Julian Barbour on does time exist

[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]

... 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.
...
...
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.

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.
https://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]

...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.

I guess that if one let's 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:

... This doesn't mean spacetime is not determined, only that we can't determine it...

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]

I guess that if one let's 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!)...

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.

...I should review some of the motivation. TT is general covariant which other kinds of physical time are not. And yet it agrees with regular physical time in several specialized cases.
I'll quote from post #74 earlier where these were mentioned.
https://www.physicsforums.com/showthread.php?p=4171588#post4171588
This is paraphrasing the Connes Rovelli paper which has 77 cites, over a third of which are in the past 4 years. So it is fairly well known and still probably the best source on TT definition and basics.
http://arxiv.org/abs/gr-qc/9406019
==quote post #74==
... 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.
== quote 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...
==endquote==

..

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/C/Class%20Quantum%20Grav_vol.10_1993_pp.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/C/Class%20Quantum%20Grav_vol.10_1993_pp.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=ZO...6AEwAw#v=onepage&q=minoru tomita math&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/C/Class%20Quantum%20Grav_vol.10_1993_pp.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.c...time-hamiltonians-kms-states-and-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]

The Rovelli-Smerlak reference (#6 of your list above) makes me wonder if thermal time might be distinguished from ordinary time experimentally...

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]

...
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...

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]

...
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...

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&...2y=2012&sf=&so=a&rm=citation&rg=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/spiface/find/hep/www?rawcmd=FIND+%28DK+LOOP+SPACE+AND+%28QUANTUM+GRAVITY+OR+QUANTUM+COSMOLOGY%29+%29+AND+%28GRAVITATIONAL+RADIATION+OR+PRIMORDIAL+OR+inflation+or+POWER+SPECTRUM+OR+COSMIC+BACKGROUND+RADIATION%29+AND+DATE%3E2008&FORMAT=www&SEQUENCE=citecount%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]

... as there is no need to ''prove'' its existence...it will continue to pervade our lives and stridently ...

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 traveling 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

 

[Last_Exile]

Hi Marcus,

Interesting discussion but I have to admit I don't follow the maths...

I just wanted to say that I remember reading, about 25 years ago or more, in the New Scientist magazine (that was when it was worth reading!) an article relating to the idea of the flow of time as a phase-change.

The general idea was that in a similar way to which a pond freezes over where you can imagine a layer of ice spreading across the surface so does time appear to us. By which I mean that to us the past is fixed (frozen) but the future is mutable and "now" is, of course, where that phase change occurs.

This idea seems to me to be consistent with your

mathematical picture in which it is a PROCESS OF CHANGE.

I'm sure the original article also had a relevant paper to go with it but it is probably irretrievable now.

Does this idea still sound viable as a layman interpretation of the current discussion?

 

[physicsguy13]

If time did not exsist, what would prevent everything from happening at once?

 

[julian]

"Time is nature's way to keep everything from happening at once." John Wheeler.

 

[marcus]

Thanks Julian, Paulibus, Exile, Detective and others for keeping us wondering about time!

There've been some more interesting papers posted on arxiv that bear on this, but first I want to recall a portion of the passage quoted in post #121, over ten days ago!

==quote page 4 http://arxiv.org/abs/gr-qc/0604045 ==
... 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==

IOW people have now developed some candidate QG theories, though it's still work-in-progress and as yet there's no consensus as to which nature prefers. But even before we have a fully developed preferred QG theory we can still take the lessons seriously that GR and QM teach us.

Our eventual QG theory will probably NOT be manifold-based. It will not be about the geometry of a space-time continuum---that would be a geometric *trajectory*. Instead it will be about probabilistic correlations between measurements.

That is, the basic math object is probably to be (M,ω) a star algebra and a function from M to the complex numbers that gives the expectation values and correlations, rather than a continuum with fields defined on it. M="measurements" and ω="state" (what we think we know about the both past and future, and our statistical uncertainty therewith.) Our notions of physics THEORY are encompassed in ω, as correlations among possible measurements we might make, as are our ideas about physical constants, past observations, initial conditions etc.

Now this gets into an area of QM foundations where a couple of researchers have recently posted new papers, so I want to quote their abstracts. Here are the links in case you want to check them out:
http://arxiv.org/abs/1211.3062
http://arxiv.org/abs/1212.3606

I have to go out briefly but will try to get back

 

[marcus]

I guess the main point to be made in connection with the TIME theme of this thread is that once you have specified (M, ω) i.e. the world of observations/measurements and what we think we statistically know about it, then we automatically get a standard time.

