The Uncertainty Relation in "Which-Way" Experiments: How to Observe Directly the Momentum Transfer using Weak Values

A which-way measurement destroys the twin-slit interference pattern. Bohr argued that distinguishing between two slits a distance s apart gives the particle a random momentum transfer \wp of order h/s. This was accepted for more than 60 years, until Scully, Englert and Walther (SEW) proposed a which-way scheme that, they claimed, entailed no momentum transfer. Storey, Tan, Collett and Walls (STCW) in turn proved a theorem that, they claimed, showed that Bohr was right. This work reviews and extends a recent proposal [Wiseman, Phys. Lett. A 311, 285 (2003)] to resolve the issue using a weak-valued probability distribution for momentum transfer, P_wv(\wp). We show that P_wv(\wp) must be wider than h/6s. However, its moments can still be zero because P_wv(\wp) is not necessarily positive definite. Nevertheless, it is measurable in a way understandable to a classical physicist. We introduce a new measure of spread for P_wv(\wp): half of the unit-confidence interval, and conjecture that it is never less than h/4s. For an idealized example with infinitely narrow slits, the moments of P_wv(\wp) and of the momentum distributions are undefined unless a process of apodization is used. We show that by considering successively smoother initial wave functions, successively more moments of both P_wv(\wp) and the momentum distributions become defined. For this example the moments of P_wv(\wp) are zero, and these are equal to the changes in the moments of the momentum distribution. We prove that this relation holds for schemes in which the moments of P_wv(\wp) are non-zero, but only for the first two moments. We also compare these moments to those of two other momentum-transfer distributions and \hat{p}_f-\hat{p}_i. We find agreement between all of these, but again only for the first two moments.Comment: 14 pages, 6 figures, submitted to J. Opt.

Electroweak baryogenesis induced by a scalar field

A cosmological pseudoscalar field coupled to hypercharge topological number density can exponentially amplify hyperelectric and hypermagnetic fields while coherently rolling or oscillating, leading to the formation of a time-dependent condensate of topological number density. The topological condensate can be converted, under certain conditions, into baryons in sufficient quantity to explain the observed baryon asymmetry in the universe. The amplified hypermagnetic field can perhaps sufficiently strengthen the electroweak phase transition, and by doing so, save any pre-existing baryon number asymmetry from extinction.Comment: 8 pages, 4 figure

Grounding Bohmian Mechanics in Weak Values and Bayesianism

Bohmian mechanics (BM) is a popular interpretation of quantum mechanics in which particles have real positions. The velocity of a point x in configuration space is defined as the standard probability current j(x) divided by the probability density P(x). However, this ``standard'' j is in fact only one of infinitely many that transform correctly and satisfy \dot P + \del . j=0. In this article I show that there is a unique j that can be determined experimentally as a weak value using techniques that would make sense to a classical physicist. Moreover, this operationally defined j equals the standard j, so, assuming \dot x = j/P, the possible Bohmian paths can also be determined experimentally from a large enough ensemble. Furthermore, this approach to deriving BM singles out x as the hidden variable, because (for example) the operationally defined momentum current is in general incompatible with the evolution of the momentum distribution. Finally I discuss how, in this setting, the usual quantum probabilities can be derived from a Bayesian standpoint, via the principle of indifference.Comment: 11 page

Large scale magnetogenesis from a non-equilibrium phase transition in the radiation dominated era

We study the generation of large scale primordial magnetic fields by a cosmological phase transition during the radiation dominated era. The setting is a theory of N charged scalar fields coupled to an abelian gauge field, that undergoes a phase transition at a critical temperature much larger than the electroweak scale. The dynamics after the transition features two distinct stages: a spinodal regime dominated by linear long-wavelength instabilities, and a scaling stage in which the non-linearities and backreaction of the scalar fields are dominant. This second stage describes the growth of horizon sized domains. We implement a recently introduced formulation to obtain the spectrum of magnetic fields that includes the dissipative effects of the plasma. We find that large scale magnetogenesis is very efficient during the scaling regime. The ratio between the energy density on scales larger than L and that in the background radiation r(L,T) = rho_B(L,T)/rho_{cmb}(T) is r(L,T) \sim 10^{-34} at the Electroweak scale and r(L,T) \sim 10^{-14} at the QCD scale for L \sim 1 Mpc. The resulting spectrum is insensitive to the magnetic diffusion length. We conjecture that a similar mechanism could be operative after the QCD chiral phase transition.Comment: LaTex, 25 pages, no figures, to appear in Phys. Rev.

