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  • Post #21

Dear Florin,

thank you very much for your prompt replies on the communities questions including my own. It's a pleasure for me to see that the discussions in the essay contest start up, for it is a main goal of the contest to stimulate discussion and fair exchange of thoughts. Thank you therefore again for this contribution to the contest.

So at first i want to say that your approach should be traced further because it could be that it will succeed, and if not, at least i would be very interesting in the question where your approach could lead us probably. Mabe we receive some new insights (i am sure that this would be the case) into the very issue of the present contest, namely the limits of physics and the physics of limits. That's important for me to say, because i am not the person who can exclude a priori some possibilities with certainty.

Although there are some aspects i want to comment on. The universal truth property for example. For me, it is evident (as surely for the most people), that one of those universal truth properties is myself (although i will die at some point of time). For me, it is really a property, not only because i exist in a very short part of the world's lifetime, but also because i am convinced that consciousness is a somewhat build-in property of ultimate reality.

Another universal truth property for me is, that when i wake up in the morning, it is granted that i am in the environment i was, before i felt into sleep. For that, the world - in the meaning of its physical behaviour and the underlying laws - stays the same with or without me. Another universal truth (but surely no *poperty* of the universe) is, that our conversation here at FQXi is and will be a truth, even if the universe fades away and somedays maybe disappears into the void nothing it possibly came out of. Well, it is an interesting question if this conclusion is really true, because if the universe came out of nothing and at some day will go into this "nothing", can we really say that the truth that we do comment on each other here and now in spacetime at FQXi will further be an undeniable fact, hence a truth out of its own existence? That question is valid also for all historical events and is only once more a rethoric question because in your framework there isn't such a thing as "nothing". In your framework "nothing" is replaced by its pure opposite, namely infinity and the special subset of it that can fully describe our physical world if your approach succeeds.

So, my question about the future status of the truth of the fact of our conversation here must have been incorporated into this subset from the very beginning of all_that_exists (because your consideration - and i want to emphasize here that it is yet only an *assumption* - is, if i got this right, that the underlying maths is "platonic" and therefore exists out of time and eternally). If the latter is true, our conversation is somewhat predetermined and all of our conclusions here too. And if in turn that would be true, Gﾃｶdel's undecidability comes into play again because we couldn't be sure that the conclusions that are immanent in the very math of the subset you are searching for, are consistent with the rest of this subset. Surely they would be consistent with all testable and perceivable physical data, but does this sufficiently mean that they are also consistent with the very framework we started from (and that is - for the case that your subset really exists - is also incorporated into this subset)? Surely, they had - for the purpose of the whole argument - to be *necessary*, but i don't think that this necessity is sufficient to conclude that there really aren't/couldn't be some other things than the laws of physics discovered at this point of time. But what, if this subset is such that it contains data that is - for whatever reasons - consistent with observation, but the a priori-conclusions correlated with this observations are of an inconsistent type?

That's what i wanted to say with my "anthropic"-argument, namely that we start with things that we are familiar for us (because we are inescapable "correlated with) and extrapolate them to the utmost level of imagination (the latter is surely also valid for my own approach).

In this context i think our both approaches aren't so much different, because you start with infinity and i start with some opposite of it, namely an undefined space of creative possibilities. And surely, my own approach could be of such a nature, that it ﾃｭs a tiny part of your subset, in the sense of a somewhat misleading conclusion that is possible because the whole subset is possible (for whatever reasons).

I want to end up with this comment with some words of Gﾃｶdel himself, who made up his mind deeply about the possible meaning of his own undecidability-results and for those i think could be a good partial end point of my comments so far. Gﾃｶdel stated that [1]

"[...] consistency with existence manifestly presupposes the axiom that every mathematical problem is solvable. Or, more precisely, it presupposes that we cannot prove the unsolvability of any problem.".

I think this lines from Gﾃｶdel are somewhat just another variation of Turing's halting problem. For circumventing it, we had to know what we yet don't know. And as Hilbert put it, we must know, - and maybe we will know.

[1]: Gﾃ-DEL, Kurt: On formally undecidable proposition of Principia mathematica and related systems I. (1931). In: Collected Works Vol. I, Publications 1929-1936. Oxford University Press, New York, 1986, pp. 145-195.

