Time travel and programming 2: paradoxes

The era of time travel has not yet arrived, and humanity has long been trying to resolve the paradoxes accompanying them. We will talk about the most obvious of them: what will happen if you intervene in the course of history? There are several options for how the flow of time responds to the actions of the traveler from the future. These models can be seen in science fiction films, more and more scientists are beginning to talk about them, but which model is closer to the truth - there is no consensus yet. We are just beginning to penetrate the secrets of time, and still do not have the opportunity to experiment with movements into the past. What can be clarified in this matter now? Under the cut we will have a tour of the basics of the mechanics of time, we will discuss paradoxes, and we will conduct a small experiment. Yes, it will be a test of a virtual time machine built on the basis of the Life algorithm!

Previous article of the cycle.

If you suddenly have not heard anything about the grandfather's paradox, its essence is as follows: the happy owner of the MW flies into the past, and by his actions interferes with his own appearance into the world. For example, interferes with the acquaintance of their parents. In the new version of the story the traveler is absent, there is no his flight into the past - it means that the story does not change. But then the traveler will still be born, and as a result will fly into the past ... - a vicious circle of mutually exclusive conditions, which is why this is called a paradox.


The paradox exists only as our misunderstanding of how time works. Surely nature does not allow the emergence of paradoxes, but how? Consider the basic models of time, noting their pros and cons.
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Models

Model 1: the impossibility of time travel

Essence: the laws of nature prohibit movement into the past, completely, or with any serious limitations. There are several variations on this topic:

• Moving into the past is not possible in principle.
• Moving into the past, or at least its serious change, leads to the rupture of the fabric of space-time, the collapse of the Universe and other total cataclysms
• Moving, say, 1 year into the past, the traveler will be at a distance of 1 light year from Earth, and will be able to reach the starting point only at the time of his flight back - thereby, without being able to influence himself in the past (i.e. does not close the ring).

Pros: the triviality of the solution. The easiest way to resolve the paradox is to exclude the conditions for its occurrence from the sphere of the possible.
Minuses: what about the time machine?) Seriously, the fundamental possibility of time travel is too vast a topic to talk about now, so consider what else we have left, hoping that they are still possible .

Model 2: Predetermined History

“At that moment he realized that he was the same Joe. Joe, whom he had already met before. It was as if lightning suddenly dawned in Bob’s head the fact that it was not just the same situation that he himself had passed through, but that was exactly the situation. Only now he perceived it from another point of view. ”R. Heinlein“ On the heels ”.

The bottom line: flying back in time is possible, but there’s nothing to change, since the pages of the story are fixed. If archaeologists have found evidence that you have visited Akhenaten in ancient Egypt, this flight will surely take place, and this will take place exactly as it was in the past. You can perform other actions there, or simply refuse to fly - due to some circumstances you cannot.
Hence the conclusion that some points in the story can be created by time travelers. For example, you decided to prevent the sinking of the Titanic - being on board, or you will encounter a lot of difficulties and will not be able to divert the ship from the iceberg, or you will realize with horror that your actions are the real cause of the disaster.
It is appropriate to distinguish two variants of the model: strong and weak. Strong predestination implies that it is impossible to change a single detail of the past. Weak admits the change of small details, but the key points of the story, the general direction of events remain.

