Dear Philip E. Gibbs,

"Information is the basic material of reality, but the processing of information raises paradoxes due to the self-referential nature of computability."

Perhaps I overlooked this statement and something that may substantiate it at the beginning, the end or even any part of your essay on "Undecidability ..."

I was lazy and looked for where you referred to [ 4] Shannon at your p. 2. Maybe you merely corrected Shannon by mentioning that the DNA is a material code. Otherwise, one is tempted to read your theory of theories as new-Hegelian idealism. Anyway, I see you obliged to take McEathern's critical arguments more seriously. He is complaining at my own essay.

Eckard Blumschein

    Thanks for your comments, references and questions.

    You make a fair point that when defining computability, infinite strings of output are required. Any finite string is computable. However for the halting problem it is easier to work with just finite output. The computation of a universe might make more sense if it is allowed to be infinite, but I am not sure I could have cleared this up in the limited space.

    For the Wick rotation I accept that this was too quick. Working with probabilities between 0 and 1 is not very good when trying to define and algebra so a switch to complex numbers works better. More work would be required to determine whether this is justified in that it would give an equivalent formulation.

    The amount of information conveyed by a statement is not the bit-length of the string that communicates it. That only sets an upper limit. What I have said at the start about information content is standard stuff, but a lot of people have a misconception that information always comes in discrete bits so I had to explain that it doesn't. It is covered in wikipedia at https://en.wikipedia.org/wiki/Information_content

    The negative log of a probability gives the information content for the outcome of a random process and it can take any real value from zero to infinity.

    That information is the basic material of reality is an axiom here. I would justify it by observing that everything is described by information in physics, mathematics and any other subject. I don't need any other substrate as a foundation and seek to derive everything else from information alone.

    I am not an expert on the classifications used by philosophers but I find much in common with both Hume and Kant and others. I would say that the underlying structure of our reality can be derived from the way we must experience it in terms of processing uncertain information. Probably this is some form of idealism but I am not sure which variety it is.

    "What I have said at the start about information content is standard stuff..." In Algorithmic Information theory, but it has little to do with Shannon's Information theory.

    As Shannon states in the first sentence of his A Mathematical Theory of Communication, he is concerned with:

    "various methods of modulation... which exchange bandwidth for signal-to-noise ratio... in a general theory of communication."

    In other words, a trade-off (exchange) can be made, that increases bandwidth in order to offset the effect (on information capacity) of a decreased signal-to-noise ratio and vice-versa. That is what he is interested in characterizing.

    On page 43, where he gives his famous Capacity theorem (Theorem 17), he states: "This means that by sufficiently involved encoding systems we can transmit binary digits at the rate (C) bits per second, with arbitrarily small frequency of errors."

    Thus, unlike any other "flavor" of "Information theory", Shannon is primarily concerned with the circumstances, under which one can correctly (without errors) recover the values of each, individual bit, encoded into a continuous, noisy waveform. It is meaningless to talk about the error-free value, of an unrecoverable fraction of a bit, precisely because a fraction-of-a-bit has no "correct" value.

    The significance of this, is that it pertains directly to "uncertainty" in physics. Namely what is the maximum number of discrete (quantized) bits of information, that can ever be recovered, without any errors, from any set of measurements of any continuous function/signal, that has a limited duration, bandwidth and signal-to-noise ratio (SNR)? In other words, what is the maximum number of bits, that you can ever be "certain" of, in measurements of any received "signal"? What happens if that maximum number happens to be exactly equal to one? What happens is - you get the Heisenberg Uncertainty principle. That is the origin of the HUP. It has nothing to do with any "weird physics", it is simply a property of any mathematical function, with a severely limited duration, bandwidth and SNR; the very properties that Shannon said he was concerned with, in his very first sentence. There are circumstances for which, there is no possible "exchange of bandwidth for signal-to-noise ratio", that will ever enable an observer to be certain of the value of any more than one, single-bit-of-information, within an entire set of measurements, of some continuous signals. That is what "entanglement" is all about.

    Rob McEachern

    Hegel (1770-1831) strongly rejected the atomism: "The atomists are thinking too materialistic". Materialism was seen close to atheism. Maybe believer in God feel attracted from your idealism.

