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Register a new userOld Game, New Rules: Rethinking The Form of Physics
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Christian Baumgarten
Publication date
2016
fields
Physics
and research's language is
English
Authors
Christian Baumgarten
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We investigate the modeling capabilities of sets of coupled classical harmonic oscillators (CHO) in the form of a modeling game. The application of simple but restrictive rules of the game lead to conditions for an isomorphism between Lie-algebras and real Clifford algebras. We show that the correlations between two coupled classical oscillators find their natural description in the Dirac algebra and allow to model aspects of special relativity, inertial motion, electromagnetism and quantum phenomena including spin in one go. The algebraic properties of Hamiltonian motion of low-dimensional systems can generally be related to certain types of interactions and hence to the dimensionality of emergent space-times. We describe the intrinsic connection between phase space volumes of a 2-dimensional oscillator and the Dirac algebra. In this version of a phase space interpretation of quantum mechanics the (components of the) spinor wave-function in momentum space are abstract canonical coordinates, and the integrals over the squared wave function represents second moments in phase space. The wave function in ordinary space-time can be obtained via Fourier transformation. Within this modeling game, 3+1-dimensional space-time is interpreted as a structural property of electromagnetic interaction. A generalization selects a series of Clifford algebras of specific dimensions with similar properties, specifically also 10- and 26-dimensional real Clifford algebras.
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Sports are spontaneous generators of stories. Through skill and chance, the script of each game is dynamically written in real time by players acting out possible trajectories allowed by a sports rules. By properly characterizing a given sports ecology of `game stories, we are able to capture the sports capacity for unfolding interesting narratives, in part by contrasting them with random walks. Here, we explore the game story space afforded by a data set of 1,310 Australian Football League (AFL) score lines. We find that AFL games exhibit a continuous spectrum of stories rather than distinct clusters. We show how coarse-graining reveals identifiable motifs ranging from last minute comeback wins to one-sided blowouts. Through an extensive comparison with biased random walks, we show that real AFL games deliver a broader array of motifs than null models, and we provide consequent insights into the narrative appeal of real games.
We review of the interface between (theoretical) physics and information for non-experts. The origin of information as related to the notion of entropy is described, first in the context of thermodynamics then in the context of statistical mechanics. A close examination of the foundations of statistical mechanics and the need to reconcile the probabilistic and deterministic views of the world leads us to a discussion of chaotic dynamics, where information plays a crucial role in quantifying predictability. We then discuss a variety of fundamental issues that emerge in defining information and how one must exercise care in discussing concepts such as order, disorder, and incomplete knowledge. We also discuss an alternative form of entropy and its possible relevance for nonequilibrium thermodynamics. In the final part of the paper we discuss how quantum mechanics gives rise to the very different concept of quantum information. Entirely new possibilities for information storage and computation are possible due to the massive parallel processing inherent in quantum mechanics. We also point out how entropy can be extended to apply to quantum mechanics to provide a useful measurement for quantum entanglement. Finally we make a small excursion to the interface betweeen quantum theory and general relativity, where one is confronted with an ultimate information paradox posed by the physics of Black Holes. In this review we have limited ourselves; not all relevant topics that touch on physics and information could be covered.
Physics of non-inertial reference frames is a generalizing of Newtons laws to any reference frames. The first, Law of Kinematic in non-inertial reference frames reads: the kinematic state of a body free of forces conserves and determinates a constant n-th order derivative with respect to time being equal in absolute value to an invariant of the observers reference frame. The second, Law of Dynamic extended Newtons second law to non-inertial reference frames and also contains additional variables there are higher derivatives of coordinates. Dynamics Law in non-inertial reference frames reads: a force induces a change in the kinematic state of the body and is proportional to the rate of its change. It is mean that if the kinematic invariant of the reference frame is n-th derivative with respect the time, then the dynamics of a body being affected by the force F is described by the (n+1)-th differential equation. The third, Law of Static in non-inertial reference frames reads: the sum of all forces acting a body at rest is equal to zero.
We study four-dimensional gauge theories with arbitrary simple gauge group with $1$-form global center symmetry and $0$-form parity or discrete chiral symmetry. We canonically quantize on $mathbb{T}^3$, in a fixed background field gauging the $1$-form symmetry. We show that the mixed $0$-form/$1$-form t Hooft anomaly results in a central extension of the global-symmetry operator algebra. We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite-size torus. We discuss the consistency of these constraints with both older and recent semiclassical calculations in $SU(N)$ theories, with or without adjoint fermions, as well as with their conjectured infrared phases.
The rare decay $Btopiell^+ell^-$ arises from $bto d$ flavor-changing neutral currents and could be sensitive to physics beyond the Standard Model. Here, we present the first $ab$-$initio$ QCD calculation of the $Btopi$ tensor form factor $f_T$. Together with the vector and scalar form factors $f_+$ and $f_0$ from our companion work [J. A. Bailey $et~al.$, Phys. Rev. D 92, 014024 (2015)], these parameterize the hadronic contribution to $Btopi$ semileptonic decays in any extension of the Standard Model. We obtain the total branching ratio ${text{BR}}(B^+topi^+mu^+mu^-)=20.4(2.1)times10^{-9}$ in the Standard Model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij $et~al.$, JHEP 1212, 125 (2012)]. Note added: after this paper was submitted for publication, LHCb announced a new measurement of the differential decay rate for this process [T. Tekampe, talk at DPF 2015], which we now compare to the shape and normalization of the Standard-Model prediction.
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