Of Dice and Divinity-discussion started by MeJennifer

[marcus]

Of Dice and Divinity---discussion started by MeJennifer

MeJennifer initiated the following discussion of a Foundations of Physics and Probability paper from our link-library

http://arxiv.org/abs/quant-ph/0611261
Concerning Dice and Divinity
D.M.Appleby
Contribution to proceedings of Foundations of Probability and Physics, Vaxjo, 2006

"Einstein initially objected to the probabilistic aspect of quantum mechanics - the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein's initial intuition was perfectly sound, and that it is precisely the fact that quantum mechanics is a fundamentally probabilistic theory which is at the root of all the controversies regarding its interpretation. Probability is an intrinsically logical concept. This means that the quantum state has an essentially logical significance. It is extremely difficult to reconcile that fact with Einstein's belief, that it is the task of physics to give us a vision of the world apprehended sub specie aeternitatis. Quantum mechanics thus presents us with a simple choice: either to follow Einstein in looking for a theory which is not probabilistic at the fundamental level, or else to accept that physics does not in fact put us in the position of God looking down on things from above. There is a widespread fear that the latter alternative must inevitably lead to a greatly impoverished, positivistic view of physical theory. It appears to us, however, that the truth is just the opposite. The Einsteinian vision is much less attractive than it seems at first sight. In particular, it is closely connected with philosophical reductionism."


It seems to me that there is a third option.
Assuming that a measurement in a given physical reality can be seen as a higher order self-expression, I don't consider it unreasonable that there would be information loss.

I hope discussion of Appleby's paper can be pursued here (as the link-library thread doesn't have room for discussions)

 

[Peter McKenna]

I was trying to find a link to Causal Dynamic Triangulation.The subject: Loop Gravity also. In the initial post you said the hyper link was in your username. No luck.

Isn't it proven that the more certain the quantum property becomes the less certain other properties become. Ergo as the discrete quantum value manifests in some tangible reality information loss becomes a necessity. Isn't this a basic tenet required of Heisenberg's uncertainty prinicple?

 

[Dcase]

Hi Marcus

I cannot discuss divinity.

I can discuss “...Einstein initially objected to the probabilistic aspect of quantum mechanics - the idea that God is playing at dice ...”

Einstein was probably right, that God does not play dice; but may play a form of celestial billiards as when Shemaker-Levy-9 crashed into Jupiter in a GR probabilistic event.
Supernovas and GRB also appear to be GR probabilistic events.

Many physics Nobels have been awarded for QM probabilistic events.

This might be accomplished through the 2T(ime)-physics of Itzhak Bars or a variant thereof.
http://physics1.usc.edu/~bars/research.html#2T

There was a recent article using discrete and continuous time “... continuous search time of robot .. discrete lifetime of odors ...” in Nature 25 January 2007 Volume 445 Number 7126, pp339-458.
http://www.nature.com/nature/journal...070125-10.html

Or see Nature editor's summary 25 January 2007 for
News and Views: Mathematical physics: On the right scent
Searching for the source of a smell is hampered by the absence of pervasive local cues that point the searcher in the right direction. A strategy based on maximal information could show the way.
Dominique Martinez doi:10.1038/445371a
and
Letter: 'Infotaxis' as a strategy for searching without gradients
Massimo Vergassola, Emmanuel Villermaux and Boris I. Shraiman
doi:10.1038/nature05464

The Nature article uses a Monte Carlo method but the terminology is that of game theory consistent with 'Dynamic Noncooperative Game Theory' (Classics in Applied Mathematics) (Paperback) by Tamer Basar, Geert Jan Olsder
[Search inside feature viewable on Amazon]
Basar is an engineer applying physics.
Olsder is a mathematician.

The n-Category-Cafe is even discussing stochastics:
February 9, 2007 Infinitely Categorified Calculus Posted by John Baez
Response. Posted by: Eric on February 9, 2007 2:54 PM, refers to
‘Noncommutative Geometry and Stochastic Calculus: Applications in Mathematical Finance’ by Eric A Forgy 20 May 2002, 13p
http://fastalgorithms.com/eric/papers/blackscholes.pdf
and
February 7, 2007 Category Theoretic Probability Theory Posted by David Corfield

It may be that space in on [continuous?] neutrino time with neutrino velocity near the speed of light while GR is on [discrete?] anthropic time as Earth moves about the sun?
In this manner QM and GR may be unified as dynamic noncooperative games in equilibria?

 

[Dcase]

Hi Peter McKenna

I do not presently have a journal copy at hand, but the website of SCIAM briefly discusses “... Causal Dynamic Triangulation...” but does not list the source.

