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Information as the key underlying physical principle

  1. Jan 9, 2015 #1
    It seems to me, at least when it comes to quantum mechanics, "information" has become the most basic unit. Like, quantum entanglement works to the point that information is extracted, and one can even revert certain things by making sure the information is destroyed. Same with the discussion about black hole evaporation etc, where the hinging point was that a black hole would destroy any information falling into it.

    My question would be, is there any material (books, papers) discussing this? I find this whole subject very tantalizing, maybe because I work in machine learning where information is the basic unit too.

    EDIT: Just to make sure what I'm asking, I'm not too interested in the specific black hole or quantum eraser experiments, but rather a slightly more "philosophical" discussion on what this shift might glean into physical "reality".
     
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  3. Jan 9, 2015 #2

    marcus

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    I think the late Asher Peres was a central figure in the development of Quantum Information Theory.

    You might check in arXiv.org for papers by Peres_A

    I'm very far from expert in this, don't know the literature. Some other people will probably answer over the next day or so, with better leads.

    I know of Asher Peres in part through mention at the end of a paper called "Relational EPR" by Rovelli and Smerlak. You'll probably get the online PDF if you just google "relational EPR". It is a well-known paper. They quote Peres at the end. Basically he nailed it. QM is about information. things evolve continuously perhaps, but they interact in discrete quanta, and all we can really say about nature is based on those interactions. there is no grand cosmic observer. reality is relational. the story is always what is seen from some observer's standpoint, IOW information. And observers can reconcile their accounts when they communicate (but that is an ongoing process limited by the speed that information can be transmitted.

    Bohr is quoted as saying something like "It's not what physical reality "IS" that concerns us, it's what we can say about it. In a subtle way, quantum reality is made of information (interactions, qubits, quantum events, maybe one could simply say "facts"). I got a lot out of the paper called "Relational EPR". but I can't pretend to broad knowledge of the quantum foundations, or quantum information theory, literature.
     
  4. Jan 10, 2015 #3
    Funny, I too work in IT and I have the exact same feeling... Please post further references if you find any....
     
  5. Jan 16, 2015 #4
    I've floated this question on PF in the past, and couldn't get much traction. I think the idea teeters too much on the edge of being purely philosophical.
    But yes, I tend to agree with the points made so far. Physical existence as described by modern physics would seem (to me anyway) to be more of an informational manifestation rather than one that we would intuitively think of as "material". I've even go so far as to ask whether Noether's theorem might be used to demonstrate some type of universal symmetry that results in the conservation of information. Couldn't get much in-put on that. Perhaps the problem is the philosophical fuzziness of trying to posit a physical existence that is really only information at the fundamental level. It obviously can lead to a discussion about what, if any, role consciousness has in this description, and that will get the thread terminated pretty quickly.
     
  6. Jan 16, 2015 #5
    Here's the problem, as I see it. It sounds like you all work in IT, or some type of computer science anyway. So, you are very familiar with the software/hardware interdependence. But how do you run computations without ANY hardware. Can you guys help me with that idea?
     
  7. Jan 16, 2015 #6

    Stephen Tashi

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    If the discussion isn't to veer into Philosophy, someone should state the precise definition of "information" in QM - if it has one.
    (I hope answering that question will be simpler than answering the question "What are the domain and codomain of a wave function?")
     
  8. Jan 16, 2015 #7
    I don't think your analogy works. Physics, however you want to describe it, doesn't need "hardware" to run on. I mean, even in its current normal description, an electron is solely described by a few parameters, none of which are embedded into "hardware".
    Similarly, the information that we're talking about, which *is* essentially the collection of parameters, wouldn't need hardware to run on.

    I don't know, I thought the initial reply was very interesting, in how physics might be eventually more about the tend relations between things than the things themselves.
     
  9. Jan 16, 2015 #8
    That's essentially consistent with Leibniz's proposition of "relational space".
     
  10. Jan 16, 2015 #9

    atyy

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    http://arxiv.org/abs/1011.6451
    Informational derivation of Quantum Theory
    G. Chiribella, G. M. D'Ariano, P. Perinotti

    But perhaps one should also remember that "information is physical" :)

    http://arxiv.org/abs/quant-ph/0610030
    Reference frames, superselection rules, and quantum information
    Stephen D. Bartlett, Terry Rudolph, Robert W. Spekkens
    "Recently, there has been much interest in a new kind of "unspeakable'' quantum information that stands to regular quantum information in the same way that a direction in space or a moment in time stands to a classical bit string: the former can only be encoded using particular degrees of freedom while the latter are indifferent to the physical nature of the information carriers."
     
