Julian Barbour on does time exist

marcus

What George Ellis (one of the world's leading cosmologists and co-author with Stephen Hawking of The Large Scale Structure of Space-Tme) says here is at once so clear and so striking that perhaps it deserves emphasis:
It follows that the existence of our specific Galaxy, let alone the planet Earth, was not uniquely determined by initial data in the very early universe.

marcus

I imagine that by now most people who might read this thread have figured out why the 4D block universe of General Relativity is incompatible with quantum uncertainty. The incompatibility is across the board---all common mainstream interpretations/formulations of QM for which uncertainty is an underlying bedrock principle. So perhaps I don't have to provide explanation (beyond what we already have in the quotes from George Ellis. But here's an excerpt from an essay by Carlo Rovelli that explains the point very clearly. This from page 4 of Chapter 1 of the 2009 book Approaches to Quantum Gravity, D. Oriti ed. published by Cambridge University Press ( http://arxiv.org/abs/gr-qc/0604045 )

==quote Chapter 1 of Approaches to Quantum Gravity==
...
In classical GR, indeed, the notion of time differs strongly from the one used in the special-relativistic context. Before special relativity, one assumed that there is a universal physical variable t, measured by clocks, such that all physical phenomena can be described in terms of evolution equations in the independent variable t. In special relativity, this notion of time is weakened. Clocks do not measure a universal time variable, but only the proper time elapsed along inertial trajectories. If we fix a Lorentz frame, nevertheless, we can still describe all physical phenomena in terms of evolution equations in the independent variable x₀, even though this description hides the covariance of the system.

In general relativity, when we describe the dynamics of the gravitational field (not to be confused with the dynamics of matter in a given gravitational field), there is no external time variable that can play the role of observable independent evolution variable. The field equations are written in terms of an evolution parameter, which is the time coordinate x₀, but this coordinate, does not correspond to anything directly observable. The proper time τ along spacetime trajectories cannot be used as an independent variable either, as τ is a complicated non-local function of the gravitational field itself. Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable. This does not mean that GR lacks predictivity. Simply put, what GR predicts are relations between (partial) observables, which in general cannot be represented as the evolution of dependent variables on a preferred independent time variable.

This weakening of the notion of time in classical GR is rarely emphasized: After all, in classical GR we may disregard the full dynamical structure of the theory and consider only individual solutions of its equations of motion. A single solution of the GR equations of motion determines “a spacetime”, where a notion of proper time is associated to each timelike worldline.

But in the quantum context a single solution of the dynamical equation is like a single “trajectory” of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues. Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory.
==endquote==

Having a block universe with some definite course of geometry would be like a trajectory.
A trajectory is a classical idea, it is not physical. We do not have continuous smooth trajectories, we have slits and detectors that is to say a finite number of measurements made along the way.

There are an infinite number of possible observations/measurements of the path of a particle or geometry of the universe. But nature does not let herself be pinned down, we can only choose a finite number of them to make. Moreover each measurement may have a range of possible values and involve uncertainty.

I suspect this is why the smooth manifold--the continuum model of the physical world including space-time--is apt to be replaced by something more like an algebra of observables, each one a package of uncertainty with its range of possible values. We see this replacement model being tentatively tried out by researchers. Time is then no pseudo-spatial "dimension" but a flow defined on the algebra.

RUTA

The problem described by Ellis, per psi-epistemism, simply reflects our inability to know the stress-energy tensor (SET) for the whole of spacetime. You need the SET to compute "a spacetime" solution (metric g) as Rovelli points out. [This is more obvious in the graphical Regge calculus version of GR where one must find a SET and metric g on every link of the graph that satisfies the graphical counterpart to Einstein's Eqns (EE).] This doesn't mean spacetime is not determined, only that we can't determine it. I don't know why that bothers him any more than the fact that we can't know the geometry of our past lightcone uniquely (per his own work in the 1980s). Does that mean the geometry of our past lightcone is not fixed? Of course not.

