"Forget time" by Carlo Rovelli

Professor Ellis wrote about Hamiltonian time evolution: "...there must for example be no dissipative processes happening, including no friction..."

but everyone knows that friction forces arise when we describe microscopic degrees of freedom with which the system is interacting with statistically.

About unitary time evolution, it is not necessary to postulate a collapse to account for any experiments. Unitary time evolution alone is enough, see .eg. here:

http://arxiv.org/abs/quant-ph/0204129

http://arxiv.org/abs/quant-ph/0205108

If such a thing as a real non-unitary collapse were to exist, then one sohuld be able to falsify the standard decoherence results based on unitary time evolution in experiments of closed systems.

Saibal,

You wrote:

"it is not necessary to postulate a collapse to account for any experiments. Unitary time evolution alone is enough".

I think this is a common misconception about decoherence. Decoherence by itself does not give a complete solution of the measurement problem, since all components of the mixed state still exist in a global superposition. To account for how this superposition jumps into one of the components in the final step, one has to invoke non-standard interpretations like the many-worlds interpretation.

Thus unitary time evolution alone is NOT sufficient to explain non-unitary quantum collapse, contrary to popular belief.

Ok, but the MWI lets the global superposition be as it is, while other "collapse interpretations" need to appeal to new unknown physics that would explain exactly how the collapse happens.

If you assume that measurements leads to a real non-unitary collapse of a wavefunction, then the whole system observer plus measured system inside a hypothetical closed box would evolve in a non-unitary way even if not measured by an external observer outside this closed box.

Since an observer is nothing more than a many particle system, one should expect that closed systems will, in general, not evolve according to the Schrödinger equation. It could be that the deviations from unitary time evolution become large only if the system is large and then the interactions with the environment get large too, making it impossible to measure such an effect.

Now, the fact that only a few papers have appeared that attempt to explain such a non-unitary time evolution from fundamental physics, suggests to me that the people who work on fundamental physics do not take it seriously.

I am going to break in here because I believe that this exchange between Saibal Mitra and Chi Ming Hung (stimulated by George Ellis) brings to a point some key issues:

(1) In practice people who do calculations in quantum theory rely essentially on projecting the wave vector -- call it collapse or not as you please;

(2) In any conventional interpretation of quantum theory it is only through measurement that we actually learn anything objective about the world (we can only predict probabilities without this);

(3) No conventional interpretation by itself tells us when measurements actually occur or are likely to occur (although various proposals supplementing interpretations have been made);

(4) Decoherence can explain correlations of measurements, but it cannot, by itself, explain the measurements;

(5) The desire to avoid taking up the physics of what precipitates measurement seems to come partly from the fact that it has been little studied, so people are somehow unsure if it is a real question, and partly from a view that if the entire world is really described by quantum theory, then where is there room for a classical measuring apparatus?

It seems clear that physicists should be able to give a physical criterion for when measurements occur, however. This criterion evidently cannot come from within a standard interpretation of quantum theory; it must be a new element. (That does not mean one needs a radically new interpretation; it does mean one needs to figure out what physics is going on.)

Hi Carlo,

I am also going to break in here, because I believe George Ellis made a crucial remark.

George explained his understanding of your claim that there is no preferred time variable in GR (George Ellis, Dec. 12, 2008 @ 20:27 GMT):

"This is correct as regards spacelike surfaces that can represent constant time. But proper time along world lines is indeed a preferred time variable in GR. The fundamental difference from Newtonian theory is that the preferred time is defined along world lines, instead of by spacelike surfaces. Proper times along timelike worldlines is what is measured by clocks ticking (p.3). So you focus on problems with surfaces of constant time, I focus on the meaningful nature of proper time along world lines."

On the other hand, in your arXiv:gr-qc/0604045v2, p. 4, you explained your understanding of 'no preferred time variable in GR' in the following fashion:

"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 x^0, but this coordinate, does not correspond to anything directly observable. The proper time [tau] along spacetime trajectories cannot be used as an

independent variable either, as [tau] 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 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 (notice the remark by George above - D.C.).

"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."

It seems to me that you and George are discussing 'apples and oranges': you are discussing the problem of time in classical GR, while he was (tacitly?) implying some yet-to-be discovered quantum gravity in which the "meaningful nature of proper time along world lines" (George Ellis, Dec. 12, 2008 @ 20:27 GMT) would be akin to "a single trajectory" (arXiv:gr-qc/0604045v2, p. 4).

