Dear Cristi,

You say "at least we know that there is room for free will." You know that and I know that, though many dispute it. But free will, in any meaningful sense, is not deterministic, and, although one may draw an analogy with random numbers, I don't think one can draw it in any detail.

Thus I see no reason to contend that free will is isomorphic to math. Even if one...

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Dear Cristi,

You say "at least we know that there is room for free will." You know that and I know that, though many dispute it. But free will, in any meaningful sense, is not deterministic, and, although one may draw an analogy with random numbers, I don't think one can draw it in any detail.

Thus I see no reason to contend that free will is isomorphic to math. Even if one can, post exercise of free will, or even concurrent with the exercise of free will, find some neural correlates. Free will partakes of causal and I don't think mathematics reaches causal. So I don't think "everything is isomorphic to a mathematical structure." You seem to think differently. With reference to time, you say, "there is no conflict between mathematics and causal explanations." But I don't believe there is an 'explanation' for free will. I don't see this as in conflict with your arguments about a theory of everything, to the effect that we cannot be living in a world described by two disconnected sets of laws. That seems to me a self-consistency argument that does not depend upon everything being isomorphic to math.

On another point you note "if it looks like a duck, swims like a duck, and quacks like a duck, then it is a duck, isn't it?"

My essay analyzes why John Bell thought that "it looked like Dirac spin, behaved like Dirac spin, and had an eigenvalue equation like Dirac spin, ['it' being the Pauli eigenvalue equation.] I argue that the Pauli equation of Stern-Gerlach is not the Dirac equation of relativistic QM, and that Bell's oversimplification of this led him to impose what he felt were reasonable constraints that prevent a local model from achieving QM correlations.

I hope you will read my essay and comment.

My best wishes to you,

Edwin Eugene Klingman

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"But can we find a property of time that can't possibly be described by mathematics? In fact, time was best understood due to mathematics, in relativity and thermodynamics."

This "understanding" is based on postulates that could be false. For instance, Einstein could have mistakenly "taken from the idea of light waves in the ether the one aspect that he needed" - then not only the...

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"But can we find a property of time that can't possibly be described by mathematics? In fact, time was best understood due to mathematics, in relativity and thermodynamics."

This "understanding" is based on postulates that could be false. For instance, Einstein could have mistakenly "taken from the idea of light waves in the ether the one aspect that he needed" - then not only the "understanding" of time, but theoretical physics as a whole would be wrong:

Relativity and Its Roots, Banesh Hoffmann, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."

Pentcho Valev

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Dear Cristi,

The introduction to your essay is very clever. Most people do not appreciate that when going from the rationals to the real numbers, one enters a whole new ballgame, so to say. I did not appreciate it until I began to study some set theory, but your example brings this home very nicely.

I essentially agree with almost everything in the essay, but would like to add the...

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Dear Cristi,

The introduction to your essay is very clever. Most people do not appreciate that when going from the rationals to the real numbers, one enters a whole new ballgame, so to say. I did not appreciate it until I began to study some set theory, but your example brings this home very nicely.

I essentially agree with almost everything in the essay, but would like to add the following comments:

1. I think that at least in part, some of the difficulties pertaining to the metaphysical status of mathematics are linguistic. Specifically, I think "exist" is simply not a good word to apply to mathematical objects (unless one subscribes to the MUH) because it has too much baggage associated with the physical world. There should be expressions which capture subtle ontological nuances, similar to how Eskimos purportedly have over a dozen different words for snow. These nuances might allow us to refer to things like physical objects, feelings, thoughts and mathematical objects in such a way that we can keep separate what it is that we are talking about from everything else, and aid in investigating how they relate to each, if they do. I do agree with you that in the specific sense that you described it, every book, piece of music, etc. is already there.

2. Taking the ability to name something in the real world to entail being able to give a list of propositions that apply to it seems intuitively pleasing, but I still have a lingering feeling that there might be something above and beyond a complete list of propositions that characterizes physical objects. One could of course simply define this relation to be just so, but that seems like a cheap way out to me.

