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A Relationship between Quantum Numbers and Quantum Information

  1. Dec 11, 2015 #1
    I would appreciate any clarification (or opinion) on the relationship between Quantum Numbers and Quantum Information. My question is related to the puzzle wether matter merely represents information or - at the basement level of reality - actually can be said to be information.

    Just to give you an idea of where this is coming from:

    It has been said that "information is neither matter nor energy, yet it needs matter for its concrete embodiment and energy for its communication". This coincides with the representational idea of information, e.g. as quantum information which is information being held in the state of a quantum system.

    On the other hand Max Tegmark has argued (in "Our Mathematical Universe") that "every [particle physics] reaction that isn’t forbidden (for violating some conservation law) appears to actually occur in nature. This means that we can think of the fundamental legos of particle physics as being not the particles themselves, but the conserved quantities [i.e. their quantum numers]." Tegmark proceeds that the quantum numbers are purely mathematical objects, but you can just as well look at them as being nothing more than a couple bits of information.

    Thanks
     
  2. jcsd
  3. Dec 13, 2015 #2

    jfizzix

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    Matter is a medium for the storage or transmission of information (quantum or otherwise).
    Quantum numbers are eigenvalues of observables with a discrete spectrum.

    The values of an observable could be used to relay information, say by preparing a stream of particles in one state, and detecting them in a corresponding state down the line. By changing the state of the input, you can change the state at the output, and so communicate.

    Matter itself is not information; how you choose to prepare an arrangement of matter so as to communicate something else (like smearing graphite on flattened bleached wood pulp) is where the information lies.
     
    Last edited: Dec 14, 2015
  4. Dec 14, 2015 #3
    Ok, I read the forum rules which explicitely discourage speculation. On the other hand, John A. Wheeler's as well as Anton Zeilinger's thoughts on the topic (just to name two of the giants) sure have been published in reputable physics journals. So the above answer is playing it extremely safe and the claim "matter itself is not information" is actually stated without any supporting argument. But instead of furthering any discussion that cannot be decided in a meaningful way, I would like to take a constructive route and follow Max Tagmarks's argument down to the bottom and ask some additional questions.

    We could write down a chemical reaction in the form

    Hydrogen + Oxygen → Water​

    but instead we prefer the notation

    2 H2 + O2 → 2 H2O​

    because it gives us additional information about what's happening in terms of what is changing (the molecules) and what is staying the same (the atoms). Chemistry is not the end of the story, so let's move one level deeper.

    We could write down a nuclear physics reaction in the form

    Uranium → Thorium + Helium​

    but we prefer the notation

    238 234 4
    U → Th + He
    92 90 2​

    because once again it tells us what is changing (the atoms) and what is staying the same (the particles). Nuclear physics is not the end of the story, so let's move one level deeper.

    We write down a particle physics reaction in the form

    n → p + e + ve

    which again tells us what is changing (the particles), but this time there is no notation that tells us what is staying the same. As Tegmark remarks, what's staying the same are the conserved quantities or quantum numbers.

    My questions:
    • Why don't we have a notation for particle physics reactions in terms of quantum numbers? Is it just for convenience because it's not easy to write them down?

    • Is there some kind of theory that gives us a picture of what is actually happening inside a particle physics reaction when particles collide and others come flying out?

    • What is an isospin of 1/2 or an electric charge of -1 if not a bit of information?
    And somewhat unrelated, but related nevertheless:
    • Quantum decoherence has been described as the loss of information from a system into the environment. Is there any theory of decoherence that contains a symbol for information in its equations?
     
  5. Dec 14, 2015 #4

    jfizzix

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    I couldn't say precisely, but if I had to guess, then it would be that fundamental particles are uniquely defined by their fundamental properties (i.e., there's no analogue for isotopes of the same element on a single particle level).
    In that case, simply knowing what the particles are gives sufficient information to describe what fundamental properties are changing/staying the same in a given interaction.
    That being said, knowing the particular quantum state of a given particle would provide more information than simply knowing what kind of particle it is.

    In my limited understanding, our current theories are only really equipped to describe what you will find at the beginning and end of an interaction.
    That being said, modern physics describes such particle interactions in terms of probability amplitudes to arrive at a particular final state given a particular initial state.
    In order to find the probability of a given interaction occurring, one must add up all the amplitudes for all possible intermediate interactions that will give the same final state.
    These intermediate processes can include such things as particle/antiparticle creation and annihilation, among many others.
    It's still up for debate as to whether these virtual particles exist anywhere other than the minds of theorists, but accounting for such things gives shockingly accurate predictions.

    A bit of information is the quantity of information contained in the answer to a two-state (e.g. yes or no) question.
    Since the charge of an electron is constant, its charge cannot be be used to convey information since its charge never changes.
    However, the spin-polarization of an electron has one of two possible values, and so by preparing a series of electrons in a chosen sequence of polarization states, one could communicate up to one bit per electron with this degree of freedom.

    There are information-theoretic treatments of decoherence (particularly in quantum information theory).
    For one thing, the measurement can be thought of as an interaction between the observed object and a measurement device.
    The quantum entropy of the object can be considered a measure of its purity or coherence (though a larger entropy means a smaller coherence). Any standard measurement of a quantum system increases quantum entropy, and decreases purity/coherence.
     
  6. Dec 15, 2015 #5
    Thank you, that was extremely helpful.

    It is a bit of information about what the particle is, not a bit of information used to represent your memory of uncle Bob's hair color.

    If I told people in the street that if you collide a football and a billiard ball, they exchange a ping pong ball and away flies a cannonball and a tennis ball, they'd call the ambulance. And even if we observed all these balls to behave exactly like this a billion times, they'd still ask for an explanation of what's going on. Which brings me to my favorite quote from theorectical physicist Lee Smolin:

    "Physics should be more than a set of formulas that predict what we will observe in an experiment; it should give a picture of what reality is."​

    In between model/reality, subject/object, observer/observed, being/representing, signifier/signified, and seer/seen we find this dichotomy everywhere. The ancient mystics in the eastern tradition told us that to hold on to these distinctions is to give in to an illusion. I think we should seriously look for some unified modelling between being and representing information in the sub-particle domain.

    I know that by now I've pushed my luck too far and you should rightfully close this thread. I'd appreciate if it could be left online so people could still contact me in private with their ideas. Thank you!
     
    Last edited: Dec 15, 2015
  7. Dec 15, 2015 #6

    Nugatory

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    yep...
     
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