LHC - the last chance for all theories of everything?

[tom.stoer]

So, the laws are identical, but initial conditions are different? If Universe is infinite, all combinations must happen. ...

Hi, I stepped out for a while, but I would like to come back now.

My question was if I can create a universe with a tenth planet simply by writing down the general equations for the solar system and introducing a tenth planet in theory. You replied that this is a problem regarding initial conditions in an (infinite) universe.

Let's assume that within the MU you have several mathematical structures describing more or less our universe. As far as I understand you the different universes with - say - nine or ten planets - would belong to the SAME mathematical mutliverse but would live in different "areas" of the "many world" multiverse. If string theory is rigth then all its solutions would still belong to the same mathematical universe but live in different branches of the "many world" multiverse. But If I introduce another system like "game of life", then I would have to refer to the mathematical multiverse (I guess game of life is not a vacuum of string theory :-)

Looking at the "game of life" it serves as a toy model. It can either be described by a (completely Goedelized) mathematical structure and it would therefore be an own universe. Or it can be simulated by computer programs within our universe, therefore it can be seen as a substructure of the mathematical structure being our universe. Therefore within MUH we have the situation that mathematical structures can be own universes, or they can be substructures of universes.

Now we can look at the "game of live" from a third perspective. It can serve as a model for a universal Turing machine. Now having said that we remember that a universal Turing machine is able to simulate all other Turing machines. Therfeore game of life is able to simulate a large class of universes.

That means that a universe can exist on its own or it can be simulated by another universe. Within the universe everything looks identical (the structure is the same), but from the outside it looks different. Whereas the abstract structure can exit w/o any context, the simulated structure lives in a certain context. That means that we can construct an infinite tower of universes containing (simulating) each other.

But as any mathematical framework shall be free of any baggage, we must identify all structures with a certain kind of "algebraic isomorphism". So we must identify the Turing machine universe with the "game of life" universe.

Now let's assume for a moment that our universe is computable. Then we could (must!) identify it with a certain Turing machine or with a universal Turing machine + certain input. But then you have to explain why our universe looks so different from a Turing machine - or "game of life"! Of course I can easily escape this reasoning by giving up the idea that our universe is computable. So the other conclusion would be that our universe is not computable. Having concluded that our universe is not computable we immediately know that our universe is either (Goedel-)incomplete or inconsistent. As our universe exists and should therefore be consistent it must be incomplete. That means there are true statements which cannot be proven within our universe.

Now what does it mean for a mathematical structure to exists? Do we need a proof? What are these structures that exist within our universe w/o having the ability to be justified by our universe?

 

[member 11137]

Hi, I stepped out for a while, but I would like to come back now.

Now what does it mean for a mathematical structure to exists? Do we need a proof? What are these structures that exist within our universe w/o having the ability to be justified by our universe?

Let us assume that our universe exists (only because we can state it) and that it is a computer then there are some mathematical motors or structures existing to give it its internal coherence even if it is not complete (of course it is in creation) ! A self evoluting machine...

 

[ConradDJ]

So my question, as you could probably guess, how you can tell a physical system from a purely mathematical one? (this question is not so easy as it sounds)

Dmitry, you are right on the money with this parenthetical remark. I think there is a fundamental – and very obvious – difference between physical systems and mathematical ones... but it is not at all easy to be clear about this difference. When I say obvious – well look, you can bang into something physical, but not something mathematical. That would presumably convince anyone but a physicist!...

But I don’t expect it to get anywhere with you or qsa, who understand physics (including banging into things) to be mathematical. If I understand you, you would say the above-mentioned difference is between mathematics that’s in your mind or in a textbook, and mathematics that really exists “out there” in Platonic eternality – one small part of which is what we experience as our physical world.

So how do we tell if the world around us is “just mathematics” or something more – and in what sense could it be “more”?

If we assume the physical world is a set of given, well-defined facts, I would say you are essentially right – or at least, right enough that there’s no point in arguing about it. Some of the facts would fall into mathematical patterns; others might just be random data, that can be located / defined in a mathematical framework. In that case I’d be happy to assume that someday we’ll have appropriate mathematics to describe all the facts... and if you want to say the facts are mathematics, fine... we’re down to semantics. In any case we would have something like a one-to-one mapping between the physical and its mathematics.

So is the physical world more than a set of describable facts? Yes – for one thing, it ’s a system that does its own describing. It’s a network of data-channels that communicates information about every part of itself to other parts. And a set of contexts that make incoming data meaningful for setting up other contexts.

There is a spacetime structure to this network, such that at any given point, information about certain other parts of the world (past light-cone) is accessible, while information about other parts is not. And there is an interactional structure such that in any given situation, certain information is measurable, while other information is not. And at any given point, the accessible / measurable information sets up a structure of possibilities (wave-function), out of which certain new information becomes “fact”, that gets communicated out as part of the base-information for other situations that create other facts.

So maybe your metaphor of “dead” mathematics and “living” physics is apt, in a certain way – though there’s nothing “magic” in this picture, this is just well-established physics. But it looks like physics is doing something that we don’t expect mathematics to do.

