Laws of Nature workshop: what can we tell from the program?

[marcus]

Christine, in case you do get around to watching the video of Ariel's talk, I want to express my preference for the 4 May version of it, over the version he gave in the Laws of Nature workshop. Here, in case you want it, is the link to the 4 May version.
http://pirsa.org/10050021/
Entropic Dynamics, Time and Quantum Theory
Ariel Caticha
"Non-relativistic quantum mechanics is derived as an example of entropic inference. The basic assumption is that the position of a particle is subject to an irreducible uncertainty of unspecified origin. The corresponding probability distributions constitute a curved statistical manifold. The probability for infinitesimally small changes is obtained from the method of maximum entropy and the concept of time is introduced as a book-keeping device to keep track of how they accumulate. This requires introducing appropriate notions of instant and of duration. A welcome feature is that this entropic notion of time incorporates a natural distinction between past and future. The Schroedinger equation is recovered when the statistical manifold participates in the dynamics in such a way that there is a conserved energy: its curved geometry guides the motion of the particles while they, in their turn, react back and determine its evolving geometry. The phase of the wave function--not just its magnitude--is explained as a feature of purely statistical origin. Finally, the model is extended to include external electromagnetic fields and gauge transformations."

For comparison, here is the same talk delivered to the LoN workshop:
http://pirsa.org/10050056/
Law without law: entropic dynamics
Maybe my reaction is too one-sided. There may be valuable aspects of both presentations.

 

[marcus]

Thanks for your comments Christine!

To be honest I was a bit dissapointed by the lack of a more detailed suggestion of how to implement mathematically the ideas Unger describes verbally quite well. I was probably expecting too much progress.

I am now getting the idea that Unger has some original thinking / not cast into quantiative form, or directly applicable to physics, that Smolin tries to "understand" and be inspired from and maybe it's Smolins job to produce the mathematics? I'm not sure if that's a correct observation or not, but it's the feeling I get.

If so, my feeling is that so far Smolin does not yet quite realize what I interpret Ungers means with reality of time, as it's apparenly not the preferred simultaneouty/global time kind of time. This was one of their points of disagreement. I still think Ungers point is good. I don't think the evolution law has to mean there is a preferred simultaneity. It's somewhat unclear to me what Smolin thinks.

But I see Ungers apperance as eccentric, extremely confident but also incredibly charming to the point of slightly amusing. I had a big grin on my face during large part of the talk from the point where Unger took the mic, mostly due to this fascinating personality.

/Fredrik

Your questions are to Christine, but I hope it will not be inconvenient for me to jump in. I think Unger has a paradigm of understanding the universe which is more like Darwin's understanding of evolution or our understanding of geology in which there is a NATURAL HISTORY without a central dominant mathematical model.
Mathematics comes in as an occasional servant, to assist the progress of natural philosophy.

One can see this paradigm in e.g. sociobiology, behavioral genetics, and in population genetics. At a critical moment of the analysis one can bring in math tools and show that given a certain diploid haploid reproductive structure one can prove that the ant or bee can evolve a program in the brain that makes it act for the common good. The mathematics of behavior evolution can get very complicated. But there is always the central, non-mathematical, reasoning process of the natural philosopher which analyzes the concepts and develops the ideas and governs the overall understanding.

A mathematical model cannot analyze its own concepts. In natural philosophy the concepts co-evolve with the undertanding. And of course to achieve greater rigor and certainty the mathematical tools should be brought in wherever and whenever possible but they are not the main course of dinner, they are side dishes.

I think that is his overall idea about how to study the universe. It is a onetime unique natural history. So we must all try to be like Mr. Darwin in how we try to understand it.

BTW earlier I could not get the video of Philip Goyal to work. So I missed sampling it. I now think his is one of the best.

My favorites are now Smolin/Unger, Caticha, and Goyal. And the 4 May version of Caticha IMHO is better than the LoN conference one.

 

[Fra]

I think I'll only have time to listen to this video next weekend.

I'll take me some time as well. I had the ambition to try watch it last night before I fell asleep but sandman beat me to it.

/Fredrik

 

[Fra]

Hello Marucs, thanks for your comments.

I think Unger has a paradigm of understanding the universe which is more like Darwin's understanding of evolution or our understanding of geology in which there is a NATURAL HISTORY without a central dominant mathematical model.
...
And of course to achieve greater rigor and certainty the mathematical tools should be brought in wherever and whenever possible but they are not the main course of dinner, they are side dishes.