Rovelli's problem is averted by finding a quantum theory of gravity that doesn't follow canonical quantization. For example, one could rather seek a theory in which one computes amplitudes for spatiotemporal units ("processes" in the language of Hiley) via the path integral approach or via an algebra of process a la Hiley. In this approach, one understands a particular SET and g on the graph of Regge calculus follow as an average of many fundamental building blocks. This can be done for the Schrodinger and Dirac eqns as shown by Hiley. Of course, these formalisms assume globally flat spacetimes, so the question becomes, how do we get spacetime curvature? We postulate that can be done by modified Regge calculus whereby large graphical links are possible. We used this approach to show a flat, matter-dominated GR solution (Einstein-deSitter) can match the type IA supernova data as well as the concordance model (Einstein-deSitter + lambda) without accelerating expansion (no lambda). You can read published presentations of these ideas in the following papers:

“Being, Becoming and the Undivided Universe: A Dialogue between Relational Blockworld and the Implicate Order Concerning the Unification of Relativity and Quantum Theory,” Michael Silberstein, W.M. Stuckey & Timothy McDevitt. To appear in a Hiley Festschrift in Foundations of Physics. http://arxiv.org/abs/1108.2261. Appeared Online First 4 May 2012.

“Modified Regge Calculus as an Explanation of Dark Energy,” W.M. Stuckey, Timothy McDevitt & Michael Silberstein, Classical & Quantum Gravity 29 055015 (2012). http://arxiv.org/abs/1110.3973.

“Explaining the Supernova Data without Accelerating Expansion,” W.M. Stuckey, Timothy McDevitt & Michael Silberstein. Honorable Mention in the Gravity Research Foundation 2012 Awards for Essays on Gravitation, May 2012. International Journal of Modern Physics D 21, No. 11, 1242021 (2012)
http://users.etown.edu/s/STUCKEYM/GRFessay2012.pdf

So while I agree that some modification of GR is needed to accommodate quantum physics, this does not entail abandoning blockworld. On the contrary, BW is necessary in these approaches to quantum gravity.

marcus

Ruta, thanks for contributing the references to your papers with Silberstein and McDevitt! It's interesting that you are able to modify General Relativity in a way that gets rid of accelerating expansion, saves (at least certain particular versions of) blockworld, and unifies your version of Relativity with Quantum theory in a highly original way!

I suspect you and I would definitely agree on at least one point: that how physics eventually comes to understand TIME and the problems associated with it will depend very much on what quantum theory of space-time geometry is eventually arrived at and accepted.

To be successful quantum theory of time will require a quantum theory of space AND time. At least this seems to be what you and your co-authors are striving to construct.

A propos of Basil Hiley, I recently started a thread on a paper of his that just appeared, but the thread elicited little interest. You may not have noticed it. I'll get a link.
http://www.physicsforums.com/showthread.php?t=651454
One of your papers with Silberstein and McDevitt was referred to in the thread, I don't recall in what connection--it may not have been clear why.

Paulibus

I guess that if one lets h go to zero, one should recover a continuous model. What happens to time as "a flow defined on the algebra" in that case? I suppose that an algebra of "states" abstracted as vectors in Hilbert space then ceases to be non-commutative. What price a quantum mechanical interpretation of time then? (if "then" has meaning!)

And is it possible that the Hubble expansion would then vanish, because "thermal time' is somehow connected with such change?

Perhaps RUTA's noting that: is useful here. It seems to imply that what is important to us is only that which we can determine or describe. But that the sub-quantum world nevertheless somehow exists. Including an algebra with a flow, and time?

marcus

Hi Paulibus, that's an astute question! It might be good to keep in mind that the TT hypothesis is not, in and of itself, a theory of QG (which should have a classical limit) but I would say rather that it is a replacement for the differential manifold that has been our basic way of modeling the world. Even though at this point it may seem contradictory, the Friedmann cosmology model used by essentially all cosmologists is CLASSICAL and was reportedly already achieved in Connes Rovelli reference [11]. Apparently when a Friedmann universe was set up in the TT (algebra+state) framework, Friedmann time was somehow recovered from the flow! Since this is just hearsay, I should go back and examine reference [11], to be sure.Here's the Connes Rovelli reference:
[11] C. Rovelli, “The Statistical state of the universe,” Class. Quant. Grav. 10 (1993) 1567-1578.
This 12-page article was published in the same issue with an 18-page article:
C. Rovelli, “Statistical mechanics of gravity and the thermodynamical origin of time,” Class. Quant. Grav. 10 (1993) 1549–1566.
Neither seems to be on the arxiv.

