Physical Invariants Research Articles

Tests of time-reversal invariance in nuclear and particle physics.

There is a theorem that states that there can be no null test of time-reversal invariance (T symmetry) in exclusive reactions; that is, T symmetry does not require any single observable to vanish. This theorem is extended to inclusive reactions. Also, a general argument, that an experimental observable vanishes from T symmetry if a corresponding operator changes sign under time reversal, is shown to be invalid.

Towards a classification of su(2)⊕...⊕su(2) modular invariant partition functions

The complete classification of Wess–Zumino–Novikov–Witten modular invariant partition functions is known for very few affine algebras and levels, the most significant being all levels of A1 and A2 and level 1 of all simple algebras. Here, the classification problem is addressed for the nicest high rank semisimple affine algebras: (A1(1))⊕r. Among other things, all automorphism invariants are found explicitly for all levels k=(k1,...,kr), and the classification for A(1)1⊕A(1)1 is completed for all levels k1, k2. The classification problem for (A1(1))⊕r is also solved for any levels ki with the property that for i ≠ j each gcd(ki+2,kj+2)≤3. In addition, some physical invariants are found which seem to be new. Together with some recent work by Stanev, the classification for all (A1(1))k⊕r could now be within sight.

The inertia tensor as a basis for the perception of limb orientation.

The ability of humans to perceive the spatial orientation of an occluded arm was investigated. It was hypothesized that this ability is tied to the arm's inertial eigenvectors, invariant mechanical parameters corresponding to a limb's axes of rotational symmetry. By breaking the coincidence between the eigenvectors of the arm and its longitudinal axis, 3 experiments were directed at the possibility that the perceived orientation of an occluded arm would vary as a function of the eigenvectors. Overall, the angles in which the arm was positioned were affected by the direction in which the eigenvectors of the limb were oriented by small appended masses. Discussion focused on the importance of physical invariants for proprioception.

The geomagnetic eccentric dipole: facts and fallacies

The geomagnetic field is sometimes approximated as that of a single dipole displaced from the geocentre, i.e. by an eccentric dipole. By investigating how the field can be represented exactly by a spherical harmonic (multipole) series at a displaced origin, it is shown how this eccentric dipole depends on the choice of criterion of best fit. In particular it is explained how, in some approximations, the ‘best’ eccentric dipole need not be parallel to, or have the same magnitude as, the geocentric dipole, despite the physical invariance of the true dipole moment to change of origin. Finally, the reader is warned about attempts to give physical significance to the position of the eccentric dipole.

The rank-four heterotic modular invariant partition functions

In this paper, we develop several general techniques to investigate modular invariants of conformal field theories whose algebras of the holomorphic and anti-holomorphic sectors are different. As an application, we find all such “heterotic” WZNW physical invariants of (horizontal) rank four: there are exactly seven of these, two of which seem to be new. Previously, only those of rank ⩽ 3 have been completely classified. We also find all physical modular invariants for su(2) k 1 × su(2) k 2 , for 22 > k 1 > k 2, and k 1 = 28, k 2 < 22, completing the classification of Ref. [9].

THE LOW LEVEL MODULAR-INVARIANT PARTITION FUNCTIONS OF RANK-TWO ALGEBRAS

Using the self-dual lattice method, we make a systematic search for modular-invariant partition functions of the affine algebras g(1) of g=A2, A1+A1, G2, and C2. Unlike previous computer searches, this method is necessarily complete. We succeed in finding all physical invariants for A2 at levels ≤32, for G2 at levels ≤31, for C2 at levels ≤26, and for A1+A1 at levels k1=k2≤21. This work thus completes a recent A2 classification proof, where the levels k=3, 5, 6, 9, 12, 15, 21 had been left out. We also compute the dimension of the (Weyl-folded) commutant for these algebras and levels.

