Section IX: Time, Motion, and Arrows, from "Is Space the Only Substance in the Universe?"

 

IX.                   TIME, MOTION, AND ARROWS

Doing Without Spacetime…and Even Without Time

The question of whether time needs to be included as a fourth dimension, as in relativity theories, deserves some special consideration. No other dimension extends in only one direction; one can go forward or backward in space but only forward in time. A few physicists have been working to abolish the four-dimensional concept of spacetime (Zyga 2012).  The concept of spacetime may be appealing in that it reminds us that both space and time are affected by velocities approaching the speed of light, as well as in powerful gravitational fields. However, the ratios between space and time are not constant (Jackson, N. 2015). The expansion of space per time is currently believed to be increasing (Rubin & Heitloff 2020).

.            One of the disadvantages of a 4-dimensional model of spacetime is that the mathematics becomes much more complicated (Wolfram 2015).  It might be possible to describe the geometry of the universe in terms of our traditional three dimensions, if we took into account their constant changes, with expansions and deletions in various locations.

            Aristotle defined time in terms of motion, and motion can occur without the need to conceive of time as a dimension (Rassi 2014). Units of time are determined in terms of repetitive movements, such as rotations and revolutions (including of the earth around the sun), clock pendulum swings, apparent movement of the sun across the sky, vibrations of springs, or electron jumps up and down among energy levels around atomic nuclei in the case of an atomic clock (Hadhazy 2010).

            A seeming obstacle to explaining time entirely in terms of events in spacial dimensions is that the repetitive motions used as measures of time must occur at regular intervals. Our common understanding of “regular” is that the interval between each repetition takes the same amount of time, thus seeming to define time in terms of itself, a circular definition. But that does not turn out to be a problem. Instead, we can compare one type of repetitive motion with another, for example, how many rotations of the earth per revolution around the sun (how many days in a year), or how many rotations from one new or full moon to another (how many days in a lunar month). A constant or almost constant ratio of one type of repetitive motion to another implies regularity, and thus time can be defined just in terms of measures in space. In fact, it is just that sort of ratio that leads humans to determine what is appropriate to serve as clocks to measure time. The number of units into which one repeated motion is divided, such as hours in a day, minutes in an hour, and seconds in a minute, is arbitrary.

            It is actually possible to make any physics equation time-free, by substituting the number of regular or recognized repeating events, or fractions thereof, that occur (such as solar days), which I shall call E_r (for events repeating), multiplied by the number of units into which each repetition is traditionally divided, which I shall call U_r. (for units in each repetition). A simple example of how repetitive events could be substituted for time is in the equation v = s/t (velocity = distance/time measured in seconds), the adjusted time-free version would be:

                                                            v = s/(E_r*U_r)                                                   (8)

            This amounts to distance divided by the product of “time” units arbitrarily assigned per repeating event, e.g., 86,400 “seconds” per rotation of the earth, times the number of events that elapse. If only one 86,400^th of a rotation of the earth has occurred, the denominator is one “second.” 

            In most of the remainder of this article, time is referred to in the usual manner, to avoid confusion. Time as we understand it in common usage is a helpful concept, which we are strongly bound to (four-dimensional spacetime being much less so), and there is no need to eliminate it to apply the “Nothing but Space” model.  However, the point made was that time is dependent on space, in order to emphasize the primacy of space as the ultimate building block of the universe.

            Meanwhile, we have advanced well beyond sundials, pendulums, and springs in the measurement of time. A second was formerly defined as 86,400^th of a rotation of the earth, but in 1967 the General Conference on Weights and Measures redefined it as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom at a temperature of 0 K. (Betts and Hosch 2007). Note that this can be considered as a repetitive motion.

Motion: Active vs. Passive, and “Real” vs. Relative

Not everything in the universe can be simplified and unified. It appears that there are three different types of motion, two passive and one active.

            We have already seen that the Hubble expansion and gravity may involve passive motion, in which space is proposed to be added or deleted. However, there are differences between these two. In the expansion, the speed of light need not be a limit (i.e., the most distant galaxies may be receding from us at a velocity greater than c), but such rapid passive motion  cannot be observed with gravity. With gravity but not with Hubble expansion, there is also slowing of clock speed when observed from a distance (UCSB Science Line 2008, Hamilton, 2006). In Hubble expansion, multiple bodies move away from each other, and only gradual acceleration is observed as the distance between the bodies increases. With gravity, multiple bodies situated around a mass rapidly accelerate toward it, without any of them needing to apply energy to do so. General relativity also implies a passive process for gravitation, and does not even consider it to be a true force, but rather the curvature of spacetime (Williams 1968).

