From: cary@carina.unm.edu (Ithlial the Archer)
Newsgroups: alt.alien.visitors,alt.sci.physics.new-theories
Subject: Supraluminal v (was Re: Elapsed Time near c )
Date: 23 Jul 92 17:23:17 GMT
Organization: University of New Mexico, Albuquerque

In article <1992Jul23.080318.25996@fys.ruu.nl> spiering@fys.ruu.nl (Geert Spiering) writes:
>I hope this adds to the discussion, but since everyone keeps repeating
>the statement that nothing can travel faster than light, i would like

Hmm, what velocity do photons travel at?  I think you mean to say
that nothing with a rest mass can travel at c.

>to bring up tachyons.
>Einsteins theory only states that nothing can travel WITH the speed of
>light. This means that you cannot accelerate to above the speed of light
>from velocities less than the speed of light. (An infinite amount of
>energy would be necessary).
>However there may be particles that ALWAYS travell at velocities > c.
>The catch is, that these particles would have to have imaginary masses.
>One could still associate real energies to these particles, that are

No, the energy would be imaginary.  The relativistic formula for total 
energy is E^2 = m^2*c^4 + p^2*c^2 = m^2*c^4 + m^2*gamma^2*v^2*c^2.
Where m is the rest mass (positive real) and gamma is the relativistic
factor equal to 1/sqrt(1-(v^2/c^2)) which for v > c is imaginary.
Thus the first term is positive real and the second is negative
real.  But the second term is larger in magnitude that the first:

	E^2 = m^2*c^4 + m^2*v^2*c^2/(1-v^2/c^2)

we're only worried about the sign so I'm going to divide out the postive
things (rest mass and c), now we have E^2 is propotional to,

	 1 + (v^2/c^2)/(1-v^2c/^2)

putting it all over a common denominator,

		= (1-(v^2/c^2) + (v^2/c^2))/(1-v^2/c^2)
		= 1/(1-v^2/c^2)

which always negative since v>c and the square root of a negative
is imaginary.

>singular at v=c. This means that these particles cannot slow down to
>velocities<c.
>Of course, no one has ever seen particles with imaginary masses....

Especially because at there extension in space in the direction of
their progation is imaginary too, which I guess would make them two
dimensional?

>
>	Geert Spierings.
>

An interesting argument that I have heard is that if time is quantized
(the hypothetical quanta of time is called a 'chronon') then you might 
be able to skip going exactly c and your next quanta of  velocity would 
be greater than c.  Mind you this is pure spectulation and I'm relating 
this since I think its relevant to the discussion not because I necessarily
think it's possible.  In any event on would have question how small the 
quanta is since te highest energy cosmic rays possess gamma factors of
10^11 (100,000,000,000) which translates into a velocity of 
0.99999999999999999999995 the speed of light, meaning that the alleged 
'chronon' is pretty damn small!  So if we are to get glose enough to
c to make the little hop to the 'other side' we're going to need
alot of energy.

Just a different way of looking at it.  Relativity and supraluminal
velocities are really strange.  And of course who knows if these
equations really describe supraluminal phenomena anyhow!

Ithlial the Archer


               XXXXX  XX   XX  XXXXX  XX  XX  XX  XX  XXXXX
               X       X   X   X      XXX XX  XX  XX  X
               X        XXX    X  XX  XXX XX  XX  XX  XXXXX
               X         X     X   X  XX XXX  XX  XX      X
               XXXXX     X     XXXXX  XX  XX  XXXXXX  XXXXX

	An Extensive Air Shower Array at the Meson Physics Facility
 			 Los Alamos National Labs


My opinions are my own, don't you dare give someone else credit for them!
Xref: sparky alt.alien.visitors:4887 sci.skeptic:13303