May I ask you to sort out this issue with 'scrupulous intellectual honesty' (C. Rovelli, arXiv:gr-qc/0109034v2, p. 9).

Please also notice my criticism of your Essay, posted earlier ( Dec. 12, 2008 @ 03:58 GMT and Dec. 12, 2008 @ 16:21 GMT): the Heraclitian Time, which corresponds to the very *generation of 3-D space*, is absent in GR.

Again, if you really believe, with scrupulous intellectual honesty, that we should "forget" time, you have to demonstrate the emergence of 3-D space from some primitive (Borel?) set of abstract mathematical points, and then prove that this *emergence* is indeed timeless.

Please act promptly: the Heraclitean Time you have by the contest ending (January 1, 2009) is running out.

Dimi

Dear Carlo,

I've read in some of your replies that you are ready ``forget space-time". In SOME sense it is possible. Please see technical detailes in

http://www.fqxi.org/community/forum/topic/327.

Best regards,

Peter

Hi Carlo,

Great essay. I think you do a great job of providing a historical reference frame for this topic before you introduce your own ideas. Very enjoyable.

You argue that the origin of time variable features are not mechanical, rather - emergent at the thermodynamical level. Do you have any thoughts as to how velocity or gravity affect the time dilation of these thermodynamical activities? It seems to me that despite all of the essays, with so many different opinions of time's true nature - we have only two possible fundamental starting points:

1) That the thermodynamical activity, or motion (or what I refer to as fundamental behaviors in my essay) is used as a measurement of "time" but plays a more passive role because these behaviors exist "in" time and their behaviors are just a visible symptom of what "time" they existed in due to their local environment.

Or

2) What we perceive as time is a macro effect of the most fundamental behaviors among particles, forces and fields. These behaviors define time and in fact are time. Now, if the most fundamental behaviors can all be accurately described as motion, then - okay. But if some behaviors on the quantum level no longer make sense to be described as motion, then it is safer to refer to the fundamental activities as "behaviors."

For those who commit to the first possible starting point, they would not appear to be in conflict with special relativity - namely Galileo's principle. The existence of time would be part of the metric that particles and forces exist "in." There would exist Einstein's inseparable connection between time and light signal velocity. There would be no "mechanism" - instead, the relative nature of time would just be a co effect of velocity and/or changing gravitational position. Time would exist as a mysterious entity (or co entity) and more questions would certainly need to be asked as to how we could get closer to determining its true nature.

For those who commit to the 2nd possible starting point (which is the one I am committed to) that motions or behaviors define time and in fact are time: Let's take a system with all of its fundamental behaviors and increase its velocity. These behaviors slow down. If the behaviors themselves "are" time and then become altered as a consequence of their increased velocity- then we need to revisit special relativity. Something is happening on the physical level that we currently don't have a description for.

Thank you,

CJ

Dear Carlo,

While I tend to agree with George Ellis' objections to your view on how time might be recovered, I do not see how any notion of objective time flow can be saved (let me note that the notion "timeless universe" is misleading; I think it should be "timeflowless universe").

It has been already realized that the traditional view of time flow - as an evolution of a three-dimensional world - is in a direct contradiction even with special relativity (the notion of a three-dimensional world is based on the idea of absolute simultaneity). Then versions of the growing block universe introduced by C. D. Broad in the twenties started to emerge - Ellis, Christian (gr-qc/0610049), Sorkin (gr-qc/0703098). All these versions claim that they do not allow any form of a preferred structure. However, I do not see how this claim can be supported if it is explicitly assumed that the existence of physical bodies is absolute. Then it becomes evident that the growing block universe model also contradicts relativity - the hypersurface (no matter how complex its shape might be) on which the birthing of events happens constitutes an objectively privileged hypersurface (existence is absolute!) and therefore an objectively privileged reference frame. To avoid such an objection Christian proposed that existence should be relativized. To my knowledge, no one has succeeded in providing convincing arguments to defend such a notion.

I have failed to see the justification of what George Ellis wrote that the "time evolution is not related to any preferred surfaces in spacetime; rather it is associated with the evolution of proper time along families of world lines" and also (Fig. 2): "The particular surfaces have no fundamental meaning and are just there for convenience (we need coordinates to describe what is happening)". If existence is absolute, the birthing of events in spacetime does constitute a given hypersurface (again, no matter how complex it might be). Let me stress - I do not mean how we describe the evolving spacetime; the point is what actually happens (and then we can talk about a description) - how the whole network of worldlines grow along the proper time of each worldline (or a family of worldlines). One can also ask additional questions about such an evolving spacetime - e.g. light-like worldlines should also evolve (obviously not in terms of proper time).

