Open System for Geniuses - by Chronostalker

27 February, 2005

What is time according to Connes and Rovelli - Part 3

Filed under: Physics

Connes and Rovelli continue:

One can still recover weaker notions of physical time: in GR, for instance, on any given solution of the Einstein equations one can distinguish timelike from spacelike directions and define proper time along timelike world lines. This notion of time is weaker in the sense that the full dynamics of the theory cannot be formulated as evolution in such a time.

For some reason they are restricting themselves to general relativity. Don’t they know about other generally covariant theories? Theories with torsion, Kaluza-Klein theories, generally covariant theories based on gauging of the Galilei group (K\"unzle, Duval)? And what about

"full dynamics of the theory cannot be formulated as evolution in such a time. "

When we are dealing with field theories, rather than theories of particles, the full dynamics is based on partial differential equations, not on "time". Now we have a footnote:

Footnote: Of course one should avoid the unfortunate and common confusion between a dynamical theory on a given curved geometry with the dynamical theory of the geometry, which is what full GR is about, and what we are concerned with here.

GR is not the dynamical theory of the geometry - as the authors would like it to have. It presupposes already certain geometry - it presupposes a manifold structure, it presupposes a particular gauge group - O(3,1), it presupposes a particular way of choosing the variables etc. There are many variations of general relativity, some of them with two metrics rather than one, some with no metric at all - they start with a general affine connection. The term "given curved geometry" is fuzzy, is undefined. What kind of geometry? The devil is always in the details.

In particular, notice that this notion of time is state dependent.

State dependent? State of what? What is state here? A particular geometry? What kind of geometry? A particular solution of Einstein’s field euqations? Which equations? Is state defined up to a diffeomorphism, or not? Are two geometries related by a diffeomorphism considered as defining the same state (as Souriau would like). The authors are not clear.

Furthermore, this weaker notion of time is lost as soon as one tries to include either thermodynamics or quantum mechanics into the physical picture, because, in the presence of thermal or quantum “superpositions" of geometries, the spacetime causal structure is lost.

Of course - if we consider families of spacetime causal structures - then one spacetime causal structure is lost. What a surprise! But things are not that easy and here again the authors are precise enough. The space-time metric, the dynamical variable of the standard, orthodox, general relativity can be naturally split into two parts: causal (or conformal) structure, and the lenght scale (or, equivalently, volume element). It is then possible to vary geometry by varying only the scale, but not the conformal structure. We still can have superpositions of geometries, while the causal structure is constant. Thus the above statement is another not precise enough.

This embarrassing situation of not knowing “what is time" in the context of quantum gravity has generated the debated issue of time of quantum gravity.

The really embarassing situation is in not understanding what quantum theory is about, and whether we really need to "quantize gravity." By the pure force of inertia we believe that once quantizing electromagnetism prooved to be largely successfull (and partly a disaster due to divergencies and inconsistencies), then we should quantize everything in view - just for fun of doing it, as we do not know what to do otherwise.

As emphasized in C. Rovelli, Class. and Quant. Grav. 10, 1549 (1993), the very same problem appears already at the level of the classical statistical mechanics of gravity, namely as soon as we take into account the thermal fluctuations of the gravitational field.

But what are the "thermal fluctuations" prior to any "time". What fluctuates, and how long it takes for something to fluctuate? What is "temperature" prior to time and prior to motion? I think the authors are using the popular jargon without giving much thought to it. If it would be Igor and Grichka rathen than Connes and Rovelli - they would be already attacted viciously for using the term "fluactuations":

Pouvez vous enoncer, avec toute la clarte mathematique dont doit savoir faire preuve un docteur en marthematique, la definition de ce que vous appelez une "fluctuation de la metrique" ?

Then we have a footnote:

Footnote: The remark of the previous note applies here as well. Thermodynamics in the context of dynamical theories on a given curved geometry is well understood - see R.C. Tolman, Relativity, Thermodynamics, and Cosmology, Clarendon Press, Oxford, 1934.

Well, Tolman is a good but rather old book. But even Tolman does not claim that "Thermodynamics in the context of dynamical theories on a given curved geometry is well understood." Tolman (ibid. Chapter V.55) writes, for example:

" The construction of a fundamentally satisfactory relativistic statistical mechanics would be in any case a complicated business and at present a somewhat dubious undertaking. Nevertheless, some progress in this direction has already been made using classical rather than quantum-mechanical statistics as a starting point.."

