One of the longest running discussions in the history of physics is that which refers to the essential nature of the fabric of reality, the universe, space-time, that is, the continuous / discrete or analog / digital dichotomy. The general impression among the best informed is that as modern physics has been developed with a mathematical formulation, especially differential and integral calculus, which assumes continuous entities (quantities represented by continuous functions), the logical thing is that the nature of reality it is the same as that of the functions that represent it so successfully in the prediction of all kinds of experiments, that is, continuous. Newton’s theory of gravity, which still allows space probes to be sent millions of kilometers away with negligible errors, or Einstein’s relativity that allows the use of positioning systems with negligible errors, and even a large part of the mathematical formulation of quantum mechanics are developed by means of continuous mathematical entities.
However, Max Planck, a hundred years ago, had to make the hypothesis that energy was transmitted by packets, that is to say in a discrete way, to avoid the appearance of infinite terms in his study of the radiation of a black body. From Planck’s constant and his assumption that all energy processes can be seen as the addition of discrete states, Planck numbers for space and time emerge, it cannot be deduced from this that the universe is pixelated with blocks the size of Planck units. They are comfortable units to operate with quantum equations, but they are so tiny that they are unattainable to the observation capacity of the best instruments of today and of the future in the long term. Many theoretical results from quantum mechanics appear suspiciously to point to a lack of continuity in the microscales of the fabric of the universe, but they do not confirm it with the desired certainty. What did become clear after Bell’s theorem is that the concept of local realism, as understood in classical physics, does not apply to quantum mechanics and this already gives food for thought.
The continuous / discreet debate applied to the small scales of reality is still open. Among these controversies is the one that refers to large scales and that could be called the infinite / finite controversy. Let’s see: logic indicates that a continuous universe, or analog in the small, should be infinite on a large scale, because if there are no simple parts in the small, there should not be them in the medium or in the large. In the same way, what is discrete or composed of simple parts cannot be infinitely added to achieve a real infinity, because we would never get there because there would always be one more part to add. This is so, and the peppers are asaos, although arithmetic allows us to abstract virtual infinities as a series of numbers in which there is always one after the last one we have written.
What is wrong is to think that the continuous / discrete debate was started by Planck or by quantum mechanics. It is a rich controversy that, after igniting with the pre-Socratics, reviving itself with the classics, and reviving itself in the era of the scientific revolution, with the famous epistolary disputes between Newton and Leibniz, seems to have fuel for a long time. The line of those that supported a discrete universe can be traced to Parmenides and was later inherited by Aristotle, who reasoned that space could not be infinite, since then it could be filled by an infinite body, of infinite size and mass, which it was absurd. The other line starts from Heraclitus and goes through Plato and Newton to reach Einstein, who always believed in a continuous space-time, or analog, at a fundamental level and concluded that the extravagances of quantum mechanics, such as the “mysterious action to distance ”of entanglement, showed that it was an incomplete description of the universe and that there were hidden variables yet to be discovered.
However, there are certain inconsistencies in the positions of these sages, who even Einstein always seem to see space and time as heterogeneous and distinct entities. If Plato and Newton thought of a continuous reality, they did not derive from it the infinity of space, nor did they have a problem in conceiving a principle for time. Plato had even been careful to define time as a kind of “mobile” copy of eternity. On the other side things weren’t completely coherent either. Aristotle thought of a finite and discrete space, however he conceived a time without beginning or end, that is, more or less eternal or infinite. But if something seems to be clear at this point in scientific history, it is that, whatever the background of reality, it will be the same for space and time, since both entities are considered one on the scales of relativity. called space-time, and since all relativistic experiments have resulted and continue to result in confirmations of the theory with a very high level of precision, it makes no sense to think that at any other scale both entities separate to the point of having different elemental make-ups, Let’s say a continuous space and a discrete time. In summary: if space turns out to be continuous on elementary scales, it seems clear that it will be infinite on global scales and that implies that time will also be continuous and eternal. And on the contrary, a discrete space implies finitude (although it is without limits) and is accompanied by a discrete and expired time.
Absolute continuity is not opposed to the unleashing of processes, but it is about infinite processes in which “nothing really happens” anywhere in space. Discrete states to jump between are required for there to be real changes in specific locations. Between these discrete states is what we could call nothingness, that is, what is not, which together with what is, forms the whole. But these are already big and not very “physical” words. It remains to be seen if the new ideas about the holographic universe and the daring, but increasingly supported ideas about the simulated universe, shed any light on this discussion.