So what about the FQXi time essay contest? It's February already.

[marcus]

http://fqxi.org/community/vote

Summer 2008 FQXi started an essay contest, about the nature of time.
They say they will announce the winners (first prize, second prize, etc...) in February 2008.
Which is half thru already.

Here's the essay context FAQ
http://fqxi.org/community/essay/faq

Does anybody have a better link to use to check to see how the judging is going and whether they've decided anything?

 

[Demystifier]

I suspect that, due to the recession, they don't have money to pay the prizes.

 

[marcus]

You've got to be kidding, Harvey

How do you rate the other essays, besides your own? Any favorites?
Which do you think have a chance of winning?

For anyone just coming in on this, here's the list, ranked by the number of public votes received:
http://fqxi.org/community/forum/category/10?sort=public

 

[Demystifier]

I think Rovelli has good chances to win. (Which does not mean that his essay is the best for me.)

 

[marcus]

I think Rovelli has good chances to win. (Which does not mean that his essay is the best for me.)

Do you have some personal favorites (besides your own entry?)

There are a half-dozen prizes to be awarded. If I remember right there are four that will be awarded based on the decisions of a select panel of judges.

And then a couple of prizes will be awarded based on the votes of members of the FQXi community.

Here's the main FQXi page, which has a "breaking news" column:
http://fqxi.org/community
If they are going to announce in February, as it says in the FAQ they will, then we should be checking that URL every now and then.

 

[Demystifier]

Do you have some personal favorites (besides your own entry?)

Well, to be honest, I have actually read only few essays, so I cannot be objective. Nevertheless, I can say that this one has intrigued me:
http://fqxi.org/community/forum/topic/318

 

[weburbia]

The blog at http://fqxi.org/community/forum/topic/402 has some info from Anthony Aguirre concerning the delay.

 

[marcus]

A news item appeared today at http://fqxi.org/community

Essay contest announcement is imminent
Mar 5, 2009
After a long and interesting process, the jury panel is wrapping up its deliberations -- expect an announcement soon!

 

[Peter Morgan]

There's also a comment that appeared just before the one Marcus mentions, at http://fqxi.org/community/forum/topic/402,

Anthony Aguirre (blogger) wrote on Mar. 4, 2009 @ 00:38 GMT

Hi All,

The time is nearly nigh. Your patience is appreciated. As John Merryman suggests, judging a contest like this is, as I have witnessed, very, very hard. But the jury is not hung, and you can expect an announcement soon.

Cheers,

-The Management

So they claim they've found a consensus on a mishmash of essays. It will be interesting to see what range of essays that consensus will include.

Presumably FQXi is engineering a splash for the media, which these two squibs are part of, but there seems to be nothing else by google, except, of course, this thread. Here's a little extra noise.

 

[marcus]

BTW Peter, weburbia, another long-awaited milestone has actually been reached. Oriti's book of collected expert articles ("Towards a New Understanding of Space, Time, and Matter") is now in stock at Cambridge University Press.

Amazon still lists it as not yet released. But copies are in stock at CUP and also at a place in Delaware in the USA, delivery time 4 to 5 days.

Sample chapters, the index and the toc can be read online at this CUP webpage
http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521860451

The amazon page that still thinks it hasn't been released (but also let's you see the table of contents etc) is here:
https://www.amazon.com/dp/0521860458/?tag=pfamazon01-20

Oriti's book should have come out 2 years ago. the wheels of scholarly deliberation turn slowly.

 

[ccdantas]

another long-awaited milestone has actually been reached. Oriti's book of collected expert articles ("Towards a New Understanding of Space, Time, and Matter") is now in stock at Cambridge University Press.

Great news!

 

[ccdantas]

BTW, what is "imminent" supposed to mean in the USA? Imminent for me shouldn't take more than 24 hrs!

 

[Count Iblis]

Since so many essays claim that time doesn't exist, the jury had decided that not sticking to the deadline would not be a problem for most participants.

 

[marcus]

Since so many essays claim that time doesn't exist,...

If so, then they are right. Indeed it does not exist, it occurs.

Let's face it, Count, time happens.

