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Dear Prof. Rovelli,

Your invocation of Tomita flow requires that the algebra of operators be, as you say, a von Neumann algebra, as well as requiring a state over the algebra. A von Neumann algebra has a Norm, by definition, which, I claim, must have a *timeless* meaning for your argument to go through.

The Norm of an algebra of observables decides what measurements are close to each other -- that is, the topology -- which allows us, by continuity, to decide whether we expect, in a given state, that the results of one measurement will be close to the results of another experiment. We can only verify that two given experimental procedures are close to each other by applying them to many different states, thereby determining that we get almost the same results (according to some Norm on the space of results) in every state. Given the statistical nature of a state -- as much in classical statistical mechanics as in quantum theory -- this requires us to construct many ensembles. Now, how are we to construct these multiple ensembles timelessly?

As an ideal world, of course, you are quite entitled to posit any mathematical structure you like, but I would like to see a Physical interpretation include at least a schematic for an operational correspondence with the world for every significant mathematical structure. In any case, given its significance to your account of time, I would like to see a relatively full account of how to understand the Norm of the von Neumann algebra in a timeless way, whether operational or not.

I apologize if this question is well understood. I don't follow the literature on quantum gravity closely at present. Please feel free just to cite a reference.

I'm perhaps simply at cross-purposes with you, since in the last sentence of section VI you assert that the world is "in" a given state rho, which suggests that you understand QFT in terms of a non-ensemble interpretation of probability. However, I would personally take a non-operational definition of probability also to be problematic for your program.

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Thank you very much for the essay. I enjoyed reading it, I expect you will expand it more.

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Carlo Rovelli's statement, "Research needs courage, wasted time and money, false directions. The history of our civilization is the proof that all this money is not wasted, in my opinion..." is a point well made.

Nature shows in all ways that waste and redundancy are assets to creativity. Efficient evolution is guaranteed by conservation laws, and not by the efficiency that we vainly try to build into a system.

Tom

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No chaff. No wheat.

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Thanks Eleni, Ray and John for the last nice posts.

Peter Morgan raises an extremely good issue, with both a technical and a conceptual side. I refer here to his post above, without trying to repeat here his points, since these are several, interconnected, and nicely expressed by Peter.

First, a technical point. It is true that Tomita theory wants a von Neumann algebra, and therefore the corresponding norm; but this is given for free by the state over the C* algebra. The reason is that such a state is enough for the GNS construction, which provides the representation, the Hilbert space, and therefore the von Neumann algebra structure. Thus, C* algebra and (appropriate) state are enough.

This does not answer Peter's questions, however; it only moves them one step back, because all the physical questions he poses about the norm, and in particular the meaning of its its probabilistic interpretation in a timeless context, can just be reformulated for the state itself.

The question, I think, raises deep issues. I'll try to answer is steps. First, regarding the operational meaning of probability. I do not want to enter the debate about probability here. I only state my preferences, without arguments. The definition of probability that makes sense to me is the one of de Finetti, subjective. Probability is something about my expectations, and the corresponding mathematical theory expresses the proper way of adjusting expectations on the basis of observations, where "proper" refers to the use of Bayes theorem, which follows from the logic structure of probabilities (expectations) themselves. We make (finite) sequences of observations, and readjust our previous hypotheses on the basis of outcomes.

This answers the question about operationalism, but not the question about the possibility of doing so in a timeless context. This is the difficult part of the question. The question is about the rationalization of experiencial temporality in a physical world. I am not sure physics in the strict sense is capable of answering it. The question pertains to that part of science that studies ourselves and our capacity to gather and elaborate informationa and conceive thoughts and representations of the world. What I am saying is that I think that timeless quantum gravity is equally blind to the temporal aspect of consciousnes as Newtonian mechanics is. What basic physics must provide, however, is a context within which it is possible to have the basic ingredients in terms of which a science of complex systems might make sense of processes of organizing information. So, here is the story: In a timeless world, a small subsystem (us) whose interaction with the rest of the universe is limited to a very small number of variables, and therefore who has no access to the exact state of the rest of the universe (that is, it has the same state for many different states of the universe), can be correlated with the rest of the world in such a way to have an imprecise information about the rest of the system (a way to express these notions precisely using Shannon information theory is in my work on relational quantum theory); then with respect to this subsystem a Tomita flow is defined; and this flow itself is the physical underpinning of the perception of the flow of time, whatever this perception is.

Maybe I should not have entered this domain, which is slipery. I think that it is better to keep as separated as possible physics and the science about cognitive capacities. Otherwise we make confusion. As an analogy: we understand the water molecules, from there the hydrodynamica behavior of liquid water, from there the floating of boats, including the boat on which we stand when we collect water from the sea on order to study its molecular strucure. But trying to write a theory of molecular structure of water thinking that within the theory we may directly see out floating boat is the bad procedure. Here the analogy is: water molecules/timeless mechanics, floating/tomita flow, collecting water from the boat/operational definition of probability.

Hope this was not too confused.