  11. Jan 16, 2015 #10

    Stephen Tashi

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    Does this imply that definition of "information" in QM is particular to that paper? Is the definition impossible to state in a concise manner?
     
  12. Jan 16, 2015 #11

    atyy

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    Yes, that's particular to the paper.

    It should be impossible to state in a concise way. Classical information theory is a branch of classical probability theory. Is quantum mechanics a generalization or a special case of classical probability?

    It depends on one's interpretation. The Chiribella et al paper stands in a long line of reformulation of quantum mechanics as a generalization of probability. In classical probability, pure states are extreme points of a simplex, which is not true in quantum mechanics.

    On the other hand, Bohmian Mechanics shows that at least some forms of quantum mechanics (eg. non-relativistic quantum mechanics) can also be interpreted as special cases of classical probability theory.

    To use an analogy from classical physics: do we live in the best of all possible worlds? :D Yes, from the point of view that it can be formulated form an action principle. However, the action is not always unique. For example, classical general relativity is the best of all possible worlds by the Hilbert action, the Palatini action, the Holst action etc.
     
    Last edited: Jan 16, 2015
  13. Jan 16, 2015 #12

    Stephen Tashi

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    Is it important to discuss the papers definition of "information"?

    I, personally, am not adverse to discussing questions in a philosophical way, but isn't the policy of the forum that discussion should deal with specific technical issues? (Perhaps "Beyond The Standard Model" has some leeway?)
     
  14. Jan 16, 2015 #13

    atyy

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    I was suggesting that paper's definition as a technical definition (to start). So we can have philosophy and technical discussion by comparing the different axiomatizations of quantum mechanics. Let's avoid Bohmian Mechanics here. Bohmian Mechanics aims to remove the notion of observers from quantum mechanics. However, the Chiribella et al paper stands in the Copenhagen tradition of quantum mechanics as an operational theory: yes observers are physical, and presumably there should be some way to describe observers and quantum systems consistently, but since in practice we have no trouble distinguishing our classical selves from quantum systems, let's describe quantum mechanics in terms of what operations we can do. Here are several alternative axiomatizations (there's old papers too, but these new ones are more readily available).

    http://arxiv.org/abs/quant-ph/0101012
    Quantum Theory From Five Reasonable Axioms
    Lucien Hardy


    http://arxiv.org/abs/1011.6451
    Informational derivation of Quantum Theory
    G. Chiribella, G. M. D'Ariano, P. Perinotti

    http://arxiv.org/abs/quant-ph/0508042
    A limit on nonlocality in any world in which communication complexity is not trivial
    Gilles Brassard, Harry Buhrman, Noah Linden, Andre A. Methot, Alain Tapp, Falk Unger


     
  15. Jan 17, 2015 #14

    Stephen Tashi

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    That would be a bit of a thread hijack, I think, unless those approaches define different types of "information". Do they?
     
  16. Jan 17, 2015 #15

    atyy

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    Yes and no. I will say no, because the Chiribella et al paper is at least partly inspired by Hardy's. The Brassard et al is about communication complexity, so I think that's easily informational. For yes - I think we could discuss the difference between the Chiribella et al axioms and Hardy's - are the former really more "informational"?

    And really, you can take the discussion wherever you want. I'm just suggesting some solid ground to stand on to start if anyone is interested.
     
  17. Jan 17, 2015 #16

    Stephen Tashi

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    Early in the Hardy paper, I have a mathematician's frustration with the language of physicists:
    The ambiguous phrase "any mathematical object that can be used to determine...of any measurement" might imply that if there exists some measurement whose probabilites a mathematical object can determine then the mathematical object is a state. Or it might imply that if a mathematical object has the property that for any measurement performed on a system, the mathematical object can be used to determine the probabilities of its outcomes, then the mathematical object is a state. From the subsequent text, the latter alternative is what is meant.

    Then there is objectionable language:
    I know of no technique to make a direct "probablity measurement". One measures observed fequencies of events. Perhaps physicists have faith that the observed frequency of an event is equal to its probability. I think no harm is done if the language is modified to say that K is defined as the minimum number of probabilities that must be "given" or "specified" in order to determine the state.