Vesselin Petkov

As many people,that many ideas about such fundamental concepts as space and time. Prof Carlo has his and so also the others. To understand the significance of both space and time, let us work out Physics without consideration of these concepts. The reality will remain elusive until we explain the observed facts with alternate concepts. After all the humans evolved these concepts and they are capable of evolving alternate ones. However, there will not be any science without some sort of precepts that lead to some logical concepts. Only then one works out the detailed explanations using mathematical tools to represent the observed facts as also to predict some that still need to be proved experimentally. As measurements will always be limited in sensitivity and accuracy, we still remain bound by such limitations. Thanks to it , we will continue to persue science as a professional activity. However, let us all always remember that we need to continue to build a better human society through our scientific endevours. If we are unable to do so, science may also collapse with humanity. The latter has got a priority over science which is just a professional activity tied to human welfare and basic curiousity about the environment around. Foundational aspects of science are closely linked to human development in a positive direction. Sorry, if it seems like a 'sermon', as i can't claim any such authority!

Addendum to my request for clarification, posted on Dec. 13, 2008 @ 13:01 GMT:

George wrote (George Ellis, Dec. 12, 2008 @ 20:27 GMT):

"But proper time along world lines is indeed a preferred time variable in GR."

May I ask you to clarify the exact meaning of your "preferred time variable in GR" by elaborating on the affine connection. Let me quote from Wikipedia:

"... parallel transport along the curve preserves the tangent vector to the curve, so

nabla_{dotgamma} dotgamma= 0

at each point along the curve, where dotgamma is the derivative with respect to t."

George: Is your "preferred time variable in GR" keeping track on *each point along the curve*? If yes, what is the mechanism of this tracking?

Also, is dotgamma the derivative with respect to some gauge-dependent coordinate time, t, or is it with respect to the proper time [tau] along spacetime trajectories?

Regarding the latter, Carlo wrote (C. Rovelli, arXiv:gr-qc/0604045v2, p. 4):

"The proper time [tau] along spacetime trajectories cannot be used as an independent variable either, as [tau] 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."

I trust Carlo will elaborate on the (timeless?) affine connection as well.

As Alan Rendall acknowledged:

"In elementary textbooks on general relativity we read that the Einstein equations imply that small bodies move on geodesics of the spacetime metric. It is very hard to make this into a mathematically precise statement which refers to actual solutions of the Einstein equations (and not just to some formal approximations)."

Perhaps Carlo Rovelli's suggestion to "forget" time and space is rooted on some 'formal approximations'. Recall Murphy's Law No. 15: Complex problems have simple, easy-to-understand wrong answers.

Dimi Chakalov

Discussion of my paper should prefereably be over in my thread, not here, nevertheless as there are two postings over here ask for answers from me, I will answer them here.

Dimi Chakalov, you ask "is dotgamma the derivative with respect to some gauge-dependent coordinate time, t, or is it with respect to the proper time [tau] along spacetime trajectories?" It is with respect to proper time $tau$: which is the meaningful physical time along world lines, and is also the curve parameter for which the geodesic equation has a zero on the right hand side (which is how it relates to parallel transfer).

Vesselin Petkov, you state "It becomes evident that the growing block universe model also contradicts relativity - the hypersurface (no matter how complex its shape might be) on which the birthing of events happens constitutes an objectively privileged hypersurface (existence is absolute!) and therefore an objectively privileged reference frame." I tried to argue that one should think only in terms of evolution at space time events or along world lines, and not try to consider the relation of times along different world lines and so on spacelike surfaces. However if one insists on doing so and considers relevant spacelike hypersurfaces, then yes, an objectively privileged time frame exists. There is nothing new in this: every physically realistic solution of Einstein's equations has preferred space sections, being just another case of the broken symmetries that are so fundamental in present day theoretical physics (the underlying equations have higher symmetries than their solutions). The classic case is the Friedmann-Lemaitre cosmological solutions of general relativity: no one in their right minds uses any time coordinate other than the preferred time coordinate that is always used! (which is of course proper time measured along the fundamental world lines). Objectively privileged hypersurfaces do indeed exist in standard cosmology, and in all physically realistic solutions. And in the end, the real-world evidence that time does indeed flow is overwhelming (example: this posting was not posted till I posted it at a particular proper time along my world line); if this demands that preferred space sections exist, so be it, too bad for any theory that denies their existence in the face of this evidence. The quote from Omar Khayam in my essay refers.