Carlo Rovelli

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The way Dr Carlo Rovelli is questioning Time is may be new in 'Quanta Theory' but not in Antique Greek Metaphysics that does analyses the connection of Time with Space in Motion precisely. This is the case of 'Eleates' (6th bc - although Eleates deduce there is no motion at all!) and Eleates are not lonely.

No doubt that the analogy between the dynamism of Time and the dynamism of Heat is one of many comparisons that are leading to new 'kinesis'. One can find that in Boltzmann's science of gas pressure for instance. Therefore the 'Question of Heat' is as 'mysterious' as the 'Question of Time'.

Such a link between Heat and Time is established by some Antique Greek scientists too.

So the good question is not in my opinion if the Antique Greek Metaphysics is up to date or not; Dr C. Rovelli's essays are just proving it is still alive.

The right question is: do Greek old masters go beyond in time analysis than actual physicians? The goal is not to rise up old Methaphysics against modern Science but to know if the Greek Metaphysics can impulse a better logic to a technological Science that seem to be possessed by doubt in the field of logic.

(I am student in an Art-School and making an writing an essay about Geometry and Newton's chromometric scale. My interest goes to the problem of Time too. Even if I am not focused on number four and 'Quanta theory' which recalls the famous trial consisting in squaring the space of the circle, I intend to publish a chapter of my own iconoclastic artistic vision in a few days on www.fqxi.org).

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Dr. Rovelli,

I agree that the issue of consciousness distracts from the question of time. I think both time and temperature are elemental to motion. That said, our mental facilities are a consequence of feedback between the source of this consciousness and motion. E.O Wilson described the insect brain as a thermostat, while the neuroscientist J. B. Taylor provides interesting insights between the 'serial processor' of the left hemisphere of the brain and 'parallel processor' of the right hemisphere;

http://blog.ted.com/2008/03/jill_bolte_tayl.php#more

I would argue that the right brained parallel processor amounts to a thermostat, in its measuring and reacting to the energies of the moment, while the left brained serial processor amounts to a clock, in that it analyses the sequential cause and effect of events.

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In traditional lore, this dichotomy was between the head and the 'heart.'

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*Another analogy: keeping as separated as possible the physics and the science about cognitive capacities is probably as difficult as for the Greek scientists keeping physics and metaphysics separated.

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Does Dr. Rivolli think my posting unworthy of a response! i am however curious to know why he consider it to be so, just because it doesn't involve detailed discussion on the mathematical treatment used or the points raised are irrelevant!

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This is more like a paper than an essay. It also seems to be way over 5000 words.

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Dear Narendra Nath, I am sorry, I did not think that your post unworthy of a response! I just did not know what to answer. Your suggestion that "distortions of time may have resulted in the release of the energy content of the Universe" is interesting, but I think is still to vague to be useful is physics. (By the way, my name is Rovelli, not Rivolli. But "Rivolli" sounds nice and funny to me... I might adopt it!)

Regarding the anonymous post "This is more like a paper than an essay. It also seems to be way over 5000 words.", I am also not sure what to say. Is this somebody interested in a scientific discussion or a contest competitor? :-) Anyway, the text alone without math gave less than 5000 words on my word counter. And I think the essay is an essay, not a "paper", whatever this means. It uses some technicalities, because I think they make the point concrete, but the main point is entirely a conceptual view about time, its absence, and its emergence.

Carlo Rovelli, (or Rivolli)

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Rovelli or Rivolli,

i enjoyed your pun, my mistake arose o/c the name of a cinema hall i use to visit in New Delhi to see western movies!

I have posted a latest one on the essay of Kyle Miller 'here and now'. That post is actually meant for we all the essays' authors. Kindly see it and then you and i will have no problem if you and i understand or not anything that any one else is saying or writing!!

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Biology is crossing Physics in motion, either you take the Dynamics of Time or the temperature's one.

And both 'Quanta theory' - think of the motion of gas depending from temperature - and Relativity are based on reflexions on the arrow of Time AND the pillar of Temperature.

Light is the 'check point' of 'Quanta theory', Einstein's theories, without forgetting Newton. And the idea of Temperature and the idea of Time are included in ambiguous light.

This is the knot. And in my artist opinion, 'pulling the time over', Dr Rovelli is cutting the knot as Alexandre did (Although Aristotle was Alexandre's advisor and not Anaximander of Miletus).

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About your comment on energy coming from distortion in time, it is already covered under Heisenburg uncertainty relations, between two conjugate pairs E & T and X & P. Both energy and mass get created as uncertainty rise in time & momentum respectively. The former provides the classical way to explain overcoming of potential barrier the alpha particle experiences inside the unstable nuclei concerned.Near zero uncertainty in time means infinite energy uncertainty!Time may have begun this way!

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Dear Carlo,

I very much enjoyed your essay. Naturally, I very much agree with its general drive too. I have a question though. As a proponent (and founder) of Loop Quantum Gravity, are you not assuming the existence of time by asserting that time (and space) are quantized, and come as minimum, indivisible atoms in LQG? I think one can see this just in general, but also that by asserting the existence of indivisible, minimum time and space intervals, one is also assuming the existence of instants in time and spatial points (things that would constitute the building blocks of time and space and which certainly do not exist) to bound and determine such intervals. I naturally have no problem with Planck time and distance - intervals beyond which clocks and rulers can no longer have meaning - but this does not mean that continuity ceases beyond this point, not does Planck time and distance require the existence of instants and spatial points.