 

[MTd2]

WINNERS!
First Juried Prize:
Julian Barbour on “The Nature of Time”
The jury panel admired this essay for its crystal-clear and engaging presentation of a problem in classical dynamics, namely to find a measure for duration or the size of a time interval. The paper argues lucidly, and in a historically well-informed manner, that an appropriate choice for such a measure is not to be found in Newton’s pre-existing absolute notion of time, but rather emerges, in the form of ephemeris time, from the observable motions and the assumption of energy conservation. The paper also suggests how this emergence of duration might be relevant to problems in quantum gravity.
Second Juried Prizes:
(1) Claus Kiefer on “Does Time Exist in Quantum Gravity?”
A fundamental problem in quantum gravity is that the “Wheeler-DeWitt Equation,” probably our most reliable equation of quantum gravity, does not refer to or even suggest anything like time or evolution. In this context time must emerge in the form of relations between a given system and some other system that may be considered a clock. Kiefer beautifully reviews this problem, and argues how, via quantum “decoherence,” time as described by the usual Schroedinger equation in quantum mechanics can emerge from this timeless substratum, via entanglement between physical systems within space, and the spatial metric that controls motion.
(2) Sean Carroll on “What if Time Really Exists?”
Drawing on recent developments in string theory, Carroll impressed the panel with an exciting account of how a gravitating spacetime might in fact be just a holographic approximation to a more fundamental non-gravitating theory for which “time really exists.” Contemplating the difficulties raised by strange recurrences in an everlasting universe, he argues for a strong condition on the set of allowed quantum states that would disallow such repetitions. Carroll closes by attempting to reconcile this picture with recent observations that indicate that the expansion of the universe is accelerating, with surprising results.

First Community Prize: Carlo Rovelli* on "Forget Time"

Second Community Prizes:

(1). George F. R. Ellis on "The Flow of Time"*

(2a). (Tie!): Rodolfo Gambini and Jorge Pullin on "Free will, undecidability, and the problem of time in quantum gravity"*

(2b) David Hestenes on Electron time, mass and zitter"

Community Runners-up: Fotini Markopoulou, Cristinel Stoica, David L. Wiltshire

(*Note: The essays by Ellis and Gambini & Pullin were also selected for a less -- and hence unawarded -- juried prize).

Third Juried Prizes:

"What Makes Time Special" by Craig Adam Callender

"Space does not exist, so time can." by Fotini Markopoulou

"On the global existence of time" by Ettore Minguzzi

"Time, TOEs, and UltraStructuralism" by Dean Rickles

"Many Times" by Steven Weinstein

Fourth Juried Prizes:

“Whither Time's Arrow?” by Gavin Crooks

“The rediscovery of time through its disappearance” by Alexis de Saint-Ours**

“Time is not the problem” by Olaf Dreyer

”Weakening Gravity's Grip on the Arrow of Time” by Maulik Parikh

“Quantum Measurement as an Arrow of Time” by Curtis Vinson**

“Condensed matter lessons about the origin of time” by Gil Jannes**

“The Production of Time” by Adam Daniel Helfer

”The Nature of Time: from a Timeless Hamiltonian Framework to Clock Time of Metrology” by Enrico Prati

”Is the notion of time really fundamental?” by Florian Girelli, Stefano Liberati and Lorenzo Sindoni
** FQXi would like to offer a special commendation to these winning essays written by either students or non-professionals. Nice work!

Now for some notes on the judging:

- First, thank you all for your participation, your interest, and your patience! I hope that it has been interesting.

- Second, note that due to the difficulty and subtlety of the issues at hand, there were numerous disagreements within the jury regarding nearly all of the essays. The awarding of a prize signifies that the jury agrees that the winner is a relevant and interesting essay: something that is well written, thought provocative, stimulating, fun, etc. It should not be construed to mean that the members of the panel believe that the approach is complete, flawless, unobjectionable etc.!

- Along somewhat similar lines, I hope that non-winners won't be too despondent. I think that many gems of insight are lurking in a number of non-winning essays, and I hope that the contest and discussion has given some of these gems and their authors exposure that would otherwise not have been possible.

- The jury will remain anonymous, and we're not going to release any details beyond what's in the above of how the jurying went. I'm sure many are curious on both counts, but equally sure you can see why we would not think either is a good idea.

- That being said, I can tell you that the jury had a tough time, and put in a lot of work. All of the essays were read and reviewed by at least two panelists (in fact, there were two panels, a screening panel that narrowed it down to 50 essays, and a judging panel that ranked them), and all of the essays that came out on top were read by all of the jurors. There was quite a lot of discussion of some pretty subtle points within a jury of quite divergent views, and not a whole lot of unanimity.

Finally, stay tuned for the imminent announcement of the NEXT essay contest topic. Thanks for your participation!

Anthony on behalf of FQXi
http://fqxi.org/community/forum/topic/426

http://blogs.discovermagazine.com/cosmicvariance/2009/03/08/the-envelope-please/

 

[marcus]

My favorites were Barbour, Rovelli, and Ellis. I'm happy that one of them got the first juried prize, one got the first community prize, and the third got the second community prize.

