Essay Abstract

If we imagine the universe as a set of data and each observer as an outcome of a series of measurement operations, then we can view ourselves as being unique series of cryptographic keys reflecting a particular track in the data (like a bubble track in a cloud chamber). We can turn to computer science for examples of perfectly deterministic systems where we regularly try to anonymize data instead of decipher it, and use insights from that field to understand physical problems. Onion routing, for example, provides a means of encrypting data so that nodes in a chain only know the node where data came from and the node data is to be sent, via the use of Chaum mixes as part of a mix network. This has implications for the information paradoxes surrounding black holes and topics of computational complexity, and how decoherence approaches which include the environment as active participant can avert the paradox and provide an additional means to connect mathematics and physics.

Author Bio

Hal Swyers holds a M.S. in Environmental Management from the University of Maryland University College. He studies physics and mathematics as a personal hobby and all content provided purely reflect his own opinions and should not be construed to reflect the opinions of others.

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Dear Harlan,

I believe that Fourier series is at the root of many of today's physics concepts, most especially those that emphasize 'superposition'. I also like very much your description of algorithms as processes that do not change with changes in language and (ideally) produce the same result. And your interesting remarks on random numbers.

You discuss von Neumann's take on hidden variables and quantum incompleteness. As you know, having read and commented on my essay, I treat a local Stern-Gerlach model that does "describe the system exactly and with certainty", and I claim that Bell is erasing the hidden variable information with his hidden constraints. Also note that the energy-exchange process effectively dissipates precession energy, ending with the particle spin aligned with the local field. But this appears to me to represent a loss of information, represented in quantum mechanics as 'collapse of the wave function'. If that is the case, then I would expect "loss of information' in a black hole.

In an earlier essay I treat information as a change in structure ('in-form'ing) effected by energy, as a record of the energy. This precludes existence of information as a 'substance' or physical entity of any kind. And my current essay brings existence of 'entanglement' into question. Finally a number of cosmologists are questioning black holes in favor of ECOs (eternally collapsing objects). So, questioning the concepts of information, black holes, and entanglement, I have not worked on the "firewall" problem, but I believe you've represented well the current state of the problem. And I very much like the way you end your essay!

Thanks for reading my essay and commenting, and thanks for entering your own essay.

Edwin Eugene Klingman

    Dear Harlan Swyers

    An algorithm as an invariant process is an interesting characterization. I have not before encountered Onion routing or Chaum mixing. They make interesting analogies. Your article left me wishing to know more about quantum mechanics. Thank you for writing your article, and thank you for commenting on mine.

    Best wishes,

    Bob Shour

      Edwin,

      Thanks so much for the response. Likewise, thank you for reading the essay and your comments.

      Best

      Harlan

      Bob,

      Likewise, thank you for your comments. I think the concept of naturally occurring algorithms is something worth contemplating. Best regards and thanks again.

      Harlan

      Dear Hal Swyers,

      For somebody who has no degree in physics your paper is remarkable. It is at a high level.

      The problem AMPS poses is the entanglement with a black hole and radiation continues. This means a crisis happens where the black holes has more entanglement information than permitted by the Bekenstein bound. There were early ideas about black hole remnants that had a huge amount of quantum entanglement information. In order to save the situation one of two things must be admitted. Either the black hole transfers entanglement with early Hawking radiation to the outside, but this requires converting bipartite entanglements into tripartite entanglements. This is a form of cloning and is not unitary. To same unitarity it must then be admitted the equivalence principle breaks down so there can be no more information transferred to the BH.

      I think that entanglement algebras are themselves uncertain. In quantum gravity there is an uncertainty as to whether an entanglement is bipartite or tripartite or GHZ entangled. I think this is a manifestation of cobordism with the structure of spacetime.

      I will have an essay here probably in the next batch that show up. I discuss some of these matters. You might find it interesting.

      Cheers LC

        Lawrence,

        Thanks for the kind words! Indeed a lot of personal time has been spent studying physics. I'll await to read your essay, I am sure there will indeed be some good discussion on this issue.

