Tachyon

Almost all of us are huge fan of Sci-Fi movies and the futuristic technologies presented by them. Those scenes are very attractive and pleasant. But, if we come to know the real explanation behind those things in the language of physics, then we can enjoy them more.

Derivation of special relativity classically relies on the use of inertial reference frames separat-ing at a constant velocity, combined with the constancy of the speed of light as a founding defi-nition of simultaneity. Einstein´s original method for derivation provides the general frame-work in which special relativity is often taught. While this approach is intuitive for students, it is nevertheless confusing in some aspects and lacks clarity in certain steps. Hence, special relativity is very often questioned with paradoxes and apparent mathematical inconsistencies. In most in-stances, these paradoxes are set up under improper mathematical frameworks, or in systems which are not invariant under coordinate transformations. Here, Minskowski space and special relativity are fully derived from an invariant tensor statement valid in any reference frame, with the simultaneity condition imposed on the 4-dimensional null vector. This approach derives Minkowski space with a very limited number of steps in tensor space without the need of in-troducing separating inertial reference frames. From it, the main features of special relativity for bradyon and tachyon trajectories are derived. This solution is particularly adequate for students of special and general relativity, as it is simple, straightforward and mathematically consistent.

According to Feinberg, superluminal neutrino velocity is:

v = +/- c (p^2 / (p^2  - m^2.c^2))^1/2 or equivalently v = c((m^2.c^4 /E^ 2) + 1)^1/2

where E is energy, p is momentum, m is neutrino scalar mass and c is light speed. The view that neutrinos have a negative mass squared are tachyonic and superluminal will be supported in this paper.

Theoretical and experimental neutrino velocities have shown that the transmission of light and neutrinos was not simultaneous for the 1987 supernova. In addition, the 2017 IceCube-170922A observation of blazar TXS 0506+056 has shown that a 290 TeV neutrino was detected before high energy gamma and x-rays during an active phase. These natural phenomena have provided supplementary evidence for the tachyonic neutrino.

According to relativity, a particle with mass cannot travel at the speed of light and must travel at either greater than or less than the speed of light with a negative or a positive mass squared respectively. In light of this, an analysis of major neutrino speed experiments including MINOS (2007), OPERA (2011), OPERA (2012) and ICARUS (2012) has revealed a number of null results.

A reduction of neutrino energy to less than 1 KeV has been suggested to enable experimental superluminal detection.

Erratum: The date of the paper should read 18th October 2019

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2+iλn corresponds physically to tachyonic-resonances/tachyonic-condensates, originating from the scattering of two on-shell tachyons in bosonic string theory. Namely, we prove that if there were nontrivial zeta zeros (violating the Riemann hypothesis) outside the critical line Realz = 1/2 (but inside the critical strip), these putative zeros do not correspond to any poles of the bosonic open string scattering (Veneziano) amplitude A(s, t, u). The physical relevance of tachyonic-resonances/tachyonic-condensates in bosonic string theory, establishes an important connection between string theory and the Riemann Hypothesis. In addition, one has also a geometrical interpretation of the zeta zeros in the critical line in terms of very special (degenerate) triangular configurations in the upper-part of the complex plane.

We study a dark energy scenario in the presence of a tachyon field $\phi$ with potential $V(\phi)$ and a barotropic perfect fluid. The cosmological dynamics crucially depends on the asymptotic behavior of the quantity $\lambda=-M_pV_\phi/V^{3/2}$. If $\lambda$ is a constant, which corresponds to an inverse square potential $V(\phi) \propto \phi^{-2}$, there exists one stable critical point that gives an acceleration of the universe at late times. When $\lambda \to 0$ asymptotically, we can have a viable dark energy scenario in which the system approaches an ``instantaneous'' critical point that dynamically changes with $\lambda$. If $|\lambda|$ approaches infinity asymptotically, the universe does not exhibit an acceleration at late times. In this case, however, we find an interesting possibility that a transient acceleration occurs in a regime where $|\lambda|$ is smaller than of order unity.