We can compare our own local observer time with that standard time. Sometimes the ratio of rates is physically meaningful.

The standard time is not a pseudo-spatial "fourth dimension", but rather it is a FLOW defined on the star algebra M. That is a one parameter group of automorphisms mapping M → M. "Time" is simply the real number parameter t that parametrizes that flow.

I want to get a quote from one of those QM foundations papers I mentioned. The one by Jeffrey Bub. Here's his introduction paragraph:

This paper is intended to be serious, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, insofar as a theory of information is essentially a theory of probabilistic correlations— not about energy being quantized in discrete lumps or quanta, not about particles being wavelike, not about the universe continually splitting into countless co-existing quasi-classical universes, with many copies of ourselves, or anything like that. To make this clear, it ...

Bub is distinguished prof at U Maryland, same place as Ted Jacobson (top-notch expert on GR and QG, and profoundly original). IMHO with people like Bub and Jacobson you take seriously what they say even if it sounds unusual, or especially if it sounds unusual. He is saying that the Hilbert space doesn't matter and all that paraphernalia, what matters is the structure of correlations. The Hilbert space is just a convenient mathematical device to represent the structure of correlations, and it's not the only possible such framework.

http://en.wikipedia.org/wiki/Jeffrey_Bub born 1942, PhD Uni London 1966, > 100 papers, several books, interpretation of qm and related.
http://carnap.umd.edu/philphysics/bub.html

 

[sshai45]

So does that mean there would be an absolute, universal time and simultaneity, and so Einstein was "wrong" in some sense? How does "only 'now' exists" jibe with "'now' depends on the observer"? How do the non-reality of the block universe and the relativity of simultaneity play with each other?

 

[Paulibus]

Marcus: your post #141 gave me a belated (by one day) birthday present.

Your reference to Jeffery Bub in his paper "Bananaworld: Quantum Mechanics for Primates", to the effect that: '...The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, insofar as a theory of information is essentially a theory of probabilistic correlations— not about energy being quantized in discrete lumps or quanta, not about particles being wavelike, not about the universe continually splitting into countless co-existing quasi-classical universes, with many copies of ourselves, or anything like that...', together with your comment that:

...with people like Bub ...you take seriously what (he) says even if it sounds unusual, or especially if it sounds unusual. He is saying that the Hilbert space doesn't matter and all that paraphernalia, what matters is the structure of correlations. The Hilbert space is just a convenient mathematical device to represent the structure of correlations, and it's not the only possible such framework.

(My emphasis), expresses, more authoritatively than I could, pretty much my sentiments. Bub's paper will compete with my Christmas reading (Bill Bryson: At Home and Paul Theroux's: St Vidia's Shadow).

Thanks for this. I plan to comment later, when I've better absorbed this gem of physics philosophy.

 

[marcus]

I'm so glad you were intrigued by Jeffrey Bub's ideas too!
I'm a bit disappointed in myself that I have a hard time following when I get into the middle of the paper. Even though he discusses in very basic terms (bananas, primates) and I'm convinced he has clear important insight, I'm still struggling. Still, it is kind of a fine Christmas present for me too!

My wife likes Bill Bryson's books, and just read "At Home". She passes savory tidbits on to me. He is a good writer and outstanding as a researcher.
==============

I also will have to comment later.

Sshai, I will get back to your comment, time permitting. I think Einstein is still right. We still have observer time. Each observer has a different time (as A.E. said) and it is interesting to compare them.
But also now we have a *state-dependent* time as well. It depends not on a particular observer but on the function omega that summarizes what we think we know (with various degrees of confidence) about the world.

Thanks to certain mathematicians of the second half of the 20th we have a chance at a new way to picture the world, as (M,ω) where M is a star algebra (observables) and omega (state) is a function from M to the complex numbers. Ordinary QFT (quantum field theory) has already been put in star algebra form. And there seems no reason that the dynamic geometry of GR should not also be put into that same form---thus combining the content of QM and GR, combining geometry with matter in a background independent or general covariant way. The (M, ω) is suitable for both.
So this (M, ω) business is quite an interesting development. Of course it is hard to get used to because such a new approach.
However in any case it does not say that "Einstein was wrong". It brings into existence yet ANOTHER version of time, which depends on the state we specify rather than on any particular observer.