        Best

        Harln

        I and some other people are working to find an equivalency, an isomorphism of sorts, between topological cobordisms of spacetime and entanglement geometries. The spacetime of importance is the AdS spacetime and the topological changes are local quantum fluctuations. These should be equivalent to the entanglement geometries of quantum states on the boundary.

        Stay tuned, maybe this will work. Then again it might of course be just wrong.

        LC

        5 days later

        Dear Harlan,

        I read your paper again. I am sufficiently impressed to give it the maximum score. This means my paper is now showing, which you might be interested in reading at:

        http://fqxi.org/community/forum/topic/2320

        Cheers LC

          Lawrence,

          Thanks much! Looking forward to reading your paper!

          Best

          Harlan

          Harlan,

          Many thanks. This is a well written and thoughtful essay.

          The idea of an observer as being the result of a unique result of a set of measurement operations is sublime. This enables me to envision the universe and the observer as single entity.

          I sometimes struggle with bra-ket notation but I found your use of it to be very effective. I think it is the supporting text and thinking that makes it understandable.

          I am something of a skeptic regarding information theory and such but you have made me reconsider this.

          I love the ending.

          Best Regards and Good Luck,

          Gary Simpson

            Thank you for your essay. I found it very interesting though I struggled on some parts (that's my fault, not yours).

            At the end of your essay, you said : "This means our environment serves as the seemingly unhackable database of information. However, human nature being what it is..."

            I have a question: If we want to make our environment even more unhackable, how would you approach the challenge?

              Sorry, I wrote my question too quickly. It should have been: "what would make our environment even more unhackable?"

              My essay is up on the essay contest list now. I don't talk about the firewall explicitly, but the brief discussion I gave on some of my work does address this.

              Thanks, LC

              8 days later

              You wrote: "At first we might see a problem in the existence of Aspect's machine, since here we have a system that can be defined and constructed with a relatively minimal number of statements, but yet is capable of producing strings of any possible length which can then be proved to be random through violations of Bell's inequalities showing their quantum origin."

              You are mixing 2 very different notions of randomness. The notion of quantum randomness is relative to the time when a device is in a specific state and ready to produce a number which will come at random in the sense that it is not determined yet, as repeating the same experiment with exact copies of the device with the same initial state may give different results. We have a physical indetermination of the choice between many possible values it is still able to take.

              On the other hand, you mentioned the notion of whether a given fixed number is a random number or not. This is a completely different question.

              Indeed by Chaitin's theorem, it is not possible to prove that any specific big number is a random one, however this does not diminish the fact that anyway most big numbers are random. Concretely, when a quantum device is going to produce a number at random (that quantum paradoxes show to be random in a physical sense, i.e. that its value is not fixed in advance but any number still has actual chances to be produced by the device at this time), there is then a provably high probability for the future yet undetermined output to have the property of "being a random number" in the sense of Kolmogorov complexity.

              This "high probability of being a random number" is related to the fact that the average expectable complexity is a high one.

              The point is that the provably high value of the average expectable complexity of the future undetermined output, does not change anything to the fact that, according to Chaitin's theorem, it is not possible to formally prove the high value of the complexity of any specific number, among all possibilities.

              To explain very simply this "paradox" which I do not even find strange, imagine a function f that will play the role of the Kolmogorov complexity, to be applied to a future output that may turn out to be either a or b with probability 1/2 each.

              Then we know that the average expectable level of complexity is high : f(a)+f(b)>2 is provable. However for each specific possibility, there is no way to prove its high complexity : neither f(a)>1 nor f(b)>1 is provable.

              Nevertheless, we have a proof of f(a)+f(b)>2 and thus of (f(a)>1 or f(b)>1).

              But this provability of (f(a)>1 or f(b)>1) does not anyhow contradict that f(a)>1 is unprovable and f(b)>1 is also unprovable, because the formal proof of (f(a)>1 or f(b)>1) does not provide any way to formally find out which of both numbers f(a) and f(b) is >1.

              Still there is a real mathematical truth about it but it is not algorithmically computable. (This non-computability should not be confused with physical indetermination.)

