Dear Flavio and Chiara

Your essay is a very high quality work, mainly as a critique of the physical sciences for determining what is fundamental.

A very in depth discussion of the Popperian falsificationism, as applied and adapted by physicists in different frontiers of physics.

It is a very good methodological application of epistemology for "demolishing the prejudices" implicit in the construction and falsification of scientific theories in physics.

But it ends abruptly without constructing or proposing an epistemological methodology for establishing what is and what is not fundamental in science, avoiding the biases of reductionism and implicitly accepted traditional conceptions. This would have made a superb closing for this essay.

    Dear Del Santo and Cardelli,

    Your paper is very well written. Your focus on no-go theorems with respect to quantum mechanics is a good overview of that area. It is as you indicate the case that modern physics does lean on such ideas. In relativity there is something similar with the invariance of the interval that gives a "no-go" theorem result that information and matter must move at the speed of light or slower.

    These bounds on quantum mechanics and no-go theorems such as no-signaling and no-cloning have interesting analogues with spacetime. For instance we have the no-cloning theorem that a quantum state |П€> can't be cloned in a unitary transformation |П€> в†' |П€>|П€>. This can be seen if we write this quantum state as |П€> = a|1> + b|2> so this cloning is

    |П€>|П€> = a^2|1>|1> + b^2|2>|2> + ab(|1>|2> + |2>|1>),

    but cloning on the basis {|1>, |2>}gives

    |П€>|П€> = a^2|1>|1> + b^2|2>|2>.

    This means cloning is basis dependent, which violates unitarity. This connects with spacetime physics if we assume we have a spacetime has a wormhole. A wormhole where one opening is transformed under a succession of Lorentz boosts or a send and return motion will exhibit closed timelike curves. It would then be possible to clone a quantum state. An observer with the quantum state |П€> will have a copy appear so that |П€> в†' |П€>|П€> if that observer later throws one |П€> into the wormhole.

    The types of spacetime solutions that may exist could then be constrained by quantum no-go theorems and restrictions on quantum measurements. I wrote a paper last year on a correspondence between the Tsirelson bound and the invariant interval of spacetime and how spacetime is built from entanglements. In general we then have that spacetime physics and quantum mechanics are mirrors of each other. The limits in both of these areas are then specific manifestations of the same constraints. It could be that the ultimate foundations of physics is just plain vanilla quantum mechanics.

    I wrote an essay that attempts to look at this correlation between quantum mechanics and general relativity. In part I attempt to look at empirical ways of supporting or falsifying this. At any rate I enjoyed your essay

    Cheers LC

      Dear Mr. Aybar,

      thank you for your comments.

      You are indeed write that we do not propose a new methodology that can open up frontiers even more.

      What we showed is that (1) we should not rely on very intutive thought, that incorporate prejudices, a reductionist approach, and naive empiricism as a methodology. Falsificationism surely brought new ways of testing a new variety of phenomena.

      We will anyway take your suggestion to further develop our ideas.

      Best wishes,

      Flavio

      Dear Mr. Crowell,

      thank you for your appreciation.

      As I state in the essay I strongly believe that results such as no-signaling theorem and its relativistic analogous no-fast-than-light-movement are the most fundamental that we have so far. They might change and be surpassed, possibly in different methodological framework (but who knows?). The fact that such constrains arise from different theories, are surely a fuerther evidence of fundamentality, in my opinion.

      I was not aware of the connectionof no-cloning with relativity that you point out. I will have a look at it.

      I look forward to read your essay. Very many thanks once again for your kind remarks.

      I wish you success,

      Flavio

      Chiara and Flavio

      Your idea that we should look for very basic assumptions and prejudices is in good agreement to my article. I regard the confusion in physics to be started before Einstein and even before Lorentz and in reality due to Stokes.

      I therefore think that it would be very interesting to here your opinions about my article. So, I hope that you will take a look at Fundamental Errors in Physics.

      Regards from ______________ John-Erik Persson

      Dear Del Santo and Cardelli,

      I found your essay very interesting, systematic and well written, and voted it very high, congratulations. Sadly I was lost in the §3.1 due the lack of mathematical tools - my formation is in philosophy.

      Anyway, you wrote that "the search for foundations is a dynamical process that aims at removing "philosophical prejudices" by means of empirical falsification.". I was wondering, could we consider also "empirical falsification" like a possible philosophical prejudice?

        Deat Mr. D'Isa,

        thank you for your very kind comments.