What we expect mathematics to do is give us coherent, more or less consistent descriptions of given structure. If we assume physics is just “a given structure”, then it’s not essentially different from mathematics. But we don’t expect a mathematical structure to create partial descriptions of itself and send them to other parts as a basis for new partial descriptions, or create measurement-contexts in which new information can be defined.

As I said above, I’m happy to stipulate that each component in this physical system will someday have a good mathematical description. My point is that there’s a functionality involved in how these components work together that amounts to “being physically real” – and that goes beyond what we think of as mathematical structure. But I admit that this functionality is very difficult to be clear about. And if anyone wants to take this as a sign that the whole idea is nonsense, I can’t very well blame them!

But here’s my question for you – if you take the physical world to be mathematical, then what in this mathematical system corresponds to a measurement? Or to the communication of information? In what way does this system provide descriptions of itself, and in what way are these descriptions made accessible only to certain parts of the system and not others?

In other words, can you really describe a mathematical system that looks anything like the world we live in, and does the kinds of things we see happening all the time? Or is it just a matter of faith that physics “must be” a mathematical structure “and nothing more,” based on our success in modeling many separate aspects of the world in equations?

 

[Dmitry67]

ConradDJ, that you for your detailed answer, even I did not understand it completely. You claim that physics is something more, then mathematics, but you fail naming that mystical "more", admitting that it is "very difficult to be clear about"

Can we agree on a simpler statements:

1. If there is a difference between mathematical and physical, that difference can't be tested experimantally by the frogs inside the universe.

2. If universe is perfectly emulated, then frogs can't detect if it is real or perfectly emulated

3. Perfectly emulated system is isomorfic to a real one.

4. Hence it is absolutely irrelevant if we are emulated or not. In fact, the emulation is an argument for MUH: if there are universes which can emulate others, then all sorts of universes MUST exist

If we agree the theory of natural numbers is the same no matter if it is written by ink, or in PDF, or scratched on a stone, so mathematics is independent from the substance, then we must agree that it is irrelevant if it is emulated or not.

(Q: ha, but what if emulator glitches or I destroy the Turung Machine?
A: We are talking about the PERFECT emulation. If you can't atop it it is not)

This is also an answer to tom.stoer (1,2,3,4)

 

[Dmitry67]

1 But here’s my question for you – if you take the physical world to be mathematical, then what in this mathematical system corresponds to a measurement? Or to the communication of information? In what way does this system provide descriptions of itself, and in what way are these descriptions made accessible only to certain parts of the system and not others?

2 In other words, can you really describe a mathematical system that looks anything like the world we live in, and does the kinds of things we see happening all the time? Or is it just a matter of faith that physics “must be” a mathematical structure “and nothing more,” based on our success in modeling many separate aspects of the world in equations?

1 Measurement is described by the physical laws of the Universe. As I said before, for the frogs inside Universe is real and measurable. It is like in MWI, narrow-minded observer in every branch would cry "only my branch is real!". The same in MUH - for any forg only "his" Universe is real.

2 You are asking for the ultimate TOE equations? Just a minute... where did I put them? ok, let me find a piece of paper where I wrote them... hope it is not in the bin...

 

[Dmitry67]

But do we know what energy is? I mean we do not really progress in labeling things of which we in fact ignore the signification.

All fundamental notions are just mere labels. They don't have any properties per se, all their properties describe their relationships with the other entities.

So the question "what is a true meaning of the Energy" either suggests just another step of an infinite reduction (like energy is made of energions, but in that case energy is not fundamental, so we have the same story again with the "energions") or is meaningless, like asking, "what numbers are made of".

 

[Fra]

I couldn't resist adding a comment on one more thing here.

So my question, as you could probably quess, how you can tell a physical system from a purely mathematical one? (this question is not so easy as it sounds)

It seems Dmitry is somewhat into Tegemarks idea of mathematical universe?

In a certain sense I can remotely connect to this, but I still see it different so I could at least comment what I mean with physical and non-physical inferece/math from my point of view because to me it has a special meaning:

Mathematics is the natural language of making quantiative predictions and calculations. So it is even more me of course. However mathematics has also evolved, just like physics. So in principle, there is no major difference. The quantiative framework is often more or less one-2-one to physics. I think Dmitry called it labels? I fully agree so far. I have no problem to imagine the class of all isomorphic constructs here.

One can even think of mathematical calculations as at least supposedly one-2-one with physical actions and processes (or inferences like I like to think of it). so far, that's fine.

So what I mean with non-physical inference, is when one observer; a human in most examples, uses some of his PHYSICAL mathematics, and try to impose it as one-2-one to a much more constrained system with very low complexity.

To me one basic conjecture is that regardless of the CHOICE of represenation or lables, there is an information theoretic abstraction where the COMPLEXITY is the same wether it's mathematics or a physical object, and this complexity constraints what are the POSSIBLE represenations.

What I for example mean is that, it does not make sense to picture a very simple low end computer to actually be able to run a a gigantic algorithem designe for a supercomputer. This is a decent analogy, since I can also accept if we choose mathematics as representation, that physical interactions are like computations. But then the question is which computations are going on in certain processes, and how does the "computers" look like?