Obviously, predestination extends not only to the past, but also to the future . After all, if the past is fixed, and contains events of arrivals of people from the future, the future is also to some extent predetermined, because it must be the circumstances for these flights. Within the framework of this model, it becomes possible to get a kind of "guarantee of history". For example, scientists find evidence of a visit to the past by people from the 20th century — this means that over the next thousand years, humanity will not only exist, but also actively develop science. Here it is important not to deviate from the laws of logic and understand that the lack of evidence for such visits absolutely does not prove anything. “If time travel is possible, then where our descendants are from the future” is, you see, not serious, many explanations can be put forward.
Examples: the movie “Hunters for the relic”, the story of R. Heinlein “On the heels”.
Pros: There is a certain elegance in this model. Maybe because it takes the middle ground between a complete denial of the possibility of travel (model 1) and their description involving not the most trivial concepts (model 3). In addition, there are indirect experimental confirmations of this model at the level of quantum informatics.
Cons: the idea of ​​predetermination of the past and the future seems at least strange. Even if it is a weak predetermination, it is not quite clear how the laws of physics limit the freedom of choice of a person to commit, and especially not to commit certain actions. It is clear that this restriction occurs through circumstances. Does every traveler in the past always have such circumstances that will not allow him to give up the flight? Something similar can still be represented at the level of quantum particles, but the work of this mechanism in the macrocosm is not yet sufficiently described.
Departing from fatalism to weak predetermination, we are faced with the question of the criterion. To what extent does history allow itself to change? What is considered a key point? To this question we will return.

Model 3: alternate realities

"-Apparently, the time continuum was broken, and a new event sequence emerged that changed reality
-Dok, you can be easier?
- Now, let me illustrate. Imagine that this line represents time, this is the present, 1985, the future and the past. Up to this point in time, somewhere in the past, the line deviated at such an angle and another 1985 appeared, another for you, for me and for Einstein, but real for everyone else. "," Back to the Future-2 "

Essence: a change in history creates a new stream of time, where an alternative scenario of events develops. The traveler himself remains in the reality he created.

Fig.1 - a classic idea of ​​the branching of reality
It is usually implied that reality branches off only if there is a serious (aha, here it is again - a criterion?) Influence on history. For example, you go into the past, and at the starting point remains the observer (H). After your quiet walk through the past as a tourist, he will see your return.

Fig. 2 - time loop closed
But if you go to make (or prevent) a revolution, then for the observer you will not return from the past, because become part of the new reality.

Fig. 3 - time loop broken

For non-programmers: the article often uses the terms "branch" (aka "branch"), "trunk", "merge" - let them not frighten you. These concepts are used in the SVN version control system, which is not necessary to understand that:
trunk - the initial, “our” flow of time, the course of history.
branch, branch - an alternative flow of time, formed by interfering with history.
merge is the process of branch injection into a trunk, i.e. the consequences of alternative history events become part of the main flow of history (the notion of the main / additional flow is conditional, here it’s rather a matter of one stream as the parent stream, and the second as a branch from it).

Thus, you can at least rewrite history from scratch - only this will be its new branch, and the old one will remain intact. A sort of GitHub with forks from any past revision.

In this model, time ceases to be a one-dimensional line, since an axis of variation of events is added. The Multiversum thus obtained (the Universe with many alternative realities) is visually depicted as a tree.
The tree can be represented in expanded form, where nodes are events, and outgoing branches are possible outcomes (Fig. 4A). When it comes to changing history, it is more convenient to take one of the tree’s routes as a reference (zero reality, trunk), portray it as a straight line, and alternative route as a branch (Fig. 4B).

Fig.4 - tree of alternative realities in two views
It is logical: after intervening in the past, the course of events develops along a new path, thereby tracing a different trajectory in the space of options . The only question is what is this space: the theoretical model, or the real parallel realities. The fact is that we are faced with the concept of an alternative course of events not only when traveling into the past. Remember the theory of the “fissile universe” Everett. In its popular exposition it is said that at each event the Universe splits into several realities, where the possible outcomes of the event are realized. Roughly speaking, when a coin is thrown, reality is cloned into three copies: in one, an eagle falls, in another tails, in the third, it rises on an edge. We threw a coin and an eagle fell - what are the other two realities? Potential states of the quantum world, or physically existing parallel worlds? This is the fundamental question of modern physics, the answer to which we do not yet have.
Examples: the film “Back to the Future”
Pros: this theory really resolves paradoxes. And she does this without causing many questions of restriction of freedom of action in the past. The notion of alternative time flows echoes a number of theories (the dividing Evevere Universe, the many-leaved Mega-Universe of Sakharov, the three-dimensional time of Bartini, etc.), and generally seems to be a logical extension of the one-dimensional time model.
Cons: brilliantly resolving some issues, the model introduced others. If a branch of history is formed only with serious interference in history, then what is the criterion for this “seriousness”? If a branch is always formed, how exactly does it flow back into the main stream, thereby ensuring the return of the traveler from the past? The hypothesis of the merging of realities is not new, but so far remains insufficiently disclosed.