And it already seems interesting to COMPARE this time with that of a given observer because it has been shown that the ratio of rates of time-passage can be physically meaningful (corresponding to a geometric temperature discovered by Tolman already in the 1930s and written about in his classic GR treatise). So it can be interesting to compare this version of time with the observer's time. It also seems to be good for other things where you can't use observer-time.

I'll try to get back to this later.

 

[marcus]

So does that mean there would be an absolute, universal time and simultaneity, and so Einstein was "wrong" in some sense? How does "only 'now' exists" jibe with "'now' depends on the observer"? How do the non-reality of the block universe and the relativity of simultaneity play with each other?

That's an intriguing question! I don't think introducing the (M,ω) picture and the corresponding state-dependent time flow on the algebra indicates that GR is wrong. But I want to take more time to answer.

Here's part of a short answer I gave to your question in post #144, with a clarifying addition in red:

Sshai, I will get back to your comment, time permitting. I think Einstein is still right. We still have observer time. Each observer has a different time (as A.E. said) and it is interesting to compare them.
But also now we have a *state-dependent* time as well. It depends not on a particular observer but on the function omega that summarizes what we think we know (with various degrees of confidence) about the world.
...a new way to picture the world, as (M,ω) where M is a star algebra (observables) and omega (state) is a function from M to the complex numbers[giving correlations between observables]. Ordinary QFT (quantum field theory) has already been put in star algebra form. And there seems no reason that the dynamic geometry of GR should not also be put into that same form---thus combining the content of QM and GR, combining geometry with matter in a background independent or general covariant way. The (M, ω) is suitable for both.
So this (M, ω) business is quite an interesting development...
However in any case it does not say that "Einstein was wrong". It brings into existence yet ANOTHER version of time, which depends on the state we specify rather than on any particular observer.
...And it already seems interesting to COMPARE this time with that of a given observer because it has been shown that the ratio of rates of time-passage can be physically meaningful ...It also seems to be good for other things where you can't use observer-time...

Basically what we are discussing in this thread are theorists' response to what is called the problem of time in GR and also in quantum GR, where the problem is broader and more formidable. Here is the best short statement I know of the problem.
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==
... 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".

There's more to say, I'll try to get back to this later. The outstanding thing to notice about the (M,ω) format (for dynamic QG geometry and simultaneously for matter QFT) is that it DOES have an independent time variable that can be used to describe the dynamical evolution of geometry+matter. The point of the quote above is that any observer's time is NOT adequate since the observer's time depends on how the geometry evolves!

When you want to describe the dynamical evolution of a system you need a time variable which is not totally at the mercy of how the system happens to evolve. So observer-time is no good.

This is why the (M,ω) formalism has come up in the context of trying to devise a fully general relativistic treatment of thermodynamics and statistical mechanics. Imagine trying to do statistical mechanics with no possibility of a physically meaningful preferred time variable. That's why it has always been done on a fixed space-time, not in a fully general covariant way. I hope to get back to this. It really interests me.

 

[Paulibus]

I've been going through Jeffery Bub's paper that Marcus pointed to in his #141 post (http://arxiv.org/abs/1211.3062). It's about stuff that I'm not at all familiar with: statistics and simplex theory. My comprehension is strictly limited, to put it mildly. Perhaps there is someone here who can straighten my thinking out.

It seems to me that Bub is trying to describing mathematically a world where the speed of information is limited and the observations that guide description are of a statistical nature --- as well as being causal, because they affect this world. He seems to show that observation inevitably generates loss of information, i.e. uncertainty, as is the case in quantum mechanics.

I think he also establishes that entanglement is inevitably associated with such loss of information. He says that all this is an expected consequence of “probabilistic correlations, (and) the structure of information”; all that is needed, I suppose, to formulate a predictive description in a holistically statistical world.

So are the mysteries of quantum mechanics forced on us because causality is a sort of statistical correlation?

But what he doesn’t clarify is for me the central mystery: the magnitude of what sets the whole shebang up, namely Planck’s constant. Perhaps his interesting approach will eventually lead to our understanding why h is of order 10^-34 J.s.in our real world? I do hope so.

