Thanks for the positive assessment. I am not sure what words I misspelled.

The point of looking at AdS spacetimes is to argue that what I did with black holes carries over to general spacetimes such as cosmologies. This is rather much a work in progress. What the open world might mean is that two cosmologies with entangled states can swap them. In other words maybe in one with a bipartite entanglement plus extra state and the other with a tripartite entanglelent can swap these. This would give the local appearance of the violation of quantum monogamy.

To show entanglement conservation suppose we have two quantum states |ψ> and |ψ'> and that we have

|ψ> = a|+> + b|->

|ψ'> = c|+'> + d|-'>.

Now suppose there is a unitary operator such that

U(|ψ> + |ψ'>) = ad|+>|-'> + bc|->|+'>,

This is then a singlet state |χ> = |ψ> + |ψ'>, with assumed normalization etc. Now we have a|+> + b|-> = |+_z> and c|+> + d|-> = |+'_z>. This means

U(|ψ> + |ψ'>) = |+_z>|+'_z>.

This runs into a problem, for we have a sort of cloning of states here for with normalization if |ψ> = |ψ'> then |χ> = |ψ> and we can with this operation clone states.

Unitary operations can't create or destroy entanglements. Entanglements have symmetries and these serve as conservation laws that conserve them. They can diffuse of course. Two states that are completely entangled with another state not entangled can evolve into partial entanglements between the three. That can happen by unitary evolution.

Read the post I wrote to S. Gupta. I give more of an idea what this means. There is a duality of some kind with the unitary principle and equivalence principle. This stems from the breakdown of predictability in this open world.

Lawrence,

You did not misspell anything ... that was the point. There were a few places where a word was probably the wrong word ... form vs from is an example although I don't specifically remember that with your essay.

Best Regards,

Gary Simpson

I will see what I can make of it. I can say that often physics or physicists do not like a lot of infinities.

Everything should be as simple as possible, but no simpler --- paraphrased from Einstein

LC

Dear Lawrence,

Probably one of the best repackage of string theory's anthropic principle. Trying to explain life in the 3-dimensional universe where we live as a consequence of the existence of the Open World aka Multiverse of hypothesized 10^500 universes out there has been long decried by many capable voices and minds.

You present the usual lot of string theory's hypotheses as facts: i.e. the complexities of quantum states in a black hole interior builds spacetime. In most other theories, and frankly to common sense, a black hole must be an implosive accident, and where not it is at the very least a singularity (not a regularity) which cannot in any way provide for a building block or elements thereof for the larger spacetime where regularities seem to be the norm.

Since black holes are dear to the theory, you find that: Quantum hair on a black hole may have mirror or dual relationship with low energy complexity we observe around . If dual relationship, we don't see any explanation of how this dual or physical relationship could possibly develop across the entire spacetime.

I like this one leap that you provide instead: it could be that be consciousness is also a truncated hyper-Turing machine that approximates the ideal of a completely self-referential system that can jump out of an algorithm, or make a leap of imagination. One is not sure if the jump is from the quantum algorithm within the black hole spacetime into our physical spacetime or into another imaginary spacetime. Or you seemingly want the quantum states within the black hole to be entangled so that their wavefunction may decohere into the larger spacetime. Should I remind the reader that quantum entanglement is between two CONJUGATE elements: can one think of separate or dual (let alone conjugate) elements within an environment that is SINGULAR?

I remind the reader that all these theories of blackhole spacetimes with entanglement states and other engenders have knowingly crashed over the discovery of an accelerating universe with a"ridiculously small"positive cosmological constant. Not to mention the very recent indictment of String Theory by the LHC because the hypothesized super-symmetry particles arising from these views have not been found within their very energy scale. I agree with you that "It is likely our inability to work quantum physics and gravity into a coherent whole is likely to be solved through new postulates or physical axioms, or the removal of current ones". Regrettably, the LHC results seem to be mandating that String Theory be one of those to be removed.

