Julian Barbour on does time exist

[marcus]

Hi Exper., Looser, Paulibus, thanks for your comments! This is a really important point. The idea of what is fundamental is comparative and provisional---depending on context some stuff is MORE fundamental than other stuff but we can't expect that anything is ABSOLUTELY fundamental.

...But let’s not kid ourselves that the words and mathematical descriptions we use have absolute eternal meanings; they just conveniently communicate concepts between us. ...

or ETERNALLY, like Paulibus says, fundamental. Because 10 years later physicists might discover something even more basic.

Emergent simply refers to something that is real and physical (maybe indispensable, necessary for our understanding) but NOT FUNDAMENTAL. Like temperature, or like the water level in a lake. If you zoom in too closely you won't see it. But it's real.

I guess you could say that all physical descriptors and features are elements of a mathematical language that we are trying to apply to nature. Some of those descriptors (the traditional name is "degrees of freedom") are more basic than others. We call them fundamental. And others are more COMPOSITE or DERIVED or only definable when we have a large unspecified number of basic objects, and we call them non-fundamental, or less fundamental, or emergent. Like the water level or the temperature.

All these things are elements of a (mathematical) language which is evolving to better fit nature.
And I have to admit the fit is astoundingly good in so many areas. But still, as Paulibus suggested, let's not confuse our descriptive/predictive language model with nature/reality itself.
=================

I think for the purposes of this thread, if someone wants to join the discussion, they should have looked at both the first--prize essays on this winners list:
http://fqxi.org/community/essay/winners/2008.1
In 2007-2008 FQXi (foundational questions institute) had an essay contest on The Nature of Time and they gave out two first prizes.
These essays are wide-audience, so some of the language in each essay is for non-specialists. And some is difficult mathematics.
The theme (what is time?) is not introductory physics. So if anyone is trying to teach themselves basic college physics this is definitely NOT a good place to start! The nature of time is one of the frontiers of physics where there is naturally the greatest confusion, disagreement, lack of clarity.

Both of the first prize essays took the position that time is NOT FUNDAMENTAL but is something you can derive from studying motion and change at a more basic level.
The two essays I'm suggesting people look at are Barbour's and Rovelli's (as a minimum, several other people in this thread have mentioned some other really good ones.)

 

[marcus]

You can get an idea of Barbour's essay by looking at the brief summary, the "abstract" at the beginning:
===quote===
The Nature of Time
By Julian Barbour

Essay Abstract
A review of some basic facts of classical dynamics shows that time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change.
==endquote==

In a nutshell, time is not needed as a fundamental concept. Time emerges. And he gives a careful concretely worked-out example of how time emerges from watching a specific system of bodies, like a solar system or a cluster of stars.
http://fqxi.org/community/essay/winners/2008.1

You can get an idea of Rovelli's essay from its abstract, or summary. Shown further down on the same list. It is also on the preprint archive: http://arxiv.org/abs/0903.3832
===quote===
Forget Time*
By Carlo Rovelli

Essay Abstract
Following a line of research that I have developed for several years, I argue that the best strategy for understanding quantum gravity is to build a picture of the physical world where the notion of time plays no role at all. I summarize here this point of view, explaining why I think that in a fundamental description of nature we must "forget time", and how this can be done in the classical and in the quantum theory. The idea is to develop a formalism that treats dependent and independent variables on the same footing. In short, I propose to interpret mechanics as a theory of relations between variables, rather than the theory of the evolution of variables in time.
==endquote==

There are actually two Rovelli essays to look at. A good non-specialists introduction is "Unfinished Revolution"
( http://arxiv.org/abs/gr-qc/0604045 ) because in about 3 pages near the beginning it takes you through the HISTORY of the gradual weakening of the idea of Newtonian time by 1905 special through 1915 general relativity to today's quantum gravity research. It is good to get that perspective. Notice that in quantum mechanics a moving particle does not have a continuous TRAJECTORY. You can only *observe* where it passed thru at some discrete locations. You cannot say what it did in between. In the dynamically evolving geometry of quantum relativity, a continuous 4D spacetime is the analog of a continuous particle trajectory. For the same reason, one cannot say that it exists. One can only make a finite number of observations of geometric observables and study/predict the correlations.

In that sense a spacetime is not any more fundamental than a continuous particle trajectory. Both are derived constructs.

 

[Paulibus]

The essays of Barbour and Rovelli that you kindly highlighted, Marcus, illuminate nicely the dangers of assuming that familiar concepts (like time) are fundamental (although Rovelli contrarily notes that “...time is one of the fundamental notions in terms of which physics is built...”).

But I sympathise with Imalooser's irritation with the somewhat shopsoiled label “emergent”. It helps when an explanation is given of what the thing in question (here the time concept) emerges from, as in these essays. Barbour plumps for Newtonian mechanics, but I get confused about what "emerges" from which: time from physics or physics from usually being parameterised by time. Rovelli, on the other hand,

...thinks that (some puzzling features of time) are not mechanical. Rather they emerge at the thermodynamical level... (they are) features that emerge when we give an approximate statistical description of a system with a large number of degrees of freedom...We represent our incomplete knowledge and assumptions in terms of a statistical state ...Time is ... the expression of our ignorance of the full microstate.

Both essays offer lots of argument, but describe no verifiable predictions. For me they represent scientific curiosity biased by special pleading; for a Newtonian perspective in Barbour’s case; for a Loop Quantum Gravity perspective in Rovelli’s case ---, rather than describing a usual cycle of scientific progress.