                Conventionally, potential energy is exchanged for kinetic when a raised object is released in a gravitational field. However, distant objects attracted by gravitation were never raised, so their apparent kinetic energy seems not to derive from any other energy, and the same applies to the apparent kinetic energy of space expansion. If there are hidden dimensions donating and receiving space from our visible universe, they are part of a complete, complex system, and the best way to think of energy considerations for both types of passive motion may be the Hamiltonian (kinetic plus potential energy) of both phases of this system combined. This should be constant if the total is a closed system, allowing the application of a version the first law of thermodynamics that apparently only applies to space, energy conservation within the entirety.

            In contrast to both of these types of passive motion, we are all familiar with active motion, applying to mechanics, in which each object must acquire kinetic energy to move, and the speed of light does impose a limiting velocity. Active motion might be a process by which waves of mass or energy somehow sweep up the units of space immediately ahead in the direction of motion, and transfer those units to positions immediately behind the wave.  Alternatively, a complex space-occupying wave combination (the mass) simply moves on to a new volume of space immediately ahead in the line of motion.

Electromagnetism, and a Potential Explanation for another Type of Passive Motion

Electrical and magnetic attraction and repulsion produce passive motion of the gravity type, with similar inverse square laws. However, unlike gravity, they can be blocked or shielded. They do not seem to involve space addition and deletion, because they neither add nor detract from gravity. Other important differences include polarity (positive and negative charges; north and south poles of a magnet), and repulsions as well as attractions.

             We are accustomed to thinking in terms of electrical and magnetic fields, but in this model a field is an area of space that is steadily conducting waves, additions or deletions, or other processes. Electromagnetic waves are often thought of as oscillating electrical and magnetic fields, the two perpendicular to each other and continually generating each other. In this model, however, they are waves with perpendicular electrical and magnetic components, and the field is space.  If a class of waves (electrical) were to have two opposite configurations, such that in juxtaposition waves of the opposite configurations were to collapse and therefore to occupy less space, the remaining waves should become passively closer together (electrical attraction).  The next closest waves then would come into contact and the process should continue. Conversely, if the interactions of electrical waves of the same configuration in juxtaposition were to cause spacial enhancement (occupying more space), the remaining waves should become passively more distant (electrical repulsion). This process should similarly continue as the next closest waves would come into contact.

             Perpendicular and integrally related to the electrical waves would be magnetic waves. Magnetic attraction and repulsion would be due to opposite and same configurations, respectively, coming into contact with each other, in a manner similar to that of electrical waves.

             Positive and negative electrical polarity could correspond to the different configurations of electrical waves. North and south magnetic polarity could similarly correspond to the different configurations of the magnetic waves. Shielding might be due to areas in space made impenetrable to electrical and magnetic waves due to the presence of different and incompatible types of waves.

             This theoretical avenue has not been explored and developed as thoroughly as the explanation of gravity in Section IV of this paper, and more work is needed in the future Meanwhile, electroweak theory (Paschos 2007) can be relied upon to continue to describe (though not to fully explain) electromagnetism, and the weak force as well.

Absolute vs. Relative Motion

The “Nothing but Space” model would imply that active motion by a body is through real units of space, changing the distances to other bodies situated in space. Let us assume that everything is in motion, that all motion is relational to that of all other bodies, that a state of “absolute rest”` does not actually exist (Huggett & Hoefer 2021), but that observers on each of two bodies in relative motion could reasonably judge themselves to be at “rest” and that the other body is moving (when no distant objects are viewed and records are unavailable).  Still, the body to which more motion has been imparted should show more change in position (however slight) relative to, or observed from, distant celestial objects.

            For both active motion and a passively falling body in a gravitational field (but not for the passive Hubble expansion), if two bodies rub against one another, there is friction. Kinetic energy is converted to molecular motion (heat), which is distributed between the two bodies prior to dissemination to the environment. The body to which more motion has been imparted has more kinetic energy to start with, and logically should provide and lose more of the kinetic energy as well as part of the resulting molecular motion of heat, a net loss of total energy.  The body to which less motion has been imparted should have less kinetic energy to lose and should gain some of the molecular motion of heat, experiencing a net gain in total energy.

            Additional differences between the two bodies should include the histories of kinetic energy imparted to them by either active motion acceleration or gravitational acceleration (the dynamics in addition to the kinematics). In addition, less time should elapse on clocks on the body to which more motion has been imparted.  In these respects, even though everything is moving relative to everything else, an increase in motion generated by the acceleration of active motion or of gravity would appear to be distinguishable as “real” rather than merely relative, resembling the concept of absolute motion.   