3. I am personally of the opinion that there is no "theory of everything". In fact, I consider the idea that there should be one as one of the last remaining vestiges of anthropocentrism in physics in the following sense: presupposing the existence of such a theory also presupposes that all processes in nature can be described using a small set of laws by one kind of observer of which we are a special example. Who is to say that there are not other kinds of observers whose observations of nature could also be described by a small set of laws but which would be *in principle* inaccessible to us? To give a specific example, who is to say that it is not possible to formulate a theory of nature from the frame of reference of an observer associated with null geodesics in spacetime? I often see the argument that it makes no sense to imagine such frames because no spacetime observer can transform to them, but that exactly makes my point: We are observers in spacetime, and to suppose that speaking of such frames makes no sense reflects a very subtle form of anthropocentrism.

Again, yours was a very thought-provoking and well-written essay.

Best wishes,

Armin

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Dear Cristi,

Thank you for your comments on my essay. I discussed your comment about the paradoxical nature of immortality in the context of a multi/maxiverse in a reply on my page.

Congratulations once again on an outstanding entry to this FQXi contest! I found myself highlighting a lot of your statements that I wholeheartedly agree with. In particular, in the section “Is there...

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Dear Cristi,

Thank you for your comments on my essay. I discussed your comment about the paradoxical nature of immortality in the context of a multi/maxiverse in a reply on my page.

Congratulations once again on an outstanding entry to this FQXi contest! I found myself highlighting a lot of your statements that I wholeheartedly agree with. In particular, in the section “Is there something that can’t be described by mathematics”, you nicely explain that, despite what mathematical universe critcs often affirm, consciousness and the flow of time could very well, in principle, “emerge” from mathematics , even if we don’t understand all of the details yet. I also agree that “emergence”, whatever it is, does not need a non-mathematical explanation (whatever that would mean), even if we, once again, do not understand all the details. There is an interesting parallel between some arguments against a mathematical universe and God-of the-gaps-type arguments : in the same way that some religious believers zero-in on the unexplained details of our scientific theories (for instance, the origin of the first life form on Earth) to see in them evidence that some sort of God is needed for that step, I think that many critics of the mathematical universe hypothesis zero-in on the parts of our understanding of the world that are not quite satisfactory (what is consciousness? why does time appear to flow?) to see in them evidence that the world cannot be fundamentally mathematical.

I agree with your conclusion that Gödel incompleteness and indecidability do not act as “show-stoppers” when one considers the fundamental relationships between mathematics and physical laws, because “to obtain an inconsistency, we should make the physical laws assert their own indecidability, but how could this be done?”

I also agree with you that the statement that our world is isomorphic to a mathematical structure is a “plain truth that doesn’t make predictions at all, and doesn’t explain anything”, and that any universe complex enough for universal Turing machines to exist could sustain our existence: that’s why, in my essay, I argue that we live simultaneously in an infinite number of larger contexts.

As I said in my reply to your comment on my page, I have some questions concerning your affirmation “at least we know that there is room for free will, whatever this may be”. While formulating them, I followed the trail from your reference pages and fallen into a rabbit hole of cross-linked articles… I will continue to think about this and come back to you soon, whether I have free will to do so or not…

Good luck in the contest… I hope you make it to the top this time!

Marc

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Christinel,

Thanks for the positive assessment of my paper. I gave your paper a pretty high score a few weeks ago. I did this while I was on travel and I don't think I had time to write a post on your blog page. I will try to write a comment, which will probably require rereading your paper.

There is a paper by Schreiber on directly applying HOTT to physics. This is a difficult and...

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Christinel,

Thanks for the positive assessment of my paper. I gave your paper a pretty high score a few weeks ago. I did this while I was on travel and I don't think I had time to write a post on your blog page. I will try to write a comment, which will probably require rereading your paper.

There is a paper by Schreiber on directly applying HOTT to physics. This is a difficult and in some ways foreign way of doing physics. I am less sure about the role of HOTT directly in physics, but rather that a simplified form of mathematics that connects to HOTT will become more important. It is in much the same way that physicists do not employ set theory a whole lot in theoretical physics. However, behind the analysis used by physicist there is point-set topology. We generally reduce the complexity of this mathematics. If I were to actually engage in this I would study the HOTT, and an introduction to HOTT with physics and related web pages on this site, are worth going through.

