About space in quantum mechanics

[Adib]

About space in quantum mechanics

 

We apply set theory with urelements ZFU to physical space, we consider

locations as urelements, elements of U (non sets).

Ui is a subset of U with number of elements n.

XiUi is the infinite cartesian product and a set of paths.

Let us consider the set of paths of all elementary particles-locations

which number is n.

If n is greater than m in CC(2through m), countable choice for k elements

sets k=2 through m, the set of paths will be the void set.

So, physical space would become void, the universe would collapse and a Big

Crunch would happen.

But the matter would have to go somewhere and indeed the Big Bang happened.

So, n is indeed greater than m.

The negation of the axiom of choice is really true because it can be

applied in physics.

 

http://jebara.topcities.com

[Martin]

We apply set theory with urelements ZFU to physical space, we consider

locations as urelements, elements of U

 

In 1915 Einstein pointed out that in his GR theory points of spacetime have no physical reality.

 

Your scheme has problems. First, you do not know that the axioms of set theory apply to the universe. Set theory is a human construct nobody says that it is right or that it is applicable to nature.

 

Second, assuming that axiomatic set theory can be applied to the universe, what set do you want to define? What do you apply it to?

 

Einstein says that in GR, spacetime is not a set of points. But GR is the prevailing theory concerning spacetime. It works very well, with high accuracy. what do you want to replace it with that will fit the observations equally well?

 

that 1915 quote (actually there are two, one from a letter and one from an article about the perihelion of mercury) is really neat---something like "the principle of covariance removes from points of spacetime the last vestige of physical reality"

Maybe you can find it by google.

 

Anyway you are being creative, but it is not so easy to get cosmology out of nothing but logic and set theory. (IMO at least, see what others say)

[Adib]

I explain why the Big Bang happened which is not yet done.

What does IMO mean ?

[swansont]

I explain why the Big Bang happened which is not yet done.

What does IMO mean ?

 

IMO = "In My Opinion"

 

common acronyms & initialisms

[CPL.Luke]

how come the universe currently isn't collapsing? you seem to be advocating a cyclic universe, however the expansion is accelerating

 

also the statement that you can't talk about points in GR isn't quite true, a point in space time is a vector which

gr will tell you how to transform into arbitrary coordinate systems

[Martin]

Adib, I think it is an ingenious highly original idea to try to apply the Axiom of Choice to cosmology. I don't want to scoff at it.

 

But I'm lazy and have limited time and braincells, so I don't want to help you explore it. There would be an immediate obstacle at the outset which would be deciding what mathematical model of the universe to use.

 

the obvious choice would be something like General Relativity and you'd run into complications there

 

There are people who do stuff that is a little bit like what you are trying to start. There is Seth Lloyd at MIT

He doesn't use the axiom of choice, he uses more modern knowledge about COMPUTABILITY. He models spacetime-and-matter as a network of events where neighbors influence each other in computable ways

 

since Turing machines and since the 1950s, a lot has been learned about the limits on computability. Some functions are harder to compute---can take infinitely long etc etc. Seth Lloyd assumes that Mother Nature has to obey some restrictions on computability of whatever functions she uses to link interacting events together. He tries to derive cosmology consequences from this.

 

He is not the only one. Some other names come to mind. they aren't doing what you are---with axiom of choice----but their work has somewhat that same spirit. There is a bunch of work called Causal Sets for example (names are Sorkin, Dowker, Henson....)

 

I wouldn't know what to advise you to do. Look up stuff on google. Look up stuff on Wikipedia. You can be proud of the originality of thinking of applying the axiom of choice but I can't honestly encourage you to pursue it.

 

Probably, if you are interested in cosmology, you should try to learn some GR.

 

There is also Carlo Rovelli's book a version of which is free online at his website. Just google Rovelli. I mean just the first couple of chapters, as an introduction to Quantum Gravity.

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

 

What I am currently most interested in are two papers by Renate Loll.

