Essay Abstract

Constructing the Theory of Everything (TOE) is an elusive goal of today's physics. Godel's incompleteness theorem seems to forbid physics axiomatization, a necessary part of the TOE. The purpose of this contribution is to show how physics axiomatization can be achieved guided by a new heuristic rule. This will open up new roads into constructing the ultimate theory of everything. Three physical principles will be identified from the heuristic rule and they in turn will generate uniqueness results of various technical strengths regarding space, time, non-relativistic and relativistic quantum mechanics, electroweak symmetry and the dimensionality of space-time. The hope is that the strong force and the Standard Model axiomatizations are not too far out. Quantum gravity and cosmology are harder problems and maybe new approaches are needed. However, complete physics axiomatization seems to be an achievable goal, no longer part of philosophical discussions, but subject to rigorous mathematical proofs.

Author Bio

Florin Moldoveanu received his PhD in theoretical physics from University of Maryland at College Park working in the area of soliton theory, nonlinear dynamics, and fiber optics. His research interests are algebraic and relativistic quantum mechanics and the foundational issues of physics. Other research interests include general relativity, non-commuting geometry, category theory, geometric quantization, Clifford and geometric algebra, and algebraic quantum field theory.

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7 days later

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  • Post #2

Dr. Moldoveanu, how can your assertion be falsified? If it cannot be falsified then can it be 'scientific' and, if not, physics? Thank you.

9 days later

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  • Post #4

Florin,

I appreciate that you touched upon the role of the heuristic approach to physics; I interpret that to mean 'creative' or 'out of the box' thinking. However, I believe that an axiomatic and mathematical approach to heuristic thinking will prove those to be mutually exclusive. There comes a time when we must ask: what is causing the universe to behave mathematically?

Jason,

Your comments touch on multiple topics. Let me try to address them all. In general, heuristic methods guide us in obtaining results when we lack the complete understanding on a subject. I did not claim I have obtained the complete physics axiomatization, only that I am proposing a way to lead us there. In this sense my essay is a research proposal backed by existing results under a new paradigm of looking at the problem. If new results will be obtained in this paradigm then the new research program will be successful, otherwise it will be a sterile approach. I have additional unpublished results I did not mention in the essay, therefore I know this new approach is fruitful, the question is to what degree?

The major problem standing in the way of physics axiomatization is the complexity of nature. Tegmark proposed he Mathematical Universe Hypothesis, and I believe this to be false. We already know we cannot axiomatize math, and the universe contains mathematicians which discover inconsistent math. If the Mathematical Universe Hypothesis is true, then the mathematical structure which explains reality should also explain the inconsistent math. However, I think he and others like Gordon McCabe are right in their understanding of reality as having a mathematical origin. So if a direct approach does not work, maybe there is a different way. And indeed there is. We use this approach in our real life. When we buy a car for example, we have requirements: price, color, etc. Requirements act as filters of desirable features.

So how do we apply this to physics axiomatization? The platonic world of math contains an infinite numbers of mathematical structures. Only a handful of them are used by reality: the Hilbert space, the Minkowski space, SU(3), SU(2), U(1) in standard model, etc. All we need is a way to filter the "good" and useful mathematical structures from the ones that play only a limited role. In other words, we need the requirements of nature. If the ultimate nature of reality is mathematics, then comparing math and reality is a good place to start. As I show in the essay this generates physics principles which I think are self explanatory. Additionally we need old fashion axioms. My current understanding is that the principles of physics acting as filters and the additional axioms helping to derive consequences from them, are complementary, not mutually exclusive as you state. Pure axioms are not enough because reality is too complex, while pure principles for now cannot have mathematical consequences without a minimum of technical axioms.

So now back to your last question: "causing the universe to behave mathematically?" my answer will be because at core, reality is only the platonic world of math arranged in a specific way.

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  • Post #6

Florin,

I consider myself a layperson, not a professional physicist. I freely admit that I have motives in terms of what the physics community should look into. I do understand that professional physicists have careers and political considerations. If I talk about hyperdrives and other crazy ideas, who cares. That's not how I earn my living. But a professional physicist has to approach physics from a completely mathematical and axiomatic point of view. It is important that real physicists approach the physical universe with cautious mathematical and axiomatic techniques. You may or may not agree, but I believe that it is my job, as the 'crack pot' to attempt to insert radical ideas that have a grain of truth in them. The advancement of physics is best served by the interplay of both approaches.