Now compare: on one hand we have Connes and Rovelli writing that according to Tolman the business is well understood, and on the other hand we have Tolman telling us that the business is complicated and dubious and that some progress have been made. Of course thermodynamics is not exactly the same as statistical mechanics. But here are getting into an even bigger trouble, because to derive thermodynamics from statistical mechanics is another serious issue - not solved satisfactorily till now.

J. M. Souriau in his "Structure of dynamical systems" uses a more precise language when he writes:

"The barycentric decomposition does not exist in relativistic mechanics. However, by using theorem (16.224) and the fact that the symplectic cohomology of the Poincare group is zero (13.73), one can show that an isolated system has no natural equilibria - except in the case, devoid of any physical interpretation, where the Poincare group leaves invariant every motion of the system."

And then he adds:

Footnote: "Of course one might call such a system "vacuum" and consider that it is a natural equilibrium for every Z. This remark ceases to be purely linguistic in quantum mechanics."

Back to Connes and Rovelli:

Thus, a basic open problem is to understand how the physical time flow that characterizes the world in which we live may emerge from the fundamental “timeless" general covariant quantum field theory - see A. Ashtekar, Lectures at Les Houches 1992 Summer School, to appear.

Note: In fact, the paper by Ashetekar is available online. See Mathematical Problems of Non-perturbative Quantum General Relativity at arxiv.org. So Connes and Rovelli think that time emerges all by itself, without ever needing the concept of an "observer" or "event", contrary to what John Wheeler and John Bell would suggest. Interesting.

26 February, 2005

Destiny Matrix

Jack Sarfatti starts his blog of February 19, 2005 :

All dynamical force fields (and geometrodynamic “force-without-force”) fields come from locally gauging a global symmetry of the dynamical action.

So first we are supposed to have a dynamical action. What is a dynamical action? How to distinguish action which is dynamical from one which is not? What is the arena where this action takes place? Why one arena rather than other? What is the pre-structure needed in order to be able to talk about global symmetry? Perhaps we will be told later on? Let’s see:

The initially dynamically broken global symmetry is restored by the compensating gauge field.

Why is symmetry broken? Who and why breaks it? Anyway, we can forget it. Probably we will never be told. So let’s start from "compenstaing gauge field". That is the original term used by Utiyama and then Yang and Mills (perhaps also Kibble) for "principal connection in a principal bundle". To have a connection we need a base space. What would it be for Jack and why? And we need a group, probably a finite-parameter Lie (Lie is name of a mathematician Sophus Lie) group. Who will give Jack a Lie group and why one rather than another one? We need also some kind of a dynamics - usually given by some kind of an action principle. But to have an action principle that is not just a topological invariant (and thus gives no real dynamics) - we need some a priori geometrical structure. Where is it coming from?

Any preferred frame is an emergent SBS effect in the lowest energy state that leaves the dynamical symmetry intact.

SBS here stands for Spontaneous Symmetry Breaking. This is a very funny term. Whenever a physicist tells you that something is spontaneous - that means he really want to say: I have no idea what and why and how this happens. Years ago a very popular term was spontaneous compactification - which was allowing physicists to discuss curled extra dimensions when they were not able to explain why some dimensions curl and some not, and how wlong it takes for a dimension to curl? So, if I would ask Jack: how long it takes for a symmetry to break? - he would give me a strange look and asked to have a glass of wine with him after his talk. So we see that we can have a preferred frame. Hmm….. I was discussing the trickyness of this subject in previous blog, when starting the discussion of Connes and Rowelli paper on time. Probably what Jack means is that he has some field equations and a preferred frame arises from a particular solution or class of solutions of field equations? But not - we have "lowest energy state" here. Lowest energy state of what? And how is energy defined when we do not yet know what is time? And what kind of a state? Did he already quantized his theory? How? It gest stranger and stranger…

Curvature and torsion in the Einstein-Cartan “tetrad”/”Ricci rotation coefficients” extension of 1916 general relativity (GR) are analogous to string vortex lines in superfluid helium.

Curvature of what? Once you have a gauge field, you have its curvature - for sure. But you do not have any torsion. The concept of a "torsion" requires a soldering form. But where it comes from? Jack is not telling us. Should I tell him?

In 1916 GR the Ricci rotation coefficients Au^bc are not independent dynamical fields, but are dynamically determined from the non-trivial anholonomic tetrads bu^a that are the compensating gauge fields from locally gauging T4 into Diff(4) (AKA GCT) because O(1,3) is not yet locally gauged as it is in Shipov’s theory.

