"Forget time" by Carlo Rovelli

I completely agree with the basic idea expressed in this essay. Let us forget about time!

In fact, I believe that if we want to understand the deepest laws of physics we have to get rid of all the unobservable quantities -- finding all the "illusory" macroscopic degrees of freedom and then quotienting them away (just like GR and gauge theories do).

Quoting Zurek, this may be called a part of the "epiontic" approach to physics (which I review in my essay).

Thanks for your inspiring work.

L. Acerbi

(The Epiontic Principle..., http://fqxi.org/community/forum/topic/333)

Including conventional Time as Superstring theoricians or C. Rovelli do can be seen as much as 'forgetting Time' than 'prescribing Time'.

Second expression is more logic until String Theoricians or Dr Rovelli do not prove that Time is not only a conventional idea but a material one that is grounding the dose of Time. A proof that is obviously lacking here, although the question was -remember- about the NATURE OF TIME.

If a 'pure theorician' does not want to prove that Time is 'something', what I can understand, in this case he MUST prove that conventional Time is dynamics.

Are Boltzmann or Planck telling us anything about the dynamism of Energy or Matter? No, they are just 'quantifying it' that is to say 'squaring the circle'.

We do not know anything more about temperature, energy or matter after Planck than before. Worst than that:idea is growing from here that ballistic measurement (the Wave) is part of Matter although it is only part of ballistic.

To make a comparison: exactly as Walras thought that his economic Diagrams grounded on thermodynamism were part of the Economy.

May I hope for an expert answer, maybe by someone else?

I consider my suspicion serious and - if justified - rather important.

Eckard

No expert, please! (Experts are blind soldiers of Empiricism E. Blumschein, taking the differential for the common principle.)

I translated for you a quoting of R. Descartes, father of Empiricism as much as Newton, a quoting that proves that C. Rovelli or Lee Smolin are about three hundred and fifty years late if not more:

"First thing one have to be worried out is that many [Scientists] are mistaking Space idea with Time idea or Speed idea... If I would have link Speed idea with Space idea, I should have give necessarily three dimensions to Force, although I gave to Force only two dimensions to leave out Time.(...)" R. Descartes, September 12th 1638.

All the problems of today Physics are still included in this letter of Descartes who does not solve them but is rationally forgetting Time in Empiricism, that is to say Force, Energy, Inertia and ballistic problems. Rovelli says he is doing it like Descartes but he is keeping Time as a convention! Nothing is more subjective.

Notice E. Blumschein that Descartes is 'anticipating' A. Einstein or H. Bergson attempts to put Time again in Empiricism (probably for cultural reasons, love of poetry and music that are changing the subtle Time in something stronger).

The question of Time and the question of what does Planck say about Einstein and Einstein about Planck, those questions we are turning around and turning around since three hundred and fifty years are in Descartes quoting.

Even if it is difficult to fight against Empiricism or Algebraic Geometry because it gives the illusion of seriousness (3,14 looks more serious than 4 or 3), my opinion is that "experts are dead already". It is still like they are speaking from the Past.

F. Le Rouge,

Even if we are at risk to forget Carlo Rovelli instead of forgetting time, your hint to Descartes reminds me of the fact that Descartes hesitated to introduce coordinates with

not just positive but also negative values. Admittedly I did not read it in the original but in a small booklet on Albert Einstein by Cornelius Lanczos (Loewy) which was translated in Russian language.

I also read somewhere that Fourier was pondering whether or not to integrate not from minus infinity to plus infinity but from zero to infinity.

Furthermore I read an argument of contemporary physicists: Restriction to past time would not be reasonable because prediction is the main goal of physics.

Hopefully you will understand my point of view from 369.

My question to Carlo Rovelli was how do we - step by step - arrive at the complex frequency domain when we start from a measurable, i.e., past function of time? Can complex frequency domain simultaneously include complex time domain?

Descartes did not have any chance but to make the first step by introducing the still ubiquitously accepted notion of Christian time which is also Christin's time. The void future "semigroup" is redundant. That's my message.

Could the consequences be like a purifying lightning? Hopefully I will still witness the failure of LHC to confirm the standard model. I guess, Nimtz will nonetheless continue to claim having proven superluminal propagation of signals.

Physicists are too proud as to take an old engineer serious.

