Progressive weakening of the idea of time since 1905 (Ch. 1 of new book from C.U.P.).

[Martin]

There's a new book out from Cambridge University Press with the subtitle "Towards a New Understanding of Space Time and Matter" and Chapter 1 is this 8 pages of non-mathematical overview piece by Rovelli which appeared earlier on the arxiv.

http://arxiv.org/abs/gr-qc/0604045

 

Here's a sample excerpt that deals with time.

 

He is talking about the gradual progressive weakening of the concept of time. From classical mechanics, to special rel, to general rel, and finally to quantum GR... I've highlighted to make the structure of the progression more obvious.

 

==quote==

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==

 

This is kind of serious. For almost 100 years Gen Rel has been the prevailing theory of how gravity works and has provided our basic idea of space time and geometry. It explains how geometry arises and why Euclidean geometry emerges as a low-density solution. Yet Gen Rel does not admit an idea of time.

Once you have a solution, a fixed geometry, you can run observers in that context and they can carry clocks and have an individual idea of time. But the system as a whole has no overall time that it evolves according to. So GR has been predominant for nearly 100 years and we maybe still didn't realize that it doesn't have have the kind of time feature we normally expect.

 

Chapter 2 of the new book is by Nobel laureate Gerard 't Hooft. It is on a similar theme, he talks about what he thinks it will take to get at the fundamental nature of space and time. In case anyone's interested, here is the chapter that 't Hooft contributed:

http://www.phys.uu.nl/~thooft/gthpub/QuantumGrav_06.pdf

 

There is a kind of consensus among the contributors to the book that space and time are macro-scale perceptions which emerge from something more fundamental, a different model of reality down at microscopic level.

 

This has been brewing in Physics for some years already, many of the chapters in this collection were posted already in 2006 or 2007 as preprints.

And there are contributors from many separate research lines (string theorists, inflation cosmologists, phenomenologists, non-commutative geometers, people from loop quantum gravity, several other non-string QG fields, particle physics, and so on...) About 20 authors in all.

 

So here's one part isolated from Chapter 1. It's about the historical weakening of the idea of time (in foundations physics, not in applied as far as I know.)

I put it out as a thread in case anyone wants to discuss it.

 

The book is expensive, aimed at the academic library market. Physics department librarians will order it on faculty request---that kind of thing.

In case anyone is curious:

http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=9780521860451

Edited April 11, 2009 by Martin

[Australo Rob.]

Martin, is it the case that a major plank of the time dilation theory is that light speed reception is constant? And is it also the case that several experiments, such as measuring light speed whilst we are rotating both toward and away from the sun, have shown this to be the case?

[Martin]

Rob, I appreciate your asking me, but that question belongs in the Relativity forum

http://www.scienceforums.net/forum/forumdisplay.php?f=20

Please open a thread there and ask that question where it can be answered without getting this thread off topic.

 

mod note: Use this thread (i.e. that's a link)

Edited April 11, 2009 by swansont
add mod note

[fredrik]

Thanks for another good highlight Martin!

 

I'll add my partly critical view to Rovelli's ideas.

 

There's a new book out from Cambridge University Press with the subtitle "Towards a New Understanding of Space Time and Matter" and Chapter 1 is this 8 pages of non-mathematical overview piece by Rovelli which appeared earlier on the arxiv.

http://arxiv.org/abs/gr-qc/0604045

 

Here's a sample excerpt that deals with time.

 

He is talking about the gradual progressive weakening of the concept of time. From classical mechanics, to special rel, to general rel, and finally to quantum GR... I've highlighted to make the structure of the progression more obvious.

...

I put it out as a thread in case anyone wants to discuss it.

 

I see the picture Rovelli paints by noting this trends, is part of the motivation for his own expectation of the future of physics. I think his idea is to argue that he takes the relational ideal, to it's extreme, but IMHO he still maintains a great deal of realism (making the revolution still incomplete)

 

Rovelli suggests that the root of some confusion is not beeing clear on what an observable means.

 

In his paper http://arxiv.org/abs/gr-qc/0110035, he tries to classify observables as partial and complete.

 

"Partial observable: a physical quantity to which we can associate a (measuring) procedure leading to a number."

 

"Complete observable: a quantity whose value can be predicted by the theory (in classical theory); or whose probability distribution can be predicted by the theory (in quantum theory)."

 

He notes that classical (ie. non.quantum) mechanics is all about relations between partial observables. Ie. the theory does not determine partial observables, it only determines relations between them, and these relations are envisioned as timeless.

 

In the QM case, he says that the theory should predict conditional probabilities, (or probability amplitudes) between partial observables. Again these conditional probabilities are timeless.

 

He says that that partial observables has a physical correspondence in that that correspond to actual measurements, such as clock readings, rod readings etc, detector readings etc.

 

The complete observables OTOH, are what the theory predicts.