To be honest it has been a while since I have studied this. I have been working on a homotopy approach to quantum gravity. I mention some of that in my essay. This concerns Bott periodicity with respect to holography. The connection though is rather apparent. There are also some similarities to C* algebra. This work of mine connects with what is called magma, which constructs spacetimes as the product on R⊕V, for V a vector space,

(a, x)◦( b, y) = (au + bv, [x|y] - ab)

where the square bracket is an inner product. This is a Jordan product and the right component is a Lorentz metric distance. This is also the basis for magma, which leads to groupoids and ultimately topos. A more convenient “working man’s” approach to HOTT is needed.

There is my sense that mathematics has a body and a soul. The body concerns things that are computed, such as what can run on a computer. The soul concerns matters with infinity, infinitesimals, abstract sets such as all the integers or reals and so forth. If you crack open a book on differential geometry or related mathematics you read in the introduction something like, “The set of all possible manifolds that are C^∞ with an atlas of charts with a G(n,C) group action … .” The thing is that you are faced with ideas here that seem compelling, but from a practical calculation perspective this is infinite and in its entirety unknowable. This along with infinitesimals, or even the Peano theory result for an infinite number of natural numbers, all appears “true,” but much of it is completely uncomputable.

Cheers LC

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Dear Cristi Stoica

Your essay is clearly written and you included all the essential notions, which are important at explanation, for instance, consciousness. I also look on physics from reductionical view. But, I disagree that neural correlates are enough to explain consciousness. Not only me, Tononi and Koch also claim for panpsychism. Thus neural correlates only explain consciousness in...

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Dear Cristi Stoica

Your essay is clearly written and you included all the essential notions, which are important at explanation, for instance, consciousness. I also look on physics from reductionical view. But, I disagree that neural correlates are enough to explain consciousness. Not only me, Tononi and Koch also claim for panpsychism. Thus neural correlates only explain consciousness in brain, but not panpsychism, primary consciousness everywhere. Thus Duck is not a Duck if everything looks like the same. I think from reductional view that various qualia in brain should be explain from one qualia. Thus despite of all, I agree that everything is isomorphic to mathematical structure of physics, because primary consciousness is only extremely reduced element, which in principle does not disturb this isomorphism. Thus, if the duck is completely the same, it is maybe not duck, but the difference is not important.

In the prolonged version of my essay [reference 1], I describe Turing experiment, which tries to distinguish conscious ''duck'' from unconscious one. The principle is:''Let us suppose that Turing experiment gives distinct answers of a duck versus computer. (Otherwise free will does not exist.) If we respect non-quantum physics, then explanation of free will needs new physics. But a quantum computer always gives distinct answers than a duck, thus free will does not need new physics.''

It is important for me, that consciousnes does not exist without free will.

I agree with you, that theory of everything thus not need two independent set of laws. But Petkov has an interesting idea that gravitational force does not exist. I gave one answer to him, but what is your answer to him?

One good example of precise words of Maluga are: ''Without abstraction, our species with a limited brain is unable to reflect the world.''

Thus math is a process of abstraction. Thus, my conclusion is that the essence of math in physics is to be abstract and simple as much as possible. Because foundations of physics should be simple, the task of math is to describe quantum gravity on a t-shirt.

Because of this reason, and because of intuition I am reductionist also.

Best Regards

Janko Kokosar

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Very boring essay. Such a filling of the maximum allowed length for so little... maybe I'm just already too familiar with the fact that mathematics is the study of structures to have any interest reading it again, but...

Despite your try to develop a visual metaphor to illustrate the question of discovered vs. invented, you did not even come up with any decent answer to this question. Your...

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Very boring essay. Such a filling of the maximum allowed length for so little... maybe I'm just already too familiar with the fact that mathematics is the study of structures to have any interest reading it again, but...

