i4=1 contains two assignments:i2=1 and i2=−1. We may supress the first assignment by the power of definition.What happens if we don't do that and accept a mathematical formulation where i2=1 could be used in certain situations?[This is a speculative notion and I am not staking a claim]. Regarding negative mass:The quantum mechanical mass of a particle may be negative . The quantum mechanical mass of an electron may be negative--this information is well known. We might have an analogous situation with the neurtrinos[ a speculative suggestion]
Imaginary mass (or negative mass squared) would lead to the effect that the potential energy in the Lagrangian has a maximum instead of a minimum which is unstable. So things with imaginary mass are rather called instabilities than particles. For negative mass (not squared) there is the example of the Dirac sea where particles below the sea level turn out to be antiparticles with postitive energy. This can be seen by considering the free space solutions of the Dirac equation where postitive mass solutions are interpreted as particles and negative mass solutions as antiparticles with positive energy.
where E is an object's energy, p is its momentum, and m is its rest mass, which we'll just call 'mass'. In case you're wondering, we are working in units where c=1. For any non-zero value of m, this is a hyperbola with branches in the timelike regions. It passes through the point (p,E) = (0,m), where the particle is at rest. Any particle with mass m is constrained to move on the upper branch of this hyperbola. (Otherwise, it is "off shell", a term you hear in association with virtual particles — but that's another topic.) For massless particles, E² = p², and the particle moves on the light-cone.
These two cases are given the names tardyon (or bradyon in more modern usage) and luxon, for "slow particle" and "light particle". Tachyon is the name given to the supposed "fast particle" which would move with v > c. Tachyons were first introduced into physics by Gerald Feinberg, in his seminal paper "On the possibility of faster-than-light particles" [Phys. Rev. 159, 1089–1105 (1967)].
For example, they accelerate (p goes up) if they lose energy (E goes down). Furthermore, a zero-energy tachyon is "transcendent", or moves infinitely fast. This has profound consequences. For example, let's say that there were electrically charged tachyons. Since they would move faster than the speed of light in the vacuum, they should produce Cherenkov radiation. This would lower their energy, causing them to accelerate more! In other words, charged tachyons would probably lead to a runaway reaction releasing an arbitrarily large amount of energy. This suggests that coming up with a sensible theory of anything except free (noninteracting) tachyons is likely to be difficult. Heuristically, the problem is that we can get spontaneous creation of tachyon-antitachyon pairs, then do a runaway reaction, making the vacuum unstable. To treat this precisely requires quantum field theory, which gets complicated. It is not easy to summarize results here. But one reasonably modern reference is Tachyons, Monopoles, and Related Topics, E. Recami, ed. (North-Holland, Amsterdam, 1978).
We can decide as we please whether or not we want to consider the second type of solution. They seem weird, but then the whole business is weird, after all.
(1) If we do permit the second type of solution, we can solve the Klein-Gordon equation with any reasonable initial data — that is, any reasonable values of φ and its first time derivative at t = 0. (For the precise definition of "reasonable", consult your local mathematician.) This is typical of wave equations. And, also typical of wave equations, we can prove the following thing: if the solution φ and its time derivative are zero outside the interval [−L, L] when t = 0, they will be zero outside the interval [−L− | t |, L + | t |] at any time t. In other words, localized disturbances do not spread with speed faster than the speed of light! This seems to go against our notion that tachyons move faster than the speed of light, but it's a mathematical fact, known as "unit propagation velocity".
(2) If we don't permit the second sort of solution, we can't solve the Klein-Gordon equation for all reasonable initial data, but only for initial data whose Fourier transforms vanish in the interval [−| m |, | m |]. By the Paley-Wiener theorem this has an odd consequence: it becomes impossible to solve the equation for initial data that vanish outside some interval [−L, L]! In other words, we can no longer "localize" our tachyon in any bounded region in the first place, so it becomes impossible to decide whether or not there is "unit propagation velocity" in the precise sense of part (1). Of course, the crests of the waves exp(−iEt + ipx) move faster than the speed of light, but these waves were never localized in the first place!
The bottom line is that you can't use tachyons to send information faster than the speed of light from one place to another. Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver. But as we have seen you can't have it both ways: localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal.
T-space is a sub universe of our universe. That means that all points in T-space correspond to a point in the real universe (R-SPACE). In addition, it is believed that all mass (R-MATTER) leaves a "shadow" in T-space, just as all T-MATTER leaves a "shadow" here.
