Oliver Thewalt

    Oliver Thewalt

    Theoretical Physics | Quantum Biology | Dark Matter Research Cluster

    Open thread: Self-accelerating Dirac particles and prolonging the lifetime of relativistic fermions: Revision

    Open thread: Self-accelerating Dirac particles and prolonging the lifetime of relativistic fermions

    http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3196.html

    A gauge field (field), let's say by its quantum phase, is able to cause quantum effects!

    Forces and effects in nature are linked to symmetries in the universe (e.g. have a look at Euler-Lagrange) and the laws of energy conservation (e.g. Noethers theorem).

    In the post above, scientists are linking the quantum world to the real world by observing the wave(function) of an electron in a region of space with zero electromagnetic field.

    This is what Dirac's equations tried to solve: when describing energy mathematically by linking real or relativistic world (Einstein) with quantum world (FTL (positrons) , Pauli, energy) the (2nd derivative of) Klein Gordon Equation induced a negative probability density which could not be explained. Aren't electrons supposed to seek for an overall equilibrium in space, just changing to a lower energy state? Shouldn't there be a Dirac Sea?http://en.wikipedia.org/wiki/Dirac_sea

    The "holes" that Dirac predicted were revealed as positrons, the opposing charge of electrons and charge of antimatter.

    We are talking by defining quantum states of energy of quantum spin, charge and different quantum states.

    http://en.wikipedia.org/wiki/Dirac_equation

    Now, the post is about the Aharonov–Bohm effect:

    "The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic field (E, B), despite being confined to a region in which both the magnetic field B and electric field E are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wavefunction, and the Aharonov–Bohm effect is accordingly illustrated by interference experiments.
    The most commonly described case, sometimes called the Aharonov–Bohm solenoid effect, takes place when the wave function of a charged particle passing around a long solenoid experiences a phase shift as a result of the enclosed magnetic field, despite the magnetic field being negligible in the region through which the particle passes and the particle's wavefunction being negligible inside the solenoid. This phase shift has been observed experimentally.[1] There are also magnetic Aharonov–Bohm effects on bound energies and scattering cross sections, but these cases have not been experimentally tested. An electric Aharonov–Bohm phenomenon was also predicted, in which a charged particle is affected by regions with different electrical potentials but zero electric field, but this has no experimental confirmation yet.[1] A separate "molecular" Aharonov–Bohm effect was proposed for nuclear motion in multiply connected regions, but this has been argued to be a different kind of geometric phase as it is "neither nonlocal nor topological", depending only on local quantities along the nuclear path.[2]
    Werner Ehrenberg and Raymond E. Siday first predicted the effect in 1949,[3] and similar effects were later published by Yakir Aharonov and David Bohm in 1959.[4] After publication of the 1959 paper, Bohm was informed of Ehrenberg and Siday's work, which was acknowledged and credited in Bohm and Aharonov's subsequent 1961 paper.[5][6] Subsequently, the effect was confirmed experimentally by several authors; a general review can be found in Peshkin and Tonomura (1989)."

    http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect

    And it says:

    "The Aharonov–Bohm effect predicts that two parts of the electron wavefunction can accumulate a phase difference even when they are confined to a region in space with zero electromagnetic field. Here we show that engineering the wavefunction of electrons, as accelerating shape-invariant solutions of the potential-free Dirac equation, fundamentally acts as a force and the electrons accumulate an Aharonov–Bohm-type phase—which is equivalent to a change in the proper time and is related to the twin-paradox gedanken experiment. This implies that fundamental relativistic effects such as length contraction and time dilation can be engineered by properly tailoring the initial conditions. As an example, we suggest the possibility of extending the lifetime of decaying particles, such as an unstable hydrogen isotope, or altering other decay processes. We find these shape-preserving Dirac wavefunctions to be part of a family of accelerating quantum particles, which includes massive/massless fermions/bosons of any spin."

    http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys3196.html

    Now, please be aware of Pauli's exclusion principle: this is a fundamental principle in order to understand how energy/charge and by that quantum spin (fermions/bosons) is partitioned by space (A Black Hole Lens, enabling antimatter to be stable at this side of an apparant horizon, antimatter is shielded by an EM-field) http://hyperphysics.phy-astr.gsu.edu/hbase/pauli.html

    The wavefunction of an electron:

    We can look upon the wave function of the electron as a confined helical wave with a forward component (zig) and a reverse component (zag), that explains the zig-zag of the electron.

    Neutrinos without any mass would be a left-handed spinor, comparable to the forward zig -wave of an electron. In case they have a tiny mass and are able to oscillate, it is possible that they interact with the vacuum field as part of a reverse zag wave.

    http://copaseticflow.blogspot.de/2013/05/solar-neutrinos-and-radioactive-decay.html

    Well, please just try to comprehend some hints I have given you. I know that my explantions are still missing the "last act in order to let people fly" on this, but you should be able to solve this puzzle for yourself, time after time..