I'll have to take a look at the Kiefer essay, since the jury had such a high opinion of it.

 

[shoehorn]

Barbour's essay was a shoo-in to win; apart from the fact he's hugely respected in this particular area, the rest of the entries were disappointing (with the exception of Claus Kiefer's paper). I appreciate the broad thrust of what the FXQi is trying to achieve with contests such as this, but several of the papers should really have been sent back to the authors with a "Thanks, but no thanks" note attached.

 

[marcus]

Anyone who liked Barbour's essay should also read Rovelli's.
The message is essentially the same: timeless mechanics.
Rovelli just goes further.
Barbour stays in a purely classic Newtonian context and shows, in a clear beautifully written and highly accessible way, that a timeless formulation is natural.
He limits himself to that and says that he hopes this will be suggestive of how a timeless quantum mechanics could be formulated.

Rovelli essentially writes chapter 2 to Barbour's chapter 1. He reviews the same natural timeless reformulation of 18th century mechanics, and then ups the ante by venturing to sketch out a generalization and a quantum version.

At the end he hazards a guess as to how a stream of time could emerge as a function of the state of the universe. But this is just the last page or two, on the "thermal time" hypothesis. The bulk of the essay is not about the thermal time hypothesis.

I think both Rovelli and Barbour were shoo-ins for first prize, and fortunately there were two first prizes!

 

[petm1]

Barbour's essay was a shoo-in to win; apart from the fact he's hugely respected in this particular area, the rest of the entries were disappointing (with the exception of Claus Kiefer's paper).


I appreciate the broad thrust of what the FXQi is trying to achieve with contests such as this, but several of the papers should really have been sent back to the authors with a "Thanks, but no thanks" note attached.

No need to worry, some of us did get that note.

 

[marcus]

No need to worry, some of us did get that note.

Unpleasant as it is to not have an essay accepted, it still does you credit to have written and submitted one. Congratulations. I think it makes sense for them to set some criteria and then try to filter. Just being accepted as an entrant is a form of publication.

I think it was a great thing for FQXi to do---really advanced their basic aims and had a positive affect.

It's important that the two firstprize essays were about time not having a fundamental existence. It's part of the GR revolution that started in 1915.
Much of the rest of physics has not caught up with that basic insight.

I wish the Wikipedia articles on hamiltonian and lagrangian mechanics could be rewritten in timeless formalism----without the dummy-variable "t" appearing all over the place.

Anyway congratulations petm1 for taking part in what I believe was a significant public science event.

 

[Peter Morgan]

It's important that the two first prize essays were about time not having a fundamental existence. It's part of the GR revolution that started in 1915.
Much of the rest of physics has not caught up with that basic insight.

Marcus, you've said this before, but I guess I don't get it in the empirical QM environment, unless we commit to a specific interpretation of the role of probability that doesn't need there to be many instances of experiments under controlled conditions. It's possible in principle to collect an ensemble of results at many places, but most experimentalists don't construct a million copies of an apparatus to collect an ensemble of a million data points, they use the same experimental apparatus at many different times, with an assumption that the individual data points are statistically independent.

If I were to agree with you that we will interpret just the mathematics, I could agree with you that diffeomorphism invariance properly leads to many of the troubled discussions of the role of time in the mathematics, but I consider that we also have to give a pragmatic description of how the mathematics models our repeatable experiments (of course no experiment is repeatable, the data points, and the statistics of all finite sets of data points, are all mathematically modeled by classical states and random variables or by quantum mechanical states and measurement operators, and the external environment is always different, just not always in a way that affects the statistics in a way that must be compensated for).

Quite a number of the other papers discussed (many of them cogently, as I thought) how there can be an experience of time for us, despite our preference for constructing models using a diffeomorphism invariant mathematics. I hope you found some of them interesting, but do you in principle deprecate those attempts to reconcile experience with diffeomorphism invariant mathematical models?

I've always found Julian Barbour too Platonist for my taste. I like Carlo Rovelli's Philosophical outlook quite a bit more.

On the issue of whether the Wikipedia entry on the Hamiltonian and Lagrangian approaches might be written in a timeless way, would it also have to be written without reference to phase space, insofar as phase space requires a foliation of space-time? It's not easy, perhaps impossible, to give a mathematically well-defined presentation even for a Lagrangian formalism without introducing a foliation of space-time, so we can discuss the action between two leaves of the foliation instead of between t=plus or minus infinity. I would say that as practical mathematics time is properly part of a description of Hamiltonian and Lagrangian formalisms; only in a perfect application to a mathematical model for the whole Universe (not just out to 10^{100000}meters) that is Platonically perfectly accurate at every scale (not just at 10^{-100000} meters, but at every scale) might we be able to eliminate time. Indeed, for this perfect model, the map would be the territory. We have to be able to describe the appearance of errors in our models, differences between the model and the world that is modeled, over time.

