arXiv subjects

B. Roy Frieden

Publications and source records attributed to B. Roy Frieden.

8 recordsLinked to original sources

arXiv2019

Spontaneous Formation of Universes from Vacuum via Information-induced Holograms

All spontaneous emergence of quantum particles from false vacuums can occur via usual energy-based Lagrangians; or, as we show, via a variational principle of minimum loss of Fisher information. By this principle all material existence in the multiverse, including its life forms, are physical manifestations of Fisher information. The information principle serially formed our universe, and all others, in the multiverse. The resulting expansionary (Big bang) eras of time t and/or space-time x_i, i = x,y,z,t (c=1) for the universes are found to obey probability densities p(t) and p(x_i) of usual exponential forms. The existence of the multiverse allows preservation of invariant values of the 26 physical constants via their relay from one universe to another by successive Lorentzian wormholes. At each relay the emerging constants are represented by the intensities of an input hologram. The information principle was previously used to derive nearly all textbook physics and much cell biology, e.g. the Hodgkin-Huxley (H-H) equations governing ions emerging into biological cells. The equations we derive governing p(t) and p(x_i) for universes coincide with the H-H equations governing ions entering these biological cells. Thus, the information concept holds over a vast range of scale sizes.

physics.gen-ph↗

arXiv2014

Derivation of Principle of Extreme Physical Information

The unknown amplitude law q(x) defining an observed effect may be found using the principle of Extreme Physical Information. EPI is derived as follows. The observations follow an information flow J --> I, with J the information intrinsic to the source and I the Fisher information level in its data, obeying (i) I=4 Integral dx q' -squared. Here q'= dq/dx and p(x) = q(x)-squared is the probability. It was previously shown, using L. Hardy's 5 axioms defining physics, that I = max. Therefore, its variation (ii) delta I = 0. Note that I is generic, obeying (i) for all source effects, whereas J is specific to the particular effect. Hence, rather than having form (i), J obeys (iii) J = Integral dx j[q(x),s(x)] with j some function of its arguments and s(x) a known source, such as of mass, biological fitness, etc. Information I decreases under any irreversible operation such as measurement, so that I l.e. J or, equivalently, I = kJ where 0 l.e. k l.e. 1. Then the variation delta I = k delta J so that property (ii) gives (iv) delta J = 0 as well. Then combining (ii) and (iv), delta(I - J) = 0. Or, I - J = L = extremum. What kind of extremum? Eqs. (i) and (iii) give (v) L=4q'^2 - j[q(x),s(x)]. Differentiating (v), (d^2 L )/(dq'^2) = +8. Then by the Legendre condition the extremum is a minimum. The unknown source effect obeys (vi) I - J= minimum, EPI.

physics.data-an↗

arXiv2006

Information-theoretic significance of the Wigner distribution

A coarse grained Wigner distribution p_{W}(x,u) obeying positivity derives out of information-theoretic considerations. Let p(x,u) be the unknown joint PDF (probability density function) on position- and momentum fluctuations x,u for a pure state particle. Suppose that the phase part Psi(x,z) of its Fourier transform F.T.[p(x,u)]=|Z(x,z)|exp[iPsi(x,z)] is constructed as a hologram. (Such a hologram is often used in heterodyne interferometry.) Consider a particle randomly illuminating this phase hologram. Let its two position coordinates be measured. Require that the measurements contain an extreme amount of Fisher information about true position, through variation of the phase function Psi(x,z). The extremum solution gives an output PDF p(x,u) that is the convolution of the Wigner p_{W}(x,u) with an instrument function defining uncertainty in either position x or momentum u. The convolution arises naturally out of the approach, and is one-dimensional, in comparison with the two-dimensional convolutions usually proposed for coarse graining purposes. The output obeys positivity, as required of a PDF, if the one-dimensional instrument function is sufficiently wide. The result holds for a large class of systems: those whose amplitudes a(x) are the same at their boundaries (Examples: states a(x) with positive parity; with periodic boundary conditions; free particle trapped in a box).