Yes, this makese sense but I tend to see a distinction here in

a) understanding our understanding, which is clearly and undeniably evolving, no same human could argue with that that,

b) and the idea that this is how nature itself works, and that the mutual interaction "rules" between parts of matter, and governed by simlarly evolving "laws"(understanding).

And in this latter view, the "mathematical systenms" somehow representing present states of "laws" has I think a deeper meaning just beyon human mathematics and just philosophy and it would also have implications beyong traditional "cosmological" models since even the actions of the SM model of particle physics is - to the inside observers - a cosmoloigcal interaction. So I think our deeper acknowledgment that this may be how nature and matter is constructed, and not just how human science is constructed, might even provide good insights into the problem of the choice of parameters even in the home-domain of regular QM or QFT.

So I'd expect to find some idea out of this, how the inside-mathematics itself evolved. This is why I have tried from the discrete perspective, to reconstruct the continuum probability (which is often the basis for entropic models) and instead consider how the complexity of the observer, in fact limits what mathematics is possible! Here fits my arguemtn for why I think the continuum is non-physical.

Here in the end I mixed in some of my personal ideas, but the point is that I expect outo smolins and ungers reasoning - in the end - some means to describe the evolving mathematics. Because something is "evolving" and not deterministically predictacble3 doesn't necessarily mean it's totally unpredictable. There should still exists like "expected" evolutions, in analogy with the schrödinger equation (in between) measurements.

So I guess wether ungers ambition at all, is to attempt anything such, or if he is content with the philosophical and verbal part? And that the hope is for SMolin to pick up the philsophical thread and construct some evolving mathematical system? (even though a you point out, the mathematical system can not rule it's own evolution)

I think that is his overall idea about how to study the universe. It is a onetime unique natural history. So we must all try to be like Mr. Darwin in how we try to understand it.

This sound like it could touch the point of controversy of smolin and unger, namely is history really unique and certain? or maybe with "unique history" you meant something different?

/Fredrik

 

[Fra]

I guess an implication of what I tried to say above, is paradoxally, that I think we need to take mathematics more seriously than we do. And with this I do not mean that the axiomatic way is right.

I mean that we must take the correspondence between mathematics and reality more serious. If we just see mathematicla as a "calculational" tool then we are loosing some of the handles I think we need to make sense out of ungers thinking.

I mean, I think if not all, at least many of physicistis would agree that the mathematical continuum isn't necessarily one-2-one with the physical reality down to inifinite resolution right? While that is true, and I agree. This should instead encourage as to find a BETTER mathematics that is better in match with reality?

If find it a bit amusing that some of the most philosophical arguments here, suggests that we should take the correspondence of mathematical and reality more serious.

/Fredrik

 

[Fra]

For comparison, here is the same talk delivered to the LoN workshop:
http://pirsa.org/10050056/
Law without law: entropic dynamics
Maybe my reaction is too one-sided. There may be valuable aspects of both presentations.

Last night I was able to watch to Ariels session.

From my point of view, Ariel describes quite well the core point of entropic inference and how it imples a flow of entropic time, and thus gives a kind of dynamics. There are good contact points with Verlinde as well. IMO this is an important ingredient in the big picture, and given that a lot of people doesn't seem to be tuned in on this reasoning at all: as was seen from the questions, people wondering what Q was.

But, apart from the basic idea of what is an entropic force, entropic dynamics and how does it yield expectations, there are many important points in the big picture that Ariel did not address at all. So I see Ariels talk as having a narrow focus, namely to present very briefly the reasoning and meaning of entropic inference, entropic dynamics and entropic forces.

The points where I have a very different view than Ariel is where he introduces QM.

In this talk you see that in the simplest case, in the way the reasoning is introduced, you just get a "simple" form of dynamics, which is basicall diffusion! So how can this inference model imply more complex dynamics, such as oscillatory phenomena or QM?

The assumptions QM uses in order to "imply" QM is not in my taste. What's good is that he illsustrates without much explanation a possible general mechanism, but I still think the connection is deeeper. I've seen several of ariels papers where QM is implied from various assumptions + inference logic, but the assumptions aren't justified IMO.