NEWS SCAN
February 2007 issue
PHYSICS
The Triangular Universe
Instead of string theory, four-dimensional tetrahedrons
By Mark Alpert
http://sciam.com/article.cfm?chanID=sa006&colID=5&articleID=16D8C673-E7F2-99DF-3D291D5627D97141

 

[Peter McKenna]

MeJennifer initiated the following discussion of a Foundations of Physics and Probability paper from our link-library


I hope discussion of Appleby's paper can be pursued here (as the link-library thread doesn't have room for discussions)

Sorry,
I'm new to this forum and was attempting to find information on CDT (Causal Dynamic Triangulation) and attempted to link through your forum signature (as suggested). Maybe you could help direct me to suitable area? Thanks in advance. I don't want to disrupt your dis. into Appleby's paper.

Peter McKenna

 

[Peter McKenna]

Sciam? Thanks I'll try it.

PM

 

[Peter McKenna]

SCIAM, ... Oh, that's the Scientific American article on CDT. I read it and was was trying to find more info. Anyone knonw anywhere to find mor info, or new/different thread?


Thanks

PM

 

[Peter McKenna]

The dichotomy between the relativistic and the quantum uncertainty is underlined in the reality of the quantum property in all frames of reference. Feynman diagrams for the probabilities of future realities are all real in those planes. However these are not planes of reference and there are no known relativistic expressions to equate them. The philosophical quandary comes in the tendencies of quantum properties to behave rationally (such as the in formation of matter). There are no relativistic planes of reference for these tendencies. There are no "observers" (unless you postulate the existence of God as a universal "observer").

Every discrete quantum particle has a specific reality which it does and will (in the future) behave in, and that reality is deterministic. The determining expressions are probabilistic and not relativistic. The difference is in Heisenberg's Uncertainty Principle. Once a respective term becomes 100% determinate, a corresponding term becomes 0% determinate. This defines the reality for that quantum particle or waveform. How is this relationship analogous to a lottery?

The metaphor of winning or not winning a lottery would be valid except that, in terms of quantum mechanics both realities of Alice winning and not winning, both postulates are real, and that reality can be expressed in probabilistic terms. In purely relativistic terms, acting upon the lottery only affects the outcome causally. Philosophically I would tend to believe that the required juxtaposition of events that would predicate application of the laws of probability for a "winner" in a lottery cannot be analogized to the probability tendencies in quantum physics.

Maybe I’m oversimplifying, or I just don’t understand the analogy.

I just don’t think that the rules of probability that apply to a juxtaposition of events as in a lottery should be applied to the uncertainties of quantum reality. I also don’t equate the uncertainty principle to God playing dice. To me it’s more like a palette of paints that only take form when called upon to form a painting, but that’s just my poor excuse for an analogy that allows me to rudimentarily grasp the concept of quantum physics.

Just my opinion. Correct me if I'm wrong.

 

[Peter McKenna]

Anyone know where info on CDT (other than the Scientific American article) can be found?

Thanks

PM

 

[marcus]

Anyone know where info on CDT (other than the Scientific American article) can be found?

Thanks

PM

http://arxiv.org/abs/hep-th/0604212
Quantum Gravity, or The Art of Building Spacetime
Authors: J. Ambjorn, J. Jurkiewicz, R. Loll
Comments: 22 pages, 6 figures. Contribution to the book "Approaches to Quantum Gravity", ed. D. Oriti, Cambridge University Press
Report-no: Spin-06/16, ITP-UU-06/19

The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence accumulated to date that a macroscopic four-dimensional world can emerge from this theory dynamically. Using computer simulations we observe in the Euclidean sector a universe whose scale factor exhibits the same dynamics as that of the simplest mini-superspace models in quantum cosmology, with the distinction that in the case of causal dynamical triangulations the effective action for the scale factor is not put in by hand but obtained by integrating out {\it in the quantum theory} the full set of dynamical degrees of freedom except for the scale factor itself.

http://arxiv.org/abs/hep-th/0509010
The Universe from Scratch
Authors: R. Loll, J. Ambjorn, J. Jurkiewicz
Comments: 31 pages, 5 figures; review paper commissioned by Contemporary Physics and aimed at a wider physics audience; minor beautifications, coincides with journal version
Report-no: SPIN-05/28, ITP-UU-05/34
Journal-ref: Contemp.Phys. 47 (2006) 103-117

A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th-century founders of modern geometry contemplated the possibility that a piece of empty space that looks completely smooth and structureless to the naked eye might have an intricate microstructure at a much smaller scale. Our vastly increased understanding of the physical world acquired during the 20th century has made this a certainty. The laws of quantum theory tell us that looking at spacetime at ever smaller scales requires ever larger energies, and, according to Einstein's theory of general relativity, this will alter spacetime itself: it will acquire structure in the form of "curvature". What we still lack is a definitive Theory of Quantum Gravity to give us a detailed and quantitative description of the highly curved and quantum-fluctuating geometry of spacetime at this so-called Planck scale. - This article outlines a particular approach to constructing such a theory, that of Causal Dynamical Triangulations, and its achievements so far in deriving from first principles why spacetime is what it is, from the tiniest realms of the quantum to the large-scale structure of the universe.