Model summary

There is another model. It is rarely found in literature, it is fundamentally different from the rest, and now you will understand why. So, the same basic data: the traveler erases himself from history, i.e. In the new scenario of events, he does not appear on the light. In this model, there are no parallel realities, the main one has changed, it is the only flow of time. Returning in due time, the traveler will be unrecognizable by anyone. The fact that now no one flies into the past does not mean that the traveler will still be born, because the change in history has already happened, and it simply remains.
Imagine that a villain went on a time machine to the distant past in order to radically change the history of mankind. We just disappear from reality, the word we never had. It is logical that already accomplished events cannot be “canceled” and just disappear like that. More precisely, this is dictated to us by intuition, but we need to think about the rationale. I propose for the time being that it is simply considered an axiom: history cannot be rewritten. All previous models are various options for implementing this protection :

1. Does not let fly into the past
2. Does not give in the past something to change
3. Does not allow to change the main flow of time, leading changes to an additional

The search for the model of resolution of paradoxes by mankind itself implies the following of this axiom. Therefore, we have 3 time models at our disposal. We will assume that this is how we outlined the contours of the first question: the protection of history against changes. What can now be done with these models? I propose to immediately exclude the first: if time travel is impossible, then all our previous and subsequent arguments are meaningless. Two models remain - which one is correct? Or maybe both are true, being special cases of a more general model? Before we talk about this, we need to look at the issue of changing the story from a different angle.

Is Ray Bradbury right

Let us forget for a second about the models considered, about the predetermination of history or parallel realities. We have a flow of history before us, a change is made in it - we are only interested in one thing: will the consequences of this influence attenuate, or will the degree of deviation from the primary scenario increase like a snowball?
In Ray Bradbury's story “And the sound of thunder” a butterfly crushed in the Jurassic period leads to large-scale changes in our time. The author develops a version about the high coherence of events, which makes history extremely unstable: even the slightest change in the past, especially the distant one, causes a serious deviation.


Now consider a small example. You are going to work in the morning, leave the house, and take the subway to it. Somehow a correction is made in history: you have learned that the subway is not working today. Taking a bike, you reach it. We make one more correction: a tire is punctured. But you will walk!

Fig. 5 - the desire of realities to unite

Chronocard shows:
1. Branch injection into a trunk occurs at different points in time, since Achieving a target state (getting to work) occurs in different ways.
2. The deformation does not completely fade, i.e. Despite the fact that in all three cases you are at work, there are some minor variations (parked bike, dirty shoes, etc.).

What happens if you abstract from the actors? If the system has a goal, it will strive for it under any scenarios, thus possessing a certain stability margin (to deflecting effects). Now I would not like to go into the jungle of philosophy and speak on the topic of purpose for material objects, people, society, etc. The fact that events in the world around us obey the laws of physics and in a certain sense are ordered - I think it is obvious. History can not be considered a set of coincidences, it has its own conditionality . After the primitive communal system, capitalism could not have come, bypassing the slave and feudal system. If the start of the war in 1939 was prevented, it would probably have started anyway later, because the world would have preserved the prerequisites for that. If a certain scientific discovery was not made by one scientist, someone else would have made it later, and so on. History events have a direction, a tendency, which means that any deviation of the course of history tends to fade.
This hypothesis takes us to the next level of understanding of the mechanics of time, because it actually combines the two models considered earlier. In one we talked about the resistance of history to change, in the other about parallel streams of time. Assuming that parallel flows of time tend to flow back into the main flow, we separate a single essence from these two models: the elasticity of the flow of time .

How is the merging of realities?

In the last article this caused a lot of questions. The question is extremely difficult, therefore, on the assumption, I clarify: it is not the objects that merge, but the events. Consider the well-known light cone, but instead of the spatial axis, we will have an axis of options.