I believe it will be necessary for someone to hold the conviction that mathematics can explain everything that is observable. This is a dynamic interactive process. You must embrace your 'mathematical physics' conviction and carry it through to its conclusion. Because ultimately, the physics community will discover that the universe is not made of mathematics; the universe is made of 'something' that has mathematical properties.

Jason,

Again you raise excellent points. There is a tension between mathematics and reality. In mathematics, we are concerned about pure abstract relationships, regardless on how they appear or not in the physical world. There is an old saying: "stones and sticks can break my bone but words will never hurt me". Paraphrasing that, we do not seem to get hurt by Pythagoras' theorem, or ... are we?

So let's put this tension on hold for a minute and discuss other points. All physics theories have axiomatizations, some with more alternative axiomatizations than others. But what is the glue that holds everything together? Nature seems unified in exhibiting all those features like relativity and quantum effects. It is therefore very natural to seek a unified axiomatization approach. So far we have none that works completely, and I am only proposing an alternative way at looking at this problem. If it works, great, if not, we learned how not to do it. However, there are rigorous mathematical results showing that this approach is at least worth of consideration.

In general it is extremely difficult to solve open ended questions like: what is existence, or what is the nature of time, etc because of the myriad of points of view one need to consider. Typically those issues are left for philosophers to discuss. As David Gross puts it, it is very easy to recognize well posed mathematical problems: those are the problems that one can give a graduate student to work on for his degree and expect an answer in a reasonable amount of time. Changing the angle on how we look at physics axiomatization has precisely this effect of making the problem mathematically tractable. Currently I have four very well defined mathematical problems (and I mention one of them in the essay: obtaining the SU(2,2) and the Klein Gordon equation in a particular case) which satisfy David's criteria. Four is not a lot, but is a start. All we have to do now is follow the math and see if it will lead us to better understanding, or to a dead end. Time will tell.

So now let's come back to the tension between reality and math. Math is relational, and the idea of reality as relational is not crazy, nor new. Loop quantum gravity takes this principle at heart. How hard is to understand reality has to have an independent existence, has to be able to change and has to be infinite in complexity? This should be self-explanatory. The hard part is deriving mathematical consequences from them. But if reality is relational and can be understood as the platonic world of math rearranged, then by looking at the differences between reality and math we should recover all the mathematical structures which describe reality. Suppose we can prove the necessity of time, space, quantum mechanics, Standard Model, and explain the origin of the universe. Then at that point we can conclude with certainty that the universe is made out of nothing but mathematical relationships.

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  • Post #8

Dear Florin,

though our both approaches to discover ultimate reality could not be much more different as they are yet, i want to mention one thing i realize as common in our both lines of reasoning. But let me say some more general things before i come to the point.

I made up myself with some (more or less) deep thoughts about the nature of maths and why it can be that our world can be so accurately described by an "abstract" system like math. For me, math is as relational as you supposed it to be. But what are the relations math deals with? Human relationships obviously deal with humans, does math therefore deal with *numbers*?

In my opinion, maths (without physics) is at first about quantities. It's about the relation between quantities and how this quantities can be transformed into one another. Therefore "rearrangement" seems quit natural for considering the nature of maths. It's about the relation between a one and the *seemingly* many. But in physics there seems to be also *qualities* in the sense of complexity and total different behaviour as consequences of total different quantities (and rearrangements) of some systems, subsystems and elementary systems. So we can surely conclude that rearrangements of quantities in some cases can abviously produce different qualities in our world, as far as human beings can conclude this out of their limited perspective that is biologically fixed. For example in chemistry, there are some fundamental entities (atoms) made out of some more fundamental entities (protons, neutrons, electrons, quarks). If you are right and nature is indeed infinite in complexity, what could this mean? Would this mean that under every "fundamental" level there exists one "more fundamental" level and so on infinitely with an infinite level of accuracy after the decimals? Well, the question is rethoric, because in yours approach the fundamentals are somewhat of math-like nature and started with bare quantities (numbers). But every number of them can theoretically be infinite in its own right. But how could this correspond to the physical world where dynamics and change govern the tide of events? More precisely: Is your view of maths, is ultimate reality just another variation of "anthropic" reasoning with respect to human observation of repeatability and lawfullness that can - for whatever reasons - be desribed mathematically?

