Snowflake wrote:

You said
“The term "distance" indicates a span of space measured by a velocity over time. Thus, ds = v*dt. However, we can also indicate the same measure of space in terms of an interval of time. Thus, dt = ds/v. This fact reveals that velocity may be interpreted as a meter of space and time wherein it, in a sense, creates space (distance), given time, or time (interval), given space.”

This confuses, for me, the difference between the meaning of distance and space. ( more specifically, note “creates space (distance)”

Defining “space” is not that easy, but blurring the distinction or meaning between the words “distance” and “space” only makes things worse. Looking ahead, once time is integrated into the relationships of spatial configurations, the description of what is Spacetime, will become particularly confusing.

Reply:

In the Reciprocal System there are two kinds of motion, scalar motion and vectorial motion. Vectorial motion is the motion of physical entities that we are all familiar with. It has magnitude and direction. Scalar motion is new to most of us. It has magnitude, but no specific direction, because, by definition, a scalar value is a magnitude that can only increase or decrease, like the prices of stock on the stock exchange.

In the case of vectorial motion between an object at point A, moving toward point B, we can quantify the distance between A and B, the magnitude of the motion, and the direction of the motion. The distance between the point A and the object increases, and the distance between point B and the object decreases, as a function of time.

On the other hand, scalar motion between point A and B does not require an object to define it. It has only magnitude, and the distance between the points A and B either increases or decreases as a function of time. An observer at point A would see point B moving directly away from or directly towards point A. However, an observer at point B would disagree and maintain that point A is moving directly away from or directly towards point B. The best example of this kind of motion is the motion of the receeding galaxies. An observer on any one galaxy will always report the same thing: all other galaxies are moving directly away from the observer, regardless of which galaxy is selected.

So, what we regard as distance between points is nothing more or less than the space aspect of a past or future motion; that is, the motion, when it occurs, creates the distance between objects. We can understand this, when we think about measuring the distance. We can't measure the space aspect of motion without repeating it somehow. In other words, to measure the distance between any set of points, we must supply a motion of some kind and measure the space aspect of the motion we are measuring. We can run a rule from one point to the other, but we have to move the rule into place. We don't care about the time aspect of the motion, so it doesn't matter how fast we move the rule. We just need to count the space aspect of the motion.

We can try all sorts of different methods to measure the distance, but all of them require motion: the light of a laser, the sound of sonar, the ambient light that our eyes use to triangulate, etc. In short, there is no way to measure distance directly. We must provide a motion of some sort to do so. Therefore, it follows that space doesn't exist apart from motion, only the motion exists, and what we measure when we measure distance is simply the space aspect of the past motion, which we recreate in the measuring process, or some future motion between the points that we contemplate.

Kesh wrote:

I have a couple basic questions I'm hoping you can clarify before this goes further, Excal:

1) What is meant by the term "background" in this context?

Smolin uses the term background to refer to the 3D non-dynamic structure of space and time required by QFT, and the 4D dynamic structure of spacetime required by GR.

2) It is stated that the relationships between these entities are relative "according to law." What law is being referred to here? How is it a law when, apparently, everything is relative?

It means that the relationships between entities are determined by events that are governed by the properties of the entities and the regular patterns of behavior, identified as physical laws, that apply to them; that is, they are causal. In contrast, the structure of space that we imagine exists, consisting of the set of points satisfying the postulates of geometry, do not meet this requirement.

3) Of course, if we think of space and time as a background, then the idea of space being the reciprocal of time seems absurd, but in considering the equation of motion, the reciprocal relationship of these two enigmatic concepts makes perfect sense.

I'm not certain that the conclusion ("makes perfect sense") follows. Perhaps you can clarify what is meant by "space being the reciprocal of time." Mathematically, I see it in the equation, but I'm not sure what this means in a practical sense.

When we think of extension space, we imagine that it consists of a set of points that satisfies specified geometric postulates. To think of this expanse as the reciprocal of time is absurd. However, when we realize that space is nothing more than a progressing aspect of motion, the reciprocal of progressing time, in the equation of motion, and that it doesn't exist as such apart from motion, as some kind of static lattice structure, for instance, then it's much easier to understand. The abstract set of points that we are accustomed to calling space, are only an abstraction of locations, to which motion can move, is moving, or has moved, things. These locations and the distances separating them do not exist in reality.

4) The model basically reduces all measurements to a form of motion, correct?

All measurements of space and time, yes.

As snowflakeuniverse points out, this seems to complicate things such as distance. In this model, how would one express a measurement such as "three feet from point A to point B" and why would it rely on a function of time? Or, is the time considered negligible somehow?

See answer to Snowflake above. The only thing that exists is motion, so to measure distance, we have to measure the space aspect of a motion. After we have measured it, we can then refer to the distance as "three feet from point A to point B." If we don't care about the time aspect of the motion separating the points, then we can disregard it as we do when using a yardstick, or tape measure. How fast we move the measure is not relevant. However, if we are measuring the distance with a laser or sound wave, then we have to know the speed of the motion we are measuring and the time involved, in order to calculate the distance.

I hope this helps. If not, don't give up. Just let me know.

Regards,

Excal