Interesting indeed, but for me less exciting than the famous emergence of Ursula Andress from the ocean in the first Bond movie!

 

[marcus]

... Barbour plumps for Newtonian mechanics, but I get confused about what "emerges" from which: time from physics or physics from usually being parameterised by time. Rovelli, on the other hand, ...

==Paulibus quoting Rovelli==
...thinks that (some puzzling features of time) are not mechanical. Rather they emerge at the thermodynamical level... (they are) features that emerge when we give an approximate statistical description of a system with a large number of degrees of freedom...We represent our incomplete knowledge and assumptions in terms of a statistical state ...Time is ... the expression of our ignorance of the full microstate.
==endquote==
Hi Paulibus, thanks for your comment! You have what is presented as a quote from that essay but I didn't understand it and couldn't find it in the essay so I figured it might be your paraphrase plus bits from several different pages taken out of context. I therefore went looking for the context. I think this is the main context, which may help me better understand what you are saying. I've highlighted some things I may want to refer to later.

==quote page 8 of "Forget time"==
This observation leads us to the following hypothesis.

The thermal time hypothesis. In nature, there is no preferred physical time variable t. There are no equilibrium states ρ₀ preferred a priori. Rather, all variables are equivalent; we can find the system in an arbitrary state ρ; if the system is in a state ρ, then a preferred variable is singled out by the state of the system. This variable is what we call time.

In other words, it is the statistical state that determines which variable is physical time, and not any a priori hypothetical “flow” that drives the system to a preferred statistical state. When we say that a certain variable is “the time”, we are not making a statement concerning the fundamental mechanical structure of reality. Rather, we are making a statement about the statistical distribution we use to describe the macroscopic properties of the system that we describe macroscopically. The “thermal time hypothesis” is the idea that what we call “time” is the thermal time of the statistical state in which the world happens to be, when described in terms of the macroscopic parameters we have chosen.
Time is, that is to say, the expression of our ignorance of the full microstate.

The thermal time hypothesis works surprisingly well in a number of cases. For example, if we start from radiation filled covariant cosmological model, with no preferred time variable and write a statistical state representing the cosmological background radiation, then the thermal time of this state turns out to be precisely the Friedmann time [21]. Furthermore, this hypothesis extends in a very natural way to the quantum context, and even more naturally to the quantum field theoretical context, where it leads also to a general abstract state-independent notion of time flow. In QM, the time flow is given by
A_t = α_t(A) = e^itH₀ Ae^−itH₀ . (19)
A statistical state is described by a density matrix ρ. It determines the expectation values of any observable A via

ρ[A] = T r[Aρ]. (20)

This equation defines a positive functional ρ on the observables’ algebra. The relation between a quantum Gibbs state
ρ₀ and H₀ is the same as in equation (14). That is ρ₀ =Ne^−βH₀. (21)
Correlation probabilities can be written as W_AB(t) = ρ[α_t(A)B] = Tr[e^itH₀ Ae^−itH₀Be^−βH₀], (22)
Notice that it follows immediately from the definition that
ρ₀[α_t(A)B] = ρ₀[α(−t−iβ)(B)A], (23)
Namely
W_AB(t) = W_BA(−t − iβ) (24)
A state ρ₀ over an algebra, satisfying the relation (23) is said to be KMS with respect to the flow α_t.
==endquote==

It may take me a little while before I can respond to your post, Paulibus. I can see you are making an effort to understand the thermal time idea and give a fair summary of it (as I am trying to do or would like to do myself!)

 

[marcus]

You see Barbour and Rovelli's pictures as contrasting but I see an underlying similarity, both dispense with time (as a basic given) and derive it from what is the case, from the timeless reality of all our interrelated observations, perhaps one could say.

The word "state" has the unfortunate mental associations that come from having heard countless times the phase "state at a given time". what one really needs is a word for the timeless state of the world. Something like what one gets from the first chapter ("Proposition 1") of Wittgenstein's Tractatus:

Proposition 1

1 The world is all that is the case.
1.1 The world is the totality of facts, not of things.
1.11 The world is determined by the facts, and by their being all the facts.
1.12 For the totality of facts determines what is the case, and also whatever is not the case.
1.13 The facts in logical space are the world.
1.2 The world divides into facts.
1.21 Each item can be the case or not the case while everything else remains the same.
=============

I don't see Barbour's vision as Newtonian because Newton's vision had an absolute time. He was closer to a 4D block spacetime in which the time coordinate had real physical meaning, was observable.
In GR the "time" coordinate is not observable and has no physical meaning, it is merely conventional. Barbour's observer derives time from watching motions. As he suggests, the idea of time as fundamental is unnecessary---I think one word for that would be "epiphenomenon".
Both Barbour and Rovelli seem in step with GR, perhaps a little out in front.

When you pass to a quantum version of GR the "state" (or "world") can no longer be a 4D continuum, for essentially the same reason that a particle cannot have a continuous trajectory. We only make a finite number of observations. We can have no mathematical representation of what is "in between" those observations. We simply have those observations and the correlations among them. The compact way to say that is with a C* algebra plus a positive (traceclass) operator ρ which represents what we think we know about it. Our knowledge and non-knowledge expressed probabilistically---as Rovelli says, "our ignorance".

