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Mathematical proof debunks the idea that the universe is a computer simulation (phys.org)
submitted 1 year ago by to c/science@lemmy.world
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Their findings, published in the Journal of Holography Applications in Physics, go beyond simply suggesting that we're not living in a simulated world like The Matrix. They prove something far more profound: the universe is built on a type of understanding that exists beyond the reach of any algorithm.

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[–] 3 points 1 year ago* (last edited 1 year ago) (10 children)

The central assertion of this paper:

Any viable F_QG must meet four intertwined criteria:

I'd argue is only partly justified. An argument for "Effective axiomatizability" is given, "Arithmetic expressiveness" is more or less self-evident, but the other two I'd say is given without justification.

Also the core concept of F_QG is defined in a very hand-wavy way. I'd like to see a concrete example of an existing theory formalized in the way they proposed in the paper. It's unclear to me how mathematical derivability from the formal system correspond to how laws of physics apply. Specifically mathematical logic is a discrete process, yet the world described by physics is generally contiguous. (Yes, there are ways for this to make sense, but they didn't provide anything for me to know how they intended for this to make sense.)

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  • [–] 0 points 1 year ago (9 children)

    Any viable F_QG must meet four intertwined criteria:

    This statement is simply defining the fundamental structure of how a full theory of everything would be composed. A consistent and complete theory must meet all four criteria.

    Also the core concept of F_QG is defined in a very hand-wavy way. I'd like to see a concrete example of an existing theory formalized in the way they proposed in the paper.

    The above four criteria are how F_QG is defined. The author, in presenting these four criteria, provides two very specific, concrete examples of theories (String Theory and Loop Quantum Gravity) while introducing the premise of his argument. He clearly affirms that these theories do meet three of these four criteria but fail on the fourth. If there were an example of a theory that meets all four criteria than that theory would be the theory of everything and the whole issue would be resolved.

    It's unclear to me how mathematical derivability from the formal system correspond to how laws of physics apply. Specifically mathematical logic is a discrete process, yet the world described by physics is generally contiguous.

    The rest of the paper explains exactly this. Mainly that the only way to satisfy all four criteria is to include non-algorithmic components that bridge the discreteness of math with the observable continuity of physics. The author goes on to describe several examples where this process can apply in modern physics theory.

    I do agree that the author is making a dramatic and bold statement regarding a proof of a theory of everything (that being that the theory of everything can never be computational) which requires heavy scrutiny. However, I am in no way an expert in these fields and so I have accept that the journal that published the proof can provide that scrutiny. It is easy to check on the reliability of that journal as a lay person, and in doing so doesn't seem to raise any flags about the validity of the arguments the author is presenting.

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  • [–] 5 points 1 year ago* (last edited 1 year ago) (5 children)

    I should've known you weren't genuinely asking a question.... You were just baiting me.

    A consistent and complete theory must meet all four criteria.

    You are doing what the authors are doing, this itself is an assertion you aren't backing up.

    The above four criteria are how F_QG is defined.

    No, these are four criteria the authors assertion F_QG must satisfy. For theories that don't satisfy all four criteria, you should still be able to at least formalize them into F_QG as proposed by the authors. Yet they didn't give a concrete example of how a theory may be so formalized.

    The rest of the paper explains exactly this.

    Uh, what, not? "The rest of the paper" is after they have already reached the point of claiming the Universe can't be simulated. My objection is way before that, which is pointing out how poorly F_QG is defined.

    It is easy to check on the reliability of that journal as a lay person, and in doing so doesn’t seem to raise any flags about the validity of the arguments the author is presenting.

    Sure, but knowing what I know I can give this paper a bit more scrutiny than a lay person can (ha ha, look at me, I am very smart /s), and this paper doesn't convince me in the slightest.

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  • [–] 1 point 1 year ago (4 children)

    I genuinely was not intending to 'bait' you. You presented an argument saying your knowledge of the subject is more robust than the experts who refereed the paper. Since I am not an expert in the subject and am curious about learning more, I was asking you to guide me in that process with your experience.

    I felt that your arguments suggesting that the author is presenting an inconsistent logical proof were not well defended and so I asked for clarification on the points you raised. I am still unclear what you are saying in this statement:

    No, these are four criteria the authors assertion F_QG must satisfy.

    These are the four criteria that establish how a computational theory is logically defined as a formal system, not an argument. The author makes this clear in addressing the notation being used:

    For clarity of notation: ΣQG is the computable axiom set; Ralg comprises the stan- dard, effective inference rules; Rnonalg is the non-effective external truth predicate rule that certifies T -truths; FQG = {LQG, ΣQG, Ralg} denotes the computational core; and MToE = {LQG ∪ {T }, ΣQG ∪ ΣT , Ralg ∪ Rnonalg} denotes the full meta-theory that weds algorithmic deduction to an external truth predicate.