Even setting the above aside, for all the "beautiful" and prolific mathematics credited to string theory, I do not find this paper to have satisfactorily delivered on the specific question of a mathematical formulation to human cognition. Because you did not relate eloquently enough, if at all, spacetime mathematical formalism to the development of human intentionality.

And pardon the long post!

    The duality I find is similar to the duality between locality and reality in Bell theorem. That this occurs across spacetime has to do with nonlocality.

    This has connections to string theory, M-theory and the multiverse. I do not particularly appeal to those in the derivation I work here. The openness I appeal to is more of a quantum openness with entanglement swapping that may occur.

    This article is largely about condition that may be necessary for the existence of consciousness. I make no detailed hypothesis on the nature of human cognition. The MH-spacetimes and truncated hyperTuring machines are invokes as something that can exist in this system. In a general open world this may lay the ground work for conscious beings.

    Sorry you are not happy with this. That is the way it goes. We will see how the cards fall in the long run.

    LC

    Hi Lawrence,

    Happy to see you again on fqxi and congratulations for your works.They are relevant mathematically and technically speaking.Good luck in this contest.You merit a prize.

    Best

      Lawrence,

      Thanks for taking a look at my essay.

      Can't pretend to understand the direction of your essay. I wonder why you need a theoretical black hole with mass, a charge, and no rotation to relate the teleological nature of humans in an open world, and how is holographical coding on gravitational differentials involved. It's all new to me.

      Jim Hoover

        Thanks for the good word. It was a bit of a stretch to take my work and bend into this question.

        Cheers LC

        It is all about the open world. In order to have systems that act in some volition you must have an open world. That is the basis from which I argue.

        Cheers LC

        Dear Lawrence,

        I've just had another read-through of your essay. It's simply amazing how many different concepts you draw on, allude to, or mention---AdS/CFT, Wess-Zumino-Witten models, quantum error correction, MERA, ER=EPR, together with Lewisian modal realism, Popper's open cosmology, and many, many more. I'm quite confident in saying that all of these concepts probably never before shared the same environment, as they do in your essay---indeed, they probably never even shared the same mind before.

        And to top that off, you preface the whole thing with a Leonard Cohen quote (and one of the best, too); that alone means I can't be too critical of your essay!

        But while the essay is very impressive in its eclecticism, it's also very hard to follow, and one fears to loose track of the central point; indeed, I'm not completely sure I can articulate what that central point is. In principle, you seem to be saying that there is a necessary openness to physical systems in the world, due to their being long-range entangled with other, in principle arbitrarily distant, systems, leading to topological order.

        Unfortunately, it's not quite clear to me how this openness is connected to goal-directedness, intentionality, etc. I get your point regarding the impossibility of making perfect predictions in an essentially open system, but I'm lost at the point where you connect this to hyper-Turing machines and pink noise as relating to consciousness (?). I'd be grateful if you could elaborate a little.

          I will confess there is a lot here. I was going to sit this essay contest out. It then dawned on me that a secondary interest in MH space I had some years ago might have a bearing upon what I am working on. The main interest I am working on is contained in sections 2 and 3. The connection to MH spaces is made in section 4.

          In statistical mechanics a closed system will approach equilibrium and there is from there no prospect for any sort of self-directed system. Closed systems simply die. As a result systems that have some self-directed properties must be open thermodynamic systems. I have been working on how cosmology is a quantum mechanically open system. They are open with respect to entanglement swapping. In the ER = EPR prespective with quantum hair it is then possible that three states in a tripartite entanglement in one timelike region can exchange themselves with a bipartite entanglement plus nonentangled state. This is connected with the firewall problem.

          I could have gone deeper on this in other directions. In particular the duality between the equivalence principle and the unitarity principle, dual in a similar way Bell's theorem indicates a duality between locality and reality, means there may be some connection with Verlinde's hypothesis on the nature of dark matter. The presence of DM may be a signature of this complementarity with quantum gravity and cosmology.

          The subject of this essay debate is huge, and a part of it is that it centers around something that we have a poor understanding of, that is consciousness. I just advanced the argument the foundation requirement of there being an open nature of the universe.

          Cheers LC

          Dear Lawrence,

          You write: Closed systems simply die.