Interesting stuff. Barbour's picture would ALSO need to be probabilistic since he doesn't know whether or not a neutron star is going to hurtle thru the solar system he is watching and disrupt his concept of time. He rightfully assumes it very unlikely but he talks as if it is completely ruled out. He sees and accounts for every body in the system, which in truth one cannot do with perfect certainty. So Barbour's picture also represents our knowledge/ignorance, just doesn't make that mathematically explicit.

I see their two visions of epiphenomenal time as somewhat akin to each other.

 

[FalseVaccum89]

In Barbour's book The End of Time, he talks about the probabilities associated with QM being represented as densities of a "fog" in Platonia (the configuration space).

 

[Paulibus]

Thanks for responding so fully to my sketchy post, Marcus. I agree that Barbour and Rovelli come to similar conclusions. I was thinking of Barbour’s emphasis on ephemeris time (a Newtonian concept used by astronomers), not of Newton’s absolute time. I also
confess I find both essays quite hard to understand, and in linking bits (as you correctly suspected) from Rovelli’s essay into a single quote I was trying to pick out the gist of his radical proposal.

Their tampering with our innate take on time won’t be easily accepted; it’s a central feature of our finite lives, and I guess our faith in its practical utility as a measure of life passing will be hard to shake. I wish Barbour and Rovelli success and look forward to the “time” when their ideas gain the gravitas conferred by testable predictions.
Maybe someone will build:

...a glittering metallic framework, scarcely larger than a small clock... (with) ivory in it, and some transparent crystalline substance

that could demonstrate Time Travel!

 

[TrickyDicky]

...
In GR the "time" coordinate is not observable and has no physical meaning, it is merely conventional...

So what are Rovelli and Barbour suggesting that must be done with the time coordinate?

 

[marcus]

So what are Rovelli and Barbour suggesting that must be done with the time coordinate?

Hi TD, Alain Connes and Carlo Rovelli have a definite proposal which they offer for consideration, called the "thermal time hypothesis". I'll excerpt a brief summary. (Someone else may be able to talk about what Barbour would say "must be done".)
As for C&R they are quite explicit already on page 2 of their paper. One just googles "connes rovelli" and gets http://arxiv.org/abs/gr-qc/9406019
==page 2==
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. 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.1 In particular, notice that this notion of time is state dependent.

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. 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. As emphasized in [4], 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.² 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 [9].

In this paper, we consider a radical solution to this problem. This is based on the idea that one can extend the notion of time flow to general covariant theories, but this flow depends on the thermal state of the system. More in detail, we will argue that the notion of time flow extends naturally to general covariant theories, provided that:
i. We interpret the time flow as a 1- parameter group of automorphisms of the observable algebra (generalised Heisenberg picture);
ii. We ascribe the temporal properties of the flow to thermodynamical causes, and therefore we tie the definition of time to thermodynamics;
iii. We take seriously the idea that in a general covariant context the notion of time is not state- independent, as in non-relativistic physics, but rather depends on the state in which the system is.
==endquote==

Note that this is presented as a hypothesis---it is proposed as one possible solution to be studied. They take the observable algebra. As given it is timeless. Any STATE is a positive functional on this algebra that gives expectations/correlations for all the observables. Then they offer a canonical way to derive a one-parameter group of automorphisms α_t of the observable algebra.
This is the modular group that you derive using the given state. Remarkably, it turns out to reproduce Friedmann time in cosmology if you use the cosmic microwave background to define the state. I have not examined the proof of this. They offer several indications that this modular group α_t corresponds to a satisfactory global idea of time. One can compare local observer-time to it and the comparison can have physical significance, which might be interesting. I have to go, back later. Thanks for the question!

 

[TrickyDicky]

Hi TD, Alain Connes and Carlo Rovelli have a definite proposal which they offer for consideration, called the "thermal time hypothesis". I'll excerpt a brief summary. (Someone else may be able to talk about what Barbour would say "must be done".)

Hmmm, that paper is almost two decades old, but I guess the concept hasn't changed much from then since you are linking it.
My question was trying to clarify what is the proposed practical implementation of considering the time coordinate "unnecessary". I guess they are not just suggesting to eliminate the time coordinate since that means doing away with Lorentzian manifolds and that seems quite wild. So is thermal time the new time coordinate?

 

[marcus]

Hmmm, that paper is almost two decades old, but I guess the concept hasn't changed much from then since you are linking it...

Yes! I do think the Connes Rovelli paper is very well written. What they say there can probably not be said much better by anybody. But the idea has developed and the most recent paper is, as you may know, Rovelli's September 2012 "General relativistic statistical mechanics".

I think the point is this is a major outstanding problem that may be nearing the time when it is ripe to work on. In a general covariant theory there is no preferred idea of time, and so one cannot do thermodynamics or stat mech as we ordinarily think of it.

One can do these things on an arbitrary fixed curved spacetime, but that is not the full GR treatment. So eventually humans HAVE to do thermo and stat mech in full GR context. Or the quantum version of that. But researchers must use their efforts wisely and not work on problems which are not ready to be addressed. For a while they only slowly chip away, or prepare some ideas to start with. that is how i see it.