What i want to say with that is that for me it is not quite clear how the relation between quantities and qualities in our world really looks like. And now i come to my point. A mathematical statement can tell us a (relative) truth about qualities which have to be related by an equality-sign in the abstract language of maths. So the left side is equal to the right side (and in pure maths at least vice verca too). An inequality for example of the Bell-type can only tell us how the things possibly *not* are. So mathematical transformations that quantitatively equal each other are in my opinion pure tautologies and therefore could be indeed interpreted as a change of the quality of a system from human perspective. The same is truth for my own approach with ultimate reality (see therefore my essay).

But a mathematical sentence does not express a thought in the sense of qualia, creativity and mindfullness. We only use mathematical sentences to mechanically conclude from sentences that do not belong to maths to sentences that also do not belong to maths. You maybe would say that that's not true in your framework because in your framework *all* sentences belong to maths. For the latter is your perspective on the whole issue.

Well, if your perspective would be true that maths is an infinite landscape and reality as well, i would perhaps agree. But i strongly assume that the very notion of "infinity" in all its historical and philosophical facets is the biggest contradiction of all: It defines itself by saying it has no definite borders. So i would say the very notion of infinity is a totally misleading tautological concept because it only says: infinity = undefined.

Insofar as you use the very concept of infinity for your approach i would say that you use an undefined space to define your lines of reasoning by an act of (honorable) creativity. For me, the latter could be the most important ingredient of reality that could have truly qualitative properties instead of only quantitative ones. But as you in my opinion said very clearly, only time perhaps can tell us. My personal conviction is, that the whole question about the ontological and epistemic status of quantum mechanics is indeed a deep issue of the relationship between quantity and quality, hence between defined and undefined parts of ultimate reality.

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  • Post #9

I finally read your paper last night and some this morning. This is an interesting proposal, I am not sure whether it will work, or even if so whether it has much applicability.

Axiomatizing physics strikes me as a case where physical states are information bits, quantum bits, which are processed by logical gates or some process. The logic gates here are quantum processes, such as unitary operations. The unitary process is similar to a Hadamard matrix, for instance This perspective is similar in a way to how I look at what might be the next level in depth with natural principles. In some ways the Turing approach to axiomatization and logical completeness has connections to physics. A Turing machine is after all a model of a physical machine. A physical process involving a change from one state to another has a computational or algorithmic element to it. So an axiomitization of physics might be thought of as some theory of processes or processors which are algorithmic. So in that setting we can certainly pose the question to what extent incompleteness results impact a program like this.

The Godel theorem indicates that no axiomatic system is able to determine the truth value of its own predicates. This is demonstrated with the predicate which acts on its own Godel number as a variable. So no axiomatic system is able to list all its Godel numbers in some complete list of provable theorems which are true. With physics there is of course the added problem that one can't identify causal sets as having a truth value. Clearly a causal set which leads to contradictions is false, but this does not mean a causal system which is consistent is necessarily true. This touches on Hume's thesis of course, but one can't establish a causal system as being true, and even if it is mathematically described empirical demonstrations don't establish its truth value (even if massively supported by such evidence), and the mathematical system used to describe it ultimately has these incompleteness with respect to foundations.

Axiomatizing physics is more of a meta-math-physics sort of idea than straight physics. It is not clear how successful or useful such a program would be. I have thought that maybe at the Planck scale quantum gravity dissolves into some self-referential system of vacuum states. I am not sure if the total chaos which may be present at L_p is really of this nature or not, but it might be. If so then this sort of program might be of some worth.

LC

Dear Stefan,

Thank you for your comments. There are many topics I would like to reply to, so I will be brief in my first reply and I will touch on additional topics later.

First about infinity. This is a huge topic and different people use it differently to derive results. For example Cantor showed that real numbers are not countable and that there are different types of infinities, while Jochen Rau uses infinity to prove the necessity of orthogonal groups. In his proof, Rau allows the local physical structure on the event manifold to vary freely. It is this critical feature that helps single out the orthogonal groups and not the unitary groups for example. If you do not have this infinite local freedom, then obtaining space time as an emergent phenomenon is a very hard problem. Also, at Chaitin puts it, you cannot obtain 20 pounds of theorems from only 10 pounds of axioms. I am bypassing this algorithmic information theory limitation using the physics principles as filters. Now from Godel we know math is infinite, and reality seems infinite as well (although we do not know it for certain). The trick is how to use this observation to derive mathematical results.