This is again just different words for my "inference system". The reason I call in uncertain inference is that the computers themselves EVOLVE _in time_ therefore they change unpredicatably (but controlled) during actualy computations!

THIS is why I don't think it's as simple as deductions. One premise giving one output for example, since during the physical process of producing the output, the calculational machinery responsds to feedback and changes.

So when *I* talk about mathematics, of course all of that is physical for me, as someone noted, at least it's represented in papers, litterature etc. However, if we are trying to impose that very complex logical system into often ARBITRARY small systems, or even points! then we are abusing the complexity constraints.

Fwiw, I supect this is not going to make any sense, but it's my differentiation. It's exactly this I mean when I object to physical redundance of mathematics, in particular a lot of the continuum mathematics.

A final note: What do You think the common say UV infinities are a symptom of?

/Fredrik

 

[Dmitry67]

UV infinities are the symptom that distances can not be infinitely small, of course, what else?

Fra, what is more complex: TOE or Standard Model? Or SR/GR? In some sense, TOE is the most fundamental (does it mean that it is more complex?) So, Standard Model emerge from TOE on low energies, like Newtonian physics emerge on our daily life limit.

We are moving from Classical physics to TOE, in opposite direction. But during the history of our Universe the 'laws' 'evolved' from TOE to Standard Model, then even heavy quarks dissapered, then classical physics... I mean, as it cooled down, the laws evolved from TOE to Classical physic.

BUT: if TOE is the most complext one, then laws did not evolve, they had actually simplified!

 

[Fra]

UV infinities are the symptom that distances can not be infinitely small, of course, what else?

It was a bit of a rhetorical question, but I meant to link the divergence calcuations with our failuer to see that the inference system - beeing the "calculations" - must scale along with the complexity of the inference systems. So I think it's more than just distance. It can also be interpreted as an "information overflow".

But let's skip this, it was pretty much a rethorical question.

Fra, what is more complex: TOE or Standard Model? Or SR/GR? In some sense, TOE is the most fundamental (does it mean that it is more complex?) So, Standard Model emerge from TOE on low energies, like Newtonian physics emerge on our daily life limit.

We are moving from Classical physics to TOE, in opposite direction. But during the history of our Universe the 'laws' 'evolved' from TOE to Standard Model, then even heavy quarks dissapered, then classical physics... I mean, as it cooled down, the laws evolved from TOE to Classical physic.

BUT: if TOE is the most complext one, then laws did not evolve, they had actually simplified!

I see your reasoning, and it illustrates also the problems you face.

Your "TOE" are necessarily pretty much infinitely complex, from which the observed simplicity follows deductively? You are faced with an enourmous initial value problem, which basically is an infinite improbable initial state. I predict that the tuning problem you are faced with is overwhealming, like the landscape problem in string theory.

The amount of information needed to represent this infinite configuration space and the computing power/time needed to make computations on in would I think stall your progress.

Ie. I do not see how your vision can lead to improved predictive power, because it seems to me you are inflating the COMPLEXITY of your inference system to the point where it violates your own complexity. I thikn only something like a god could make use of your master plan.

BUT: if TOE is the most complext one, then laws did not evolve, they had actually simplified!

I have the requirement of beeing able to make computable predictions. A theory that isn't mangable in the complexity and computability sense simply isn't viable to me. I am taking his seriously in my view.

So in this view, there were no coherent very complex inference systems during this supposed big bang, this is why the complexity you envision (from which simplicity emerged) is not a proper inside view. It's to me an imaginary external view that lacks physical meaning.

So A TOE as seen relative to a human today would be complex, but a TOE seem from the emergent inference systems during say the big bang, would have been very simlpe. Simple mathematics and therefore also simple laws.

The question is instead not how an improbable initial conditions in an infinite configuration space evolves to the probable present, it's how during this process an ARBITRARY initial condition, constrained by a very limited configuration space, INFLATED the configurations space and while doing that evolved new interactions that was originalkly indistinguishable from each other.

/Fredrik

 

[Dmitry67]

Regarding the "improbable initial state" - this is a problem for Bohmians. As you probably remember, I am fanatical MWIer, so for me this problem doesn't exist - Universe started at very simple initial state (probably with null or very simple initial conditions) and the total amount of information in the Universe is probably 0

"but a TOE seem from the emergent inference systems during say the big bang" - wait, do you deny the existence of heavy quarks soon after the BB? If not, do you think that the laws they obeyed were simpler then the Quantum Chromodynamics they obey now?

 

[Fra]

Regarding the "improbable initial state" - this is a problem for Bohmians. As you probably remember, I am fanatical MWIer, so for me this problem doesn't exist - Universe started at very simple initial state (probably with null or very simple initial conditions) and the total amount of information in the Universe is probably 0

I have to admit that since I find a lot of the MWI reasoning a bit weird, I do not in detail follow the supposed logic there.

But in a certain sense, the "zero information" starting point is not too unlike my view.