Now we have Ricci rotation coefficients Au^bc. I’ve never seen them defined. Using terms that are not defined is atypical trick. Shipov used it with great success. Whatever you write using such terms - no one will be ever able to criticise you for being wrong! So our Ricci rotation coefficients - which we are not told what they are - are dynamically determined from the non-trivial anholonomic tetrads. OK, I know what are anholonomic tetrads - probably Jack means a soldering form, which he, for one reason or another, assumes to be non-degenerate? Where are his tetrads comind from? And why tetrads rather than funfbeins? And what does "dynamically determined" mean? And now we are locally gauging T4 into Diff(4). Allright Jack probably would like to speak about the Poincare group (including translations) as a "gauge group". But wait, no, he wants to have Diff as the gauge group. But what is the principal bundle for Diff to act on? We are not told.

There is a curious cross-play in that the disclination-curvature strings are characterized by rotations of a vector parallel transported around a closed loop, whilst the dislocation-torsion strings are gaps in second order in the attempt to close the loop. Roger Penrose shows that gaps in third order appear even in torsion-free 1916 GR.

Now we have another animal that is coming to the zoo by a back door: disclination-curvature strings. Would it be nice to define them? It would make life so much simpler in our already uptight world.

The curious cross-play is that the curvature disclination rotations about closed loops come from the local-gauging of the translational group T4 of special relativity generated by total energy-momentum Pu, whilst the torsion dislocation gaps come from the local-gauging of the Lorentz group O(1,3) of special relativity generated from the spin-orbital angular momentum J = L + S (space-space rotations) and the boosts connecting coincident inertial frames in instantaneously uniform relative motion.

This is a looooong sentence. It reminds me some sentences produced by a random Markov algorithm that you can find on the blog by Robert Helling:

sigmamodel has no chiral ring write down to symmetric massless states with matter and consistency of the effects of mtheory in the help of motion of those of supersymmetric type ii orbifolds including the newly formed in kkltlike vacua we investigate the transition in the acceleration we consider the presence of a tensionful codimensionone brane is finite k coincident branes wrapping cycles on the usual finetuning between the black supertubes of the edges evolve through the presence of gravitation together with a mass with qdeformed harmonic oscillator with scalar field coupled to end of spinorbit interactions for communication here

Now there comes another long sentence:

The curious cross-play is this dual switching between T4 locally gauged to Diff(4), and O(1,3). The lack of preferred space-time frames with “absolute velocity”, as in the usual interpretation of the Michelson-Morley experiment, means that the vacuum symmetry is not spontaneously broken with respect to the boost sector of O(1,3).

We have "dual switching", which sounds like another Markov term, then we have T4 (I understand it is the translation group of a flat 4-dimensional affine space? Then it becomes Diff(4) - probably the idea being that generators of diffeomorphisms are vector fields rather vectors - but everybody knows it, then why to use strange terms. Then we have another Markov term "boost sector of O(1,3)", and also we have our old friend, but this time not spontaneously broken vacuum symmetry. Enough for now. Let’s take a break ….

All this being said - I do like Jack. In fact I adore him. He makes our lifes more interesting. The point is that he should not be put into the same category as “professional theoretical physicists” - that is those who have “real jobs”, who have to take care of “getting grants” and “being promoted”. Jack is more like Igor and Grichka Bogdanovs - he is using an “impressionistic style” - as Daniel Sternheimer described it. Of course the case of Jack is somewhat different - jack has a different set of friends and enemies than Igor and Grichka. So John Baez will not dare to attack Jack - though having some Sokal-kind of fun would also be justified in this case. Yet there are hidden links that leave Jack outside of the range of attackers who spare no time and energy trying to destroy Bogdanov’s brothers.
In fact the problem is not with Igor and Grichka, and it is not with Jack. The problem is with narrow views of the so called “scientists community”, with politics, with jealousy. And it is much easier to destroy than to create. It is not my intention to destroy Jack by my critical comments. My aim is to help him. Jack posts his vague (yet more and more sharp with each year) for a public scrutiny. He heared a metallic voice long ago - and there is something inside that tells him that a ceratin bell is ringing. Except that he doesn’t know which church it is in. Neither do I… Curiosity and a continuous search for knowledge. Correcting our course again and again. And not being afraid of laugh and criticism from others - that is the only way towards the Truth.

