Facts about the past and present are either true or false. Can knowledge of the future provide the same degree of certainty?
Qe sera sera
Which have not be avoided
We are not allowed to see the future
Que sera sera
So Doris Day sang in 1956, expressing almost the general opinion of mankind that it is impossible to know the future. Even if this is not everyone's opinion, people, based on common human experience, believe that we do not know the future. That is, we do not know him directly and directly, as we know the constituent parts of the past and present. We see how something is happening in the present, we remember something from the past, but we do not see and do not remember the future.
However, impressions can be deceiving and memory unreliable. And even this kind of direct knowledge is not something certain and unchanging. In addition, there is indirect knowledge of the future, which is as certain as what we learn through direct perception or memory. I'm sure I know the sun will rise tomorrow. I know that if you throw a stone hard at my kitchen window, it will break. On the other hand, last year, on Christmas Eve, I didn’t know that my hometown of York was going to have a heavy downpour on Christmas, and on the second day of Christmas it would be almost completely cut off from the rest of the world due to flooding.
In the ancient world and, as it seems to me, in our childhood, events such as the flood in York make us confident that we cannot know the future. I may know something about the future, but not everything. I am sure that there will be some events tomorrow that I have no idea about. In the past, such events could be attributed to the inscrutable will of the gods. York was flooded because the rain god was in a bad mood or wanted to play with us. In my insurance policy, such disasters are called "force majeure." When we feel that it is impossible to predict the winner of the elections, we say that "the result is only known to God."
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Aristotle formulated the evidence of the future in the language of logic. In Athens, where he lived, an invasion from the sea was always possible at that time. He expressed his arguments with the following sentence: "Tomorrow there will be a sea battle." One of the classic laws of logic is the “law of the excluded middle”, according to which any statement is either true or false. Two judgments, one of which formulates the negation of the other, cannot be simultaneously false. That is, either the judgment itself or its negation is true. But Aristotle stated that the statements "there will be a sea battle tomorrow" and "there will be no sea battle tomorrow" are not ultimately true, for both possibilities lead to fatalism. For example, if the first statement is true, then no one can prevent a naval battle. Consequently, these statements belong to the third logical category,and are neither true nor false. In our time, such a conclusion is reflected in a multi-valued logic.
But some of the statements in the future tense do seem to be true. I gave the example "tomorrow the sun will rise", and when I throw a stone, "this window will break." Let's take a closer look at this. In fact, none of these forward-looking statements are 100% true. The sun may not rise tomorrow if some galactic stellar trawler arrives in our solar system today, grabs our star and flies away at the speed of light. When I throw a rock out the window, my older brother, who is a responsible family member and a great goalkeeper, can walk by. He will see me throw the stone and will catch it to save the window.
We didn’t know the sun would not rise tomorrow morning as usual; I didn’t know my stupid prank would fail. But such ignorance is not a specific consequence of the fact that we are talking about the future. If the Spaceguard program of protection against space bodies had a wider area of responsibility, we would know about the approach of a star trawler, and accordingly, we would know that we will see the sun for the last time. If I knew where my brother was, I would have predicted that he would rush to save the window. In both cases, ignorance of the future is reduced to ignorance of the present.
The success of modern science has led to the emergence of the idea that the following is always true: ignorance of the future can always be associated with ignorance of something from the present. An increasing number of phenomena are subject to the laws of physics; in the same way, an increasing number of events can be explained by the previous events that caused them. In this regard, the confidence appeared that if it is enough to know about the present, it is possible to predict with great certainty any event in the future. The most famous manifestation of such confidence was the statement of the French mathematician Pierre-Simon Laplace, made by him in 1814:
We must consider the present state of the universe as a consequence of its previous state and as the cause of the subsequent one. The mind, which would have known for any given moment all the forces that animate nature, and the relative position of all its constituent parts, if, in addition, it turned out to be vast enough to subject these data to analysis, would embrace in one formula the movements of the greatest bodies of the Universe on an equal footing with the movements of the smallest atoms: there would be nothing left that would be unreliable for him, and the future, just like the past, would appear before his gaze.
This idea was expressed by Isaac Newton, who had a dream in 1687:
It is a pity that we cannot deduce other natural phenomena from the principles of mechanics through the same reasoning, for for many reasons I am inclined to suspect that they can all depend on certain forces, due to which, for reasons hitherto unknown, they either are attracted to each other, forming the correct figures, or pushing off and moving away from each other.
From this point of view, everything in the world consists of particles of extremely small sizes, and their behavior is explained by the action of forces that make these particles move in accordance with Newton's equations of motion. The future movement of particles is completely predetermined if their position and speed are known at one time or another. This is the theory of determinism. Therefore, if we fail to know the future, it is only for the reason that we do not know enough about the present.