Also, another point which I think Ariels reasoning is not complete, is that his idea of the evolving statistical manifold is that the prior is updated, the manifold is updated. I think this "mechanism" is sort of right, but there are other mechanisms that I think is lost in ARiels and Jaynes reasonings since they start by assuming the the relative entropy measure that defiens hte measure on the manifold give the prior is unique. But I find the assumptions that go in there weak and ad hoc.

Instead I think the entropy measure itself is result of evolution.

So I disagree with quite a bit of Ariel says, buy I think his main message in the LON session here was to illustrate the most BASIC parts of what entropic dynamics is and how the general connection between dynamics on a statistical manifold, and the dynamics of the statistical manifold is connected. I share that, but to make sense of this and get the physics connection you end up questioning a lot of what Ariels is putting in as premises. ARiel doesn't seem to deny that though.

I *think* that it could be easy for some people to reject the reasoning since they don't see the big picture. Ariel does not line out the entire picture in that talk IMO.

I'm not sure how the other version of the talk Marcus referred to is different.

/Fredrik

 

[Fra]

Also, another point which I think Ariels reasoning is not complete, is that his idea of the evolving statistical manifold is that the prior is updated, the manifold is updated. I think this "mechanism" is sort of right, but there are other mechanisms that I think is lost in ARiels and Jaynes reasonings since they start by assuming the the relative entropy measure that defiens hte measure on the manifold give the prior is unique. But I find the assumptions that go in there weak and ad hoc.

Instead I think the entropy measure itself is result of evolution.

At first when Ariel argues that the manifold defined by the prior is fixed and when the prior is, and this is relaxed it sounds like if he has removed all background dependence, but he has not, because the entropic measure that defines the "set of manifold" of the transformation that generates the new manifolds is FIXED, this is still a background information.

This is something I object to and this is also evolving as I see it. Beucase the assumptiosn that goes into defining the equiprobability hypothesis and the space of probabilities based on continuuum probabilities is just too big and is IMO unphysical. From the point of view of pure inference and probability this is nothing strange, but I suggest that the connection to physics starts already here. Apparently Ariel does not think so.

Instead of adding uncelar constraints such as conservation of something we call energy, one could instead argue for conservation of complexity where the complexity is needed to encode all structurs. And no finite complexity can encode an infinite infinitedimensional space of continuum probability. This is one of my strong objections. This is something ariel probably didn't think a lot about since it traces all the way back to E.T Jaynes. But as I've rambled many times before on here I think the problem is in the first part of JAynes book, where he simply ASSUMES an apparently innocent (but I claim it's not) thing that "degree of beleif" is represented by a real number.

Surely, even rational numbers are real. but that's not the problem. The problem is not that degrees of believes are NOT real numbers, the real problem is the key property that you use in entropic inference, namely that the SET of all POSSIBLE degrees of beliefes suddenly is uncountable! For me that makes no physical sense!

/Fredrik

 

[Fra]

I listened to Philip Goyal's talk since the title was interested and Marcus mentioned it. I didn't actually watch the video or slides, I just used the mp3 while laying on a spike mat.

The general connection between classical logic, quantum logic and the corresponding properties of the real and complex numbers reminds me of some of the connections ariel has done in some papers where you can "dervice" QM formalism, by assumping properties of the complex number. This is not too unlike Jaynes, "derivation" of probability theory as an extension of inference but were you use the assumption the degrees of beleif is represented by real numbers.

But as I see it, while the connection is there (when you postulate that degrees of beliefs are represented as per aq particular number system, you do get a particular inferece logic - but what chooses the choice of mathematics in the first place?), the interesting problems were just metioned in the question part in the end. Royal seems to prefer the continuum because he is more familiar with it. I think what someone suggested, to make this "reconstruction" from rational numbers would be interesting.

He also said it's not clear to hime why the complex numbers and their properties seem to be prefered. I personally expect that question (why certain number systems are more FIT) is better addressed if reconstruct also the continuum rather than assume it.

/Fredrik

 

[ccdantas]

(...)

I still have to watch the video, no time yet.

Finally, only now I was able to watch this video.

Very interesting. Lots of material to think about, and potential points of convergence with other ideas. I am curious on how far the idea of time as a "change of change" is connected with H. Bergson's idea of "duration". Hopefully, the book will be released soon. It might have some reference to Bergson.

For those who have not watched it yet, it's not a waste of... time.