Her team in Holland is running simulations of small universes, which assemble themselves out of microscopic interacting components, come into existence, grow, do a passable imitation of Einstein spacetime, then collapse and go out of existence. Because it is quantum cosmology (not classical) it is unpredictable and different each time.

 

there is no overall guidance. only some simple rules of interaction between neighbors----so it is a little like an ant nest that seems to behave intelligently tho it has no brain, or a flock of birds that seems to flow like a fluid as each bird is just responding to his immediate neighbors.

 

the secret is in the choice of microscopic rules by which the little buildingblocks interact. in a sense they have to embody a quantized version of the einstein field equation of GR, down at micro-level, from which the largescale classical behavior can emerge

 

It is a quantum model of spacetime, not a classical one, and it is uncertain geometry which gets fractal at small scale and only has the illusion of smooth at large scale. very neat.

 

if you want to look here are two recent papers (which have references to earlier ones)

 

http://arxiv.org/abs/0711.0273

(The Emergence of Spacetime: Quantum Gravity on Your Desktop)

http://arxiv.org/abs/0712.2485

[foodchain]

About space in quantum mechanics

 

We apply set theory with urelements ZFU to physical space, we consider

locations as urelements, elements of U (non sets).

Ui is a subset of U with number of elements n.

XiUi is the infinite cartesian product and a set of paths.

Let us consider the set of paths of all elementary particles-locations

which number is n.

If n is greater than m in CC(2through m), countable choice for k elements

sets k=2 through m, the set of paths will be the void set.

So, physical space would become void, the universe would collapse and a Big

Crunch would happen.

But the matter would have to go somewhere and indeed the Big Bang happened.

So, n is indeed greater than m.

The negation of the axiom of choice is really true because it can be

applied in physics.

 

http://jebara.topcities.com

 

My opinion is that QM might also have convergent histories.

 

So if you were at a specific history you might be able to view so much, but over differentiation you can find more and more a discrete nature to individual parts. Decoherence using environment as a witness or I guess what is doing the measuring? So the question to me is if you can use decoherence to obtain a convergence. For instance when looking at any particular geological structure, like hand size rocks. I would imagine that at some point those atoms or molecules might have been in a liquid state. So phase wise what allowed for each individual chunk eventually end up where its at state wise currently, such as geometry.

[CPL.Luke]

well to a certainn extant your talking about the probabilities of large numbers where the state of the system converges to the state of highest probability, (which is also the average).

 

also your talking about histories then the most probable path will be the path of least action, as the paths that neighbor this one will add constructively and the paths that are further away tend to add destructively.

[foodchain]

well to a certainn extant your talking about the probabilities of large numbers where the state of the system converges to the state of highest probability, (which is also the average).

 

also your talking about histories then the most probable path will be the path of least action, as the paths that neighbor this one will add constructively and the paths that are further away tend to add destructively.

 

 

Well I don’t know anything for sure, most all of this is rather new to me. Right now in my free time I am reading up on superconductivity. I read an interesting paper on arvix about decoherence, or the use of such after two decades of existence. Its made some really good progress is what I generally understood from it. I like the idea of a pointer, but I got confused as to exactly what the pointer was. My ideas on the subject where pointers are an observed point value, or particle?

 

What I think is scary is that relativistic wave equations exist. To what extent in those due you apply as an environment? Basically where can you denote the extent of a field? More so with issues like entanglement.

 

Like I said a lot of this is really new to me.

[fredrik]

What I am currently most interested in are two papers by Renate Loll.

Her team in Holland is running simulations of small universes, which assemble themselves out of microscopic interacting components, come into existence, grow, do a passable imitation of Einstein spacetime, then collapse and go out of existence. Because it is quantum cosmology (not classical) it is unpredictable and different each time.

 

there is no overall guidance. only some simple rules of interaction between neighbors----so it is a little like an ant nest that seems to behave intelligently tho it has no brain, or a flock of birds that seems to flow like a fluid as each bird is just responding to his immediate neighbors.