Best wishes

Peter

PS: I should note that, considering its emphasis on background independence and its adherence to 4-d, I find LQG the most promising current approach to quantum gravity. It is just the "atoms of time and space" that I have a real problem with. I'm not sure if LQG could be reformulated without this feature and still be "LQG" however.

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Dear Peter,

thanks for rising this key point. You say: "Are you not assuming the existence of time by asserting that time (and space) are quantized, and come as minimum, indivisible atoms in Loop Quantum Gravity"? Very good point. Here is what I think:

Einstein great discovery, of course, is that the two things are in fact the same. The two things are: on the one hand, the gravitational field, and on the other the two "entities" that Newton put at the basis of his picture of the world, and called "space" and "time". Now, when you discover that mister A and mister B are the same person, you can equally say that mister A is in reality mister B, or that mister B is in reality mister A. Books like to say that the gravitational field, in reality, is nothing but the spacetime, which happens to curve and so on. I prefer the opposite language: namely that the entities that Newton called "space" and "time" are nothing else than the gravitational field, seen in the particular configuration where we can disregard its dynamical properties, and assume it to be flat. The choice is not just a choice of wording. My understanding is that the deep discovery of Einstein with general relativity is not that the gravitational field is very special, but, the other way around, that it is just a field on the same ground as the other fields. The key novelty with respect to pre-general-relativistic physics is that all these fields do not live "in" spacetime: they live, so to say, "on top of one another". (In fact, I think that this was also Einstein view. He writes for instance "Spacetime does not claim existence on its own but only as a structural quality of the [gravitational] field", in "Relativity: The Special and General Theory", page 155.) So, I think that the clearest way of thinking about general relativity, or, more precisely, the general relativistic theory that , at best as we know, describes our world, and which includes the gravitational field and all the other physical fields, is to view it as a theory of interacting fields, without any need of making reference to space and time. What we have is observable quantities that are functions of these fields.

Now, from this point of view (which is mine), the "atoms of space" of loop quantum gravity are truly just quanta of the gravitational field. The reason we call them "quanta of space" is only because we use to call "space" the quantity measured my a meter. But a meter only measures the gravitational field. And the same with time and a clock. The reason we keep talking about "space" and "time" in loop quantum gravity is only because these are traditional names for indicating aspects of the gravitational field. But these names are ill-used, if we assume them to carry all the heavy ontological significance of Newtonian space and Newtonian time. They represent observable variables (measured by clocks and meters), on the same ground as many other quantities observed in nature.

This is why I think that in order to have a clear picture the easiest thing is to "forget space" and "forget time", and only to talk about relations between observable quantities. The "atoms of space" and the "atoms of time" of LQG are only figures of language, to indicate that certain physical observables aspects of the gravitational field have a discrete spectrum.

I am very glad you have raised this point.

Carlo Rovelli

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Dear Carlo,

Thanks. I thought that was an excellent response. I agree with everything you said as well. It's also nice as, with your interpretation of time and space in LQG, we both get to come away happy; no time, no space, no quantizaion of "time" or "space" etc. If only physics worked out this way all the time!

Best wishes

Peter

PS: I use that Einstein quote in my essay. It is remarkable how this point has been lost on so many.

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Dr. Rovelli,

One question with regards to space; Is this gravitational field ultimately a singular entity, as in Big Bang theory, or is it ultimately distributed, as in a fluctuating vacuum?

Given you describe it as "flat," I assume you think it is distributed.

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Drs. Rovelli, Merryman and other postings from public,

my comments here will concern the theme 'TIME'.Giving a meaning to life introduces time as a concept. It is at the root of life. Timelessness means that there is total freedom and complete randomness around. The latter is the scenario for all the physical processes/phenomena, as these have been understood only on probabilistic considerations. No individual event can be pre-detemined in time!

Now let us see what space is. If no location is desired, we have the spaceless situation. Only if one exists, it is enough for it to know it exists, no need for location. However, if two or more exist simultaneously, there is need for location in space. If we all agree to say that we are one then where is the need to assign different locations.

In psychology/logic, we deal with just 0 & 1 as the numbers. In fact, all other so-called digit numbers are obtainable through some manipulation of only these two digit numbers.The existence and non-existence can thus be treated as two sides of the same coin, both equally significant or insignificant. Such is the problem before us o/c the duality nature of all worldly things/matters.

An interesting combination of two set of terms and traits may be provide us with some humor! Let us take a set of service, love, knowledge and life. Then, let us take another set of attitude. reason, intellect and time. If we combine the corresponding terms and traits with words 'with' and then 'without' in turn, the net result comes out to be selfish,false,ego and finite in the first option. The other option provides us with selfless, true, ego-free and eternal. The latter is a desired ( theoretical) set of objectives while the former results in a factual( practical) situation.

Hope i have posted something down to earth with regard to TIME and its sister SPACE!!!