We propose a holographic tachyon model of dark energy with interaction between the components of the dark sector. The correspondence between the tachyon field and the holographic dark energy densities allows the reconstruction of the potential and the dynamics of the tachyon scalar field in a flat Friedmann-Robertson-Walker universe. We show that this model can describe the observed accelerated expansion of our universe with a parameter space given by the most recent observational results.

It is a Chapter of the Book "Italian Studies in the Phylosophy of Science", edited by M.Dalla Chiara, belonging to the Boston Studies series. It is discussed the question of Causality and Superluminalmotions, with attention to physical fundamental problems and even to phylosophical implications

In this paper we show, through the study of concrete examples, that, depending on the cosmic dynamics of the energy density of matter degrees of freedom living in the brane, Randall-Sundrum (RS) brane effects can be important not only at short distances (UV regime), but also at large cosmological scales (IR regime). Our first example relies on the study, by

involves the spacetime metric g_{mu nu} as well as the induced metric \bar{g}_{mu nu} proportional to \eta_{a b} \partial_{mu} \phi^a \partial_{nu} \phi^b where \phi^{a} (a=0,...,3), as we call it, break all four diffeomorphisms spontaneously via the vacuum expectation values < \phi^a > proportional to x^a. In this framework, we construct and analyze the most general action density in terms of various invariants involving the curvature tensors, connexion coefficients, and the contractions and the determinants of the two metric fields. We show that this action admits a consistent expansion about the flat background such that the resulting Lagrangian possesses several novel features not found in the linearized Einstein-Hilbert Lagrangian with Fierz-Pauli mass term (LELHL-FP): (i) its kinetic part generalizes that of LELHL-FP by weighing the corresponding structures with certain coefficients generated by invariants, (ii) the entire Lagrangian is ghost-- and tachyon--free for mass terms not necessarily in the Fierz-Pauli form, and, (iii) a consistent mass term is generated with no apparent need to higher derivative couplings.

It has been shown earlier that Noether symmetry does not admit a form of corresponding to an action in which is coupled to scalar-tensor theory of gravity or even for pure theory of gravity taking anisotropic model into account. Here, we prove that theory of gravity does not admit Noether symmetry even if it is coupled to tachyonic field and considering a gauge in addition. To handle such a theory, a general conserved current has been constructed under a condition which decouples higher-order curvature part from the field part. This condition, in principle, solves for the scale-factor independently. Thus, cosmological evolution remains independent of the form of the chosen field, whether it is a scalar or a tachyon.

Friday, May 22, 2020

''' However, there is nothing in Einstein’s theory that forbids a particle
to move faster than light. You just don’t know how to accelerate
anything to such a speed. So really Einstein did not rule out faster
than light motion, he just said, no idea how to get there. However,
there is a problem with particles that go faster than light, which is that
for some observers they look like they go backwards in time.
Really, that’s what the mathematics says''
/ by Sabine Hossenfelder /

http://backreaction.blogspot.com/2020/05/is-faster-than-light-travel-possible.html
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Quantum Tunnels Show How Particles Can Break the Speed of Light
Recent experiments show that particles should be able to go faster than light when they quantum mechanically “tunnel” through walls.
Natalie Wolchover, Senior Writer/Editor,
October 20, 2020

''In short, quantum tunneling seemed to allow faster-than-light travel, a supposed physical impossibility.''
Tunneling seems to be incurably, robustly superluminal.

“How is it possible for [a tunneling particle] to travel faster than light?”
Quantum tunneling: “There’s a mystery there, not a paradox.”

