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Einstein’s
Special Theory of Relativity predicts that nothing can accelerate
and exceed the speed of light, i.e. the speed of light, c,
is the upper limit of speed in the universe. This is the direct
consequences from relative mass equation:

It is obvious
that when velocity, v approaches c, relative mass
increases. Thus if any object can reach the speed of light, its
relative mass will be infinite at that moment. It will then need
infinite amount of energy to move. This is unimaginable. This is
why ordinary object cannot travel at the speed of light.
Superluminal travel ( faster-than-light travel ) thus remains to
be science fiction.
Ordinary Particles
The graph below is sketched by Graphmatica Version 1.60e. It shows
momentum (p) on the x-axis
and energy (E) on the y-axis.

The
two lines that cross the origin show the 'light cone'. For
simplicity, we treat c to be 1 space unit per time unit. We
also have to assume that space is one-dimensional. So, in real
four dimensional spacetime, the light cone is a “hypercone”. Here,
the equation is E = ± p.
The region above and below the two lines is known as 'timelike',
and the region to the left and the right is known as 'spacelike'.
We have
E2 = m2c4 + p2c2
from Special Theory of Relativity. Note that m here refers
to rest mass or .
Since we have already assumed that c = 1, we reduce
the equation to E2 = m2 + p2.This
is an equation that describes a parabola, as shown in the graph
below:

To sketch this
graph, m is taken to be 2. But it depends on the mass of
the given particle. The parabola crosses the E axis at
m. This is indeed consistent with
since c = 1. These ordinary particles move at
subluminal speed, and are called
tardyons or bradyons ( "slow particles" ).
Massless particles are called luxons, i.e. “light particle”
and they travel at the speed of light – on the light cone itself.
Examples of luxons are photons, gravitons ( theorized particles
that transmit gravitational force ) and possibly neutrinos ( some
physicists think that they have very small mass ).
Property of Tachyons
Now we will consider a class of extraordinary particles:
tachyons. These particles travel faster than light! Now how is
that possible? Isn’t special relativity does not allow particles
to exceed speed of light? No. This is not true. It was predicted
that nothing can accelerate and exceed the speed of light. Nothing
was mentioned about particles that are already traveling faster
than light since they are created. They don’t have to accelerate
to exceed the speed of light since they are always
traveling at such speed. These particles can never slow down to
the speed of light or below the speed of light, or else it will
contradict the special relativity. For tachyons, c is the
lower limit of speed.
From the equation

We see that for
tachyons, v > c. And hence denominator is imaginary.
The mass of tachyons is therefore imaginary. From ,
it follows that there energy must be imaginary as well. Thus
E2 = m2 + p2
becomes p2 - E2 = M2,
where M is real. The solution to this equations are again
parabola as shown below:

Note that the
solution set is below the p-axis as E < 0 for
tachyons. What is the observation that we can make from the graph?
Well, we see that when their energy decreases, the momentum of
tachyons increases! This is really weird.
Tachyons will
not contain any electrical charges. This is because charged
particles will gives off energy as it moves through a transparent
medium with superluminal speed. The energy is called Cherenkov
radiation. This will decrease their energy, and thus
accelerate them. This leads to endless emission of energy.
From quantum physics, we know that tachyon and anti-tachyon pairs
were formed spontaneously in vacuum. The energy released in this
manner will cause the vacuum to become very unstable.
Transmitting Information From The Future?
Some people will argue that psychics might be using some special
tachyons to bring information for future, and hence predicting
the future. However, even if psychics have real ability to predict
the future, they are not using any tachyons as messengers.
If we can send information by tachyons, it really leads to some
paradoxes. For an example, we can invent a machine that can send
out tachyons containing information to blow itself up into the
past ( according to Special Theory of Relativity, time stops
at the speed of light, and reverses when one exceed the
speed of light ) before the tachyon is sent out!
Fortunately we might not be able to build such machine anyway due
to known law of physics. The mathematics is beyond the scope of
this article. It suffices to say that it is impossible to send a
message using tachyons.
Reference:
http://www.morleysoft.freeserve.co.uk/physics/tachyons.html
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