25 February, 2005

Les-Mathematiques contra Bogdanovs

Filed under: Physics

Over 1 MB of a discussion about Igor and Grichka Bogdanovs on the Forum Les Mathematiques - mathematical forum hosted by the University of Strasbourg. The level of the discussion is depressing. The discussion has just been closed - fortunately. To give an example of the level: jc has a problem with some of the explanations by Igor and Grichka:

Auteurs: jc (—.w193-252.abo.wanadoo.fr)
Date:   02-23-05 10:48

bonjour MM Bogdanov,

J’ai lu ce que M SPI 100 a йcrit et j’ai bien vu que c’йtait une citation, mais si vous citez ce texte c’est que tout doit кtre clair pour vous dedans… Ensuite, vous pouvez me dйfinir ce qu’est cette trace? Il s’agit bien de:

$ g_{00}+ g_{11}+g_{22}+ g_{33}$ ?
car si c’est le cas, combien mкme ce physicien est docteur en physique thйorique et respectable et que je respecte autant que vous ou d’autres, cette quantitй n’est pas intrinsиque par rapport а la base…il y a du y avoir un confusion de vocabulaire sans doute comme le laisse penser:

«alors vous pouvez gйnйraliser et dire qu’en tout point de l’espace, le tenseur mйtrique а une trace (+++-).
»

Notez bien que mon ton est on ne peut plus courtois que d’autres ici… D’autre part, pour une fois j’avais trouvй ce texte assez clair et faisant percevoir assez bien cette notion de fluctuation de mйtrique…j’aimerais savoir?

Кtes vous capable d’expliquer des choses $ \textbf{simplement}$ sans faire appel а des copiй collй d’autres?

e>

to which another participant replies:

Auteurs: jc (—.w193-252.abo.wanadoo.fr)
Date:   02-23-05 10:48

bonjour MM Bogdanov,

J’ai lu ce que M SPI 100 a йcrit et j’ai bien vu que c’йtait une citation, mais si vous citez ce texte c’est que tout doit кtre clair pour vous dedans… Ensuite, vous pouvez me dйfinir ce qu’est cette trace? Il s’agit bien de:

$ g_{00}+ g_{11}+g_{22}+ g_{33}$ ?
car si c’est le cas, combien mкme ce physicien est docteur en physique thйorique et respectable et que je respecte autant que vous ou d’autres, cette quantitй n’est pas intrinsиque par rapport а la base…il y a du y avoir un confusion de vocabulaire sans doute comme le laisse penser:

«alors vous pouvez gйnйraliser et dire qu’en tout point de l’espace, le tenseur mйtrique а une trace (+++-).
»

Notez bien que mon ton est on ne peut plus courtois que d’autres ici… D’autre part, pour une fois j’avais trouvй ce texte assez clair et faisant percevoir assez bien cette notion de fluctuation de mйtrique…j’aimerais savoir?

Кtes vous capable d’expliquer des choses $ \textbf{simplement}$ sans faire appel а des copiй collй d’autres?

able>

Somehow nobody notices that the answer does not apply because we are dealing with the is a covariant tensor, not 1-covariant and 1-contravariant. Lot of noise, lot of chaos. Any real discussion is completely impossible in such circumstances, when some pf the participants are coming here with a pre-established agenda (as YBM, whose only goal is to destroy as much as he can, using whatever means). Moderators of this forum did a very bad job.

24 February, 2005

Notes on Bohmian Mechanics

Filed under: Physics

I am reading "A survey of Bohmian Mechanics" :

Authors: K. Berndl, M. Daumer, D. Dürr (LMU Munich), S. Goldstein (Rutgers), N. Zanghi (Genova)
Journal-ref: Nuovo Cim. B110 (1995) 737-750

This web page contains my notes and thoughts - I will be writing while I am reading. So this page will grow with time.