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  • Post #22

I failed to state that what obeys first order logic are the combinatorics of the state space or state of the universe. Godel's theorem is in a way a combinatorial result. To skirt the Godelian problem with a cosmological structure that is quantum computational this restriction or something similar seems necessary. It is not that hard to arrive at from a mathematical perspective. Most mathematical developments of late, proofs of Fermat's conjecture and Poincare's homology conjecture, don't run into Godelian problems.

The conservation of quantum information with black holes and other quantum gravitational systems requires there be some great quantum error correciton code that underlies quantum gravity. This leads in some sense to the idea of the universe as a grand quauntum computer. While issues of consistency and completeness in the Godel-Turing sense are not my primary focus I can well imagine these problems coming to the stage. This then does seem to require the domain of computation, the state space, must be some primative recrusive or first order. Quantum cosmology might well have to be of this nature to within some cut-off in energy E < E_{planck}, which is curiously only about 1/2 Planck units of energy below E_{planck}.

Lawrence B. Crowell

Dear Stefan,

Thank you for your time to read my essay and comment on it. I am too very glad that finally the discussions started happening and I found them very stimulating. The universal truth property (for lack of a better description) expresses the concept of independent reality of the world. The world is still out there regardless of what I may think about it or how I perceive it. But if reality emerges from pure math, then this property is absolutely remarkable because this does not exist in general in the Platonic world. Because of the existence of time, reality can have this property, otherwise all sorts of paradoxes and contradictions can ensue. Those contradictions are OK in the Platonic world, precisely because this world exists outside space time.

Now you raise a very interesting point by asking if our discussion for example will simply vanish with the disappearance of our universe. A related problem is why our universe is happening only once. From composability, there are only 3 solutions possible: quantum mechanics, classical mechanics, and hyperbolic quantum mechanics. The hyperbolic quantum mechanics does not satisfy the universal truth property because different pseudo-unitary representations are not isomorphic (unlike in the regular QM). Consequently we do not see any hyperbolic quantum mechanical effects in our universe. However, this is a very good property for a hypothetical "universe nursing ground" where new universes just like ours can be born, evolve, and die. This is a wild speculation at this point, but maybe our universe started by quantum tunneling form a chaotic hyperbolic QM domain into a regular QM domain. So now for the answer, our current discussion can have reality only in a domain where the universal truth property holds (meaning in our universe - frog eye view), but it does not have reality from a hyperbolic QM perspective - bird eye view. (There is no such thing as reality from the bird eye view: reality is a concept made possible only when the universal truth property holds). Also the mathematical relationships that are making our discussion possible will still live forever in the frozen Platonic world of math. In other words, our discussion was potentially possible from before our universe was born, but it could became actuality only within a coherent universal truth property domain, if this makes sense.

Lawrence,

Thank you for your clarifications. I still think the Turing idea is an unnecessary complication. Quantum mechanics is based on unitary groups which preserve information. There are isomorphisms between orthogonal and unitary groups and I think the most important one is SO(2,4)~SU(2,2). I think those isomorphisms play the central role in your quantum error correction code idea for quantum gravity.

A critical question is then how should we understand the relationship between classical and quantum mechanics? Is 't Hooft right in his idea of emergent quantum mechanics, or is Zurek right in his decoherence approach? By the way, browsing the fqxi site I have read the Azores' talks, and in particular Joy Christian's amazing claim. Were you aware of his claim and if yes, what do you think of it? If no, I would highly recommend his papers and replies to criticisms on the archive.

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  • Post #25

Dear Florin,

thanks again for answering. I think i expressed myself a little bit ambiguous in my last post concerned with the "reality" of our current discussion.

I ment this not in respect to reality, but in respect to the property of "truth", hence to logics and its truth/false-values. My question is, is it further true that we corresponded at Aug. 4. 2009 16:05 GMZ when our universe doesn't exist anymore in a far away future? I mean, our conversation at Aug. 4. 2009 seems to be a bare fact to me in the sense of an unalterable truth. What happens to this truth if the physical basis of this truth does disappear? You answered that this truth is still possible in the platonic realm, but is it still true that we both commented at each other for the case that the physical basis for that all has vanished away completely and nothing is left then - well, nothing but maths?