    Science is not made by gathering just knowledge, but a result of curiosity and passion.

    I will provide some more useful links:

    http://www.nature.com/nature/journal/v463/n7277/full/nature08688.html

    http://www.hep.phy.cam.ac.uk/~thomson/partIIIparticles/handouts/Handout_2_2011.pdf

    http://www.physics.ucdavis.edu/~cheng/teaching/230A-s07/rqm3_rev.pdf
    "



    I would like to quote +Randy Curry (Google Plus) here, who wrote this fabulous comment on this shared post in his stream:

    "This would reduce the cost of particle colliders like the LHC, and make funding research into the basic structure of the cosmos much easier. This has the potential to progress our understanding, and therefore technology, faster than ever thought possible. Testing theories such as M-Theory would cost a fraction of what it took to accelerate the first particle. The possibilities are all but endless." Thanks a lot for this, Randy!

    Quote: "Similarly, the Aharonov–Bohm effect illustrates that the Lagrangian approach to dynamics, based on energies, is not just a computational aid to the Newtonian approach, based on forces. Thus the Aharonov–Bohm effect validates the view that forces are an incomplete way to formulate physics, and potential energies must be used instead. In fact Richard Feynman complained[citation needed] that he had been taught electromagnetism from the perspective of electromagnetic fields, and he wished later in life he had been taught to think in terms of the electromagnetic potential instead, as this would be more fundamental. In Feynman's path-integral view of dynamics, the potential field directly changes the phase of an electron wave function, and it is these changes in phase that lead to measurable quantities."

    http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect#Global_action_vs._local_forces

    I was thinking of this quantum effect of Aharonov-Bohm could be related to the exchange of phonons and superpositional states by electrons in space vacuum. There is also a close relation of solenoidal (maths) and source free (physics, maxwell), because the fields in vacuum are changing their density (energy is like a perfect fluid, hence the relativistic quantum vacuum is behaving like a bubble of air below water in aphelion and perihelion phases, changigs its density, the fine structure constant alpha is chaning, even radiation decay rates are chaning with sun activity (neutrinos are oscillating)):

    We might encounter here an effect by phase transition of real world to quantum world (FTL!) : the photon is an information boson ...

    Any yes, on Wikipedia there is this thought of a source free space vacuum...

    Monopoles and Dirac strings

    The magnetic Aharonov–Bohm effect is also closely related to Dirac's argument that the existence of a magnetic monopole can be accommodated by the existing magnetic source-free Maxwell's equations if both electric and magnetic charges are quantized.
    A magnetic monopole implies a mathematical singularity in the vector potential, which can be expressed as a Dirac string of infinitesimal diameter that contains the equivalent of all of the 4πg flux from a monopole "charge" g. The Dirac string starts from, and terminates on, a magnetic monopole. Thus, assuming the absence of an infinite-range scattering effect by this arbitrary choice of singularity, the requirement of single-valued wave functions (as above) necessitates charge-quantization. That is, 2\frac{q_\text{e}q_\text{m}}{\hbar c} must be an integer (in cgs units) for any electric charge qe and magnetic charge qm.
    Like the electromagnetic potential A the Dirac string is not gauge invariant (it moves around with fixed endpoints under a gauge transformation) and so is also not directly measurable.

    http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect#Monopoles_and_Dirac_strings


    http://en.wikipedia.org/wiki/Gauge_fixing

    And this one, me thinks that there is a correlation to this post:

