With the development of science and technology, understanding of our universe turn into comprehensive perspectives and more extensive reasonings. Changing in the concept of dimension and acceptance of time as a dimension allowed us to examine our universe in a more distinctive angle.
Today, we discuss the possibility that our universe may be more multidimensional than we perceive as well as existence of different universes – parallel universes – and travelling amongst each such universes. We can think of parallel universes in two distinct ways; either as universes embedded in different dimensions of our universe, or as other universes with different dimensions and parameters independent of our universe.
When we speak of the parallel universe, we will be talking about the former since the latter is far beyond our understanding. Well, what does universes embedded in our universe mean? Let’s explain this with an example. For instance, if we realize our world as 4 dimensions, shall we say, this does not mean that our universe has 4 dimensions. It might be of 10 dimension and we could be living in its 4 dimensional part and only be able to understand these 4 dimensions. So, there could be parallel universes in the other 6 dimensions which is also embedded in our 10 dimensional universe. I believe, this example clarify what we mean with parallel universe..
Before we talk about the dimensions and parallel universes more, we will do some math without going into the details. Those who do not like mathematics can skip this part. We will interpret what those mathematical terms might imply after we are done with it. Mathematics will help a lot in understanding time which is accepted as a dimension in our universe after Albert Einstein’s observations..
Totally Ordered and Partially Ordered Sets
A set is a collection of different elements. A totally ordered set is a set with a relation satisfying mild axioms that helps us to order elements in it. More precisely, if A is a totally ordered set, then for any elements a,b in A either a<b or b<a or a=b. For example our number system is totally ordered. If you pick any two numbers a,b then either a<b or b<a or a=b. Another example is time! Time is a totally ordered set. If you pick any two timeline then either one or the other is in the past (or present) or they define the same time period.
A partially ordered set is a set with a relation satisfying some axioms that helps us to order some parts of the sets. That’s why we call it partially ordered.. In general, we cannot order any two elements in this kind of set. A typical example is given by sets. Two sets, A and B, may have an intersection as well as elements which only belong to themselves. In this situation we cannot order these two sets using inclusion as an order structure. However we can order these sets with their unions. Both sets are ‘smaller’ than their union set. So, although we don’t have a total order, we have a partial order!
The crucial observation is, any totally ordered set can be thought as a subset of a partially ordered set in a larger dimension (Note: If you are familiar with math, just consider product spaces with a componentwise ordering in each projections). I will not go into details, this is enough with math!
What Does Math tells us?
Time can be seen as a totally ordered according to our perception so that one of the two timeline is in the past or they are over the same time period. On the other hand, math tells us it might be considered as partially ordered and we cannot, in general, order any two timelines; instead we could only order parts of them. Therefore, while we perceive time as we can, it may have more dimensional than we presume and it might not be possible always to compare two timelines!
When we transfer the concept of time into number system we get two directions since we understand it as totally ordered. While the left part of the line describe the past direction, the right part of the line illustrates the future direction. However, what if time is not totally ordered, but partially ordered. Instead of one direction to the left (or right), we might have several, in fact even may have infinite, directions (See Figure above). Each direction may have its own ‘past’ and ‘future’ concepts. These directions can be defined as parallel universes such that each of them has their own (totally ordered) notion of time which has completely different meaning in the other parallel universes. Thus, our universe might have more than one time concept each of which may define a parallel universe whereas we can only understand one of them. All these small (parallel) universes might be considered as a part of our universe. Now, let’s talk about time travel.
Time Travel – Grandfather Paradox:
The most known paradox about time travel is Grandfather paradox. If you go to past and kill your grandfather, you will not be able to go back to your future. Alternatively, some theoretical physicists argue that killing your grandfather would not be possible. What is really happening? Is it really a paradox?
First of all, going back to past itself cause the same paradox (if this is indeed a paradox) whether you kill your grandfather or not. Because when I go back to my past, I shouldn’t be in there as an individual who is not born at that particular timeline! This is exactly the same paradox with going back to future after killing your grandfather..
What are we missing here? I think the problem here occurs because of our concept of ‘time’. We interpret time as 1-dimensional totally ordered set so that two timeline can be ordered and we can thus only move to either ‘past’ (left) or ‘future’ (right). However, as we explained, time could be multi-dimensional and so moving along the time could have happened in different directions rather than going only left and right (See Figure above). In that scenario, we can travel to ‘past’ with multiple, maybe even infinite, routes. Therefore, it may not be necessary to travel to ‘past’ through our understanding of time which is nothing but moving towards left in the figure above. In particular, perhaps, this may never be possible because of the paradoxical situation. Hence, time travel might be possible through the time perception of parallel (different) universes.
Though the notion of time travel is not a concept we can grasp today, when we consider time more extensively it makes more sense to me travelling through other dimensions (parallel universes) than our own time notion.