Despite your try to develop a visual metaphor to illustrate the question of discovered vs. invented, you did not even come up with any decent answer to this question. Your illustration by points of a line is more confusing than explaining, since if you take a physical line made of aligned atoms, a physical point in this line as defined by a particular atom can only encode a few words, not even an ordinary sentence. To encode whole texts you need a mathematical line, far from anything concrete or visual (would you qualify this as visual ? I don't). There are not even enough atoms in the visible Universe to be in bijection with all possible meaningful texts of 1 page length. But a decent answer is possible as I explained in my essay : by making the difference between mathematical existence (where all possibilities exist but can be lost in a huge pool of alternatives as soon as they are a bit complex) and the conscious act (or contingent event) of pointing out a particular possibility here and now (which is what the notion of "brilliant text" is actually about).

"Some may hope that there are things in the universe which can’t be described by mathematics. But can you name those things? To name them, you would have to provide a list of their properties, of propositions which hold for them. If the universe is describable by a list of propositions, then there is a mathematical structure describable by the same propositions. But then, couldn’t we find something to say which is true about our universe, but not about the mathematical structure? The answer is no."

Example : the sensation of the red color. I can name it (as I just did). I can list its properties : this is the empty list, since it does not have any mathematical structure. Or maybe I can say that I do not like this color : would you classify it a property of this sensation ? We can also say that it is the color of blood. However, if the sensation of the red color is a property of the sight of blood, I doubt the relevance of this link as a description of the sensation of red itself. So, some things can be said about the sensation of the red color, which does not mean that it admits any mathematical description as a mathematical structure.

"If we can’t [describe it completely by a list of true propositions], it’s only because of practical limitations."

Disagree: if I can't describe the sensation of the red color completely by a list of true propositions, it is not because of any practical limitations, but on the contrary because the list of mathematical structures it is made of is trivial: an empty list.

"We know what a feeling is: some chemistry of the brain"

Disagree. The sensation of the red color surely has neural correlates which can be described mathematically, however these mathematical structures will never account for what this sensation actually is. And it is found in NDEs that many feelings occur far away from any chemistry of the brain. As for the idea that a feeling is some chemistry of the brain, it is still pure speculation from a scientific viewpoint. Feelings must have correlates in the brain of course, but these concepts of chemical correlates in the brain did not achieve any actual scientific understanding of what feelings are and how they work, and I think they never will (if psychiatrists think they do, they are just hallucinating).

"any kind of world, as long as it is free of contradictions, is isomorphic to a mathematical structure"

Unfortunately, this claim looks much less like an expression of amazement at how deep mathematical concepts are involved in physics, than like an expression of lack of imagination to consider any other possibility. In my essay I explained how I consider the world as not a mere mathematical structure since it includes the non-mathematical component of consciousness, even if mathematics takes a large part in it.

"...maybe the universe obeys two or even more sets of laws. This doesn’t make much sense, since if the universe obeys two or even more independent sets of laws, there must be two or more disconnected mathematical structures modeling them. But we can’t live simultaneously in two disconnected worlds."

Looks like you never heard of any intermediate possibility for 2 sets between being equal or disjoint. I see no contradiction in having a world made of a combination of the fundamentally different ingredients of maths and consciousness, as I described in my essay.

You don't even seem to understand what is Godel's incompleteness theorem actually saying. You wrote: "To obtain an inconsistency, we should make the physical laws assert their own undecidability". What the incompleteness theorem says, is that "To obtain an inconsistency, we should make a mathematical theory able to express arithmetic, stating (among its theorems) its own consistency". I admit that your claim is rigorously correct, since, actually, and still according to this incompleteness theorem, the claims of consistency and incompleteness (in a theory able to express arithmetic) are logically equivalent. But... the reason for the correctness of your formulation is so indirect that it makes things even more twisted to figure out than they basically are. Especially given your previous sentence: "If a man states the undecidability of some problem in physics, would this introduce an inconsistency in the universe? No, since the statement can simply be wrong". If consistent theories able to express arithmetic are unable to prove the claim of their own undecidability, it is not because this claim can be wrong, but on the contrary because it is right: these theories are undecidable, which is why they are unable to prove some true facts, such as the fact of their own undecidability.

And I see no justification for your implicit assumption that the laws of physics should be able to express arithmetic, as I disagree with this claim (see my essay).