For two centuries, Newton's dream seemed to come true. The material world more and more fell under the influence of physics, since matter was analyzed at the level of molecules and atoms, and its chemical, biological, geological and astronomical properties were described in Newtonian terminology. The particles of matter that Newton spoke of had to be replaced with electromagnetic fields in order to show a complete picture of what the world consists of. But the basic idea that they all obey the laws of determinism remained. The vagaries of nature, such as storms and floods, which previously seemed an unpredictable whim of the gods, became possible to predict. And if some phenomena such as earthquakes still cannot be predicted, then we say with confidence that thanks to the emergence of new knowledge in the future, such predictions will become possible.
This scientific program has been so successful that we have forgotten about the other ideas about the future. University of Washington physicist Mark G Alford writes about it this way:
In ordinary life, as well as in science before the advent of quantum mechanics, it was assumed that any uncertainty that we encounter … is the result of ignorance.
We completely forgot that the indefinite world was inhabited by the human race long before the 17th century, and we perceive Newton's dream as a natural view of the awakening reality.
Well, it was a beautiful dream. But everything turned out differently. At the beginning of the 20th century, Ernest Rutherford, studying the newly discovered phenomenon of radioactivity, realized that it demonstrates random events occurring at the fundamental level of matter in the atom and in its nucleus. But this did not mean that Newton's dream should be abandoned. The nucleus is not the lowest level of matter, but a complex object consisting of protons and neutrons. If we knew exactly how these particles are located and move, then we would probably be able to predict when the radioactive decay of the nucleus will occur. However, other, more bizarre discoveries of the time led to a radical departure from Newtonian physics, represented by quantum mechanics. They confirmed the view that phenomena of the smallest scale are indeed random, and that it is impossible to know the future for sure.
The discoveries that the new physics of the 1920s had to oppose were twofold. On the one hand, Max Planck's explanation of the distribution of wavelengths in radiation emitted by hot matter, and Albert Einstein's explanation of the photoelectric effect, indicated that energy comes in discrete form, and does not vary continuously, as it should be according to the rules of Newtonian mechanics and the electromagnetic theory of James Maxwell. On the other hand, experiments on electrons by George Paget Thomson, Clinton Davisson, and Lester Jermer showed that electrons sometimes behave like waves, although it was previously firmly established that they are particles.
These perplexing facts found a systematic, coherent and unified mathematical explanation in the theory of quantum mechanics, which arose from the work of theorists after 1926. Quantum theory itself is so mysterious that it is not clear if it can be called an "explanation" for the perplexing facts that it classifies. But its most important feature, which seems irrefutable, is that when predictions about physical effects are made on the basis of this theory, they do not give exact numbers, but a percentage of probability.
While not everyone admits it. Some people believe that there are more subtle details in the composition of matter, which, if we recognize them, will again allow us to accurately predict its behavior in the future. From the point of view of logic, this is certainly possible, but in this theory there are certain aspects that will make most physicists think that it is extremely unlikely.
The format of quantum theory is very different from previous physical theories such as Newtonian mechanics and electromagnetism. These theories work with mathematical descriptions of the state of the world or some part of it. They have equations of motion that, through such mathematical descriptions, tell us what it will become after a certain period of time. Quantum mechanics also works with a mathematical object that describes the state of the world. It's called a state vector (although it's not a three-dimensional vector like velocity) and is often denoted by the Greek letter Ψ or some other similar symbol.
But this is a different kind of mathematical description, different from descriptions in mechanics and electromagnetism. Each of these theories uses a set of numbers that measure physical properties, such as the speed of a specified particle or an electric field at a specified point in space. On the other hand, the quantum state vector is a trickier thing, and its relation to physical quantities is indirect. From the state vector, we can get the values of physical quantities, but not all: we can choose which values we want to know, but we cannot completely select them all.
Moreover, when we decide what values we want to know, the state vector will not give us a specific answer, but will only give a percentage of the probability of possible different answers. This is how quantum mechanics differs from determinism. Oddly enough, in its attitude to change, quantum mechanics is similar to the old deterministic theories. It also has the equation of motion, the Schrödinger equation, which will tell us what the given vector of the state of the world will become in a given time. But since we can only get a percentage of the probability from this vector, it will not show what we will see after a given time.
In general, the state vector is a strange and obscure thing, and it is completely unclear how it describes physical objects in the real world. But some of the descriptions correspond to those descriptions that we are able to understand (if we do not look at them too closely). For example, among the cat state vectors, there is one that describes a seated and rather purring cat. And there is another one describing a dead cat poisoned by a devilish device invented by physicist Erwin Schrödinger.
