VI Expanding the Expansion and The Cosmological red shift   The spectra of an element is the distribution of the various colors or wavelengths of light an element produces when either absorbing a photon or emitting a photon. The spectra are unique for each element.   The cosmological red shift is the increased wavelength observed from the spectra of stars in distance galaxies.  Generally, the further away the galaxy, the longer the wavelength of the spectra is observed.  Since this effect was noticed first visually, the initial descriptions were described as a “red shifting”.  The cosmological red shift is also often called a “recessional red shift” and even a “Doppler shift”.  All such observations of the increased wavelength of light are associated with the expansion of space.   Doppler shift   The Doppler effect was first mathematically expressed in the mid 1800’s by Christian Doppler who worked on relationships in which the motion of a “source” and an “observer”  would affect the observed frequency of light and sound. When Sir Edwin Hubble first discovered the “reddening” of galaxies he interpreted the increased wavelength of the spectra as a result of the actual motion of the galaxies away from our location, resulting in a Doppler shift.  It is still common practice to refer to the recessional red shift of galaxies as a Doppler shift but to do so is somewhat misleading in that the physical explanation has changed with the acceptance of General Relativity.  (Although Hubble never accepted the “Doppler shift” as being the result of the expansion of space-time). Cosmological red shift and General Relativity The Cosmological red shift is now generally interpreted as the result of the interaction of a photon of light as it travels through an expanding space time field, due to the principles of General Relativity. How the wavelength of light increases can be explained with a few analogies.  If a bowling ball is rolled to some pins at the end of an alley, the ball will hit with a certain amount of energy, based upon the relative velocity of the ball to the pins.  If the bowling alley was stretched while the ball was rolling down the alley, the relative velocity of the ball when it reaches the pins will be less since the pins will have been moving away from the ball while the ball was rolling to the pins. While there is no relative change in velocity for a photon of light, there is still the loss of energy, which is evidenced by the increased wavelength. ( E = h x v; Energy = Plank’s constant  times the frequency of light, and the frequency v= c/wavelength).  Another way to visualize the effect is to imagine the wavelength of light to be a physical property of a photon that is part of the structure of space-time.  As space-time expands, the wavelength of light is increased.  Another way to visualize the relationship is to assign the photon with a specific amount of energy and as space-time expands, it draws energy away from any system within the expanding space, just as atoms or molecules in a balloon loose kinetic energy when the balloon is stretched and the balloon expands.  Figure 20.  The net result is that “The cosmological red shift is a direct consequence of the diminishing energy and momentum of photons in an expanding space.” (Quote from a section of a book integrating the concept of General Relativity with the cosmological red shift called “Constructing the Universe” by David Layzer Scientific American Library 1984 page 239). Does a uniform expansion of space-time result in no cosmological red shift? The proposed model allows atoms to also expand with the expansion of space-time.  This would alter the energy released as an electron drops from one energy level to another.  The curvature of the electromagnetic field around an atom increases the closer to the nucleus one measures, so an electron dropping from an S2 orbital to an S1 orbital pattern produces a photon with more energy than an electron dropping from an orbital pattern further from the nucleus such as an electron dropping from an S3 to an S2 orbital pattern. By allowing atoms themselves to be part of the expansion, the energy imparted to a photon, when an electron drops a level,  would have to have been greater in the past.  The same orbital patterns are maintained, but the energy associated between levels decreases with the passage of Absolute time. Since the same inverse square law describes both the relationship between the electron and the nucleus and that of gravitational interaction, the same Ratio of Time formulas would be in effect.  For example, when the universe was half it’s present absolute age, the energy imparted to an escaping photon dropping from one energy level to another would be greater. E2/ E1 =  (T1/T2) ^(2/3)        Eq III-11 Eq VI-1 E2/ E1 =  (1/2) ^(2/3) = .63  , The energy of a photon drooping from one energy leval to another would be 1/.63 =1.6 times greater in the past.   As the photon travels through an expanding space-time field, its energy would be reduced.  The amount of reduction would be E2/ E1 =  (T1/T2) ^(2/3)                                Eq III-11 E2/ E1 =  (1/2) ^(2/3) = .63  ,           Eq VI-2 The amount of increase in energy imparted to a photon in the past is exactly equal to the amount of energy the photon looses as it travels to our present location. Eq VI-1= Eq VI-1This seems to imply that there would be no observed cosmological red shift.  To resolve this problem the nature of the expansion of space-time will be “expanded”. Dimensionally expanding the uniform expansion of space. One of the problems with the proposed uniform expansion of space as presented so far is that the relationships predict that no cosmological red shift should be detected.  A number of possible explanations or additions to the proposed model could be proposed that would result in creating a cosmological red shift but the preferred explanation will be to extend the basic relationships proposed so far.  This is done based upon an epistemological desire to establish a set of uniform “rules” upon which physics is based. The fewer and more universal the application of the same basic set of rules the better.  It is proposed that the same set of relationships that describes how space-time expands regions of space-time or matter, also describes the motion of space-time itself.  As an object is expanding, it is also moving along an “unobserved” or absolute dimension.  (This is also consistent with the explanation given earlier regarding the measure of time with a light clock). Three-dimensional space moving in an unobserved dimension In order to resolve the apparent prediction that a uniform expansion results in no observable cosmological red shift, it is necessary to develop another aspect of the uniform expansion of space-time. The unobserved dimension also describes the actually motion of space-time along the unobserved dimension. Three-dimensional space is moving along a locally unobserved dimensional measure. This motion along an unobserved dimension is geometrically tied to a uniform expansion of space-time. This concept is illustrated in Figures 21,22 and 23. Not only is space expanding, space itself is moving in an unobserved dimension.  Note the expansion of the Notation used in Figure 21 and 22 by the inclusion of “A” to indicate motion in the absolute reference frame.   Galaxies motion in an unobserved dimension results in a red shift   Extending the concept of a two dimensional space moving along an unobserved dimension to that of a three dimensional space moving in an unobserved dimension allows the assigning of intrinsic velocities to galaxies since the galaxies are “carried” by the motion along the unobserved dimension. This then allows the Cosmological red shift to be the result of a Doppler effect. The following figure represents the spatial relationship of two galaxies including the unobserved dimensional measure. Note that the shaded ellipses are not describing a flatland universe this time but galaxies carried by motion along the unobserved dimension.   Uniform Rules   The next assumption of the proposed model is that the same set of rules that describes the uniform expansion of space-time also describes the uniform motion of space-time along the unobserved or Absolute dimension.  The primary reason for adopting this idea of uniform rules or laws is based upon simplicity.  If given a choice between one set of rules to describe reality or two sets of rules to describe reality, the simpler choice is preferred. It also is consistent with the description regarding the speed of light and time as developed in Part V in this section.  The final justification of such an assumption rests upon the conformance of the theoretical behavior to the observational.    The Absolute Expansion of Space Time   The observed cosmological red shift of the spectra from distant Galaxies is directly associated, in this model, with the expansion along the absolute Dimension. It does not correspond to local motion observed within our three dimensional observation of reality. It is tied to our motion of three-dimensional space itself as it moves in an absolute or unobserved dimension.    Absolute Distance, Velocity and Acceleration and Absolute time   Absolute distance, velocity and acceleration between two points vary as a function of cosmic time as developed in Equations III-5, 6, and 7.  These relationships resulted in the formulation in the Ratio of Time Equations. Again, while the equations were derived based upon a uniform expansion of points in space-time, the model proposed has the same relationship describing the motion of space itself. The Ratio of Time Equations are listed again for convenience.   Note the addition of the A in the expressions to indicate motion in the Absolute dimension.    The Absolute Ratios of Time   DA2/DA1 =  (T2 /T1)^(2/3)               Eq III-8                        Eq VI-3 VA2/ VA1 =  (T1/T2) ^(1/3)              Eq III-9                        Eq VI-4 AA2/AA1  =  (T1/T2) ^(4/3)              Eq III-10          Eq VI-5 EA2/ EA1 =  (T1/T2) ^(2/3)              Eq III-11          Eq VI-6   Graphically the equations are expressed in Figure 25.   The cosmological red shift   The cosmological red shift observed between galaxies now becomes the result of the difference in the Absolute velocities of the galaxies.  The further away a galaxy is, the faster it is moving in the “unobserved” dimension.  This increased speed “away” form the observer causes a Doppler like effect resulting in the Cosmological Red shift.  The following figure illustrates how the observed velocity would be perceived for increasing distances away from the observer. (Figure 26)   Sign Convention   Starting line + + Eye of observe at “Absolute” reference frame at starting line describing motion of cars Positive measures are ascribed to motion Starting line - Eye of observer observing absolute reference frame, (starting line) while tied to moving object Negative measures are ascribed to motion Figure 27 Selection of observation direction and location alters “sense” of motion Looking to the “Future” Looking to the “Past” Note, the slope of the acceleration of space is negative, which corresponds to a deceleration of space. While figure Figure 25 seems to indicate a positive value, this is actually the result of dividing a negative by a negative, which looses the sense of the relationship.  A review of the actual acceleration of a point is found in Eq. III- 7 (A = k (-2/9) x T^(-4/3)).  A negative value is indicated.             This initially seams contrary to the popular description of the expansion of space in which space is accelerating.  The difference is simply the result of the frame of reference used, as illustrated in the following Figures. (Figures 27,28)   Is space accelerating or decelerating?   The rate of expansion of the universe, and its divergence from a linear rate of expansion is based upon the information from the red shift, the light curve and the observed brightness associated with type 1a supernovas.  The rate of acceleration/deceleration will be a separate topic in the applications section of this work, which addresses the decreasing duration of the light curve associated with high red shifted 1a novas.  For now the discussion is general.    From a relative reference frame, the further away a galaxy, the faster it is moving away. Given that high red shift  type 1a supernovas are dimmer than what would correspond to a linear rate, these supernovas imply an “acceleration”. It is important to note that this  “Positive” sense tied to the acceleration of space is based upon a local reference frame that looks “backwards” in time.  From an absolute reference frame, space is decelerating.  Objects moving faster in the past than the present are defined as decelerating.  Since galaxies are moving faster in the past than the present, then the expansion of space is decelerating.