              If you are amazed that physical devices may produce random numbers, well, remember that a physical quantum device is NOT a classical deterministic Turing machine, which Chaitin's theorem exclusively refers to. As I explained in my essay, I interpret quantum randomness as having a non-physical source (conciousness). See also my arguments against the hidden variable approach.

              You wrote: "As photons are generated by excited atoms, we can only state the exact polarization of photons is indeterminate prior to measurement. Since the polarization states are generated from some quantum source, then Aspect's machine contains a component that is indescribable in the formal language that can describe its construction and prove its result."

              It all depends on the precise experiment. Some kinds of excited atoms may have a spin that determines the polarization of the emitted photon. In practice the result is usually indeterminate because systems are made of many atoms whose spins are randomly distributed, full of entropy.

              You wrote: "real numbers can be characterized as being rational functions, which are simply the ratio of polynomials"

              Looking at the reference you gave where this amazing result on the simple nature of real numbers comes from, the explanation is this one:

              "the real numbers are a subset of the rational functions" where "By a rational function in the variable t, we will mean a function of the form p(t)/q(t), where p(t) and q(t) are polynomials with standard real coefficients", so that "for instance, the number 7 can be viewed as 7/1, where 7 and 1 are both polynomials of degree 0". So more generally in this way, we can get any real number u in the form of the rational function u/1 where u and 1 are seen as polynomials of degree 0 with real coefficients. Wow !

                7 days later

                Joe,

                Thank you for the insightful comments.

                Every point in space time is assigned some set of operators as defined in quantum field theory. At the instant prior to the big bang, there is no apriori definable energy distribution. We are force to view this as a singularity. After the big bang the universe evolves, and some parts of space end up having higher probabilities of particles being measured than others. However, the process of measurement itself is only definable for subsets of the larger system. It is ignorance that makes us think their is anything real at all.

                Good luck out there.

                Cheers!

                Harlan

                Sylvain,

                Thanks for the nice editorial.

                I am quite aware of the difference, but perhaps wasn't clear in the write up.

                Aspect's machine is designed to signal whether there are two photons with coincident polarizations. The set up looks to measure one set of polarizations from a larger set. That means that over a period of time, while the generation of photons pairs can be controlled to occur at some constant rate, the photon pairs that cause coincidence must fire at random. There can be no discernible pattern if ones and zeros measured within any given interval at a specific polarization. This sequence is provably random because it can be proved to be part of a quantum process. No classical means can discern this.

                I am sorry you read more into what I was saying, but if you check the reference to Sidney Coleman's video, these things should be clear to you.

                Thank you for the comments.

                Cheers!

                Harlan

                Gary,

                Thank for the nice comments.

                The best way I have been able to understand Bra-ket notation, is to just remember that the Bra is always the conjugate of the ket.

                In complex terms, if a ket represents a complex number like 3+4i then the bra is 3-4i. Or for instance if the ket is eix the ket is e-ix[\sup].

                A bra and its conjugate ket will the squared norm (expected value) unless there is an operation (O) that changes the ket into some other number . In this case you would see the the average value of the operator. In QM, because we are dealing with probabilities, the squared norm is always equal to one.

                Hopefully that helps.

                Cheers!

                Harlan

                Your work is tech-driven and it goes on to say very detailed structures of environs in greener way!

                Sincerely,

                Miss. Sujatha Jagannathan

                Dear Harlan,

                I enjoyed reading your essay, particularly as I am interested in the phenomena of quantum entanglement.

                In your essay you make the point that: 'This serves to enforce the locality on interacting fields, e.g. it ensures that faster than light interactions do not occur.'

                To take the case of a photon interacting with an electron, my understanding is that during transmission, the photon always travels at the speed of light, but at the point of interaction (observation) effects can occur at faster than the speed of light. So my understanding is that non-local effects can occur at the point of measurement while protecting the fact that useful information cannot be transmitted at a speed faster than the speed of light.

                Is this in line with your thinking on the subject of non-locality in quantum entanglement?

                Regards

                Richard