        It could well be the case that falsification is not the definitive methodology (and indeed, as you know even better than I do, most of modern philosophers of science do not adhere to falsificationism). What our essay tries to show is that within falsificationism we can strive for a systematic demolition of prejudices in our theories. And also with our examples we support the idea that falsificationism is what scientists are doing every day (or at least what they are convinced to do). But surely, a different methodology can lead to possibly surpass this.

        However, if is the empirical part that you would like to remove, than I cannot agree, because otherwise we are not doing natural science: we can do mathematics, art, or any kind of beautiful and imaginative activities, but that have nothing to do with the "world".

        I will read soon also your essay, that is in my list of the ones worth reading.

        Thank you again, and I wish you the best of luck!

        Flavio

        Dear Flavio,

        thank you for your reply. I understand your point, and as I said I find your theory useful and well argument. I agree that within falsificationism we can strive for a systematic demolition of prejudices in our theories.

        I have to partially disagree in what you said in the last part of your comment: it's true that empirical facts are necessary to natural science, but it's not true in my opinion that mathematics, art or other disciplines have nothing to do or to say (and I mean something true) about the world, even if within different languages. But maybe I misunderstood your statement.

        Thank you again, I wish you luck! In bocca al lupo (by your names it looks like you are Italian) ;)

        Francesco

        Dear Francesco,

        thanks for your further reply.

        Surely I didn't mean that maths is useless or meaningless in natural science. Far from me this! I only meant that is somethnig different, but I think we pretty much agree.

        I am reading your essay and will comment in the dedicated page.

        Crepi il lupo! And in bocca al lupo anche a te!

        Flavio

        p.s.

        Sono nato e cresciuto a Firenze, dove vedo che tu hai studiato

        Thank you for your reply as well.

        (Crepi! Allora oltre che connazionali siamo anche concittadini, perché sono nato e cresciuto a Firenze pure io, e attualmente ci abito :)

        Hi Stefan,

        What is fundamental? I see it my business to ask whether or not so called no-go theorems may be questionable. In other words, are these claimed theorems and their interpretation in physics really fundamental or are they merely the fundaments of something called by Einstein's castles in the air?

        I tried to explain without any emotion why I consider causality a most indispensable basis.

        I am however disappointed if experts ignore my strict distinction between established theoretical constructs and what I defined in a previous essay as conjectured reality. Wigner's delayed choice gedanken didn't persuade me that it isn't reasonable to accordingly strictly distinguish between ideal past and ideal future in reality.

        An ear is definitely not aware of the chosen reference point for time.

        I consider this a most fundamental in the sense of undeniable fact, and I hope, at least you will agree on that.

        Eckard

        Flavio and Chiara--

        I found your essay very interesting and stimulating. Although your essay is more rigorous and technical than mine, we actually cover some of the same ground and arrive at some similar conclusions (e.g. about the limits of reductionism). Also, in addition to being less formal, my essay argues for some conclusions that are a bit different than those you argue for here. I hope you will have a chance to read my essay and comment on it, I'd be interested in your analysis.

        Meanwhile, I have a few brief comments on your essay to offer some (hopefully) constructive criticism. Regarding what you call "fundamental constraints," my issue is that I don't believe that we can establish those reliably. Historically, what seemed like a fundamental constraints in one time period was sometimes found to not be so--how can we know what we don't know? Regarding Popper, it's true that philosophers dispute his approach and that scientists typically quote him approvingly, but I disagree with the contention that scientists behave in accordance with Popper's dictums. If you examine what scientist do instead of what they say, you find very little to support Popper. For a more sophisticated alternative view, I think Polanyi was a much better thinker. On a related note, it seems like you are not taking into account at all the Quine-Duhem thesis and underdetermination more generally. Well, I'll leave it at those comments for now. Thanks.

          Dear Gregory,

          many thanks for your kind words, and for the very interesting end relevant comments.

          About 'fundamental constraints', you write "I don't believe that we can establish those reliably". Indeed, as I point out several time, this is a methodology-dependent definition. What is important is actually that we have defined a dynamical process that is irriversible, due to the falsification (so far accepted methodology in some form). As I showed, the problem with phenomena the likes of violation of no-signaling theorem would violate a cause-effect relation and, as such, they undermine the very possibility of empirically test them. However, I do not exclude that a possible methodology beyond falsificationism can in principle test such constraints and remove them. But until there is the most fundamental we can think of.