 

[sshai45]

This is why the (M,ω) formalism has come up in the context of trying to devise a fully general relativistic treatment of thermodynamics and statistical mechanics. Imagine trying to do statistical mechanics with no possibility of a physically meaningful preferred time variable. That's why it has always been done on a fixed space-time, not in a fully general covariant way. I hope to get back to this. It really interests me.

By a "preferred" time variable, does this mean that this time forms an "absolute time" in some sense (i.e. a "universal clock" that is not tied to a particular observer, sort of like in "old" pre-Einstein physics), or what?

 

[marcus]

Paulibus, bravo for tackling Bub! I'll be interested to know what you make of it. So far what I can get is for the most part merely what delighted me so much in the introduction (and I quoted.) But I'm trying to do too many things at once (family Christmas letters, and our community chorus has given several performances of Moz. mass in c-minor!, not to mention physics-watching)

By a "preferred" time variable, does this mean that this time forms an "absolute time" in some sense (i.e. a "universal clock" that is not tied to a particular observer, sort of like in "old" pre-Einstein physics), or what?

Maybe we need a new word to use instead of "preferred". I think it's different from going back to "old" pre-Einstein time ideas. In the old days there was an absolute time and all observers clocks were supposed to follow it and agree on simultaneity and stuff.

Now we still have all the observer-times and a democracy of disagreeing clocks, but IN ADDITION we have one more clock, which we can COMPARE the various observer clocks with. The ratio of rates can even be physically meaningful, correspond to something measurable.

This one additional clock is distinguished by the fact that it is not observer-dependent it is, instead, state-dependent. It depends on what we think we know about the world--on our degree of (un)certainty about correlations amongst observations---what we posit to be the case, with varying degrees of confidence. If you like, picture the state as a density matrix defining a function on the observables.

Each observer still gets to keep his own individual clock and nobody is presumed to be RIGHT, but there is this one additional clock, which has one particular advantage: the world can be analyzed as a fully relativistic system evolving according to THIS time.

Which is something you CAN'T do with some particular observer time, because the observer's history itself depends on how the system evolves---so there is a kind of logical circularity. The observer's time is not truly an independent variable.

So as I see it, this is not going back to the old picture, but instead is adding one more disagreeing clock to the general temporal madhouse and anarchy---which however has a nifty feature that you can do a fully general relativistic statistical mechanics and thermodynamics using IT as the independent time variable---something you cannot do with any other clock as far as I know. So it is subtly different from going back to the old picture and it does not imply that "Einstein was wrong". Or so I think.

Maybe instead of preferred we could say "distinguished" time variable. Distinguished by the fact that it can be used as independent variable in a fully general relativistic quantum statistical mechanics and suchlike fully relativistic analysis (rather than have to first choose a fixed solution to the Einstein equation and then do the analysis "on curved spacetime".) This gives the variable a definite "distinction" without applying that it is somehow "absolute" and the only right choice :big grin:
The key paper for understanding it in this light is http://arxiv.org/abs/1209.0065
But also maybe re-read the "Chapter 1" quote in post #145. It's short and to the point.

 

[mattmars]

Dear Marcus

Hi, I`m new to this thread, and I think it is very well conducted, and please excuse my butting in.

But I would like to respectfully say that I question/disagree with your view...

“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.”
(post #135)

...at a fundamental level.

If we take the simple working view that ‘time’ is apparently 'real', and thus something that in the most simple terms consists, at least, in some way of components described as ‘the past’ and ‘the future’ then at the most basic level we would need...

A- some initial reason for suspecting or assuming the existence of these things/places ('past', 'future'), and,

B- some proof / reason or experiment, to sensibly show how or why they exist.

It seems to me that if the universe is such that it is just filled with a quantity of matter/energy that ‘just’ (as in ‘only’) exists, moves, changes and interacts, (without leaving a 'past' behind us, and without heading into a 'future'), then this would explain all that we think implies the existence of a past and future – if we misinterpret, or over extrapolate, what we observe.

Specifically – if as that matter moves and changes, it also moves and changes the contents of our minds, we may look at some of the contents of our minds, and ‘call’ those contents ‘memories’, and add to this (possibly wrongly) that those contents (memories) are not just things that exist and prove that matter can exist, but are also proof that another thing called ‘the past’ -also- exists.
(And thus also proof that a thing called 'time' exists).

As such we may (imo wrongly) imply that some existing matter, in a particular formation, gave us good reason to suspect that as things move and change the universe ‘also’ creates and stores some kind of ‘record’ of all events in a place or a thing called ‘the past’.