But there are other state vectors obtained mathematically by combining the above two vectors. Such a combined state vector can be composed of a part describing a live cat and a part describing it as a dead one. These are not two cats: the meaning of Schrödinger's story is that one and the same cat is described as living and dead at the same time. And we cannot understand how such states can describe something that occurs in the real world. Physicists of different generations ask: how can we believe in this theory if we have never seen living-dead cats?
There is an answer to this riddle. If I open the drawer in which Schrödinger dissected the poor cat, the ordinary laws of everyday physics do the following. If the cat is alive, the image of a live cat will remain on my retina and in the visual area of the cerebral cortex, and the system consisting of me and the cat will end up in a completely understandable state in which the cat will be alive, and I will see a live cat. If the cat is dead, I will have the image of a dead cat, and the system consisting of me and the cat will end up in a state in which the cat will be dead, and I will see the dead cat.
In accordance with the laws of quantum mechanics, it follows from this that if the cat in superposition is alive and dead, then the system consisting of me and the cat will be in a superposition of the two final states described above. In such a superposition, there is no state of the brain that sees the unusual state of a dead-living cat. The usual states of my brain are familiar, in which I see a live cat and I see a dead cat. This is the answer to the question from the previous paragraph; it follows from quantum mechanics that if cats have states in which they seem both alive and dead, then we will never see a cat in such a state.
But a combined system of me and a cat is one of the strangest superposition states in quantum mechanics. It is mathematically represented by the + sign and is called the confusion state of me and the cat. What does it mean? Maybe the mathematical sign "+" only means "or"? It makes sense. But unfortunately, if this value is applied to the states of an electron, it is incomparable with the facts of interference observed in experiments showing the wave behavior of an electron. Some people think that this "+" should be understood as "and". When the cat and I are in a state of superposition, there is a world in which the cat died and I see the dead cat. And there is another world in which the cat is alive, and I see a living cat. Others do not find such a picture useful. Perhaps we should just accept this (in a certain sense) as a true description of the cat and me,the meaning of which is beyond our understanding.
Let's now expand our horizons and consider the entire universe, which contains each of us, viewed as a being, observing the physical system. According to quantum mechanics, there is a description of a state vector in which the system of a being is entangled with the rest of the universe, and several different sensations of the system of being are involved in this entanglement process. The same general vector of the state of the entire universe can be viewed as an entangled state for every system of beings within the universe; they are simply different points of view on the same universal truth.
But the claim that this is the truth about the universe seems to contradict my knowledge of what I see. To illustrate this, let's consider again a small universe consisting only of me and a cat. Suppose that when I ran Schrödinger's experiment, the cat survived. In this case, I know what my state is: I see a live cat. From this I know what the state of the cat is: he is alive. The confusion of my little universe as a result of my experiment also contains a part with a dead cat and my brain, which is full of remorse.
But seeing a live cat, as I do, I believe that such a different picture is not part of the truth. She describes something that could have happened but did not happen. In general, looking at the entire universe, I know that I have only one definite feeling. But this contradicts what was said in the previous paragraph. What then is the truth of this?
This contradiction is of the same type as many of the familiar contradictions between objective and subjective statements. In The View from Nowhere, Thomas Nagel shows how some of these contradictions can be resolved. We must acknowledge that there are two positions from which we can state facts or meanings, and that statements made in these two contexts are not comparable. This applies to the puzzle presented by quantum mechanics as follows. In an external context (the point of view of God, or "a look from nowhere") we go beyond our specific situation and talk about the entire universe. In the internal context (from here and now) we make stating statements as physical objects within the universe.
Thus, from an external point of view, the confused universal vector of state is all the truths about the universe. The components that describe my different possible sensations and the corresponding states of the rest of the universe are (unequal) parts of this truth. But from an inner point of view, from the standpoint of some particular sensation that I know I am experiencing, this sensation, together with the corresponding state of the rest of the universe, is real truth. I can find out what the other components are, since I can calculate the universal state vector using the equations of quantum mechanics; but to me these other components represent things that could have happened but did not happen.
Since I cannot see the future, I am unable to isolate any of the worlds of such a future.
Now we can see what quantum mechanics tells us about the future. As far as we can now expect, there are two answers, one for each of the two points of view. From an external point of view, the universe at any given moment is characterized as a universal state vector, and the state vectors at different times are related to each other in accordance with the Schrödinger equation. Given the current state vector, the Schrödinger equation gives a unique state vector for any moment in the future. This is a deterministic theory, fully consistent with the Laplace worldview (in the quantum version).
But from an internal point of view, everything looks different. We now need to indicate a specific observer (in the above discussion it was me, but it could also be you or anyone, or even all of humanity taken together), in relation to which we can divide the universal state vector, as indicated above. And we also need to indicate the specific state of sensations of this observer. From this point of view, it is by definition true that the observer has certain sensations, and that the rest of the universe is in a corresponding certain state.