Post-Newtonian gravity: its theory--experiment interface

The local non-gravitational physics of matter possesses, to very high degree, two observational features: (1) cosmological constancy of its dimensionless numbers in Earth laboratories as well as throughout spacetime, and (2) rotational invariance. This strongly implies that cosmological--gravitational physics is metric. We review the properties of metric gravity---which represents a broad class of theories of gravity including general relativity, a highly unique metric theory which also fulfils the strong equivalence principle, i.e., spacetime invariance of local gravitational physics, as well. Although the more general parametrized post-Newtonian (PPN) gravitational metric field is considered, and its empirical status is reviewed in the appendix, particular attention is given to the most viable degrees of freedom in metric gravity which are parametrized by two of the PPN coefficients and , both presently experimentally determined to a part in to be in accord with general relativity's predictions. A new determination of and using existing radar ranging data to Viking Mars landers is described which involves the simultaneous fit of two post-Newtonian effects---Shapiro time delay of radar propagation and polarization of inner planet orbits if the Sun's gravitational-to-inertial mass ratio differs from 1. Methods for measuring these aspects of gravity to a part in in the future are discussed, and the special theoretical significance in reaching this precision is outlined. Second post-Newtonian order renormalizations of first post-Newtonian order gravity effects at the level (the Sun's fractional gravitational self-energy) are illustrated as new measurement objectives for the future.

Hierarchical order of Galilei and Lorentz invariance in the structure of matter

The structure of matter shows a hierarchical order: (1) from Lorentz invariance in high-energy physics; (2) to Galilei invariance in the low-energy nonrelativistic limit of high-energy physics; and (3) again to Lorentz invariance in condensed matter physics (where the velocity of sound takes the place of the velocity of light). The hierarchical order can be continued downward further to: (4) non-relativistic (velocity small compared to the velocity of sound) condensed matter excitons, obeying Galilei invariance; and (5) to excitonic matter obeying Lorentz invariance with an excitonic matter sound velocity. It was previously conjectured that Lorentz invariance of high-energy physics is preceded by Galilei invariance at the Planck scale. Still further, the conjectured Galilei invariance at the Planck scale may be the result of an underlying five-dimensional non-Euclidean conform invariant metric structure, with three spatial and two time dimensions, compactified onto three spatial and one time dimension.

Null tests of time-reversal invariance.

It has been proved1 that there exists no null test of time-reversal invariance (TRI) in nuclear and particle physics in any reaction with two particles in and two particles out. That is, there is no single experimental observable that is required to be zero by TRI. This follows from the fact that TRI equates a reaction observable to an observable in the inverse reaction, so the difference (or sum) of the two is zero. Even in elastic scattering, which is its own inverse reaction, two different observables are related by TRI; e.g., polarization and analyzing power, so that Ay − Py = 0. Because of this requirement to compare two experimental observables, one of which is often difficult to measure with precision (say 1%), it is easy to understand why such tests of T-symmetry have rarely attained the 1% level of experimental accuracy. In strong contrast, since null tests of parity conservation are available, e.g. Az = 0 from P-symmetry, the weak-interaction parity non-conserving contribution to Az in pp scattering has been determined to the truly remarkable accuracy of 2.2 × 10−8 (ref. 2). Thus, it is clear that a comparable null test of T-symmetry would permit an improvement in experimental precision of several orders of magnitude.

A Possible Origin of Gauge Invariance in Low Energy Physics

A Possible Origin of Gauge Invariance in Low Energy Physics

A possible origin of gauge invariance in low energt physics

It is pointed out that a part of the gauge invariance in the low energy region, say, lower than the GUT or the Planck energy could be an induced symmetry describable with the Berry phase potential due to partial compactification of a higher dimensional space-time. A model lagrangian with a U (1) gauge symmetry in six dimensions is shown to double the symmetry in four dimensions to enjoy U (1) X U (1) in a limit where the compactification mass scale is sent to infinity. The generalization to non-abelian theories is discussed.

Monte Carlo simulation of CPN-1 models.