          About your statement: "If you examine what scientist do instead of what they say, you find very little to support Popper", I actually agree in some cases (not always, though). However, in my essay "We just assume as a working hypothesis

          - build upon a number of instances - that this is what scientists do, or at least what they are convinced to do: this is enough to lead them to pursue certain (theoretical) directions." What I mean by this is that scientists actively propose their line of reseach with an aim and a (more or less consciously) methodology in mind, and this actually has tangible consequences on scince (i.e. my example of no-go theorems).

          thank you again, and I will have a look at your essay soon.

          Good luck!

          Flavio

          Dear Gregory,

          many thanks for your kind words, and for the very interesting end relevant comments.

          About 'fundamental constraints', you write "I don't believe that we can establish those reliably". Indeed, as I point out several time, this is a methodology-dependent definition. What is important is actually that we have defined a dynamical process that is irriversible, due to the falsification (so far accepted methodology in some form). As I showed, the problem with phenomena the likes of violation of no-signaling theorem would violate a cause-effect relation and, as such, they undermine the very possibility of empirically test them. However, I do not exclude that a possible methodology beyond falsificationism can in principle test such constraints and remove them. But until there is the most fundamental we can think of.

          About your statement: "If you examine what scientist do instead of what they say, you find very little to support Popper", I actually agree in some cases (not always, though). However, in my essay "We just assume as a working hypothesis

          - build upon a number of instances - that this is what scientists do, or at least what they are convinced to do: this is enough to lead them to pursue certain (theoretical) directions." What I mean by this is that scientists actively propose their line of reseach with an aim and a (more or less consciously) methodology in mind, and this actually has tangible consequences on scince (i.e. my example of no-go theorems).

          I will read your essay soon.

          Best of luck,

          Flavio

          Dear Flavio and Chiara,

          Thank you for a beautiful essay and well done criticism of some of the current prejudices in science. I agree with most of your criticism, including of conventionalism, reductionism, the pop-Popperianism which pervaded much of current research. Not that I would find the current situation wrong, I think that it was expected (1) since we departed so much of the possibility to easily falsify our ideas, much of the gestation of a theory can inevitably be based much more on deduction and mathematics and less to physics than it used to be, and (2) we need to develop and explore so many possibilities to explain the world, that it is unavoidable that a large part of them would simply fail. These problems, along with the current pressure to publish, led to a very difficult situation. So it is important to go at least once in a while back to square zero and reconsider our methodology. Maybe I look a bit like devil's advocate of conventionalism, but I am not, I just try to understand the reasons of this situation. After all, despite a spread belief that Popper invented the scientific method, I think what he actually did was to describe it by looking at the most successful theories of that time, particularly special and general relativity. Since 100 years passed since then though, we should expect an improvement of the scientific methodology, but this didn't happen. By contrary, due to the current crisis, more and more voices advocate an evasion from Popper's demarcation. And it is in fact what already happened in practice.

          I like the proposed solution, which you exemplified with no-go theorems about quantum mechanics and explained very well. In the previous edition, in my essay, I used these no-go theorems as illustration of what I meant by metalaws, not in the same way as you did though.

          I like how you closed, "We have shown that the search for foundations is a dynamical process that aims at removing "philosophical prejudices" by means of empirical falsification." Of course, some may want to conclude from this that, to avoid "philosophical prejudices", one should avoid philosophy, but I would say by contrary. Even though some philosophers are caught themselves in some prejudices about various ideas in physics, and a handy example is the quote you gave from Feyerabend, who seems to adhere to a widespread idea among philosophers that the debate about the foundations of quantum mechanics was about determinism, when this was in fact just incidental. If he was right, then for those who accept indeterminism there should be no foundational issue in QM, but there still are.

          Very good essay, I wish you success!

          Best wishes,

          Cristi

            Dear Cristinel,

            I am flattered by your kind words. Thank you for your very interesting comments.

            As you have pointed, I accept indeed the descriptive, and not the normative, aspect of Popper's falsificationism. I truly believe that whether it is what scientist do or otherwise, their conviction is enough to lead them to pursue a falsificationist approach to foundations of science. No-go theorems are in my view the clear expression of this research program, they would not arise from simple inductive observations. And, in fact, falsificationism it is a deductive process that start with "bold conjectures" and as you highlight from mathematics. Then it requires as a final judje the experiment though, but I don't see a strong divergence between our views.

            Thanks so much again.

            I wish you the best of luck!