http://arxiv.org/abs/hep-th/0505154
Reconstructing the Universe
Authors: J. Ambjorn (NBI Copenhagen and U. Utrecht), J. Jurkiewicz (U. Krakow), R. Loll (U. Utrecht)
Comments: 52 pages, 20 postscript figures, added references
Report-no: SPIN-05/14, ITP-UU-05/18
Journal-ref: Phys.Rev. D72 (2005) 064014

We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.

http://arxiv.org/abs/hep-th/0505113
Spectral Dimension of the Universe
Authors: J. Ambjorn (NBI Copenhagen and U. Utrecht), J. Jurkiewicz (U. Krakow), R. Loll (U. Utrecht)
Comments: 10 pages, 1 figure, added reference
Report-no: SPIN-05/05, ITP-UU-05/07
Journal-ref: Phys.Rev.Lett. 95 (2005) 171301

We measure the spectral dimension of universes emerging from nonperturbative quantum gravity, defined through state sums of causal triangulated geometries. While four-dimensional on large scales, the quantum universe appears two-dimensional at short distances. We conclude that quantum gravity may be "self-renormalizing" at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction.

http://arxiv.org/abs/hep-th/0411152
Semiclassical Universe from First Principles
Authors: J. Ambjorn, J. Jurkiewicz, R. Loll
Comments: 15 pages, 4 figures
Report-no: SPIN-2004/22, ITP-UU-04/40, TPJU-19/2004
Journal-ref: Phys.Lett. B607 (2005) 205-213

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in the Euclidean sector of this theory is a bounce which satisfies a semiclassical equation. After integrating out all degrees of freedom except for a global scale factor, we obtain the ground state wave function of the universe as a function of this scale factor.

http://arxiv.org/abs/hep-th/0404156
Emergence of a 4D World from Causal Quantum Gravity
Authors: J. Ambjorn (1 and 3), J. Jurkiewicz (2), R. Loll (3) ((1) Niels Bohr Institute, Copenhagen, (2) Jagellonian University, Krakow, (3) Spinoza Institute, Utrecht)
Comments: 11 pages, 3 figures; some short clarifying comments added; final version to appear in Phys. Rev. Lett
Report-no: SPIN-2004/05, ITP-UU-04/11
Journal-ref: Phys.Rev.Lett. 93 (2004) 131301

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over geometries in nonperturbative quantum gravity, with a positive cosmological constant. We present evidence that a macroscopic four-dimensional world emerges from this theory dynamically.

========================

The above are the core research papers that have appeared since 2004. You can read the full paper free simply by going to the page and clicking "PDF". Then you get a download. CDT has only become generally visible since 2004 but it goes back to around 1998, and before that the "non-causal" version goes back to early 1990s. There was a breakthru in 2004 when CDT computer simulations of the universe produced something that was macroscopically 4D and had other realistic features.

The dimensionality was not FORCED to be 4D and actually it degenerated to around 2D at very very small (Planck, microscopic) scales. But at larger scale an illusion of familiar 4D emerged. this is what one might expect if space is actually made of something simpler at a fundamental level---a web of relations, a network, a fabric of something we don't know-------so then it could be a fractally mess at small scale but a nice 4D could emerge at larger scale.

this was the suggestive result of 2004. So one can say that the CDT approach is comparatively NEW because it only started going places in 2004.
people worked on it earlier but they were always frustrated because never getting a nice 4D space to emerge (or the analogous thing in lower dimension toy models)
===========================

here is Loll's website
these people work with her at University of Utrecht Holland
http://www.phys.uu.nl/~loll/Web/group/group.html

here are some press/ wide-audience media pieces
http://www.phys.uu.nl/~loll/Web/press/press.html

 

[Peter McKenna]

Cdt

Marcus,

Thanks for the relply. Very interesting stuff.

PM

 

[Peter McKenna]

Are the two dimensional constructs strings?

 

[marcus]

Are the two dimensional constructs strings?

read for yourself

they do not vibrate, they do not live is some pre-determined fixed surrounding space (the way strings) they ARE space

they fork and branch in complex whiskery cobwebby fashion

they are made of little simplex chunks (in the computer approx but of course might not be that in reality)

several people have described the way the CDT microscopic view looks to them as like a "fractal"

you have to decide for yourself if you think it has any point of similarity to string-thinking (besides getting down to a more one-dimensional kind of object which several QG approaches do besides these----LQG for example)

I would advise scanning the 2004 papers to get the flavor without bringing your own preconceptions to it at first, try to get at what is different about it

the computer simulations of the entire life of a small universe from appearance to disappearance----that is a fairly unique CDT thing

for example, string does not describe the dynamics of space itself, it takes a certain dimensionality space for granted as a GIVEN and let's strings run around in it.