"the only prediction made by the mathematical universe hypothesis is that our universe has to be Turing complete"

I answered about the issue of predictions of the MUH in reply to Marc Séguin's essay.

In your previous essay "Flowing with a Frozen River" you described a possibility for free-will in a way that seems to be the same as I support, except that you seem to attribute free will to a retroactive effect on the initial conditions. Maybe because you use your own variant of quantum mechanics, "Smooth quantum mechanics", while I accept quantum mechanics in its standard formulation, and I attribute randomness to the event of wavefunction collapse by conscious observation, which I qualify not as a physical event but a metaphysical one (so that the discontinuity is not something physical, it is not located in the physical space-time). It looks like your interpretation is just a twisted rewording of the "discontinuous collapse of the wave function" into a "retroactive discontinuous collapse of the initial conditions" from which the present state would be a posteriori re-determined by the continuous quantum evolution, and which is just mathematically equivalent to the former, but only coming as an illusory way to deny that anything here is discontinuous.

So it looks like, your special way of wording your interpretation through this mathematical reformulation is just hiding the fact that we have essentially the same interpretation, which I invite you to read in my essay.

But... no, there is still a difference, by which I would qualify your version as incoherent: the problem I see with your interpretation is that the new observations do not just complete the previous ones, but can also be incompatible with them (in the sense of non-commutation). Thus, the new initial conditions are turning past states into thermodynamically incoherent states (such as with the story of "liar states" which I commented there), retrospectively changing past clear observations into indeterminate ones, and finally, changing the big bang into a combination of initial conditions mixing the smooth big bang that normally explains things (the thermodynamic time arrow) with highly chaotic initial states with multiple singularities and so on, where the thermodynamic time arrow cannot be found anymore.

In your text "Modern physics, determinism and free will", you make a distinction between "branching time" and "choice time". But what is the role of a "branching time", that would not be the same as "choice time" ? I cannot see a role for it. Nothing in the formalism of quantum physics, speaks about "branching" as a fundamental event. Proponents of the Many-worlds interpretation saw it well, as they just dismissed the existence of any branching, to conclude that different possible measurement results keep coexisting, not really as branches from any specific branching event (as might be intuitively said for approximative descriptions), but as emergently separable components of the unitarily evolving state, which remains a unique physical state that only happens to be equal to a combination of these practical measurement results (without being directly affected by this fact). As David Wallace wrote : there is no such a thing as a well-defined "number of branches". Instead, in my view, all what plays the role of a branching time, is what you call the choice time; it needs not be retroactive, but only non-local (see details). So, since other interpretations (Bohm and Many-worlds) just deny the existence of any special measurement times at all, I think that introducing 2 different special times, one for branching, the other for choice, is a bit too much.

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Dear Cristinel,

Lots of sweeping statements in this essay and many attempts to refute other arguments without sufficient logic or evidence and more of of attempts to persuade with a general sweeping comment (where is your evidence for "Even if we manage to extend the list with new truths about the universe, there is a mathematical structure which is isomorphic to the universe described by...

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Dear Cristinel,

Lots of sweeping statements in this essay and many attempts to refute other arguments without sufficient logic or evidence and more of of attempts to persuade with a general sweeping comment (where is your evidence for "Even if we manage to extend the list with new truths about the universe, there is a mathematical structure which is isomorphic to the universe described by the extended list of propositions" or "Any phenomenon related to time, for example memory, can in principle be described mathemat- ically.").

The main issue I think you should consider is the evolutionary character of mathematics. Mathematics is not a constant where the universe could or could not be isomorphic to it. Mathematics and physics have grown together. For a couple millennia Euclid's fifth postulate was considered to be True, yet a little over 150 years ago it was shown to be one of a few options (it was only true in certain circumstances, so not all circumstances everywhere). Can we say that the universe was isomorphic to Euclildean geometry in 1800, but not now? Our current physics would not be possible without this fundamental change in mathematics beyond Euclid. Since we are all limited to our current time in history, we are limited in what we know of mathematics, which could be, even today, a very small amount.

You also seem to think mathematics is itself consistent and complete, which is impossible to prove (and Godel's proof indicates otherwise for completeness).

