 Yes, first I would like to thank the organizers for inviting me and also for a very nice lunch today with plenty of wine, which undoubtedly should improve quality of presentations today. My talk today is a little bit strange, but the good news is that I didn't have any problems in publishing it. If I try to publish something similar, say, ten years ago, I would expect a lot of objections. The reasons are that, say, ten years ago, if something published in one of the same nature journals, which would indicate some microscopic quantum retrocazality, at the end, there would be a legal disclaimer which would say, this work must not be considered as evidence for causality violation. That's a must. This kind of disclaimer, they disappeared now. So there is not a problem discussing causality in one way or the other. So we're approaching technological evolution. There will be big changes, and I expect paradigm changes in science. And one of the areas in which we expect these big changes probably would be our understanding of time. So let us try to discuss what this understanding of time is and what's different concepts of time. First, of course, what we all like is the river of time, as a flow of time. Paetic words, they're very well aligned with our intuition. But in fact, of course, we understand that time cannot flow. It cannot change because there is no other variable so that time can change with respect to. What happens is that some sequence of events, and this sequence, which is shown here, changes in time. So it's a change of events in time, which we perceive as a flow of time, as a river of time. And again, each of these events probably causes the next one to appear. So now we speak about causality and what causality is a big question. First, of course, we've got a very good understanding, an intuitive understanding of what this causality might be. So if we have this vase falling down and then it's broken, the A is a consequence. The A is a cause and B is a consequence, obviously. That's what we intuitively understand. We also can conclude that these two events, A and B, they're connected to each other. But Y, A is a cause and B is a consequence. And philosophies, they try to define what is cause, what is consequence for a very long time. And they could not, to such a simple and intuitively understood relationship between these events, they could not give relatively strict and clear and simple definition. There are hundreds of papers published on this. Now, the one conclusion which we can draw is that, okay, A precedes B, so by definition, A is a cause and B is a consequence. But then we come to a circle of arguments. We define time, error of time, direction of time, in terms of cause and consequences. And we define cause and consequence in terms of the direction of time. So we need to break this loop somehow. If we want to break something, we should go to some ideas which were expressed long time ago. And these ideas were first expressed by Boltzmann. As they were repeated many times over and over again, but perhaps the idea in form which was expressed by Ludwig Boltzmann was the deepest. He identifies, he identifies the direction of time with the second law of thermodynamics. All laws, all physical laws, we know that time symmetric. Mechanics is time symmetric. Relativity is time symmetric. General theory of relativity is time symmetric. Quantum mechanics is time symmetric. Relativistic quantum mechanics is time symmetric. There is only one law that we know which is time asymmetric. That's the second law of thermodynamics. His statement is very deep. It's not just identifying the time as we perceive it with the direction of the second law. He's saying that the time as we perceive it is the direction of increase of entropy. And he goes as far to say if it was some part of the universe in which entropy would be decreasing, then people living there would perceive our past as a future and our future as a past. Okay, so how this, how, what, how time works? First, if we deal with say a mechanical system of large dimension, then according to conventional laws, what we have, we have Hamiltonian systems, the volume would not increase. But generally, if we start from some initial conditions and go forward in time or backward in time, we will have something like a sponge. That's what I brought as illustration, as a prop from Australia. So the volume of material can be quite small, but sponge can occupy much larger volume. So in this case, the phase volume remains constant, strict phase volume. And entropy, which is logarithm of this phase volume, roughly speaking, does not increase or decrease. It stays constant forward in time and backward in time. Now, what is time? Time is a little violation, tiny violation. It's so small, we cannot measure it directly. We don't know what it is. It's a time primary. It's a process, a known process, which violates these idealistic, idealistic properties of conventional mechanics. And it makes a small deviation from these laws, which allow for increase of the volume forward in time and decrease of the volume backwards in time. It violates symmetry of time. And it creates direction. It wasn't suggested by me. It's suggested by many other people, and Pinrose will be one of this. And they have all different explanation what it is. I don't believe in the explanation. I simply think that the law is not known why we have... What process is actually responsible for direction of time? What physical process? All right. Now we need to go down to quantum mechanical level. At quantum mechanical level, we have unitary evolutions. And these unitary evolutions are time symmetrics. They can go forwards and backwards. And they don't increase or decrease entropy. It's analog of classical mechanics. But then there are some other processes. And these other processes are usually associated with the coherence. And coherence when we convert a pure state into mixed state. And then if you start from a pure state, then unitary evolution would convert it into another pure state, no entropy change. But the coherence would make it a mixed state. And now you don't know in which state you are. You can't be in any of these states in ideal, make sure this would be with equal probability. Entropy increases. There