Fig. 6 - the present, as a projection of alternatives of the past and the root of the options for the future
The upper cone is the future, these are possible outcomes from the current state, the lower cone is the past, it is a certain spectrum of possible previous states. The walls of the cones define the boundaries of reachability, i.e. to go beyond the limits of the cone means to go into a state (delta along the b axis) that cannot be reached from the current state in a given period of time (delta along the t axis).
The merging of events of the cone of the past at the point of the present means a common result for them. But how does this happen at the level of changing the structure of objects, how do they overlap? Perhaps something similar is happening as shown in “Back to the Future”, where the headline of the newspaper is smoothly changing right before our eyes — this is “brunch to trunk”.

Quantum coin

Two people are sitting in the room: Alice and Bob. Five minutes ago, Alice threw a coin and fell tails, they both saw it. We have a time machine, and we make history correction: an eagle drops out five minutes ago. As a result, we have two realities:

Fig. 7 - experiment with two observers
Alice and the coin cannot be separated, since the result of a coin toss does not exist in isolation from his observation . But we still have Bob, who with some delay also finds out the result of the coin toss, and he and Alice exchange a pair of replicas. Two outcomes, and two realities - we see this in the diagram.
Let's change the conditions of the experiment: Bob does not see the result. From the point of view of Bob, these two realities are identical, in both of them he sees a coin toss, but does not know the outcome. Important detail (thanks to Agent_J for the amendment): Alice does not tell the result to Bob, then for him the course of events is really the same in both cases. Bob can leave in two brunches too, as soon as Alice tells him the result of the experiment. Let's try this in 5D:
Fig.8 - experiment with one observer
Think about it, it is really curious! As if two Alice communicate with one Bob, but simply pronouncing a single phrase initiates the division of the listener's time flow.

Here we come to understanding the role of the observer in the model of parallel realities. The line on the chronocard is not a reality, it is the state of a group of objects , the observation of any of which includes the observer in this line. Nature does not make a complete copy of the universe, it simply keeps a dif of their differences.

So after all, how is the merger?

First: the merger should not be interpreted literally, as if the worlds are becoming identical. The two worlds are somewhat different, somewhat similar - and this similarity is something like a junction in the space of options. As in the example where, in three ways, a person still got to work — at this moment the three realities had this junction, they partially merged. Of course, it is incorrect to speak of a complete fusion of realities, because reality itself, as has already been shown in the paradox of the quantum coin, is just a slice of the state space. How different objects can be in different joints, pockets and streams of options space is a good exercise for the imagination!

Frequently asked question: why do brunches merge, where does the idea of ​​elasticity of history come from? I will answer in other words and briefly: system stability. This is a universal property of almost any more or less complex system, be it a person, a country's economy, world politics, etc. The system has a goal (in one form or another), and the system works like an automatic regulator that corrects movement towards the goal. Therefore, disturbances introduced into the past will encounter resistance to the stability of the systems of the world. The points of bifurcation is quite another matter, the impact on them can drastically change the course of events. But the damping of the dif will still be, just on a larger scale.

In the course of the discussions, MrSeventh proposed an interesting hypothesis : what if the physical carrier of the brunch of differences of brunch is dark matter and / or energy?

Single model

And now we connect all the above. Two models of time (predetermination of history and branches) actually merged into one: "branches with merg". Any changes in the history (even the fact of being in the past) draw alternative routes in the space of options, but the flow of time has the property of elasticity, which manifests itself as a gradual desire of alternative routes to join the main one. At the same time, the observed world is a cross-section of a complex quantum interweaving of time flows, when objects in the same space can belong to different time flows (as long as there is no observation between them).

Mathematical model

So, we need to simulate the attenuation of the deviation of history that occurs when interfering with the past.