First of all: why I got interested in the subject? Mostly because the idea has some similarity with my own EEQT, namely that fo a more complete desription of quantum systems we need to use both classical degrees of freedom AND quantum wave function. Therefore, EEQT is dualistic and Bohmian mechanics is dualistic. This dualistic nature of Bohmian mechanics is stressed explicitly in "Quantum Equilibrium and the Origin of Absolute Uncertainty":


The conventional wisdom that the wave function provides a complete description of a
quantum system is certainly an attractive possibility: other things being
equal, monism—the view that there is but one kind of reality—is perhaps
more alluring than pluralism. But the problem of the origin of quantum
randomness, described at the beginning of Section 1, already suggests that
other things are not, in fact, equal.
Moreover, wave function monism suffers from another serious defect, to which the
problem of randomness is closely related: Schrodinger’s evolution tends to produce
spreading over configuration space, so that the wave function $\psi$ of a
macroscopic system will typically evolve to one supported by distinct, and
vastly different, macroscopic configurations, to a grotesque macroscopic
superposition, even if $\psi$ were originally quite prosaic. This is
precisely what happens during a measurement, over the course of which the
wave function describing the measurement process will become a superposition of
components corresponding to the various apparatus readings to which the
quantum formalism assigns nonvanishing probability. And the difficulty with this
conception, of a world completely described by such an exotic \wf,
is not even so much that it is extravagantly bizarre, but rather that this
conception—or better our place in it, as well as that of the random
events which the quantum formalism is supposed to govern—is exceedingly
obscure.\footnote{What we have just described is often presented more
colorfully as the paradox of Schrodinger’s cat\recite{cat paper}.}
What has just been said supports, not the impossibility of wave function monism, but
rather its incompatibility with the Schrodinger evolution. And the allure of wave function
monism is so strong that most interpretations of quantum mechanics in fact involve the
abrogation of Schrodinger’s equation. This abrogation is often merely implicit and,
indeed, is often presented as if it were compatible with the quantum
dynamics. This is the case, for example, when the measurement postulates,
regarded as embodying “collapse of the wave packet,'’ are simply combined
with Schrodinger’s equation in the formulation of quantum theory. The “measurement problem'’
is merely an expression of this inconsistency. (…)

The theory of GRW modifies Schrodinger’s equation by the incorporation of a random
“quantum jump,'’ to a macroscopically localized wave function. As an explanation of
the origin of quantum randomness it is thus not very illuminating,
accounting, as it does, for the randomness in a rather ad hoc manner,
essentially by fiat. Nonetheless this theory should be commended for its
precision, and for the light it sheds on the relationship between Lorentz
invariance and nonlocality (see\recite{Bellj}).
A related, but more serious, objection to proposals for the modification of
Schrodinger’s equation is the following: The quantum evolution embodies a deep
mathematical beauty, which proclaims “Do not tamper! Don’t degrade my
integrity!'’ Thus, in view of the fact that (the relativistic extension of)
Schrodinger’s equation, or, better, the quantum theory, in which it plays so
prominent a role, has been verified to a remarkable—and
unprecedented—degree, these proposals for the modification of the quantum
dynamics appear at best dubious, based as they are on purely conceptual,
philosophical considerations.
But is wave function monism really so compelling a conception that we must
struggle to retain it in the face of the formidable difficulties it entails?
Certainly not! In fact, we shall argue that even if there were no such
difficulties, even in the case of “other things being equal,'’ a
strong case can be made for the superiority of pluralism.

But back to "A survey of Bohmian Mechanics". The abstract starts with:

"Bohmian mechanics is the most naively obvious embedding imaginable of Schrodinger’s equation into a completely coherent physical theory."

I have doubts about "coplete coherence" of the resulting theory. My guess is that Bohmian mechanics, and understood and as presented today is not a coherent theory. But in order to be able to prove this hypothesis I need to study Bohmian mechanics in some details.

Next the following paragraph comes:

Suppose that when we talk about the wave function of a system of N
particles, we seriously mean what our language conveys, i.e., suppose we insist that
“particles'’ means particles. If so, then the wave function cannot provide a
complete description of the state of the system; we must also specify its
most important feature, the positions of the particles themselves!

Now, why only "positions" rather than "positions and momenta"? Probably the authors were trying to answer my natural question, but they did not come with a right answer. Notice that there is a difference between the way Bohmian mechanics is presented by Bohm himself and the way it is being presented by the authors. In "Undivided Universe" (Chapter 3.1, point 4.) Bohm and Hiley state explicitly:

4. The particle momentum is restricted to p= gradient S.

But Berndt et al. skip this and prefer not mention it (even if it is an automatic results of their postulates). The question is why is the momentum constrained? Of course, once the momentum is constrained, the resulting dynamics is non-Newtonian, that is clear. But why it must be non-Newtonian? What would happen if we would like to remove the constraint and replace it by some dynamical equation? Did anyone try it in the past? Personally I did not like constraints that are postulated without giving any reason. We do not really understand our theories if we can’t explain our constraints.

