Where is every time traveler?

Perhaps nowhere, since they simply don’t exist, as time travel is impossible–but Einstein’s twin paradox (time dilatation, if you prefer) is nonetheless real. Notice that the time dilatation is not a proof of time travel; and that time travel and time dilatation are different questions. The first one is about whether time is similar to space in a certain sense, the second one is about what happens at very high speeds.
Obviously, time is a problematic field of modern physics. As far as we know, “the second law is the only fundamental law of physics that distinguishes between past and future” [Melanie Mitchell: A Guided Tour to the Complexity, p. 43]. Obviously, it has a kind of physical background, as the rise of entropy wouldn’t be possible without an early phase of high order (=Big Bang) but entropy’s concept is purely mathematical. I.e. in the case of the law of gravity, the gravitational force is inversely proportional to the square of distance–and this proportion cannot be deduced solely from the mathematical equations. But to understand the second law is enough to know that there are more ways to make disorder than order. What is to say, in this case there is no an additional physical law to determine the results over the logic of mathematics (opposite to gravitational law where there is a second “layer” over the mathematical description to determine that the connection between the distance and force is not, say, linear. By the way: if Newton’s law is two-layered (physics over math), then it is interesting question whether exist laws with tree, four etc. layer).
The second law creates the “time of arrow”. So since there is no any physical effect to modify its mathematics, time can be regarded as a result of the mathematics which is the basis of our time description.
British historian Arnold J. Toynbee said that history was regarded to be nothing but "one damned thing after another.” According to the logic of our argumentation, it is defendable that although time, using a kind of mathematical abstraction, can be represented as a dimension, in reality it is nothing more than “one damned thing after another”. So the meaning of travel in time is simply uninterpretable: It has no meaning at all, but it doesn’t exclude the time dilatation where according to the observers of a different frame, events follow slower each other if your speed is close to the speed of light.
Of course, it can be argued that it is a natural law that there is no an additional natural law over the level of mathematics in connection with entropy, and it can be asked why.

Complexity and alien intelligence

From a complexity approach there are some different kind of “intelligence” and they have two components: individual building blocks (ants, neurons, humans etc.) and their societies (ant hill, brain, human society etc.). These components can be either simple or complex.
In short: in search for alien intelligence, we have to take into consideration not only the complexity of an individual agent, but its societal environment, as well. Incidentally, it raises the question whether a traditional, “lonely” computer could produce a kind of intelligence similar to ours, since all intelligent form known by us is embedded into a societal networks, bit it isn't.
Regarding the possible combinations, it is a self-contradiction a complex system with simple building blocks and similarly simple society, so we have to ignore it.
The second possibility is represented by ants. They aren’t intelligent individually, but their societies can show complex and adaptive behaviors.
The third category is the human-like complexity: we are complex individuals who live in a complex society.
Theoretically it seems to be possible a fourth solution: it would be a huge, complex and adaptive being. A similar entity appears in Stanislaw Lem’s novel Solaris (where the whole planet sems to be intelligent) without any societal environment.
This taxonomy raises some questions.
First of all, it is a cliché that how intelligent an ant colony, although a sole ant isn’t. They can build anthills with regulated temperature, defend their descendants etc. It is a central problem of complexity science that there is no an exact measurement for complexity (Melanie Michell: a Guided Tour to complexity, p 95), but is seems to be unquestionable that there is no ant-like intelligence with consciousness on our planet. They can monitor their environment but from this point of view they are on the level of cockroaches. They never reached the second level: the self-reflexivity or reflective self-awareness: to know that you know. (Clayton: Emergence and Mind 110)
Since there are more insect races and individual insects than mammals, they would have more opportunity to evolve into an intelligent system than mammals. Ergo it is a plausible hypothesis that a mammal-level intelligence (=intelligent agents, complex society) unreachable by ant colonies (=simple individuals, complex society). And not only their intelligence, but their ability for environment modification is limited, as well. They can build ant hills, but cannot able to build spaceships. In other words: ant like system cannot reach the level of consciousness and consciousness is the only way to develop really effective technologies. Opposite to some SF writers’ ant like, intelligent technological societies, an alien intelligence presumably would similar to us in the sense that they would be individually complex entities. After all, technology reachable only if you are both a complex entity and are supported by a complex society–it is not a surprise that computing is not a Paleolithic invention.
Following this train of thought, it seems to be probable that there are no Solaris like mega brains, since they wouldn’t have complex societies. But who knows–perhaps their mega complexity can substitute a complex society’s influence.
Or not.