I have not been able to find online copies and so may have to visit the stacks at the Physics Department library here.

EDIT: YAY! I found an online copy.
http://siba.unipv.it/fisica/articoli....1567-1568.pdf

marcus

It's great that earlier article is available online! Thanks to someone at University of Pavia. I printed a copy immediately---in some cases availability is sporadic, so just to make sure. The paper is historically important and it would be nice if it were on arxiv. Here is the abstract:
http://siba.unipv.it/fisica/articoli....1567-1568.pdf
==quote==
Class. Quantum Grav. 10 (1993) 1567-1578.
The statistical state of the universe
Carlo Rovelli

Abstract. The idea that the cosmological state of the universe can be described in terms of a statistical state is discussed. A dynamical model with infinite degrees of freedom that describes a Robertson-Walker universe with non-homogeneous electromagnetic radiation is defined. Its statistical mechanics is studied by using the covariant statistical theory developed in a companion paper. A simple statistical state that represents the cosmic background radiation is constructed. The properties of this state support the general theory; in particular, the idea, introduced in the companion paper, that a preferred time variable, denoted thermodynamical time, is singled out by the statistical state can be tested within this model. The-thermodynamical time is computed and shown to agree with the standard Robertson-Walker time. In addition, an application of the general theory to a simple special relativistic system, and a proposal for an application to full general relativity are also presented. The relevance of this application for the physics of the very early universe is discussed.
==endquote==

Here's an excerpt from the introduction:

In this paper, we discuss the statistical mechanics of a dynamical model that represents the universe filled with an arbitrary non-homogeneous electromagnetic field. The purpose of this investigation is twofold. In the first place, we wish to introduce the idea of a statistical description of the state of the universe. In the second place, the model is presented as a first application of the general theory of covariant statistical thermodynamics that has been introduced in a companion paper...

An excerpt from the conclusion section:

In addition, we have discussed the application of the general theory to a simple special relativistic system, and we have introduced a perturhative expansion for computing an exact statistical state of the full Einstein theory that should represent a Robertson-Walker universe filled with gravitational radiation. We expect this model to be relevant for the description of the thermodynamics of the very early universe.

We conclude with a general comment about thc definition of the thermodynamical time. Thermodynamical time is an extension of the non-relativistic Hamiltonian time, which is defined whenever the system is in equilibrium. The thermodynamical time agrees with the natural definition of time in several physical contexts in which a preferred time exists. In particular, we have considered the following cases:

• in non-relativistic systems, if the system is in a Gibbs equilibrium state, the thermodynamical time is the standard Hamiltonian time;
  
• in special relativistic systems, the thermodynamical time is the Lorentz time of the specific Lorentz frame in which the heat bath is at rest;
  
• in the cosmological example considered, the thermodynamical time determined by the physical cosmic background radiation is the Robertson-Walker proper time.

Our conjecture is that in the general covariant universe in which we live, the thermodynamical time selected by (3) is the natural variable to which the notion of time may be associated.

marcus

I think it's important to grasp what Rovelli says here, regarding time in General Relativity and the further weakening of the time concept that must accompany any quantum theory encompassing GR, on basic grounds regardless of what theory one considers. First one needs to appreciate this fact, repeated below in larger context:

" Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable."

This is best understood in context---it is from page 4 of Chapter 1 of the 2009 book Approaches to Quantum Gravity, D. Oriti ed. published by Cambridge University Press ( http://arxiv.org/abs/gr-qc/0604045 )

==quote Chapter 1 of Approaches to Quantum Gravity==
... Before special relativity, one assumed that there is a universal physical variable t, measured by clocks, such that all physical phenomena can be described in terms of evolution equations in the independent variable t. In special relativity, this notion of time is weakened. Clocks do not measure a universal time variable, but only the proper time elapsed along inertial trajectories. If we fix a Lorentz frame, nevertheless, we can still describe all physical phenomena in terms of evolution equations in the independent variable x₀, even though this description hides the covariance of the system.