Blah, blah, blah.

 

[marcus]

... I don't get it in the empirical QM environment, unless we commit to a specific interpretation of the role of probability that doesn't need there to be many instances of experiments under controlled conditions...

I don't understand your objection, Peter. First to consider the classical case, there is no need to give up the privilege and pleasure of performing many instances of the same classical experiment.

Have a look both at Rovelli's general formalism and at his model of a simple pendulum.

As long as the pendulum is treated as an isolated system, the model of it is the same on Wednesday as it was on Tuesday.

A good explanation of the general formalism starts on page 105 of his book. See particularly page 107.

Maybe you see some problem that I don't, so I'd like it if you could spell things out explicitly. Maybe take some concrete example.

Rovelli's model allows clocks, as I expect you realize. It just does not allow a distinguished Clock. It can't be that. I'll re-read your post and try to understand.

Is the problem with the quantum version of his timeless model?

The discussion begins on page 177 (section 5.2 "Relativistic QM")

You might want to go back to some immediately preceding sections
page 172 section 5.1.3 "Partial observables and probabilities"

and
page 169 section 5.1.2 where he sets up quantum versions of the simple pendulum, and the timeless double pendulum. Describes the Hilbert spaces, the Hamiltonian operator, and so forth.

I'll have a look at your essay on the nature of time and see if there is anything that can help me understand what you think is wrong with the timeless approach to mechanics presented here.

 

[Count Iblis]

About rewriting wikipedia entries for Lagrangian/Hamiltonian formulations of (classical) physics, I think it would be best to start new wiki articles about the timeless formulation. Make sure everything is well referenced using peer reviewed publications.

 

[Peter Morgan]

I have no problem with there not being a distinguished clock in the mathematical models. There is always, however, a question of what is in the model and what is not in the model.

In the quantum mechanical case the data gathering phase of an experiment is typically modeled as a single time-slice in space-time. I'm thinking here, for example, of Bell's classical model for Gregor Wiehs' experiment that violates Bell inequalities. Bell's model has four random variables associated with two regions in space-time (specifically, the "The theory of local beables" model, which most Physicists take to be definitive for classical field theories), the real experiments have two data-points in each of hundreds of thousands regions in space-time, which we take it we can model as an ensemble, from which we can extract statistics to compare with expected values predicted by the probabilistic model. [A quantum mechanical model could be presented as a Wigner function, from which we extract various probabilistic models as marginals, but we would need to make the same reduction from hundreds of thousands of regions of space-time to two regions of space-time.]

What is the nature of the move from hundreds of thousands of regions of space-time to two regions of space-time? In classical Physics, a lot of discussion and mathematics has sought to justify this kind of move through the ergodic theorem, but I believe it's ultimately pragmatic. When we have a probabilistic or quantum-mechanical theory, we don't even have the individual events in the mathematics, we don't even have statistics, we only have expected values. Of course there are engineering rules for how we should make the comparison between statistics and expected values, and some people are much better at using those heuristics than others.

In classical deterministic mechanics, there was always a pretense that we could model the hundreds of thousands of regions of space-time, but a probabilistic model cannot even pretend that we can. [If we introduce a much bigger model of minutes of operation of the whole experimental apparatus during which hundreds of thousands of events take place, we would have to construct an ensemble of hundreds of thousands of those minutes long runs of the experiment to verify it.] This is not the measurement problem of QM, it's also an issue for a classical probabilistic theory. We cannot even have a discussion of something like the ergodic theorem in a probabilistic theory, the nature of probability instead derives quite loosely from "correspondence" with the classical world (parenthetically, I find Landsman's take on Bohr eye-opening: http://www.math.ru.nl/~landsman/EBpubl.pdf" ).

Note that I'm not hankering for a return to deterministic physics, I'm just saying that once we move to a probabilistic/quantum-mechanical model as our fundamental theory there is a level of the world that we are admitting we cannot model. If we can't model it, we can't talk about it (if I talk about it, and claim to make sense, I'm claiming that my words constitute a model). This is also, I consider, not precisely the incompleteness argument, again because it also applies to classical probabilistic physics.