Eckard Blumschein

As a physical mathematician (the converse of a mathematical physicist), my view of mathematics often differs from my pure mathematician colleagues. Nowhere is this more noticeable than when I teach calculus, which, as traditionally taught, is about functions. But science is about equations, that is, about relations between physical quantities, not about dependent and independent variables.

Never in my wildest dreams did I imagine that all those related rates problems in fact contained a possible resolution to one of the universe's most vexing questions, namely what the nature of time is, or perhaps what it is not.

Dr. Rovelli

yes, time is not a fundamental physical reality

time is an observer effect

yours amritAttachment #1: 1_THE_THEORY_OF_ATEMPORALITY__SORLI_2008.pdf

Tevian Dray,

Maybe, you didn't write an essay, maybe I overlooked it. My essay is nearly the opposite of what prefers the majority from Baez to Wheeler. The majority is strong enough. It does not need your support. Why do you deny the distinction between cause and effect in physics?

A key argument of mine is the limitation of original physical quantities to quantities that cannot change their sign.

I am calling it not an equation but an inequality if for instance pressure is always positive except when measured on log scale while sound pressure alternates around the dc component, and the elementary electric charge is negative. Likewise one can not measure negative distance and also not negative duration.

I asked Carlo Ravelli to explain step by step how the i in his equations 5, 19, 24, 26 can be derived from reality.

I was not surprised that he refused to do so because already Charles Francis in spf was also unable to do so.

While they could do it quite easily, they were forced to admit that some strangeness of quantum mechanics could be explained as consequence of improper interpretation of complex quantities.

Apparently they prefer taking quantum mechanics a gospel and deny the elapsed time instead. Carlo Ravelli even suggests to forget time in general. Mors certa, the clock is uncertain.

Eckard Blumschein

Dear prof. Rovelli,

I liked your radical approach to a description of physical phenomena. You suggest a timeless description. I believe, that your approach is insufficiently radical. In my opinion, one should use coordinateless description for the space-time geometry. Such a description is used in the Euclidean representation of the geometry, which is used for a teaching in the middle school.

However, the main problem of contemporary physics lies in the fact, that our knowledge of geometry is poor. We cannot describe discrete geometry. We cannot describe geometries with restricted divisibility. We know only axiomatizable geometries, which can be deduced from some system of axioms. However, the axiomatizable geometries form only negligible part of all possible geometries, which are mainly nonaxiomatizable. In particular, the true space-time geometry admits one to consider the principles of quantum mechanics as needless.

Let me explain the situation in a simple example. Let us imagine a person N, who does not know, that the quadratic equation has two roots. (He thinks, that the quadratic equation has only one root). I understand, that such a situation is rather unreal, but nevertheless, let us consider this situation. Constructing theories, the person N may meet such a situation, when one needs two roots of the quadratic equation. In this case he should think about his knowledge of algebra.

But the person N is self-opinionated. He invented new hypotheses, which admit him to compensate his poor knowledge of algebra. These new hypotheses are simple fittings, but in some cases these fittings work successfully. In other situations these fittings cease to work, and the person N is forced to search for other fittings.

Principles of quantum theory and, in particular, the quantum theory of gravity are such fittings, generated by our poor knowledge of geometry. There is a lot of papers on this subject (look in Aricheves, searching my name "rylov". It is enough). There is also my essay on this contest.

My slogan is: "Find and correct mistakes! New ideas are needless!"

Sincerely yours,

Yuri Rylov

Dear Carlo,

I've been reading your essay with interest. There are some points I'd like to understand. (Sorry about the long post -- that's what you get for writing a stimulating essay!)

(a) Am I right in thinking that you adopt the Schroedinger rather than the Heisenberg picture in order to try to pass to a theory of quantum gravity? (If we limit ourselves to, say, quantum fields in curved space-time, then the Heisenberg picture is more naturally relativistic, does not distinguish a particular time parameterization, and seems to meet most of your concerns -- although it does not explain the nature of time.)

(b) My main question is, What is the significance of thermal time? Your hypothesis is that this is "what we call 'time'" and "physical time." Since, however, as you emphasize, no relativistically invariant notion of "time" in general, it seems it must be some sort of cosmic time, or time somehow collectively generated by a system. Under what circumstances could we expect thermal time to approach one of our other notions of time?