So – is it correct to say , either,

1- Matter just exists moves and changes, or

2- There is also a (temporal) past, and thus a thing called ‘time’ that also may be considered.

Many people seem to assume that Relativity tells us something about the nature of a thing called ‘time’.

From what I have read, as far as I can tell, relativity only seems to actually tell us about the way, and ‘rates’ at which things may move and change differently under various conditions.

As far as I can tell no part of relativity ever proves or demonstrates the existence of things (or places etc) such as ‘the past’ or ’the future’. Although it is written in a way that seems to imply or suggest ‘time’ and these places naturally or obviously exist, or make sense.

While relativity seems to correctly show that matter may intrinsically 'change at different/reduced rates' while at velocity, in acceleration, gravity, etc, I don't see any proof that such matter 'sinks into a past' or 'surges into a future', or that relativity indicates the existence of these concepts.

I would suggest 'time' is not real, but only a false idea borne out of us incorrectly interpreting what the contents of our minds prove and do not prove.

If I am wrong could you point me to a link that shows how the existence of these entities ( 'the' past and 'the' future) has been demonstrated (in relativity or otherwise), as opposed to have just been assumed and untested?

Yours M.Marsden, London

 

[marcus]

Hi Matt, welcome to PF and thanks for contributing to this discussion. I'll try to respond...
I think your critique is mainly focused on the 4D "block universe" idea. You offer reasons to be skeptical about the existence of time as a DIMENSION, extending back into past and forward into future.

You are skeptical of the idea that pastpresentfuture exists as a kind of 4D crystal with time as a kind of pseudospatial dimension. That's how I read what you say. You seem dubious regarding the presumed real existence of SPACETIME.

You are certainly in good company as far as that goes. There was even a conference in Capetown South Africa this month bringing together people critical of the 4D block spacetime idea. We discussed that earlier in this thread. Your message also doesn't seem basically at odds with what I've been saying.
You may have misunderstood what I've been trying to get across about time as a real process of change, rather than a spacetime dimension.

I think the best argument against the actual existence of spacetime was given in Chapter 1 of that book, also available online at "arxiv.org". I gave the link in post #145, and quoted a passage that comes on page 4 of the essay. A 4D block spacetime seems incompatible with quantum uncertainty. You have to fiddle around with the concepts too much to get them to live with each other.

Look back at post #145 right on this page, where it says:
Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime...
Which is to say, because we are talking about what is the best most fundamental mathematical description of the world, spacetime does not exist.

This does not mean that TIME AS A PROCESS OF CHANGE isn't real. The math representation of a process of change is as a flow defined on the set of all observations. That is where transition probabilities and correlations between measurements (now and a few seconds later or a few years later) are defined.

When you treat time as a process the math formalities are not as familiar to most people as when you treat it as a dimension, but that just takes getting used to. There is an observable algebra M consisting of all the possible measurements, and a numerical function ω giving correlations amongst the possible measurements, representing our knowledge. It's more abstract than most people are used to, but maybe that will change. (M, ω) is one possible formulation of any quantum theory about the world. John von Neumann is the main person who developed that approach back in 1930s. It does not necessarily assume a space-time.

And then given (M, ω) as the world, TIME is represented as a process that stirs M around.
This kind of picture can be constructed using matrices of numbers. People can build examples of what I'm referring to. Already did this in the 1930s. von Neumann again. and others. Nowadays you can put this kind of model of the world into a computer and run it. Time becomes a process of change defined on M, and is itself represented by matrices of numbers that you multiply other stuff by to change it.

It may be that the "spacetime" or block universe picture simply is not realistic enough and people will have to go with this (M, ω) picture of the world, where time is not a pseudospatial dimension of a block of eternity but is a process of change instead. That block may simply not be realistic enough (with its eternally existing past present future.)

That is what was being argued in that quote I mentioned where it says
Therefore in quantum gravity it is likely to be impossible to describe the world in terms of a spacetime.

Quantum gravity means quantum *geometry*, the quantum theory of the geometry in which matter and everything else lives. So the QG program is aimed at constructing and verifying the most fundamental picture of the world. If you cannot incorporate a block space-time in QG, then that is as much to say a block spacetime does not exist, and time is not a 4th dimension.

So we have to see how the QG research program goes, and how it turns out.