Interpretation
of Quantum Mechanics.
Sec. IV: "Central to it is the doctrine that *the only
proper subject of physics are correlations among different parts of the
physical world*. (...) There is no absolute state of being; there are only
correlations between sybsystems."
[Ref. 5] Jeeva S. Anandan. Causality,
Symmetries, and Quantum Mechanics.
[Ref. 6] Rodolfo Gambini, Rafael A. Porto.
Relational Reality in Relativistic Quantum Mechanics.
==================
RE: Carlo Rovelli. Partial observables. Date (revised
v3): Mon, 21 Jan 2002 13:22:53 GMT,
"But how can a correlation between two non-observable quantities be observable?" Dear Professor Rovelli, A correlation may be prepared in the putative global time mode, i.e., without an explicit time parameter [Ref. 1], but it is *not* observable, http://members.aon.at/chakalov/Stachel.html See also http://members.aon.at/chakalov/Rovelli.html and http://members.aon.at/chakalov/Ashtekar.html I will appreciate your comments and insights, as well as those of all recipients of this email. Sincerely yours, Dimiter G. Chakalov
--
"The most significant feature of this equation is that
it contains absolutely no reference to time whatsoever.
It is usually argued that "time", or more precisely,
the physical systems that we use to measure time, are containedalready
in the gravitational and matter fields [3,4,5]. While this is veryplausible
it leaves us with the question as to how to extract interesting
physical predictions from this wave function, given the absence
of the time coordinate that plays such a central role
in standard quantum theory."
==================
Dear Professor Rovelli, May I ask two questions regarding your gr-qc/0111016 [Ref. 1], particularly the extended configuration space and the inevitable "retrodictions" from it, as advocated by Jim Hartle (gr-qc/9304006). 1. Can you compute something related to QFT and gravity that other people can't? 2. Specifically, can you resolve the problem of gravity and QED? The discrepancy is quite huge, 120 orders of magnitude. If you're on the right track, I believe you should be able to say something, from your perspective, and solve the puzzle of the energy density of the vacuum, http://math.ucr.edu/home/baez/vacuum.html Sincerely, Dimiter G. Chakalov
Reference [Ref. 1] Michael Reisenberger, Carlo Rovelli. Spacetime
states and covariant quantum theory. Tue, 6 Nov 2001
18:16:53 GMT,
"We observe that the preferred role of time in quantum theory is the consequence of an idealization: that measurements are instantaneous. Canonical quantum theory can be given a covariant form by dropping this idealization. States prepared by non-instantaneous measurements are described by "spacetime smeared states". The theory can be formulated in terms of these states,without making any reference to a special time variable. "Our aim is to support the view that general covariant
quantum mechanics is consistent. That is, we
can consistently use quantum theory without abandoning
the covariant treatment of spacetime which is characteristic of general
relativity. More precisely, we can define a quantum theorycorresponding
to a covariant system without necessarily having to single out a
preferred time variable. In our opinion, the often alleged profound
inconsistency between the way time is treated in general relativity and
in quantum mechanics is not real. It is not more real
than the inconsistency between general relativity
and *classical* hamiltonian mechanics: we expectthat quantum mechanics
admits a fully general covariant formulation, just as classical hamiltonian
mechanics does.
"This formulation clarifies some issues in the formulation
of the quantum theory of a single relativistic particle,
and in relation to the time of arrival problem, and
it helps us to give a consistent interpretation to quantum
cosmological models.
"We shall call the normalizable state |f> labeled by the spacetime function f(X,T) a "spacetime-smeared quantum state", or simply a "spacetime state". It is important to notice that this denomination refers simply to the representation that the state is given. It is a perfectly ordinary normalizable quantum state in the ordinary Hilbert state of the theory. "It is clear that the spacetime-smeared representation
is highly redundant -- many different spacetime functions
$f$ give rise to the same state -- while the
instantaneous representation is unique. This situation is a bit reminiscent
of that found in electromagnetism, where the gauge freedom can be
essentially eliminated in the Coulomb gauge, but at the cost of making
the formalism non-covariant.
"We need an interaction hamiltonian H_int , representing
the interaction that gives rise to the measurement.
H_int must have the following properties. First,
it must cause the transition |0> --> |1> . Second, the particle should
interact only at or around the spacetime position X=0, T=0 . Thus
the interaction hamiltonian must be time dependent,
and vanish for late and early times. We have to concentrate
the interaction around T=0 . However, we cannot
have a perfectly instantaneous interaction because this would require infinite
force. We must therefore assume that the interaction is non vanishing for
a finite period of time. Putting these requirements
together, and requiring also that the hamiltonian
is self-adjoint, we arrive at an interaction hamiltonian
of the form (...).