However, in my view information can be created and destroyed, if you ackonwledge the intrinsic view, it's just that no observer EXPECTS it, and therefor all stable laws does conserve information. But information conservation doesn't apply to the case where the inference systems is either loosing or gaining complexity.

The zero information in my view, simply means that there are not yet any coherent observers. There is no information because there are no "memory devices" to put it crudely.

"but a TOE seem from the emergent inference systems during say the big bang" - wait, do you deny the existence of heavy quarks soon after the BB? If not, do you think that the laws they obeyed were simpler then the Quantum Chromodynamics they obey now?

This is a difficult question and for sure my ideas are not yet developed enough to explain quark interactions :)

But as a generic "prediction" of my vision, I certainly expext a unification of QCD, electroweak AND gravity. And the inside view of this must be simpler, at least in the sense of explaining a lot of the paramters parameters.

At the point where spacetime is emergent, there is unavoidably also emergent inference systsm that I associate with matter or "confined energy" systems. If this is new particles, or some of the existing standard model particles is way too early to see. But if my vision is to make sense, then there must be a level of a simple inference system from which QCD gravity and electroweak follows as the scaling of the inference system complexity/mass grows.

It's just prematute for me to have any expectations on this. But given the formulation of the standard model, as based on QFT, I think the explanation must start already at the emergent of the continuum and dimensions. And to assume that some non-trivial massive stuff like heavy quarks appear in the first part of reconstruction I find quite unlikely, unless they are the FIRST non-trivial systems to emergen as spacetime is formed. But I really can not comment on that at this point.

But it is definitely things that should be answered from a theoretical point of view..

/Fredrik

 

[Dmitry67]

The zero information in my view, simply means that there are not yet any coherent observers. There is no information because there are no "memory devices" to put it crudely.

No, system can be infinitely complex - and yet - contains no information!

Take an empty chessboard. It has only 1 possible state, so it contains no information.
Put 1 figure on any of 64 squares. Now you have 64 possible states and it contains some information.
Put 2nd figure - you have 64*63 possible states.
Adding more and more figures, you add more and more information, until.. until you start to approach the UNIVERSUM (in our case it is a full board)
There are only 64*63 configurations with 62 figures, 64 with 63 figures, and only 1 - with 64 figures.

'Something' is equivalent (on information level) to UNIVERSUM minus something.
Empty set is equivalent to the UNIVERSUM and contains no information.

In MWI Universe contains zero information not because it is void, but because it contains all possible states. Interestingly enough, for any frog the amount of information in the universe is huge.

P.S.
It would be interesting to develop a theory of relativity of information. For example, for observer who is aware that 2 particles are entangled, the amount information in such system is less than for an observer who is not aware of it.

 

[ConradDJ]

When a complex molecule is simulated on a computer with mathematical modeling, you can see how it vibrates and responds to environment, it looks alive... What we conjecture, that by a similar process we the “physical” become alive because of computation. The only difference is we can see the simulation of ourselves by ourselves without a computer screen.

Can we agree on a simpler statements:

1. If there is a difference between mathematical and physical, that difference can't be tested experimentally by the frogs inside the universe.

2. If universe is perfectly emulated, then frogs can't detect if it is real or perfectly emulated.

3. Perfectly emulated system is isomorfic to a real one.

4. Hence it is absolutely irrelevant if we are emulated or not.

Thanks for the lovely argument! But talking of “simulation” or “emulation” raises an issue that’s much easier to argue than what I was being incomprehensible about above.

There is no analytic solution to a problem as simple as the Newtonian 3-body problem. In other words, if I understand correctly, in a classical universe even very simple physical systems would constantly be finding exact solutions to problems that a computer can solve only approximately – and would be doing so in real time, with no expenditure of energy.

We don’t live in a classical universe, and it’s not clear how that affects the computation problem. On the one hand, the properties of systems don’t have to be specified by an infinite amount of information, and on the other hand the equations are a lot harder to compute.

But I think we can agree that any system capable of emulating the behavior of 3 particles is going to be a lot more complex than the 3 particles themselves, and it has to behave in much more complex ways. And of course, the computation problem becomes vastly more difficult if we have 4 or 5 particles – not to mention the number involved in any realistic physical situation.

The existence of computer simulations makes it easy for us to imagine that we also inhabit a simulation. But it’s easy to see this is really just a fantasy, if you think about the magnitude of the problem involved in, say, computing the paths of individual molecules in 1cc of air over the course of a second. This is something the physical world handles just fine, but no computer ever will.

I think your original idea was not about one system simulating another one, though... it was more like, the world does not need to be “simulated” or “computed” because it already is a mathematical pattern.

 

[ConradDJ]

Measurement is described by the physical laws of the Universe.

I would say this is a statement of faith, not fact.

Our closest approximation to a description of measurement is given in quantum “wave-functions” – which are mathematical entities, but rather vague ones. They refer to physical situations in which certain outcomes are possible – but the mathematics doesn’t actually say very much about those situations, it just assumes they are there, and that they can distinguish the various outcomes.

You certainly could not “emulate” a physical measurement-situation in any level of detail, by manipulating the wave-function used in connection with it. The math of QM is a very useful tool for predicting measurement-outcomes, but it doesn’t actually tell us much about what’s physically involved in a measurement.

