Time

V Measuring Time   Time is physically measured   Fundamental to any measurement of local time is the assumption of regular repeating intervals. Figure 16 shows a light clock used to establish an interval of relative time. This measuring device will be used to establish the temporal relationships between relative and absolute time.  Both reference frames must describe the same physical phenomena identically for congruence.   Relative measures of time remain constant   The relative length of the light clock in Figure 16 remains constant.  In order to preserve the relative relationships of Special Relativity, the relative speed of light must also be preserved.  The local increment of time described by a cycle of the light clock remains locally the same.  One second always locally appears to be one second.   Absolute measures indicate variation in increments of time   Viewed in from the absolute reference frame, the light clock changes with the expansion of space.   Figure 17 illustrates that the length the light must travel is longer since the length of the light clock increased with the expansion of space.   The change in absolute length over the passage of absolute time is   D2/D1 =  (T2 /T1)^(2/3)        Eq III-8  (Eq V-1)   The velocity of light, from the Absolute reference frame, is also not constant, C1 does not equal C2, (note capitalization).  It’s absolute velocity conforms to the uniform expansion of space. Just as the velocity of an orbiting object is altered by the Uniform expansion of space-time, so too is the velocity of light. (This is because the speed of light is geometrically described by the expansion of space. This will be discussed later.) Applying the same “rules” developed earlier the absolute velocity of light changes by the following relationship.                           V2/V1= C2/C1 = (T1/T2)^(1/3)                    Eq V-2   The interval of time it takes for a photon to travel a given distance is the distance measure divided by the velocity, Ti = D/V. Comparing the interval of time Ti at two historical measures, T1 and T2 yields the following               T2i =   D2/D1 =  (T2 /T1)^(2/3)                   Eq V-3 T1i =                       C2/C1 = (T1/T2)^(1/3)   Which reduces to   T2i/T1i = T2/T1  Equation V-4   Based upon absolute measures established in the present, cyclic events or processes take longer in the future, and happened more quickly in the past.   If it presently takes 1 second for a light to travel back and forth between two points, how long will it take when the universe is 2 times as old?   Relative measures of the time interval remain constant, so it will still take 1 second of locally measured time for the photon of light to describe a cycle Absolute measures of time are based upon equation Eq V-4 T2i/T1i = T2/T1 which yields  T2i = T1i x T2/T1  Given T1i is presently 1 second, (T1i =t1i), and T2/T1 =2 yields T21 = 2 x T1i   Based upon absolute measures, established at T1, it takes the photon of light twice as long to pass the length of light clock in the future.  Based upon Absolute measures, the speed of light decreases with the passage of time, and the distance the light must travel must also increase.    Another derivation describing relative time- The pendulum   The above relationship describing Relative and Absolute intervals of time based were made based upon the assertion that the absolute speed of light varied with the passage of cosmic time.  This extension of the effects of a uniform expansion to even include light indicates the universal effect the expansion has. The following example yields another verification of the temporal relationships that is based upon gravitational considerations.   The period of a pendulum clock is proportional to the square root of the ratio of the length of the pendulum divided by the local gravitational constant. The interval of time described by the pendulum describes a locally observed constant interval of local time, t.   Ti , t sec = 2 pi x (l/g)^(1/2)  Eq V-5   (T and t are used together indicating the “present”, which is where ti =Ti) The absolute length of the pendulum increases with the passage of time, and the effect of gravity decreases with the passage of absolute time, so from the absolute reference frame, relative time slows with the expansion of space time.   D2/D1 =   (T2 /T1) ^ (2/3)     Eq III 8   (Eq V-6) A2/A1  =  (T1/T2) ^(4/3)                    Eq III 10 (Eq V-7)   Establishing a ratio at two different absolute times, T1 and T2 for the period, yields T2i/T1i = (L1/A1)^(1/2) / (L2/A2)^(1/2)  , and with D = L  this leads to   T2i/T1i =( D2/D1/ A2/A1)^(1/2)  = ((T2 /T1) ^ (2/3) / (T1/T2) ^(4/3))^(1/2) = T2/T1 (Eq V-8) This is the same relationship previously established using a light clock. Based upon absolute measures, if the age of the universe doubled, the time involved for a cycle to complete is twice as much. This effect is universal. Since even matter is proposed to also be a part of the expansion, those timepieces that depend upon elastic properties, or atomic regularities are also similarly affected. Even biological processes are described by the same relationships.   The time it takes for the Earth to orbit the Sun represents a relative measure called a year, the time it takes for so many cycles of a crystal to vibrate a specific number of times represents a relative second.  All are examples of relative cyclic measures.  These locally observed cyclic measures will essentially remain the same with the expansion of space-time.  