To visualize T-space, imagine a large sphere, the surface of which is a 2-dimensional representation of our universe. A representation of T-space would be the surface of a smaller sphere placed inside the R-sphere. A line from the T-space surface to the R-space surface, perpendicular to both surfaces is called the TRANSIT LINE and shows the correspondence of points in the two universes.
Tachyons travel through T-SPACE at some indeterminate speed. Most scientists agree that this speed is probably C, but this is more out of deference to Mr. Einstein than any observed property of T-space or tachyons. What can be observed is that the shadows of tachyons in R-space travel faster than the speed of light. In fact, tachyon shadows travel about 20 LY/day.
Because of their imaginary mass, tachyons are actually slowed by energy added to them. If their velocity drops below that of light, they would presumably enter R-space. However, because of the tachyon's imaginary quantum state, no amount of energy will bring this transition about. The tachyon's velocity "bottoms out" at (1.06)C @ 31.4 Gigawatts.
To overcome this limitation, several coils of the element Salidnium are used. The coils are magnetically suspended and placed in a geometric pattern, with neighboring coils being as close as 5 cm. Electric current is pushed through the coils and an outside magnetic field is applied. The magnetic moments of the tantalum atoms align themselves with the magnetic field. After this alignment occurs, the polarity of the magnetic field is reversed at a frequency of 1.5 MHz. However, the magnetic fields of the current through the coils interferes with this flicker effect, causing the different coils to have slightly different frequencies.
Just as when two tuning forks of slightly different frequency are struck next to one another, there are beats in the magnetic field produced by the flickering Salidnium coils. Most of these "beats" are called mundane beats and have no useful effect on the drive unit. A few of these beats have a resonance that is imaginary. These resonances, coupled with the influx of energy needed to start this process, allow tachyons to slow to sublight speeds and appear in the real universe.
These tachyons clump at these imaginary resonance points. The flicker frequency is changed slightly and the clumps move into the Salidnium coils where they follow the energy stream into the web of fine Salidnium wire that extends throughout the hull of the ship. When the ship is surrounded in T-matter, the energy in the web is reduced causing the tachyons to increase in velocity. When they reach light speed, the ship bridges the gap between R-space and T-space. This is called TRANSIT. The ship is now in the sub universe of T-matter.
The starship is in a delicate state of existence where it is neither R-matter or T-matter. Scientists call R-matter in a tachyon field RETON particles. Retons can exist in T-space, but do not exhibit all the same properties of tachyon material. For example, retons do not increase velocity as they approach zero energy. They do however, exchange momentum with T-matter and therefore can be "pushed" by tachyons. The tachyons in the web actually push the ship through T-space. If the energy in the web decreases below a certain point however, the tachyons will escape the web at 20 LY/day. The retons will be pushed, but only momentarily as the tachyon field will be lost and the ship reverts to R-matter with potentially unpleasant results.
The FTL EFFICIENCY of the drive unit is a measure of how many tachyons can be captured. With more tachyons comes more momentum that can be transferred to the retons and more speed for the reton ship. The actual speed of the starship comes from the supercurvature of T-space. Imagine a ship at a point in T-space and its corresponding point in R-space (the intersection of the transit line with R-space). If a ship moves a certain distance on the surface of the T-sphere, then it moves a corresponding distance on the R-sphere. However, it has a much greater linear displacement on the R-sphere (try drawing it with two circles and see) and if time is equal in both dimensions, a greater velocity -- in fact much greater than the speed of light.
As a Reton object moves through T-space, the pseudo-matter interacts T-space and TERON particles begin to build up on the ship. Teron matter are sort of anti-particles of retons. Terons can exist in R-space, but do not interact with most forms of matter there. The number of terons that build up in the ship is proportional to the distance the ship travels in T-space.
When a ship comes out of T-space, its tachyon field is lost and the ship's retons revert to protons, neutrons and electrons, giving off TWEEN PARTICLES in the process. These tween particles can interact with the residue of terons and excite them, producing high-energy photons and more tweens as the teron is destroyed. If enough terons are present, a chain reaction is started and the ship can be irradiated to deadly levels. The retons seem to congregate in the Salidnium web of a ship, and the subsequent radiation will destroy the drive components (as well as the crew). Experiments and accidents have shown that the critical limit is 12 LY. If a ship travels more than this distance in T-space, the reton level will be high enough to cause a chain reaction as soon as the ship makes transit from jump.
In layman's term please.
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