Undercomputing

Hypercomputing is about the hypothetical extension of the capabilities of traditional Turing-machines. I.e. how to go beyond Turing-compatibility? How to calculate infinitely many steps within a finite amount of time (these are supertasks, see i.e. the Thomson lamp) and how to solve a mathematical problem which is unsolvable by Turing machines? Obviously, these are mainly thought experiments, but the main point is to exceed certain limits of Turing-computing.
But we can turn into another direction and we can examine the limits of physically existing computers. A Turing machine is an abstract construction originally with to aims: to model how a “human computer” can solve a problem (in the year of publication of Turing’s paper about Turing machines (1936) the computational processes were performed by humans with paper and pen); and to create a mathematical construction to describe it–this was adopted to electromechanical/digital computers around the end of WWII. In other worlds: it was based on an abstract conception about mathematics.
According to this approach, every Turing machine which are capable to solve a problem are equal, since they give the same answer using the same logic and it is indifferent if one of them is a super fast computer while the other one is a slow, mechanical model made of tinker toy.
But–opposite to the physical reality–mathematics does not contain time as parameter and it explain why one of the central problems of Turing machines is the “halting problem”. The question is whether the computer halts because of a given input sometime at all, but it is irrelevant whether we have to wait either a second or one trillion years.
Penrose makes a distinction between hardware and software (Emperor’s new Mind, p. 24.). The previous one is “the actual machinery involved in a computer” (circuits, processors, etc.) while the software “refers to the various programs which can be run on the machine”. So Turing machines are equal regarding their software–after all, they are based on the same logic. But they aren’t equal in the real world, since it is not the same to wait for a result a second or to a longer time than the earth would exist. It is indifferent from a practical point of view that we don’t know the answer since a Turing machine unable to solve the problem or because it takes too long time.
But making a distinction between the abstract mathematics of computing and the real, physically existing machines makes possible to introduce a neologism called undercomputing. Similarly in a certain way to the concept of the Landauer number, it is about the limits determined by the physical reality, and while hypercomputing is to exceed the traditional Turing machine, undercomputing is to take into consideration the physical limits of every physically existing computer.
Bennett and Landauer [The fundamental physical limits of computation. Scientific American 253(1), 1985] have studied some fundamental physical limits of information processing pointing out that, for example, PI doesn’t have an exact value in reality, since it cannot be calculable to the last decimal. So we can interpret computers as machines with performing capacities influenced by their hardware that are determined by the physical laws.

Living in an extremely big Universe

Fred Adams and Greg Laughlin distinguish (in their book entitled Five Age of the Universe) four “windows” from an astronomical point of view which are opened to observe the physically existing Universe.

• The first level is the planets;
• the second is the solar systems;
• the third one is the level of the galaxies and
• the last one is the Universe itself.

One can question why the level of galaxy clusters ignored and it is unquestionable that this scale is influenced by our special circumstances. An intelligent being living in the interstellar space probably would not regard either the planets’ or the solar systems’ level as important (although she could recognize their existence.)

Another example for the observer-dependent nature of scales/taxonomies is the megatrajectory theory. It is based on the evolutionary mile stones and

• the emergence of life is the first so-called megatrajectory;
• the second is the prokaryote diversification;
• then eukaryotic cells appear;
• it is followed by the rise of the multicellular life forms;
• the “invasion of the land” is the 5th and
• the rise of intelligence is the 6th megatrajectory that gave an opportunity for the invasion of every possible environment

–perhaps including the outer space (A.H. Knoll, R.K. Bambach: Directionality in the history of life: diffusion from the left wall or repeated scaling of the right. Paleobiology, 2000).
The post biological intelligence can be interpreted as the 7th megatrajectory (Cirkovic, Dragicevic and Beric-Bjedov 2005).
This taxonomy is focuses at least partly on parochial details of earthly evolution, since its aim is to give a description of the history of life on earth: I.e. the fifth megatrajectory would never occur on a water covered planet.
We can reinterpret this megatrajectory concept focusing on those factors that are presumably universal. Freeman Dyson distinguishes three classes of phenomena which can occur in our universe: “normal physical processes”; “biological processes” and radio (or another forms of) “communication between life forms existing in different parts of the universe.”(Disturbing the Universe, 1979) These factors can be interpreted as “gigatrajectiores,” because they–opposite to megatrajectories–can be typical in any universe which is populated with intelligent observers.

• The first gigatrajectory is characterized by the domination of lifeless matter;
• the appearance of life was the second gigatrajectory and
• finally intelligence rose.

Robert Batterman mentions in his article about “The Tiranny of scales” (in the Oxford Handbook of Philosophy of Physics) that it is a reductionist approach to believe that “whatever the fundamental theory is at the smallest, basic scale, it will be sufficient in principle to tell us about the behavior of the systems at all scales.” Regarding the second gigatrajectory, after its appearance life was able to conquer our whole planet and, what is more, thanks to the relative small size of the earth, we can visit any point of it–even on foot. It is imaginable a bigger planet where its habitants too small and/or too short lived to do it individually, but it is questionable whether it is imaginable a so big planet that there isn’t enough time for life to occupy every part of it, since their sun goes out before the end of it. In short: the size of our earth is consistent with life’s abilities.
What is more, if you accept one or other form of panspermia hypothesis, then it seems to be possible that life which appeared on the surface of a planet can spread in our Galaxy. But it seems to be impossible even to the microbial life to sail to the closest galaxy, since it would take billions of years. So the spread of life is localized for ridiculously small parts of the Universe. In other word: to believe that other galaxies inhabited with intelligent beings, we should believe that both life and intelligence arose independently from us somewhere in in the Universe.
Similarly, technology seems to be provide an opportunity (theoretically, at least) to conquer not only our planet, but both our solar system and our galaxy–after all, even the Fermi Paradox is based on the presumption of its possibility (if we are able to, then they should be able to visit any stars, including the sun, as well). But notice that even the SETI is mainly about the search for alien intelligence within the Milky Way. Although we have a theoretical chance to observe a super civilization’s energy emission from another galaxy, it is impossible to visit even the M31, since it would take million years even with 0.9 c. And although the time dilatation would make slower the aging on the board of the spaceship, its construction should survive an unimaginably long period of time (notice that the Homo sapiens itself didn’t existed a million year ago). This long travel seems to be not theoretically, but technically impossible. So unless we invent a revolutionary new form of travel (i.e. a warp driver, but it is only an unfounded dream today without a chance to build it), we will never leave the Milky Way and it means that the Universe is extremely huge compared to our possibilities.
In short: the spatial structure of the Universe limits the possibilities the spread of life and intelligence. It raises a question whether it would be possible a universe which can be conquerable by its habitants.