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Quantum mechanics and determinism

  1. Apr 8, 2012 #1
    im currently writing a paper for one of my classes, and part of that paper requires me to "Discuss also the question of determinism in Newton’s theory: explain why Newton’s mechanics suggests the “Clockwork” Universe. Briefly mention resolution of these issues in the modern developments of Quantum Mechanics in the 20th century. "

    i have researched and understand determinism and the clockwork universe, however i am yet to find an article that explains how quantum mechanics helps resolve the suggestion of determinism and a clockwork universe. part of that reason is i am only in early physics and calc classes and have never done any quantum mechanics. im not asking anyone to write my paper, but i really have no idea how to answer this question and im having a hard time finding answers.

    please help.
     
  2. jcsd
  3. Apr 8, 2012 #2
    Well, that actually depends on your interpretation of Q.M., so I'll explain the observation:

    We observe, upon measurement, the destruction of determinism because of wave function collapse, which suggests a literal random process that decides which of the infinite possible scenarios is the one where we live. This is what you observe, and should be enough to discuss the breakdown of determinism.

    Now onto the interpretation:
    Some interpretations say collapse is an actual process (most of them, however, do not state and lack the means to state when it happens), and is the only breakdown of determinism in known physics. The main such interpretation is the Copenhagen.
    Other interpretations say collapse is an epiphenomenon of something else (most notably, quantum decoherence), and that in fact determinism is never lost in the whole universe, and there is a constant superposition of wavefunctions all the time. The main such interpretation is Relative State (better known as Many-Worlds).

    Regardless of your interpretation, what is observed is what was described above: loss of determinism/true randomness in wavefunction collapse. How you deal with that is the personal matters of interpretation.
     
  4. Apr 8, 2012 #3
    This is a novel and natural interpretation of QM based on determinism. The idea is a 'conceptual' reconsideration of the wave-particle duality: "Similarly to a "particle in a box" or to a "vibrating string", the constraint of intrinsic periodicity can be used as semi-classical quantization condition, with remarkable matching to ordinary relativistic quantum mechanics." ... without introducing any hidden variable.

    Title: Clockwork quantum universe (IV prize, FQXi, 2011)

    Author: Donatello Dolce

    Abstract: Besides the purely digital or analog interpretations of reality there is a third possible description which incorporates important aspects of both. This is the cyclic interpretation of reality. In this scenario every elementary system is described by classical fields embedded in cyclic space-time dimensions. We will address these cyclic fields as "de Broglie internal clocks". They constitute the deterministic gears of a consistent deterministic description of quantum relativistic physics, providing in addiction an appealing formulation of the notion of time.

    http://www.fqxi.org/community/essay/winners/2011.1#dolce


    You might also readsome of most recent publications of the same auhor.



    Title: Compact Time and Determinism for Bosons: foundations (Foundations of physics, 2011)

    Abstract: Free bosonic fields are investigated at a classical level by imposing their characteristic de Broglie periodicities as constraints. In analogy with finite temperature field theory and with extra-dimensional field theories, this compactification naturally leads to a quantized energy spectrum. As a consequence of the relation between periodicity and energy arising from the de Broglie relation, the compactification must be regarded as dynamical and local. The theory, whose fundamental set-up is presented in this paper, turns out to be consistent with special relativity and in particular respects causality. The non trivial classical dynamics of these periodic fields show remarkable overlaps with ordinary quantum field theory. This can be interpreted as a generalization of the AdS/CFT correspondence.

    http://arxiv.org/abs/0903.3680

    http://www.springerlink.com/content/g324131430841515/


    Title: Gauge interaction as periodicity modulation (Annals of Physics, 2012)

    Abstract: The paper is devoted to a geometrical interpretation of gauge invariance in terms of the formalism of field theory in compact space–time dimensions (Dolce, 2011) [8]. In this formalism, the kinematic information of an interacting elementary particle is encoded on the relativistic geometrodynamics of the boundary of the theory through local transformations of the underlying space–time coordinates. Therefore gauge interactions are described as invariance of the theory under local deformations of the boundary. The resulting local variations of the field solution are interpreted as internal transformations. The internal symmetries of the gauge theory turn out to be related to corresponding space–time local symmetries. In the approximation of local infinitesimal isometric transformations, Maxwell’s kinematics and gauge invariance are inferred directly from the variational principle. Furthermore we explicitly impose periodic conditions at the boundary of the theory as semi-classical quantization condition in order to investigate the quantum behavior of gauge interaction. In the abelian case the result is a remarkable formal correspondence with scalar QED.


    http://www.sciencedirect.com/science/article/pii/S0003491612000255

    http://arxiv.org/abs/1110.0315


    Title: On the intrinsically cyclic nature of space-time in elementary particles (Journal of Physics: Conference Series, 2012)

    Abstract: We interpret the relativistic and quantum behavior of elementary particles in terms of elementary cycles. This represents a generalization of de Broglie hypothesis of intrinsically "periodic phenomenon". Similarly to a "particle in a box" or to a "vibrating string", the constraint of intrinsic periodicity can be used as semi-classical quantization condition, with remarkable matching to ordinary relativistic quantum mechanics. In this formalism the retarded and local variations of four-momentum characterizing relativistic interactions can be equivalently expressed in terms of retarded and local variations of "de Broglie internal clock" space-time periodicity.

    http://iopscience.iop.org/1742-6596/343/1/012031


    Title: de Broglie Deterministic Dice and emerging Relativistic Quantum Mechanics (Journal of Physics: Conference Series, 2011)

    Abstract: Generalizing the de Broglie hypothesis of intrinsically periodic matter fields, it is shown that the basic quantum behavior of ordinary field theory can be retrieved in a semi-classical and geometrical way from the assumption of intrinsic periodicity of elementary systems. The geometrodynamical description of interactions that arises in this theory provides an intuitive interpretation of Maldacena's conjecture and it turns out to be of the same type of the one prescribed by general relativity.
    http://iopscience.iop.org/1742-6596/306/1/012049/

    http://arxiv.org/abs/1111.3319
     
    Last edited: Apr 8, 2012
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