I think one should not immediately think of a 4D lorentzian manifold (just my private opinion) I think one should think of the observable algebra, possibly abstractly as a C*-algebra. And the state embodies what we think we know and expect about all the observations. The fine thing is that this state itself uniquely specifies a one-parameter flow on the observables---the modular group of automorphisms of the algebra---uniquely up to some equivalence relation.
that is very abstract, but then one can in various cases make it specific using the familiar tools of the Hilbertspace, the 4D manifold, the fields written on the manifold, and so on. Or (I don't know) maybe LQG tools and Hilbertspace. At the moment I do not see any suggestion of a connection with LQG, it seems like an entirely separate development. (Except for sharing the general covariant GR perspective.)

 

[marcus]

I must repeatedly stress that this is only a hypothesis put forward to be tested, but C&R just could have hit on the way to handle time in a generally covariant quantum system. Remember that all we actually have is an algebra of observables. A 4D differential manifold is sheer mathematical fiction, as far as anyone knows. All we really have are our observations, a finite number of them, of which we can multiply and add together some to predict others (because they form an algebra).

==quote http://arxiv.org/abs/gr-qc/9406019 page 14==
Let us now return to generally covariant quantum theories. The theory is now given by an algebra A of generally covariant physical operators, a set of states ω, over A, and no additional dynamical information. When we consider a concrete physical system, as the physical fields that surround us, we can make a (relatively small) number of physical observation, and therefore determine a (generically impure) state ω in which the system is. Our problem is to understand the origin of the physical time flow, and our working hypothesis is that this origin is thermodynamical. The set of considerations above, and in particular the observation that in a generally covariant theory notions of time tend to be state dependent, lead us to make the following hypothesis.

The physical time depends on the state. When the system is in a state ω, the physical time is given by the modular group αt of ω.

The modular group of a state was defined in eq.(8) above. We call the time flow defined on the algebra of the observables by the modular group as the thermal time, and we denote the hypothesis above as the thermal time hypothesis.

The fact that the time is determined by the state, and therefore the system is always in an equilibrium state with respect to the thermal time flow, does not imply that evolution is frozen, and we cannot detect any dynamical change. In a quantum system with an infinite number of degrees of freedom, what we generally measure is the effect of small perturbations around a thermal state. In conventional quantum field theory we can extract all the information in terms of vacuum expectation values of products of fields operators, namely by means of a single quantum state |0⟩. This was emphasized by Wightman...

...Given the quantum algebra of observables A, and a quantum state ω, the modular group of ω gives us a time flow α_t. Then, the theory describes physical evolution in the thermal time in terms of amplitudes of the form
F_A,B(t) = ω(α_t(B)A) (26)
where A and B are in A. Physically, this quantity is related to the amplitude for detecting a quantum excitation of B if we prepare A and we wait a time t – “time” being the thermal time determined by the state of the system.

In a general covariant situation, the thermal time is the only definition of time available. However, in a theory in which a geometrical definition of time independent from the thermal time can be given, for instance in a theory defined on a Minkowski manifold, we have the problem of relating geometrical time and thermal time. As we shall see in the examples of the following section, the Gibbs states are the states for which the two time flows are proportional. The constant of proportionality is the temperature. Thus, within the present scheme the temperature is interpreted as the ratio between thermal time and geometrical time, defined only when the second is meaningful.⁶

We believe that the support to the thermal time hypothesis comes from analyzing its consequences and the way this hypothesis brings disconnected parts of physics together. In the following section, we explore some of these consequences. We will summarize the arguments in support the thermal time hypothesis in the conclusion...
==endquote==

C&R are telling us that in a fully generally covariant system without making some additional arbitrary choices, *the modular group flow is the only definition of time we've got*.
Further, it gives us transition amplitudes.
Further, if we go ahead and arbitrarily make a choice of geometry (e.g. Minkowski) then we can compare that time with the inherent modular group time, and the ratio can have a physical meaning.

 

[Paulibus]

I think that the central idea of Rovelli’s essay “Forget Time”; his proposed “thermal time hypothesis” ; is a “timely”, important and thought provoking reminder of an uncomfortable truth, namely that the way physicists describe reality (which is their job description!) is dominated by our anthro’centric perspective. We are a species distinguished by our peculiarly elaborate communication skills.

Rovelli persuasively argues that:

... what we call “time” is the thermal time of the statistical state in which the world happens to be, when described in terms of the macroscopic parameters we have chosen.

(My emphasis.) Thermal time is taken as the variable that the system is “in equilibrium” with respect to. In the case of say, a gas, his thermal time, I gather, reduces to our ordinary time (to within a proportionality factor). Since our macroscopic-scale description of equilibrium hinges on the statistically and thermally defined concept of temperature, in this case “thermal” is a very appropriate label.

What about situations where we are as yet unable to quantify entropy, but just trust the Second Law implicitly? As Rovelli says: “Time is ... the expression of our ignorance of the full microstate”. Is Rovelli suggesting that our concept of time is an statistical artefact of the scale we human beings inhabit? Just a tool; a parameter that physics uses to describe quantitatively our human circumstances, with thermodynamics as a sort of catch-all background?

Roll on the next chapter in this story.

 

[marcus]

... In the case of say, a gas, his thermal time, I gather, reduces to our ordinary time (to within a proportionality factor)...
What about situations where we are as yet unable to quantify entropy, ...?
...
Roll on the next chapter in this story.

Your post raises several interesting issues, I'm focussing on one right now---the cases where thermal time "reduces to our ordinary time". It seems important to list those offered in the Connes Rovelli paper, since the good consequences of the thermal time hypothesis (TTH) support one's suspicion that it is possibly right and worth investigating.