    *Fibre Bundle, Gauge Theory, Instanton Moduli Space and
    Instanton Tunneling Effect*
    The connection between gauge theory and the geometry of fibre bundle is very dramatic. The
    non-Abelian gauge theory was proposed by theoretical physicists Chen-Ning Yang and Robert
    Mills in the early middle of 1950s [1]. At that time, the fibre bundle theory had already developed
    ripely in differential geometry, but physicists almost know nothing about it. It is until
    early 1960s that a theoretical physicist Elihu Lubkin realized that the classical Yang-Mills gauge
    theory and the affine geometry of fibre bundle are identical [2]. A gauge field is actually the
    pull-back of the connection to the base manifold of a certain principle fibre bundle and the gauge
    field strength is the pull-back of the curvature of principle bundle, while the gauge group is the
    structure group of principle bundle. Further, matter fields can be considered as the sections of
    some associated bundles of the principle fibre bundle, and the gauge transformation is the action
    of structure group on the section of associated bundle. However, these facts had not been taken
    3seriously by physicists. The extensive application of fibre bundle geometry in gauge theory was
    caused by an article on the global structure of electromagnetic field written by Tai-Tsun Wu
    and Chen-Ning Yang in 1975 [3]. In this article, they defined the electromagnetic potential on
    two half spheres S
    2 with overlapping and avoided the singular string problem in the magnetic
    potential produced by the Dirac monopole [4]. In the overlapping region of two spheres, the
    magnetic potentials are related by a U(1) gauge transformation. The geometry of this physical
    system is precisely a principle U(1)-bundle with base manifold S
    2
    [3]. In the the same year Wu
    and Yang published their paper, A.A. Belavin, A.M. Polyakov, A.S. Schwartz and Yu.S. Tyupkin
    from the former Soviet Union found a solution to the classical SU(2) Yang-Mills theory with
    finite action in the Euclidean space [5], which is now called the BPST instanton (due to the
    physical effect it produces which will be mentioned later). This solution describes a gauge field
    configuration with (anti-)self-dual field strength, and its geometrical description is the principle
    SU(2)-bundle on the base manifold S
    4
    . Further, it had been realized that this solution has
    topological meaning, and it is characterized by a topological index, which is precisely the Chern
    number of the second Chern Class in fibre bundle theory [6]. The BPST instanton is actually
    a classical solution to the Euclidean SU(2) Yang-Mills theory with the Chern number equal to
    one. In the following years, theoretical physicists including Edward Witten [7], E. Corrigan and
    D.B. Fairlie [8], Roman Jackiw, C. Nohl and Claudio Rebbi [9] found multiple (anti-)instanton
    solution with Chern number |k| > 1. Especially, Jackiw and Rebbi showed that the classical
    Yang-Mills theory has not only non-Abelian gauge symmetry and the Poincar´e space-time symmetry,
    but also a larger conformal space-time symmetry [10], which consists of the Poincar´e
    symmetry composed of translational and Lorentz rotational invariance, dilatational invariance
    and special conformal symmetry. As we know, if a field theory has a certain symmetry, then the
    symmetry transformation on a space-time dependent classical solution should lead to another
    solution to the equation of motion. This means that there exists a family of solutions to a field
    theory with symmetries. The inequivalent solutions under symmetry transformations constitute
    a finite-dimensional space, which is called the moduli space of classical solution. Concretely
    speaking, if a space-time dependent solution to the classical equation of motion cannot manifest
    a certain symmetry of the field theory explicitly, then there must have some parameter in the
    solutions to characterize the symmetry. The number of independent parameters in the solution
    is the dimension of the moduli space of the classical solution. At the late stage of 1970s, both
    theoretical physicists and mathematicians employed various distinct methods to determine the
    dimension of instanton moduli space. A.S. Schwartz [11] and Michael Atiyah, Nigel Hitchin and
    Isadore Singer [12] used the celebrated Atiyah-Singer index theorem in algebraic geometry to
    have identified the dimension of SU(2) instanton moduli space as 8|k| − 3. At the same time,
    Jackiw and Rebbi [13], Lowell Brown, Robert Carlitz and Choon-Kyu Lee [14] determined the
    dimension by analyzing degrees of freedom in the instanton solution and calculating the number
    of fermionic zero-modes of the Dirac operator in the instanton background, respectively.
    Moreover, the number of independent parameters for the instanton solution to the Yang-Mills
    theory with a general gauge group was worked out by theoretical physicists Claude Bernard,
    Norman Christ, Alan Guth and Erick Weinberg [15] as well as mathematician Atiyah, Hitchin
    and Singer [16]. Further, mathematicians [17] solved the problem how to construct an instanton
    solution for an arbitrarily given Chern number by using Roger Penrose’s twistor description [18]
    to Yang-Mills theory. This construction showed the power of algebraic geometry in gauge theory
    [17]. Finally, mathematicians proved that the finite action solution to a Yang-Mills theory on a
    compactified Euclidean space in four dimensions must be an instanton solution [19]. At the end
    4of 1970s, all the puzzles on instanton solution and the instanton moduli space had been cleared.
    To summarize, the joint efforts made by both physicists and mathematicians at the late of 1970s
    had laid the foundation for the breakthrough made in 1980s in understanding differential topological
    structure of a simply-connected smooth four-manifold.
    On the other hand, in the same time theoretical physicists started investigating physical