'' Researchers stress that superluminal tunneling is not a problem as long as it doesn’t allow superluminal signaling. It’s similar in this way to the “spooky action at a distance” that so bothered Einstein. ''
. . . when you see where a particle ends up, then . . . that it was doing before.
Tunneling “almost seems weirder than entanglement.”

https://www.quantamagazine.org/quantum-tunnel-shows-particles-can-break-the-speed-of-light-20201020/?fbclid=IwAR29TG5lFQOkruakxLpijwpm_075miPD4tKYZlNsibtwg0JPX65xY6HlgKs
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Instantaneous action is possible when the action is faster than the constant speed of light.

==================

What that mathematics says is that it is impossible for a particle with a real,
(classical) nonzero rest mass to be accelerated from less than c to c or faster
than c. To do so would require infinite energy and infinite force. This is not
some sort of practical obstacle that could be overcome. It is a mathematical impossibility.
#
The possibility of tachyons is a mathematical curiosity, but such particles would
have to have an imaginary (as in √-1) rest mass, and could ONLY move at speeds
higher than c.
Most physicists do not believe that such particles exist, as objects with
measurable properties that are imaginary are problematic. There is
no reason to believe that they are real, . . .
---------
Notice, that if mass-particle has speed  v > c its  energy becomes an imaginary number. 
. . .  Modern opinion:  this  makes no sense . . .
. . .  but Dirac's imaginary  energy  -E=mc^2  does make sense . . .
We ignore to use imaginary numbers as real component of reality 
. . . . and therefore . . .
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  Vacuum -- Light -- Imaginary Tachyons    / by Israel Socratus / 
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1 -  In the cosmic vacuum the speed of light is constant and minimally (c=1)
2 - Light can travel faster than (c=1) -- (tachyon)
3 - At the speed (c>1) all proportions of light are ''imaginary''
4 - There is a universe of ''imaginary'' tachyons - such universe is vacuum
5 -  The universe as a whole is homogenous, isotopic, smooth, flat and cold vacuum.
6 - The vacuum is filled with ''imaginary-negative-virtual''  particles
 7 - The ''imaginary and  transcendental''  particles are real stuff in the vacuum.
Why?
1 - First: 
In 1927  Dirac found an imaginary  positron-antielectron energy particles
 ( -E=mc^2 ). Many years they were abstract particles, but today  these particles
are accepted as real particles. . . . maybe, with time, the tachyon will repeat
 the positron story . . .
We ignore to use imaginary numbers as real component of reality 
. . . . and therefore the truth of nature is hidden 
2 - Second:
There are concrete physical laws that confirm this opinion.
Cold vacuum has a temperature about T=0K . . . then . . .
a)  Then, there is a possibility to use the ''theory of ideal gas''
 (has temperature T=0K) and say, '' according to the J. Charles law -
the law of volumes -  (1787)  that  says : when the temperature falls 1 degree,
the volume decreases 1/273. And when the temperature reaches -273 degrees
the volume of the particle  disappears and the particle  becomes a flat figure.
From all flat figures the circle (membrane) has the most optimal form
 (C/D= pi = 3,14159 )
The Charles law  was confirmed by other physicists: Gay-Lussac,
Planck, Nernst, Einstein.
b) - The vacuum (as a whole) is homogenous, isotopic, smooth (flat)
and very cold (the temperature is about zero).  Then, there is possibility
to use the ''theory of ideal gas'' ( that has temperature T=0K) and say,
 ''the cosmic  space is filled with Boltzmann's mass-molar particles (k)'
 c) - The cosmic space is very cold (the temperature is about zero).
Then, there is the possibility to use Kirchhoff '' black body'' image.
Max Laue called  '' black body'' as ''Kirchhoff's vacuum''  ( has temperature T=0K)
 Planck solved the ''  black body - vacuum'' problem by the quantum
  energy particles of action (h) 
d) - According to Dirac the ''vacuum sea'' is filled with ''negative - virtual'' particles
  ( - E=Mc^2) ,
3 -    Three :
 From a strictly mathematical viewpoint the Lorentz Transformations
are completely analogous to a circular rotation . . .  of a single point
This point-particle according to the SRT cannot be rigid, it must be
 elastic particle - can change its form.
The maximum space of a single point is the size of pi-circle =3,14159 . . .
Now take the rotation of the pi-circle . . . in the Lorentz equation . . .
the result will be imaginary . . . from our (earthy) point of view,
but this result will be positive from the  Cosmic view.
And the Lorentz transformation will show the geometric changes
of the circle and physical changes between (h) and (-E=mc^2)
======
Best wishes.
Israel Sadovnik Socratus
========
P.S.
It seems that from the Cosmic view, it is we, who live in the Imaginary World
=============== 