And of course... the wave–function gives us only a set of probable outcomes, whereas in the physical world we get a random selection of an actual outcome. Yes I know, from an MWI perspective there is no “selection” and all the outcomes are equally “there”. In other words, in the big picture measurements don’t actually happen, and the wave-function is the complete picture. But this doesn’t get us closer to mathematics and physical laws describing what happens in a measurement.

From the perspective of any observer in any universe, the world is constantly offering up new facts that could not in principle be predicted on the basis of prior facts, and which often have profound consequences for what can be observed in the future.

So I think mathematics gives us wonderfully effective partial representations of many different (highly simplified) aspects of the physical world. If we take any small part of a measurement-situation, a photon or an electron, say, we can give a good mathematical description of it. But that doesn't mean we've described the structure of the situation as a whole, or described how it does what it does.

I don’t doubt that our ability to model more and more of the world mathematically will continue to improve. But the leap to the idea that mathematical structure per se explains what’s going on in the world is a long leap of faith... or maybe, a default position based on the difficulty of imagining alternatives.

It’s not clear what’s going on in quantum measurement-processes... but to me, MWI just offers a nice way to avoid dealing with the problem. That’s a sensible choice to make based on a faith that the world is mathematical, and that issues we don’t know how to frame mathematically can’t be really important. But I don’t believe there’s a strong argument there.

 

[Fra]

No, system can be infinitely complex - and yet - contains no information!

I know what you mean, but then your certain information measure and state space is a baggage. This baggage carried background information in my view. So your information measure is "relative to" the context, which is fixed in your view.

I don't think there is an innocent background, in my view the context is evolving. Therefore there exists a feedback between information, and information carrier.

I know you can define microstructure of infinite size, and an information measure. Then zero information is simply the equipartitioning.

But the ergodic hypothesis is not unique, this choice does carry background information. In my view I am trying to account for this.

This is why I also talked about a reconstruction of information theory, which is pretty much on the same table as the reconstruction of probabiltity theory.

The ambition is exactly a theory of relativity of information (and inference) that you mention! So if you like that, then there might be some grains in here that you can like as well. Now, I think a theory of relativit for information necessarily evolves, because there exists no static fixed solutions. The inference processes resulting from this relativity, are physical ones, that possesses things like inertia etc in my view. This is how I intend to extract physics from the actual inference process, and the evolution of matter (and distinguishable law) from the evolution of infernefce system, by the requirement of preservation. "Consistenctly inconsistent" systems are not present in the equilibrium "population", however "transient inconsistency" is unavoidalbe and part of the evolution/development.

Edit(with regards to post 331): The connection to the holographic principle is an interesting lead, there is actually some interesting connections to that and to my abstraction of inference system, but currently I'll be away for some days and it's unclear wether I will have any internet access. There is actually a mathematical abstraction of an inference system, and in there there is something you can call a communication channel, and this has as size measured by the distinguishable states. This "size" or area, together with some other stuff, like the information capacity on one side of the "screen" limits the inferrable information of the other side. But this is a pure abstraction so far, the screen is not interpreted as a space-area. OTOH, this would clearly turn into something interesting as spacetime emerges. This is one of the things I'm working on and it's not yet finished. But there are at least potentially very interesting links.

In particular am I interested in finding information theoretical interpretations to several constants.

About overestimating information, that is also an interesting direction of discussion.

/Fredrik

 

[Dmitry67]

The ambition is exactly a theory of relativity of information (and inference) that you mention! So if you like that, then there might be some grains in here that you can like as well.

I have 2 questions to that future theory - may be someone can give a reply?

1. As I mentioned, when you look at 2 particles you overestimate the amount information in that system, if you unaware of the fact that these particles were entangled. But in the past many particles had interacted somehow, so they are mutually bound by some conservations laws, and further in the past we look, the more bounding interaction we find.

The question is, to what extent do we overestimate the amount information in the typical system? Is it near 0 if we go back to the BB?

2. Based on the http://en.wikipedia.org/wiki/Holographic_principle
the amount of information in a given volume in proportional to the surface of the boundary of that region. Specifically, to the number of Planck-size 'pixels'.

The interesting thing is that if you increase the radius by 10x, the volume grows as 1000x, but surface (and information inside the region) grows as 100x. So average information density per voxel (volume pixel) decreases as you increase the volume!

On the bigger scales Universe becomes more and more primitive. We started to draw these spheres from the Earth. But it is illogical to assume that Universe in complex here but is more and more primitive far from us - there is no center of the universe.

So looks like the only option is to conclude that on large scale regions of the Universe start to repeat themselves.

 

[qsa]

Thanks for the lovely argument! But talking of “simulation” or “emulation” raises an issue that’s much easier to argue than what I was being incomprehensible about above.

There is no analytic solution to a problem as simple as the Newtonian 3-body problem. In other words, if I understand correctly, in a classical universe even very simple physical systems would constantly be finding exact solutions to problems that a computer can solve only approximately – and would be doing so in real time, with no expenditure of energy.