I'm unsurprised you didn't much understand my first complaint, indeed I'm rather surprised you took it seriously. This is longer, so I hope it's better, but I rarely reach the heights of clarity in my writing (sad smiley)? I think worries about timelessness are a result of a relatively Platonic interpretation of the mathematics that we currently use to model nature that ignores the richer pragmatics of empiricism, and by doing so becomes moderately scholastic.
All the best,
Peter.

 

[ccdantas]

I think there is a need at some point to move from our present "input-process-output" style of thinking in mathematics, which is actually quite a good type of mathematics for the classical world, but limits our representation of the quantum world. I think we should move to a concurrent mathematics-type of reasoning: my point of view is that the quantum world is a fundamentally concurrent world, and determinism can be retrieved from it if we re-think physics in concurrent terms. For the moment, this is just a feeling and I have no worked out proof, nor I believe I will have a satisfying one. But I do believe it is an idea worthy to wonder about.

Well, my essay raises that exact issue because, from my ideas, time should arise as a unique deadlock avoidance constraint from the quantum substrate. My essay however has been practically ignored in the FQXi contest (as far as I know I did receive at least one restricted vote; I'm happy that someone thought the idea was somehow worthy). I am aware that my essay does not raise any specifics or formal models to express the idea, it is much of a philosophical essay and I just scratch the surface of the idea. I thought, however, that such a style would reasonably match the theme in question, because the nature of time is truthfully a philosophical issue per se -- physics will be always behind it and always be an incomplete or poor description of it (this is also raised in my essay). But now I realize that most people focused in choosing the essays that could better convince the reader on the point of view offered. I do not have the style of convincing anyone of anything, but to simply share some possibilities that I find intriguing and that I know that are not being considered elsewhere, even if they are incipent ones. Now I realize that such an approach has little value.

I am not saying that the awardees did not deserve their prizes; on the contrary, I congratulate them for their very good work. The point that I raise here is how really far the ideas proposed there are really original or new or intriguing; sincerely, there is evidently very good work in those essays, but I did not see anything really *new*. I have accepted the final result from the FQXi judges and I am not complaining. In fact, it is great to see many people thinking about such a difficult issue. I'm just one more curious person and could be completely wrong. Yet, I must be convinced otherwise. The FQXi is just a prize and you win it or not. I didn't, but I feel really sad when people mention that almost all essays apart from the first winners were disapointing or complete trash. Yes, of course, there were many essays that lacked quality. But I cannot accept that mine was one of those. One may not agree with the ideas there, but I am certain my essay has minimum quality. I accept not to have won a prize, but I do no accept general depreciative remarks from people that have not read my essay.

Thanks,
Christine

 

[Peter Morgan]

Dear Christine,
Yours was one of the papers that I downloaded and read fairly carefully. I went back to it today. I didn't have anything constructive to say before, but your comment here may have crystallized your point of view a little for me. I found your invocation of Bergson interesting but difficult to encompass in my own flawed worldview. I take it that your ideas are pre-mathematical, but I think that your ideas can be put in a mathematical form.

I note that you distance yourself from Wolfram in your paper, but you also say, on page 6, "It would be a fundamental step to examine how to restore realism under the concurrent hypothesis here addressed (realism not towards local spacetime locations, but towards a lower level of reference)." I consider that this sentence puts you as much in conflict with Bell inequalities as Wolfram is, if you introduce any sort of mathematization that would be describable at a higher level by probability densities. I hope you might find my http://arxiv.org/abs/cond-mat/?0403692" of interest. This paper shows that the assumptions that Bell has to make in order to construct Bell inequalities for random fields are far more powerful than are justified if there are thermal or quantum fluctuations. In other words, if you are willing to introduce an explicit model for quantum fluctuations, then, with only a few provisos, Bell inequalities cannot be derived.

I may have misunderstood your intentions, but random fields may be adequate to mathematize your ideas. The above paper and others you can find through my homepage (Physics Forums gives you a link) should give you an idea (one of the papers is my over-mathematical FQXi contest entry). If random fields are not what you need, then sadly I think you need to find some other mathematics.

A fundamental mathematical idea in my work is to give a Hilbert space presentation of classical random fields that is as close as possible to the Hilbert space mathematics of quantum field theory. By doing so, we clarify what is quantum mechanical and what is a consequence of using probability measures over fields. It is fundamentally the case that classical random fields are not generally describable in terms of particle properties. Superposition, entanglement, quantum fluctuations, and the violation of Bell inequalities are all as much properties of classical random fields as they are of quantum fields.