In general relativity, when we describe the dynamics of the gravitational field (not to be confused with the dynamics of matter in a given gravitational field), there is no external time variable that can play the role of observable independent evolution variable. The field equations are written in terms of an evolution parameter, which is the time coordinate x₀, but this coordinate, does not correspond to anything directly observable. The proper time τ along spacetime trajectories cannot be used as an independent variable either, as τ is a complicated non-local function of the gravitational field itself. Therefore, properly speaking, GR does not admit a description as a system evolving in terms of an observable time variable. This does not mean that GR lacks predictivity. Simply put, what GR predicts are relations between (partial) observables, which in general cannot be represented as the evolution of dependent variables on a preferred independent time variable.

This weakening of the notion of time in classical GR is rarely emphasized: After all, in classical GR we may disregard the full dynamical structure of the theory and consider only individual solutions of its equations of motion. A single solution of the GR equations of motion determines “a spacetime”, where a notion of proper time is associated to each timelike worldline.

But in the quantum context a single solution of the dynamical equation is like a single “trajectory” of a quantum particle: in quantum theory there are no physical individual trajectories: there are only transition probabilities between observable eigenvalues. Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime, in the same sense in which the motion of a quantum electron cannot be described in terms of a single trajectory.
==endquote==

So the problem is on two levels, classical and quantum. Already at the classical level
there is no observable independent time variable that can be used to describe the evolution of a (general) relativistic system.

And at the quantum level the problem is even more severe, since one cannot realistically assume some fixed metric solution--i.e. a geometric "trajectory".

marcus

This is the log-jam which the (M, ω) formulation breaks thru. I'm using the notation from the Princeton Companion to Mathematics article which I quoted back few posts. M is the *-algebra of measurements/observations and ω: M→ℂ is a positive linear function defined on M, called the "state". It summarizes what we think we know--including statistical uncertainties--about the means variances and correlations of the elements of M. Physical theories and constants boil down to correlations among measurements. Uncertainty about the precise values of constants boils down to variances--all that is comprised in the state ω. Along with observational data and predictions.

The Companion article explains how a unique idea of TIME arises from (M, ω) as a one-parameter subgroup or flow defined on M, which in this thread I've been writing α_t: M→M.

marcus

I should gather together some of the main source links for thermal time (= Tomita flow time).
This is to page 517 of the Princeton Companion to Mathematics
http://books.google.com/books?id=ZOf...20math&f=false
It's a nice clear concise exposition of the Tomita flow defined by a state on a *-algebra. For notation see the previous post: #128.

Here's the article by Alain Connes and Carlo Rovelli:
http://arxiv.org/abs/gr-qc/9406019

Here is Chapter 1 of Approaches to Quantum Gravity (D. Oriti ed.)
http://arxiv.org/abs/gr-qc/0604045
Page 4 has a clear account of the progressive weakening of the time idea in manifold-based physics, which I just quoted a couple of posts back. I see the inadequacy of time in manifold-based classical and quantum relativity as one of the primary motivations for the thermal time idea.

The seminal 1993 paper, The Statistical State of the Universe
http://siba.unipv.it/fisica/articoli....1567-1568.pdf
This shows how thermal time recovers conventional time in several interesting contexts.

Here's a recent paper where thermal time is used in approaches to general relativistic statistical mechanics and general covariant statistical QM.
http://arxiv.org/abs/1209.0065

It can be interesting to compare the global time defined by the flow to a local observer's time. The ratio between the two can be physically meaningful.
http://arxiv.org/abs/1005.2985

Jeff Morton blog on Tomita flow time (with John Baez comment):
http://theoreticalatlas.wordpress.co...d-tomita-flow/

Wide audience essays--the FQXi "nature of time" contest winners:
http://fqxi.org/community/essay/winners/2008.1
Barbour: http://arxiv.org/abs/0903.3489
Rovelli: http://arxiv.org/abs/0903.3832
Ellis: http://arxiv.org/abs/0812.0240

Paulibus

The Rovelli-Smerlak reference (#6 of your list above) makes me wonder if thermal time might be distinguished from ordinary time experimentally by folk familiar with isotope enrichment via the centrifuge method. Could high centrifuge accelerations, combined with cryogenic temperatures, perhaps amplify the fractional difference between the two Times sufficently to alleviate the pesky 1/c^2 factor?

