What is space?
Space is a concept which indicates relationships between positions. What does this mean?
Suppose that we consider a room in our house, say the living room. The living room is a part of the house between four walls and between those four walls is some “space”.
The “space” within that room indicates relationships between the positions of those four walls. One wall is over here, another wall is over there and the other two are there and there. In between is all this space.
The space essentially refers to the separation between objects. And “separation” is a sum of positions (or places) within the boundaries, relative to the boundaries.
Space is the sum of positions between the boundaries of some kind of container or some otherwise defined set of bounding objects.
For instance, you can walk into the living room and say “Well, we have these walls. They are in different positions, forming the boundaries of the room.
There are other positions in between the walls.” The sum of those other positions is the “space” inside the room.
Does this imply that there are not other things in those positions? No. The concept of position only applies to entities and only entities can have a position.
There is no position of a “non-entity” or of nothing. Position is a quality and a quality is a quality of something.
Is this space some kind of absence of being? Early philosophers tended to think so. But, this is not the case. There is no such thing as empty space.
What would empty space refer to? Some kind of “here” where there are no entities. Where nothing exists. But, how can there be any here without something that exists?
How can there be any here separate from anything that exists? Unless there is a something, there is no here.
Hence, there is no such thing as “empty” space. Or in other words, there is only space where there are things with position.
To allege the existence of empty space is to talk about position without entities to have position. It is to allege that you can have a sum of positions without anything that has a position.
That is, that you can have a sum of positions without any position! It is a contradiction in terms.
If you want it put simply, then space is a sum of positions. But there has to be something with position for there to be any space. You cannot divorce the concept of space from things with position.
No, space is not the absence of objects. It is not some backdrop upon which you can lay things that exist. For there to be any space, something must already exist.
Is space a combination of dimensions, as alleged by modern physics?
Most certainly not. What would that even mean?
The word dimension has two primary uses in the sciences. The first is geometrical. It assigns some position in space as a starting point. And then measures the relative position of other objects relative to that starting point or frame of reference.
It measures the relative position of something, relative to that starting point, by measuring in three directions: up/down, left/right or back/forward. The details are not all that important.
The essential fact is that the measurement is performed by a combination of performing measurements in three different directions. Each of these directions is a separate dimension.
What does this measure? The position of that object relative to the starting point. The concept of dimension is a mathematical abstraction which represents relative positions.
(That is three-dimensions. You can, of course, perform similar measurements in two dimensions if you wish to ignore the separation between objects in the direction that corresponds to “depth”).
Dimension is a mathematical abstraction which allows relative positions to be numerically quantified.
The concept “dimension” is a mathematical abstraction used for the purpose of measurement.
Hence, space is not composed of mathematical abstractions used for measurement, that is space is not a combination of dimensions.
The second use of the word dimension is far more mathematically abstract and we will not go into it here. Suffice to say that it too is a mathematical abstraction and also does not justify considering space a combination of dimensions.
We may use the concept of dimensions to perform measurements on space but the concept of space is a more fundamental concept than that of “dimension”.
What about the idea that there are more than three dimensions of space?
Well, the three dimensions of space are sufficient to indicate the relative position of any point. Any dimensions after the third would be some combination of one of the first three and would be redundant.
String theorists and other physicists assert that there are more than three spatial dimensions. And that the extra ones are “rolled up really” small so that we cannot detect them. This is an entirely arbitrary claim without any merit. For a few reasons.
Firstly, it reifies the dimensions by treating them as anything other than abstractions used to measure relationships. What does it mean to have abstractions rolled up so that they cannot be detected? Nothing.
Earlier on I mentioned the more mathematical and abstract use of the word dimension. In string theory, they equate the mathematical use of the word dimension is equated with the kind of physical dimensions that physics considers the first three spatial dimensions to be.
This is supposed to tie the otherwise completely arbitrary mathematics of string theory back to reality.
However, it goes without saying that this fails.
They say they are “rolled up” so that they can explain why we do not detect them. But, we do not detect any of the dimensions.
We form the abstraction of dimension to describe relationships. The reason spatial dimensions other than the first three ones does not make sense is because they are redundant.
What about time, what is that?
Time measures motion or change. For instance, it takes two motions or events or changes and identifies a relationship between them.
For instance, suppose we are talking about how old I am. What fact of reality does my age refer to?
Well, we take two events, my birth and the writing of this article. And identify the fact that there is a certain relationship between these two. My birth happened during a particular revolution of the Earth around the Sun. This moment is occurring within a different revolution of the Earth around the Sun.
While I write this, 37 such revolutions have happened. And so I have thus identified a relationship between my birth and the writing of this article.
I could do something similar with myself starting a race and ending it. Except, presumably I would use a second to measure the relationship between the start and end of this event; a second as measured by the motion of a second hand around a clock or by a digital equivalent.
In any case, I am measuring motion or change.
Many people define time only in terms of measuring motion. However, we can use the same concept to measure the amount of change. Perhaps an example would make this more clear.
Suppose we want to know how long it takes for someone to wake up. What are we measuring here? We are not measuring motion as such. We are measuring a change in state, from a state of sleep to one of being awake. The concept of time applies to this just as it does to motion.