"Thus we can conclude that if we prepare a state concentrated around X=0, T=0 by means of a physical measurement procedure like the one described, we necessarily obtain a spacetime-smeared state defined by a function f(X,T) with support in a finite region R around X=0, T=0 . The size of R is determined by the accuracy of the measuring apparatus in resolving distances*and time intervals*. ... "A (well known) crucial observation is that most interesting physical systems, and in particular all gravitational systems, such as full general relativity with or without matter, cosmological models ... are not given in terms of a hamiltonian: they are given directly in the covariant formulation. Therefore not only the covariant formulation of mechanics appears to be more generalthan the hamiltonian one, but such a wider generality is required for the theories that better describe our world. "One can try to "deparametrize" these theories by picking one of the configuration space space variables and identifying it as the time variable. It is sometimes claimed that such a deparametrization is necessary in order to understand the quantum properties of the these systems. But such a deparametrization adds an element of arbitrariness which is certainly not part of the classical dynamics. Since the classical dynamics of these systemsdoes not select any preferred independent "time" variable T , we think that their quantum mechanics should not select a preferred time variable either. "To understand their quantum dynamics, we must therefore have a formulation of quantum theory in which time plays no special role. This is the motivation for the definition of covariant quantum theory that we give in this section. ... "This completes the definition of general covariant quantum
theory.
"Finally, consider the case in which R^prime is in the past of R . Strictly speaking, this case refers to a situation which has no meaning in conventional quantum mechanics: it refers to a situation in which the measurement is made at an earlier time than the preparation. Therefore the general theory given in Section {general} gives more predictions than the ones usually considered in conventional quantum theory. The additional predictions can be more accurately denoted "retrodictions", since they are statements about a time which is in the past with respect to the time at we assume to have information about the state. "Jim Hartle has long argued that such retrodictions can be added to standard predictions of quantum theory, and in fact, that they have to be added, if we want to make sense of any statement about the past deriving from our knowledge of the present. Either we give up the possibility of making *any* statementabout the past, or we take retrodictions as these statements. We refer to Hartle's paper \cite{}{Hartle} for a detailed discussion. ... "Here we are more interested in the interpretation of
the theory once the propagator is given, than in the
actual construction of the propagator. Let us nevertheless
say something on the derivation of W(x,y) itself. There is
a number of ways of constructing this object starting
from the classical theory. For instance, W(x,y)
may be defined as a sum over classical histories \cite{}{Hartle}
.
"The technical ingredient to be added to the quantum formalism
is the notion of spacetime-smeared quantum state.
This is a state generated by a measurements that is
not instantaneous. In particular, localization measurements
can be naturally described in terms of states associated to spacetime
regions, or, more in general, regions in the extended configuration
space. The key element of the theory, from this point of view, is the propagator
W(x,y) . This quantity is a two point function on configuration space,
it is strictly related (but not identical!) to the "probabilityamplitude
for the system to be detected in x if it was detected in
y ".
"The remaining conceptual difficulty regards the possibility
of associating probabilities to sequences of measurements.
We see two possible solutions to this difficulty.
The first by reducing any such sequence to a single measurement
or, equivalently, to sets of commuting measurements, by including
the apparatus in the theory. The second by introducing the notion of time
ordering of the observer."
Note: Carlo Rovelli posted today a very interesting dialog between a grad student, Sal, and a professor in theoretical physics, Simp. My comments labeled with D.C. are inserted with red. Carlo Rovelli, A dialog on quantum gravity, hep-th/0310077 v2, October 14, 2003 [snip] Simp - Is loop gravity unitary?
Simp - And if there is no background
time, there cannot be unitary evolution, right?
Simp - Alright, I accept this. But we have been digressing... can we try to wrap up? Sal - Alright. I suppose your conclusion is that loop gravity is (a) too different from usual QFT, (b) not completed and (c) not yet able to recover low energy physics... D.C. - Did you say "not yet"? The hardest thing of all is to find a black cat in a dark room, especially if there is no cat, says Confucius. Simp - And your conclusion is that string theory (a) does not describe the real world in which we live, (b) is not predictive because it can agree with any experimental outcome, (c) it requires an immense baggage of new phenomenology like supersymmetry, and extradimensions, which we do not see, and (d) it has not lead to a true conceptual merge of QM with the GR’s notions of space time... D.C. - I think loop gravity and string theory are just Barbies. My daughter would say "I want this Barbie, and that's it."
... Many thanks to Ted Newman, Gary Horowitz, Abhay Ashtekar, Daniele Oriti, Lee Smolin, Warren Siegel, Simone Speziale and Juan Maldacena for corrections and suggestions.
D.C. Hey, you missed me! Will
check out your third, utterly revised version of
hep-th/0310077.
A great mathematical physicist and visionary,
Carlo Rovelli, said the following: "But
success, I think, can only be granted by scrupulous intellectual honesty."
Read all about it above.
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