I've moved over to and am working from the Connes Rovelli paper, since it is the main source and considerably more complete than any of the other papers (including the wider-audience FQXi essay.) The C&R paper has 77 cites, over a third of which are in the past 4 years. It is the root paper that other thermal time papers (including by Rovelli) refer to for detailed explanation.

So what I would propose as a "next chapter in the story" is to make sure we get the main points that C&R are making. I'll run down the main corroborative cases they give on page 22, in their conclusions. These are explained in the preceding section, pages 16-21.
== http://arxiv.org/abs/gr-qc/9406019 ==
...
• Classical limit; Gibbs states. The Hamilton equations, and the Gibbs postulate follow immediately from the modular flow relation (8).
• Classical limit; Cosmology. We refer to [11], where it was shown that (the classical limit of) the thermodynamical time hypothesis implies that the thermal time defined by the cosmic background radiation is precisely the conventional Friedman-Robertson-Walker time.
• Unruh and Hawking effects. Certain puzzling aspects of the relation between quantum field theory, accelerated coordinates and thermodynamics, as the Unruh and Hawking effects, find a natural justification within the scheme presented here.
...
==endquote==

They also include three other supporting points. One that is not discussed in the paper and they simply mention in passing is the widely shared notion that time seems bound up with thermodynamics and there are indeed hundreds of papers exploring that general idea in various ways (far too numerous to list). Their idea instantiates this widely shared intuition among physicists.

Another supporting point is that the thermal time formalism provides a framework for doing general relativistic statistical mechanics. Working in full GR, where one does not fix a prior spacetime geometry, how can one do stat mech? A way is provided here (and see http://arxiv.org/abs/1209.0065 )

The sixth point is the one they give first in their "conclusions" list---I will simply quote:
==quote gr-qc/9406019 page 22==
• Non-relativistic limit. In the regime in which we may disregard the effect of the relativistic gravitational field, and thus the general covariance of the fundamental theory, physics is well described by small excitations of a quantum field theory around a thermal state |ω⟩. Since |ω⟩ is a KMS state of the conventional hamiltonian time evolution, it follows that the thermodynamical time defined by the modular flow of |ω⟩ is precisely the physical time of non relativistic physics.
==endquote==

There is one other supporting bit of evidence which I find cogent and which they do not even include in their list. This is the uniqueness. Have to go, back shortly.

 

[marcus]

The way I see the uniqueness point is that once you have a C*-algebra A of all your observables, and a (positive trace-class) state functional ρ representing what you think you know about the world, then there is only one time evolution that you can define from the given (A,ρ) without making any further choices.

It is the natural canonical flow of time, given the world as we know it. We know the world as a bunch A of observables/measurements that are interrelated by adding subtracting multiplying etc. that is what an algebra is. And as a probabilistic functional ρ defined on that algebra, representing our information about what values those observables take. Given those two things (A,ρ) there is a unique flow defined on the algebra, taking each observable along to subsequent versions of itself.

I'm not entirely clear or comfortable with this, but it seems reasonable to try thinking along those lines. GR is timeless, QM says what counts are the measurements, we take those hints seriously and we say that the world exists (timelessly) as an algebra of observations A. Specifically a C* algebra (abstract form of von Neumann algebra) and such an algebra has a natural idea of state defined on it representing what we think we know and expect. So this pair (A, ρ) is the world. And that pair gives you a unique time flow. The one-parameter group of automorphisms on the algebra that takes any observable to the next, to the next, to the next. There is a natural built-in way to make the observables flow. That's time. Or one idea of it.

 

[marcus]

I think perhaps the essential thing about time-ordering is it makes a difference which measurement you do first. All these differences are encoded in the non-commutativity of the algebra of observations, so time-orderings are already latent in the algebra. We shouldn't be too surprised that an algebra of observables, helped by a timeless state function to define the world, would have a preferred flow.

 

[Paulibus]

...it seems reasonable to try thinking along those lines. GR is timeless, QM says what counts are the measurements, we take those hints seriously and we say that the world exists (timelessly) as an algebra of observations A. Specifically a C* algebra (abstract form of von Neumann algebra) and such an algebra has a natural idea of state defined on it representing what we think we know and expect. So this pair (A, ρ) is the world. And that pair gives you a unique time flow. The one-parameter group of automorphisms on the algebra that takes any observable to the next, to the next, to the next. There is a natural built-in way to make the observables flow. That's time. Or one idea of it.

Sounds sensible to me, put this way (barring C* algebra; new to me). But for a long time I've thought of time as a "dimension", one of four absolutely mysterious and fundamental such items in the "Universe Lucky Packet" that when unwrapped, started stuff off with a singular bang, or a softer bounce, neither of which we understand properly yet.

What are simple folk like me to think if Connes and Rovelli's approach turns out to be right?

Time is part of the flexible spacetime geometry responsible for gravity. Time curves as one of the four dimensions described by the Riemann tensor. So I've understood. Or is it ct, which dimensionally is space-like, that curves? Or perhaps just c that changes from place to place, so bending light around galaxies? Strange thoughts pass by.

 

[marcus]

... it seems reasonable to try thinking along those lines. GR is timeless, QM says what counts are the measurements, we take those hints seriously and we say that the world exists (timelessly) as an algebra of observations A. Specifically a C* algebra (abstract form of von Neumann algebra) and such an algebra has a natural idea of state defined on it representing what we think we know and expect. So this pair (A, ρ) is the world. And that pair gives you a unique time flow. The one-parameter group of automorphisms on the algebra that takes any observable to the next, to the next, to the next. There is a natural built-in way to make the observables flow. That's time. Or one idea of it.