The first option: the most trivial, we believe that the brunch attenuation occurs with some constant acceleration. It is described by a uniformly accelerated motion formula.
The second option: more likely, where the flow of time is compared with the spring, and then the force (and hence the acceleration) is proportional to the current deviation. That is, the further the flow of history went to the side, the more he seeks to go back. Described by the damped sinusoid formula.
The third option: here is an interesting story. The first version of the article contained
Thanks to Strepetarh , Sayonji , mayorovp , an error was noticed: the calculation is based on a uniformly accelerated motion formula, which is not suitable here. But this formula, as it turned out, is well suited for describing the observed picture (see below).

1. Equal acceleration attenuation.
2. Attenuation according to the correct "spring" formula.
3. The third is the old formula.

And now it's time to move from theory to practice.

Experiment

What if history data can be modeled? We need some kind of simplified model of the world, consisting of a set of interacting elements. We will record the course of events, then wind it back, make changes to the "world", run a simulation, and observe a new scenario. It will only be necessary to quantify the difference between these two realities and to give it out in the form of a graph. Then we get an experimental, rather than theoretical, decay curve for the deviations of history.

It remains to come up with an algorithm that would fit the role of a "model of the world." After going through several options, I settled on Conway’s “Life” algorithm. I had heard almost nothing about him before, so I sat down to search - and I was surprised to find many articles on Habré on this topic. It remains to understand how to assess the difference between the worlds. I wanted to build a solution on a certain evolutionary principle, since the history of the real world is still progress and improvement, and not an established “cell boiling” mode. Maybe something like a genetic selection mechanism., or something like that, which would introduce into the world some measurable characteristics that allow you to compare different versions of the story (for example, "the number of cells of the 42nd level"). On top of the algorithm Conway turned out to be quite difficult to screw something. He chose the optimal parameters of "Life", and my attempts to add my own rules to the algorithm made the world unstable. After some time, I chose the simplest solution: to use the classic version of the algorithm without any frills, and simply subtract pixel-wise one world from another (Hamming distance) - this will be the degree of divergence of the story.

I have embodied what was said in the project: https://github.com/TimeCoder/LifeTime

There you can also download the collection for Windows: https://github.com/TimeCoder/LifeTime/raw/master/bin/lifetime.0.0.0.12.bin .win32.zip
And also under Linux (thanks to vershov ):
lifetime.1.0.0.12.bin.linux.x86.tar.gz
lifetime.1.0.0.12.bin.linux.x64.tar.gz

Video:


Before launching our time machine, let's get acquainted with the UI and program code.

Fig. 10 - controls
The program interface consists of 4 areas:

1. World - here the process of life development is displayed, after an accidental filling, the cells are formed and broken up according to the Conway algorithm “Life”. The edges of the world are "stitched" among themselves.
2. Chronocard - in fact, here we see the chrono-wood, Multiversum, the space of options - call it what you want. Initially, we have one straight line - the primary flow of time, zero reality (green). When we move into the past, a tunnel (blue) forms over the main stream, and a new scenario will be represented by a curve (yellow).
3. The control unit where the time machine is turned on and the movement starts.
4. The output area of ​​various data about the world, the traveler and the movement.

Now consider the procedure for working with a time machine:

1. Immediately after launching the program, you will see the boiling ocean of life and a running time counter. Wait a bit and press the "Begin" button.
2. , . ? . , . , , .
3. , , . , . : .
4. Click "Leap" - forward to the past! The object is transferred to your chosen time point, becomes part of the world, and the simulation will continue from this point. The graph will show the deviation of the new scenario of the story, and in the place where the object was, its light will be highlighted. When the time reaches the top of the loop (the point where the transition was made to the past) - the program will pause, a series of data will be displayed on the monitor.

In this version there are some features:

• Only one flight in the past for one session of the program. The possibility of multiple brunches in the program is laid, but is still disabled, including due to the unresolved “three-branch” task , see below.
• There are no journeys to the future (I did not see the point in them).
• You can switch between threads only after a loop.
• After you have started moving the time slider, you cannot select another object for movement (you need to add a little code).
• On large world sizes, the program slows down (needs to be optimized).
• Rendering occurs using OpenGL (sort of like a normal solution).