    There is mathematical question of whether a finite minimum exists. If we have infinite sets of probabilities, it may take an infinite number of "given" probabilites to determine it. So are we asssuming K must be a finite number? [Edit: He seems to say yes afterwards - if "N" represents a finite number.]
     
  18. Jan 17, 2015 #17

    atyy

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    marcus mentioned Rovelli's RQM in response to the OP, while my instinct was to mention Chiribella et al. I'd like to mention that although they are different in technical details, they are similar in spirit, in that both are about being able to consistently shift the "Heisenberg cut" between observer and quantum system. Rovelli's RQM is a radical view of reality that is meant to also solve the measurement problem, but while everyone who knows quantum mechanics will feel its spirit is right, it is less clear if such a radical view really works (Rovelli needs a technical kludge in his paper). On the other hand, the Chiribella paper does not solve the measurement problem, and so while also dealing with the consistency of shifting the "Heisenberg cut", does reproduce orthodox QM (in finite dimensional Hilbert spaces).
     
  19. Jan 17, 2015 #18

    atyy

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    Your complaint is unfounded, since you seem you to have understood the languauge after all :p

    One limitation of these axiomatizations of QM is that (I think) they only reproduce QM in finite dimensional Hilbert spaces. From the physics point of view, this is mostly considered ok, since we should be able to make the Hilbert space large enough for all practical purposes.

    I should mention that Ken G here on PF has pointed out some problems with the Hardy paper (nothing that cannot be fixed). Hardy also has a later slightly different axiomatization, but I listed the 2001 paper because it is considered a classic.
     
    Last edited: Jan 17, 2015
  20. Jan 17, 2015 #19

    Stephen Tashi

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    From Hardy:

    I don't know what a "single shot measurement" is. Is it a measurement consisting of a single number which might be one of many possible values that can be realized from a probability distribution? Or does a single shot measurement give a value that represents a probability?

    Does this refer to the dimension N of a system" or is it referring to a dimension N of a state? If , for each state of a system, a "single shot" measurement( taken on whatever state the system is in) allows us to distinguish between N states, then N would be a number associated with the "system" If the number N depends on the particular state the system when the measurement is taken, then N is a number associated both with a particular state and the particular system. Different states might have different "dimensions N".



    That's Ok for a physicist to say, but it is not what the mathematical Law Of Large Numbers says unless we elaborate the meaning of "in the limit". The type of limit mentioned in the Law Of Large Number is a statement involving a limit of a probability of an observed frequency, not the limit of an observed frequency (with no mention of the probability of the observation.) Later Hardy says that Axioms I-V give classical probability theory. Mathematically speaking, Axiom I doesn't, but Axiom I is a practical way of thinking about the world.

    As I understand the paper, each state has a "degrees of freedom K" and there is no comment on whether K may vary from state to state. To say K is a function of N might mean one of the following:

    1. For a given system , the K for a state in the system is a function K(N) of the N for the state. But for a different system K might be a different function of N.

    2. There a single function K(N) that gives the value of K for a state in a system as a function of the N for the state and this function works for all systems.

    3. Each state in a given system has the same value K and the system has a single value N. There is a function K(N) that gives K as a function N as N varies from system to system.
     
    Last edited: Jan 17, 2015
  21. Jan 17, 2015 #20
    Probability theory tells how to derive a new probability distribution from old probability distributions…….. It does not tell how to get a probability distribution from data in the empirical world.

    In the theorem of large numbers, the existence of the probability distribution is not deducted, it is postulated. In mathematic this is an evidence like if we say : The arithmetic tells us how to calculate a new number from old numbers ... It does not tell us how to get a number from the information of the "real world".

    Patrick
    PS
    It seem (page 10) that Kolmogorov write « I have already expressed the view ...that the basis for the applicability of the results of the mathematical theory of probability to real random phenomena must depend in some form on the frequency concept of probability, the unavoidable nature of which has been established by von Mises in a spirited manner.....(But) The frequency concept (of probability) which has been based on the notion of limiting frequency as the number of trials increases to infinity, does not contribute anything to substantiate the applicability of the results of probability theory to real practical problems where we have always to deal with a finite number of trials » in Shankhya, 1963.
     
    Last edited: Jan 17, 2015
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