Dear Nora

Good question, Usually the imaginary velocity for a particle, means its impossible to be measured with full precision. In fact there is a new theory that assumes complex Lorentz transformations and gives the complete derivation of them assuming complex velocities for quantum particles, its in the following link:

https://www.researchgate.net/publication/259996539_Solving_the_instantaneous_response_paradox_of_entangled_particles_using_the_time_of_events_theory

Best regards

Article Solving the instantaneous response paradox of entangled part...

Dear Nora,

I recommend reading the following text:

A tachyon particle is a hypothetical particle that always moves faster than light. The word comes from theGreek:  meaning rapid. It was coined in 1967 by Gerald Feinberg. The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than light), which both exist. The possibility of particles moving faster than light was first proposed by O. M. P. Bilaniuk, V. K. Deshpande, and E. C. G. Sudarshan in 1962, although the term they used for it was "meta-particle". Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according tospecial relativity) would lead to violations of causality. Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier. In the 1967 paper that coined the term, Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,and instead represent an instability known as tachyon condensation.Nevertheless, negative squared mass fields are commonly referred to as "tachyons", and in fact have come to play an important role in modern physics.

Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found. In September 2011, it was reported that a tau neutrino had travelled faster than the speed of light in a major release by CERN; however, later updates from CERN on the OPERA project indicate that the faster-than-light readings were resultant from "a faulty element of the experiment's fibre optic timing system".

Speed

One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, approaches zero when approaches infinity. (For ordinary bradyonic matter, E increases with increasing speed, becoming arbitrarily large as v approaches c, the speed of light). Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below.

As noted by Einstein, Tolman, and others, special relativity implies that faster-than-light particles, if they existed, could be used to communicate backwards in time.

References:

Feinberg, G. (1967). "Possibility of Faster-Than-Light Particles". Physical Review 159 (5): 1089–1105. Bibcode:1967PhRv..159.1089F. doi:10.1103/PhysRev.159.1089. See also Feinberg's later paper: Phys. Rev. D 17, 1651 (1978)

Bilaniuk, O.-M. P.; Deshpande, V. K.; Sudarshan, E. C. G. (1962). "'Meta' Relativity". American Journal of Physics 30 (10): 718. Bibcode:1962AmJPh..30..718B. doi:10.1119/1.1941773.

Lisa Randall, Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions, p.286: "People initially thought of tachyons as particles travelling faster than the speed of light...But we now know that a tachyon indicates an instability in a theory that contains it. Regrettably for science fiction fans, tachyons are not real physical particles that appear in nature."

Tipler, Paul A.; Llewellyn, Ralph A. (2008). Modern Physics (5th ed.). New York: W.H. Freeman & Co. p. 54. ISBN 978-0-7167-7550-8. ... so existence of particles v > c ... Called tachyons ... would present relativity with serious ... problems of infinite creation energies and causality paradoxes. Cite error: Invalid tag; name "Tipler" defined multiple times with different content (see the help page).

Aharonov, Y.; Komar, A.; Susskind, L. (1969). "Superluminal Behavior, Causality, and Instability". Phys. Rev. (American Physical Society) 182 (5): 1400–1403. Bibcode:1969PhRv..182.1400A. doi:10.1103/PhysRev.182.1400.

A. Sen, "Rolling tachyon," JHEP 0204, 048 (2002). Cited 720 times as of 2/2012.

Hoping this will be helpful,

Rafik

Dear Nora,

Maybe these can be also useful for you:

Recami, E. "Classical Tachyons and Possible Applications: A Review." Riv. Nuovo Cim. 9, 1-178, 1996

http://dinamico2.unibg.it/recami/erasmo%20docs/SomeRecentSCIENTIFICpapers/ExtendedRelativity/RNCreview1974RM.pdf

arXiv:1602.03743

O M P Bilaniuk and E. C. G. Sudarshan, Phys. Today 5 43 (1969)

T Alv¨ager and M. N. Kreisler, Phys. Rev. 171 1357 (1968)

M V Davis T. Alv¨ager and M. N. Kreisler, Phys. Rev. 183 1132 (1969)

Irina