    On your p.8 you stated like an axiom: "Physicists have so far failed ... because they still cannot relinquish certain cherished philosophical beliefs ... objective physical reality ... and causality".

    I am ready to agree concerning reality because I see it just a successful conjecture. However by questioning causality you lost me. Aren't you aware what you are saying with words like process and processing?

    Have you any idea how to apply your axioms?

    It is perceptive of you to pick up on the philosophical side of this essay. It is very important. I am not going to allow myself to be identified with any particular philosopher because there is none that matches my whole outlook. As you point out, much of philosophy is historically built around the debate of religion vs atheism rather than what physics needs or tells us.

    I wrote a whole essay on causality under the topic of giving up assumptions. It was my least successful essay in the community voting, but that does not mean it is wrong.

    I also reject materialism, determinism and reductionism, for starters. People don't like that. They want to keep these things. These are concepts that are built into our education, our language and therefore our psych. You say that using words like processing implies that I really accept causality, but I disagree. You can process and compute the universe in any order. It is hard to express this in language because our everyday language is built around the assumptions that I am giving up. It is only in the mathematics that the real picture can be understood.

    "You can process and compute the universe in any order."

    The essence of mathematics is its freedom (Cantor). This makes it just a tool that even allows, to some extent, reasonable backpropagation.

    You raise an interesting point about the finitude of information. In an idealist philosophy my reality is determined only by the finite amount of information in my mind. The external world is an ensemble of possible worlds consistent with that information. I dont allow that there is one external physical reality for the state of the whole universe around me because that would require an infinite amount of information, but each possible state of the universe would require a large or infinite amount of information to describe it. What this provides is an illusion of an external reality described by more information than I really possess in my mind.

    I think that symmetry is important to how this works. Suppose that all objects in the universe were distinguishable so they can be labelled in some way. If the universe is infinite and I know that the object with label X is in the room with me then I have an infinite amount of information about it. This can't be right. The paradox is resolved because elementary particles are indistinguishable. All I can really know is that there is an object in the room made up of elementary particles in some configuration. This requires only a finite amount of information. The indistinguishability of particles is a permutation symmetry.

    You are right that I have identified information entropy with action, even if I did not say it explicitly. It is an interesting conclusion, and not one that I would have expected.

    At least I am not alone in linking action to entropy

    https://arxiv.org/abs/physics/0106081

    https://www.researchgate.net/publication/239614590_The_concept_of_entropy_Relation_between_action_and_entropy

    https://physics.stackexchange.com/questions/483580/is-it-there-any-relation-between-an-action-and-entropy

    etc

    Philip,

    philosophy has always been discussed along contemporary hot topics and of course by using contemporary vocabulary. The only constant I can find in it right from its start is:

    - Time versus Time-lessness (not eternity!)

    - a posteriori versus a priori

    - empiricism versus rationalism

    which all mean the same.

    The other point I want to address is that REAL progress has been made when a scientist cannot decide whether he has discovered or invented something. Then what he discovered/invented is Absolutely free from contradiction. The formal description of this state of 'universal validity' exceeds the capacity of logic, but not the capacity of the scientific metaphor.

    Heinz

    Phil,

    Thanks for clarifying the difference between yours and MUH. And thanks for pointing out that your approach is "indistinguishable from the'multiverse' of wavefunctions in QM which is really just one field." I'm actually glad to hear that as I like your ideas, but felt they were the extreme opposite of mine. I do believe that good ideas should generally converge to a "correct" idea.

    Best,

    Edwin Eugene Klingman

    In the light of some of the great comments above, I want to clarify the philosophical position in this essay.

    When physics students learn quantum mechanics they often feel unsatisfied with the formulation. I know I did. In-determinism is not the problem. The real difficulty is the role of the observer. In the standard interpretation the wave function collapses when an observer makes a measurement. The problem with this is that our traditional philosophy of science is materialism. Everything is made of particles and fields which exists independently of us. we are just configurations of these material structures that happen to have a highly evolved brain capable of self-awareness. How can we even define what we mean by an observer that is consistent with this philosophy? This is the question that leads to the famous statement by Feynman that nobody understands quantum mechanics.