Finally what about evolution along lightlike world lines? yes this can in principle take place; but in my paper I tried to indicate that while this is a possibility, in real situations such as cosmology, signficant effects almost always propagate along timelike world lines rather than null ones. The only physically significant case where influences along null curves are important are in relation to lasers; but they themselves are physical objects that move on timelike world lines.

Dear Carlo Rovelli,

Very interesting approach: there is no time - there is no problem. Remaining within the bounds of the special theory of relativity, we cannot refuse the relativity of simultaneity, which concerns to events at a quantum level also. In the general theory of relativity the time plays a key role, therefore the quantum theory of gravitation without time in principle cannot be constructed on the basis of the general relativity. However, hopeless situations do not meet. The quantum theory of gravitation can be constructed as the alternative theory of gravitation. One of many alternative approaches to time and gravitation is presented in essay The Theory of Time, Space and Gravitation.

Regards,

Robert Sadykov

I suppose I will throw in my 2 cents on this. I don't think that science can tell us about the existential status of geometric entities. If one considers a point x in spacetime, one can chose two different spatial surfaces S and S' where one pushes this point x to x' and x" which are not equal. General relativity is not about geometric entities, such as points, but it is about the relative motion of particles, such as the goedesic deveiation equation

x^a_{ss} = R^a_{bcd}U^bV^cU^c,

where x_{ss} = 2 derivatives with respect to proper time. So GR does not tell us about the existence of points, or as in the old perspectie "events," but it does tell us about intervals between them (proper time) and permits us to compute the dynamics of particles.

Quantum mechanics and general relativity involve two different notions of time. In quantum mechanics a Hamiltonian is defined by specifying a coordinate time. The Hamiltonian in a Neotherian perspective is the generator of time translations. Yet in general relativity this coordinate time is just a bookkeeping device we impose.

So we are caught with two different concepts of time in our two pillars of physics. There is a third pillar which is thermodynamics, and the so called arrow of time due to the second law of thermodynamics.

In #370 I suggest that time is a scaling principle. Imaginary time t = hbar/kT, for T = temperature in an AdS/CFT setting plays the role of a possible renormailization group. If we think of spacetime as composed of Sakharov oscillators (pregoemtry) the temperature T tells us how many of these modes are excited, which in turn can determine the scaling principle for the phase of spacetime.

I don't know if physics can ever tell us whether time exists or not, but it is an aspect of model systems that is useful.

Lawrence B. Crowell

George,

Thank you for your partial reply from Dec. 15, 2008 @ 05:16 GMT.

Is your "preferred time variable in GR" identical to what you just dubbed 'the meaningful physical time $tau$ along world lines'?

Is the latter observable (=read by a physical clock), or is it "the explicit (but unmeasureable) time" suggested by Bill Unruh?

Can you solve the Cauchy problem for Einstein field equations with your "preferred time variable in GR" or 'the meaningful physical time $tau$ along world lines'?

What is your 'test of the pudding', actually?

Dimi

Lawrence B. Crowell wrote " So we are caught with two different concepts of time in our two pillars of physics. There is a third pillar which is thermodynamics, and the so called arrow of time due to the second law of thermodynamics".

May be, GR operates with ensemble of particles only. On the one hand, the ensemble has statistics of interaction (i.e. it has thermodynamic time); on the other hand it has gravitational mass.

The QM examines wave function microparticle on a background of temperature time of this ensemble.

On Dec. 12, 2008 @ 13:11 GMT, Carlo Rovelli wrote:

"I apologize for the posts I am not answering to. I am tryng to catch up..."

No rush, please take your time. I believe have showed that your approach is logically inconsistent -- please check out my postings above from Dec. 12, 2008 @ 16:21 GMT, Dec. 13, 2008 @ 13:01 GMT, and Dec. 14, 2008 @ 14:01 GMT, and follow the links.

In a nutshell, your logical error would be similar to the following claim: Fish cannot ride bicycles, therefore we should "forget" about bicycles.

More on the intrinsic limitations of GR in my posting to Gavin Crooks from Dec. 13, 2008 @ 20:55 GMT.

Dimi Chakalov

Dear Carlo,

Thanks for clarifying your use of the Heisenberg representation. (I now see I had too quickly jumped to a misinterpretation of some of your notation.)

I also appreciate your comments that thermal time is meant to get at concepts of flow and irreversibility. If it is possible to be more precise (for example, to say how thermal time is measured, or to what systems the concept of thermal time applies), that would be helpful.