Sounds sensible to me, put this way (barring C* algebra; new to me). But for a long time I've thought of time as a "dimension", one of four absolutely mysterious and fundamental such items in the "Universe Lucky Packet" that when unwrapped, started stuff off with a singular bang, or a softer bounce, neither of which we understand properly yet.

What are simple folk like [us all] to think if Connes and Rovelli's approach turns out to be right?

Time is part of the flexible spacetime geometry responsible for gravity. Time curves as one of the four dimensions described by the Riemann tensor. So I've understood. Or is it ct, which dimensionally is space-like, that curves? Or perhaps just c that changes from place to place, so bending light around galaxies? Strange thoughts pass by.

I imagine we're all rather much in the same fix as you describe, or at least I am. Geometrizing time as a pseudo-spatial dimension works so well! It's become part of how we think.

And it may be right! This approach proposed by Connes and Rovelli may be wrong. It is just an hypothesis which they argue should be thought through.

You put the mental dilemma very precisely---and the business of light bending around galaxies and clusters of galaxies is very beautiful. As well as being essential to observational cosmology nowadays---they depend on the magnification produced by lensing. The whole business of 4D geometry is compellingly beautiful...

It's a challenge to hold two contradictory ways of thinking, at least for a while, in one's head. I can't say it any better than you just did.

 

[marcus]

Paulibus, I don't want to raise false hopes. But I am beginning to find thermal time understandable and (for me) it comes of reading pages 16 and 17 of the Connes Rovelli paper. I'm comfortable with ordinary operator algebra on ordinary hilbertspace. this is undergrad math major level. there are many steps of algebra but you just have to go thru them patiently. IFF you also are comfortable it might work for you. Then you wouldn't have to feel mystified by it. Maybe in a day or two I will try to make INTUITIVE sense of the 20 or so steps of algebra on those pages. In case you don't like vectors and matrices and would find it tedious to work thru.

What it does is go thru the NON relativistic case where there is already a hamiltonian and it shows that the jazzy new thermal time flow RECOVERS the conventional hamiltonian time evolution. IOW the jazzy new idea of time specializes down to the right thing---it is a valid generalization of what we already think of as time-evolution flow.

So for me, the pages 16 and 17 are the core of the Connes Rovelli paper and at least for now the core and the whole business. It's not so unintuitive now.

 

[marcus]

here ( gr-qc/9406019 pages 16,17) we have a conventional situation with hilbertspace H and hamiltonian H. Of course we have the algebra A of observables, the operators on the HAnd the quantum state ω is a density matrix: that's what we want to study and finesse a time evolution from. And of course we have the algebra A of observables, the operators on the H

Imagine it in positive diagonal form, we'll need its square root k_o = ω^1/2.
Now the trick is the "GNS construction" which is like obviously a bunch of matrices can themselves form a vectorspace! You can add two and get another matrix. You can multiply by a scalar.

If we want to think of k_o as an operator we write it k_o. If we want to think of it as a vector in a vectorspace where the vectors are actually matrices we write it | k_o>

This (which appears kind of dumb at first sight) is actually the cleverest thing on the whole two pages. I've seen this in math before, something that looks utterly pointless turns out not to be. It is so pointless that it takes clever people like Gelfand Naimark Segal to think of it. We can make a mixed state (a matrix) into a pure state (a vector) in a "higher" hilbertspace this way.

Now all the operators A which used to act on H can act on vectors like k_o, call a generic such "vector" k. The key analytic condition is that k k* have finite trace (equation 30).
Define the new action of any operator A by
A |k> = |Ak>
It's obvious. k WAS an operator, so A by k is another operator so |Ak> is a vector. It is the vector which |k> gets mapped to.

So now we can do something a little interesting. We can define the set
{ A |k_o> for all A}
I think I've seen that called the "folium" of |k_o>. Anyway the set of all vectors that |k_o> gets mapped to, using all possible operators in the algebra. that is a vectorspace and it has |k_o> as a "cyclic" vector. I don't like the term "cyclic" for this but it has historical roots and is conventional. Call it seed or generator if you want. It generates the whole vectorspace when operated on by the algebra A. Above all algebra requires patience, now we are at the top of page 17, where things begin to happen. I'll continue later.

|k_o> is going to play the role of a "thermal vacuum state". the vanilla state from which the thermal time arises. the authors say a little about it at the top of page 17 that could provide extra intuition. But I'll continue this later.

 

[rjbeery]

Here's my two cents;

IF:
1) All observers share a reality
and
2) There is some definition of "state" or "now" describing physical existence which extends beyond those observers (which utilizes the concept of Time in any way)
and
3) We consider what Relativity does to our usual definitions of Time

THEN:
Applying the definition of #2 for all observers in #1, taking #3 into consideration, we conclude that the entirety of the history/future of the Universe eternally exists as a physical representation in what is literally a static 4D Block Universe; the flow of time and the concept of becoming are emergent properties of being sentient.