Magnetic field generation from non-equilibrium phase transitions

We study the generation of magnetic fields during the stage of particle production resulting from spinodal instabilities during phase transitions out of equilibrium. The main premise is that long-wavelength instabilities that drive the phase transition lead to strong non-equilibrium charge and current fluctuations which generate electromagnetic fields. We present a formulation based on the non-equilibrium Schwinger-Dyson equations that leads to an exact expression for the spectrum of electromagnetic fields valid for general theories and cosmological backgrounds and whose main ingredient is the transverse photon polarization out of equilibrium. This formulation includes the dissipative effects of the conductivity in the medium. As a prelude to cosmology we study magnetogenesis in Minkowski space-time in a theory of N charged scalar fields to lowest order in the gauge coupling and to leading order in the large N within two scenarios of cosmological relevance. The long-wavelength power spectrum for electric and magnetic fields at the end of the phase transition is obtained explicitly. It follows that equipartition between electric and magnetic fields does not hold out of equilibrium. In the case of a transition from a high temperature phase, the conductivity of the medium severely hinders the generation of magnetic fields, however the magnetic fields generated are correlated on scales of the order of the domain size, which is much larger than the magnetic diffusion length. Implications of the results to cosmological phase transitions driven by spinodal unstabilities are discussed.Comment: Preprint no. LPTHE 02-55, 30 pages, latex, 2 eps figures. Added one reference. To appear in Phys. Rev.

Speculations on Primordial Magnetic Helicity

We speculate that above or just below the electroweak phase transition magnetic fields are generated which have a net helicity (otherwise said, a Chern-Simons term) of order of magnitude $N_B + N_L$, where $N_{B,L}$ is the baryon or lepton number today. (To be more precise requires much more knowledge of B,L-generating mechanisms than we currently have.) Electromagnetic helicity generation is associated (indirectly) with the generation of electroweak Chern-Simons number through B+L anomalies. This helicity, which in the early universe is some 30 orders of magnitude greater than what would be expected from fluctuations alone in the absence of B+L violation, should be reasonably well-conserved through the evolution of the universe to around the times of matter dominance and decoupling, because the early universe is an excellent conductor. Possible consequences include early structure formation; macroscopic manifestations of CP violation in the cosmic magnetic field (measurable at least in principle, if not in practice); and an inverse-cascade dynamo mechanism in which magnetic fields and helicity are unstable to transfer to larger and larger spatial scales. We give a quasi-linear treatment of the general-relativistic MHD inverse cascade instability, finding substantial growth for helicity of the assumed magnitude out to scales $\sim l_M\epsilon^{-1}$, where $\epsilon$ is roughly the B+L to photon ratio and $l_M$ is the magnetic correlation length. We also elaborate further on an earlier proposal of the author for generation of magnetic fields above the EW phase transition.Comment: Latex, 23 page

A complete 3D numerical study of the effects of pseudoscalar-photon mixing on quasar polarizations

We present the results of three-dimensional simulations of quasar polarizations in the presence of pseudoscalar-photon mixing in the intergalactic medium. The intergalactic magnetic field is assumed to be uncorrelated in wave vector space but correlated in real space. Such a field may be obtained if its origin is primordial. Furthermore we assume that the quasars, located at cosmological distances, have negligible initial polarization. In the presence of pseudoscalar-photon mixing we show, through a direct comparison with observations, that this may explain the observed large scale alignments in quasar polarizations within the framework of big bang cosmology. We find that the simulation results give a reasonably good fit to the observed data.Comment: 15 pages, 8 figures, significant changes, to appear in EPJ