I think QM describes a world in which there are no outright deadlocks, insofar as the evolution is modeled by the action of a unitary operator on states in a Hilbert space, which we use to generate evolving probability measures associated with particular observables. As a matter of experience, a unitary evolution is a good mathematics for generating evolving probability measures. The Copenhagen interpretation of course advocates not worrying about what underlying mechanism there might be for the evolving quantum state. By adopting a Hilbert space presentation for classical random fields, in which evolution is also unitary, classical random fields also have this no-deadlock property. However, I tend to agree with Copenhagen that a probabilistic random field approach to Physics is as much as we can verify by experiment. I can't see how we could verify any particular classical deterministic model (such as Nelson mechanics, de Broglie-Bohm trajectories, etc.). I'm sure people will still try, but I worry about epistemology.

I'm very conscious that I'm seeing a connection where you may well see none. It's rare that anyone makes connection with anyone else in foundations of physics, so I won't hold my breath for you seeing much of what I see in this. There are numerous other mathematical tools available, particularly the categorical methods that FQXi is so keen on at present, which I suppose you may have already considered and found wanting.

Hunting for more connection with Bergson, I hope not too desperately, I note that ideas of interpenetration can be found within the mathematics of Fock space, through the pervasive (necessary) use of test functions and of products of creation operators, however not many people find it easy to think in terms of test functions (I have a ten year head start on you, and they are definitely still not easy).
Peter.

 

[marcus]

... I think it would be best to start new wiki articles about the timeless formulation...

Exactly, Count. That is what I meant to suggest.
Leave the old "time-ful" treatments just as they are and create new articles on the same topics---giving them the timeless treatment.

BTW (in case anyone's interested) according to the Wikipedia article back in the 18th century a timeless version of the action principle was proposed by Maupertuis (Moe-per-twee.)

He also got the idea, which turned out to be right, that the Earth might be slightly pumpkin-shape instead of perfectly round.

 

[ccdantas]

Dear Peter Morgan,

Thank you for your thoughtful comments and feedback. I will read your papers carefully. You seem to have developed an interesting material, as you have certainly thought about the foundations of quantum mechanics for a quite longer time than I have (I certainly consider myself a newcomer on these matters). So I find your comments here of great interest.

I have not much to say at the present time. I have to think about your considerations. Thank you very much!

Christine

 

[marcus]

Christine, both you and Peter too are definitely to be congratulated* on your essays and on helping to make the contest a highly visible and worthwhile event. I am impressed with how well it turned out. The level of essays did not have to be that high. I would not have expected so many good ones. The response definitely puts a spotlight on fundamental issues in physics.

*and thanked.

As Peter has pointed out, I am excited by the increased visibility that the contest has given to a timeless approach to physics.

I was just now reading the Wikipedia translation of Euler's 1744 book where he proposes the timeless action principle. (Which apparently also appeared in some unpublished papers of Leibniz from around 1705.)

It comes as a shock to realize that not only
1. does General Relativity have no place for a distinguished time, so we are required to dispense with time (if we take GR seriously) but also
2. a timeless approach to mechanics as been around since the 18th century. And moreover
3. the push to develop a general-relativistic quantum field theory (or to define field theory free of an underlying spacetime) has now brought this to a head.

For me, the two first-prize essays sum up the "message" of the FQXi contest, as it turned out. Julian Barbour's shows clearly how classical physics can be done without assuming time---the measure of duration arises simply as a byproduct of the collective motions of the system.

So one is free to do physics without a time variable. And then Carlo Rovelli's essay goes ahead and suggests how to extend and generalize this. I'll get some links. There is also a very interesting footnote on page 5 of Rovelli's essay.

Here's Euler's original 1744 Latin (Appendix 2 of Euler's Methodus)
http://math.dartmouth.edu/~euler/docs/originals/E065h
Here's the English translation:
http://en.wikisource.org/wiki/Methodus_inveniendi/Additamentum_II

 

[marcus]

... This is longer, so I hope it's better, but I rarely reach the heights of clarity in my writing (sad smiley)? ...

To the contrary, I would have said that clear writing was one of your strong suits. The odds always favor the sober pessimist over an optimist---more apt to be right every time (exuberant smiley)! But let me get the link to Rovelli's footnote #6.
http://fqxi.org/data/essay-contest-files/Rovelli_Time.pdf

==quote==
It appears that all elementary physical systems can be described by hamiltonian mechanics.⁶ Once the kinematics --that is, the space
C of the partial observables q^a-- is known, the dynamics --that is, Γ and f-- is fully determined by giving a surface Σ in the space Ω of the observables q^a and their momenta p^a . The surface Σ can be specified by giving a function H: Ω → R. Σ is then defined by H = 0.⁷ Denote $$\tilde{\gamma}$$ a curve in Ω (observables and momenta) and γ its restriction to C (observables alone). H determines the physical motions via the following

Variational principle.
A curve γ connecting the events q^a₁ and q^a₂ is a physical motion if $$\tilde{\gamma}$$ extremizes the action

$$S[\tilde{\gamma} ] = \int_{\tilde{\gamma}}p^a dq^a$$

in the class of the curves $$\tilde{\gamma}$$ satisfying H(q^a, p^a) = 0 whose restriction γ to C connects q^a₁ and q^a₂.

