A Model of Time and Space

Prologue

This model was madzenoe mostly as an interesting exercise. I do not claim it is a correct model, or that I even believe in it. However, the fact that I can make such a model, that cannot in any way be disproven, does tell us something interesting.

Ideally, one would look at all facts and start building a model to explain them. The world is unfortunately not ideal. Such a model begins always by an idea, which one tries to match the facts with.

Then the game has taken a small but crucial turn: one does not ask the question: “which model explains this?” – but, “how can this be explained through this model/idea?”. Usually one can find an answer to the latter question – by introducing some new element, by adjusting some details.

One admits that yes, there are other explanations that are models. Still one interprets everything through one’s model – lives according to one’s model. The admission on the rational plane means very little. In the process of making and thinking about this model, I was almost pulled towards it – beginning to feel that this is how it is. Almost automatically, I started to try explaining everything through the model, make examples and analogies, and I had to resist the urge to keep adding details and information.

A model is not consciously assumed, but something one is drawn towards. Since the bond one has to one’s model is not formed consciously, it is hard to consciously break it. Not only because the bond is unconscious, but because the model is hard to contradict. A detail can always be changed, but the larger idea of it can rarely be disproven.

Assuming the existence of an almighty God, everything can be explained from this. Arguments about plausibility do not affect the bond; since the model is not logically contradicted, why abandon it? Not to mention, that it must be contradicted on its own terms. And the implausibility of assuming God – how can it be implausible without assuming some model? There is little reason to be convinced by “according to my way of thinking, your way of thinking is not sound”. One does not really understand another way of thinking without immersing oneself in it, and how to do this consciously – is unknown.

The model below cannot, I hope, be in any way disproven. It may be possible to make several other models for the same, that while different, also cannot be disproven. This means nothing more than that we do not have enough knowledge available to know. Nor is it necessarily possible for us to attain such knowledge. If we are God’s creatures, why would God reveal everything to us? If we are a product of evolution, why would we have evolved to see and understand all dimensions?

A Model of Time and Space

Imagine time being frozen. Everything in the universe, from galaxies and planets to electrons and quarks is locked in its current position. We have no problems imagining this. It is even easy. In this intuitive model, things do not come into existence as you travel around and see them: you discover them. If you do not see them, we still imagine them as being there, fixed. This matches our daily experience.

This is a three dimensional space, and the world at the point P will remain the same until something there moves. But now we have movement, and movement does not make sense without time. Time – is a fourth dimension.

Let us model the three first dimensions by x-,y- and z-coordinates, and time by t. A coordinate system does not really contain anything by itself. We can talk of the point (x,y,z,t), but there is nothing there. A coordinate does not tell us what is there. Think of temperature. When you say that there is 20 degrees in the room, you are associating a number to a place in space and time. Temperature is a function.

Think of the universe as a function F of space and time. It associates material to an area in space and time – spacetime. A bird flying past your window is a value of F in that area of spacetime. It associates energy to points in spacetime. It associates ideas and thoughts; consciousness. Your thoughts are values at an area of spacetime. At each point in time, we intuitively imagine everything in x, y and z directions as being completely fixed: we commonly say and think: at that time, it was like that. I was like that. My house was like that. I felt like that. This is the same as saying that if the time t is given, say t=t’, F(x,y,z,t’) is fixed for every point (x,y,z).

Regarding the past and present, we intuitively think this way. Two days and three seconds ago, it was like this. It is determined. However, for the future, we do not think so. One thing is to admit that we do not know the value of F(x,y,z,t) for t in the future, but we often think that this value does not exist a priori. It is not determined until we get there.

The problem here is “we”. For times in the past and present, we think that F(x,y,z,t) has determined value, regardless if we observe it or not. Fixing y, z and time t and moving in direction x, we do not imagine things as happening or coming into being as we travel, but simply as being observed. When imagining as in the first paragraph, we imagine exploring the plot of F(x,y,z,t) over all (x,y,z) with t fixed. When imagining the past, we imagine the values of F at (x,y,z,t) for “previous” values of t. It is fixed.

With future, we imagine things as happening, as coming into being, as we move. There is no logical basis for this, only a natural bias stemming from how we perceive the world. We can observe a large part of the space dimensions at any time – but in the time dimension we can observe only in a different way. In time dimension, we can only look, to some extent, in one direction.

