I Newtonian "schema/paradigm" != Newton's mechanics

[gentzen]

Just wanted to make a short comment on this.


IMO, the idea to explain the non-dynamical evolution as an entropic flow, still shares a problem with the newtonian schema, which is that it's explanatory value builds on that we have an low entropy initial condition in a timeless statespace, but where the statistical average may imply a hamiltonian flow on the macrostate levels.

IMO, most of us here (me included) are more interested in the exact meaning of Newtonian "schema/paradigm" than in its supposed problems. Can we just agree that stuff like David Deutsch's constructor theory does not follow the Newtonian scheme? And that thermodynamics and its second law is maybe only halfway as different from the Newtonian scheme, but still different?

For me this problematic, because the "explanation" presumes and improbable (low entropy) premise and "true" evolution that I think is the deeper sense Smolin refers aims to explain more without that premise. My firm opinion is that trying to "solve this" but thinking it's just emergence in terms of entropic flows is really missing part oft he core issue.

The past entropy doesn't need to be extremely low, it only needs to be noticably lower than the current entropy. And like David Wallace observed, it would actually be more surprising if this were not the case. So no fine tuning is required for that assumption/premise.

But here we get into various reasons why newtonian schema is problematic and there I think we again get many interpretations on this. An example is already the paper I randomly cited to describe the term, Ken Wharton argues in ways I wouldn't but that is a seaparate discussion I think.

Exactly!

 

[Fra]

IMO, most of us here (me included) are more interested in the exact meaning of Newtonian "schema/paradigm" than in its supposed problems. Can we just agree that stuff like David Deutsch's constructor theory does not follow the Newtonian scheme? And that thermodynamics and its second law is maybe only halfway as different from the Newtonian scheme, but still different?

Yes.

Deutsch also likes to contrast his constructor theory with this himself

Constructor Theory of Information
"...The basic principle of constructor theory is that

I. All other laws of physics are expressible entirely in terms of statements about which physical transformations are possible and which are impossible, and why.

This is in contrast with the prevailing conception of fundamental physics,which seeks to explain the
world in terms of initial conditions and laws of motion, and whose basic dichotomy is therefore between what happens and what does not.

Constructor theory describes the world in terms of transformations involving two kinds of physical systems, playing different roles. One is the agent causing the transformation, which we refer to as the constructor, whose defining characteristic is that it remains unchanged in its ability to cause the transformation again. The other consists of the subsystems—which we refer to as the substrates—which are transformed from having some physical attribute to having another."
-- https://royalsocietypublishing.org/doi/10.1098/rspa.2014.0540

This is indeed the newtonian schema/paradigm, although he doesn't label it as such.

So loosely speaking he instead of a "statespace" and a "lawspace", he seems to entertain some "set of possible substrates" and "set of possible constructors".

The past entropy doesn't need to be extremely low, it only needs to be noticably lower than the current entropy. And like David Wallace observed, it would actually be more surprising if this were not the case. So no fine tuning is required for that assumption/premise.

I can't comment on what Wallace arguments was I am not familiar with it, but it's not just about the entropy associated to the initial condition of the state space or phase space, but also about the priori probability of having all the laws tuned, to what they are in "theory space". The latter contains massive amounts of prior information that is tactically hidden and not made explicit in the fine tuning of the laws temselves, in the newtonian schema.

/Fredrik

 

[Morbert]

The past entropy doesn't need to be extremely low, it only needs to be noticably lower than the current entropy. And like David Wallace observed, it would actually be more surprising if this were not the case. So no fine tuning is required for that assumption/premise.

In Penrose's Conformal Cyclic Cosmology (CCC) treatise, he makes the argument that symmetry implies we should expect entropy to increase both into the past and the future. E.g. our evolutionary history is more surprising than a history where we spontaneously came into existence as our physical state moves from a higher-entropy to a lower-entropy region. This is one of his motivations for CCC as it would predict a low entropy early universe and hence a breaking of this symmetry.

Does Wallace argue that no such explanation is necessary and we should just expect our past to be lower entropy anyway?

 

[gentzen]

The past entropy doesn't need to be extremely low, it only needs to be noticably lower than the current entropy. And like David Wallace observed, it would actually be more surprising if this were not the case. So no fine tuning is required for that assumption/premise.

I can't comment on what Wallace arguments was I am not familiar with it, but it's not just about the entropy associated to the initial condition of the state space or phase space, but also about the priori probability of having all the laws tuned,

Does Wallace argue that no such explanation is necessary and we should just expect our past to be lower entropy anyway?