We have learned from SR and GR that coordinate measurements are ambigous because the coordinate lacks physical basis. This is what we get if we think in terms of geometry. The parameterization of a section of a curved surface has no relevance for it's geometry. The geometrical properties OTOH, are those that are diffeomorphism invariant, and thus observer invariant.

 

So what's the possible objection to this picture which seems to be the basic lesson from the relational tradition from Mach to Einsten? My objection is that it's not relational enough, in particular does it ignore the relativity of the observers internal structure.

 

In SR and GR, an "observer" is reduced to a choice of coordinate gague. A reference frame equipped with clocks and rods. No attention is ever payed to how the physical manifestation of these clocks and rods are actually to be realized, in sharp situations, and wether there are constraints on the freedom to build accurate clocks and rods, and what happens to the observational data, once observed? IS there any hidden memory storages somewhere?

 

In QM and observer is reduce to a choice of measurement operator.

Then the geometrical picture means, that what a single observer is completely arbitrary since in the geometrical picture the observer is simply an arbitrary gauge fix. It's only the relations between all possible observers that we can predict from a theory. But how do we know when we have distilled the full symmetry transformations between all observers? And more important, how can an single observer acquire and hold this information?

 

There is a birds view here, that breaks the relational ideal. It implicitly makes use of a birds view that IMO is principally no more sophisticated that newtons idea of absolute space.

 

I don't think such an abstraction acknowledges the meaning of the observer. It is still true that an observer can only be characterized by it's interactions with other observers. And thus we expect that our theory should predict how observers interact. In a sense this is what gauge theory does, two different observers, corresponding to different gague choices, are related by the gauge transformation.

 

So the gauge symmetry, predicts how any two arbitrary observers relate.

But this isn't good enough. What we need is one observers view, of how two OTHER observers relate. Not Gods view, of how two observers relate?

 

The first point is that we can not so easily dimiss the concept of observer, a fundamental object in any theory of scientific inquiry, to the status of an arbitrary gauge choice. There is something deeply wrong with that, that seems to imply a hidden birds view, where you picture "all possible observers" and that the collective somehow describes a geometry. But the only one that can be at a single moment, be informed about this is an omnipresent observer that can see everything, but without interfering.

 

But somehow, the very notion of theory, belongs in the context of scientific inquiry itself. Thus the idea of observerindependent laws, are an almost religious realist idea I can't accept.

 

I would expect that laws are what an observer infers from measurments, as per some scientific method, and not ONLY the other way around. I think there IS a infinite regress here, that is unavoidable. And this regression IS evolution.

 

The question I have at my hand, is not how the unknown laws of physics can explain my observations, but rather how I can infer from them, knowledge that allows me to LEARN about the laws.

It's here the internal structure of the observer comes into play. To make a comparasion between partial observables, some sort of memory structure is needed. Also the amount of memory limits what is possible to see. These things are not even mentioned in Rovelli's reasoning. Which I find surprising.

 

Therefore, i think that an alternative reasoning than that of rovelli, is to consider evolving and emergent laws. And these laws, an in particular, different observers differing VIEW of law, explains their relation, and mutual impact. This could be an alternative logic, still effectively consistent with all we know of SR, GR and QM. It might however, suggest a different way forward, that is even more relational that the geometric view rovelli advocates. In that it totally does away with the realism of geometry as well. And not only in the probabilistic sense, that we only know nthe probabiltiy for the geometry, but in a even deeper sense of evolving law.

 

This paradox here between the fundamental importance of the observer, and on the other hand the geometrical view that hte observer is ambigous and that only the relationas to other observers, can justify it needs to be resolved. I can't see that rovelli tries to. The gods view may seem like a technical possibility, but I think it's conceptually inconsistent with a fit method of scientific inquiry.

 

The person I think is at least starting to acknowledge some of these questions is Smolin. He seems to have a chapter in the later part of the book, but it doesn't seem to focus on this.

 

I think the relational ideas, and relations between partial observables, is a good perspective. But I think something is missing.Rovellis seems to want to tie up that sack in a realist manner. I think the picture, in which the actual complete observables emerge, must be an inside view, not a birds view, which in turn imples that the basis of this view is evolving. Rovelli on one hand, seems to try to very much acknoqledge the deep lessions from relativity, but when he tries to merge it with measurement theory, I can't see that his synthesis there is satisfactory. I think another way to do it, would instead place the typical symmetry views, in a dynamical context, and thus the emergent symmetries would correspond to emergent observable law. The concept of an observer independent law should not be needed, no more than an external embedding space is needed to describe differential geometry.

 

So the early part of Rovellis abstraction of mechanics, as well as the early part of his relational QM(http://arxiv.org/abs/quant-ph/9609002), is I think good, but when this is to be cast into the form suitable for a theory of scnetific inquirry, it does not quite do to reduce the observer to a arbitrary gauge choice and be done with it.

 

I'll end with noting that I think that Rovelli's RQM paper is one of not so many favourite papers of mine. Not because I like all of it, but because it contains part that speaks for themselves.

 

/Fredrik

Edited April 13, 2009 by fredrik