    Different people come to terms with this in different ways. Some people claim that the wave-function does not collapse and it is just decoherence. This is nonsense. Others look for an underlying deterministic hidden variable theory to eliminate the probabilistic part altogether. Some develop a pluralistic philosophy where consciousness is something more than just high level brain power so that the observer can be counted as something special. For me it was the many worlds interpretation that allowed me to accept a more comfortable materialistic view where the wave function collapse is an illusion of our own experience.

    I now think that all these ideas are wrong.

    The only viable solution to the measurement problem is to replace materialism with idealism. The observer is not just something different, it is everything. Before quantum theory philosophers proposed various types of idealism: subjective idealism, objective idealism, transcendental idealism, etc. what we are considering now is best termed quantum idealism. This is not some religious or spiritual philosophy. It is pure science.

    In this view our reality is determined by the information we have in our mind. This is a slightly fuzzy quantity because we are not conscious of everything at once and the boundary of our mind is not absolute but we can allow for that. Our brains can only hold a hundred terabytes of information which is tiny compared to what is required to determine the physical position of all the particles around us, and yet it is everything.

    In a sense the detail in the world around us is an illusion. There are really many possible worlds. All the worlds that are consistent with the information we possess. The real amount of information out there is no more than the amount in our head. It is as if a giant quantum computer is continuously computing all universes consistent with what we know, not just in the present but also in the past and future. New information from these worlds comes back into our mind through our senses when we make observations providing the illusion of a world containing much more information than is really there. This computer is not a real thing. That would be a materialistic interpretation. It is not part of our mind either. Our brain is not powerful enough. It is just the force of consistency which makes our reality operate in this way.

    I know this will not be a popular view, just as my views on causality and many other things are not popular, but if I am right then the very nature and structure of reality must be determined by the mathematics of the information calculus required to describe this process. In my essay I tried to show that we can get to the emergence of quantum mechanics, space, time, particles and fields just starting from an algebraic analysis of information and how it works in a self-referential system. Obviously there is more work to do but lie to think that I have made a promising start.

      Thank you for your kind words and encouragement.

      For the FLRW metric with k = 0 the spatial surface of the Hubble frame is R^3. A similar situation occurs with how one defines coordinates in de Sitter spacetime. There is no serious problem I see with that sort of infinitude. The limit to observing an infinite amount of stuff, first pointed out by Olber in his paradox, is the expansion of the universe and cosmological horizon. The expansion factor e^{Ht} in the FLRW, or cosh(Ht) in de Sitter, defines a limit for the expansion of a Planck length at the earliest quantum gravitation stage to the scale of the CMB or cosmological horizon. This is an enormous factor e{Ht} = 8Г--10^{60}, but Ht = 140. This gives r = 140Г--в€љ{3/О›} ≈ 1800 light years.

      The hunt for B-modes in the CMB is a form of this. Graviton production or gravitational waves produced in inflation should leave a polarization signature on the CMB. In this way the most distant and earliest quantum information we may receive or observe is on the CMB as a sort of cosmic quantum gravitation detector. Anything beyond this scale is sealed off from view. As a result, any observer can access only a finite amount of information.

      There is a curious sort of renormalization of scale with information. As we observe further outwards the number of qubits available decreases, until at some final scale of the Planck wall there may only be one qubit. Of course, observers, or we, find themselves in a local world filled with information. The cosmological horizon at the time of inflation has an area of around 10^{15} Planck units of area. This is the amount of information potentially available from this epoch. Pushing further back to the Planck era this approaches one unit.

      Cheers LC

      erratum, r = 140Г--в€љ{3/О›} ≈ 1800 light years is meant to read r = 140Г--в€љ{3/О›} ≈ 1800 billion light years.

      LC

      Feynman was right about Fredkin. He is an original thinker who appreciated the importance of computation in physics long before others. He has inspired a number of people including myself. I also know him personally and have heard many of the incredible stories of his adventures first hand.

      I have cited his work in some of my other essays. There are many lessons to be learnt from his approach that have affected mine, even if I do not agree with his deterministic vision of reality.

