Digital physics is grounded in one or more of the following hypotheses; listed in order of decreasing strength. The universe, or reality: History The hypothesis that the universe is a digital computer was pioneered by Konrad Zuse in his book Rechnender Raum (translated into English as Calculating Space). Related ideas include Carl Friedrich von Weizsäcker's binary theory of ur-alternatives, pancomputationalism, computational universe theory, John Archibald Wheeler's "It from bit", and Max Tegmark's ultimate ensemble. Overview Digital physics suggests that there exists, at least in principle, a program for a universal computer which computes the evolution of the universe. Some try to identify single physical particles with simple bits. Loop quantum gravity could lend support to digital physics, in that it assumes space-time is quantized. Weizsäcker's ur-alternatives Pancomputationalism or the computational universe theory Wheeler's "it from bit"
Fredkin finite nature hypothesisIn digital physics, the Fredkin Finite Nature Hypothesis states that ultimately all quantities of physics, including space and time, are discrete and finite. All measurable physical quantities arise from some Planck scale substrate for multiverse information processing. Also, the amount of information in any small volume of spacetime will be finite and equal to a small number of possibilities. Conceptions Stephen Wolfram in A New Kind of Science, Chapter 9, considered the possibility that energy and spacetime might be secondary derivations from an informational substrate underlying the Planck scale. Fredkin's ideas on inertia According to Fredkin, "the computational substrate of quantum mechanics must have access to some sort of metric to create inertial motion. See also References External links
Non-orientable wormholeIn topology, this sort of connection is referred to as an Alice handle. Theory "Normal" wormhole connection Matt Visser has described a way of visualising wormhole geometry: take a "normal" region of space"surgically remove" spherical volumes from two regions ("spacetime surgery")associate the two spherical bleeding edges, so that a line attempting to enter one "missing" spherical volume encounters one bounding surface and then continues outward from the other. For a "conventional" wormhole, the network of points will be seen at the second surface to be inverted, as if one surface was the mirror image of the other—countries will appear back-to-front, as will any text written on the map. "Reversed" wormhole connection The alternative way of connecting the surfaces makes the "connection map" appear the same at both mouths. This configuration reverses the "handedness" or "chirality" of any objects passing through. Consequences Alice universe Notes
Lamb–Oseen vortexIn fluid dynamics, the Lamb–Oseen vortex models a line vortex that decays due to viscosity. This vortex is named after Horace Lamb and Carl Wilhelm Oseen. Vector plot of the Lamb-Oseen vortex The mathematical model for the flow velocity in the circumferential –direction in the Lamb–Oseen vortex is: with The radial velocity is equal to zero. An alternative definition is to use the peak tangential velocity of the vortex rather than the total circulation where is the radius at which is attained, and the number α = 1.25643, see Devenport et al. The pressure field simply ensures the vortex rotates in the circumferential direction, providing the centripetal force where ρ is the constant density Jump up ^ Saffman, P.Scharnhorst effectThe Scharnhorst effect is a hypothetical phenomenon in which light signals travel faster than c between two closely spaced conducting plates. It was predicted by Klaus Scharnhorst of the Humboldt University of Berlin, Germany, and Gabriel Barton of the University of Sussex in Brighton, England. They showed using quantum electrodynamics that the effective refractive index, at low frequencies, in the space between the plates was less than 1 (which by itself does not imply superluminal signaling). They were not able to show that the wavefront velocity exceeds c (which would imply superluminal signaling) but argued that it is plausible. Explanation Owing to Heisenberg's uncertainty principle, an empty space which appears to be a true vacuum is actually filled with virtual subatomic particles. The effect, however, is predicted to be minuscule. Causality References
Cabibbo–Kobayashi–Maskawa matrixThe matrix A pictorial representation of the six quarks' decay modes, with mass increasing from left to right. In 1963, Nicola Cabibbo introduced the Cabibbo angle (θc) to preserve the universality of the weak interaction. Cabibbo was inspired by previous work by Murray Gell-Mann and Maurice Lévy, on the effectively rotated nonstrange and strange vector and axial weak currents, which he references. In light of current knowledge (quarks were not yet theorized), the Cabibbo angle is related to the relative probability that down and strange quarks decay into up quarks (|Vud|2 and |Vus|2 respectively). In particle physics parlance, the object that couples to the up quark via charged-current weak interaction is a superposition of down-type quarks, here denoted by d′. Mathematically this is: or using the Cabbibo angle: Using the currently accepted values for |Vud| and |Vus| (see below), the Cabbibo angle can be calculated using . θC = 13.02°. or using the Cabibbo angle: λ = s12
Lorentz groupThe mathematical form of Basic properties The Lorentz group is a subgroup of the Poincaré group, the group of all isometries of Minkowski spacetime. Mathematically, the Lorentz group may be described as the generalized orthogonal group O(1,3), the matrix Lie group which preserves the quadratic form on R4. The restricted Lorentz group arises in other ways in pure mathematics. Connected components Each of the four connected components can be categorized by which of these two properties its elements have: Lorentz transformations which preserve the direction of time are called orthochronous. The subgroup of all Lorentz transformations preserving both orientation and the direction of time is called the proper, orthochronous Lorentz group or restricted Lorentz group, and is denoted by SO+(1, 3). The set of the four connected components can be given a group structure as the quotient group O(1,3)/SO+(1,3), which is isomorphic to the Klein four-group. P = diag(1, −1, −1, −1) where
Pontecorvo–Maki–Nakagawa–Sakata matrixIn particle physics, the Pontecorvo–Maki–Nakagawa–Sakata matrix (PMNS matrix), Maki–Nakagawa–Sakata matrix (MNS matrix), lepton mixing matrix, or neutrino mixing matrix, is a unitary matrix[note 1] which contains information on the mismatch of quantum states of leptons when they propagate freely and when they take part in the weak interactions. It is important in the understanding of neutrino oscillations. This matrix was introduced in 1962 by Ziro Maki, Masami Nakagawa and Shoichi Sakata, to explain the neutrino oscillations predicted by Bruno Pontecorvo. The matrix On the left are the neutrino fields participating in the weak interaction, and on the right is the PMNS matrix along with a vector of the neutrino fields diagonalizing the neutrino mass matrix. The PMNS matrix describes the probability of a neutrino of given flavor α to be found in mass eigenstate i. Based on less current data (28 June 2012) mixing angles are: where NH indicates normal hierarchy and IH and
Homogeneity (physics)The definition of homogeneous strongly depends on the context used. For example, a composite material is made up of different individual materials, known as "constituents" of the material, but may be defined as a homogeneous material when assigned a function. For example, asphalt paves our roads, but is a composite material consisting of asphalt binder and mineral aggregate, and then laid down in layers and compacted. In another context, a material is not homogeneous in so far as it composed of atoms and molecules. A few other instances of context are: Dimensional homogeneity (see below) is the quality of an equation having quantities of same units on both sides; Homogeneity (in space) implies conservation of momentum; and homogeneity in time implies conservation of energy. In the context of composite metals is an alloy. Homogeneity, in another context plays a role in cosmology. Fundamental laws of physics should not (explicitly) depend on position in space. Translational invariance