It is shown using numerical simulation that classical charged tachyons have several features normally thought to be unique to quantum mechanics. Spin-like self-orbiting helical motions are shown to exist at discrete values for the velocity of the tachyon in Feynman-Wheeler electrodynamics and in normal causal electrodynamics more complex closed orbits also appear to exist. Tunneling behavior of the classical tachyon is observed at classical turning points depending on the angle of incidence. The equations of motion appear to be chaotic and effectively indeterministic when the tachyon crosses its own past light cone. It is argued that self-interacting tachyons moving in a tight helix would behave causally, and that they could be a basis for a hidden variable description of quantum mechanics. A procedure is proposed which could determine the fine structure constant.
It is shown using numerical simulation that classical charged tachyons have several features normally thought to be unique to quantum mechanics. Spin-like self-orbiting helical motions are shown to exist at discrete values for the velocity of the tachyon in Feynman-Wheeler electrodynamics and in normal causal electrodynamics more complex closed orbits also appear to exist. Tunneling behavior of the classical tachyon is observed at classical turning points depending on the angle of incidence. The equations of motion appear to be chaotic and effectively indeterministic when the tachyon crosses its own past light cone. It is argued that self-interacting tachyons moving in a tight helix would behave causally, and that they could be a basis for a hidden variable description of quantum mechanics. A procedure is proposed which could determine the fine structure constant.
By now the “chaos revolution” has reached nearly every branch of the natural sciences. In fact, chaos is everywhere. To name but a few examples, we talk about chaotic weather patterns, chaotic chemical reactions and the chaotic evolution of insect populations. Atomic and molecular physics are no exceptions. At first glance this is surprising since atoms and molecules are well described by the linear laws of quantum mechanics, while an essential ingredient of chaos is nonlinearity in the dynamic equations. Thus, chaos and atomic physics seem to have little to do with each other. But recently, atomic and molecular physicists have pushed the limits of their experiments to such high quantum numbers that it starts to make sense, in the spirit of Bohr's correspondence principle, to compare the results of atomic physics experiments with the predictions of classical mechanics, which, for the most part, show complexity and chaos. The most striking observation in recent years has been that quantum systems seem to “know” whether their classical counterparts display regular or chaotic motion. This fact can be understood intuitively on the basis of Feynman's version of quantum mechanics. In 1948 Feynman showed that quantum mechanics can be formulated on the basis of classical mechanics with the help of path integrals. Therefore it is expected that the quantum mechanics of an atom or molecule is profoundly influenced, but of course not completely determined, by the qualitative behaviour of its underlying classical mechanics.
During the 20th century, two new ways of describing physical sys tems emerged to thwart scientists' hopes of ever completely predicting nature's behavior. First, the theory of quantum mechanics uncovered ram pant uncertainty at the tiniest scales of matter?in the canonical example, an electron's precise position and momen tum cannot simultaneously be known at any particular moment. The second body of thought is what we now call chaos theory. Some phenomena, it turns out, depend intimately on a sys tem's initial conditions, so that an im perceptible change in the beginning value of a variable can make the out come of a process impossible to pre dict. Chaos appears in examples as dis tinct as the frequency of drips from a faucet and the motion of planets. Given the unpredictability that char acterizes both chaos and quantum me chanics, one might well wonder what would happen if these phenomena were merged. Utter chaos, perhaps? Probably not; in fact we have tools for approaching the modeling of quantum chaos, or chaotic behavior on the quan tum scale. Early attempts to under stand this exotic realm have produced results that are both mathematically and scientifically important. Having
The tachyon model of neutrino is constructed, basing on the statement that quantum description is a statistical description of stochastically moving particles. Besides, the tachyon model contains two conceptual points: (1) universal formalism of particle dynamics, describing uniformly all particles: deterministic, stochastic and quantum, (2) discrete space-time geometry and skeleton conception of particle dynamics. The universal formalism is a result of a logical reloading, when the statistical ensemble becomes to be the basic object of particle dynamics instead of a single particle. Such a reloading admits one to describe uniformly the quantum, stochastic and deterministic particles in terms of a statistical ensemble without a reference to principles of quantum mechanics. Besides, one uses a relativistic state of a particle, when the state is described by the particle skeleton (several space-time points) instead of the point in the phase space, what is nonrelativistic concept of the particle state. Representing the Dirac equation in terms of the statistical ensemble, one concludes that in the deterministic approximation the world line of the Dirac particle may be a spacelike helix with timelike axis. The rotational component of the relativistic Dirac particle is described nonrelativistically. It shows that the world line may be spacelike, and the Dirac particle may be a tachyon. Neutrino is a Dirac particle, and it is a tachyon.
A number of years ago, Bohm postulated the existence of a quantum potential in order to create a completely causal description of nonrelativistic quantum mechanics. It is shown that this quantum potential must be a tachyon field. An experimental test of the identification of tachyons with Bohm's quantum potential is described. It is shown that though in the above experiment spacelike intervals are investigated, the information arrives after timelike intervals. The experiment thus provides an example where tachyons can affect a measured quantity though they cannot be used to violate causality.
Sidney Coleman has noted that superluminal particles or observers would be able to go back in time and have no definite trajectory according to subluminal observers, while not violating Lorentz invariance [1]. Recently, Dragan and Ekert have significantly developed similar ideas even further, which lead to formulation of ``quantum principle of relativity'' that intimately links the two theories [2]. However, field theory descriptions of an on-shell tachyon, described by scalar field φ with negative mass squared parameter, lead to violation of basic principles of relativity or quantum mechanics. In this work, we investigate whether purely virtual tachyons can be consistent within the fakeon framework--the only known viable formulation of purely virtual particles. We show that the supports of the real part of the tachyon Feynman propagator, which is also the principal-value propagator (PVP), and the Wheeler propagator intersect only on the light cone. We show that PVP cannot be time-ordered two-point function of a local Hermitian field, excluding the direct extension of the canonical formalism to free fakeon tachyon. Finally, with an imposed tachyonic PVP, interactions with electrons generate composition-dependent accelerations that violate the weak equivalence principle, and we provide a quantitative bound on this scenario. Our analysis identifies obstacles to formulating covariant quantum field theory of interacting virtual tachyon.
The classical equations of motion of a charged point-particle with intrinsic spin under the influence of an external electromagnetic field are restated and compared with the Heisenberg equations of motion derived from the Dirac theory. The partition of angular momentum between particle and field in the classical theory is contrasted to the Dirac theory of electron spin. The analogy between the Dirac equation and the theory of parametric amplification is pointed out.A free spinning point particle moving according to the laws of classical relativistic point-particle mechanics may move along a helix. The sum of the intrinsic spin $\ensuremath{\sigma}$ and the angular momentum of the helical motion in this classical analog of zitterbewegung is an effective spin vector S which is a constant of the motion. Because of this internal motion, the effective mass M of the particle differs from the mass m which is ascribed to it in the equations of motion. Solutions are found in which S is parallel or antiparallel to the momentum, and the sign of M is determined by the helicity. When placed in a uniform electromagnetic field, the particle behaves as if it had a rest mass M and a magnetic moment $\frac{e\ensuremath{\sigma}}{\mathrm{Mc}}$, in addition to any explicit magnetic moment that may be ascribed to it.