Numerical simulations of two-dimensional ${\mathrm{CP}}^{N\ensuremath{-}1}$ models are performed at $N=2, 10, \mathrm{and} 21$. The lattice action adopted depends explicitly on the gauge degrees of freedom and shows precocious scaling. Our tests of scaling are the stability of dimensionless physical quantities (second moment of the correlation function versus inverse mass gap, magnetic susceptibility versus square correlation length) and rotation invariance. Topological properties of the models are explored by measuring the topological susceptibility and by extracting the Abelian string tension. Several different (local and nonlocal) lattice definitions of topological charge are discussed and compared. The qualitative physical picture derived from the continuum $\frac{1}{N}$ expansion is confirmed, and agreement with quantitative $\frac{1}{N}$ predictions is satisfactory. Variant (Symanzik-improved) actions are considered in the C${\mathrm{P}}^{1}$ \ensuremath{\cong} O(3) case and agreement with universality and previous simulations (when comparable) is found. The simulation algorithm is an efficient mixture of over-heat-bath and microcanonical algorithms. The dynamical features and critical exponents of the algorithm are discussed in detail.

Klein's group-theoretic conception in the mechanics of a material point

The aim of this paper is to show that the physical principle of invariance and the condition that mechanics be Lagrangian make it possible to extend Klein's conception, originally proposed for geometry, to the mechanics of a material point. It thus becomes possible to place the known systems of mechanics (classical and relativistic) on a unified theoretical basis, after proving their uniqueness, and to outline a way to construct new, alternative systems. This may prove useful for the interpretation of new experimental factors. It should be borne in mind that transformation groups are one of the most natural and universal tools for investigating and classifying fundamental phenomena in the exact sciences. As a mathematical object, groups can be studied theoretically in advance, independently of experimentation. Hence physical invariance principles, which develop Klein's conception, may be considered to be one of the simplest and most aesthetically justified sources of scientific predictions with a claim to reliability.

Adiabatic invariance, the cornerstone of modern physics

The article by M. Greenspan on the Boltzmann‐Ehrenfest adiabatic principle [J. Acoust. Soc. Am. 27, 34 (1955)] is used as the starting point for discussing the role of adiabatic invariance (or integrability) in modern physics. These conserved properties of open systems constitute the key concept upon which all advances in modern physics have been focused. These include the origin of thermodynamic irreversibility for Hamiltonian systems and the quantization of motion. Delauney (1860) was first to employ adiabatic invariants as dynamical variables with an aim toward determining the stability of the solar system. This issue eventually culminated in the work by Kolmogorov, Arnold, and Moser on the stability of nearly integrable systems. The solution to the problem of soliton motion by the inverse scattering transformation is in fact a transformation to the adiabatic invariant as the canonical momentum. Recent acoustical applications of adiabatic invariance include a determination of the potential in an acoustic levitator and a prediction of second sound in acoustic turbulence.

Should the classical variance be used as a basic measure in standards metrology?

Since a measurement is no better than its uncertainty, specifying the uncertainty is a very important part of metrology. One is inclined to believe that the fundamental constants in physics are invariant with time and that they are the foundation upon which to build internationl system (SI) standards and metrology. Therefore clearly specifying uncertainties for these physical invariants at state-of-the-art levels should be one of the principal goals of metrology. However, by the very act of observing some physical quantity we may perturb the standard, thus introducing uncertainties. The random deviations in a series of observations may be caused by the measurement system, by environmental coupling or by intrinsic deviations in the standard. For these reasons and because correlated random noise is as commonly occurring in nature as uncorrelated random noise, the universal use of the classical variance, and the standard deviation of the mean may cloud rather than clarify questions regarding uncertainties; i.e., these measures are well behaved only for random uncorrelated deviations (white noise), and white noise is typically a subset of the spectrum of observed deviations. The assumption that each measurement in a series is independent because the measurements are taken at different times should be called into question if, in fact, the series is not random and uncorrelated, i.e., does not have a white spectrum. In this paper, studies of frequency standards, standard-volt cells, and gauge blocks provide examples of long-term random-correlated time series which indicate behavior that is not “white” (not random and uncorrelated). This paper outlines and illustrates a straightforward time-domain statistical approach, which for power-law spectra yields an alternative estimation method for most of the important random power-law processes encountered. Knowing the spectrum provides for clearer uncertainty assessment in the presence of correlated random deviations, the statistical approach outlined also provides a simple test for a white spectrum, thus allowing a metrologist to know whether use of the classical variance is suitable or whether to incorporate better uncertainty assessment procedures, e.g., as outlined in the paper.