            This should be susceptible to experimental testing, and seems at first to be at odds with both special and general relativity (Williams 1968). However, the philosophical basis for the notion that all motion is relative is complicated by the consideration that Minkowski spacetime (the geometric framework for special relativity) includes a background structure. There could be “real motion” in relation to that structure. In addition, general relativity can distinguish locally which of two objects is accelerating (Huggett & Hoefer 2021). Absolute vs. relational motion is thus another Philosophy of Science topic appropriate for ongoing analytical discussion.

The Three Arrows: Expansion, Thermodynamics, and Time

There seem to be 3 "arrows" in physics, processes which in our common experience only progress in one direction. One is the expansion of the universe (which according to the “Big Bounce” model is a phase that will eventually be reversed, but not for billions of years). Another is the second law of thermodynamics, which dictates that entropy or disorder will tend to increase. It is not difficult to conceptualize that as the size of the universe increases, existing matter and energy can disseminate throughout that increased space and become diluted, increasing entropy. However, things may not be that simple, because the space addition adds the energy of the expansion to our universe, and might even be related in a causative manner to the creation of mass and energy (see above in Section V, under the topic “ ‘Big Bang’ vs. ‘Big Bounce’ ”).

            The third "arrow" is time. If all three "arrows" are related, the direction of time, too, may be due to a general expansion of space. Time has been defined in terms of repetitive motion, but space expansion could be related to why, in our common experience, it only goes forward. However, the relationship between space expansion and time passage should not be oversimplified. The inconstancy of this relationship has already been noted at the beginning of this section. Also, in gravitational fields where space is being deleted, time does not flow backward, although it might theoretically under the extreme gravitation of a black hole, see below.

            Time reversal is not a concept foreign to physics.  Ernst Stuekelberg and later Richard Feynman proposed an interpretation of the positron (an antimatter electron) as an electron moving backward in time (Schwartz 2015). Negative time should reverse the direction of movement and hence of repetitive motion, which could backtrack over previous repetitions.  The theoretical hidden dimensions would currently be contracting, and time might be running backward there. Antimatter waves seem to be rare in our “observable universe,” because they are annihilated by more numerous units of conventional matter waves. However, they might be more common in the alternate dimensions.

Time and Black Holes                      

Within a black hole, time might also hypothetically run backwards. The "event horizon" of a black hole is considered to be the spherical surface at which objects being pulled in could no longer escape (with the exception of some electromagnetic radiation as postulated by Hawking). The radius of the “event horizon” is called the Schwarzschild radius, and its defining equation is r_s = 2GM/c². According to general relativity, to an outside observer, as an object is pulled in by the immense gravity (very rapid space deletion in this model), closer and closer to the “event horizon,” its clocks slow more and more, and at that Schwarzschild radius, they seem to stop altogether. That can be explained by light no longer reaching the observer, but it may also represent the extreme gravitational effect of the black hole on time (UCSB Science Line 2008, Hamilton, 2006). 

            So what might happen if the object were to pass the “event horizon” and continued to move closer toward the center of the black hole?  Positive time having reached zero at the “event horizon,” at least from the perspective of an outside observer, as the object traveled further inward it might be moving in negative time. This would mean that actual motion would be back outward toward the inner margin of that horizon. This might be a real phenomenon rather than just an observational artifact, if the arrow of time is related to overall space expansion. 

            The velocity of an object subject to gravitational force is v = g*t where g is gravitational acceleration, defined in equation (2) as Gm/r², with G being the gravitational constant, m the mas toward which the acceleration is occurring, r the radius from the center of gravity of the mass, and t the time. Substituting for g, and assuming that time would be flowing in a negative direction, we get:

  v = Gm*(-t)/ r²)                                                           (9)

            Multiplying both sides of equation (9) by -1, we see that the velocity would be backwards:

  -v = Gm*t/ r²                                                               (10)

            Thus, everything might collect at that “event horizon.” All the things sucked into the black hole, including stars, might fit there because of the tremendous amount of space deleted from them. As mentioned, this is conjectural, and would be contrary to a common view that there is a “singularity” at the center of a black hole, into which things fall, causing space and time to disintegrate (Sutter 2020, Impey 2020). In a small black hole, the event horizon would not be far from the center.

            Assuming that all gravity deletes space, a black hole might be defined by a critical rate of deletion. The Schwarzschild radius might be where the instantaneous rate of volume deletion   reaches that critical value.