 

[marcus]

Hi RJ, block universe was discussed some earlier in posts #50 and 52 of this thread. Here is a link to post #52
https://www.physicsforums.com/showthread.php?p=4140332#post4140332

 

[rjbeery]

Hi RJ, block universe was discussed some earlier in posts #50 and 52 of this thread. Here is a link to post #52
https://www.physicsforums.com/showthread.php?p=4140332#post4140332

Ahh, thanks marcus. I was too lazy to work through 4 pages of comments. Also, there wasn't much mention of Block Universe that I could see (even in your referenced posts).

A block universalist might say I can't make a decision as the future is already present in some sense. But he/she seems unable to say how many essays that eventually will have been read by me

This is because an observer in the "now" has access to information which has been stored in some manner accessible to the observer in the current state; this information gets stored via entropic processes. What this means is that entropy doesn't increase with time, but rather information is available for storage as entropy is increased. Any observer in the "now" might naturally conclude that states to which he has information (i.e. the past) are of a different character than those states which reveal how many essays you have or will read, but that isn't the case (IMHO).

 

[marcus]

If one accepts GR then the decay of a radioactive nucleus will affect the geometry of the universe (as the distribution of mass always does, in GR) and according to QM the time when the nucleus will decay has not yet been determined (unless you postulate "hidden variables") and cannot in principle be predicted. Thus the geometry (the metric) of the universe is not predetermined.
So if one accepts ordinary physics (GR and QM) there can be no block universe.

George Ellis put this amusingly in his FQXi essay that I linked to above. He described a massive rocket powered sled zooming back and forth along a track under the control of a radioactive decay (Schrödinger Cat) mechanism that tells it when to go east and when to go west.

In ordinary GR, the "coordinate time" is not physically meaningful. Not measurable. One needs to break general covariance by introducing an observer, or e.g. a uniformly distributed gas of particles, as is done in cosmology.

A good discussion of the status of time in modern physics is provided in a few pages of the Rovelli essay that Naty linked to earlier in this thread. It is called "Unfinished Revolution" and was posted on arxiv in 2006 or 2007. Google "rovelli revolution" and you should get it. It is wide audience. I don't personally know of any working physicist who takes the traditional block U idea seriously. The prevailing question is where do we go from here.
=========================

What I've been gradually working thru, in the past few posts, is the idea that there IS an intrinsic time-flow on the space of observables, which arises from specifying a STATE ω of the universe. This is akin to what Barbour has been saying: time is certainly real but not as a pseudo-spatial dimension or as something fundamental. It arises from more basic stuff. In this case it arises as a one-parameter group of transformations of the space of observables. What I'm trying to understand better is how this socalled "modular group" α_t or "flow" arises from specifying the algebra of observables A and the state ω. The formalism we are working with here is compatible with BOTH QM and GR, it is used to delve into "general covariant statistical quantum mechanics" which definitely seems interesting.

 

[marcus]

Sources
http://arxiv.org/abs/gr-qc/9406019 pages 16,17
WikiP: "Gelfand-Naimark-Segal construction"
WikiP: "KMS state"
WikiP: "Tomita-Takesaki theory" (not so good I think, but at least article exists)
WikiP: "Polar decomposition" (article exists, I haven't used or evaluated it)

The basic situation that general covariant quantum physics deals with is an algebra A of observables. That's the world. After all QM is about making measurements/observations. And a temporal flow α_t is a oneparameter group of automorphisms of that algebra.

automorphism means it maps an observable A onto another observable α_tA which you can think of as making the same observation but "t timeunits later".
oneparameter group means that doing α_s and then doing α_t has the same flow effect as doing α_s+t. the parameter t is a real number.
And automorphism means it preserves the algebra operations, it is linear etc etc.

Observables are in fact an algebra because you can add and multiply observables together to predict other observables or to find how they correlate with each other.

The statistical quantum state of the world is represented by a positive functional on the algebra which we can think of as a density matrix ω and its value on an observable A can be written either as ω(A) or as trace(Aω). The state ω is what gives the observables their expectation values and their correlations.

A nice thing about a density matrix ω is that it has a square root ω^1/2. Think of writing it as a diagonal matrix with all positive entries down the diagonal, and taking the square root of each entry.

More about this later. From an algebra A and a state of the world ω it is possible to derive a unique flow α_t on the algebra. Taking each observable A into a progression of "later" evolved observables α_tA, for every timeparameter number t.

 

[rjbeery]

If one accepts GR then the decay of a radioactive nucleus will affect the geometry of the universe (as the distribution of mass always does, in GR) and according to QM the time when the nucleus will decay has not yet been determined (unless you postulate "hidden variables") and cannot in principle be predicted. Thus the geometry (the metric) of the universe is not predetermined.
So if one accepts ordinary physics (GR and QM) there can be no block universe.

George Ellis put this amusingly in his FQXi essay that I linked to above. He described a massive rocket powered sled zooming back and forth along a track under the control of a radioactive decay (Schrödinger Cat) mechanism that tells it when to go east and when to go west.

The hidden variable problem goes away in a Block Universe; nothing remains to be determined because it already exists. The unknown variables are hidden from us locally but reside local to the respective particles in the future. "When" a nucleus decays relative to an observer is a problem of information availability, not some intrinsic Universal randomness.

I emboldened the words in your post which show that we have problems thinking without a "flow of time". Technically, neither GR nor QM have any mechanism for a FLOW of time whatsoever. They are completely time-symmetric theories, yet you are suggesting that one direction is preferred over the other. The time parameter is only a marker along the 4D Block Universe in my view.