David Wallace simply said that he doesn’t understand why such an explanation should be necessary.
https://www.preposterousuniverse.com/podcast/2021/08/02/158-david-wallace-on-the-arrow-of-time/

0:43:31.7 SC: Good. ... There’s this feeling that you say something like, “Look, it’s just a black body radiation, that’s high entropy. How could it… It had the highest entropy it could have had, given that it was tiny,” but when you turn on gravity, that’s not true. So am I right to say that it’s fair to say the early universe had low entropy compared to what it could have had?

0:44:10.6 DW: Yeah.

0:44:11.2 SC: And gravity had something to do with that.

0:44:12.7 DW: But look, here’s something I don’t understand about this, these conversations with cosmologists. Absolutely, the early universe had low entropy compared to what it could have, but one really quick way to tell that is the early universe had low entropy compared to the current universe. If it didn’t, the second law of thermodynamics is empirically wrong. And no one thinks that.

0:44:34.1 SC: Well, yes, but the…

0:44:35.4 DW: So it’d really better be the case that the early universe was lower entropy than the present universe. We shouldn’t need to give some subtle transcendental argument as to why it must be lower. It’d better be lower in order not to blow our entire thermodynamic theory out of the water.

The main argument Sean Carroll advanced against this was that the empircally observed entropy of the early universe is even lower than can be explained by this "of course the entropy in the early universe had to be noticably lower than in the current universe".

 

[physika]

The Borde–Guth–Vilenkin theorem poses insurmountable obstacles to cyclic universe models.

Vilenkin:
"A cyclic universe runs into the second law of thermodynamics, which says that any system left to itself eventually reaches the state of maximum disorder, called thermal equilibrium. So if the universe were cyclic, then in every cycle, the disorder in the universe would increase. Eventually the universe would reach this thermal equilibrium state, which is a totally featureless mixture of everything—this is not what we see around us."



.....

 

[Morbert]

The Borde–Guth–Vilenkin theorem poses insurmountable obstacles to cyclic universe models.

Vilenkin:
"A cyclic universe runs into the second law of thermodynamics, which says that any system left to itself eventually reaches the state of maximum disorder, called thermal equilibrium. So if the universe were cyclic, then in every cycle, the disorder in the universe would increase. Eventually the universe would reach this thermal equilibrium state, which is a totally featureless mixture of everything—this is not what we see around us."

This is true for models like Friedman's oscillating model, where each big bang obtains via a prior big crunch. Penrose's proposal is that each big bang obtains via a conformal rescaling that permits a continuous increase in entropy. His proposal has been around a while, and so far it hasn't been evidenced by any experiment, but it's motivated by the peculiarity of a lower-entropy early universe. This is in contrast with Wallace who seems to just take it as a brute fact.

 

[Fra]

David Wallace simply said that he doesn’t understand why such an explanation should be necessary.
https://www.preposterousuniverse.com/podcast/2021/08/02/158-david-wallace-on-the-arrow-of-time/

I must say these arguments doesn't add much insight to me at all as they don't consider the force unification problem, and the observer problem which is a major factor for me in the ponderings that for me is entangled with the issue of time. This makes me think the various reasons for looking for a new paradigm is very different.

Wallace at 0:22:49.6 says

"Within physics, if you’re going to break that symmetry, I think you can only logically, you can only really do it in two ways, your dynamics needs to violate the direction of time, needs to distinguish past from future, or your boundary conditions needs to distinguish past from future. So the former approach needs you to change deep physics, put that aside for the moment. That’s another conversation we’ll have, and it gets on to something I think we’ll talk about later..."

Did they ever talk about this? I admittedly skimmed, but couldnt see they did?

/Fredrik

 

[physika]

This is true for models like Friedman's oscillating model, where each big bang obtains via a prior big crunch. Penrose's proposal is that each big bang obtains via a conformal rescaling that permits a continuous increase in entropy. His proposal has been around a while, and so far it hasn't been evidenced by any experiment, but it's motivated by the peculiarity of a lower-entropy early universe. This is in contrast with Wallace who seems to just take it as a brute fact.

https://doi.org/10.1103/PhysRevD.109.043519
Phys. Rev. D 109, 043519 – 16 February 2024.

"The Borde-Guth-Vilenkin (BGV) Theorem states that any spacetime for which the net expansion is positive is
necessarily geodesically past-incomplete. This has profound implications for cosmological model building, since it applies not only to trivially past-incomplete spacetimes such as matter- or radiation-dominated Friedmann-Robertson-Walker (FRW) cosmologies, but to inflationary models as well."


https://iopscience.iop.org/article/10.1088/1475-7516/2022/06/011/
Journal of Cosmology and Astroparticle Physics
Volume 2022, June 2022.