I do insist in this question because in that platonic realm which has the universal truth property there could be myriads of constellations that wouldn't have become actual until the universe vanishes away and are also possible and true in a certain sense. But these certain - mathematical truths - are they of the same ontological level as the actual truths? So what happens with truths as we know them after a physical universe collapses back to the "ground" where it came from? I guess your answer is that the universal truth property is the borderline of it all. But that seems to be somewhat circular for me, because the universal truth property could only be true because the universe itself is true, and the universe itself is true, because the universal truth property is true (insofar you derivate this universal truth property from the properties of the seemingly true universe in which we live).

Sorry for my insisting on your clarification, but i try to understand where all these truths come from and what/who has defined what is universally true and what not. I am aware of maths as a possible source of truth and falseness, but i am still not aware of the answer what/who inspired the breath into the equations, say exposing an if-statement that has consequences if this statement is true. Consistency alone cannot do this because consistency is a matter of fitting together some elements in a certain way that they do not contradict each other. So for example Curry's paradox:

*If* this sentence is true, then the world is made of nothing than pure maths (or cheese or whatever).

Well, therefore the world is made of nothing but pure maths or cheese because the antecedent could be true. We do not necessarily have to belive that the antecedent is indeed true, it is sufficient that it could be true.

With all this in mind i cannot conclude at this point that

"*if* we prove the necessity of time, space, quantum mechanics, Standard Model and explain the origin of the universe *then* we can really conclude with certainty that the universe is made out of nothing but mathematical relationships."

Why? Because it only says "if the universe is made out of nothing but mathematical relationships, then the universe is made out of nothing but mathematical relationships (what surely would be true in this case), but excludes the one thing that it originally wanted to explain: the origins of the universe and hence the origins of maths itself.

Dear Stefan,

You raised many valid points, which would take a long time to answer, so let me start answering a few critical questions first. Based on your satisfaction with my answers here I can provide further clarifications if needed.

You asked: "My question is, is it further true that we corresponded at Aug. 4. 2009 16:05 GMZ when our universe doesn't exist anymore in a far away future?" The short answer is NO. Only mathematical truths exist forever, and they exist within an axiomatic framework. Our discussion framework is our reality, and if this reality vanishes, so is our conversation, along with everything that ever happened in our universe. But it did happen you may say. Indeed, but if reality's origin is mathematical, then reality is relational just like math and it requires something to have a reference to, in other words an independent observer. If there is no possible observer to witness our discussion, or its future consequences, then the existence of our conversation is an ill defined concept. We exist only in space-time; this is the canvas of reality. To ask about events in a vanished universe is the same as asking what is south of the South Pole? The universal truth property is "universal" only in reference to our reality, and not across multiple universes.

You also say: "But that seems to be somewhat circular for me, because the universal truth property could only be true because the universe itself is true, and the universe itself is true, because the universal truth property is true". Well..., I do not know the meaning of the sentence: "the universe itself is true". This is either metaphysics or wild speculation at best. What I do know is what I can observe around me. And what I see is that the events that make our universe have an extra property which is unlike any we have seen in mathematics. The three physics principles are true statements about our universe, and they are validated by all experiments, so this is still physics, not philosophy.

I do not derive the existence of our universe from the 3 principles. Just because I write them on paper, I cannot command them: "fly" and a new universe will form. I do not play God here. They are only used to select the desirable mathematical structures which describe out universe. The success of this program is to show that this heuristic rule generates principles which in turn will select precisely all the math which is validated by experiments and nothing else. If by working out the math consequences I predict a universe with 2 times, or a universe with 3 more elementary forces besides the ones we observe, then my heuristic rule is wrong. If I only predict the electroweak force and not the strong force, then my heuristic rule is incomplete. Only if we successfully derive exactly only the core physical characteristics of our universe, then we can fully believe the heuristic rule and extract the meaning of reality from it. (We can still do it now, but we are not yet sure of the likelihood of the correctness of our speculation). If the heuristic rule fulfills its promise, then we can say with 100% certainty that reality is based on nothing but relational mathematical objects.

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  • Post #27

Between 't Hooft, Zurek and Christian I choose Zurek for sure. I tend not to give much interest in ideas about hidden variables and other ideas which purport to have quantum mechanics wrong. If quantum mechanics goes oft aglee it will likely do so in the quantization of gravity.

A bit of interesting calculation I did. A shild's ladder construction is describable by a Galois field GF(4). Curiously the spin 1/2 system in QM is described by the same Galois field. GF(4) is the Dynkin diagram for SO(8), which is a central root with three others at 120 degree angles. This has triality for SO(8). So QM and GR are on a Galois level equivalent, and further they are both SO(8), or spacetime is SO(7,1), which are contained in SO(16), or Cl_{16}(C) = Cl_{15,1}(R)xC.