A year will always be measured to be a year and a second will always be locally observed to be a second, despite the changes observed from the absolute reference frame.   From the Absolute reference frame, the rate of physical processes or cyclic events slow with the expansion of time.  From the local frame of reference there is no slowing since all the local clocks have also slowed. Cumulative Time elapsed The two measures of an interval of time, at the present, always describe the same interval, but when the two measures of time are compared with a historical separation, the cumulative time elapsed will be different for the two measures of time.  If the absolute reference frame is used to measure temporal events with the present as a point of reference, relative process transpires slower in the future and quicker in the past.  This results in two different descriptions associated with age. If the present age of the universe, Tu, is used to compare the relative measure of intervals of time in the past to the present, formula Equation V-4  becomes   t1i = t2i x  Tu / T1       Eq V-9   Assigning the interval measure in the present to be 1 year, t2i = 1 year, Eq V-9 now becomes..   t1i =  Tu / T1 years. Eq V-10   This hyperbolic relationship is illustrated in Figure 19. We live in a universe in which we measure things relatively, yet the proposed uniform expansion formulas are based upon Absolute measures.  This means that if relationships are expressed based upon Absolute measures of time, there must be a transformation to our relative measures of time.  When comparing a system of the past to the present, allowance for the faster passage of relative time must be considered. What represents an Absolute interval of time equivalent to 10 billion years since the beginning of time represents a longer period of time based upon relative measures.   The relationship expressing a specific interval of absolute time to a specific interval of relative time can be established by finding the Integrated Mean or average over specific intervals of absolute time.  The average rate of passage of relative time over the interval of Absolute time will yield the relative time elapsed te. over the absolute interval of time considered.   For graphic of Integration check "Integration graphic"

Example.  Assume the universe is 10 billion Absolute years old.  Five absolute years in the past represents how many relative years in the past?  te = Tu (ln10 – ln5) = Tu ln2 = 10 x .69 = 6.93 billion years. Eq V-13 If we thought of this as in relationship involving Earth, calculations based upon absolute measures of time 5 billion years ago would chronologically be measured on Earth as representing almost 7 billion relative years in the past, the Earth would have made 7 billion rotations around the sun. (Ignoring other gravitational factors.) An everlasting universe with a beginning and end. The nature of the relationship between absolute and relative time is somewhat surprising.  This is revealed by considering Figure 19.  If it is assumed the 10 demarcations associated with the x axis in figure 19 are correlated to a measure of 10 billion absolute years, the intervals of relative time that pass for each measure of 1 billion years absolute time will vary depending upon where on the x axis the one billion years of absolute time is considered. When the universe was 1 billion absolute years old, one absolute year equals 10 relative years.  The closer to the beginning of time events are considered, the more relative time passes for every measure of absolute time.  One second of absolute time near the beginning of time could correlate to millions of years of relative measures of time.  Based upon relative measures of time, the universe is very old.  Looking to the past, the total number of years elapsed form now to the beginning of the universe, based upon relative measures of time, approaches infinity, the universe appears to be infinitely aged. Looking to the future, relative measures of time pass slower and slower, compared to absolute measures of time.  Eventually, what now takes one second to happen will take trillions of relative years to pass. This is a very old, everlasting universe, at least in terms of relative measures. This is in stark contrast to the description of the universe based upon absolute measures.  The universe has a definite beginning, and it will have a definite end. Asserting that the universe has a beginning is not too controversial, particularly with the near universal acceptance of the “big bang”.  Even the assertion of an end to the universe is not that radical, except the end, according to this model, will occur sooner than thought.  This topic will be disused in more detail in the applications section of this work.  For now the main point is to describe the correlation between absolute and relative measures of time.  If “predictions” are made based upon absolute measures, they generally should be translated to relative measures of time in order to achieve an understanding of the perceptual interval of time described. (For biological creatures, a universe with no end does not mean that life is perpetual.  The correlation between absolute and relative times is real.  Eventually the bonds between atoms will become so weak that atomic structures will become unstable.  When this happens can be determined in Absolute measures, then translated to Relative measures of time.  The biologic implications will be discussed in more detail in the applications section of this work.)