"We consider recently proposed bouncing cosmological models for which the Hubble parameter is periodic in time, but the scale factor grows from one cycle to the next as a mechanism for shedding entropy. Since the scale factor for a flat universe is equivalent to an overall conformal factor, it has been argued that this growth corresponds to a physically irrelevant rescaling, and such bouncing universes can be made perfectly cyclic, extending infinitely into the past and future. We show that any bouncing universe which uses growth of the scale factor to dissipate entropy must necessarily be geodesically past-incomplete, and therefore cannot be truly cyclic in time."

BTW, if desired, a new thread could be opened in the cosmology section, since it does not go with the original question or approach of the thread.

 

[Morbert]

@physika I'd be happy to participate in another thread. For now I'll remark that, at first glance, these papers are raising issues of geodesic completeness of CCC models rather than their entropy dissipation. My reason for bringing up CCC models in this thread was a potential contrast between Penrose's and Wallace's position on the 2nd law. Not to argue that CCC is correct.

 

[gentzen]

I must say these arguments doesn't add much insight to me at all as they don't consider the force unification problem, and the observer problem which is a major factor for me in the ponderings that for me is entangled with the issue of time. This makes me think the various reasons for looking for a new paradigm is very different.

Who is looking for a new paradigm? Sean Carroll and David Wallace just had a normal conversation, and talked about their different views on entropy and the second law of thermodynamics. They knew before that they don't agree on it.

And I just want to know and clarify the meaning of Newtonian "schema/paradigm". I argued that "thermodynamics, including its second law, is" not "categorized in Newton Schema", because there is not necessarily a dynamical law. I could also quote Wheeler:

But when Everett produced his many-universes interpretation for quantum theory you changed your mind for a while. Why was that?
...

What attracted you to this remarkable idea?

... But I also have a deeper objection: the Everett interpretation takes quantum theory in its present form as the currency, in terms of which everything has to be explained or understood, leaving the act of observation as a mere secondary phenomenon. In my view we need to find a different outlook in which the primary concept is to make meaning out of observation and, from that derive the formalism of quantum theory.

So you think that the many-universes approach may still be useful?

Yes, I think one has to work both sides of the railroad track.

But in the meantime you're siding with Bohr.

Yes. As regards the really fundamental foundations of knowledge, I cannot believe that nature has 'built in', as if by a corps of Swiss watchmakers, any machinery, equation or mathematical formalism which rigidly relates physical events separated in time. Rather I believe that these events go together in a higgledy-piggledy fashion and that what seem to be precise equations emerge in every case in a statistical way from the physics of large numbers; quantum theory in particular seems to work like that.

But do you think that quantum theory could be just an approximate theory and that there could be a better theory?

First, let me say quantum theory in an every-day context is unshakeable, unchallengeable, undefeatable - it's battle tested. In that sense it's like the second law of thermodynamics which tells us that heat flows from hot to cold. This too is battle tested - unshakeable, unchallengeable, invincible. Yet we know that the second law of thermodynamics does not go back to any equations written down at the beginning of time, not to any 'built in' machinery - not to any corps of Swiss watchmakers - but rather to the combination of a very large number of events. It's in this sense that I feel that quantum theory likewise will some day be shown to depend on the mathematics of very large numbers. Even Einstein, who opposed quantum theory in so many ways, expressed the point of view that quantum theory would turn out to be like thermodynamics.

It is an excerpt from "The Ghost in the Atom" (1986). The questions are from Paul Davies.

 

[Fra]

Who is looking for a new paradigm? Sean Carroll and David Wallace just had a normal conversation, and talked about their different views on entropy and the second law of thermodynamics. They knew before that they don't agree on it.

That explains it. I was hoping for something subtle that probably wasn't there, which explains why i didn't see it.

/Fredrik

 

[gentzen]

My nephew told me two years ago that he cannot conceive how there was no time before the big bang. I could immediately relate to that, because I also tried to understand this when I was a small kid. I told him about Stephen Hawkin's image of a sphere, I guess you know what I mean. Then he asked me why we remember only the past, but not the future. I didn't really believe him that this was his own question. Christoph Zenger had asked me that question before. But he liked to ask that question to see the reactions, not because he really believed to get a satisfactory answer. I answered that this is complicated: sometimes we are better at accurately predicting the future than at accurately remembering the past.

But for me, it was even more complicated. We can sometimes predict the future, because we created a highly ordered state in the space around us before. And nature has a way to create local smoothness and order. That smoothness and order is the essence of the Poisson equation, and of analytic functions, and function theory. And if you have some intuition about gauge theory, that is a large part of what happens there too. You might think that this is easy, but it is frustratingly hard to simulate: There are always those local feedback mechanism, actio equals reactio, which work on time scales that you don't really want to resolve in your simulations. But even nature cannot smooth out everything, so curvature and topological effects remain.

This is not a Newtonian "schema/paradigm". A Poisson equation doesn't work with initial conditions. It needs boundary conditions. And it is not fine tuned at all. It just locally smoothes out everything. Like a river grids down mountains on its way to the sea.