In effect I think general relativity and quantum mechanics are functorially equivalent. This little bit above indicates something of that sort of going on.

LC

Lawrence,

I know clearly now what mistake is Christian making in his attempt to disprove Bell's theorem. Unfortunately for me, two of his critics discovered the same thing from different perspectives and therefore my explanation is spurious and has only a pedagogical value.

I have never learned Galois theory, but I highly doubt relativity and QM are functorial equivalent. QM is a combination of a Lie algebra with a Jordan algebra and the Jordan side does have shared characteristics with relativity. The Lie side however is where the main differences arise. Hence I cannot see how QM and relativity are functorial equivalent. And if they were, then I would expect quantum gravity to be a trivial problem.

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  • Post #29

Dear Florin,

thank you very much for your comments.

"the universe itself is true" - i ment it in the sense of being necessary, means, all the properties you mentioned are necessary (time, space, quantum mechanics, Standard Model). Necessary to fit with our observations and mesurements made to this point in time.

Surley they are necessary too in the meaning of being valid and in effect, even if our theories would change/are modified (in the way our theory changed from Newtonian description of the laws of gravity to Einstein's description/interpretation).

But if not only our theories change but also our interpretations, what would this mean for the property of necessarity? Would it mean that these properties are still necessary out of the fact that the underlying maths is necessary to exist or would it mean that it is further necessary because our lack of observation of exceptions of the physical laws until now have not changed yet? I write this in respect to QM, which for me seems to be an exception of the deterministic laws discovered by Newton and Einstein.

My point is, though even it is necessary to use maths to be able to give a strict proof of the necessity of a future Newtonian/Einsteinian physical event that we already can describe mathematically correct, is this sufficient to conclude or even to prove that the existence of maths is all that exists/can exist in general and our universe is merely a mathematical machine that came into "actuality" by the very necessities we already observed as physical behaviour? Please consider that this could be a circularly line of reasoning. Please also consider that the necessity of a future Newtonian/Einsteinian physical event is not the same as the necessity of these laws to have been implemented just like they are and not totally different. It is only our in-built filters, generated by the evolutionary filtering process, that lets us conclude that what we observed yet has to be all that can be observed, not more and not less. Surely, we have expanded our perceptions with the help of technical apparatuses, but these apparatuses don't exist a priori but are again designed to *filter* a small area of interest. And the latter is obviously also true for observers like us, because we live in the middle between the microcosmos and the macrocosmos and are biologically adapted with all our senses to this area.

This would mean for me, that the crutial criterion for the provability of successfully filtering out the ingredients (namely the universal truth property) for your proof (namely, reality is based on nothing but relational mathematical objects) is the bare fact of our very existence and the bare and astonishing fact of not only existing but also understanding, explaining and comprehending this existence. Otherwise, as you wrote, all we discuss here would be ill-defined from the very start. Because, as you wrote, without an observer it is senseless to speculate about things that can't be observed in general (i can't agree with the latter in general, but for the purpose of the argument, i write it here). But once such observers become actual, is it necessary for them to discover your version of ultimate reality? My answer to this question is: If you are right with your approach, then it is indeed necessary, because if you are indeed right, this would prove that your personal discovery of ultimate reality is implemented in a frozen manner in the platonic realm of ultimate reality. So what you implicate with your assumptions is

1. Observers are a necessary ingredient of ultimate reality

2. Ultimate reality is such that it (and due to your lines of reasoning it is only made of nothing but mathematical relationships) implies and comprehends its own fully rational understanding by being able to become "actual" (i don't ask for the mechanism for that all to become actual because i think you have no answer to that).

3. Being able to discover, explain and to prove itself is a built-in feature of ultimate reality, but can only be recognized if it becomes actual.

For me, it seems that there is still a certain inconsistence in your lines of reasoning, because "becoming actual" is just another word for "becoming conscious of something" and becoming conscious of something does not guarantee that the actually conscious contents are the only ones that can be true/valid/provable.

The latter is self-evidently also valid for my own - actual - consicous contents i tried to expose here.