Finally, you appear to think that the universe does not have contradictions in it, something that defies all evidence we have at the moment (if reductionism is correct, why is an intelligent being at our scale needed to understand it and to affect the very small as part of the understanding process?) - so this must be an article of faith on your part, which extends as much to mathematics as to the known universe.

Thank you for your essay, but I an unconvinced by your arguments.

Donald

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Now I more closely examined your article "Modern physics, Determinism and free-will", for properly replying to what you actually put there (sorry I was not careful enough last time). Indeed, I confused between your "interpretation" that you support, and your (incorrect) description of the wave function collapse with the role of free will in wavefunction collapse (that you criticize). I see now...

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Now I more closely examined your article "Modern physics, Determinism and free-will", for properly replying to what you actually put there (sorry I was not careful enough last time). Indeed, I confused between your "interpretation" that you support, and your (incorrect) description of the wave function collapse with the role of free will in wavefunction collapse (that you criticize). I see now they were separate sets of concepts.

About your own "interpretation":

"even though the states |ψ^j₀ 〉 were obtained by a unitary operator from the orthonormal states |ψ^j₁ 〉, they are not necessarily orthonormal, and may even become dependent. In fact, in our case they all become at t₀ equal to |ψ₀ 〉. The operator U is a unitary operator on the total space of |ψ〉|η〉, but not on the space of |ψ〉. This shows that it is possible for |ψ〉 to satisfy the constraints of both observations, and still have unitary evolution"

Assuming for a moment that such ideas make sense, then why do you need the evolution to be unitary in the "total space" |ψ〉|η〉 ? After all, this system is only a subsystem of the Earth. So, if all we need is that the evolution is unitary for the Earth system then the evolution of its subsystems do not need to be unitary. By the way, where is the assumption of unitarity in QM ?

Now seriously : according to the rules of established QM, what your claim rigorously means is that the first measurement device (that made the first measurement) keeps physically interacting with the system during the time between measurements, so as to progressively align it with the basis of the second observable. Such a claim of interaction is just plain wrong. In reality, after the first measurement, the system no more interacts with the first measurement device, and even if a little bit of influence might subsist, it would be ridiculous to assume that this interaction systematically manages to align the system to one eigenvector of the second observable. You seem to attribute this coincidence to final causes: you seem to argue that there should exist possible initial conditions that make the evolution fit this condition, so that the presence of the second measurement will retroactively arrange the initial conditions to make all things fit so as to achieve this evolution of the system from the eigenstate of the first observable to the eigenstate of the second observable. I consider this as a mere dream since anyway, in good approximation, there is not supposed to be any interaction between the first measurement device and the system after measurement, so that no fine-tuning of the apparatus can make its non-existing interaction with the system succeed to align it with eigenvectors of the second observable.

"In UIQM I acknowledge that the observed system is in fact entangled with all systems with which it interacted in the past."

Not entangled, but in continuous physical interaction. You are confusing between (the mathematical expressions of) entanglement and physical interaction.

In conclusion, your "interpretation" of QM is not an interpretation at all but some fantasy, another theory far from what QM actually says. Now since you did not explicitly claim to reject QM to develop your own theory, but kept giving the illusion that you respect it and only try to interpret it by keeping superficial similarities ("unitary evolution"...), it just shows that you have no serious understanding of quantum physics.

Now about your discussion of standard QM and the mind makes collapse interpretation:

"If humans base their choices on random inputs, then this by itself doesn’t make them free."

Of course but only under the assumption that the inputs are actually random in the case under consideration. As I explained in my interpretation of QM, I consider that the same process of wave function collapse usually obeys randomness in non-living systems, but departs from it in the cases of brain processes where free will applies. And I explained in length why I see this sort of "discrepancy" between the kinds of outputs of the same physical process of wavefunction collapse (normal randomness in "purely physical systems", vs. free will in the brain), to be not a discrepancy at all but a very elegant, coherent solution. (I also like the explanation by the last reply of that thread).

