The Arrow of Time
Friday, November 7, 2008 at 08:50AM
Doug

Philip Gibbs, in his FQXI essay, “This Time – What a Strange Turn of Events!” writes: 

Minkowski used the symmetry in the Lorentz transformation to bring together space and time making them merely different dimensions of spacetime. Yet time is somehow different in our mind. This difference is characterised by an arrow of time that defies the symmetry. In our conscious experience our past is clear and fixed but our future is uncertain. From the laws of thermodynamics we learn that this difference is due to entropy which always increases as time passes. Entropy is a measure of information and by the rules of quantum mechanics information of (sic) conserved. There is a paradox, but information can be as clear to us as the letters on this page, or as hidden and disordered as the states of the molecules in the air around it. As time passes, the disorder increases and entropy measures this change.

Time can distinguish itself from space in this way because the spacetime metric has a Lorentz signature that assign a different sign in the time dimension versus the three space directions. Thus in locally flat Minkowski spacetime distances are measured by the invariant quantity

ds2 = dx2 + dy2 + dz2 – c2dt2

Part of the mystery of time is to understand where this signature comes from. Why three plus signs for space and only one minus sign for time? Even with this separation of dimensions there should remain symmetry under time reversal t -> -t, but the arrow of time breaks this symmetry. What is the origin of this arrow? From what bow did it take flight?

When we understand that the progression of time is only one aspect of the space/time progression, and that the progression of space is its reciprocal, we can understand the broken symmetry. It’s broken when the uniform motion is quantized by the continuous reversals in the space, or the time, aspect of the progression, as shown in the graphic of the previous post below, which is shown again in figure 1.

Figure 1.Two Fixed Reference Systems Created by Pseudoscalar Oscillations.

In figure 1, we see the arrow of time is created when the s/t pseudoscalar oscillations nullify the space progression, and the arrow of space is created when the t/s pseudoscalar oscillations nullify the time progression. Of course the two systems are separated by the unit space/time progression, which is c-speed from the 0 point of both systems.

From the perspective of either system, the zero speed (or frequency) of the inverse system is four times its own zero speed (or frequency); that is, 1/2 * 4 = 2/1. Another way to say the same thing is that, if we take the frequency of one system as the fundamental, the frequency of the inverse system is two octaves above that frequency, regardless of which one we select as the fundamental (i.e. 1/2 + 1/2 = 1 and 1 + 1 = 2).

If fermions are triple combinations of s/t and t/s pseudoscalars, whose net frequency is at the fundamental, or whose net motion is at the spatial zero, then a natural question to ask is, “What effect does vectorial motion have on their time (space) flow?” Einstein’s theory shows that time slows down relative to inertial systems in motion. We can illustrate this effect as shown in figure 2.

      

Figure 2. Vector Motion Slows Down Time.

Of course, the difference between the space/time of figure 1 and the spacetime of figure 2 is that, in figure 1, both space and time are progressing, whereas, in figure 2, only time is progressing, and while the change in space of figure 2 is a vectorial motion of an object, a one-dimensional change of x, y, z, locations, tied to events that are separated by spacetime, the events in one inertial frame happen slower (height of green arrow), relative to the events in another inertial frame, depending upon their relative speed (length of the purple and blue arrows).

In figure 1, we see that it’s the oscillation in the space progression, effectively nullifying it, that creates the inertial frames of figure 2. So, a more accurate representation would show the oscillation of an inertial frame, in both the s/t and t/s cases, as shown below in figure 3.

 

 Figure 3. The S/T and T/S Pseudoscalar Oscillations in a World Line Chart

The space/time progression of the oscillating s/t pseudoscalar is illustrated in the vertical bar of figure 3, where the space aspect of the continuous expansion is oscillating, while the time aspect continues its uniform increase. In the horizontal bar, the oscillation of the t/s pseudoscalar is illustrated, as, in this instance, the time aspect oscillates, while the space aspect continues its uniform increase.