Second, about the relationship between quantity and quality: I am not a philosopher, and I am not qualified to discuss this. As a physicist however, if we can make predictions that are ultimately validated by experiments, then we are making progress I can explain. Now in the conceptual area of physics, we already know the basic properties of nature and we should try to prove mathematically their unique necessity. If we achieve that, then the conceptual problems are solved. If from those results we can find the solutions to well known problems of physics like quantum gravity, then even better.

Case in point, quantum mechanics. I do not know how to explain the relationship between quantity and quality, but I can explain QM in an intuitive way without the recourse to hidden variables. Just recently I discovered Joy Christian's claims of disproving Bell's theorem. Very interesting papers, but I think I know where he makes a mistake. The mistake is not mathematical as his critics tried to prove so far, but conceptual in the way that he does not understand why hidden variables should commute. He is using a Clifford algebra hidden variable, and he thinks he obtains a local realistic theory, but in fact his model has a continuous state space and it is only QM in disguise in quaternionic language. He can do that because of 2 things: 1. geometric algebra can allow a representation of all classical Lie groups, and 2. there are a handful of isomorphisms between orthogonal and unitary groups SO(3)~SU(2), SU(4)~SO(6), SO(2,4)~SU(2,2). He is using the first isomorphism, but his argument will not work for SU(3) for example with no such isomorphism and his hopes to rewrite all QM in terms of hidden variables are wrong. His model is intuitive and very nice, but I think I can prove all QM is intuitive.

Lawrence,

Thank you for taking the time of reading my essay. I know this program works because of all the results obtained so far. The real question is can it generate anything else? I am very hopeful it will work because for me it helped framed the physics intuition behind Connes' results and also pointed the way towards obtaining the Standard Model parameters. I do need to properly obtain the local gauge symmetry principle from the three axioms, but gauge theory is basically dimensional analysis. Being algebraic, the composability principle is stronger than that. Also the composability principle is best understood in category theory framework, and quantions can be cast trivially as a Hopf algebra.

About Godel's result, I showed how its roadblock is avoided, but I am not sure about nature as a Turing machine. In math research right now there is a new area called inconsistent math. One can arrive there for example by considering the Peano arithmetic in conjunction with an axiom of a maximum number (like the maximum representable natural number in a physical computer). Then we can ask questions of how we can obtain anything valuable while avoiding the inconsistencies? I am thinking in this case one can always convert this into a Turing machine because we necessarily need to introduce the idea of a state that will protect us from contradictions and we can also do recursive manipulations. But then if this is true and the universe is just a giant Turing machine, we cannot tell this apart from a brain in the vat case. And I think simulating reality is not the same thing as reality itself. A computer program can have logical errors and crash, but reality seems to be able to avoid all logical inconsistencies.

Dear Stefan,

You ask: "Is your view of maths, is ultimate reality just another variation of "anthropic" reasoning with respect to human observation of repeatability and lawfullness that can - for whatever reasons - be desribed mathematically?"

I am not sure what anthropic reasoning is, but I can explain my understanding of the anthropic principle. This will also tie up with your earlier mentioning of complexity. So let's start at complexity. In this area you have emergent phenomena that cannot be explained by the individual parts only. For example one of the millennium problems asks for a rigorous proof of the so called mass gap, while the Yang Mills lagrangian has no mass term to begin with. The anthropic principle is borrowed from biology and is suppose to explain the fine tuning of the physics parameters that makes our universe livable. I view this not as clarification, but as a way to hide our lack of understanding in a catch all explanation, not unlike the idea of God. Life takes advantage of the emerging complexity which appears during the evolution of our universe. In a different universe, maybe the complexity there will have a completely different scales and nature. Why is life suppose to exists only at scales of 10^-3 - 10^1 meters? Why not at the Plank space-time foam level, or at the astrophysical scales in other universes for example? The anthropic principle seems to bind us into imagining life similarly to what we see around us, not unlike how B-rated movies imagine aliens: with 2 feet, two hands, 2 eyes, etc. Wherever there is enough complexity, life will emerge in one way or another. But is our universe unique, and do we really need the anthropic principle? I believe our universe is the way it is because there is no other mathematical way it can be. Not if you want to satisfy the three principles. There is only one conceptual problem remaining. If the universe is unique, why does it happen only once as Guth asks? I can only offer a wild speculation at this point: there must be some "universe nursery" where all the universes get born, live, and die. This "nursery" should not have the universal truth property, and from composability, apart from standard QM and classical mechanics there is a QM-type theory based on split complex numbers which satisfy this. I suspect hyperbolic QM may be responsible for generating universes very much like ours.