quant-ph↗

arXiv2005

Ab initio yield curve dynamics

We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success of the Nelson Siegel approach to fitting static yield curves and the empirically observed modal structure of yield curves. A practical numerical implementation of this equation of motion is found by using the Karhunen-Loeve expansion and Galerkin's method to formulate a reduced-order model of yield curve dynamics.

physics.data-an↗

arXiv2005

Power laws of complex systems from Extreme physical information

Many complex systems obey allometric, or power, laws y=Yx^{a}. Here y is the measured value of some system attribute a, Y is a constant, and x is a stochastic variable. Remarkably, for many living systems the exponent a is limited to values +or- n/4, n=0,1,2... Here x is the mass of a randomly selected creature in the population. These quarter-power laws hold for many attributes, such as pulse rate (n=-1). Allometry has, in the past, been theoretically justified on a case-by-case basis. An ultimate goal is to find a common cause for allometry of all types and for both living and nonliving systems. The principle I - J = extrem. of Extreme physical information (EPI) is found to provide such a cause. It describes the flow of Fisher information J => I from an attribute value a on the cell level to its exterior observation y. Data y are formed via a system channel function y = f(x,a), with f(x,a) to be found. Extremizing the difference I - J through variation of f(x,a) results in a general allometric law f(x,a)= y = Yx^{a}. Darwinian evolution is presumed to cause a second extremization of I - J, now with respect to the choice of a. The solution is a=+or-n/4, n=0,1,2..., defining the particular powers of biological allometry. Under special circumstances, the model predicts that such biological systems are controlled by but two distinct intracellular information sources. These sources are conjectured to be cellular DNA and cellular transmembrane ion gradients

q-bio.CB↗

arXiv2003

Financial Probabilities from Fisher Information

We present a novel synthesis of Fisher information and asset pricing theory that yields a practical method for reconstructing the probability density implicit in security prices. The Fisher information approach to these inverse problems transforms the search for a probability density into the solution of a differential equation for which a substantial collection of numerical methods exist. We illustrate the potential of this approach by calculating the probability density implicit in both bond and option prices. Comparing the results of this approach with those obtained using maximum entropy we find that Fisher information usually results in probability densities that are smoother than those obtained using maximum entropy.

cond-mat.stat-mech↗

arXiv2000

Classical trajectories compatible with quantum mechanics

Consider any stationary Schroedinger wave equation (SWE) solution $psi (x)$ for a particle. The corresponding PDF on position QTR{em}{x} of the particle is QTR{em}{p}$_{X}(x)=|psi (x)|^{2}$. There is a classical trajectory QTR{em}{x(t)} for the particle that is consistent with this PDF. The trajectory is unique to within an additive constant corresponding to an initial condition QTR{em}{x(0).} However the value of QTR{em}{x(0)} cannot be known. As an example, a free particle in its ground state in a box of length QTR{em}{L} obeys a classical trajectory QTR{em}{x/L - (1/2}$pi)sin (2pi x/L)+t_{0}=t.$ The constant QTR{em}{t}$_{0}$ is an unknowable time displacement. Momentum values, however, cannot be determined by merely differentiating QTR{em}{d/dt} the trajectory QTR{em}{x(t)} and, instead, follow the usual quantification rules of Heisenberg's. This permits position and momentum to remain complementary variables. Our approach is fundamentally different from that of D. Bohm.

quant-ph↗

arXiv1998

Fisher's arrow of `time' in cosmological coherent phase space

Fisher's arrow of `time' in a cosmological phase space defined as in quantum optics (i.e., whose points are coherent states) is introduced as follows. Assuming that the phase space evolution of the universe starts from an initial squeezed cosmological state towards a final thermal one, a Fokker-Planck equation for the time-dependent, cosmological Q phase space probability distribution can be written down. Next, using some recent results in the literature, we derive an information arrow of time for the Fisher phase space cosmological entropy based on the Q function. We also mention the application of Fisher's arrow of time to stochastic inflation models

gr-qc↗