Phil,

Very nice article. My argument for why the black-hole information paradox is not true would rest largely on the idea that the orthogonal states of the density matrix are at best approximate in nature. So while the density matrix can be defined as a collection of pure states of a statistical ensemble, the pure states are at best approximations of the system itself. The underlying uncertainty ensures that there is a retention of information even when that system is thought to "collapse" into a definite state. It is only at the limit of measurements of single particle systems that we can be definite about the purity of states.

In other words, the nature of the yes/no questions are always hampered with a distribution. We can say they are mostly true or false based on observation, but only with including a confidence interval about those mean states.

On Constrained Perception

    This is the only essay I have read so far that required me to look up word definitions in the English (Oxford of-course) dictionary. Leave it to a Scot to keep an American informed about the proper use of English. Well written. Introduce me to the notion of bi-geometry. A strong attempt to further relate Lie-geometry to (super)string theory.

      Mauro, the digital vs analogue question was the topic of the essay two years ago so it is not my emphasis in this essay. There as here I take the view that quantised information made of qubits has analogue as well as digital features. It has never been my position that the foundations of physics are based on pure digital information in the form of bits.

      The analogue side comes from the uncertainty which is realised through quantisation or multiple-quantisation. I think I could not have made the importance of this clearer given the title of the essay. If I had to give my own short slogan it would be more like "it from qubit" or even "it from ...quququbit"

      The "It from Bit" question is not so much about digital vs analogue as about emergence. This has also been a common theme in all my previous essays where I have discussed emergence of locality, causality, space and time. My contention is that the foundations of physics take an purely algebraic form where space and time are emergent. I have argued in this essay that the holographic principle implies a large redundancy of information when physics is viewed as a theory in space and time which suggests that a "complete" symmetry plays a role in the emergence. My fundamental formulation is therefore in terms of pure algebras defined by multiple quantisation but independent of space and time. These are infinite dimensional Lie-algebras defined over the complex numbers so there is an analogue nature to physics already at this level. I do not expect the analogue nature of physics to be purely emergent.

      As for the reference to string theory you should be aware of the modern view that string theory is just part of the larger framework that includes quantum field theories. It is of interest because of its ability to bring gravity into the picture. I do not adhere to the view that it will provide a conveniently unique formulation of particle physics. I think that is a view which is fading in popularity. We now have to accept that such a theory is a long way off and concentrate instead on the underlying principles to understand the relationships coming from dualities and how these lead to emergence. Hoefully when new experimental BSM data is forthcoming we will be in a position with the theory to understand it.

      I have been looking at necklace lie algebras in this way for nearly twenty years and have seen many new ideas appear in the mainstream that follow the same principles. Permutations of the qubits extend to larger infinite dimensional symmetries which should resolve to diffeomorphism invariance as space and time emerge. You can compare this to what happens in quantum graphity for example. More recently we have seen new work on scattering theory in planar 4D SYM where permutations of states are of fundamental importance. The super conformal symmetry in space-time is joined by a new dual superconfirmal symmetry in momentum space and the completion of these symmetries defines an infinite dimensional Yangian symmetry which is similar to a necklace lie algebra. It is natural to turn this round and assume that the Yangian symmetry is the fundamental idea and that space and time are emergent along with locality, causality and unitarity. In the last few years this has become a very active field of research which is philosphically and mathematically very similar to what I have been looking at for many years.

      Iterated integration also arises in scattering theory as a process that recursively generates the polylogarythmic amplitudes. I have recently learnt that the free Lie algebra is a simple form of necklace algebra that can be mapped to a continuous space using iterated integrations. This is what I have described in my essay. It is just a small part of the whole picture which is too big and as yet incomplete to describe in more detail. The hope is that similar mappings could be used on my earlier necklace lie algabras in the same way.

      I hope this gives you a better picture of how my ideas fit in to the bigger picture. I am sorry that you seem to have gotten a completely upside down impression of what I was trying to say. Others have graciously complemented me on the clarity of my exposition so perhaps you just need to read it again more carefully.

      Dear Philip

      thank you for your thorough response. I believe in the value of simplicity of the starting principles of a theory. It seems to me that the Lie algebras are not good starting principles: they relate to continuous symmetries of something else. But I surely miss the conceptual points within the math. Also, we have too different background and motivations.

      My best

      Mauro

      Mauro, yes we seem to have different approaches. I do not place a high value on simplicity. I like consistency arguments where we try to put known theories together to form a new theory consistent with both in places where they clash. The maths this generates is not always simple but the constraints of consistency can be strong and lead to mathematical structures you would not find by any other means.

      Sorry I missed this earlier as the post was collapsed in the thread.

      I thank you for your train of thought but I think I am tuned into a different frequency from you where philosophy goes. For example I dont invoke God in my reasoning either for or against. This means I differ on too many fundamental points to try and address them.

      One thing I will say is that this essay is about emergence in general and causality is just one small part of that mentioned only briefly. It was much more important in my previous essay where these discussions would have been more relevant. They are still of some relevance here but the emergence of space and time is the bigger issue.

      best, Phil

      Philip,

      I have had physicists contact me about the holographic principle for they feel that the findings of a 12 year experiment I have recently concluded has provided empirical evidence to validate it. I find your statement, "Sometimes the most brilliant step towards a great discovery is asking the right question to begin with." is indeed the issue at hand.

