I wonder what we can learn about this, probably one of the most fundamental questions facing humanity, if we just use our common sense and call on just a few basic, everyday experiences?

First, we need to clarify in what sense we are examining the infinity of the world. As a first approximation, and this will probably be sufficient, we can consider three types of infinity. Infinity in space, time and events. The latter perhaps needs some further explanation, by historical infinity I mean the number of states of the world, i.e. the inexhaustibility of the world’s phase space, i.e. whether the same thing can happen in the same way again. We will talk more about this later. Of course, the three infinities mentioned are related to each other, as we will see.

Perhaps the simplest is the issue of temporal infinity, and it can certainly be surprising. I myself never thought how simple this question could be handled, until I read the thoughts of an ancient Greek philosopher (I don’t remember who this brilliant philosopher was, only the clarity and simplicity of the thought caught my attention right away). He thought that the world’s past could not be infinite, because infinite time simply could not have passed until the present moment. Infinity is a possibility. If we start counting from one up, it is easy to imagine that we can continue counting to infinity, but we will never reach the last number. Infinity is therefore a possibility that will never be realized, therefore it is infinite. If time is infinite in the past, it is, on the other hand, an embodied infinity, an infinity of which we grasp one end, but the other end is not just a possibility, as in the case of numbers, but a realized infinity. And for this we think that it cannot exist. In fact, the problem with all three infinities is that one can only deal with objects in one’s thoughts that have some kind of equivalent in reality. And infinity is not like that. We have no experience of infinity, we can imagine the possible infinity, but not the actual infinity. Everything in our life has a beginning and an end, but these things with a beginning and an end follow each other in time, seemingly without end, but for us it is a possible infinity and not an actual, experiential infinity, since with our mind being finite in temporal and spatial sense, as well as finite in complexity, we cannot experience infinity.

But I have to admit, now that I’ve tried to explain why it’s clear that infinite time couldn’t have passed until now, I really feel I can’t. I feel it’s simply obvious, but I can’t give a completely exact argument for it. Fortunately, we can list physical arguments against temporal infinity. It looks very much like the Universe is developing in one direction, from hydrogen to helium, from that to carbon and oxygen, and the line ends with iron. Iron is the end of the fusion life of stars, even heavier elements can be created in a supernova explosion, but the fusion era of the Universe will end sooner or later, this requires a finite amount of time, so if the Universe is infinitely old, then there would be no more stars. The world would be filled with black holes, in thermodynamic equilibrium, in the state of heat death, and would actually be in this state for an infinite time, since compared to its infinite past, the finite star age would actually be a flash of time. This is also the problem with the infinite past, that compared to it, any finite duration is actually as if it never happened, compared to infinite time, any finite time shrinks to zero duration.

So let’s accept that the world had a beginning. Unfortunately, we are not helped by this either, because we have no experience of what it is like when nothing exists and the world suddenly pops out of nowhere. Our everyday experiences all show that every consequence has a root cause that precedes it, so we can’t do anything with the image of the world that appears out of nowhere without a cause.

It can therefore be concluded that the more likely answer is that the world has a beginning and is not infinitely old, but we humans cannot be satisfied with this answer either. It can be safely stated that we can have thoughts and opinions about the temporal infinity of the world, but no real reassuring answer to the question can be given.

In fact, we can get to the same point in relation to spatial infinity, the likely answer to this is that the world is not infinite in space, but we cannot be satisfied with this answer either, since we have no experience of what it is like to reach the end of the world and there is no more to go, even though there is nothing to prevent us from doing so. We could accept only one imaginable finite world as it is: in a finite but limitless world, we can never reach the edge of nowhere, on the other hand, if we start in one direction, sooner or later we will return to our starting point without turning around. Although this is very strange, it is conceivable and acceptable. This spatial world is incompatible with temporal infinity, because, for example, the gravitational effect of the mass in it circles the world endlessly, in the same way photons also circle endlessly, which would result in a world multiplying itself infinitely.

Regarding the spatial and temporal infinity of the world, there is a very ancient experience that precludes the world from being infinite both in space and time, and this is none other than the dark night sky. And although our ancestors have always lived under such a dark sky ever since they became conscious as humans, it took a doctor named Olbers to think about this simple fact and to draw far-reaching conclusions from it. If there are an infinite number of stars in space, then no matter which direction we look in the sky, sooner or later our eyes will come across a star. Dust and gas nebulae can hide stars for a while, but what absorbs light sooner or later emits that light, so this cannot cause the darkness of the sky. The world is therefore certainly finite either in space or in time, or if it is infinite in space and time, it cannot contain an infinite number of stars, so the infinite space beyond a limit is already completely empty. At least we can state this much with absolute certainty.

Finally, let’s look at the issue of infinity in events. This is a very important question, because there is a popular misconception that in an infinite universe everything can happen, even an infinite number of times, in other words, there can be an infinite number of copies of us, in an infinite variety of environments, one of us is currently writing Chinese, and the other of us he lives in a Hungary whose borders are washed by three seas. However, the fact that the world is infinite – we have seen that it is probably not – does not mean that all kinds of events take place in it in an infinite number of ways. It is also possible to imagine an infinite world in which only Earth has life, all the other, infinite number of planets are lifeless. And not only is there not an infinite number of human histories, but there is only one, the one that takes place here on this one Earth. Infinite space and time does not necessarily mean infinite variety, although this may provide the basic idea of many sci-fi books or movies, but it is not necessarily true, an infinite world can also be infinitely simple and bleak also.

However, the repetition of events can raise another interesting question, and that is the theme of eternal return, if the Universe reaches a state identical to its previous state, does this mean that everything will repeat itself from then on? If the world is deterministic, then yes. However, many signs point to the fact that quantum mechanics is the guarantee that the world is not deterministic, so the repetition of a previous state does not mean that the entire sequence of events will take place again, as this would result in a Universe that repeats its fate endlessly. According to our current knowledge, the Schrödinger equation, which describes the behavior of the micro world, is not deterministically responsible for the production of measurable macro states, so different outcomes of the same events are possible.

The infinity in events raises another question, which is related to another aspect of infinity, namely the problem of infinite divisibility. If time and space are infinitely divisible, this may raise problems at least as serious as the infinite extent of space and time. Perhaps it is no coincidence that energy cannot be divided into arbitrarily small portions, perhaps the same situation with space and time, it is not continuous, but quantum. Such a world, if it is not infinite in either space or time, and now it seems very likely, it results in a finite state space, i.e. the finitude of events is also ensured, i.e. the Universe can repeat its previous states. It follows from indeterminacy that if you step into the same river once, you will not go through your own fate over and over again, but it is still possible that the same states will repeat themselves over and over again, if not in the same order, i.e. it is possible , that the complexity of the Universe is finite.

Is this world of finite complexity capable of take all of its states, or does it only repeat a small subset of them over and over again, even if the individual events follow each other in different orders?

And is the event when a conscious mind suddenly understands the functioning of the Universe part of the event field of the Universe? Or is this exceptional event part of a subset that the Universe state vector never reaches?

*February 2, 2013*