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Space and Time
By Thomas M. Miovas, Jr.

I think throughout history, the concepts of “space” and “time” have not been derived from that which is observable, leaving them as floating abstractions. By “floating abstractions” I take Ayn Rand’s definition as those concepts that are not connected to reality – to that which we observe – and therefore are almost mental only and not of reality. To be objective, a man must ensure that his mind forms concepts from that which he observes instead of starting off in mid-stream. For example, Kant held that Space and Time were the ultimate fundamentals of reality because he could think of both time and space without either containing any material things in it; but I think this is incorrect, and a wrong approach.

What we observe starts off as the basic axioms: existence, identity, and consciousness; which we get simply by opening our eyes or observing reality (say if we are blind), and then conceptualizing what you notice. And, as Dr. Peikoff pointed out, the basic axioms can be put into a fundamental sentence – there is something there that I am aware of – there is (existence) something there (identity) that I am aware of (consciousness) – and these are fundamentals because they are universal. It does not matter what one observes – trees, people, insects, frogs, emotions, thoughts, memories, etc. – One observes it being something and that one is aware of it. But this is not true of Space and Time the way Kant and other philosophers would have you believe. One cannot directly observe Space or Time with the senses; rather what we observe are entities (derived from the observation of things having identity), attributes (what a thing is made of or its color or shape), and motions or changes (as is given in observation, see my essay on the topic). So everything we observe is something, is something specific, like a car, a boat, a pen, a nail, a computer, an idea, a thought, or a memory (those these later concepts of consciousness are not made of matter, so they don’t have the attributes of material entities, like weight and height or density; nonetheless they are something specific and formed as something specific by the human mind).

So, if we do not observe Space and Time, what are they? I think they are higher-level concepts developed by observing entities and their locations (here versus there) and motions or changes (before and after). The following example might prove to be motivational: Let’s say one rolls a ball at the far wall, and then tries to catch up with it. One can do this without the concepts of here, there, before, and after, let alone Time and Space. In other words, one is simply observing something here moving over to there and getting there (at the wall) before we do, or that we get there after the ball gets there. So, as Aristotle first pointed out, the concept of “time” is based on “before” and “after” while space is derived from “here” and “there.” In other words, “here”, “there”, “before” and “after” are all *lower concepts in the hierarchy than is the concept of “time” and “space.”* That means that one must form those concepts before one can form the concepts of “space” and “time.”

The concept of “space” integrates the similarities of here versus there (a certain distance from you observed, like a meter), while “time” integrates a certain state of being before or after an event used as a standard (like a clock). Actually, at first one only has here and there and not a specified distance and only before and after (without a specified unit of motion); because that is what we observe. We do not observe even duration (one second, or one minute, or one hour) or one unit of distance (one meter or one foot, or one mile, or one kilometer) until someone conceptualizes those and makes measuring sticks and measuring clocks. And what these tools measure is not space and time, but rather specific relationships between that which is being measured (motion or place), but not space or time per se. These are developed from more basic concepts such as here and there and before and after.

So, I totally disagree with Kant, who presented the idea that Space and Time were fundamentals, but rather we observe with our senses that which exists (entities) that are here or there, and moving before or after some other comparative motion or change. We can use a clock to measure how long it takes for the ball to get to the wall (say ten clicks of the second hand) or how far away something is from us (say three meters) which gives rise to the concept of duration / measured time; or distance / measured by comparison to a yard stick. But a clock does not measure time, and a meter stick does not measure distance – not until a man compares the distances and the motions to something else within the purview of his observations using either a clock or a meter stick to measure those motions or changes or distances.

For a much earlier attempt of reconciling these issues, see my essay An Example of Rationalism.