      "The real amount of information out there is no more than the amount in our head." If it is only "out" there, then it is not "in" our head. Where did your "information about physics" come from, if it was not in papers, books and the minds of your professors, before it got copied into your head, and probably had to overwrite older information stored there, in order to make room for it?

      "Our brains can only hold a hundred terabytes of information which is tiny compared to what is required to determine the physical position of all the particles around us" - Or in us. The information content of either a computer or a brain, is not just that stored in its "memory". It requires much more information, to specify how to construct the computer, or brain, in the first place.

      "This computer is not a real thing." That is your illusion. The universe merely "computes" itself, by simply being itself, just like every other computer, brain or being; things can only be whatever they are, and can only do whatever it is that they do. Humans do not have enough information storage capacity, to ever store all the information contained within all these other beings. That is no cause to believe that such other things, do not exist.

      Information has nothing to do with consciousness, thought or life. As Shannon stated on the first page of his A Mathematical Theory of Communication: "semantic aspects of communication are irrelevant to the engineering problem." In other words, his conception of "information" has nothing to do with "meaning", it is simply a "quantifiable", observable pattern, encoded into an observable, physical "substance", waiting to be correctly recognized, by some other entity in the future. The fact that such an entity may not have appeared yet, and correctly copied and "decoded" that information into its circuitry, or brain, has no bearing on the existence of the information "out there"; if I write a note on a piece of paper, and cast it into the wind, the fact that some other being does not yet know that it exists, much less know what I wrote on it, is irrelevant to the fact that the paper, with its writing, does exist, and may be eventually discovered and "correctly decoded", by something.

      You seem to be totally ignoring the fact that the key word in the title of Shannon's paper, is the word communication - thus, Shannon's "information" is entirely concerned with a possibility, the potential, to transfer (AKA communicate) "information", from one inanimate entity to another, without any "thought" or "meaning" entering into the process - such as the process embodied in an inanimate radio receiver. Some other entity, like a human being, may subsequently come along and attempt to attach some "meaning" onto this acquired "information", but as Shannon stated, that is "irrelevant to the engineering problem", involving the "information transmission" itself.

      Rob McEachern

      "Some people claim that the wave-function does not collapse and it is just decoherence. This is nonsense."

      If I recall correctly, someone else called even the wave-function collapse itself a nonsense. Don't get me wrong. I don't support the two "nonsensical" opinions. I just dislike the word nonsense in a scientific discussion.

      Eckard Blumschein

      Your mini-prolegomena has ideas I too have pondered. I am not quite as disposed to this idea of idealism. However, locality and realism are dual constructs and Frauchiger and Renner showed how the observer of observers can have disparate reports to the observed outcomes. This illustrates how this duality can have a non-realism wing. Thus, nonlocality can give way to some element of locality if realism is weakened or dropped.

      The thrust of my paper is there is no computable or dynamical reason for how outcomes of measurements obtain. What are quantum interpretations are then auxiliary postulates that share properties similar to what happens in geometry when Euclid's fifth axiom is negated. Nagel and Newman illustrate how this is an undecidable axiom, and if one includes this as an unprovable statement you get a consistent system, whereas the negation leads to a bouquet of geometries that are not consistent with each other. In QM, as I see it, there is a similar situation, where one can do the Mermin "shut up and calculate," or one can decide between whether QM is ψ-epistemic, Bohr CI or Qubism, or ψ-ontological, such as MWI. There is then a branching of various interpretations, which if they are not inconsistent with QM are workable.

      I am not certain what role to give mind. I am not sure about "all idealism," but on the other hand QM has this idealism prospect. Trying to eliminate idealism might be a sort of "whack-a-mole" exercise. Penrose has in his Road to Reality a suggested triality between physical reality or materialism, mathematics and consciousness. Of course, Penrose is at an age with the stature that he can propose something like this. I am not entirely certain about these ideas. It is evident the universe existed long before biology, at least on Earth, and certainly long before intelligent life or consciousness. There are many reasons and evidences that force me to not completely throw my lot towards idealism. This is even if the door for idealism is slightly open.

      Cheers LC