"The configuration after the branching has to evolve, so that the agent can see where it is going"

Where does that idea come from ? I see no reason for it. My view is that the collapse occurs at some time after decoherence, when the different possibilities are meaningfully distinguished by the observer; there is no need to assume any branching to have occurred before that time, nor to assume that the observer has any explicitly conscious perception of the alternative possibilities among which he is actually (more or less) choosing.

"in the case of quantum mechanics, where the unitary evolution governed by Schrödinger’s equation is interrupted from time to time by the wave function collapse. Assuming that an agent uses this randomness to perform free choices, she must act precisely at the appropriate moment and position where the branching appears."

"(The discontinuous jump) has never been directly observed. There is no known explicit process leading to the discontinuity. In fact, all interactions we know fit well in the Hamiltonian description, and the measurement devices are made of systems which obey it. So, where does the discontinuity come from?"

Indeed, if taken separately, these 2 issues would be problems. However, taken together they become zero problem as they resolve each other. Indeed, there is no definition of when the collapse occurs ? It looks like a mystery how the time of free choice may coincide with the time of collapse ? No problem : let the "time of collapse" be conventionally defined as given by the time of free choice. Then, there is no more mystery when and how the collapse occurs, and there is no mystery either how the time of choice may happen to coincide with it.

"It would violate the conservation laws". This is one of my objections against spontaneous collapse theories. But my interpretation of the collapse is different : I think it occurs not by projection but by selection of a world after decoherence (this is an emergent condition, that fits with my idea of collapse as a non-physical, non-local process) : it is still non-unitary but resolves some defects of the projection postulate. It does not satisfy the conservation laws if taken in a naive sense (expressed by averages) that you wrongly assume to be the necessary form of expression of the conservation laws, but does satisfy a more subtle understanding of the conservation laws that I explained there.

Generally, my page on the mind makes collapse interpretation replied to all of your objections in your "2.2. The internal tension of quantum mechanics".

"I find hard to believe that the environment is the cause of selecting the eigen‑states, because these depend only on the measurement device. Change the measurement device, and leave the rest of the environment unchanged, and the eigen‑states change too."

You missed that the role of the environment in decoherence happens by interaction with the measurement device. So, change the measurement device, leave the rest of the environment unchanged, then the environment will interact with the new measurement device to do the decoherence according to the new eigenstates given by the new measurement device.

You speak about the "decoherence interpretation" as if it was an option to accept or reject it. The reality, well-known by all serious participants in QM interpretation issues, is that decoherence is NOT an interpretation but a logically necessary consequence of established QM, completing the picture of what needs to be interpreted.

I stopped reading your article here. I consider that I found enough fatal flaws in it already. And I see it as a big bug in the academic system, to find such an incompetent "physicist" have any position as physicist there.

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Dear Cristi

I really enjoyed reading your beautiful essay.

Here some considerations.

(1)" A universe in a dot". This is a lovely peace of writing. It reinforces my conviction that the principle of finite information density must hold, as Feynman himself believed (see his 1982 Int. J. Th. Phys.) The continuum is paradoxical: you can write the whole history of the universe on...

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Dear Cristi

I really enjoyed reading your beautiful essay.

Here some considerations.

(1)" A universe in a dot". This is a lovely peace of writing. It reinforces my conviction that the principle of finite information density must hold, as Feynman himself believed (see his 1982 Int. J. Th. Phys.) The continuum is paradoxical: you can write the whole history of the universe on a single atom. This is also related to the following point (3)

(2) I totally disagree with Smolin on many things, even if I enjoyed reading most of his books, in particular Time Reborn where he already expresses his new ideas that you can also find in his current essay taken from his last book. The two main things I disagree on are: (2a) the physical laws are not constant; (2b) mathematics cannot describe “particularities”. I think that both assertions are unscientific according to Popper.

(2a) Imagine a physical law that changes every minute, and you don’t know how it does. It is not a law anymore, right? What about if it is valid for a year, or a billion of year, or not valid e.g. two billions light-years from our planet. What should be the validity time (and space) of the law? If we state a law, it is supposedly eternal. This, however, does not protect the law from possible falsification, which will ask for another law, yet supposedly eternal. In particular, the new law maybe a “meta-law“ which regulates the change of the falsified law.