is uncertainty now. Information is destroyed. Again, what's the physical mechanism behind this coherence? It can be discussed. There are different theories. But what's important for us? There is coherence. It's present. It acts. It changes the world forward in time. Now, what it means for us? We remember the past, but we don't remember the future. Why? We look at a photograph and we see an image. This image tells us about the past, but it does not tell us anything about the future. And let us see an example, which is, I think it's very good example. You see footsteps in the sand. These footsteps tell you about somebody walked on the sand. Or somebody will walk on the sand. Of course it tells you about the past, but why? So if somebody walked, then footsteps appear, but they would be washed away slowly. Entropy increases. Information is cleared. And if you see, and if you see footsteps somewhere here, you always assume somebody walked. Let us try to assume somebody will walk on the sand in the future. So he will walk. Again, both lines are in accordance of conservation of energy. They don't violate any energy relationships. But here, instead of disappearing, it would appear from nowhere. And this line does contradict, does contradict to the law, to the second law of thermodynamics. It's impossible. That's why intuitively we always assume that's what happened. Somebody walked on the sand. And these footsteps can be seen here and then disappear. Nothing like this can appear without a cause. That's what we perceive. The second law of thermodynamics we perceive as causality. Causality helps us to understand this action of the second law of thermodynamics intuitively. Anyway, also initial and final conditions. You can set, for small intervals, you can set probably initial conditions as well as final conditions. But generally, you are much better off setting initial conditions than the final conditions. Because when these footsteps disappear, it's very difficult to solve a problem backward in time. This probably would be ill-posed. So also you start from this condition or that condition and you finish up with equilibrium. Information is cleared. It's very difficult to go backward in time if you are going to set the final conditions. So that's, again, it's a consequence of the second law of thermodynamics. But it gives us a very simple, very simple rule how we should apply. We should use initial conditions, not final conditions. And that's nothing else but the principle of causality. We should start from initial conditions and we should proceed forward in time. That's the safest way of obtaining correct solutions. Now, matter and antimatter. What we know about particles and antiparticles. According to quantum mechanics, antiparticles are particles moving backwards in time. There is, in the microscopic world, in quantum world, it's a CPT symmetric. So when you switch from particles to antiparticles, you need to reverse the direction of time. And then you get exactly the same solutions. This universe is full of matter and radiation. It has particles and antiparticles, but there is no antimatter present at all. No one has ever seen it. And we are very lucky because can you imagine what would happen if a little stone made of antimatter would just fall somewhere nearby? There would be very large explosion. But no one, no one has ever seen any substantial quantities of antimatter. So what I'm saying is that we know properties of matter and thermodynamic properties associated with microscopic objects. And we know these properties quite well. But we don't know anything about properties of antimatter because it doesn't exist. No one has ever seen it. We know about microscopic properties in quantum mechanics. And we know particles and antiparticles. We know that this microscopic world is CPT symmetric and is not CP symmetric. But we don't know much about what these antimatter properties would be. And if we can see the microscopic properties, thermodynamic properties, they don't exist for elementary particles, but they exist for macroscopic objects. There are two possibilities. One possibility is conventional thermodynamics, which is valid for matter, can be extended into antimatter in two different possible ways. The time, thermodynamic time, can run for antimatter either forward in the same direction as it runs for the matter or backward in opposite direction. This gives two fundamental possibilities. How thermodynamics, how conventional thermodynamics that we know, can be extended from matter into antimatter. It's either symmetric or anti-symmetric case. In some way, matter and antimatter are equivalent, but we don't know which of these cases, they are mutually exclusive. They cannot be valid at the same time, but at least one of them is correct and the other one is not. Okay, what it means for reaction mechanisms? Say we have reactants. We have two molecules. One has some energy and other one does not. They react and they exchange energy. Excited A at the beginning and non-excited A and excited B at the end. The reaction rate, as we know, is proportional to concentrations of reactants, but not concentrations of the products. And it's strange why we put reactants in, but never put the products. An explanation, of course, is this process of decaherence. Because before every reaction, these particles go through running time represented by decaherence. And decaherence actually distributes these particles equilibrium equivalently between all possible phase states. Now the probability, the probability of finding two particles in the same box determines the reaction rate. Determines the reaction rate. So the simple rule that we take decaherent components which are in conventional thermodynamics value of components before the reaction and product, product of number of particles would determine the reaction rate. Now what would happen if one goes forward in time, one decaheres and another one decaheres? Then concentrations which would determine the reaction rate would be A star and B star. Decaherent components, as you see, expression would be different. Now what it means for us in terms of energy exchange between matter and antimatter? What it means for us if we can see the conversion of matter and we allow for conversion