 

the secret is in the choice of microscopic rules by which the little buildingblocks interact. in a sense they have to embody a quantized version of the einstein field equation of GR, down at micro-level, from which the largescale classical behavior can emerge

 

I find the idea that spacetime (any structure in general) is self-emergent and self-organised as per some "logic" of self interaction right in line with my personal thinking. I like this!

 

But I have some problems to picture a the implementation of this "microscopic rule" withour prior structure. It is a bit ad hoc IMO. Not as ad hoc as many other things but still not quite satisfactory. So I think the idea is right on, but more needs to be done.

 

I think that the extension of this idea is to also show how the microscopic rules themselves are emergent and that in principle rules and structures are unified. I haven't found much papers on this but it's what occupies my mind at the moment.

 

I think that to expand the ideas of Loll, one must also take into account the observer, and the microstructure of the observer. I am starting to think the rules are implicit in the microstructure (not microstate; I make a distinciton here) of the observer, and the evolution of the rules go hand in hand with evolution of observers (which as essential in my thinking self-preserving microstructures that interact with their environment) and since basically everything is observers in mutual interaction (if you consider particle interactions as two observer inteacting) these things (structures and rules) tend to find it's common base.

 

I'm starting to be convinced that the path integral concept can be given an explanation from a pure information processing perspective. But it seems very difficult to find the formalism.

 

I don't like the fact that in that paper the rule are put in manually. You have to start somewhere, but I think taking the idea to the next level would IMO need to show how the rules are also emergent, and how the rules and structure are unified. I am naive enough to think it can be done but I don't know how.

 

/Fredrik

 

I am starting to think the rules are implicit in the microstructure (not microstate; I make a distinciton here) of the observer

 

The idea then is that observer emodying inconsistent "rules" simply won't survive. There is a negative selection for them. And ultimately the selected rules will be what "most observers" agree upon, which means that the rules may not be completely homogenous.

 

/Fredrik

[Martin]

 

I don't like the fact that in that paper the rule are put in manually. You have to start somewhere, but I think taking the idea to the next level would IMO need to show how the rules are also emergent,..

 

I think I see where you are coming from. You would like to arrive at a new microscopic action rule based on fundamental principles.

 

their approach is extremely conservative, by comparison. they just take over the Einstein-Hilbert action-----going back to around 1915

and the adaptation by Regge made in 1961

 

so they do a nonperturbative IMPLEMENTATION of the EinsteinHilbertRegge action, that has been around for 45 years.

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

 

in science many ways must be tried

 

I cant say their way is right or that it is wrong, but it makes sense to try a very conservative approach

 

the action they are using is essentially General Relativity which has a long record of working well

 

so they say WHAT IF YOU DON'T HAVE TO INVENT ANY NEW STRUCTURE? what if there are no loops or strings or extra dimensions or any exotic jazz?

what if good old Einstein GR continues all the way down?

 

the only difference is that they are using a nonperturbative strategy that was pioneered with the (successful) QCD of the some decades back, the perturbative treatment of GR failed, so they are doing something analogous to what the QCD people did, and trying a nonperturbative strategy.

that gets into techniques of regularization, and into the business of how you calculate. But the basic approach is conservative and extremely uninventive.

 

they don't say the triangles exist. they just use triangulation to regularize their numerical work and then they shrink the size of the triangles to zero.

 

all they say exists is the relational dynamics already present in classic Einstein Hilbert Regge GR.

 

Regge was the guy who figured out how to do GR without a system of coordinates. Hilbert (you know) was the guy that Einstein was racing to the finish line in 1915. They all contributed

 

Have you read Loll's paper "Quantum Gravity on Your Desktop"?

I think you must have been looking at it. Great paper, yes?

[Adib]

We have drifted far from the subject.

Why don't you ask for instance if the time needed to reach a Big Crunch

is infinite ? It is.

[fredrik]

I think I see where you are coming from. You would like to arrive at a new microscopic action rule based on fundamental principles.

 

Something like that yes. But my suggestion is also extremely conservative, and I'd like to think it's _in a certain sense_ way more conservative than that paper.