This direction we call the past, and the other future. We “observe” the past only through memory: having stored values of F at previous times, or through deduction about the behaviour of F – assumptions about how F at a point (in space and time) depends on the points around. If we find ash, we think there must have been a fire at a previous point in time. If something is falling, it must have been higher up the moment prior. F does not make arbitrary jumps. Again mathematics give a good intuition about this: if a function f is continuous we know that the value of f at points around a point P must be close to the value of f(P). That F(X,Y,Z,t) contains ash means that F(X,Y,Z,t-s) contains fire, for some s>0. But, just like in mathematics, the sets (X,Y,Z,t) and (X,Y,Z,t-s) and the values of F at these sets exist at the same time.

Like Africa occupies a different place than Europe on earth, (X,Y,Z,t-s) is just a different area of time-space than (X,Y,Z,t). I cannot observe Paris without being at its spatial coordinates, but it still exists. I cannot observe Paris in the past even if I am at its spatial coordinates, because I am not in the right time coordinate. At every moment we think of the whole universe as existing and being fixed in the Now. Paris and all that goes on there exists now. What is now cannot be changed – it may be different at a later point in time, but at this point it already is. We think of the past of something that was, that has existed; everything in Paris yesterday was. And what was cannot be changed. The future is something that will come into existence. And this we think we can control – change.

Why do we treat the time dimension as essentially different than the other dimensions? Not knowing the value of F at a point in the future, is it not senseless to say that we can change it? If t is now and we think of F(x,y,z,t) as existing for all (x,y,z), should we not also think that if we fix say x, F(x,y,z,t) exists for all (y,z,t)? And then, why fix anything: F(x,y,z,t) exists for all (x,y,z,t). You are just a value of F. The thought that the past does not exist is a value of F at a given place in timespace.

There is no movement, change or events, only different points in a four dimensional space, and a function defined on this space. “You” is only a value of this function at specific points and times. When you are making a prediction about something in the future, i.e. saying that the value of F will be at some point in spacetime, this is a value of F at your spatial position at the time you had this idea. You and your idea is a value of F at this set in spacetime. You do not occupy a place in spacetime, you are a value that F takes at a point in spacetime – when saying your position this is only meant to help intuition. That you have memory of “the past” means that the value of F at your position in spacetime contains information about the value of F at another point in spacetime, and only for values of t less than the current value. Or greater – positive direction in mathematics is just a convention.

That the value of F at your spacetime position does not contain the idea “the value F at spacetime position P contains X” does not mean that it does not contain it. When we say “I could have chosen differently”, we are saying that the value of F at a point in spacetime could have been something else than it is. The value of F contains the idea that the value of F could have been different. This does not mean it could.

I can define a function f by sending a number x to the set with two elements {x, f(10) contains the number 15}. Thus the value at 1 is {1, f(10) contains the number 15}. Imagine your mind as being f(1): you have the idea that 15 is one of the elements of f(10). But f(10)={1, f(10) contains the number 15}, and 15 is not an element. (in common set theoretic notation, elements are separated by comma).

In mathematics one says that a function f at a point x depends on f at y if changing the value of f(y) changes the value of f(x). In a sense this is a nonsensical statement: if one changes the value of f(y), then f is not the same function anymore. In other words, one is saying that if one changes f then f becomes something different – a tautology.

If you did something different then F at some point would be different, but your actions are just values of F – they cannot be different.

Nothing moves. If f(x)=5 and f(y)=5, we do not say that 5 moved from x to y. Nothing changes. F(x,y,z,t) does not change if (x,y,z,t) does not change. The universe tomorrow is different than the universe today because it is the value of F at a different value of t, but the universe at a certain time is the universe at that time.

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2 thoughts on “A Model of Time and Space

  1. Do we also assume that time exists in the other dimensions, or just the three physical ones that we know of? If time exists in the other dimensions is it time that we would recognize? Is it chronistic?

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    • First, I want to apologize for the very late reply.
      Here, we assume that time is a seperate dimension from the others. For those familiar with mathematics, this is easy to imagine, since one oftes works with equations u(x,t), where x=(x,y,z) is the spatial dimension, and time t. And for every fixed time t1, the graph of u(x,t1) plotted over x is the state of the system at that time. Mathematically, there is no difference between t and x or y or z, it is just common convention to treat space and time differently, because in applications one is interested in describing a system as we perceive it, and we perceive space and time differently.

      And, I am ashamed to admit, but I could not find a clear definition of chronistic, so while I can guess what you are asking about, I am not sure. English is not my first language.

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