Therefore, quantum mechanics tells us that there are several different worlds at the moment. But I know that one of them stands out especially as the world that I know, and whose finer details I discover during the experiment. But when we look to the future, the situation is different. Since I cannot see the future, I cannot specifically distinguish any of the worlds of the future. Even if there is only one world now, and what I see is consistent with the universal state vector of quantum mechanics, it may happen that the laws of quantum mechanics will give us the superposition of worlds in the future. For example, if I start with the sensations from the preparation of Schrödinger's experiment with a cat, then at the end of the experiment the universal state vector will be an overlay of what we have already encountered, and one part containing me will see a living cat,and the other part containing me will see the dead cat. And then what can I say about what I see in this future?
When I first encountered this, I was quite perplexed. I used to think that something awaits me in the future, even if I cannot know what it is, and even if there is no law of nature that determines what it is. Truly, what is to be cannot be avoided. But Aristotle already knew that this was not true. Future tense statements do not follow the same logic as present tense statements. They don't need to be either true or false. Logicians, following Aristotle, admitted the possibility of a third true meaning in addition to "true" and "false", calling it "indefinite" or "unresolved."
However, Aristotle also noted that while no statement about the future is truly true, some are more likely than others. Likewise, the universal vector of a state in the future tense contains more information for me than just the sensations that I may have at this time. These sensations, appearing as part of the universal state vector, contribute to it to varying degrees, and are measured by coefficients that are commonly used in quantum mechanics to calculate probabilities. Therefore, we can imagine the future universal state as giving information not only about what sensations I may have in such a future tense, but also about how likely each such sensation is.
Further, truth and falsity can be expressed numerically. A true statement has a truth value of 1, and a false one is 0. If the future event X is very likely, and therefore the probability of X is close to 1, then the statement "X will happen" is very close to the truth. If event X is unlikely, and this probability is close to 0, then the statement "X will happen" is almost false. This suggests that the future tense value of the statement must be between 0 and 1. A true statement has a truth value of 1; a false statement has a truth value of 0, and if the statement in the future tense "X will happen" has a truth value between 0 and 1, then this figure is an indicator of the probability of event X.
The nature of probability is a long-standing philosophical problem that scientists also need to find an answer to. Many researchers are of the opinion that the probability of an event makes sense only when the circumstances in which the event can occur are repeated many times, and we develop a proportion of time that says that it will happen. But what has just been stated seems to be the calculation of a single event in time, which will occur only once. In everyday life, we often talk about the likelihood that something will happen only once: that it will rain tomorrow, that a particular horse will win the race tomorrow, or that there will be a sea battle. The standard view of the likelihood of such a single event is that it refers to the strength of the conviction of the person who claims to have such a probability, and can be measured by the rates,offered by people betting on such an event.
But the probability described above is an objective fact about the universe. It has nothing to do with the faith and convictions of a person, and even of the person whose sensations are being discussed. This person is told the fact of his future sensations and experiences, whether he believes it or not. The logical theory gives an objective meaning to the probability of an individual event: the probability of a future event is the true meaning of the assumption in the future tense that such an event will happen. I analyze this view of probability and how quantum mechanics validates the associated multivalued logic of temporal assumptions in my work The Logic of the Future in Quantum Theory.
It has now become clear that the description of the physical world in quantum mechanics, namely the universal state vector, plays very different roles in the internal and external context. From an external point of view, it is a complete description of reality; it tells what the universe is at a given time. This total reality can be analyzed in relation to any given sentient being, which gives a number of components applied to the various sensations of the chosen sentient system and being parts of the universal reality.
However, from an internal point of view of the system, reality consists of only one of two sensations; the component applied to such a sensation is the absolute truth about the universe for the sensing system. All other non-zero components are what could have happened, but did not. In this perspective, the role of the universal state vector at a later time is not to describe what the universe will be like at that time, but to indicate how the current state of the universe might change between the present and the future. This gives a list of possibilities for the future with the likelihood that each of them will become true.
It may seem that we at least know such probabilities of the future, since we can calculate them based on certain knowledge from our current sensations, using the Schrödinger equation. But even that is uncertain. Our current sensations may well be only a part of the universal state, and the entire vector of the universal state will have to be introduced into the calculation of future probabilities. What could have happened but did not happen (we may not even know something about this) can still influence the future. However, if these things are quite different from our real feelings at the macroscopic level, then quantum theory assures us that the impact they can have on the future is so small that it can be neglected. The consequence of this theory is known as decoherence.
Hence, knowledge of the future is fundamentally limited. The point is not that there are true facts about the future, but knowledge about them is beyond our reach. There are no facts, and certain knowledge that should be there is simply not there. Nevertheless, there are facts about the future with a partial degree of truth. We can get knowledge about the future, but this knowledge will always be uncertain.
Tony Sudbery