Loll is interested in how SPACE ITSELF can arise, generated by certain primitive rules, and change curvature, expand, and contract dynamically.
She does not have particles running around in a fixed chosen-ahead-of-time space.

 

[marcus]

there are some curious things going on in Lolls simulations

there are no "2D constructs",

the dimensionality is something that happens and that you MEASURE (important: understand hausdorff dimension) at various scales and the dimens. is DIFFERENT AT DIFFERENT SCALES

you can take a 4D topological space and divide it up into 4D simplexes and (as long as you are not working with differentiable manifolds) the dimensionality does not have to be 4D down at small scale

the micro-picture can be fractally and have a fractional dimension like 1.9 or 2.1

this may seem paradoxical, it is something that just HAPPENS in the Monte Carlo random universe runs.

when you relax the smoothness requirements of differential geometry and just go to topological spaces, without the usual infinite differentiability smoothness assumptions (like you have in string think on manifolds) then all kinds weird stuff can happen. you give up the ability to do differential calculus at small scale, but in exchange you get a lot of new micro stuff.

to some extent same trade-off in other newer nonstring QG approaches

maybe it is how nature is and maybe it isn't, have to try to test these newer QG theories---not clear how.

 

[marcus]

we should talk about the Appleby paper that Jennifer spotlighted
here are all Appleby's papers going back to 1998.
he is a published researcher
http://arxiv.org/find/quant-ph/1/au:+Appleby_D/0/1/0/all/0/1

I liked the abstract of Dice and Divinity, thought it made a lot of sense.
havent read the full paper yet

why don't some other people take a look, and we compare reactions?

Look, this makes a lot of sense!
=====================
Originally Posted by MeJennifer
http://arxiv.org/abs/quant-ph/0611261
Concerning Dice and Divinity
D.M.Appleby
Contribution to proceedings of Foundations of Probability and Physics, Vaxjo, 2006

"Einstein initially objected to the probabilistic aspect of quantum mechanics - the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein saw as the abandonment of physical realism. We argue here that Einstein's initial intuition was perfectly sound, and that it is precisely the fact that quantum mechanics is a fundamentally probabilistic theory which is at the root of all the controversies regarding its interpretation. Probability is an intrinsically logical concept. This means that the quantum state has an essentially logical significance. It is extremely difficult to reconcile that fact with Einstein's belief, that it is the task of physics to give us a vision of the world apprehended sub specie aeternitatis. Quantum mechanics thus presents us with a simple choice: either to follow Einstein in looking for a theory which is not probabilistic at the fundamental level, or else to accept that physics does not in fact put us in the position of God looking down on things from above. There is a widespread fear that the latter alternative must inevitably lead to a greatly impoverished, positivistic view of physical theory. It appears to us, however, that the truth is just the opposite. The Einsteinian vision [i.e. naive realism] is much less attractive than it seems at first sight. In particular, it is closely connected with philosophical reductionism."

Jennifer said:
It seems to me that there is a third option.
Assuming that a measurement in a given physical reality can be seen as a higher order self-expression, I don't consider it unreasonable that there would be information loss.
===================

I say that Apple is RIGHT and that QM way of describing the world does NOT have a single reality ("in the eye of God"), it HAS to give up naive realism because it is basically an INFORMATION theory or a LOGICAL theory (logic is Logos, greek for talk, it is about talk, what you can properly SAY).

Sure, it is possible that there is a deeper more fundamental theory from which QM emerges, and that deeper theory might have a simple unique reality!

It might have a lot of surprising stuff we haven't thought of yet :-)

But as long as we are doing QM then it is about what various observers can know about various systems, it is not about some unique bedrock reality.

And that's fine.

that's my opinion just based on Appleby's abstract :-) hope someone else can do better

 

[MeJennifer]

http://arxiv.org/abs/hep-th/0604212
Quantum Gravity, or The Art of Building Spacetime
Authors: J. Ambjorn, J. Jurkiewicz, R. Loll
Comments: 22 pages, 6 figures. Contribution to the book "Approaches to Quantum Gravity", ed. D. Oriti, Cambridge University Press
Report-no: Spin-06/16, ITP-UU-06/19

I like the start of the document until on page 6 it states:

"Of the diffeomorphism-invariant quantities one can consider in the quantum theory, we have chosen a particular proper-time propagator, which can be defined constructively in a transparent way."

Sure we can, but should we?
On what ground should such a preferred perspective be the basis of a space-time building block?

 

[marcus]

I like your Appleby paper too. The Dice and Divinity one.

we could try talking about both Loll and Appleby in alternation:-)