The Impact of Special Relativity on Theoretical Physics

As one of my colleagues put it, “Asking about the impact of special relativity on theoretical physics is like asking about the impact of Shakespeare on the English language.” An impossibly large, even senseless, task. Special relativity is a fact of life, part and parcel of the way nature is. If its impact on everyday life is slight, its impact on physicists' thinking is profound. Space and universal, inexorable time were rudely united into space‐time by Albert Einstein's discovery of special relativity. Explorations of the properties of space‐time, of the covariance of physical laws, and of the physical invariants of nature, together with quantum mechanics, led to the formulation of relativistic quantum field theories. The external symmetries of space‐time were augmented by abstract spaces for internal symmetries corresponding to invariant (conserved) quantities such as isospin, strangeness and charm. The whole worldview of modern theoretical physics can be traced back to the fundamental postulate or idea that physical phenomena do not change just because you happen to be moving by, instead of standing still, when observing them. Rotations and other transformations in internal spaces have replaced “moving by,” but the idea is the same.

The Bayliss-Isaacson algorithm and the constraint restoration method are equivalent

Summary Bayliss and Isaacson (1975) method of modifying any given difference scheme so as to ensure total conservation of the appropriate physical invariants is shown to be equivalent to the constraint restoration method of Miele et al. (1968, 1969) subject to the requirement of least-square change of the statevector coordinates. Both methods are applied to enforce conservation of total energy and potential enstrophy in global shallow-water equations models. Some algorithmic differences between the methods are discussed as well as some implications of a posteriori enforcement of conservation of integral invariants on the performance of meteorological numerical weather prediction (NWP) models and the internal energy distribution.

Realist Principles

We list, with discussions, various principles of scientific realism, in order to exhibit their diversity and to emphasize certain serious problems of formulation. Ontological and epistemological principles are distinguished. Within the former category, some framed in semantic terms (truth, reference) serve their purpose vis-à-vis instrumentalism (Part 1). They fail, however, to distinguish the realist from a wide variety of (constructional) empiricists. Part 2 seeks purely ontological formulations, so devised that the empiricist cannot reconstruct them from within. The main task here is to characterize “independence of mind”. A pair of notions, “physical invariance” and “anti-determination”, seem to work. They enable us to assess anew “the problem of constructing the physical out of the phenomenal” (yielding certain clarifications demanded by Goodman). Modern cosmology, especially, is seen to present insuperable obstacles to such empiricist approaches to science. The final section on epistemological principles reveals a morass better avoided in favor of an elementary claim about perception, together with a rejection of any absolute observation/theory dichotomy. Finally, a positive, realist notion of “observable-in-principle” is sketched, and it is suggested that, from the perspective of relativistic cosmology, even this defines no boundary to potential knowledge.

Interpretation of Tests of Time-Reversal Invariance

Some of the most sensitive tests of time-reversal invariance in particle and nuclear physics involve the measurement of certain polarization quantities in elastic scattering which are thought to be exactly zero when time-reversal invariance holds. It is shown that a nonzero result for such quantities need not indicate a violation of time-reversal invariance, but can be the consequence of a dynamics which is time-reversal invariant but which violates rotation or Lorentz invariance. These two alternatives can be told apart by subsidiary measurements.

The role of syllables in speech processing: infant and adult data

An empirical account is offered of some of the constants that infants and adults appear to use in processing speech-like stimuli. From investigations carried out in recent years, it seems that syllable-like sequences act as minimal accessing devices in speech processing. Ss are aware in real time of syllabic structure in words and respond differently to words with the same initial three phonemes if the segmental one is CV /... and the other CVC /---- Likewise, infants seem to be aware that a ‘good’ syllable must have at least one alternation if it is composed of more than one phoneme. When the segment is only one phoneme long, its status is necessarily somewhere between that of the phoneme and the syllable. An important problem that arises with the syllable is that it is an unlikely device for speech acquisition. Indeed, there are a few thousand syllables and the attribution of a given token to a type is far from obvious. Even if physical invariants for syllables in contexts were to be found, the task facing the child still remains one of sorting thousands of types from many more tokens. Issues concerning acquisition versus stable performance will be addressed to further constrain possible models. In addition, I try to show that even though information processing models are useful tools for describing synchronic sections of organisms, the elements that can account for development will have to be uncovered in neighbouring branches.