# IS OURS ONLY ONE OF THREE UNIVERSES?

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CIA-RDP79-00999A000200010088-9

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RIPPUB

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K

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5

Document Creation Date:

November 4, 2016

Document Release Date:

January 9, 2014

Sequence Number:

88

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Publication Date:

January 16, 1974

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OPEN SOURCE

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s ours only one of three universes?
y Dietrick E. Thomsen
The usual big-bang cosmology con-
ected with Einsteinian general rela-
vity has the universe starting from a
oint of space-time that is called the
ingularity. "Singularity" is a mathema-
cian's euphemism for something dif-
cult to deal with, a point at which
hysically the universe has no dimen-
ions and infinite density. From this
oint the universe expands as time pro-
eeds, extending its dimensions and
mering its density.
Such is the usual picture of the ex-
anding universe. But this universe oc,
upies only one region of the space-
me that physicists are used to dealing
ith, the region that lies to the future
f the singularity. The question arises:
/hat happens in the other regions of
mce-time that physicists are able to
nagine? Does anything happen in the
ngularity's past? Can anything happen
cside it, so to speak in the regions of
pace-time called spacelike?"
The answer, says J. Richard Gott III
f California Institute of Technology,
; yes. Writing in the latest ASTROPHYS-
,/iL JOURNAL (Vol. 187 No. 1), he
,iows that if we look for the most gen-
1-al solutions of Einstein's equations,
t flat space-time, we come up with
ree universes. One is our own, which
e have just described, lying in the
gularity's future and dominated by
dinary matter. Let us call it Universe
Universe II lies in the singularity's
St and is dominated by antimatter.
iverse III lies in the spacelike region
space-time and is inhabited by ta-
yons, particles that travel faster than
ht.
To understand the geometry of this
her mind-boggling concept, it is nec-
ary to spend a few words on a gen-
1 description of space-time. In true
ce-time there are three spacelike
ensions and one timelike dimension.
r graphic purposes two of the space
ensions are suppressed, and a two-
ensional graph is drawn in which
vertical axis is time and the hori-
tal space.
very point in this two dimensional
ce-time represents an event: It speci-
both the location and the time at
'eh something happens. The start of
articular particle's flight may he one
nt; its finish, another. The slope of
line that joins them represents the
city of the flight.
.alculation shows that the lines run-
at 45 degrees to the time and
1-1,-ceifiari in Part -
Space-time
diagram of Gott's
proposed three-
universe cos-
mological model.
Gott/Astrophysical
Journal
?
f:=411
F..-
174,
frz.
space axes are of particular importance.
They represent objects moving at the
speed of light (they define what is
called the light cone), and in ordinary
physics one cannot cross them in going
from event to event. The light lines
(or the light cone in more than two
dimensions) divide space-time into two
reaions, the timelilce (in the upper
and lower quadrants) and the spacelike
in the right and left quadrants.
For two events in the timelike region
(where we live) it is possible to find
an observer moving in such a way
that the two events seem separated in
time only. If observer A sees a particle
moving from x to y while the time
goes from t1 to t2, observer B, who
happens to be going along with the
particle, will see the time change only.
If the particle was in his hand at the
start of the flight it will be in his hand
at the end. In the spacelike region, in a
similar way one can find an observer
for whom two events are simultaneous
but appear to represent an instantane-
ous translation in space. Thus in the
spacelike region our usual perceptions
of space and time and cause and effect
are overthrown, but we need not worry
about it since we can never get there.
When observer B moves with respect
to observer A, from A's point of view
the motion represents a skewing of his
time axis in the direction of the light
line. It can also be shown that his space
axis will skew and also in the direction
of the light line. The faster B goes, the
narrower becomes the angle between
his space and time axes. When he
reaches the speed of light his space
and time axes meet in a grand flash
of?well that's the singularity, as Gott
considers it.
There's no crossing it. Gott puts our
universe in the upper quadrant to the
future of the singularity. His time-re-
versed antimatter universe lies in the
lower quadrant to its past. And his
tachyon universe lies in the spacelike
region, which is not two regions but
one. This can be seen if we add a
third dimension and imagine the dia-
gram rotated around the time axis: Re-
gions I and II become cones; region
III becomes a wedge-shaped ring.
There is no communication across
the singularity. Antimatter and tachyons
can exist in our universe occasionally
and ephemerally?they are not visitors
from the other universes. They are pro-
duced here. There are differences in
perception: Our view of Universe II,
if we could see it, would be that it is
dominated by matter and contracting.
To its own inhabitants it looks as if
antimatter dominates and it is expand-
ing. Finally the principal of causality,
which says that neither information nor
energy can be transmitted faster than
light, is not violated in the tachyon
universe. Though the tachyons them-
selves go faster than light, their radia-
tion, which is the only way they can
transmit energy or information, does
not.
Gott concludes: "The mode! we have
presented is a unified, time-symmetric
model treating matter, antimatter and
tachyons in a natural and equal fashion.
The model is consistent with our pres-
ent observations of the universe and
could gain support from an experimen-
tal discovery of tachyons. . . ." 0
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U C?
rest frame precess
x a (11.54)
ialid if v < c. We
)recession by noting
acceleration. If a
2n there is a Thomas
sion of the magnetic
xt by the screened
ocity is
iv
Ir
(11.55)
contribution to the
spin-orbit coupling
), yielding
/V
(11.56)
dr
mnic electron.
:elerations due to the
es are comparatively
nucleons as moving
attractive, potential
iddition a spin-orbit
ctromagnetic contri-
(11.57)
[Sect. 11.6] Special Theory of Relativity 369
(11.58) is in qualitative agreement with the observed spin-orbit splittings
in nuclei.
11.6 Proper Time and the Light Cone
In the previous sections we have explored some of the physical con-
sequences of the special theory of relativity and Lorentz transformations.
In the next two sections we want now to discuss some of the more formal
aspects and to introduce some notation and concepts which are very useful
in a systematic discussion of physical theories within the framework of
special relativity.
In Galilean relativity space and time coordinates are unconnected.
Consequently under Galilean transformations the infinitesimal elements
of distance and time are separately invariant. Thus
ds2 dx2 dy2 _F dz2 = ds'2
dt2 = de2
(11.59)
For Lorentz transformations, on the other hand, the time and space
coordinates are interrelated. From (11.21) it is easy to show that the
invariant "length" element is
ds2 = dx2 dy2 dz2 ? c2 dt2 (11.60)
This leads immediately to the concept of a Lorentz invariant proper time.
Consider a system, which for definiteness we will think of as a particle,
moving with an instantaneous velocity v(t) relative to some coordinate
system K. In the coordinate system K' where the particle is instantaneously
at rest the space-time increments are dx' = dy' = dz' = 0, di' = dr. Then
the invariant length (11.60) is
? c2 dr2 = dx2 dy2 -1- dz2 c2 di2 (11.61)
In terms of the particle velocity v(t) this can be written
) ..., ----1
1. The form of o32, is i /. z- i 11 /?--e-