 

the action they are using is essentially General Relativity which has a long record of working well

 

so they say WHAT IF YOU DON'T HAVE TO INVENT ANY NEW STRUCTURE? what if there are no loops or strings or extra dimensions or any exotic jazz?

what if good old Einstein GR continues all the way down?

 

I agree completely that this should be tested, but the opinion is open as to whether extrapolating GR to a domain where we have pretty much no empirical support, is the least speculative (most conservative) strategy?

 

Have you read Loll's paper "Quantum Gravity on Your Desktop"?

I think you must have been looking at it. Great paper, yes?

 

Yes I read it and I like the fact that they try to compute something without ordinary perturbation theory. The most interesting thing IMO is the dynamical dimensional reduction they found.

 

As should be clear from the discussion above' date=' [/font']in a scheme of this sort one is by no means ensured that what comes out is the correct theory of quantum gravity. However, thecomputational handle we have on such models can give us a very good idea of whether we may be on the right track or whether the formulation is fatally flawed. This is something that is very difficult to tell if one only has pen and paper at one’s disposal to evaluate a sum over such geometries nonperturbatively

 

But I am not personally satisfied with their starting points, and I don't think it's anywhere like a revolutionary paper in any way.

 

Reading this papers makes it clear how ambigous and poorly understood the path integral and action principle is. They also refer to principal measurements with clocks and rods. I would expect to see the distinguishable rods and clocks in the micro world emerge out of the data.

 

I'm not sure I follow their conclusion(?) how their choice of regularization and gluing rules have no impact on the resulting expectations (theory)? I suspect this is based on some implicit manually put in ergodic hypothesis and that type of reasoning is speculative IMO. It seems more like an assumption to me, and one I'm not sure I share.

 

I think the ergodic inductions should come from a revised action principle. The ergodic hypothesis should IMO be supported in a history, and in this history the support should be quantifiable. And I think this quantity is closely relatey to the concept of intertia.

 

Also they have made the blocks 4D by hand. Wouldn't you expect that there should be able to be exist transition between topologies? I think that it is possible to rate possible topologies according to their expected fitness, and this induces from the observers history a prior expectation, so no ergodic hypothesis is needed in the ordinary sense. I think this should also solve the regularization issues, because the options themselves are normalized one by one. I always felt this is a missing detail in feynmanns formalism. Still the formalisms is too nice and too good to be a conicidence, but I think we still await the ultimate polishing on this, and my personal expectations is that in that respect gravity will emerge. Now if such a procedure could be shown to reproduce einsteins equations in the appropriate limiting case it would be interesting.

 

I totally agree that all options should be tested for viability in relation to expectations. But what I look for is to me is even more conservative in that it tries to implement the essence of the scientific method in the "micro rules"! This means that I envision that these microrules are sort of nothing but the essence of scientific reasoning, or scientific inductive reasoning, and the laws of physics should be the micro-implementation of what human philosophers consider to be the "science"

 

I have had the impression that it's extremely hard to communicate the ideas at this proto-stage. I hope to be able to find an explicit realisation of it but it's hard with so little time. I try to be as conservative as possible, given that I hope to be able to get something at least within a lifecycle.

 

/Fredrik

[Martin]

Fredrik, I appreciated your thoughtful response based on a reading of the paper and enjoyed following parts of your argument. My only worry is that if I respond here as I would like, it would be off topic from the original post! I am thinking of starting a thread about the Triangulations approach and possibly moving some of our posts out of here and into the new thread. Otherwise we run the risk of abusing the hospitality of Adib, the O.P.

[Adib]

Thank you for remembering the topic, a new idea about space in quantum mechanic.

Some posts are very complcated, I wonder if it is necessary that they be so.

[fredrik]

I'm sorry for the diversion Adib.

 

I personally didn't quite follow the line of reasoning in your original post, but I agree that the nature of "space and spacetime" in QM is an interesting topic to reflect upon.

 

/Fredrik