      I hope you find time to review my findings to see if they coincide with your conclusions:

      http://fqxi.org/community/forum/topic/1809

      Best wishes,

      Manuel

      Phil,

      I am digging deeper into your essay, and getting a better understanding of the necklace algebra you are proposing: "it can be interpreted as the emergence of

      string field theories in continuous space and time from algebras based on quantised information,"

      I think I am in agreement with the general idea. In my definitions, I associate information with uncertainty (which is consistent with Shannon). I am associating knowledge with what most people view as information, which is the sense of Wiener. In any case, the relative information, e.g. shared knowledge is what we are interested in. That is limited by quantum mechanics. In my interpretation of what you are saying, the idea is that we could build algebras based on the quantization of mutual information, which must be limited, which I am taking to mean there is a least element that can be defined. I like the idea of algebra building in general, so I find your essay to be very helpful.

      On another note, what are your thoughts on the apparent similarity of ideas that seem to be popping up from different corners?

        I must add one more response. You say that symmetries relate to something else. This is not necessarily the case. A Lie algebra can act on itself via the adjoint representation. This is what I have called complete symmetry. It means that the field that generate the symmetry are the same as the fields they act on so it is simply a principle of unification. It also implies that the degrees of redundancy match the degrees of freedom. This is exactly what is required for a holographic principle.

        Notice that I am following a train of logic to draw a conclusion (with assumptions that are reasonable but not watertight) I think this is better than just looking for something that is simple according to our tastes.

        Dear Philip,

        I had the alias name QSA before, my essay has been finally posted.

        http://www.fqxi.org/community/forum/topic/1877

        As we discussed before and after some research I am convinced that your theory is nothing but mine in disguise, however it may be hard to see. I will discuss that some other time once you got some good feel of my theory. I think my advantage is that time has been taken out naturally, and after some thinking I feel that it can be incorporated in the end.

        The rating is low but I am not concerned at all in that respect. I am only looking for few good people with deep understanding of physics plus some programming skills to run and test my programs to check that what I claim is true. The programs are so simple and should take you 15 minutes to figure them out. These programs are listed(can be downloaded) in section 11 of my website with additional detail in my postings

        http://www.qsa.netne.net

        I am specifically looking for the following:

        1. Can you understand the derivation of the model

        2. I claim that the model produces some results of QM, do you see it.

        3. the mass of the electron appears using the same model

        a. do you believe the result

        b. assuming that is the case ,do you think that can be significant.

        I will soon add the programs that you can run to see the Bohr model, the mass of the electron and how the fine structure constant is produced naturally within the system with only three lines of code. The code separates the number of hits between all the successful accepted hits and divides by the hits that happened only in the particle(electron) Compton wave region. That is very similar to the probability interpretation of the FSC.

        I am really counting on you because I feel that my chance is very small with others. Besides my theory is very close to yours as I said earlier. But If you can't find the time, I understand.

        Thank you.

        Adel

        Dear Philip

        I vaguely remember hearing the name Weizsacker as a president of Germany, but not as a theorist of matters quantum. JAW was the one who led me into the labyrinths of quantum mechanics. It was through his contributions in "Some Strangeness in the Proportion", a book of essays from the Centennial Celebration of the Achievements of Albert Einstein that quantum mechanics became alive for me. Before that only the catechisms of Schrodinger Equation and Heisenberg Uncertainty Principle!

        In my essay "Analogical Engine" I tried to draw the parallels between Analogy (as a thought process) and Quantum Mechanics (as a physical process) from a premise "What quantum is to classical" is similar to "What analogy is to rationality." With the help of a thought-experiment, I came to this conclusion: "Planck constant is the Mother of All Dualities, and a necessary condition for the existence of thoughts and things."

        Then entering the FQXi Essay Contest I found your essay, and wow you are saying: "With multiple quantisation the values of the probabilities themselves are replaced with further wave-functions ad infinitum." and "Bringing together different theories often forces almost unique conclusions."

        Very deep and very interesting I said to myself. Unable to jump the maths huddles, I can feel only the resonances that I can barely articulate. I do not like to impose, but I am curious to know what do you see from your side of the fence if you were to look at mine.

        Good luck!

        Than Tin

          Dear Philip,

          It is clear you have worked long and hard on remarkable essay, but I have a few comments and questions:

          A clear and concise definition of the "holographic principle" was never given. What I get from context: the holographic principle - all information within a closed surface can be reproduced by knowing the flux of all the fields going through that same surface.

          A clear definition of "information" is needed.

          Is the same information bit used for all fields? If there is just one type of bit then how does one know which field the bit is producing? If there is a different bit type for each type of field then how does saturation in one field (gravity as seen in a black hole) saturate another field such as the electrical field?

          Why do we not see a black hole-like saturation due to other types of fields?

          Any volume of space could have many streams of information going through it at any given moment. At the shopping mall, you can buy glass paperweights with an imbedded pattern of tiny bubbles made crossing laser beams which over-drive phonons in the material. Over-driving phonons is many orders of magnitude less than the Plank density, but in theory, we could reach that information flow density. Could we create a black hole by beam crossing?

          Pions violate chiral symmetry. We have more matter than anti-matter, so charge symmetry is violated. Symmetry breaking is sometimes said to define a field, yet you declared that entropy is declared not fundamental because it violates time-reversal symmetry. Entropy might not be fundamental, but violation of symmetry cannot be the reason it is not fundamental.

          All the best,

          Jeff