Magnetogenesis and the dynamics of internal dimensions

The dynamical evolution of internal space-like dimensions breaks the invariance of the Maxwell's equations under Weyl rescaling of the (conformally flat) four-dimensional metric. Depending upon the number and upon the dynamics of internal dimensions large scale magnetic fields can be created. The requirements coming from magnetogenesis together with the other cosmological constraints are examined under the assumption that the internal dimensions either grow or shrink (in conformal time) prior to a radiation dominated epoch. If the internal dimensions are growing the magnitude of the generated magnetic fields can seed the galactic dynamo mechanism.Comment: 27 in RevTex style, four figure

Disorder-specific functional abnormalities during sustained attention in youth with Attention Deficit Hyperactivity Disorder (ADHD) and with Autism

Attention Deficit Hyperactivity Disorder (ADHD) and Autism Spectrum Disorder (ASD) are often comorbid and share behavioural-cognitive abnormalities in sustained attention. A key question is whether this shared cognitive phenotype is based on common or different underlying pathophysiologies. To elucidate this question, we compared 20 boys with ADHD to 20 age and IQ matched ASD and 20 healthy boys using functional magnetic resonance imaging (fMRI) during a parametrically modulated vigilance task with a progressively increasing load of sustained attention. ADHD and ASD boys had significantly reduced activation relative to controls in bilateral striato–thalamic regions, left dorsolateral prefrontal cortex (DLPFC) and superior parietal cortex. Both groups also displayed significantly increased precuneus activation relative to controls. Precuneus was negatively correlated with the DLPFC activation, and progressively more deactivated with increasing attention load in controls, but not patients, suggesting problems with deactivation of a task-related default mode network in both disorders. However, left DLPFC underactivation was significantly more pronounced in ADHD relative to ASD boys, which furthermore was associated with sustained performance measures that were only impaired in ADHD patients. ASD boys, on the other hand, had disorder-specific enhanced cerebellar activation relative to both ADHD and control boys, presumably reflecting compensation. The findings show that ADHD and ASD boys have both shared and disorder-specific abnormalities in brain function during sustained attention. Shared deficits were in fronto–striato–parietal activation and default mode suppression. Differences were a more severe DLPFC dysfunction in ADHD and a disorder-specific fronto–striato–cerebellar dysregulation in ASD

Hypermagnetic Knots, Chern-Simons Waves and the Baryon Asymmetry

At finite hyperconductivity and finite fermionic density the flux lines of long range hypermagnetic fields may not have a topologically trivial structure. The combined evolution of the chemical potentials and of pseudoscalar fields (like the axial Higgs), possibly present for temperatures in the TeV range, can twist the hypercharge flux lines, producing, ultimately, hypermagnetic knots (HK). The dynamical features of the HK depend upon the various particle physics parameters of the model (pseudoscalar masses and couplings, strength of the electroweak phase transition, hyperconductivity of the plasma) and upon the magnitude of the primordial flux sitting in topologically trivial configurations of the hypermagnetic field. We study different cosmological scenarios where HK can be generated. We argue that the fermionic number sitting in HK can be released producing a seed for the Baryon Asymmetry of the Universe (BAU) provided the typical scale of the knot is larger than the diffusivity length scale. We derive constraints on the primordial hypermagnetic flux required by our mechanism and we provide a measure of the parity breaking by connecting the degree of knottedness of the flux lines to the BAU. We rule out the ordinary axion as a possible candidate for production (around temperatures of the order of the GeV) of {\em magnetic} knots since the produced {\em electromagnetic} helicity is negligible (for cosmological standard) if the initial amplitude of the axion oscillations is of the order of the Peccei-Quinn breaking scale.Comment: 30 pages in Revtex style, 8 figure