Towards a Coherent Theory of Physics and Mathematics: The Theory–Experiment Connection

The problem of how mathematics and physics are related at a foundational level is of interest. The approach taken here is to work towards a coherent theory of physics and mathematics together by examining the theory experiment connection. The role of an implied theory hierarchy and use of computers in comparing theory and experiment is described. The main idea of the paper is to tighten the theory experiment connection by bringing physical theories, as mathematical structures over C, the complex numbers, closer to what is actually done in experimental measurements and computations. The method replaces C by C_n which is the set of pairs, R_n,I_n, of n figure rational numbers in some basis. The properties of these numbers are based on those of numerical measurement outcomes for continuous variables. A model of space and time based on R_n is discussed. The model is scale invariant with regions of constant step size interrupted by exponential jumps. A method of taking the limit n→∞ to obtain locally flat continuum-based space and time is outlined. Also R_n based space is invariant under scale transformations. These correspond to expansion and contraction of space relative to a flat background. The location of the origin, which is a space and time singularity, does not change under these transformations. Some properties of quantum mechanics, based on C_n and on R_n space are briefly investigated.     

The BaBar Experiment‘s Distributed Computing Model

In order to face the expected increase in statistics between now and 2005,the Babar experiment at SLAC is evolving its computing model toward a distributed multitier system.It is foreseen that data will be spread among Tier-A centers and deleted from the SLAC center,A unifrom computing enviromment is being deployed in the centers,the network bandwidth is continuously increased and data distribution tools has been designed in order to reach a transfer rate of -100 TB of data per year,In parallel,smaller Tier-B and C sites receive subsets of data,presently in Kanga-Root[1] format and later in Objectivity[2] format,GRID tools will be used for remote job submission.     

The Nuclear Spin Scissors Mode—Theory and Experiment

A new type of nuclear collective motion—the spin scissors mode—was predicted seven years ago. Promising signs of its existence in ²³²Th were found. We perform a systematic analysis of experimental data on M1 excitations in rare earth nuclei to find traces of the spin scissors mode in this area. Obvious signs of its existence will be demonstrated. We propose new criteria to attribute the observed 1⁺ states to the scissors mode, entailing that the agreement of the experimental data with the results of our calculations and with the sum rules is improved substantially.     

Emergence of Classicality in Stern–Gerlach Experiment via Self-Gravity

Emergence of classicality from quantum mechanics, a hotly debated topic, has had no satisfactory resolution so far. Various approaches including decoherence and gravitational interactions have been suggested. In the present work, the Schrödinger–Newton model is used to study the role of semi-classical self-gravity in the evolution of massive spin-1/2 particles in a Stern-Gerlach experiment. For small mass, evolution of the initial wavepacket in a spin superposition shows a splitting in the magnetic field gradient into two trajectories as in the standard Stern–Gerlach experiment. For larger mass, the deviations from the central path are less than in the standard Stern–Gerlach case, while for high enough mass, the wavepacket does not split, and instead follows the classical trajectory for a magnetic moment in inhomogeneous magnetic field. This indicates the emergence of classicality due to self-gravitational interaction when the mass is increased. In contrast, decoherence which is a strong contender for emergence of classicality, leads to a mixed state of two trajectories corresponding to the spin-up and spin-down states, and not the classically expected path. The classically expected path of the particle probably cannot be explained even in the many-worlds interpretation of quantum mechanics. Stern–Gerlach experiments in the macroscopic domain are needed to settle this question.     

Complex Modulation in Plasmon-Assisted Transmission Spectra of a Two-Slit Structure

We study the plasmon-assisted transmission of two kinds of slit structures in a 290-nm-thick silver film on a glass substrate. For the two-slit structure, the total transmission intensity spectra displays a complex modulation, which is attributed to different propagation constants of the surface plasmon polaritons （SPPs） on the silver-air and silver-glass interfaces. Replacing one of the two slits by a shallow corrugation results in a simple sinusoidal intensity modulation because of the only effective SPP excitation and propagation on the silver-air interface. These confirm the role of different SPP propagations and interference in the transmission properties of metal nanoslits.     

The Linux Based Distributed Data Acquisition System for the ISTRA＋ Experiment

The DAQ hardware of the ISTRA experiment consists of the VME system crate that contains two PCI-VME bridges interfacing two PC‘s with VME,external interrupts receiver,the readout controller for dedicated front-end electronics,the read-out controller buffer memory module,the VME-CAMAC interface,and additional control modules,The DAQ computing consist of 6 PC‘s running the Linux operating system and linked into LAN.The first PC serves the external interrupts and acquires the data from front-end electronics,The second one is the slow control computer.The remaining PC‘s host the monitoring and data analysis software.The Linux based DAQ software provides the external interrupts procssing,the data acquisition,recording,and distribution between monitoring and data analysis tasks running at DAQ PC‘s.The monitoring programs are based on two packages for data visualization:home-written on and the ROOT system.My SQl is used as a DAQ database.     

The rock–paper–scissors game

Rock–Paper–Scissors (RPS), a game of cyclic dominance, is not merely a popular children’s game but also a basic model system for studying decision-making in non-cooperative strategic interactions. Aimed at students of physics with no background in game theory, this paper introduces the concepts of Nash equilibrium and evolutionarily stable strategy, and reviews some recent theoretical and empirical efforts on the non-equilibrium properties of the iterated RPS, including collective cycling, conditional response patterns and microscopic mechanisms that facilitate cooperation. We also introduce several dynamical processes to illustrate the applications of RPS as a simplified model of species competition in ecological systems and price cycling in economic markets.     