There are other candidates for the role of the basic algorithm, instead of "Life", for example Tierra or Avida. Development of the project continues.

The problem of three branches

The problem is that we quantify qualitative quantities. So imagine 3 worlds: the main flow of time, and two alternative ones. What to take for the frame of reference when depicting the deviations of history? In the case of 2 branches, everything is simple: the first is drawn as a straight line, the second is depicted as a curve showing the degree of deviation from the basic reality. But now we need to draw the third curve. Suppose this reality spun off from a trunk, and differs from it as much (quantitatively) as the second - it turns out that the trajectories of the second and third streams coincide - but qualitatively different events take place in them! Another option: the third reality spun off from the second, and in it the course of history quickly comes to the trunk variant (for example, first the past was changed, reality 2 arose,then they flew into the past in order to return everything as it was - a reality formed 3, almost identical to the 1st). The deviation of the third reality from the second is the same as the second from the first. The task is to come up with an optimal method of drawing chrono-cards, taking into account such nuances.

Code

A brief look at the architecture of the project, and the key points of individual fragments. Below is a diagram of the main classes of the project:

Fig. 11 - simplified class diagram.
Everything begins with the life calculation algorithm implemented in LifeModel . This piece contains the current state of the world (to work with which there is a World class ), can fill the world with random cells (this is necessary for the first start) or continue the “frame by frame” simulation from a given world (this is necessary when making changes to the past). The LifeView class is responsible for the visual display of the model of life, they are connected via signals / slots.
Life is simulated, but this is only a fleeting “present”, we will need to know all the past states of the world, i.e. we need to go from three dimensions to four: the class TimeFlow appears (the flow of time, the branch of reality). It aggregatesLifeModel , contains a collection of World (history of the past), as well as points for constructing a curve of deviation of history. He also has a pointer to the parent stream, from which he spun off.

Of course, there can be a lot of time streams, and all of them are stored in a TimeModel , which is actually a tree of time. It is TimeModel that provides an interface for viewing the past and moving at a given moment. It stores not only the collection of streams and the number of the current one, but the time traveler (collection of cells). In the TimeView class, a chrono- render is rendered with dynamic scaling.

At the topmost level, we have the class MainWindow. It contains all the view and TimeModel, is responsible for the logic of the UI, and connects the model with the representations by means of signals \ slots. The working cycle is organized by a timer, which is called up by TimeModel’s next ticks, and it is already running through all the time streams that currently require the next call (after all, we can be in the past and our native stream is already calculated for a certain number of steps forward) .

All other details are easier to look directly at the code. Yes, since this is my first development experience on the Qt framework, constructive comments on the code are welcome)

Run!

Let's make a trial launch, the size of the world is 300x300:

Fig. 12 - The example of the time travel of
History turned into an intense deviation not immediately, having reached a maximum, some decline took place. The ratio of the deviation at the starting point of the journey (“loop top”) to the maximum deviation can be seen on the monitor, the Dif coef parameter. Here it is equal to 0.82, that is, the deformation of history has managed to decrease by almost 20%.

Dif and nature of the branch curve

Having set the size of the world to 100x100, I made a leap into the past, and I got this schedule:

Fig. 13 is one of the variants of the time flow curve. The
yellow curve is an alternative history flow computed by the program, and on top of it I have superimposed the graphics discussed in the mathematical model section. Of course, he had to scale them along both axes, because they do not respect the actual dimensions. They are simply not known to us: we do not know the coefficient of elasticity of time, and we do not know the coefficient of scaling the graph along the time axis.

The graph shows that the first option (equal acceleration attenuation) is clearly past, the second (“spring” formula) looks more like the truth, but the curve starts to fade too early. The third option (the formula obtained as a result of an error) for some reason reflects the nature of a real curve more than others.

In fact, I was just lucky on the first attempt to get such a curve. Not always dif fades out, sometimes the deviation constantly grows, including after the top of the loop. In order to accurately identify what it depends on, we need to refine the program and careful experiments. So far, I have not noticed that the size of the world, the object, the range of transfer, influenced the nature of the curve. Most likely, as in the real world, it is all about the specific circumstances of the journey, i.e. those "events" among which there is an alien from the future.