Suppose I have a simple spin 1/2 system, which I prepare in a (constant) state

epsilon |up>

[The following seems to have gotten cut off my last post.]

epsilon |up>

[O.K.; the blog parser seems to be selecting against my states! Here goes again, with less technical notation.]

rho = epsilon (pure up) (1-epsilon ) (pure down).

After preparation, the system does not evolve (it is insulated). What meaning, then, am I give to thermal time? It does not, with H_rho, generate evolution (the state remains constant). Does it connect with another, familiar, sense of time?

(c) Your program turns on the idea that the system considered is in a statistical state, which reflects "our ignorance of the microstate." How objective is the concept of "our ignorance of the microstate?"

I am guessing that you intend that there is at least a semi-objective way of quantifying this. Two possible approaches occur to me. One is some sort of coarse-graining (as in conventional thermodynamics). If that is what is intended, is it possible to give an idea of what this coarse-graining is?

The other possible approach to objectify knowledge of the microstate would be to consider the effects of quantum measurements as restricting the state. But those lead, not just to statistical restrictions, but to actual projections of a state vector (rather than a density matrix). (One could also consider some sort of mixed approach.)

One reason I am wondering about this is that the thermal Hamiltonian, being - log rho, would be very sensitive to the precise probabilities assigned to very unlikely states. Thus it seems that one has to spell out fairly precisely how to determine the statistical state in order for the thermal Hamiltonian to be well-defined.

Thanks,

Adam Helfer

To Blumschein:

-I will read your essay as soon as possible.

-Even if it is more serious from Descartes, father of the Algebraic Geometry to 'forget Time' when you say you want to forget it, although Rovelli is keeping it as nothing less than a dimension!?, nevertheless Descartes is trapped by the Potential Infinity postulate (see my forum) where Black Holes ideology is diverted. There is a Discontinuity in the Standard Model and where Descartes is speaking about 'slipping', Quanta Physics is speaking about 'black holes'.

Hello Dr. Rovelli,

while i can fully appreciate an apparent confusion in identification of relationships in time with time itself and an interest in recognizing that what is referred to as time in physics is typically relative associations and wishing to do away with 't' in considering the relationships (essentially, i see no problems inherent in the math with conclusions 1 and 2), but, relative as they may be, the relationships are not spatial in nature.

an example i used in a post elsewhere here:

we can toss a hula hoop out on a lake, put a little drop of oil in the center of the ring, monitor it's dispersion, note that it eventually fills the ring fairly evenly, watch the rainbows, have great fun 'till someone from the EPA shows up.

our calculations all include the expression "on the water".

we can set a couple of marker buoys on the lake and race a couple of boats around them, calculating their relative position to one another and the marker buoys all the while, and noting that, on the boats, they are always moving forward, regardless of which way they may turn.

our calculations all include the expression "on the water".

somewhere around the middle of the shoreline, wherever the middle of of a shoreline might be, we hop in an inner tube and go dog-paddling across the lake. it's a big lake. we paddle and paddle... count the number of strokes, intending in this way to measure how big the lake is... lose site of the shoreline... never find an end to the water... maybe somewhere in the wee hours of the morning we slip exhausted from the inner tube and disappear.

again, our calculations include the expression, "on the water".

our local situation may be compared to a bunch of people on a raft being towed around the lake by the sun, much as a water-skier might be towed.

some have gotten to looking at the calculations and wonder just what that "on the water" means in them; some ask if the calculations prove that water exists, others whether or no one can dispense with the idea of "on the water" in the equations and some get to questioning if there even is any water.

another example:

it is possible to define points of data on a hard drive in terms of relationships to one another. it is possible to run programs on the hard drive and describe then in more or less the equivalent of thermodynamic processes.

but it is not possible to have the data points without the hard drive.

the concept of time is somewhat a perceptual problem.

we have what is referred to as consciousness.

if we had just that, there would be no perception of time.

we might say that, with rotating consciousness through one dimension, we have memory.

this permits of an impression of 'duration' otherwise unavailable. it is only in that impression of 'duration' that a notion of 'time' arises at all.

yet it is only a vague sense of something there - akin to what a fish might have of water.

there is no way of parameterizing the perception - perceptually, there is no 'contrast' (required for perception) in that we cannot step outside of time. it would require another dimensional rotation of memory to be able to acquire an appropriate perspective and that is rather difficult to visualize.

