From: sarfatti@well.sf.ca.us (Jack Sarfatti)
Subject: Star Trek Physics 3
Organization: Whole Earth 'Lectronic Link
Date: Mon, 25 Jan 1993 06:43:52 GMT


Part 3
Review of Part 2 basics:
 >Gamma is defined as (1 - v^2/c^2)^(-1/2).  For our train (for
which v = 0.6 c), gamma is 1.25.  Lengths will be contracted and time
dilated (as seen by the outside observer) by a factor of 1/gamma = 0.8,
which is what we demonstrated with the difference in measured time (8
seconds compared to 10 seconds). Gamma is obviously an important number
in relativity, and it will appear as we discuss other consequences of
the theory.

>Another consequence of relativity is a relationship between
mass, energy, and momentum.  By considering conservation of momentum and
energy as viewed from two frames of reference, one can find that the
following relationship must be true for an unbound particle:
        E^2  =  p^2 * c^2  +  m^2 * c^4
Where E is energy, m is mass, and p is relativistic momentum which is
defined as
        p  =  gamma * m * v     (gamma is defined above)
By manipulating the above equations, one can find another way to express
the total energy as
        E  =  gamma * m * c^2
Even when an object is at rest (gamma = 1) it still has an energy of
        E  =  m * c^2
>Many of you have seen something like this stated in context with the
theory of relativity

Hinson continues: (Comments by Sarfatti ((Rashi II?)) between *...*)

>It is important to note that the mass in the above equations has
a special definition which we will now discuss. As a traveler approaches
the speed of light with respect to an observer, the observer sees the
mass of the traveler increase.  (By mass, we mean the property that
indicates (1) how much force is needed to create a certain acceleration
and (2) how much gravitational pull you will feel from that object).
However, the mass in the above equations is defined as the mass measured
in the rest frame of the object.  That mass is always the same.  The
mass seen by the observer (which I will call the observed mass) is given
by gamma * m.  Thus, we could also write the total energy as
        E = (observed mass) * c^2
That observed mass approaches infinity as the object approaches the
speed of light with respect to the observer.

*This same equation is true for the superluminal particle in real time with
a different gamma = 1/(v^2/c^2 - 1)^1/2 for v/c > 1 and v = v(particle) =
c^2/v(wave).  The equation is also true for a transluminal particle in
imaginary time with gamma = 1/(v^2/c^2 + 1)^1/2 for 0<=v/c <= infinity.
Note v/c = 1 is allowed in imaginary time. There is no light cone barrier
in imaginary time. Hawking mentions this in his book, A Brief History of
Time. The idea is that any elementary massive particle (quark, lepton, W,Z,
X mesons) of frame-invariant mass m can exist in three phases, subluminal,
superluminal and transluminal. Only the subluminal obeys causality in the
sense of vanishing quantum field commutators across spacelike intervals.
Only the subluminal obeys the familiar spin-statistics connection in which
spin 0,1,2 are bosons (coherent superfluid condensates) and spin 1/2,3/2
are fermions (Pauli exclusion). The field commutators for superluminal and
transluminal phases form the "exotic" and cosmological "dark matter" that
support the traversable worm holes for Star Ship "warp drive" and the
highly efficient fuel for "impulse power" allowing subluminal travel near
the Einstein barrier relative to the global frame of the "Hubble flow" of
the expanding universe in which the cosmic blackbody radiation is
isotropic. Note, that the local speed of the star ship through the worm
hole is subluminal. The effective global speed is superluminal because the
worm hole provides an extra-dimensional short cut connecting widely
separated space-time regions.*