of matter into antimatter and vice versa? I would just go to conclusion. So in case of symmetric thermodynamics, matter and antimatter are equivalent. Thermodynamics would predict equal quantities of matter and antimatter present. In case of anti-symmetric thermodynamics, it would favor full conversion of antimatter forward in time into matter and it would favor any conversion of energy from antimatter to matter. In very simple terms, according to anti-symmetric thermodynamics, antimatter is extremely hot. It's hotter than some, it's hotter than any other object you can imagine. It would just, any heat associated with any thermal energy associated with antimatter should be transferred to matter forward in time. Now how this agrees with equivalence of matter in antimatter and if you look, then this transition occurs forward in time as we go. We are matter observers, but if we imagine ourselves as antimatter observers, backward in time the same amount of energy and the same amount of mass would be, would be transiting from matter into antimatter. So antimatter and matter are still equivalent in some way. Now let's forget about matter and antimatter because no one has ever seen antimatter, although they, they actually tried to make it and there are some attempts to create antimatter atoms and it's not very far from here when sooner or later some quantities of antimatter will be created and then we'll see what kind of thermodynamic properties they have. Are they the same or different from properties, from properties of matter? But let us discuss something else is interaction between radiation and, and matter. And as you know, there is a classical theory which was published exactly 100 years ago by Einstein and it introduced two processes of emission, spontaneous emission, when you have excited atom which produces a photon and then induced emission. When you have excited atom and it produces another photon and this emission is induced by a photon and finally you have two photons. Absorption of course you have a photon and then it's absorbed by an atom in ground state and this atom becomes excited. If you calculate reaction rates, all these reaction rates they actually consistent with the classical Bose-Einstein distribution for photons. Photons are bosons and they need to have this distribution. But as engineer I always had these doubts about, no it's a correct theory of course. It's, it predicted many things including lasers. It was a great, great vision of Einstein, who actually formulated this theory a long time ago. But from engineering perspective you see this one reaction, that's another reaction. The one is the reverse of another one but there is no reverse reaction for this one. It's very strange. It's very strange. And I always thought why is the case? Why is this reaction is missing? It's correctly missing. It should not be here. If you put another reaction like this it would not work because then you wouldn't have this consistency with Bose-Einstein statistics. Now let us look what it means from these general rules that we just derived, that we always must use decayed components to determine the reaction rates. Irrespectively if they decayed forward in time or backward in time. And we try to apply different rules and see if we can get results which are consistent with the great theory of great Einstein. And first of course we would assume that say photons always decay here and then it would produce correct, correct equation for absorption and incorrect equation for emission. Another assumption would be okay, so it didn't work, let us try recurring photons. Maybe photons should behave like antimatter. And in this case again the reaction rates are wrong. The reaction rates are correct for emission but incorrect for absorption. And finally we choose something which matches Einstein's theory of radiation. We assume that decoherence neutral radiation interacts with matter. What it means? It means that on emission, when emission occurs radiation ricoheres and when absorption occurs radiation decoherence. Decoherence here and ricoherence there. This produces exactly the same results as Einstein's theory. So it gives another interpretation why it should be written in this form. It doesn't introduce any new theory of course. It just gives an explanation. It shows consistency between what we considered from general principles of decoherence and general principles of thermodynamics with existing knowledge about interaction of matter and radiation. Also this ricoherence is not just imagination. It's not just a mathematical trick. Recoherence is possible and is observed in lasers when photons form a coherent beam and they ricohere into unique structure. It's a physically observed phenomenon. All right, so what kind of conclusion we draw? From this perspective there is no difference between spontaneous and induced emission. Both are the same. Spontaneous emission is nothing else but emission which is induced by photon which is emitted but it's induced from the future into the past. Why? From the future into the past because it ricoheres and we know that this ricoherence process is possible because it's observed in experiments. So with this kind of topic I probably should leave some time for discussion but the last slide I want to show is this. That's a summary. That's a conclusion and fundamentally we have two possibilities. We live in one of these worlds. It cannot be both of them. It's one or the other. It's either anti-matter has opposite direction of time. Opposite direction of time as shown here. Direction of thermodynamic time of course and radiation must be neutral then. That's one possibility and another possibility is here when anti-matter and matter have the same thermodynamic directions of time but radiation does not. It appears to be ricoherence neutral. It must be there. So what tell a mechanism what tell a mechanism and next direction of time it does not affect radiation in the same way as it affects matter and anti-matter. Again I'm not saying which one is correct. I'm saying just there are two principle fundamental possibilities. We live in one of these two worlds and I believe sooner or later and probably more likely sooner than later we will know the answer. It would be one or the other.