We don’t live in a classical universe, and it’s not clear how that affects the computation problem. On the one hand, the properties of systems don’t have to be specified by an infinite amount of information, and on the other hand the equations are a lot harder to compute.

But I think we can agree that any system capable of emulating the behavior of 3 particles is going to be a lot more complex than the 3 particles themselves, and it has to behave in much more complex ways. And of course, the computation problem becomes vastly more difficult if we have 4 or 5 particles – not to mention the number involved in any realistic physical situation.

The existence of computer simulations makes it easy for us to imagine that we also inhabit a simulation. But it’s easy to see this is really just a fantasy, if you think about the magnitude of the problem involved in, say, computing the paths of individual molecules in 1cc of air over the course of a second. This is something the physical world handles just fine, but no computer ever will.

I think your original idea was not about one system simulating another one, though... it was more like, the world does not need to be “simulated” or “computed” because it already is a mathematical pattern.

ConradDJ, solutions for differential equations or results of computing any algorithms are already there (that is exactly our point), so you are right in your last sentence. When we talk about us computing (simulating) we are trying to simplify the bizarre notion that existence is mathematics, and people have hard time accepting. As for accuracy, physicists say that in principle any classical problem can be solved accurately, even throwing a dice. You can do numerical solution and find out to any arbitrarily high accuracy provided you have formulated the problem correctly. Formulating the problem is a different issue, it is basically a human intelligence (and logistic) problem, not fundamental.

As for the accuracy of QM and the formulation issue, now you are talking about the really interesting part, which may bear directly on the postulate of math&reality. QM theory is very accurate –up to experimental set up accuracy-, but QFT is a different issue all together. The rapping about TOE in PF is all about not knowing a good (final) theory that describes nature. For me (I know people will through anything close to them on me now), the unification of forces and particles is not the biggest issue. I will not settle for anything less than complete description of interactions, be it one or many particles (with gravity, high-low …etc). The problem is that in QFT the operators are no more representing observables as in QM but the particle creation/destruction representation, the wave function represent the probability of creation/destruction and so on. The spatial information is lost. I don’t know why this issue has not been raised (it is difficult because SR is involved). But my program http://www.qsa.netne.net has the first very modest attempt at tackling this problem. Of course, most attempts at TOE are been concentrated in the Regularization/Renormalization problem, just aspirin if you ask me. Although, if somebody was suffering from a brain tumor and no cure were in sight, aspirin will do. If we are able to model reality in a highly accurate way, I would say we will be 80% (or 100% who knows) there to the theory of “existence is mathematics”. I can elaborate, but I think it is prudent to stop.

 

[Fra]

1. As I mentioned, when you look at 2 particles you overestimate the amount information in that system, if you unaware of the fact that these particles were entangled. But in the past many particles had interacted somehow, so they are mutually bound by some conservations laws, and further in the past we look, the more bounding interaction we find.

The question is, to what extent do we overestimate the amount information in the typical system? Is it near 0 if we go back to the BB?

I think we approach this in different ways. Entanglement and particles, conservation laws etc makes me think of the standard QM or QFT framework. Since I consider the notion of information we have in that framework to be inappropriate my reasoning doesn't start from that, I'm focused on finding a coherent framework.

For me, a measure of information is only defined differentially and locally with respect to an observer, so that the information defines a differential evolution (by the action). The feedback from a definite evolution, sometimes not only revises the information but also the information measure itself.

To see a link between GR and a relativistic theory of information here is a association:

When I insist that all information is inferred, I am suggesting a link between inference system and the information state. A link between state and "law" of change, if you like. This connection as I see it, defines a self-evolution. This self-evolution is pretty much the correspondence of a geodesic. Ie. given no conflicting information or unexpected interactions, the systems evolves as per a sort of geodesic in hypothesis space.

Even when the geodesic is curved, with respect to another observer, the inside view is still that it simlpy follows the geodesic. However, there will be differential forces that curves the inference system during a definite progress.

So, the inside observer does not perceive it's own path as curved, because the curving is a natural process where new information updats the expectaion of what the self-evolution is like.

So the inside view is just evolution in the forward direction, but where there is a new forward direction after each step so that the direction is always straight as judged from the inside. The inside view is that of evolving inference system.

Now, consider a second sufficiently complex obserer observing this from an external position, he will instead infere that there is a law that describes how the first observer deforms. Given the correct circuumstances about complexity of the second observer and ability to monitor the first sstems environment, then the first systems "inside evolving law" can be consistently described by fixed laws with respect to the second observer.

There is no conflict here. So in effect, there are dualities here when you transform between observers, you also transform the laws, but to find THAT transformation you need yet another third observer :) and he has to be even more COMPLEX to be able to infere with certainy this transformation. This is the sene where I insist that symmetry transformation are emergent, and the complexity of systems limits to what exten this is possible. When the limit is reached, the remainder are simply evolving law, wether we like it or not.

Now for me the whole point is that seeing how the real inside view is like, we can actually understand it's ACTION better, if you use the rational action conjecture which suggest tha the action take is the one that is minimally speculative from the point of view of self-preservation.