concerns with such a modeling involving 'forgetting time'...

in part the psychological impact this may have, leading to a further disassociation with the natural world. i can see this happening quite easily with our growing absorption in entirely human activity and a dwindling identification with the world in which we actually live. the cultural stage is ripe for such a break as appears evidenced in the popularity of your paper. is this an inevitable result of the evolution of consciousness? no 'home'?...

and the attitude toward the world further disassociation with it would likely bring...

science's successes in augmented prowess has occasionally also been its disasters in a lack of wisdom involved in application. what is lost is frequently not possible to see until the 'disaster' aspect has evolved.

the unnaturalness of the thermodynamic interpretation - seemingly putting the cart before the horse.

if adopted, a potential for limiting consideration of possibilities by removing a contextual component capable of pointing to potential additional possibilities; something akin to how a loss of memory would result in no temporal perception. that time, gravity and space are actually not terribly well understood raises some concern in eliminating reference to one of them simply because it does not appear to have any specific effect in itself other than being a potential for data to exist.

a sense of time appears fundamental in living creatures. even the most basic of life forms.

http://discovermagazine.com/2009/jan/071 (slime mold have a sense of a length of time)

from cognitive science, that consciousness is clearly capable of accessing distant past, distant elsewhere present and distant future events information with considerable fidelity, there is a strong suggestion of a space-like dimensional character to time seemingly unaccountable for with a simple thermodynamic model.

to say that 'time flows' appears to be a slight misapprehension; that we flow in time would appear more precise.

while i am in full agreement with the majority of your observations and do not see any real reason why your proposed approach could not be employed effectively, i remain unclear about the extent of desirability of advantages this may afford beyond a sort of Swiss 'neat and tidy' and have some concerns about potential unintended disadvantages.

please forgive me if this all has already been addressed somewhere in the posts here. i've still got a lot of reading to do elsewhere here and it's not easy to keep up.

please forgive me also if i have misinterpreted your paper in any way. my own background is a little different from yours.

thank you,

matt kolasinski

Regarding my posting from Dec. 2, 2008 @ 08:21 GMT above: Let's recap on the facts.

As of today, Carlo Rovelli's essay "Forget time" got 6 Registered Votes, and 103 Public Votes.

Yet he hasn't made any effort to explain what may happen to 3-D space in case we choose to "forget time". I do hope he will do this until the contest ending date, January 1, 2009.

Please correct me if I got it wrong: In the canonical formalism of today's GR, the foliation of spacetime into 3-D spacelike hypersurfaces enables the distinction of two infinitesimally neighboured hypersurfaces, so if we "forget" about [delta]_t, we must "forget" about the whole 3-D spacelike hypersurface as well. It's a package -- see the drawing attached.

Carlo Rovelli has been manifestly silent on this fundamental issue.

He wrote (Oct. 24, 2008 @ 17:53 GMT): "... 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."

And in his latest posting (Nov. 9, 2008 @ 10:42 GMT), he added even more confusing remarks: "... 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."

It is totally unclear why would the "observable quantities" care about each other's relational stance, nor what would be the driving force that implements the unitarity principle.

For if Nature chooses to "forget time", the "observable quantities" would need human consciousness to get their job done. Or maybe Carlo Rovelli should re-write his essay?

If he chooses the latter, there is a simple way to convince us that we should indeed "forget time": The very mechanism which shapes '3-D space' should be proven non-existent.

Carlo: If you believe can kill the Heraclitian Time, you should first kill the generation of 3-D space.

Please do not "forget" the event of contest ending, January 1, 2009.

Dimi ChakalovAttachment #1: adm.jpg

Many questons to reply to!

Let me start from the last one, by Dimi Chakalov. Dimi asks "what may happen to 3-D space in case we choose to forget time". And comments "I do hope he will do this until the contest ending date, January 1, 2009." Here I am.