In this connection (trying to understand just what thermal time was) I raised some other questions (about the objectivity of the concept, and about its application to simple systems) in my previous post, and if you get a chance I'd be interested in the answers.

Thanks,

Adam

What does "the real-world evidence" support - an objective flow of time or the block universe view?

As what George Ellis wrote above "the real-world evidence that time does indeed flow is overwhelming" is quite relevant to the topic of this contest and especially to Carlo Rovelli's position I will comment here. But my comments on his statement "Objectively privileged hypersurfaces do indeed exist in standard cosmology, and in all physically realistic solutions" will be posted on his thread. Lawrence Crowell's "I don't think that science can tell us about the existential status of geometric entities" will be addressed on my thread.

Yes, of course, the evidence that time flows is indeed overwhelming, but that evidence is not physical. If the evidence is analyzed rigorously it becomes clear that it boils down to the fact that we realize ourselves and the world at the constantly changing moment 'now'. But it does not necessarily follow from that undeniable fact that the world itself also exists only at (or up to) the present moment. That is why Hermann Weyl, who certainly was aware of "the real-world evidence", conjectured that it was our consciousness crawling along the worldtube of our body that creates that evidence and the feeling (illusion) that time flows. I would suggest that all who disagree with the block universe view analyze only Weyl's conjecture and try to find just one example (or even a hint of an example) when it fails to explain what we perceive as flow of time.

To avoid any misunderstanding, George Ellis' "The time reversible picture of fundamental physics underlying the block universe viewpoint" (p. 3 of his essay) is not quite correct. The block universe view does not follow from the reversibility issue; that issue was known before Minkowski introduced the concept of spacetime. It is the spacetime idea that underlies the block universe view - if spacetime is not just an abstract mathematical space but represents a real four-dimensional world, we call that world a block universe.

Also incorrect, in my view, is another statement: "This irreversibility is a key aspect of the flow of time" (p. 1 of his essay). I think the majority of relativists will agree that the irreversibility of physical processes demonstrates the anisotropy of spacetime and does not imply an objective flow of time. Let me specifically stress - we are not asking how to describe spacetime in terms of the idea of time flow (based on our three-dimensional language); we ask the fundamental question - is the future as real as the past, or more precisely, is the world four-dimensional (a block universe)?

The real situation is, in fact, opposite to what George Ellis wrote -- the macro scale evidence supporting the block universe view is overwhelming. Consider even special relativity and ask whether the experiments (not just the theoretical results), which confirmed its kinematical predictions (relativity of simultaneity, length contraction, time dilation, twin paradox), would be possible if the physical objects involved in these experiments were three-dimensional or growing four-dimensional worldtubes.

Here is a very quick example of such an analysis in the case of length contraction. First, take into account that an extended three-dimensional body is defined in terms of simultaneity - all its parts taken simultaneously at a given moment of time. Then, as length contractions turns out to be a specific manifestation of relativity of simultaneity, while measuring the same rod two observers A and B in relative motion measure two different three-dimensional rods (two different sets of the rod's parts) since A and B have different classes of simultaneous events. Is this would be possible if the rod were a three-dimensional object? Is this would be possible if the rod were a growing worldtube (see the attached diagram)?

In the case of the growing worldtube one might argue that we will always see only the completed part of the worldtube since we always see past events. That is, of course, correct but try to imagine how many tough questions the growing or evolving block universe has to answer (even tougher than the questions the block universe view itself has to answer) - (i) we are interested not only in what we observe (from what we observe we try to understand the world itself), (ii) how to explain, for example, the EPR-Bell-Aspect type of experiments, (iii) how to explain the inescapable conclusion that the evolving block universe is as predetermined as the block universe since the growing block universe will be merely actualizing the forever given events of the block universe (take into account the EPR-Bell-Aspect type of experiments, for example, to see why), etc.

And one last point - the probabilistic behaviour of quantum objects does not necessarily contradict the forever given spacetime picture of the world. To see why this is so, assume that the quantum objects do not exist continuously in time (which means that they would have an internal frequency).

Vesselin PetkovAttachment #1: Growing_4D_World.pdf

Correction

I am sorry for this correction (the error was caused by editing at the last moment). The last two sentences of the third paragraph from the bottom should read:

Would this be possible if the rod were a three-dimensional object? Would this be possible if the rod were a growing worldtube (see the attached diagram)?

Vesselin Petkov