In the Reciprocal System of physical theory created by Dewey B. Larson, there exists
i) 3-dimensional time (in contradistinction to 1-dimensional time)
ii) clock space (in contradistinction to clock time).
My question is
i) How can we feel a 3d time since we only sense time as a linear course of events?
ii) Since a clock has a physical motion to indicate the passage of time, what kind of clock has a physical motion to indicate the passage of space?
To understand the Reciprocal System, you have to think in terms of
motion, the
ratio of space to time, not the individual aspects. Motion is the "rate of change" of space to time (speed) or time to space (energy). As a ratio, space and time are inseparable; you cannot have space without time, nor time without space. The Reciprocal System starts with
three dimensions of motion, with each dimension of
motion having
aspects of space and time.
In order to measure a rate of change, you need to specify a
datum, the origin of the system of measurement. Because the ratio is a multiplicative inverse, it's identity is unity, not zero, so the datum of motion in the RS is the ratio of unity, 1/1. In the RS, this is the concept of the "clock"--not an independent entity, but a specific magnitude of motion in which to take measurements from.
With three dimensions of motion to "build in" and a fixed reference from which to make measurements from, you can start to construct a Universe as a theoretical model. Because a ratio has two aspects, a numerator and denominator, we can measure "change" in either aspect (or both). But which aspect is space, and which is time? Larson's solution was BOTH: one sector of the universe is based on s/t and the other based on t/s, since s/t x t/s = 1/1. Measurements can be made in either direction. He refers to the s/t basis as the "material sector," our conventional frame of measurement and the t/s basis as the "cosmic sector," the "universe of antimatter" as it has been commonly described (though it is technically "conjugate matter").
Our consciousness, in order to be effective as observers and able to communicate with each other, creates another datum of measurement that is uniform for all observers--it normalizes all the dimensions of motion so they have t=1, matching the corresponding aspect of our "clock datum." For example, I can have a ratio of motion as 4/2, which means time is "flowing" twice as fast, as compared to my clock reference of 1/1, and normalize it to 2/1. (Because we are comparing two ratios--a cross-ratio--it remains "projectively invariant.") So what we end up with is 4/2 (scalar motion) --> 2/1 (normalized for the same "flow of time") --> 2 (a length). This is how we end up with 3D space and clock time.
The cosmic sector is the same, with the aspects reversed. There, you normalize space and extract coordinate dimensions for 3D time and clock space.
i) How can we feel a 3d time since we only sense time as a linear course of events?
In our material reference frame, clock time is a
scalar--just a magnitude from which we take measurements from. It does not have a geometry, so it is not "linear." Space (what Larson calls "extension space") is linear, and linear divided by a scalar = linear: the
ratio of motion, s/t, appears to us as linear. With all the denominators of motion set ot unity, it
appears we have a 3D spatial reference system, with a constant "flow" of clock time, measuring how things change. (This is the Euclidean stratum of projective geometry.)
The same situation occurs with clock space--it is a scalar that is used to normalize the dimensions of motion to give us the equivalent of a length or distance
in time. This is NOT clock time, it is coordinate time, 3D time with the "flow" of clock space.
There are two answers to your question. The first involves the "outside world" and what Larson terms "equivalent space," how temporal motion alters space. The material and cosmic sectors exist 90 degrees out of phase with each other, like the sine and cosine relationships. When one is at its maximum or minimum, the other is at zero. As a consequence of the way our consciousness measures spatial structures, temporal structures appear
between spatial locations as
forces and
force fields, determined by the number of dimensions involved with the temporal aspect of motion: 1D = electric, 2D = magnetic, 3D = gravitational. So any time there is a "rate of change" in the temporal aspects of the three dimensions of motion, field effects are observed--and these field effects include two components: orientation and magnitude. Equivalent space is a 2nd power "space" in coordinate space--rotational--so the effects of equivalent space cause things to orient (as in the case of ferromagnetism) or spin. The magnitude determines how strong the effect is, as in interatomic distances. (Equivalent space = integral (temporal displacement), so we see it as t
2/2.)
The second answer is the "inside world." Biological life, Larson's "life units," are composed of a stable combination of material and cosmic atoms, and therefore have existence in BOTH sectors. We recognize this in psychology as the split between sensation and intuition,
sensation being how we detect spatial change that is valued by
thinking (the material half), and
intuition, how we detect temporal change, valued by
feelings (the cosmic half). (Concepts from Carl G. Jung.) Your intuition is providing you with 3D temporal data, but you've probably never been taught how to use that temporal geometry (the study of psionics).
ii) Since a clock has a physical motion to indicate the passage of time, what kind of clock has a physical motion to indicate the passage of space?
The speed of light in a vacuum, which is the "clock" in the Reciprocal System--unit motion. All measurements in the RS are taken from the speed of light, which is 1/1 in natural units. So the speed of light works as a clock for both clock time and clock space.
Every dogma has its day...