This complexity constraint also explains STABILTY in a remarkable way, because to a bounded system, it's action is CONSTRAINED by the fact that from our point of view not all "mathematically realisable" possibilities are distinguishable! And to such a system the rational action conjecture of mine required the action to be invariant with respect to those possibilities!

This means these "paths" simply aren't part of whatever inference calculation you have, feynmann style path intergral or similar.

This means that the inside-actions, or naked actions of any system is BOUND to get simpler and simpler as it looses mass. But the external view is still complex, because the baggage there is physical with respect to the outside observer, but most of that baggage is something the system of study is invariant to. So in order to know what symmetres to apply, to get rid of the redundancy this idea will certainly help. Since it contains clear ideas and clear constraints. But it's still complicated of course.

This link I am suggesting, is totally absent in the standard framework, and this link is IMHO at least what makes the information theory including a sort of feedback to the context, and thus making it intrinsically relative; rather than just relative in the sene of a fixed relation with a kind of god-like background.

/Fredrik

 

[qsa]

ConardDJ, here is a website link that gives an interesting argument about physical and non-physical which gives a hint of what we have been talking about. The author is an excellent QFT teacher plus he has many unconventional research.

http://www.scientificexploration.org/journal/jse_14_2_klauber.pdf

 

[jal]

update:
http://www.interactions.org/cms/?pid=1028531
Media information for LHC running in 2009-2010

 

[tom.stoer]

Can we agree on a simpler statements:

1. If there is a difference between mathematical and physical, that difference can't be tested experimantally by the frogs inside the universe.

2. If universe is perfectly emulated, then frogs can't detect if it is real or perfectly emulated

3. Perfectly emulated system is isomorfic to a real one.

4. Hence it is absolutely irrelevant if we are emulated or not. In fact, the emulation is an argument for MUH: if there are universes which can emulate others, then all sorts of universes MUST exist

If we agree the theory of natural numbers is the same no matter if it is written by ink, or in PDF, or scratched on a stone, so mathematics is independent from the substance, then we must agree that it is irrelevant if it is emulated or not.

...

This is also an answer to tom.stoer (1,2,3,4)

I see your point. It seems rather straightforward but I still have problems with it.

Do you know the "Chinese Room" from Searle? Let there be a a room with a Chinese person locked inside and answering questions written in Chinese language. Now replace the chinese person with an english speaking person equipped with Chinese books and procedures written in English how to use them. Again you hand over questions written in Chinese language - now to the "room", not directly to the person. Assume that the questions and written answers are the same as before.

Question to you: in the latter case, who does really understand the Chinese language: the room, the system "room + books + person"? My answer would be neither, it's the person who prepared the experiment, wrote the books and procedures and set up the experiment!

Of course you can refuse to comment on this because it's not really a question regarding ToEs or physics in general but a question regarding consciousness, the mind-body-problem etc. You can respond that the emulation is not perfect. I don't claim that this analogon is perfect - far from it. I only want to illuminate why I still have problems to accept your statements 3 and 4. If two systems are isomorphic that does not automatically imply that they are identical. You can interpret this as mathematically identical, but not necessarily as ontologically identical.

Tom

 

[Dmitry67]

Of course, "Chinese room" depends on if you accept "Strong AI" or "Weak AI" hypotesis. But your argument is a good one. The only difference between 'real' and 'unreal' universe could be in the solution to the "Hard problem of consciousness", so 'unreal' universe can contain nothing but P-zombies.

 

[tom.stoer]

what are P-zombies?

 

[Dmitry67]

check: http://en.wikipedia.org/wiki/Philosophical_zombie
it is closely related to the "Hard problem"

 

[tom.stoer]

OK, I agree that the Chinese room and the P-zombies are somehow related. I repeat my question: in the case of the "Chine room", who does really understand the Chinese language: the room, the system "room + books + person"?

 

[Gear300]

When is it that the LHC will start operating at or near its highest energy?

 

[Dmitry67]

OK, I agree that the Chinese room and the P-zombies are somehow related. I repeat my question: in the case of the "Chine room", who does really understand the Chinese language: the room, the system "room + books + person"?

Answer: entity "room + books + person"

Imagine human brain enlarged to a size of a city: you will be walking on the 'streets', looking at working neurons, asking: but WHAT EXACTLY is responsible for the qualia?

Imagine some conscious microbes-scientists living in your body. As scientists they will discover many interesting patterns: for example, activity during the day is higher then during the night, there is a strange 7-day pattern, when some signals (pain) comes into brain, soon there is a response sent to muscles. They will study cells and neurons, and they will get a lot of information about them. But they will not believe that all these neurons are conscious. As that consciousness is on another size and time scale, they will not be able to communicate with that conscious.

In fact, I am sure there is ALREADY a sort of cheneese room: it is a network of 2 types of nodes: Internet + humans. Human work not only as nodes, but also as senses: photocameras, youtube, forums, etc. They also process that information (by typing a word in Google pictures you can see how any object look like even there is no object recognition software)

'Thoughts' of that system exist in form of blog posts, emails, etc. Some fade, some spread over the whole network (much slower then we think, so it is on a different timescale). For elementary nodes (us) everything in that system is reducable to some elementary facts: emails, characters in the blogs etc. So it is very easy to deny the existence of somethign extra. It is very easy to say: "there is nothing except us - humans, computers and the link between them".