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  • Post #30

Quantum mechanics and relativity as similar within a partial functor. A spin 1/2 quantum system and the Schild's ladder construction in general relativity are both Galois constructions of GF(4). So there is what I might call a functorial overlap. Their commonality with Jordan algebra of octonions works because there is a triality centered around SO(8). The Dynkin diagram of SO(8) is FG(4).

I have not read Christian's argument, but I tend to think that quantum mechanics is pretty secure. I don't think that there is some underlying flaw in it, at least on the level of photons, atoms and so forth. The measurement problem is still outstanding in some ways. I think that Zurek's decoherence and einselection model is most likely correct. I am not much on quantum interpretations, such as Bohm or Many Worlds, and Zurek's approach seems to offer the least in the way of metaphysical ideas these interpretations bring.

Lawrence B. Crowell

Dear Stefan,

It is I who need to thank you for your insightful comments. Let me present in this post the framework of my thinking, and I will come back in a second one to reply to your specific questions.

Suppose for the sake of argument that my heuristic rule is indeed fruitful and it will lead to complete mathematical understanding of our universe. (A tall order for, unlikely to happen in my lifetime). What does this mean for the nature of reality? What is reality and why is there something rather than nothing?

If our universe is at core mathematical, then looking at the differences between reality and the platonic world of math is all that is needed to derive our universe's mathematical necessity.

So let's list a mathematical structure characteristics:

1. It is abstract

2. It is relational

3. It is frozen

4. Truth is defined within the boundary of its axiomatic system

Let's list our universe characteristics:

1. It is concrete

2. It is relational

3. It is changing

4. Truth is defined within our universe

So our universe shares some characteristics of an axiomatic system (items 2 and 4), but can change because it is made out of many mathematical structures. In a way, the difference between the platonic world of math and our universe is like the difference between ice and water. Same components, different ways of arranging them; one is frozen, the other one is fluid.

Truth and reality are universal in our universe but they cannot be defined from outside our universe. Truth is a relational concept, just like the rest of math. The same way it does not make sense to say "my speed is 3 m/s", it does not make sense to ask about the events happening in our universe from another universe, you need a frame of reference, or an observer.

Now the famous question: why is there something rather than nothing? The answer: because it can be. Not very satisfying, but this is all there is to it. A more interesting question is: why is our universe happening only once? Or: what was before the beginning of the universe?

To answer those questions, we need to eliminate one of the 3 principles of physics: the universal truth property. If is this principle that confines us to a universe. From composability, there is a solution: hyperbolic quantum mechanics which violates this principle and I highly suspect that it is in this framework we need to work when addressing those questions. In hyperbolic QM, there is no time, no objective reality, and no universal truth property. This is a "chaotic" domain from which universes just like ours are born, evolve, and die. Quantum cosmology should try to work out the mechanism in which elliptic QM can arise from a hyperbolic QM domain (maybe via quantum tunneling).

And for the answers, our universe is happening only once, but many other universes are happening as well, we just cannot say when, because in hyperbolic QM there is no such thing as time. What was before the beginning of the universe? This is an ill posed question like what is south of the South Pole?

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  • Post #32

Dear Florin,

thank you very much for exposing your ideas. It's a pleasure for me to read your lines of thinking and to grasp more and more the framework you are working with.

I agree with your answer to the question "why is there something rather than nothing?". As you surely noticed, your answer to that question is a plain fact. Though i still cannot see wherefrom the dynamics of the formerly frozen maths comes from when it "becomes" "liquid", i agree with the points 1, 2 and 4 of the mathematical structure characteristics and with the points 2 and 3 of the universe's characteristics. If maths or at least a part of it has the property of "becoming liquid", i would suppose to call it further with the term "animathed".

I just want to make another short notice.

Your argumentation goes like this:

1. There exists a platonic realm of fixed relationships, unanimated.

2. There exists a universe which is dynamic and in some parts animated.

3. Hence, there must be a difference between both, because the term animated and the term unanimated cannot be the same at the same time and working out these differences proves the necessity of both, the animated and the unanimated realms.

4. Because of the fact that it is indeed possible to divide reality in animated and unanimated parts, the necessity of the points 1. and 2. are proven and therefore also point 3.

I would like to contrast the above points by the following:

1. The existence of a platonic realm of fixed realationships is a possibility, but not a necessity that can be proven with certainty.

2. The existence of a universe that is only animated in some parts is a possibility, but not a necessity that can be proven with certainty.