Berndl et al. propose then:

Suppose, in fact, that the complete description of the quantum system—its state—is given by
(Q,psi)

where Q = (Q_1,…,Q_N) is in R^3N with Q_k the positions of particles, and psi=psi(q) is the wave function.

Now, here we have a problem. We more or less know what are positions, how to observe positions, even with some errors. We can use photographs, cloud chambers, microscopes and telescopes to register what we think are positions. But how do we observe a "wave function"? What kind of microscope or telescope we are supposed to use to even guess what psi can be? And why only Q instead of (Q,P)? We can observe positions and we can observe velocities. Why are we choosing here positions only?

Then we shall have a theory once we specify the law of motion for the state (Q,psi). The simplest possibility is that this motion is given by first-order equations—so that (Q,psi) is indeed the state in the sense that its present specification determines the future.

Well, if the equations of motion are supposed to be deterministic, how are we going to account for apparent randomness observed in Nature? Lack of knowledge? But what is "knowledge"? How "knowledge" is modelled in Bohmian mechanics?

We already have an evolution equation for psi, i.e., Schrodinger’s equation,

Consciousness Unexplained

Filed under: Metaphysics

A particurarly interested piece on Mental Deviance.

I don’t buy it when scientists say that the brain creates consciousness or awareness.

I don’t buy it either. Quantum theory is telling us that observer is an important element in the participatory universe.
It all boils down to this: the brain is a system of particles and energy. The brain can only do what other hunks of particles and energy do — obey the laws of physics.

And if so, where do the laws of physics are coming from? Are laws of physics part of the material brain? Popper and Eccles understood that the world of knowledge and information is different from the world of matter.

When a photon of light hits your eye and triggers an electric impulse down a neuron which then sends electrons bouncing around in your brain, that’s just a series of physical reactions. It’s the same as kicking a rock and seeing it bounce off a tree. If the system of someone kicking a rock into a tree isn’t a conscious entity, then why am I? Why isn’t a computer?
First of all what is a kick? Does Nature, the material one, understands the concept of a kick? When, exactly a kick starts, and when it does it ends? It seems that consciousness is necessary to introduce the very concept of a kick. And kicks are particular cases of events. Quantum theory, the orthodox one, knows nothing about events. John Bell understood it well.
Which brings me to my next issue. The Observer. Why are we aware? Why is there an internal observer that suffers and feels pain and feels pleasure? We certainly aren’t necessary to our bodies’ survival.
But, as Wheeler points it out - we may be necessary for the Universe to become . See for instance: Towards the theory of matter, geometry and information.
The brain is simply a computer that our “soul” or awareness uses to process input into meaningful patterns and store them. Saying that our brain creates our awareness is like saying that computers created us so we could surf the internet for porn.
It seem to me that while consciousness as such is timeless, matter involves the concept of time. How precisely it happens, I do not know. This brings us back to the question: what is time? Can we read and interpret Signs of the Times?

23 February, 2005

What is time? Part 2

Filed under: Metaphysics

In the Introduction the authors, Alain Connes and Carlo Rovelli, write:

Our approach is based on a key structural property of von Neumann algebras. The links between some of the problems mentioned and central aspects of von Neumann algebras theory have already been noticed. A prime example is the relation between the KMS theory and the Tomita-Takesaki theorem [7]}. Rudolf Haag describes this connection as “a beautiful example of `prestabilized harmony’ between physics and mathematics" ([7], pg. 216). Here, we push this relation between a deep mathematical theory and one of the most profound and unexplored areas of fundamental physics much further.

It is clear from the above that the authors will be seeking the solution in the formal mathematical concepts, not in expanding our conceptual framework. That should be not a surprise as Alain Connes is a mathematician and Carlo Rovelli did not show a deep understanding of philosophical and conceptual problems either. Consider for instance the following sentence from page 2:

The problem we consider is the following. The physical description of systems that are not generally covariant is based on three elementary physical notions: observables, states, and time flow.