All known physical (relativistic and nonrelativistic) hamiltonian systems can be formulated in this manner.

Notice that no notion of time has been used in this formulation. I call H the relativistic hamiltonian, or, if there is no ambiguity, simply the hamiltonian. I denote the pair (C, H) as a relativistic dynamical system...

6 Perhaps because they are the classical limit of a quantum system.
7 Different H’s that vanish on the same surface Σ define the same physical system.
==endquote==

 

[Peter Morgan]

I won't repeat my inchoate comments on timelessness. Not exciting to do it again.

Christine, how long someone has thought about a subject makes rather little difference to the novelty of their thought. I'm sorry that the "I've been doing this for a long time" slipped into my comment. If a good mathematician ever applies themselves to random fields, they will be past my ten year head start in a week.

 

[marcus]

I won't repeat my inchoate comments on timelessness...

Not so inchoate! I will look back at your comments specifically as regards the main points of the "Forget time" essay. The gist of the essay is summed up in the conclusions section at the end:
==quote==
I have presented a certain number of ideas and results:

1. It is possible to formulate classical mechanics in a way in which the time variable is treated on equal footings with the other physical variables, and not singled out as the special independent variable. I have argued that this is the natural formalism for describing general relativistic systems.

2. It is possible to formulate quantum mechanics in the same manner. I think that this may be the effective formalism for quantum gravity.

3. The peculiar properties of the time variable are of thermodynamical origin, and can be captured by the thermal time hypothesis. Within quantum field theory, “time” is the Tomita flow of the statistical state ρ in which the world happens to be, when described in terms of the macroscopic parameters we have chosen.

4. In order to build a quantum theory of gravity the most effective strategy is therefore to forget the notion of time all together, and to define a quantum theory capable of predicting the possible correlations between partial observables.
==endquote==

I don't feel I can paraphrase your views at all adequately, Peter. But I am guessing that the only engagement is with points 1. and 2. We can set aside the other two because either they are more speculative or they have to do more with ideas about constructing a quantum theory of gravity.
Looking just at 1. and 2. I would guess that you wouldn't object to point 1. That doesn't involve probabilities arising from quantum amplitudes. It is purely classical, and just says a timeless formalism is possible and (in the case of GR) natural.

Point 2. is where you might strongly disagree, unless I'm mistaken. You might grant that it is possible to formulate a quantum mechanical system in the timeless way proposed, depending on what one expects to get out of doing this. But you might question the fundamental validity, or the practical point, of doing that. You especially emphasized probabilities. In Rovelli's setup one can, I believe, repeat the same experiment over and over, so one can accumulate empirical probabilities. The probabilities describe correlations between observables.
One can repeat the experiment, varying only a few parameters, or no parameters.
Perhaps I am mistaken, and you will disagree.

To me the setup looks pragmatic and empirical. This may not be so from your perspective.
That is where I sense possible disagreement.
===================

I just read the article by N.P. Landsman you linked to:
http://www.math.ru.nl/~landsman/EBpubl.pdf
great quotes and a fascinating writer---too much to assimilate in one sitting, but too interesting to stop reading.

 

[Peter Morgan]

"All known physical (relativistic and nonrelativistic) hamiltonian systems can be formulated in this manner." Non-Hamiltonian systems cannot be formulated in this way, but all Hamiltonian systems can be.

Only if the model is of everything in the universe should the model be conservative, and hence Hamiltonian. A truly fundamental model does model absolutely everything in the universe, no degrees of freedom at any scale left out, the map really is the territory, so that would be alright. If, for trivial example, there's a fractal structure, turtles standing on turtles all the way up and down, with the turtles at different scales always of a different kind, I think it's problematic.

I find the approximate relationship between ideal models and experimental results, which is all we've ever had in the past, very different from a discussion of ultimate, perfect models.