3. Hence, even if your approach is sucessfull in the sense of filtering out our laws of nature, your filter was build of at least two freely-chosen axioms, namely your points 1. and 2., has therefore 2 free parameters and therefore cannot be considered as necessary in a strictly mathematical sense that has it's axioms out of space-time.

Your approach doesn't work without the good old additional axioms within space-time, just like my approach too. The question is, which approach is more lucid. I think, this is deeply a question of personal taste instead of straight-forward reasoning.

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  • Post #33

Newton discovered the universal gravitation law without using any heuristic rules. Einstein also discovered relativity without using Florin's heuristic rules. Why are you sure that the future constructor of TOE is in need of your heuristic rules? If you wish to contribute in physics, you may propose a model of TOE or quantum gravity, but not rules and advises how to build it.

Lawrence,

A partial functor is probably right.

Christian's argument is very interesting, but as one of its critics pointed out from Bell's result hidden variables in QM cannot be real and local. Bohm's theory is real but nonlocal; Christian's theory is local but not real. Christian proposes using a Clifford algebra element to describe his hidden variable and obtains all the violations of Bell's inequalities precisely like QM. From this he concludes (incorrectly) that Bell's inequalities can be violated by a real local hidden variable theory. If you are interested I can tell you what his mistake is; it is subtle. Finding the mistake was fun, I only wish I were aware of his results two years ago.

Dear Stefan,

Let's see if I can convince you of point 3 for math and 1 and 4 for the universe.

Point 3 is as follows: in math, all theorems are already there just waiting for mathematicians to reveal them. It is only an accident of history that Pythagoras theorem is named like that. This mathematical fact was there the moment you specify the axioms. Frozen means that in one axiomatic system mathematical statement do not have a transitory existence: they do not switch between true and false and mathematical objects do not pop in and out of existence. In this sense, math does not evolve; it is only our understanding of it that evolves. The history of math is only the history of mathematicians. Godel's theorem was still true in ancient Greece, but the people living in that time did not discover it.

Point 1 of reality: You can hear on the radio that x people died in a car crash, never that x people got hurt by the theorem that there are an infinite numbers of primes. We can touch, see, feel the world around us; it is made out of concrete, not abstract things. This is precisely the opposite of mathematical structures. A complex number for example it is not a pair of a real and an imaginary numbers. This is just one possible representation of it. You can represent complex numbers by 2X2 matrixes and this is even a better representation because it has a natural explanation of sqrt(-1) (which was the main roadblock in the acceptance of complex numbers as a valid mathematical structure). Complex numbers and mathematical structures in general are just abstract objects independent of their concrete representation. In the real world a concrete instance is what matters: a physical chair, not the idea of a chair. In the real world we try to make ideas and dreams reality, a mathematician distills the essence by considering only formal abstract structure.

Point 4 of reality: What we observe in the real world has the same truth value for all observers. The Roman Empire did fell, and its impact was different from different people's points of view: the common citizen of Rome, the soldier in the invading army, etc. but they all can agree on this fact. To shorten the explanation, please see my earlier reply to Georgina on Aug. 4, 2009 @ 02:24 GMT (the car in the garage "counter example" for how the world might look if events were contextual and appearing different for different observers.)

Now back to your questions. You say:

Your argumentation goes like this:

1. There exists a platonic realm of fixed relationships, unanimated.

>Yes

2. There exists a universe which is dynamic and in some parts animated.

>Yes, but I disagree with some parts. (It is in all parts)

3. Hence, there must be a difference between both, because the term animated and the term unanimated cannot be the same at the same time and working out these differences proves the necessity of both, the animated and the unanimated realms.

>This is not what I am saying.

4. Because of the fact that it is indeed possible to divide reality in animated and unanimated parts, the necessity of the points 1. and 2. are proven and therefore also point 3.

>This is not what I am saying.

You also say:

1. The existence of a platonic realm of fixed realationships is a possibility, but not a necessity that can be proven with certainty.

I disagree with this. See my point 3 above. The value of pi as 3.141... was 3.141... regardless of our universe, regardless on when we discover its value, and regardless of other mathematical structures like topological and logical structures. This value exists outside space and time. A universe, a star, a child can be born, not the value of pi or the theorem that the sum of the angles in triangle in flat geometry is 180 degrees.

What I am doing is ultimately old fashion physics and not a subjective interpretation. I only present the philosophical implications here, but I am not a philosopher and I am only doing it to explain my new paradigm.