Let us analyze this: systems that are not generally covariant. This expression is meaningless. To say that a "system is generally covariant" is to convey no information at all and is meaningless. For instance, our solar system is a physical system. But is it generally covariant? Simply the concept of general covariance does not apply here. Our solar system system is neither generally covariant nor "not generally covariant". The concept of "general covariance" applies only to certain descriptions of certain mathematical models. But even then the concept is rather tricky. Every model, even one that at first may look as being not generally covariant, can be, if we wish so and if we are smart enough, to be reinterpreted as "generally covariant." I am sure that Connes and Rovelli know about it, as they must have read discussions of general covariance published in the literature and talked about at length at conferences, and yet here they take an easy path and forget about the necessity of being clear an precise. They go on to say:

Observables and states determine the kinematics of the system, and the time flow (or the 1-parameter subgroups of the Poincare’ group) describes its dynamics.

Here we have another wrong statement. For a physical system described through a classical mechanical model it is not so much observables and states that describe kinematics, but the symplectic manifold and its symplectic structure. We may have the same set of observables and states - and yet completely different kinematics, if we choose a different symplectic structure. Moreover, for a time dependent systems the time flow is not described by a 1-parameter subgroups of the Poincare’ group. What more one has to distinguish between passive and active "time flow". For instance for a dissipative system we can have a 1-parameter group of "passive time translations" and "1-parameter semi-group" of active time translations. These subtleties are important and it is not a good start when the authors make errors and oversimplifications already at the very start of their paper.

Next laputan statement:

In a general covariant theory there is no preferred time flow, and the dynamics of the theory cannot be formulated in terms of an evolution in a single external time parameter.

A general covariant theory may have a preferred time flow as one of its variables. It may have, for instance, a vector field - as a kinematical or a dynamical variable. This vector field will define a "preferred time flow" and yet the theory will be "general covariant". Moreover, as mentioned above, the question of whether a given theory is generally covariant or not is a tricky question. If I declare that my vector field is "fixed" - I will be told that my theory is not generally covariant. But if, for exactly the same theory, I will declare that my vector field is "arbitrary" and that my "configuration space" includes "all possible vector fields" - then my theory (the same as before) may be even admitted into the "generally covariant zoo." Some will still argue and ask me whether my vector filed is "dynamical" or "only kinematical", but even so they will not be able to define precisely what they mean by "dynamical" as opposite to "purely kinematical". They will try all kind of little tricks - but they will not succeed. Connes and Rovelli, I am sure, know about it, yet they repeatedly fall into a trap of following the popular slang that really deep thinkers have to "unlearn" if they want to really understand what is this theoretical physics all about.

What is time? Part 1

Filed under: Metaphysics

What is time - I don’t know. But it’s time to start to know.

Until one is committed, there is always hesitancy, the chance to draw back, always ineffectiveness. Concerning all acts of initiative there is one elementary truth, the ignorance of which kills countless ideas and endless plans: That the moment one commits oneself, then providence moves, too.

All sorts of things occur to help one that would never otherwise have occurred. A whole stream of events issues from the decision, raising in one?s favor all manner of unforeseen incidents and meetings and material assistance which no man could have dreamed would come his way.

Whatever you can do or dream you can, begin it! Boldness has genius, power and magic in it. Begin it and the work will be completed.
Johann Wolfgang von Goethe

I’ll begin this blog with an analysis of the paper by Alain Connes and Carlo Rovelli: Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories, published in Class.Quant.Grav. 11 (1994) 2899-2918. The paper is available on the web in PDF form from arxiv.org. The title may suggest that the paper is rather technical and incomprehensible for a general public. Yet I am going to make my comments on the paper as comprehensible as possible. Here is the claim made by the authors:
[…]a basic open problem is to understand how the physical time flow that characterizes the world in which we live may emerge from the fundamental “timeless” general covariant quantum field theory [9]. In this paper, we consider a radical solution to this problem. […]
I will analyse the paper in some details pointing out its weaknesses, those that I see and that I consider important. The reason for my criticism is twofold. First of all the subject is important - therefore to get to the truth of the subject is important. Second, the authors are famous (especially Alain Connes) and there is a double standard in the community of professional scientists: those who just begin their adventure with science are criticised for every mistake they make, while those who are “famous” are being forgiven for any nonsens or even stupidity they can write or say. A typical example is Albert Einstein. You can find statements by serious physicists that his years devoted to his Unified Field Theory consisted either of plagiarizing other physicists’ work, or making errors after errors, neglecting achievements of quantum theory, and trying to stop the progess of physics. And yet this information and these opinions are not as easily available to the general public as apologetic and uncritical stories are. [Note: For a good and deep overview see On the History of Unified Field Theories by Hubert Goenner ]


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