 

[marcus]

nothing remains to be determined because it already exists...

You are on your own, RJ. Working physicists assume QM. Your picture is incompatible with QM. I've tried explaining this to you but it doesn't seem to get across.

How about you read a few pages of Rovelli's wide-audience essay Unfinished Revolution, that I suggested you look at earlier?
Section 1.2 "Time" is less than a page long. It starts at the bottom of page 3 and covers part of page 4.

Google "rovelli unfinished revolution" and you get the arxiv version: http://arxiv.org/abs/gr-qc/0604045

 

[rjbeery]

You are on your own, RJ. Working physicists assume QM. Your picture is incompatible with QM. I've tried explaining this to you but it doesn't seem to get across.

How about you read a few pages of Rovelli's wide-audience essay Unfinished Revolution, that I suggested you look at earlier?
Section 1.2 "Time" is less than a page long. It starts at the bottom of page 3 and covers part of page 4.

Google "rovelli unfinished revolution" and you get the arxiv version: http://arxiv.org/abs/gr-qc/0604045

I will, and I will also read George Ellis' FQXi essay but I could not find your link to it. I assume I can Google it without much problem. Regardless, I'm not speaking from a position of naivete; QM is not incompatible with Block Time and I'd be happy to discuss specifically why you think this (other than referencing others' papers).

 

[marcus]

I will, and I will also read George Ellis' FQXi essay but I could not find your link to it. I assume I can Google it without much problem. Regardless, I'm not speaking from a position of naivete; QM is not incompatible with Block Time and I'd be happy to discuss specifically why you think this (other than referencing others' papers).

I gave the link in the post I pointed you to:
http://fqxi.org/community/essay/winners/2008.1
go there, scroll down to "second community prize", there is Ellis's abstract and a link to the PDF.

I already explained the incompatibility using the same example Ellis did, radioactive decay changes the distribution of mass---Ellis's rocket sled just makes it more colorful.

 

[marcus]

I need to plug ahead with how time (as a flow on the observable algebra) emerges. For continuity, here are the essentials of the last post:

Given an algebra A of observables and a state of the world ω it is possible to derive a unique flow α_t on the algebra. Taking each observable A into a progression of "later" evolved observables α_tA, for every timeparameter number t.

A nice thing is that this "thermal time" construct RECOVERS ordinary time when we start with a conventional Hamiltonian H and hilbertspace H. this is what Connes Rovelli show on pages 16 and 17 of their paper. See link:
Sources
http://arxiv.org/abs/gr-qc/9406019 pages 16,17
WikiP: "Gelfand-Naimark-Segal construction"
WikiP: "KMS state"
WikiP: "Tomita-Takesaki theory" (not so good I think, but at least article exists)
WikiP: "Polar decomposition" (article exists, I haven't used or evaluated it)

The basic situation that general covariant quantum physics deals with is an algebra A of observables. That's the world. After all QM is about making measurements/observations. And a temporal flow α_t is a oneparameter group of automorphisms of that algebra.

automorphism means it maps an observable A onto another observable α_tA which you can think of as making the same observation but "t timeunits later".
oneparameter group means that doing α_s and then doing α_t has the same flow effect as doing α_s+t. the parameter t is a real number.
And automorphism means it preserves the algebra operations, it is linear etc etc.

Observables are in fact an algebra because you can add and multiply observables together to predict other observables or to find how they correlate with each other.

The statistical quantum state of the world is represented by a positive functional on the algebra which we can think of as a density matrix ω and its value on an observable A can be written either as ω(A) or as trace(Aω). The state ω is what gives the observables their expectation values and their correlations.

A nice thing about a density matrix ω is that it has a square root ω^1/2. Think of writing it as a diagonal matrix with all positive entries down the diagonal, and taking the square root of each entry.

The observable algebra (think matrices) IS a vector space. You can add matrices entry-wise and so on. The celebrated GNS construction makes a vectorspace out of |ω^1/2⟩ together with all the other density matrices and their like which you can get by applying elements A of the algebra to that root vector. that is called the FOLIUM of ω
|Aω^1/2⟩ for all A in A
It is a hilbertspace. The special good things about this hilbertspace (they give it a name, K) is that the algebra acts on it, after all it was MADE by having the algebra act on the single root vector |ω^1/2⟩ and seeing what you get, and the other thing is just that: it has what is called a "cyclic vector", a root or generator: the whole hilbertspace is made by having the algebra of operators act on that one |ω^1/2⟩, as we have seen.

ω(A) = ⟨ω^1/2|A|ω^1/2⟩

Now what C&R do is they construct an operator, by giving its polar decomposition. This is what happens on page 17. And the operator obtained by putting the polar decomp. together has the effect of doing a matrix transpose, or mapping A → A*. They call this operator S.

SA |ω^1/2⟩ = A* |ω^1/2⟩

There is some intuition behind this (there is already something about it on page 7 but I'm looking at page 17). It is like swapping creation and annihilation operators. Undoing whatever an operator does. Partly it is like getting your hands on what is implicitly an infinitesimal time-step, except there is no time yet. More importantly, transpose is tantamount to commuting
(AB)* = B*A*
So if we can just take the anti-unitary part out of the picture it's almost like swapping order: AB → BA. Yes very handwavy, but there is some underlying intuition, will get back to this.

We are going to build from that swapping or reversal operator S. In particular we will use the positive self-adjoint part of the polar decomposition. More about this later.