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Impact on Special Relativity
Tachyon in Physics
Neutrino as Tachyon or Sterilized


Appearance of a Tachyon Tachyon is any object moving with greater than light speed. By this definition the object reaches the observer (at point P in Figure 01) before being seen. After such object passed over, there are two images coming to view. There is first a bluish one with an elongated shape created by the Doppler shift and the aberration of light as it approaches to the observer. The second image is in red color and shrunk by the same kind of effects for a receding object. Figure 01 also shows the Cerenkov radiation, which is the bluish light produced by charged particles moving through a

Figure 01 Appearance of a Tachyon [view large image]

transparent medium at a speed greater than the speed of light in the medium. This is the optical equivalent of a sonic boom. In theory even though the object is not charged, it would induce gravitational radiation via the interaction with the mass in the medium.

Physics books before 2011 invariably consider tachyon as non-existing. If such object appears in a theory, then there must be something wrong with the analysis, or the system is unstable and would quickly decay to a state without such annoyance. This kind of view has changed somewhat as OPERA (Oscillation Project with Emulsion-tracking Apparatus) announced in March 2011 that they have detected neutrino moving slightly faster than the velocity of light. See Update.


Impact on Special Relativity

Mass and Velocity Space-time Diagram In Einstein's first paper on Special Relativity, he pointed out that as the velocity of an object or frame of reference v approaches the velocity of light c, many formulas in the theory become infinity. He then went on to declare that nothing can move pass the speed of light, and moving just at the speed of light is also impossible as it requires infinite amount of energy to attain that. This statement has been accepted by all text books in physics as self-evident. What had been neglected to mention is the fact that photon moves with the speed of light at the moment of its creation, since it doesn't need to go through the barrier. Similarly, a tachyon can be created

Figure 02 Mass and Velocity [view large image]

Figure 03 Space-time Diagram

conceivably with a speed exceeding the velocity of light - again there is no barrier to cross (the barrier is shown in Figure 02).

Since there is some sort of symmetry between the under and over velocity of light objects, Special Relativity for tachyon can be better illustrated by referring to those properties for under the barrier objects (see appendix on Relativity). Special attention has been given to distinguish the velocity of the object v and the velocity of the frame of reference V. In order to simplify the formulation, the followings deal with only the case where velocity of the frame V < c and velocity of the object v > c.


Tachyon in Physics


Neutrino as Tachyon or Sterilized

The concept of measuring the velocity of neutrino is rather simple involving distance and time. The difficulty is in the precision of the measurement to detect a very small difference from the well established value of 2.99792458 x 1010 cm/sec (Review of Particle Physics, Particle Data Group, iopscience.org/jphysg). The distance between the labs is 730.5 km, the timing is relied on GPS to synchronize the clocks at the two ends. The departure and arrival of the signal is recognized from the profile of the proton beam,
Velocity of Neutrino Explanation of Superluminality which generates the neutrinos. Experimenters determined the flight time by comparing the shape of the proton signal at CERN to that of the neutrino signal received at Gran Sasso (Figure 10). After considering details like the curvature of the Earth, the tidal effects of the moon, the general relativistic effects on the GPS synchronization, and a lot of checking for experimental errors (Figure 11), they still left with 60 nanoseconds arrival time earlier

Figure 10 Velocity of Neutrino [view large image]

Figure 11 Explanation of Superluminality

than if the neutrinos were traveling at the speed of light.

P-brane and Bulk Although superluminal neutrino is apparently a tachyon (if confirmed by later experiments), another equally exotic explanation involves the extra-dimension invoked in the superstring theory. According to the theory our world is on a 3+d11 dimensional brane, which floats in a higher dimensional space-time called the bulk (Figure 12). Only the gravitons and possibly the sterile neutrinos can jump over to the bulk (since they are closed string). The shorten arrival time of the neutrinos is attributed to the short-cut taking by the sterile neutrinos when they appear in portions of the flight path due to neutrino oscillation. It is suggested that confirmation of the OPERAs result

Figure 12   3+d11-brane and Bulk [view large image]

would provide support for the existence of sterile neutrino, the first glimpse of extra-dimensions, and a step forward to vindicate the superstring theory.

Test for Superluminal Neutrinos A study in September, 2011 shows that the superluminal neutrinos would lost energy (at the high end) through the process of bremsstrahlung (braking radiation) producing electron-positron pairs :
+ e- + e+
The ICARUS team (in the same location of OPERA) follows up the idea with their data but for a different process in which the neutrino turns into a muon. Figure 13 compares the data (blue points) with a theoretical model (in red) for non-superluminal neutrinos. The result indicates that there is no superluminal neutrinos, otherwise the data would deviate a lot more from the theoretical curve.

Figure 13 Test for Super-luminal Neutrinos

A report in "Nature News" November 2011 by the same OPERA team indicates that their conclusion about superluminal neutrino remains unchanged even though the proton (used to generate the neutrinos) pulse length has been reduced from 10.5 microseconds to 3 nanoseconds (more than 3000 times shorter). The reduction in pulse length would minimize the uncertainty in arrival time.

Detection Errors Another report in "Nature News" on February 2012 by the OPERA team indicates that there are possibly two problems involving the use of GPS. The first is the incorrect calculation of the time interval from the GPS to the synchronize atomic clocks at each end of its neutrino beam. The other involves a possible faulty connection between the GPS signal and the OPERA master clock. The two errors together can account for exactly the 60-nanosecond difference.

Figure 14 Detection Errors

It is reported in Nature Online on March 16, 2012 that the ICARUS experiment located just a few meters from OPERA has clocked neutrinos traveling at roughly the speed of light, and no faster. This experiment should be more accurate since the pulse length is only 4 nanoseconds - much shorter than the original OPERA measurement, which used 10-microsecond pulses. It seems that the case is closed, the speed of light is not broken by the neutrino.

According to April 2, 2012 Nature Online : OPERA's physics coordinator Autiero resigned from the collaboration on 30 March, a day after OPERA spokesman Antonio Ereditato of the University of Bern. The moves followed months of internal tension and media leaks and, last week, votes of no confidence in Ereditato and Autiero by OPERA's collaboration board, which consists of representatives from its member institutions. After the motions won a majority - although not the two-thirds of votes required to force the leadership out - the two men stepped down voluntarily.