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  • Post #13

Florin,

If I understand you correctly, identifying all of the mathematical properties that are valid in the physical universe might have benefits. Physical properties and observations can, without our even noticing, deceive us because of some influence that we didn't account for. At least with a set of physically confirmed mathematical axioms, we can break everything down into axiomatic building blocks. That will make it a little easier for physicists to give engineers more powerful mathematical tools to work with. For crazy laypersons like me, I known which axiom I need to counteract to get somthing fun like a hyperdrive. Another advantage to creating axiomatic building blocks is that, if they really are absolute, then we truly know what we can ever expect to observe. In contrast, if the physics community ever confirms an observation that should never be observed (e.g. transmitting information FTL; consistent thermodynamic violations; etc...) then we can find the fault line in the mathematics, and either remove that axiom, or figure out why we observed something that should be observable.

I say make a list of axioms. It makes it easier to track anomalies, anyway.

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  • Post #14

Florin,

I have only just begun reading your essay.

You have said "In the physical world truth is usually defined as something corresponding to reality and has a ubiquitous and non trivial universal property."

This is a statement about how the term truth is used in general parlance rather than a statement about the nature of truth itself. Truth is tied up with perception. Truth that is perceived may in fact be untrue, due to lack of evidence to draw contrary conclusions or misinterpretation or deception etc.

There is also the whole conundrum of what is meant by the term reality and is this in any way a universal objective truth or just subjective interpretation of sensory input by each individual.

You also say "In physics events are true for all observers and across all contexts." I would also have to disagree here, as due to relativity, different observers may disagree about the order in which events occurred and when they occurred. So there is no single truth that will apply universally.It once again comes down to perception. If one observer closed his eyes, at the very moment the event could have been observed by him, he might not observe it at all.For him it is true that no event was observed and therefore he may conclude that the event did not occur.

Why do you assume that there is a "universal truth property" of the "real world" as you put it?

I intend to continue reading your essay and will try to give further thought to it and feedback on it but have limited time available to me at the moment.

Jason,

I hate to disappoint science fiction fans, but there is no time travel, faster than light communication, warp drives, etc. (I continued to be amazed at how serious physicists like Kip Thorne, and Karl Svozil take those things seriously.) Finding the final axioms is work in progress, but we already know what is possible in principle. One very interesting frontier is quantum computers, quantum cryptography and quantum information. This is an area in physics were we are genuinely surprised by what is realistically possible to achieve in practice.

Georgina,

I follow your posts on the blogs, but in general I do not have the qualifications to discuss your posts which are more on the philosophical side. I will try however to reply to your questions here to the best of my (modest philosophical) abilities. Let me start with an easy answer. In relativity, different observers disagree about the order of events if they are spatially separated. But I was not talking about 2 events which can be compared, but about a single event in general which by itself is the same for every observer. If a star goes supernova, observers from different galaxies see the same thing, not one see the explosion while others do not (taking into consideration the time it takes for the light to reach different observers).

I cannot provide an answer regarding my universal truth property idea in the Vienna circle framework, or Hillary Putnam's approach, but I can tell you this is simply an elementary observation. In the real world, (historical) events are the same for everyone: monarchy was abolished in France and everyone agrees with that: the universe did not split itself in two copies and for some observers France remained a monarchy while for others it did not. (maybe it did split in two copies according to Everett, but within each copy everyone observed the same thing). Another way of looking at this is universal non-contextuality: it does not matter how we observe something, it is the same for everyone (not the same in math).

Perhaps a "counter example" can clarify this. In special relativity suppose you have a car of a given length, and shorter garage with two front and back automatic doors. Now suppose the car is entering the garage at a relativistic speed. For any stationary observer, the car undergoes a Lorentz contraction and they will observe the car inside the garage with both doors closed. From the car driver's perspective, it is the garage that becomes shorter and he will never see the car completely inside the garage. In this case the "car fits completely inside the garage with both doors closed" statement has different truth values for the two kinds of observers (stationary with regards to the garage or the car) and both are right (they can even take pictures to show as evidence).