The Tsallis–Laplace transform

We introduce here the q$q$-Laplace transform as a new weapon in Tsallis’ arsenal, discussing its main properties and analyzing some examples. The q$q$-Gaussian instance receives special consideration. Also, we derive the q$q$-partition function from the q$q$-Laplace transform.     

The quasi–abelian limit

A new, non perturbative, eikonal method called the “quasi abelian limit” (QAL) is suggested for high energy quark (nucleon) scattering involving the exchange of all possible, non interacting, non abelian gluons (mesons). With this method, those functional integrals defining, e.g., the exchange of color cooordinates in quark–quark scattering, are replaced by a finite number of quadratures over a subset of their coordinates. Mathematically, this procedure is not rigourous, because an unjustified interchange of limits has been performed; physically, it corresponds to the observation that the non perturbative sum over all color–moment fluctuations can vanish at arbitrarily high energies. The QAL generates a result in agreement with a corrected, “contiguity” calculation, when the latter is summed over all perturbative orders. Received: 30 August 1999 /Published online: 17 March 2000     

The fluctuation–dissipation theorem

A system in equilibrium will in general exhibit microscopic fluctuations about the equilibrium state. The fluctuation–dissipation theorem relates the spectrum of these fluctuations to a solution of the macroscopic equation describing the approach to equilibrium from a non-equilibrium state. The aim here is to show exactly what the theorem is and how it is to be used. An account of the quantum version of the theorem is given in three parts, depending on the solution of the macroscopic equation used to express the fluctuations: the relaxation function, the response function or the Green function for continuous systems. Each part is illustrated with an example: charge fluctuations in an RLC circuit for the first two and electric field fluctuations in vacuum for the last.     

The Born–Infeld sphaleron

We study the SU(2) electroweak model in which the standard Yang–Mills coupling is supplemented by a Born–Infeld term. The deformation of the sphaleron and bisphaleron solutions due to the Born–Infeld term is investigated and new branches of solutions are exhibited. Especially, we find a new branch of solutions connecting the Born–Infeld sphaleron to the first solution of the Kerner–Gal'tsov series.     

A Rigorous Analysis of the Clauser–Horne–Shimony–Holt Inequality Experiment When Trials Need Not be Independent

The Clauser–Horne–Shimony–Holt (CHSH) inequality is a constraint that local hidden variable theories must obey. Quantum Mechanics predicts a violation of this inequality in certain experimental settings. Treatments of this subject frequently make simplifying assumptions about the probability spaces available to a local hidden variable theory, such as assuming the state of the system is a discrete or absolutely continuous random variable, or assuming that repeated experimental trials are independent and identically distributed. In this paper, we do two things: first, show that the CHSH inequality holds even for completely general state variables in the measure-theoretic setting, and second, demonstrate how to drop the assumption of independence of subsequent trials while still being able to perform a hypothesis test that will distinguish Quantum Mechanics from local theories. The statistical strength of such a test is computed.     

Experiment to Test Whether We Live in a Four-Dimensional Physical Space–Time

For quantum systems, whose energy ratios E_n/E₀ are integers, and |E₀| is the smallest energy, the time dependent wavefunctions and expectation values of time independent operators have time periodicitiy with a time period T equal to T = h/|E₀|, where h is the Planck constant. This periodicity is imposed on the wavefunctions due to undersampling in energy, but following a similarity with aliasing in signal analysis, it may allow to probe future and past events under the condition that our world is in reality a true four-dimensional, “static” space–time. We suggest an experiment to test that possibility. A positive result will indicate that we live in a four-dimensional space–time. A negative result (not getting signals from the future) will indicate that four-dimensional space–time is not physical one and that we live in a three-dimensional space with a time.     

The Measurement of Glass Elastic Modulus by Using of Newton＇s Ring Experiment

弹性模量是衡量物体抵抗形变能力的重要物理量,本文在对牛顿环这一大学物理经典实验研究的基础之上,对牛顿环仪进行了改装,从理论上分析光学平板玻璃与平凸透镜接触端暗斑大小与外力的关系。测定弹性模量,同时利用MTALAB进行数据处理。     

The phenomenology of Dvali–Gabadadze–Porrati cosmologies

Cosmologists today are confronted with the perplexing reality that the universe is currently accelerating in its expansion. Nevertheless, the nature of the fuel that drives today's cosmic acceleration is an open and tantalizing mystery. There exists the intriguing possibility that the acceleration is not the manifestation of yet another mysterious ingredient in the cosmic gas tank (dark energy), but rather our first real lack of understanding of gravity itself, and even possibly a signal that there might exist dimensions beyond that which we can currently observe. The braneworld model of Dvali, Gabadadze and Porrati (DGP) is a theory where gravity is altered at immense distances by the excruciatingly slow leakage of gravity off our three-dimensional Universe and, as a modified-gravity theory, has pioneered this line of investigation. I review the underlying structure of DGP gravity and those phenomenological developments relevant to cosmologists interested in a pedagogical treatment of this intriguing model.     

The Vlasov–Poisson–Boltzmann System Near Vacuum

Global classical solutions with small amplitude are constructed for the Cauchy problem to the Vlasov–Poisson–Boltzmann system, which describes the dynamics of charged particles interacting with their self-consistent electrostatic potential as well as with themselves through collisions. Received: 29 September 2000 / Accepted: 27 November 2000     

The Lagnese–Stellmacher Potentials Revisited

We give a new proof of a classical result of Lagnese and Stellmacher, characterizing all Huygens’ operators of the form , where q(x) depends on only one variable. The proof amounts to characterize the Schrödinger operators with a finite heat kernel expansion.