hull@hao.UUCP (Howard Hull) (10/23/83)
Just what I wanted! A nice quiet sophomoric discussion about Relativity.
Enter absurdium mode |-}
The Special Theory of Relativity deals with "inertial frames", and two sets
of formula pairs are used so that one may choose real or imaginary numbers
to deal with as one requires. If one wishes to write an expression in which
energy is described in a manner that is "time-like", and momentum is described
in a manner that is "space-like" one can use the following:
Energy - Momentum
R = SQR(E^2-(cp)^2) P = SQR((E/c)^2-p^2)
[Fermion Form] [Boson Form]
In these equations, p is the magnitude of the relativistic momentum vector,
calculated from the product gamma*mass*velocity for Fermions, or the h*nu/c
expression, for instance, for photons. E is the relativistic energy, and c
is the velocity of light. All are measurable quantities (in any inertial
frame) except for one, which must be calculated as gamma = 1/(1-(v/c)^2) for
a Fermion moving through the coordinate system defined by any observer.
In th event of a collision at relativistic speeds (of the intruder with any
massive object in the inertial system), E is the available energy, part of
which will be retained as the adjusted rest masses of the resultant Fermions.
The R invariant is the "proper energy", or rest energy. R = mc^2, and is
thus the familiar, favorite way of expressing things.
The P invariant will be definded, for the purposes of this discussion, as the
"proper momentum". Notice that P will be zero for photons, and a positive
real number for Fermions. The Energy - Momentum four vector is *almost*
symmetrical with the Time - Space four vector described below, except that
P would be imaginary for real mass situations if the sign of the terms were
adjusted to create the symmetry.
Time - Space
T = SQR(t^2-(d/c)^2) S = SQR(d^2-(ct)^2)
[Time Separated Form] [Space Separated Form]
This set of equations has been discussed before on the net. In summary, d is
the measurable magnitude of the incremental distance vector between two events
seen by any of several observers. The measurable time difference between the
two events is represented by the t value.
The T invariant is that which represents the "proper time" separation
between two temporally separated events, and has a minimum real value for
the observer who is not moving with respect to two temporally separated events.
The events may or may not be co-located from his point of view. If any of the
observers reports T as an imaginary value, then the events are not likely
"properly temporal" in their separation.
The S invariant represents the "proper space separation" between two events,
i.e., the minimum real spatial separation seen by any observer, and usually
that seen by an observer who is (if possible) not moving with respect to two
simultaneous (to him, at least) spatially separated events. If any observer
reports this as an imaginary value, then the events are not likely very well
characterized as "properly spatial" in separation. The preferred form (T or
S) is the form which yields a real (as opposed to an imaginary) value.
Einstien once said, "It followed from the Special Theory of Relativity, that
mass and energy are but a participant manifestation of the same thing, a
somewhat unfamiliar conception for the average man. Furthermore, the equation
E is equal M C square, in which energy is put equal to mass multiplied by the
square of the velocity of light, showed that a very small amount of mass may
be converted to a very large amount of energy, and vise versa. The mass and
energy were, in fact, equivalent. According to the formula mentioned before;
this was demonstrated by Cockcroft and Walton in 1932, experimentally."
It should be no surprise to any of you, upon inspection of the time-space
expression, that space and time are but a participant manifestation of the same
thing as well, and that a very small amount of time may be converted to a very
large amount of space, and vice versa! Walla! We have the time-space bomb.
One need only "take a few seconds" to lower the density of the enemy to the
state of a rather nebulous threat. That, I presume, has not been verified
experimentally by anyone. It is possible, however, that we have simply not
looked in the right place. On a cosmological scale, we see at apparently great
distance objects whose spectra appear to be red shifted. We have decided, for
the time being, anyway, that photons do not "get tired"; they, experiencing no
time of their own relative to *any* frame of reference, do not change their
momentum until they are absorbed. If, however, there is conversion of time
into space to fill the continuum between us and such objects, we would indeed
see an effect similar to what is seen. One may then ask, for the expected
conversion rate, what might be the Hubble constant, and how does that agree
with what is measured experimentally?
Leave absurdium mode :-{#} "In the dark and whistling Dixie"
The above discussion is with respect to the Special Theory of Relativity.
Tempered by the General Theory of Relativity, the exchange of space and time,
in the presence of accelerated mass and radiated energy may perhaps become
more explicable. Certainly, the wanton creation of space between objects
held together by force has rude implications with respect to the conservation
of energy unless the force is reduced in a way that no work is done, or the
masses or momenta are reduced to provide the energy.
Be forewarned concerning the speed of light; it is a dimensional *ratio* of
measurable quantities. Entities that are expressed in ratio are more likely
by their very nature to be invariant.
It should be noted that the space-time formula is derived from a situation
in which two or more observers are experiencing the expansion of a photon
wavefront from a point source. Since this will occur with the velocity of
light, c, then I presume it is implicit in the formula used that the light
will "create" the required space as it expands.
The formula dictates that with the passage of time, space will be created
at the rate of one linear radial light-year per year of propagation of the
wavefront. The question raised here concerns the reverse of this process;
that is, can time be "vice versa" created from space? If so, in what way
will this be manifested? Will it look like a "black hole"? or will it be
a gnaB giB?
Regards, Howard Hull
{ucbvax!hplabs | allegra!nbires | decvax!brl-bmd | harpo!seismo | menlo70}
!hao!hullguy@rlgvax.UUCP (Guy Harris) (10/26/83)
A minor quibble: your distinction between bosons and fermions should be
between "luxons", i.e. massless particles travelling at C, and "tardyons",
i.e. massive particles travelling slower than C. There are both massive
and massless bosons, and there may be massive fermions (the rest mass of
the neutrino is currently being debated).
Guy Harris
{seismo,mcnc,brl-bmd,allegra}!rlgvax!guy