Now compare this with the event's universal truth property. The situation above will never happen when one considers only one event. This is the meaning of the universal truth property. (So can we reconcile the universal truth property with this seemingly counter example? Yes, because the "paradox" in easily explained away by noting that the sentence about the car inside the garage actually contains two events: front door closes, and the back door opens and it all boils down at the relativity of simultaneity)

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  • Post #17

The axiomatization of physics is useful within a physical theory which has the universe as a universal quantum computer which computes its own states. A unitary operator can be thought of as rotating a state vector from one basis to another, and a coupling between two fields as being a CONTROL-NOT operation. So the universe itself is a great universal Turing machine.

This of course leads to all sorts of questions, for it demands that the physical states be recursive or first order logical. This must hold at least to within some cut-off in a renormalization group flow. The cut-off might be the Planck scale, where beyond that Godelian chaos might take over.

The world of structured spaces has only four types R, C, H, and O, according to the Cayley number sequence. We are pretty familiar with R and C, and H is a bit odd. However, quaterionic systems

i^2 = j^2 = k^2 = ijk = -1

do exist in physics with Dirac matrices and Clifford algebras. The failure of closed loops to close up vectors under parallel transport according to an algebraic structure or roots is some Clifford basis. Octonions are of course the really odd man in the crowd. It is not hard though to think up some nonassociative logical operations. It we make Q some logical process, such as a Hadamard gate, it is not hard to wee that inputs ABC into two O's, where A--Q--B means "A and B feed into Q" which gives the immediate symbol on the other side of the equal sign: A--Q--B = D. The nonassociativity is then

A--Q--B = D--Q--C =/= A--Q--E' = B--O--C,

so that nonassiative structures

So the universe can be consdered to be a system which operates according to the algebra A, some self dual error correction code which defines a Hilbert space. The E_8 has the [8,4,4] which computes the Hamming distance 4, which is a quantized system. The Leech lattice has [24, 12, 12] and [24. 8, 8]. So the universe is a quantum universal Turing machine.

For this machine to operate without Godelian influence it must be first order in logic and recursive. That is the requirement for any axiomatization program. The 3 principles you outline must then satisfy this requirement with in the Church thesis or Lambda calculus.

Lawrence B. Crowell

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  • Post #18

Florin thank you for your prompt reply.

History is also a question of perspective, reflecting the bias or interest of the historian, who subjectively "paints a picture of the past"for the reader.He does not just amassing an impartial collection of equally objective, verifiable facts without supplying any subjective selection or interpretation of those facts.Some events are recorded, some are given significance, others are forgotten.I can not personally verify all historical facts that I am told or read, but may accept some of them as truth without any verification.

Perception varies between individuals, who perhaps vary in the amount of attention they give to an event, or who pay attention to different features of the event. So the qualitative experience and description of the same event also varies.The police are well aware that eye witness accounts of events may vary significantly. Too much similarity or too little discrepancy between accounts may in fact be suspicious, indicative of fabrication of the truth.

Although there may be an objective reality external to experience, no one has access to that objective reality.It is not therefore the "real world" that we experience, but our own subjective "fabrication".

However I accept that there may be a general consensus as to those singular events that have happened. The consensus of a significant number of independent witnesses or agreement of a significant number of independent replications of an experiment may be accepted as likely evidence in favour of an approximation of an underlying objective truth.

Florin, I would like to read the rest of your essay. I intend to write again when I have done that. I am interested to see how you have developed your ideas. The beginning part of your essay just caught my attention because of the way in which I perceive certain concepts such as truth and reality, which you already understand having read some of my previous posts.

Lawrence,

The universe may be a giant universal Turing machine, I do not know, but what consequences can you derive from that? On the other hand, in an UTM, you can make copies of the state you are in, but in QM you have the no clone theorem so I cannot see how the two can agree. First order logic is also very constrictive and why this should be the case in general is not clear. You seem to agree with Tegmark's approach though, but I have deep reservations about his assertions.

There were some attempts to obtain QM from information theoretical approaches by Bub and others, but as of today I am not aware that this approach succeeded completely.