Some such connection between mathematical ratiocination and observation might also help to dissipate the frustration of theorists in general, engendered by many years of sterile string theory.

marcus

That's a constructive line of questioning and I got intrigued thinking about it and while looking thru Smerlak's recent papers I found a VIMEO of a talk he gave last year about thermal time. It was interesting to see the person himself in action, and it helped round out how I see thermal time because some of the speaker's personal view of it comes across. A propose, he said in the talk (as I recall) that with merely *earth gravity* (i.e. low curvature regime) the difference would too small to measure, and he mentioned the c² factor, as you did.

But that was just a passing remark, I wouldn't take it terribly seriously. There could be other regimes in which it is measurable. Putting that issue aside for the moment, I think you might enjoy the talk. Unfortunately it cuts off after 15 minutes. So we don't get the last 10 or 15 minutes of his presentation. Anyway, just in case you're interested, here's the link.
http://vimeo.com/33363491
It's from a 2-day workshop March 2011 at Nice, France.

marcus

As regards observational tests of LQG, I think the main focus is on higher resolution maps of the microwave background. These should show traces of a bounce and a brief pre-inflationary era which have been worked out. Much of the relevant early universe phenomenology literature can be accessed simply by a search like this:

marcus

As regards observational tests of LQG, I think the main focus now is on higher resolution maps of the microwave background. These should show traces of a bounce and a brief pre-inflationary era which have been worked out. Much of the relevant early universe phenomenology literature can be accessed simply by a search like this:
http://inspirehep.net/search?ln=en&a...=50&sc=0&of=hb
That gets 428 quantum cosmology papers (2009 to present) about half of which are loop. And among them are quite a few phenomenology---about observable effects---though you have to look for them.

There's a more selective link that is sometimes slow. I'll get that in a moment.
http://www-library.desy.de/cgi-bin/s...tecount%28d%29
It just now timed out on me twice and then worked the third time. It came up with 66 recent Loop cosmology papers that are more consistently oriented towards observational testing.

I would very much like to see the Loop cosmology bounce modeled using Tomita flow time.

detective

....hello all...a most fascination take on time, and for simplicity's sake the theory of time will give me endless hours of enjoyable argy bargy...it's the mathematics that seems to have to creep in ...and we all know that mathematics are the tools for proving a theory, but once again time will confound us on that account as there is no need to ''prove'' its existence....it will continue to pervade our lives and stridently make us have to grapple with it.....seeya

marcus

Hi Tec, I would certainly agree with what I quote from your post here but that doesn't seem to be the issue. I think everybody in the thread would go along with the idea that time is real and vitally important---both in physics and in our everyday experience.

The phrase "does time exist?" is just a way of getting attention---it's not a useful way to frame the discussion---not really what we're talking about.

The main thing driving the discussion seems to be dissatisfaction with the (outmoded, I believe) way of imagining time mathematically as an "axis" i.e. as a pseudo-spatial dimension.

The title of the Capetown conference, held this week, was Do we need a physics of 'passage'? IOW instead of a static picture with time as an AXIS (analogous to spatial coordinate axes) shouldn't we develop a mathematical picture in which it is a PROCESS OF CHANGE.

For a substantial part of the last century the prevailing tendency was to geometrize time--put it on an axis--leading to a static picture in which our experience of time's passage is apt to be disregarded or explained away as merely psychological. Now the pendulum seems to be swinging the other direction (away from the static geometrization of time.)

I wouldn't disparage mathematics. The meat of the discussion here is actually about competing mathematical representations of time. Math can represent process in various ways, it's not restricted to describing location along a coordinate axis.

You might be interested to read what the organizers of the "Passage" conference wrote about it:
http://prce.hu/centre_for_time/jtf/passage.html
http://prce.hu/centre_for_time/jtf/FullProgram.pdf

In the html index page they quote some famous 19th and 20th century physicists to exemplify what they, the organizers, are NOT happy with and want to try to change. You might even like the tack they are taking.

detective

...thanks for the clarifications marcus .. could i pose this thought ....to a photon or any other massless object, time has no usefulness or relevance to their being, as their travelling at the speed of light renders time to stand still...

...when we start to include mass into the physics there is automatically a need to invoke the constant of time....but this leads us to at least two sets of rules, which is repulsive to a pure theory of time.....

....any thoughts?...i hope i'm not over simplifying things....cheers