          Are you sure? I thought the laws of conservation required that closed systems, systems with no exchange whatsoever with their immediate environment, that is, would be preserved and enjoy stability. That closed systems tend to evolve into thermodynamic equilibrium, as opposed to open systems. So if life is for you viability, instead of death, and viability a chance for emergence of consciousness, then one would think that you would give preference to closed or stable systems in the pursuit of inception of intelligence.

          I can't make sense of your argument.

          Now of course perfectly closed systems do not exist. And life has developed on the basis of highly stable systems but not "absolutely" stable systems. It is within the "small window" of instability (1% perhaps) that give and take occurs, that which we call metabolism and interaction with the medium mediated by cognition.

          Am I wrong...

          Joseph

            The rule in biology is that equilibrium is death. A system that reaches equilibrium is not at large evolving.

            With gravity there is a subtle matter with the definition of equilibrium. An anzatz involving a black hole in a world with the same background temperature illustrates the point. A black hole with mass M has a Bekenstein-Hawking temperature T = 1/8πM (in naturalized units) will absorb a unit of mass δM or by quantum tunneling emits a unit of mass δM. It is then clear that in the case the black hole absorbs a unit of mass that its temperature is a tiny bit lower than the background temperature and it will statistically more likely absorb energy from the background. Conversely, if the black hole emits a quanta of radiation it will get hotter and statistically be more probable for quantum decaying away. Equal temperature does not mean equilibrium.

            There are open questions still concerning the nature of thermodynamics and certainly quantum mechanics with gravitation. My interest with this has been of late with BPS black holes that have gauge charges. The induced "quantum hair" has consequences for the universe as a quantum open system. Quantum open systems are to open thermodynamics, what Poincare recurrence in classical systems is to the recurrence of quantum systems. It is where the real fun lies.

            Cheers LC

            10 days later

            You are welcome Lawrence.

            I understand,difficult sometimes to resume a general work.Your mathematical plays are always surprising and relevant.Your posts on blogs and forums lack us Lawrence.:)

            Best

            Hi thinkers,

            Lawrence, I have difficulties to accept the reasoning of Verlinde about MOND.The fact to modify our newtonian mechganic is odd,it is also odd that the fact to consider the quantum gravitation like an emergent electromagnetic force.All searchs this weakest quantum force.It is well like that,that boosts and catalyses the compétitions,we have so many interesting works searching answers.But I don't understand why so many scientists insist only on photons and only on this luminiferous aether ???? it is a prison this special relativity and if a main primordial causality has created an universe, I am doubtin,g that it is a prison ??? the aether is gravitational and the universe is more complex than our standard model.It is really odd that all insists in this prison and these chains .Like if in 200 years of sciences we had all understood and concluded ,only the photons exist ??? the cold and heat .....The consciousness and the gravitaztion has nothing to do with our standard model in logic.

            psd verlinde tells that dark matter does not exist in fact and that the reasoning that Zwicky has found in galaxies inventing dark matter is not necessary.So Verlinde wants to explain gravitation in all the sense, entropical this, now mond, and this and that.Well is it a joke ? has he a team of business men behind him??? all the pappers pondered become irrational.Sometimes competition is well sometimes no, and a little of holidays also sometimes is well for the Heath and the pression :)

            Dark matter seems essential ,this matter baryonic permits to balance the standard model when we consider the zero absolute,the cold.

            MONDS OR emergent electromagentic gravity ...are not really universal.

            Best Regards

            I have read Verlinde's paper on this MOND-like theory. Over all I gave the paper an attention level of 5, where I studied the initial idea pretty closely and some of the later development not so much. I would file this hypothesis into the maybe file. It is not an entirely crazy idea.

            The idea is that with anti-de Sitter spacetime entanglement corresponding to Einstein-Rosen bridges (ER = EPR) connect on the boundary or conformal boundary. If a de Sitter spacetime emerges from a causal wedge of the anti-de Sitter spacetime these entanglemnts do not necessarily connect on the horizon. This means that entanglement is a structural mortar for spacetime. This results in curvatures in spacetime. This Verlinde interprets as a MOND-like modification of gravity.