In either case, the orthogonal paths of the oscillations show that the indicated system is at the zero point of their respective fixed reference system, created by the oscillations. Now, let’s give the same vector motion to the pseudoscalars as that shown it figure 2. Notice, depending on the vectorial speed, that the vertical bar will slant toward the horizontal, just as the green arrow does in figure 2, and the horizontal bar will slant toward the vertical.

However, there is a difference in how the x, y, z, spatial dimensions are to be understood in the two figures. In figure 2, the change in locations is defined by 1D motion, whereas, in figure 1, every point in the graph is a 3D change in the size of the locations; that is, vectorial motion causes the bar to slant to the horizontal, but it’s a physical impossibility to represent vectorial motion in three directions at once.

Therefore, we have to understand the oscillations of figure 3, not as 3D psuedoscalar oscillations of figure 1, but as 1D pseudoscalar oscillations. On this basis, it would take a composite of three charts like that in figure 3 to illustrate all the vectorial motion possibilities (this has important implications later.) But, to illustrate the relation of vector and scalar motion, we can imagine a 1D pseudoscalar oscillation, affected by high-speed 1D vectorial motion, as shown in figure 4 below.

 

Figure 4. 1D Pseudoscalar Vector Motion

In figure 4, the red space/time arrow increases diagonally, to the upper right, as the s/t pseudoscalar expands, in space and time equally. Subsequently, it increases diagonally to the upper left, as the s/t pseudoscalar decreases in space, as time continues to increase.

Inversely, the blue time/space arrow increases diagonally, to the lower right, as the t/s pseudoscalar contracts, in time, but continues to increase in space, while it subsquently increases diagonally to the upper right, as the t/s pseudoscalar expands in time, while space continues to increase.

Hence, we can see the perfect symmetry of the space/time | time/space relationship. But now, when we add vectorial motion to these pseudoscalars, the vertical, s/t, pseudoscalar rotates right, to the unit speed diagonal, while the horizontal, t/s, pseudoscalar rotates left, to the unit speed diagonal, represented by the green boxes with green arrows.

The most interesting thing to note at the unit boundary is the directional changes of the red and blue arrows. As the s/t pseudoscalar’s speed increases to c-speed, the time component of its expansion arrow disappears. It increases in space only, while on the contraction part of the cycle, the space component of the contraction arrow disappears, indicating that only the time component is increasing in this half of the cycle.

The full implications of this development are not well understood as yet, but it seems clear at this point that any increase in vectorial speed of the s/t pseudoscalar, beyond the unit level, crossing the c-speed boundary so-to-speak, is tantamount to a decrease in the vectorial speed of a t/s pseudoscalar. Moreover, we can see that, what would appear to be an increase of s/t vectorial speed, is actually a decrease in t/s vectorial speed, which completely transforms the red diagonal arrows of the s/t pseudoscalar into blue diagonal arrows of the t/s pseudoscalar and vice-versa!

Thus, the arrow of time, the arrow that defines the entropy on the s/t pseudoscalar side of unit speed, reverses direction, as the arrow of space, on the t/s side of unity, defining a reverse entropy! (note to John: is this not tantamount to the direction of matter’s time arrow (s/t) being opposed to the direction of energy’s time arrow (t/s), described by you?)!

To underscore that the directions of the two scalar arrows (i.e. the two “time” arrows) progress in opposite “directions,” a final graphic serves to more clearly illustrate it geometrically, in figure 5 below.     

Figure 5. The “Directions” of the Two Arrows of “Time” in Our RST-based Physical Theory are Opposed.

While our RST-based theory differs from Larson’s, in that his theory doesn’t incorporate the principles of the tetraktys in its development of the consequences of the RST, yet it continues to amaze me how the trail he blazed continues to be our guiding light.

Not only was he the first to solve the problem of the asymmetry of the “arrow of time,” and in the process uncover the t/s side of the universe, but he went on to show how high-speed vector motion, with the dimensions of scalar motion, and the unit c-speed datum, produces a cosmology of such beauty and grandeur that the contemplation of it is in itself almost a religious experience.

Of course, there is much, much more to learn about it. We have scarcely begun.

Article originally appeared on LRC (http://www.lrcphysics.com/).
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