(2b) A theory cannot describe “reality as it is”. It can describe/predict only connections between known conditions/preparations/events and observed facts. Inferring initial conditions in the past needs an increasingly larger knowledge of the current state, the more distant is the past from the now. We can only connects known facts with known facts, or predict facts from known facts: the theory cannot provide the initial conditions. If we want to predict what will happen, we need information about the past. Accounting for the Smolin’s “particularities” requires the knowledge of the initial conditions, otherwise it is not science: it is magic.

I love your ideas about “Is everything isomorphic to a mathematical structure?”. I agree with you that the answer is positive, and I enjoyed very much this part of your essay. I think that the point, however, is another one, and again it is about “what is theory”. A theory is a reduction of complexity of connections between events/observations. Transforming a set of observations (a peace of “reality”) into a list of propositions does not necessarily entail a complexity compression, it is not a theory. Suppose I give you the observation made of the following digits:

3.1415926535897932384626433832795028841971693993751058209749
445923078164062862...

A good theory would be the Plouffe formula that fits in few bits.

Also, as Poincaré says, the power of mathematics stays in the induction method, which produces an infinite compression of true statements. This is also the case of a physical law.

It would be too long to write everything I would like to say ..,

I hope to meet you again very soon and have a long discussion of philosophy of physics at a dinner table.

My best regards

and compliments again

Mauro

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Daer Cristinel

I find your essay very interesting, indeed, I consider mine an extension to it. I agree on almost everything.

I believe, that the universe is "an hyper-equation". "A mathematical structure inside an other, and depends on another external"

"Mathematics and physics are two sides of the same thing. numbers and physical entities in motion”.

Now, I think...

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Daer Cristinel

I find your essay very interesting, indeed, I consider mine an extension to it. I agree on almost everything.

I believe, that the universe is "an hyper-equation". "A mathematical structure inside an other, and depends on another external"

"Mathematics and physics are two sides of the same thing. numbers and physical entities in motion”.

Now, I think we need concrete things from which we can start. For this. I proposed The Paradigm Bi-iterative: a concept that goes beyond quantum mechanics and general relativity.

Quantum mechanics is not enough, General Relativity is not correct. Maybe, that's why it was impossible to combine the two branches of modern physics. Therefore, it was necessary to introduce the mechanics iterative, as the source, to justify the origin of acceleration, force and time. In addition, the rhythm and the polarization.Two mechanics seemingly separate, connected with a constant, only in this way, we can unify them.

I am convinced that reality is made up of thin numbers and geometric shapes. For this, I have proposed a Theorem and various mathematical structures (see Annex), which in my opinion, could be the true universe's mathematics.

The Bi-iterative system's calculation considers reality multi-directional and multi-dimensional. with (1) we mean (1 * 1 * 1). while, the recursive computation and the Fibonacci series uses only the first, the fractal uses the first and the second. So, are wrongly linear, interprets reality on a bi-dimensional sheet. Instead, the system Bi-iterative uses all three.

Let's take an example:

(1 + 5 + 7 + 12) =

                           = 1 + 5 + 7 + (6 + 8 + 10)

                           = 1 + 5 + 7 + (3 + 4 + 5) + 8 +10)

                           = 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10

                           = 1 + 5 + 7 + (3 +4 +5) + (1 + 6 - 9) + 10

                           = 1 + 5 + 7 + (3 +4 +5) + (1 + (3 + 4 + 5) - 9) + 10

                        

     
                      = 13

= 2197

This structure is compact, inside it could coexist other structures indipendent.

which can be expressed also in a linear fashion:

(1 + 5 + 7 + 12) = 13 = 2197

                            
= (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5) + (6,5): A straight line.

“A complex and varied reality , can be described only with a structure capable of transforming”.

This sequence is like a clock going always forward, or rather, reflecting itself, coping itself.

( a + b + c + d ) + K

(1 + 5 + 7 + 12) + K

In agreement with the concept of light propagation and the distribution of mass and energy, fairly, K is a constant equivalent to (1) ....... + 1, + 1, + 1, + 1, + 1 ........

"The universe was born so, one bit after another, and continues to do it today."

Sincerly yours

Bannouri

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