In any case, the curves obtained are closer to the truth than the usually accepted conventional representation of reality in the form of a straight line. First, the deviation of reality is hardly linear. One event takes place, an insignificant in itself, which after some time causes (or does not cause) another, which is much more powerful. It's like in the I-th part of “Back to the Future”: first, Marty pushed his father away from the car - the deviation curve of reality slightly went away. And only then events begin to develop rapidly. Secondly, fluctuations constantly occur, the worlds become closer, then further (in terms of similarity).

Does the size of the world matter?

All the tests I conducted on the square worlds of dimension 100-1000. Of course, the larger the world, the more fully it simulates the real world, while there is only one problem: the program slows down on the big worlds. Need optimization. But now some quite logical laws are clear. In a small world, the spatial focus of a history change spreads faster. Take the world 100x100:

Fig. 14 - comparison of a trunk and a branch
An object of 4 cells was sent to the past, and for some 200 generations the world has changed almost completely (two realities are shown in the figure).

Let's see the world 1000x1000:

Fig. 15 - spreading the area of ​​change
If you impose two variants of the world in 500 generations, then you can see quite a clear spot of difference (everything else is identical). The spot radius increases with time, i.e. changing history encompasses more and more space. But then again, not always. Sometimes there is a strange series of events, and all changes are smoothed, sometimes even to zero, and the worlds become identical .
By the way, after reaching the top of the loop, you can click “Play” and continue the simulation to see the further behavior of the branch. As a rule, if dif grows monotonously inside the loop, it continues to grow after (the radius of the spot increases). However, growth is rather slow, and for large world sizes, the relative radius of spatial changes is extremely small. .

Three types of loop time

In the course of the article, we have several times been faced with the question: what is considered a “serious” intervention in history and what is not? Perhaps, already in the foreseeable future, we will learn to calculate the trajectories of reality as Calculators in A. Azimov's “The End of Eternity”, but for now you need to start at least with something.
Let's start with the concept of a reference system. They are two, although they are inextricably interconnected: the world and the traveler. You can go back in time and make tremendous changes in the neighboring galaxy, but this will not affect the past of the traveler here on Earth. Another example: a traveler can go back a day and add some trifle to the stream of events of his twin, as a result of which he does not fly in a day
t in the past. The deviation of history in the first example is enormous in the world’s reference system, but imperceptibly from the traveler’s point of view. In the second example, the opposite is true: for the world, this is a vanishingly small fluctuation, and from the point of view of the traveler a completely different scenario of events has started.

Measuring the deviations of history in the world’s reporting system is an extremely interesting and important topic, only so far there are more questions in it. History flows affect too many people until the necessary models are developed to quantify the significance of world events. Say, what a change in history is more significant: saving President Kennedy or preventing the Chernobyl accident?

The simplest thing we can do now is assess the degree of history change by the effect of these changes on the top of the time loop. And then it is logical to distinguish 3 degrees of history change:

Fig. 16 - three types of time loop

1. The change almost completely fades to the top of the loop. For example, they made a picnic in the Jurassic period, even plastic will not be preserved to this day.
2. Towards the top of the loop, the change fades, but not completely, some trace remains. For example, they flew in yesterday and in their notebook they drew a picture. Returning, open the notebook, and see it (the main thing before the start of the experiment is not to look at the notebook).
3. The rejection of the story is so powerful that it can cancel the flight itself.

It is important to understand the relativity of these degrees, i.e. any change in the history fades, the only question is how much it will have time to fade by the time of departure to the past. However, the attenuation continues after this point.

In the program, for some reason, I did not succeed in catching a type II loop on the move:

Fig. 17 - examples from the program

The loop type on the monitor is displayed in the Leap Type parameter. Almost always there is number 3. What happens? When the simulation reaches the point from which the descent into the past was accomplished, the object (which flew away) to the current world (brunch) is superimposed. If the cell arrangement is the same, i.e. in the new version of history, this object has this object - the “invariance coefficient” is 1. If no cells match, then it is 0. So far, the code sets the conditional thresholds of this coefficient, which delimit 3 types of loop (absolutely "from the ceiling").