Added on edit 02/26/2020:

"Duration" is not a given by perception phenomena; that the ball that you rolled gets to the far wall before you do is directly observable. I think that was the point Ayn Rand was trying to make in that clip presented in ITOE 2nd edition. Duration, I think, is based upon measuring how many times the pendulum goes back and forth before the ball hits the far wall; so one needs a standard repetitive motion and counting to get the concept of "duration" after omitting the measurements of the clock, pendulum for several different rolling of the ball towards walls. And "Time" is a bit higher up the hierarchy in that it omits the measurements of several types of clocks (pendulum, ball bouncing up and down, something acting consistently like the sun going round the earth) and various different types of motions or changes as compared to the standard; so, in a way, "time" is the measurement omission of clocks and motions or changes as compared to a unit of duration.

Added on edit 03/01/2020:

I define "time" as the concept that designates that various clocks (pendulums, rotational clocks, sun dials, etc.) can be used to measure the duration of all sorts of every motion or change (a tree growing, a ball rolling towards the way, a girl holding a pretty pose, reading a book, changing one's mind, thinking about it for a while, etc.) with all the measurements of both groups (clocks and actions) being omitted. A clock does not measure time, and it is based on duration, which is a measurement of motion – it is a recognized relationship between a standard motion or change and what is being measured with respect to it with regard to “before” and “after,” and then “duration” (how many times the clock ticks) with regard to the measured motion.

Space-Time in Relativity 09/02/2020

Now if time is a measure of a relationship (of a periodic motion to all other motions with regard to before and after) and space is a measurement of a relationship (of a thing being over here or over there), then what is space-time? I think it is a concept of a higher-level relationship between the concepts of time and space – in other words, it is the measurement of a relationship between before and after *and* here versus there; and it is based on Einstein’s understanding that the speed of light is finite and that the speed of light is not dependent upon the motion of the source of the light (unlike a ball which moves faster if it is thrown out of a car moving forward relative to a ball being thrown from the ground), and that neither time nor space nor motion nor measurements have a set point of measurement – not fix place in time or space in which to measure what something is doing or when it is doing it. What Einstein thought about was how clocks (as measuring devices of time, of before and after) behaved when one moves near the speed of light, and it turns out that the relationship between time and space does change with high relative motions. If the speed of light is a constant in all frames of reference, and we observe clocks in differing types of motions near the speed of light relative to the measurer, then we notice that time is shortened as measured and space is compressed as measured. But Einstein held that as measured meant as it really is, just as when one measure a piece of paper as being 8 ½ x 11, that is the size it is, and using light to measure time and space relationships, that is what they really are. There is no “true motion or true time or true space” just as we measure it to be. No special frame of reference in which one can claim that his measurement is accurate but another’s who is moving relative to the other observe is not a true measurement, because there is no fixed background as a reference point. So, this is a higher-level relational concept and not a physical thing as an object, but a relationship with respect to objects.

So, what does it means to say space-time is curved of necessity? It simply means that in a non-accelerated frame of reference, all motions must follow a curved path *without any forces acting on them in a non-accelerating frame of reference*. It is not a physical thing that is curved – space-time does not exist as a physical object, but is rather relational. It is not that the concept makes things move in funny ways, but things move and we measure them as following a curved path if no forces are acting on them. As an example, we have the astronauts orbiting the earth in free fall – in Newtonian physics, they are falling at the same rate as their spaceship, and so they float; in Relativity, if any forces were acting on the spaceship or the astronauts, then they would be driven up against the side of the spaceship, just as you are pushed to the back of your seat in your car when you hit the gas. Since this does not happen, then Relativity states that there is no accelerating force acting on them and they are naturally following a curved path. This curved path has an effect on the measure of time as well, since as we observe clocks moving relative to us, they are moving slower than if they were both moving at the same rate. And this is born out by measurements of things moving at close to light speeds, like cosmic rays and particles streaming to the earth from outer space. Their decay rate is delayed relative to the decay rate of such particles on earth that are stationary relative to us.

In other words, there is nothing spooky going on, no attractive forces in gravity, and no way to synchronize clocks moving a high rate of speed to one another or in a gravitational field context.