Why is this physics and why it is not subjective? Because all the 3 principles are validated by all experiments performed to this date. In my heuristic rule I am asking for the differences between math and reality. This means that whatever differences are found (the 3 principles so far) they have to pass all past, present, and future experimental tests. This is why this is ultimately objective physics and not subjective philosophy. In computers there is the GIGO principle: garbage in, garbage out. If the 3 principles are invalidated by experiments, they are the garbage in and the conclusions will only be the garbage out. Next, the 3 principles generate mathematical consequences and they have already proven a large chunk of the necessity of our universe. By a leap of faith now, I am speculating that ALL core characteristics of our universe will be obtained in this way. If true, this will mean that our universe cannot be except in the way it is: it has uniqueness and this is big. If true then we have mathematically succeeded in proving that there is no God. God's hands were tied at the moment of creation and he had no freedom into creating this universe, the blue print for the universe was already there just like the value of pi: there was no other way possible except to have 3 spatial dimensions, one time dimension, quantum mechanics, electromagnetic, weak, strong, and gravitational forces, etc, etc.

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  • Post #36

Sure enough let me know. I only heard about J Christian a few weeks ago.

LC

Dear Septickii,

I love pointed questions. I think there are three things to consider here.

1. More important than answers is asking the right questions. Before Galileo and Newton people considered rest as the natural state of objects, not uniform motion. The mathematics in Einstein's general relativity was discovered in the prior century, but Einstein overcame the conceptual barrier that even empty space can bend. By asking the right question, a new paradigm can form. My heuristic rule is just this, a new paradigm at this point. Is it going to be fruitful? I surely hope so and this leads me to the second point.

2. No Nobel Prize was ever given in physics for new paradigms, but for solving concrete problems. Even Einstein did not get the prize for relativity. But if the question is right, result will surely follow. Can we imagine discovering relativity and not solving real physical problems? No, because relativity is a real physical phenomenon and its discovery were bound to lead there. So how can we approach the quantum gravity problem? This leads me to the last point.

3. String theory is a very consistent, beautiful, and coherent theory, but with not much to show for all the effort that was put in. A common misconception is that ALL good ideas in physics are in there. I believe the right approach for quantum gravity is non-commuting geometry and I do intend to contribute in this area. Viewed through my heuristic rule paradigm, non-commuting geometry becomes suddenly very intuitive. But there are easier problems to solve first: obtain the strong force and the electroweak force beyond the semi-classical approximation and solve the Standard Model parameter values problem. Based on AdS/CFT correspondence, if we completely understand gauge theory, quantum gravity should follow.

I am currently working on four problems suggested by the new paradigm. It is not much, but it is a start. Suppose I will be successful and I will publish the results. Will anybody pay any attention? How many people paid attention to Grgin's structural unification of quantum mechanics and relativity? How many people noticed Jochen Rau's results based on dimensional analysis of Lie groups? How many people are aware of David Hestenes' zitter phenomenon which was experimentally confirmed?

How can I compete with 30 years of effort by many bright physicists working in string theory and come up with the solution for quantum gravity overnight? The time for quick theories like electromagnetism has passed. Rome was not built in a day, neither was quantum mechanics, general relativity, or string theory. A coherent new paradigm will attract the critical mass of researchers to make significant progress if there is indeed progress to be made.

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  • Post #38

Dear Florin,

Thank you very much for your effort to write back at length and elaborated.

To your point 1:

Imagine that at some day in the future all observers have died but two of them.

Imagine further that these two observers have a conversation and after that suddenly both die (not trouth a car accident, but perhaps trouth a natural desaster).

After that happened there is nothing which/who can wittness the former conversation of these both observers. Due to your former lines of reasoning, if there isn't an observer that can witness the mentioned conversation or its physical consequences in the future, the concept of this conversation having been real is ill-defined. So must be the whole concept of physical reality in general and the universe has to abruptly vanish if my scenario happens, because it would also be an ill-defined concept because inconsistent with the necessity of observation.

Your point seems to be not so unsimilar to mine, because it seems to me that to circumvent this you assume nature to be animated not only in some parts of it, but in all parts of it. This is interesting for me.

To your point 3:

Knowing that pi and the whole maths is an eternal, "frozen" thing would mean that someone has access to an area out of space-time. I at least believe that i understand your argument, that both, space-time and the (mathematical) realms out of space and time must be interwoven in a specific manner.