    effects induced by instanton. In the middle of 1970s, Jackiw and Rebbi [20], Curtis Callan,
    Roger Dashen and David Gross [21] found the vacuum structure of a non-Abelian gauge theory
    is highly nontrivial: the Yang-Mills theory with gauge group SU(2) has vacua with an infi-
    nite number of degeneracies. These vacua are classified into distinct homotopy classes by the
    mapping from S
    3
    to SU(2) and characterized by topological indices. People usually thought
    these topological vacua should be absolutely stable since topological numbers should prevent
    the vacuum from decaying. However, the existence of instanton breaks this naive physical pattern.
    Gerard ’t Hooft first studied quantum gauge theory in the instanton background [22].
    He found that an instanton can cause the transition between two topological vacua if the difference
    of their topological indices equals to the Chern number of the instanton. This is the
    famous tunneling effects produced by instanton in a quantum gauge theory. A clear physical
    interpretation on the tunneling effect in quantum chromodynamics was further given by Callan,
    Dashen and Gross [23]. The tunneling phenomenon has lifted the degeneracy of topological
    vacua and the true vacuum state is the so-called θ-vacuum, the superposition of the topological
    vacua. However, if the theory has massless fermions, then the tunneling effect produced by
    instanton disappears. The reason for this phenomenon is that a massless fermion carries not
    only usual fermionic charge (electric charge, lepton number or baryon number, depending on
    physical objects fermionic fields represent), but also a fermionic charge which changes sign under
    mirror (parity) transformation. In physics, it is called that the massless fermionic theory has
    a chiral symmetry (or equivalently axial vector UA(1) symmetry). However, in the presence of
    instanton configuration, this symmetry is violated by quantum correction. Thus the fermionic
    charge that flips a sign under mirror reflection transformation is not conserved and acquires a
    contribution proportional to the instanton number, which is induced by quantum correction.
    This phenomenon in physics is called that UA(1) symmetry suffers from chiral anomaly [24].
    At the late stage of 1970s, it was realized that chiral anomaly is independent of perturbative
    calculation of quantum field theory and has a topological origin. The violation of the axial
    fermionic charge is equal to the difference of the left- and right-handed fermionic zero modes of
    the Dirac operator in the instanton background [25]. This means that the Dirac operator acting
    on the massless fermionic fields in the instanton background must have non-paired zero modes.
    Since a fermionic field is represented by a Grassmann quantity, so the existence of non-paired
    zero modes leads to vanishing integration over fermionic fields and hence the tunneling effect
    is suppressed by massless fermions. ’ t Hooft used the integration property of the Grassmann
    quantity to have realized that this phenomenon is actually a topological section rule for the
    physical process. Some gauge invariant quantities carrying the fermonic charges which change
    sign under parity transformation can absorb the fermionic zero modes and present non-vanishing
    expectation values, and hence contribute to the ’t Hooft quantum effective action. ’t Hooft used
    this idea to have solved the notorious UA(1) problem in particle physics.
    The instanton background can also cause zero modes for the operators acting on bosonic
    fields such as scalar and vector fields. However, the origins of these bosonic zero modes are
    5completely different from the fermionic ones for the Dirac operator. As mentioned before, the
    instanton solution must contain some parameters to manifest gauge and space-time symmetries
    of the theory. The variations of these parameters do not alter the action or potential energy of
    the theory. Therefore, the bosonic operators have zero modes along the directions represented
    by these parameters. In physics one can consider these bosonic modes as the Goldstone modes
    corresponding to the breaking of certain global symmetries in the directions represented by the
    parameters. Viewed from the geometry of instanton moduli space, these bosonic zero modes
    are actually tangent vectors to the moduli space and hence the number of these zero modes
    is the dimension of the instanton moduli space, since the dimension of a tangent space to
    a manifold is equal to the dimension of the manifold. One usually makes use of a so-called
    collective coordinate method to handle the bosonic zero modes in quantum field theory. In the
    path integral description of quantum field theory, the essence of collective coordinate method
    is separating the integrations over zero modes from those non-zero modes. After the non-zero
    modes have been integrated out, the path integration over the bosonic fields reduces to an
    integration on the instanton moduli space and the key point in this process is how to define
    the integration measure on the instanton moduli space. Note that this is actually the physical
    idea used by Witten to describe the Donaldson invariant with a quantum gauge theory. It
    should emphasize that the above mentioned ’t Hooft’s instanton calculus is a pioneer work in
    non-perturbative calculation. During these past thirty years, most of important developments
    in non-perturbative quantum field theory such as instanton calculus in supersymmetric gauge
    theory [26, 27, 28, 29], topological quantum field theory [30] and the Seiberg-Witten duality [31]
    are somehow the prolongs of ’t Hooft’s instanton calculus. ’t Hooft converted the complicated
    calculation in the instanton background into a central potential problem in quantum mechanics,
    and it is still not an easy task to repeat his calculations for a beginner despite that more than
    thirty years have passed.

    4 Supersymmetry, Supersymmetric Gauge Theory, R-symmetry
    ....

    http://arxiv.org/pdf/0803.1340v2.pdf