Does this mean that any movement into the past leads to paradoxes? I think not, just the “Life” algorithm is extremely sensitive to the changes being made. He gives a model of the world in a very rough approximation, without goal-oriented processes, while human activity somehow has its own vector. Due to this, as I assume, the effect of damping dif in simulation is less than in the real world .

Readers have a lot of questions like "whether history fades away, didn’t modeling in the program disprove this?". I think that is not refuted, but partially confirmed. There are no more cases when the deviation monotonously grows than when the deviation fades out, at least by 5-10%. Even the fact that these cases are registered indicates that history can “straighten out” in principle, has elastic properties. Some have noticed specific conditions under which a branch is particularly quickly merged into a trunk - and these conditions can be interpreted in two ways. Yes, the history of the world in the program, like that of the real world, is heterogeneous, consists of several “epochs”:

• high density of life and its homogeneity
• life thins and more complex structures form, isolated groups of cells
• balance era

But doesn't it look like the evolution of our cosmos and the planet? And yes, moving within the same epoch, moving between epochs give a different result. This can be interpreted as a feature of the algorithm that prevents us from conducting correct experiments. And it can be considered a reflection of the real processes of the universe.

Conclusion

Can we say that in general, history most often seeks to return to its own course? At a minimum, such an effect is registered, and to talk about its frequency, more experiments are needed. Of course, experiments should be carried out in an automated mode, i.e. instead of UI, implement API programs + scripts, where to set different test scenarios with multiple repetitions. What will it give?

At a minimum, we can evaluate the dynamic characteristics of the flow of time. As the decay curve of the deformation of the history depends on the size of the object, the size of the world, what is the most general form of this curve?

Having made a reusable time machine, we will be able to simulate complex paradoxes , and see what really happens. Undo cancel history change? Groundhog Day? Paradox statues? All this can be seen “live” in the form of real (more precisely, virtual) 5D tracks.
Maybe you have ideas and suggestions, in what other direction can the project be developed?

In addition to conceptual tasks, there are a number of purely technical improvements, in particular:

• There is an acute need for optimization, it is necessary to finish the algorithm (for example, to implement HashLife) - I hope that someday they will reach their hands.
• Can someone build binaries for Linux?
• Automated experiment system.
• Transition to Qt5, C ++ 11
• And many small improvements on the interface, the ability to save the world, select an object from the past, teleport it when flying into the past, etc.

The main thing is to understand the fundamental principle of the question! Now there are quite a few “myths”, alas, that shape many people’s ideas about time. One time I read about "if you move a second ago, you will find yourself in space, because the Earth is moving." Or the state of “chronostasis”, when the world around “freezes”, is called “time dilation”, whereas, on the contrary, the acceleration of the observer’s time. But such questions are easily solvable even without any experiments, at the level of elementary logic! What I mean is that a huge amount of time research work can (and should) be carried out even without working chronotechnologies, armed with common sense. Plus, it is not the first time that programming comes to the rescue.

Today we touched the tip of the iceberg, briefly examining one of the paradoxes of time. The theme of time is infinite, in a variety of questions and its fascination. If anyone is interested in participating in this work - please open several projects. Without a drop of irony, I will say that in the matter of studying time, not the last human hope for habra people, whose ability to think logically and burn creatively will help make new discoveries!

Yes, the article does not disclose the topic of event laws (eventology), does not list various ways of observing the past (because the article is about travels), and of course many people have questions: are travels to the past possible at all, is there time? In order not to go into just one philosophy (and as a result - holivar), it is necessary to make assumptions. First of all, we allow the possibility of flying into the past. Then we have the opportunity not only to discuss this topic and express the most "crazy" ideas, but also to bring the stream of thoughts into the system, and even try to confirm our theories experimentally. So, step by step, we are approaching the solution of the greatest mystery - time!