I left a comment on Rovelli's FQXi paper, which he answered but I didn't have the will or the skill to pursue, more-or-less to the effect that a von Neumann algebra, which is required to be able to construct a Tomita flow, is too potent an analytic structure to introduce without far more justification than I think he gave. [In part, I so liked the way that he responded, and that he responded so nicely to other people too, that I didn't want to rain on his parade.] Particularly I don't think we can introduce such a potent analytic structure in the same breath as a Hamiltonian formulation of quantum field theory, which can be constructed as an interacting model only in an ill-defined way, at least as far as we know. We could note, though this is not at all definitive because we can manage unbounded operators if we are very careful about their domains, that the Hamiltonian is never a bounded operator, whereas a von Neumann algebra only contains bounded operators. We can calculate renormalized Wightman functions in perturbation theory that for some experiments match to many orders of magnitude, but introducing an analytic structure is a very different game. The big conclusion in his FQXi paper, the application of Tomita flow, is very flawed, in my opinion, though it conceivably might be justifiable nonetheless.

I think I disagree with 1, 2, and 3, making 4 moot.

I dunno, Marcus. My very flawed attempt at a constructive mathematics, in the easy territory of quantum field theory, is very different from Rovelli's constructive approach, in the much harder terrain of quantum gravity, so I'm very little competent to engage with this.

 

[marcus]

...I left a comment on Rovelli's FQXi paper, which he answered... [In part, I so liked the way that he responded, and that he responded so nicely to other people too, that I didn't want to rain on his parade.]

You keep pointing me in interesting directions. First the Landsman paper, and now you gave me some motivation to read the comments and discussion of Rovelli's paper at FQXi:

http://fqxi.org/community/forum/topic/237

I was just looking at the 13 October post where he replies to a bunch of comments.
"...In any case, I am aware that the thermal time hypothesis is highly speculative. I would like the readers to keep it separate from the main idea defended in the essay, which is that mechanics can be formulated without having to say which variable is the time variable..."
The thermal time and the Tomita flow business are indeed speculative and seem secondary to his main idea.

Ah! I see your comment at 16 October and Rovelli's reply of 19 October which begins"
"...Peter Morgan raises an extremely good issue, with both a technical and a conceptual side. I refer here to his post above, without trying to repeat here his points, since these are several, interconnected, and nicely expressed by Peter..."

Wow! There is some remarkable material in these comments which I had no idea was there! There is a comment from the Other Peter (Peter Lynds) of 22 October, and Rovelli's 24 October reply which sheds light on his personal view of LQG

==quote==
Dear Peter,

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

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

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

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

I am very glad you have raised this point.

Carlo Rovelli
===endquote===

 

[marcus]

Peter, I can see why you might have wanted to exercise restraint and not "rain on the parade". The way Rovelli is handling the questions is a class act. Nice and clear at the same time. Here's a 9 November post that clears up a problem people often have.
==quote==
Dear Bob,

thanks for the question, which is very appropriate. Let me give a dry answer first, and then explain:

> In the timeless picture you propose there is no unitarity, right?

Right: more precisely, there is no unitarity in the usual sense.

> Does this mean that probability conservation can be violated?

No: probability conservation is not violated.

Let me explain. In usual quantum theories, unitarity is the request that the change of the state *in time* is given by a unitary operator. It follows that probability is conserved *in time*. In a theory in which there is no preferred time variable, this request obviously looses its meaning. This is why unitarity in the usual sense is not present in the timeless formulation. Nonetheless, probability must be "conserved". This means that the probabilities of all the possible specific-measurement's outcomes predicted by the theory must sum up to one. Unitarity in *this* sense must of course be implemented by the timeless theory, and it is.

The answer is different in the statistical context. In this context, thermal time emerges, and therefore we have a unitarity requirement again. In this case, the evolution in thermal time turns out to be unitary by construction.

Thanks also for bringing back the discussion to the actual content of the essay. I do not think that this forum is the proper place for discussing alternative points of view, especially if discussed in other FQXi essays, or issues which are too general.

Carlo Rovelli
==endquote==

Also noteworthy is George Ellis' post of 12 December which challenges several of the points made in the essay. It's fairly long. I'll just post the link again and encourage people to read it.
http://fqxi.org/community/forum/topic/237
George Ellis is a world expert in cosmology, relativity, and foundations. He also submitted an essay to the FQXi contest

This was an amazing contest. It may have had a subtle transformative effect on the conceptual weather. Thanks to Peter Morgan for clueing me to look into those FQXi comments.

George Ellis takes the "time is real" line, and his essay won the second Community prize.
In case anyone is interested I'll get the link to that as well.
http://fqxi.org/community/forum/topic/361
http://fqxi.org/data/essay-contest-files/Ellis_Fqxi_essay_contest__E.pdf