    After that paragraph the author uses several very specific examples in modern physics theory describing how the findings apply starting with the paragraph:

    Crucially, the appearance of undecidable phenomena in physics already offers empirical backing for MToE. Whenever an experiment or exact model realises a property whose truth value provably eludes every recursive procedure, that property functions as a concrete wit- ness to the truth predicate T (x) operating within the fabric of the universe itself. Far from being a purely philosophical embellishment, MToE thus emerges as a structural necessity forced upon us by the physics of undecidable observables. Working at the deepest layer of description, MToE fuses algorithmic and non-algorithmic modes of reasoning into a sin- gle coherent architecture, providing the semantic closure that a purely formal system FQG cannot reach on its own.

    Again, I am trying to approach the authors bold claims with skepticism and scrutiny, not argue with you. But you have to be a little more humble, the paper wasn't published in order to convince you. Just because you weren't convinced doesn't mean that the proof is invalid.

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  • [–] 1 point 1 year ago (3 children)

    Actually, F_QG is itself an assumption which isn’t backed up. See the paragraph before the one you quote when defining it. The beauty of axioms is that we can assume whatever we want but we need to either show nothing goes underneath it (eg Peano axioms) or have a very compelling case to make them (eg non-Euclidean geometry like parallel lines meet at infinity). This is a metasumary of some similar research at best. It’s not a proof in the way you think it is. Just because you don’t understand what you’re responding to doesn’t mean you’re right.

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  • [–] 1 point 1 year ago (2 children)

    Thanks for responding! I never meant to claim that I am right. The whole purpose I am engaged in here is that I do not understand the proof at all and am trying to understand it better.

    Here is where F_QG is introduced in the proof:

    As we do not have a fully consistent theory of quantum gravity, several different axiomatic systems have been proposed to model quantum gravity [26–32]. In all these programs, it is assumed a candidate theory of quantum gravity is encoded as a computational formal system FQG = {LQG, ΣQG, Ralg}

    Here, LQG a first-order language whose non-logical symbols denote quantum states, fields, curvature, causal relations, etc. ΣQG = {A1, A2, . . . } is a finite (or at least recursively- enumerable) set of closed LQG-sentences embodying the fundamental physical principles. Ralg the standard, effective rules of inference used for computations

    Is this not just saying that it is the existing theories (string theory, LQG, etc.) that are assuming gravity takes the form of a formal computational system? And so, F_QG as it is defined above is how any formal computational system is logically constructed, as in it has to have those three components in order to logically be a formal computational system?

    I am not a logician and do not understand what a first-order language is, or closed sentences or all those logic terms in the definition of notation. However, is F_QG in this case not just logically how any theory would need to be constructed in order to logically be a formal computational system? Is there an assumption being made here with regard to those three components in how formal systems are logically constructed?

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  • [–] 1 point 1 year ago (1 child)

    You’re missing the initial step.

    1. Assume that these proposals are correct.
    2. Given the proposals are correct, all of them contain a common structure.
    3. Given the common structure…

    Both OP commenter and myself take umbrage with #1 (if I can speak for them; they make disagree with me). I assume that if we trace the sources for the letter that we’ll see the reasons we’re able to make all of these logical leaps using other results in the field that come out of these proposals. I also assume that, if one of these systems is the foundation for a fully consistent theory of quantum gravity, then its conclusions are valid. This paper doesn’t address that initial assumption though so things like the article summarizing it are begging the question.

    There are many situations where we just have to agree to assume. If you read 14 and 36, you’ll find some of the core assumptions that go into this letter (both interesting ideas and the same authors so you can understand why they’d continue). An assumption Faisal makes is the rejection of objective observability which is one of those things you either believe or don’t believe. It’s analogous to the axiom of choice in that it could be contested but could be generally accepted.

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  • [–] 1 point 1 year ago

    Thank you, this is helping. However, I am still not following your logic here, I do not know what you are referring to when you say I am missing the initial step?

    1. Assume that these proposals are correct.

    Is this the initial step? And if so, what are the proposals that are being assumed?

    There are many situations where we just have to agree to assume. If you read 14 and 36, you’ll find some of the core assumptions that go into this letter (both interesting ideas and the same authors so you can understand why they’d continue).

    I have read through the abstracts and fail to see a connection regarding assumptions in those papers and the assumptions in this proof. Can you please clarify further for me? What are the specific assumptions being made in these papers that are also being made in the proof?

    An assumption Faisal makes is the rejection of objective observability which is one of those things you either believe or don’t believe

    There are several different interpretations of quantum mechanics. There are very valid arguments in favor of and against every one of them. If you accept one interpretation over an other, would that not just imply you believe that the arguments in favor of that particular interpretation are more logically valid than the other arguments? And so, it follows that you would continue that line of logical reasoning in further interpretations of theory?

    I don't understand how favoring objective collapse theory over objective observability is in any way making assumptions about how formal computational systems are logically constructed.

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  • [–] 1 point 1 year ago* (2 children)

    It is easy to check on the reliability of that journal as a lay person

    Is it, really? How does one check if a journal is one of those rigorous ones, without being an expert in the field? Some journals change from legit to predatory.

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  • [–] 1 point 1 year ago (1 child)

    https://en.wikipedia.org/wiki/Journal_ranking

    It isn't a perfect system, but it is a place to start.

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