            I do think that if there are these entanglements not connected to horizons exist there should then be some interpretation according to elementary particles. A pure spacetime physical perspective and a particle perspective might have some sort of duality to them.

            I have read several ideas also and pappers about these MOND.We search of asnwers after all and all works seraching these answers are always important for the evolution of sciences.We know so few still about our universe and its gravitational laws.The universal mechanic is so complex and we analyse at this moment a so small part of this puzzle,detrministic and objective.We are so youngs still,our knowledges are so weak still.This universal sphere is an incredible splendor of evolution of matter energy.

            Thanks for sharing your thoughts Lawrence,I am wishing you all the best in this contest, your ideas are always relevant.

            Friendly

            Excellent essay Lawrence!

            I tend to agree with your main thesis, that an open universe favors emergence of consciousness. I also see some overlap of your black hole analysis with my current areas of interest. But this essay is jam-packed with ideas and information, to the point where I pity folks who are not savvy about the abbreviations for technical terms, or conversant enough to see what you are trying to show with the Math. An impressive tour de force! But I will have to go back over it a few times, to absorb it all.

            This work is pretty much tied into a particular view of quantum gravity and black hole research, involving String Theory. Luckily; I got to hear Maldacena's talk on entangled black holes at GR21, along with a few others like Don Marolf, which seem to have a direct tie-in with what you are trying to prove. I think you win your point, in any case, but it somewhat rises and falls with the fate of the AMPS firewall BH model. There is a big 'it from qubit' resurgence these days, where a lot of researchers are focusing on entangled spacetime. Some of that work appears a little artificial to me.

            In the larger view; Padmanabhan has recently argued that the same thermodynamic considerations that create an open universe also require gravity to be quantum mechanical. So it argues for the necessity of quantum gravity. If the fabric of spacetime itself emerges from entanglement on a higher-dimensional boundary, this supports some models of induced or entropic gravity that might otherwise fail. But I am more in the camp of Ashtekar, where I see a need to put many models of quantum gravity on an equal footing, in order to make progress, rather than focusing only on String Theory. We shall see what comes of it.

            All the Best,

            Jonathan

              I had also wanted to mention,

              One does not have to rely on thermodynamic considerations, to have an open universe. In some scenarios, as with the DGP model, it can happen due to purely geometric considerations. That occurs in a brane-world formulation where the prior space is 5-d, presumably AdS5, which spawns a 4-d spacetime when a 5-d black hole implodes to become a white hole in our universe.

              There was a Scientific American article "The Black Hole at the Beginning of Time" which was interesting except for the misleading title (not at time's inception, but as above). There was a paper in JCAP "Out of a White Hole..." also in 2014, with technical details. But this could show where the AdS background comes from, and explain why the universe is open.

              On the other hand; recent work by Dvali and colleagues focuses on an analogy between BEC formation and the event horizon of a Schwarzschild black hole. They derived that BHs are the most powerful efficient possible quantum computers, but also that physical limitations prevent us from using them to obtain useful information or perform meaningful calculations. Care to comment?

              Regards,

              Jonathan

              Thanks for the positive response. I will comment more tomorrow. It is getting a bit late for a long writing session. This is in line with the approach with Raamsdonk that spacetime is built from entanglements. I wrote an answer on stack exchange that connects with this perspective with regards to Hawking radiation.

              The open world emerges from the existence of gauge hair and BPS charge. The hair of the black hole is entangled with particles in a vast number of other black holes in the universe. In the unique situation where there are two black holes maximally entangled one would have a complete Einstein-Rosen bridge connection to the interior of the other black hole in this other world. The openness comes from the fact the spatial surface in region I has an ambiguity with respect to being connected to other cosmology or the black hole interior region. For maximal entangled Bhs one in principle can avoid the singularity and travel around to other worlds.

              I will write more tomorrow. I have been recovering from influenza, and today it the first day I feel not utterly horrible. I am not that familiar with DGP model, but I will see what I can make of it.

              Cheers LC