I think that the fate of space is precisely the same as the one of time. I think we better forget both space and time, in order to understand better understand the structure of reality at the Planck scale. So; why all the fuss about time, and little abut space? Because the idea that space is not an entity is a very old and much discussed idea in the past, while the absence of time is much less so. In fact, when Newton based his theory on the existence of space, he did so *against* the prevalent thinkinf, from Aristotle to Descartes, which was to conside space not as an entity but only a relation between existing things. For Aristotle and for Descartes, the world is *not* a big space inside which matter moves (like for Newton and for the ancient atomists). Rather, it is just an ensemble of things that can happen to be in a relation of being "touching" one another. So, getting rid of space at the fundamental level is not very new. I think that what general relativity does is precisely so. It is the realization that the Newtonian "space" is nothing else that one of the physical fields that make up reality. Relality is not a space inside which things moves, but rather an ensemble of fields in interaction. So, my answer is that we must forget space and forget time. Forgettin space is easy; we have centuries of traditions that give us exemples about how to think the world without a fundamental space. Forgetting time is more difficult, and it is what we are discussing here.

Dimi writes "Carlo Rovelli has been manifestly silent on this fundamental issue." No, I am not, I have written often about that, including earlier in this discussion.

I do not understand the other points raised by Dimi. He says my statement about unitarity is confused, but dos not say what he finds confusing. The statement is simple and technical. The theory must give predictions, namely associate probabilities to alternative measuremenet outcomes. These probabilities should sum up to one. This, in my understanding is unitarity.

Dimi also writes: "For if Nature chooses to "forget time", the "observable quantities" would need human consciousness to get their job done." No! certainly not. I do not want to bring consciousness into these problems. The quantities that I call relational are not relationas because they are perceived by consciousness. They are relational because they pertain to two systems and not one. For instance, velocity is relational. An object has a velocity only "with respect" to another object. I walk on a train and I have a velocity of 1meter per second "with respect to the train". This does not mean that the train has a cosciousness to be aware of my velocity!

Adam Hefler asks: "Am I right in thinking that you adopt the Schroedinger rather than the Heisenberg picture in order to try to pass to a theory of quantum gravity? " No, it is the other way around. I adopt the Heisenberg picture, which remains well defined in the absence of a preferred time. I am told by friends who were there thatin his last publc lecture (in Sicily) Dirac had a single slide, with the Heisenberg equations dA/dt = i hbar[A,H] and the text "Heisenberg picture is the right one". These equations generalize to timeless quantum dynamics, as I have discussed in the essay.

Second question by Adam: "My main question is, What is the significance of thermal time? " Thanks for this question. I think that the origin of the problem with time is that many of the characteristic feautures of time (flowing, irreversibilty, and so on) seem totally absent from the picture of the world given by dynamics, especially when this includes relativistic gravity. The thermal time is an attempt to find the physical baisis for *these* additional features of time.

I loved the post by Tevian Dry, above (Dec 8). Nice, Tevian!

Thanks also to the kind post by Luigi Acerbi.

Petr Frish writes "I would like to make it stronger = a conjecture: Flowing of time a a property of the observer. Any decent observer of course has a memory. An object (complex particle with no memory) does not experience a flow of time. etc" I do not disagree. In fact, if thermodynamical time depends on the statistical description, hance on the coarse graining, to some extent it *it* observer dependent. By I would not know how to implemenet this concretely in physics.

Dimi Chakalov (already mentioned above), in an earlier post writes "It seems to me that Rovelli's recipe for quantum gravity is this: take Quantum Mechanics and General Relativity in their current formulation, with all their well-known problems, blend them into some new theory with "patrial observables", and hope that the problems of QM may be solved from GR, and the problems of GR may be solved from QM." Very good point. How could there be a change that this recipe works? The reason, I think, is because it has worked wonderfully in the past. When there was a problem between relativity of velocity and the Maxwell equations, many wanted to change one or the other. Einstein didn't do either. He kept both, and found that the two would work together, if we drom some other implicit common sense assumption (simultaneity). Dirac found antimatter by simply taking special relativity and quantum theory, and seeing where did they take if taken together. Newton took seriously Galilo's acelleration and Kepler ellipses... and so on. Very often physics advances by *taking seriously* theories that have proven empirically effective, and making an effort to merge then. Sometimes the merge requires new idea. One of the new ideas I advocate (with many others) is that to merge QM and GR we need to forget time. The result is that some say I am too radical; others, like Dimi in this post, say I am too conservative... I don't know what I am; I am just trying to find tentative solutions to the problems on the table ....

Thanks for the interesting comment, Cristi.