Let me shortly comment on this.

For having access to the spaceless and timeless realms, there had to be some conditions to be fulfilled. One condition could be that these eternal truths exist in both sets you mentioned (the mathematical platonic realm and the concrete universe - that could be for example your Point 2, namely "relationality").

Another condition could be, that the insight of human beings into the spaceless and timeless realms was set up at the very beginning of the physical universe. These could have been happend for example by some subtle initial conditions of the universe that necessarily (in the case of a strictly deterministic evolution of the further universe) are correlated (entangled?) with the right and consistent propositions, when used in the most consistent way and results in the right deductions. I am not convinced of this possibility.

A third condition could be, that your belief in the eternal realm of maths and in pi has been exclusively generated by local, realistic, and space-time dependend, chemical processes in your brain. I am also not convinced of this possibility and i prefer the first possibility. Please see therefore my comment to your question at my essay page.

Your wrote:

"The value of pi as 3.141... was 3.141... regardless of our universe, regardless on when we discover its value, and regardless of other mathematical structures like topological and logical structures. This value exists outside space and time. A universe, a star, a child can be born, not the value of pi or the theorem that the sum of the angles in triangle in flat geometry is 180 degrees."

As long as observers can prove pi by drawing a circle in the Egyptian sand and calculate the ratio, this is true in your framework. But what happens when there isn't nomore an observer to do so? Doesn't this mean that the cited lines of reasoning above, made by you, are in this case also ill-defined? This must be the case in your framework, because your framework is built on the dualism of the universal truth property and some fixed eternal truths.

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  • Post #39

The notion of paradigm shift has been over used IMO, but there are occassions where this happens according to some definition. The concept was advanced by T. Kuhn in this "Structure of Scientific Revolutions," and while it has some validity to it, I also think the idea is overblown.

However, running with this football, there does seem to be a paradism shift waiting in the wings. Maybe several changes are required. Such paradigm shifts usually involve the removal of excess baggage that keep two categories distinct. As indicated above I think that QM and GR have similar structure, or are equivalent under a partial functor. I will also say I think that in GR the distinction between inertial and accelerated frames is a stumbling block.

I wrote a paper last spring concering the zitterbewegung, and communicated with Hestenes about this. I have not submitted it for publication yet. If you are interested in it I can transmit it. Zitterbewegung may be telling us something about the end of renormalization group flows and the onset of mass at low energy. The leptons and quarks all have masses ~ .5 to 100 MeV, and sitterbewgung suggests this mass is associated with a confining potential at the Compton wave length of a particle.

Lawrence B. Crowell

Lawrence,

Christian's argument is as follows. The hidden variable in spin measurements in his theory is the pseudo-scalar from the Clifford algebra Cl 3,0 (a trivector). From this he very nicely obtains the GHZ state and the Bell's inequality violations precisely like QM does. This is the valid part. The interpretation is completely wrong however. He completely misunderstands what QM, classical mechanics, and real hidden variables are about. His main points are 3:

1. The trivector contributes only counterfactually towards his final answer.

2. All possible orientations should be considered when averaging over hidden variables in a realistic theory. (This is his main point in the recent Azore conference.)

3. The non-commutativity of the trivectors only reflects the fact that two rotations do not commute.

So what are his mistakes?

1. If the trivector contributes counterfactually only, this is not a realistic hidden variable theory in the sense of Einstein and Bell. In experiments we read real numbers from dials or other devices. When you generalize the statistic to go beyond real numbers you are no longer in the Kolmogorof's realm or the realm of realistic hidden variable theory. You can either be in the realm of QM, or in an inconsistent statistical theory.

2. Considering all possible orientations will generate a continuous state space, the Bloch sphere in his case and this is precisely the distinguishing factor between classical and QM and it is no wonder he recovers all QM predictions.

3. Non-commutativity of hidden variables is also a distinguishing characteristics between classical and QM. In fact he is only casting the EPR experiment in the language of quaternions, hardly a novel thing after Adler's results. So why can he use geometric algebra and why does his model look realistic? Because Cartan's classification of classical Lie groups can be done in the language of geometric algebra and he is only benefitting from a particular isomorphism between orthogonal and unitary groups: SO(3)~SU(2). In general his method will not work for SU(3) for example.

The other thing he does is that he uses a very obnoxious and aggressive tone in his rebuttals.