But it is exactly the cheneese room argument, or saying that there is nothing except the neurons in a perception of the microbe-scientist in our body. So I am sure that superconsciousness already exists on Earth but we will not be able to communicate with it, because it is on a different scale.

 

[tom.stoer]

OK, that's where I have a different opinion. For me the knowlede regarding Chinese language somehow disappeared from the system. I would say that it's not system "room + books + person", but the person who prepared the experiment.

Now let's come back to TOE: the question was if a mathematical system that is equivalent (isomorphic) to the universe, is identical with the universe. Again that's where we differ. I would say that I believe in some metaphysical entity which IS the universe (object, entity, stone, human, ...). A mathematical system being isomorphic to that universe is still different.

You can turn it the other way round and state that mathematics exists w/o any physical existence. Let's come back to my simple universe with only gravitational law. I do not believe that it exists in a physical sense "anywhere", but of course it exists in a mathematical sense. Therefore mathematical existence transcends physical existence.

I think there is nothing illegitimate or contradictory in your reasonung; it is simply the fact that I am not (yet) prepared for the dark side ...

 

[friend]

Now let's come back to TOE: the question was if a mathematical system that is equivalent (isomorphic) to the universe, is identical with the universe. Again that's where we differ. I would say that I believe in some metaphysical entity which IS the universe (object, entity, stone, human, ...). A mathematical system being isomorphic to that universe is still different.

The universe is something we observe or measure. Mathematics is something we calculate. The mathematics would be a kind of language or description of the universe. And no equation we could write would account for every single particle or field at any time. We use math to figure out different configurations or general features that we are interested in. Math only tells us that given some input some output results. It doesn't tell us that a given input IS the case.

 

[tom.stoer]

thanks

 

[Dmitry67]

The universe is something we observe or measure. Mathematics is something we calculate. The mathematics would be a kind of language or description of the universe. And no equation we could write would account for every single particle or field at any time. We use math to figure out different configurations or general features that we are interested in. Math only tells us that given some input some output results. It doesn't tell us that a given input IS the case.

It tells us if it IS a case - if initial conditions are included in the axiomatic system, or if initial conditions are null

 

[qsa]

Friend, the initial condition issue is a side advantage of the idea, and it is being explained as there is no need for it, for the theory is multiverse and all possible configurations are possible.

As to you tom, you have made the most beautiful statement so far in this discussion

“You can turn it the other way round and state that mathematics exists w/o any physical existence”

But if that is true, how this mathematical existence does manifest itself? It can not hang in thin of nothing and exist. Well then, I don’t need to repeat how its existence is manifested.

 

[qsa]

tom
As to the isomorphic issue you can look at it from different perspectives, I’ll give the easy one and leave the harder one to later. If I do have isomorphism then I can go to a computer and program the properties which I discovered and plot them so to speak, i.e. simulate. Notwithstanding accuracy and computer time issues, and so on. Let’s assume we can approximate and maybe we get a universe that small numbers of galaxies and algae appear. That would give you a strong hint, wouldn’t it? Now, if you get in argument with me about if a computer has enough power or the accuracy needed, then you have to admit that isomorphism issue was put on the shelf by you.

 

[moniker2]

OK, that's where I have a different opinion. For me the knowlede regarding Chinese language somehow disappeared from the system. I would say that it's not system "room + books + person", but the person who prepared the experiment.

Now let's come back to TOE: the question was if a mathematical system that is equivalent (isomorphic) to the universe, is identical with the universe. Again that's where we differ. I would say that I believe in some metaphysical entity which IS the universe (object, entity, stone, human, ...). A mathematical system being isomorphic to that universe is still different.

You can turn it the other way round and state that mathematics exists w/o any physical existence. Let's come back to my simple universe with only gravitational law. I do not believe that it exists in a physical sense "anywhere", but of course it exists in a mathematical sense. Therefore mathematical existence transcends physical existence.

I think there is nothing illegitimate or contradictory in your reasonung; it is simply the fact that I am not (yet) prepared for the dark side ...

do you think the toe could have holons of matter and energy?

 

[tom.stoer]

tom
As to the isomorphic issue you can look at it from different perspectives, I’ll give the easy one and leave the harder one to later. If I do have isomorphism then I can go to a computer and program the properties which I discovered and plot them so to speak, i.e. simulate. Notwithstanding accuracy and computer time issues, and so on. Let’s assume we can approximate and maybe we get a universe that small numbers of galaxies and algae appear. That would give you a strong hint, wouldn’t it? Now, if you get in argument with me about if a computer has enough power or the accuracy needed, then you have to admit that isomorphism issue was put on the shelf by you.

But that brings us back to the Chinese room. The question is if the output of the computer IS a universe (then the usual output devices are not sufficient) or if it's only isomorphic to our universe. Then my belief is that isomorphism is not the same as identity.