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November 4, 2016
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January 16, 1974
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/4) Declassified in Part - Sanitized Copy Approved for Release 2014/01/09: CIA-RDP79-00999A000200010088-9 FEI 1-11N !DENT! AL ? SECRET _ ROUTING AND RECORD SHEET SUBJECT: (Optional) FROM: EXTENSION NO. S TAT? DATE TO: (Officer designation, room number, and building) DATE OFFICER'S INITIALS COMMENTS (Number each comment to show from whom to whom. Draw a line across column after each comment) RECEIVED FORWARDED / ry ( 2. v, S cr, . 3401 ... 3. 4. 5. .6. ? 7. 8. 9. 10. 11. 12. 13. 14. 15. 610 USE M -19 ni ? crrorr rnur nrtrri A I INTERNAL Declassified in Part - Sanitized Copy Approved for Release 2014/01/09: ONLY CIA-RDP79-00999A000200010088-9 UNCLASSIFIED 414,-P 11U nrie fixdWin." Declassified in Part - Sanitized Copy Approved for Release 2014/01/09 : CIA-RDP79-00999A000200010088-9 . ? ILT 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 Sanitized Copy Approved for Release 2014/01/09: CIA-RDP79-00999A000200010088-9 Declassified in Part - Sanitized Copy Approved for Release 2014/01/09 : CIA-RDP79-00999A000200010088-9 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-