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

Carlo Rovelli

Dear all,

Since Carlo Rovelli has been "manifestly silent", I will take issue concerning some positions by Le Rouge and Yuri Rylov uttered here and comments on Carlo and others made elsewhere. Please goto http://fqxi.org/community/forum/topic/369

You are welcome,

Eckard Blumschein

Hi Carlo:

You wrote (Dec. 12, 2008 @ 13:11 GMT): "The result is that some say I am too radical; others, like Dimi in this post, say I am too conservative... I don't know what I am; I am just trying to find tentative solutions to the problems on the table .... "

1. I never said that you are "too conservative". What I actually suggested (Dec. 12, 2008 @ 03:58 GMT) was this:

If you believe can kill the Heraclitean Time, you should first kill the generation of 3-D space.

2. We all are trying to find tentative solutions to the problems on the table, but I'm afraid your approach is logically inconsistent: you "derive" statements about time and space from a theory -- GR -- that cannot say anything about those same statements. Your whole essay is tantamount to speculating on the precise conditions "inside" a singularity, knowing very well that GR cannot be extended outside its applicable limits.

I also suggested you to consult Prof. Karel Kuchar. If he is busy, I can quote from his research papers.

As to your relational ontology, please check out the so-called Buridan donkey paradox.

Dimi

Hi Carlo,

Your essay is of course beautifully written and argued. Thank you.

Now in this essay competition, there is an important split between a number of papers putting the view that time is an illusion/does not exist, yours being a prime example, and a number saying time is not an illusion/does indeed exist, mine being in the latter category. Recently I have been under some pressure from colleagues to explain how I could maintain my position in the face of your expert arguments. So I decided, a bit reluctantly, that I'd better point out where I disagree with your paper, else I will lose the argument by default.

I think there are four areas where we have different views.

First, on pages 2/3 of your paper, you state that there is no preferred time variable in GR. 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. To some degree this accounts for our differing positions on the nature of time.

Second, you focus on timeless evolution described by a Hamiltonian. I suggest firstly that physical evolution is described by a Hamiltonian in the way you propose only for some forms of matter content: there must for example be no dissipative processes happening, including no friction. Your `general structure of dynamical systems' does not, I think, describe simple realistic systems with friction, e.g. a pendulum with air resistance. Once the pendulum has stopped, you cannot follow it backwards and determine its previous motion. So I do not concur with the statement at the top of page 5: "It appears that all elementary physical systems can be described by Hamiltonian mechanics" (at least not by the time reversible dynamics you describe). Secondly, I suggest that in the quantum case, the Hamiltonian only describes part of the dynamics, the other part being handled by {the measurement process/collapse of the wave function/ decoherence}, however one conceives of and describes it [see Penrose, The Road to Reality, sections 21.8 and 22.1, 22.2, and Chapter 29, and Isham's book Lectures on Quantum Theory].

Thirdly, and related to the last point, your `timeless quantum mechanics' (Section 5) has no prescription for when projection (i.e. measurement) will take place [lines after equation (9)], and the Probability statement (7) has no prescription for when anything occurs. But that is the place where time and time irreversibility enters. This is Roger Penrose's key point, developed in The Road To Reality and The Emperor's New Mind. So I suggest that your formulation of QM is timeless because it is incomplete: your dynamical description does not include any way of determining when unitary development will be replaced by projection (in Penrose's terms, when unitary evolution U will be replaced by state vector reduction R).

Finally, the discussion of the recovery of time [section VI] parallels Penrose' discussion of coarse graining [The Road to Reality, pp 686-707]. But the Thermal Time Hypothesis [p. 8] only applies to statistical systems with many particles interacting [`these features are not mechanical , they only emerge at the thermodyamical level']. It does not seem to apply to single particles, or pairs of particles that collide, or planetary motion. I disagree with this hypothsis: I don't see that thermodynamics is needed to describe the motion of the Earth around the sun, for example. You say 'time is the expression of our ignorance of the full microstates." I do not agree; in my view [following Boltzmann, Oliver Penrose, and others] it is *entropy* that expresses that ignorance. The following equations [(19)-(26)] describe how the time variable works in some situations. That does not imply what the *origin* of time is; it merely shows how it works.

So that's how I see the differences betwen our views. I am sure I still have much to learn that may change my view.