 

[gentzen]

My nephew told me two years ago that he cannot conceive how there was no time before the big bang. ... I told him about Stephen Hawking's image of a sphere, I guess you know what I mean.

And such a "parabolic" end similar to a sphere is also what you would get near a minimum of the entropy. And as for the sphere, it suggests that time should be multi-dimensional, not one-dimensional. That was my answer to Christoph Zenger back then, a multidimensional time. But not because I believed in it, but because I wanted to show that I can be creative and clever. Not sure why Hawking suggested a sphere, instead of a circle (which would have been one-dimensional). Maybe the minimum of the entropy was also his reason for his image.

 

[Fra]

I see you look for a precise definition of newtonian schema from a mathematical perspective. And now I am not as sure anymore if there are variants as the typical description as initial conditions and an ODE system seems incomplete imo.

But it is not newtons mechanics. The problem with newtonian schema is a conceputal one

From my perpective a boundary condition is a kind of "constraint" in the generalized sense just like a diffequation is. For me its the fixed nature of constraints and fixed space of input that defines the newtonian paradigm.

I dont recall how carefully smolin elaborates that. It was some years since I read all his books. But i recall that also smolin main point is that laws evolve. I probabaly would need to refresh that to properly reconsider smolins exact scope of "newtonian schema.

/Fredrik

 

[gentzen]

From my perpective a boundary condition is a kind of "constraint" in the generalized sense just like a diffequation is. For me its the fixed nature of constraints and fixed space of input that defines the newtonian paradigm.

Are you aware of the general behavior of elliptic partial differential equations, and the role boundary conditions have for them? Such type of behavior is simply fundamentally different from ordinary differential equation, and any intuitions you might have developped in their context.

Also, I fear that you want to enlarge the meaning of the newtonian paradigm so much that it essentially becomes an empty concept. If you alone are the only one who can use your concept correctly, then your concept is not of much use for anyone else.

 

[Fra]

I fear that you want to enlarge the meaning of the newtonian paradigm

You fear is correct that the paradigm that have issues with, is indeed larger than the basic phrasing.

The discussion about how its not beeing empty is another topic, but IMO closely related to one possible critique of newtonian paradigm. I planned to dig up some references of the rough connection I had in mind, but one of my problems is that I should do a better job of maintaining proper reference lists to papers or books I read for future reference than I currently do, to not have to spend so much time finding it when you need it

/Fredrik

 

[pines-demon]

The discussion about how its not beeing empty is another topic, but IMO closely related to one possible critique of newtonian paradigm.

you mean Newton Schema, I really refuse to lose the usual meaning of "Newton paradigm" to something vaguely defined by Smolin.

 

[Fra]

Yes, i admit that I myself used both "paradigm" and "schema" before without thinking about it, but i meant the same thing (and it wasnt newtons/classical mechanics, although i consider classical mechanics to of course be of that paradigm)

If someone suggests a difference between paradigm and schema, im not sure what it is.

/Fredrik

 

[Fra]

Smolin's Newtonian Schema is too similar to Newtonian paradigm or any other common use of Newtonian "System of the world". When scientists use those terms it refers to the differences between Newton mechanics and modern physics (relativity and quantum mechanics) in terms of both equations and philosophy.

Just to clash again a bit on the terminology. I checked Kuhn's work who is the one that introduced the concept of paradigms shifts in science. Newtonian paradigm is mentioned many times in different ways, mostly to say that it is different from that of Einstein and Aristotle. However Kuhn himself recognizes that he is sometimes not clear if "Newton's paradigm" includes or not all classical mechanics, in the postcript on his own book, Kuhn says

He then continues with long sections to explain the difference, but I cannot tell if I am unable to understand it or if he does not solve it either in the postcript.
Source: T. Kuhn, The Structure of Scientific Revolutions, 2ed..

I see now, that you did indeed make a difference between schema and paradigm, I missed that before, sorry.

While I haven't read any of Kuhns writings I find it highly unlikely, given when his book came out, that Kuhn is using "newtonian paradigm" in any sense of what smolin refers to or what I mean, especially if he contrast it to "quantum paradigm".

So yes, I likely do not mean what Kuhn means by "Newton's paradigm". So lets call it schema, and we have at least sorted that out.

(While I think the philosophy and foundation of science is important, after making the mistake to read Poppers book to end, hoping to be enlightened, I was so dissapointed of all the things I expected but that was dismissed in his disgust for inductive reasoning, I have since avoided any writings from actual philosophers I prefer "philosophical writings" of actual physicists rather than "professional philosophers", as the latter tend to loose focus, where the philosophy becomes the main topic rather than a tool for understanding the real world, I don't like that.)

/Fredrik