SRT
The speed (v) belongs to microworld of classical objects and the
speed (c) belongs to microworld . . . there are two different systems . . .
and  the interaction between these two  different systems is not solved . . .
we only now the border between them is the constant speed (c)
#
SRT ---    the communication can be instantaneous  . . . if  c>1  (EPR)
Simultaneity as a consequence of Lorentz transformations . . .
The notion of simultaneity is perfectly sensible, one can
indeed infer this directly by looking at the Lorentz transformations
  in special relativity
---------------------

'"Inertial frames are related by Lorentz transformations,
and if you apply a Lorentz transformation for a speed v greater
than c you get imaginary coordinates. I asked before how your
wrist watch would indicate sqrt(-1) seconds."'

Remember that the Lorentz transformation contains approximations
for v/c<<1. So you cannot even think of getting meaningful results for v>c.
---------
the Light travel applies to events in spacetime - 4D
the Light travel applies to vacuum (SRT)
the Light travel applies to events in inertial frames
in all space coordinates (with respect to the time coordinate) the speed (c)  is equal
-----------------

Never EVER question the herd . . . !
#
To do a career in physics I need to ignore crazy ideas like:
1 - zero vacuum is the source of everything
2 - big bang is scientific fiction
3 - quarks (QCD) is an abstract idea
4 - string theory is mathematical play
5 - CERN / LHC is an useless project
6 - Gravity is local effect of mass and energy
7 - electron and light are one and the same particle
8 - Einstein/Lorentz  SRT is about behaviour of light/electron
9 - the constant speed of light is minimal
10 - . . .
---------------

For negative roots we have Euler's e**(i*Pi)=-1.
So sqrt(-1)=(e**(i*Pi))**1/2=e**(i*Pi/2)=i, which means a rotation
by 90 degrees, counterclockwise.
/  by Gerd Termathe /
-------

Lorentz transformation is rotation frame
Euler's e**(i*Pi)=-1 is rotation frame
Can be an unity between them?
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Israel Quiros1, a and Eduardo Testé2, b 1División de Ciencias e Ingeniería de la Universidad de Guanajuato, AP 150, 37150, León, Guanajuato, México. 2Departamento de Física, Universidad de La Habana, Habana, Cuba. (Dated: 27 de mayo de 2010) We perform a thorough ...

We construct D=4 Type I vacua with massless content remarkably close to that of the standard model of particle physics. They are tachyon-free non-supersymmetric models which are obtained starting with a standard D=4, N=1 compact Type IIB orientifold and adding the same number of Dp-branes and anti-Dp-branes distributed at different points of the underlying orbifold. Supersymmetry-breaking is felt by the observable world either directly, by gravity mediation or gauge mediation, depending on the brane configuration. We construct several simple three generation examples with the gauge group of the standard model or its left-right symmetric extensions. The models contain a number of U(1) gauge groups whose anomalies are cancelled by a generalized Green-Schwarz mechanism. These U(1)'s are broken but may survive as global symmetries providing for a flavour structure to the models. The value of the string scale may be lowered down to the intermediate scale (as required in the gravity mediation case) or down to 1-100 TeV for the non-SUSY models. Thus the present models are the first semirealistic string vacua realizing the possibility of a low string scale. The unbalanced force between the pairs of Dp- and anti-Dp-branes provides for an effect which tends to compactify some of the extra dimensions but no others. This could provide a new mechanism for radius stabilization.