            Flavio

            Interesting essay, but I have found something to object:

            " forPopper, a statement is scientific if and only if it can be formulated in a way that the set of its possible falsifiers (in the form of single existential statements) is not empty"

            I disagree because this misses the important distinction between particular statements and scientific theories. Particular statements are almost always unfalsifiable, to obtain falsifiable statements one needs complete theories, and (if one takes into account Quine's arguments for his holism) even a lot of different theories. Popper has discussed this somewhere in Conjectures and Refutations.

            Then, there is no "impossibility of instantaneous signaling implied by both quantum formalism and special relativity". The impossibility is purely relativistic, non-relativistic QM has no limiting velocity.

            "Indeed, a theory that would violate this condition allows for instantaneous signaling and it thus would mean a failure of the scientific method as we conceive it. It would be in principle not falsifiable"

            This is wrong. Only a particular observation which falsifies relativity would not falsify this theory. The theory could make a lot of other falsifiable predictions. For example, such superluminal signaling would define a preferred frame. A natural falsifiable prediction would be that this is the CMBR frame.

              Dear Schmelzer,

              let me start replying from the most unfortunate of your comments. You say:

              "Then, there is no "impossibility of instantaneous signaling implied by both quantum formalism and special relativity". The impossibility is purely relativistic, non-relativistic QM has no limiting velocity."

              What you say is just wrong. The no-signaling theorem, which I have illustraded in my assay too, is derived ONLY using the non-relativistic quantum formalism. It proves that QM lies within the boundaries of instantaneuos signaling. Your comment that make use of the word "velocity" is obviously inappropriate because it is clear that I never made any claim on speed limits, but on the possibility of having instantaneous signals.

              Also your comments on Popper's I think are based on some common misconceptions, but I will comment separately on them.

              Regards,

              Flavio Del Santo

              Hi Flavio Del Santo

              Hi Chiara Cardelli

              Wonderful demonstration... "how the current scientific methodology entails a certain kind of research for foundations of science, which are here regarded as insurmountable limitations." to get to the foundations dears Flavio Del Santo and Chiara Cardelli............. very nice idea.... I highly appreciate your essay and hope for reciprocity.

              I request you please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

              Some of the Main foundational points of Dynamic Universe Model :

              -No Isotropy

              -No Homogeneity

              -No Space-time continuum

              -Non-uniform density of matter, universe is lumpy

              -No singularities

              -No collisions between bodies

              -No blackholes

              -No warm holes

              -No Bigbang

              -No repulsion between distant Galaxies

              -Non-empty Universe

              -No imaginary or negative time axis

              -No imaginary X, Y, Z axes

              -No differential and Integral Equations mathematically

              -No General Relativity and Model does not reduce to GR on any condition

              -No Creation of matter like Bigbang or steady-state models

              -No many mini Bigbangs

              -No Missing Mass / Dark matter

              -No Dark energy

              -No Bigbang generated CMB detected

              -No Multi-verses

              Here:

              -Accelerating Expanding universe with 33% Blue shifted Galaxies

              -Newton's Gravitation law works everywhere in the same way

              -All bodies dynamically moving

              -All bodies move in dynamic Equilibrium

              -Closed universe model no light or bodies will go away from universe

              -Single Universe no baby universes

              -Time is linear as observed on earth, moving forward only

              -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

              -UGF (Universal Gravitational Force) calculated on every point-mass

              -Tensors (Linear) used for giving UNIQUE solutions for each time step

              -Uses everyday physics as achievable by engineering

              -21000 linear equations are used in an Excel sheet

              -Computerized calculations uses 16 decimal digit accuracy

              -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

              - Many predictions of Dynamic Universe Model came true....Have a look at

              http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

              I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

              Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

              In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

              I request you to please post your reply in my essay also, so that I can get an intimation that you replied

              Best

              =snp

              Dear Flavio and Chiara,

              What a lovely and insightful essay! We have reached remarkably similar conclusions. I have written more extensively in reply to your comments on my essay, "Reductionism Is Not Fundamental."

              A few additional comments: I was especially impressed by your treatment of Bell-type theorems, which you have done very elegantly and philosophically. In addition, I read and studied your arXiv paper on the new no-go theorem, your ref. [30]. It is exactly the type of "outside the box" thinking that modern theory needs.

              And Chiara, your algorithm for the correct folding of proteins is fascinating. It's neat that you can get a reasonable M just with directionality added to the toy blocks. Does adding additional characteristics of specific amino acids, such as the potential for hydrogen bonding, limit the value of M to one or a few "correct structures? Organic and/or biochemists should like your model, for they are adept at playing with realistic toy structures.

              All in all, a very impressive piece of work.

              Cheers,

              Bill