Time and Space: PLERWA
Hermann Bader Emeritus, Medical School, University Ulm, Germany January 2005
Last changes January 2007
email: Hermann.Bader@baderbuch.de
Abstract: Based on the spacetime continuum Minkowskis^{25}, called “WORLD”, where according to Einstein^{11} the usual time coordinate is replaced by the imaginary magnitude , which has the dimension of a length, it is proposed, that our three dimensional space moves with the help of the time as tool like a slice through the fourdimensional WORLD. The time behind our space slice is our past, the time before this slice is our future. This fourdimensional WORLD is us well known as Period like the period of the 20^{th} century, which means not only the time between 1900 and 2000, but also all changes of space during this time as for instance the destructions caused by both world wars or the invention of the automobile. However, we can only remember the past and try to forecast the future. But we can not change the past and we do not know exactly how our doing really will effect our future. We only will know it, when the future becomes for us the past.
Our body, a threedimensional creation, is situated in a likewise threedimensional space, which additionally is exposed to a forth of gravity because of the pull of the earth (gravitation). Thus we divide the three dimensions of the space with our senses in width, depth and height. This organization applies however only relative to the location on earth and not relative to the cosmos. Both our body and the perceptible space change with time. In our memory however the past form remains and by our fantasy and presentiment we can design a future form (for example a house). Where however did the former form remain, where the future come from? What is the time? Augustinu^{4} admits: If nobody asks me for it, I know it; if I want to explain it to someone asking, I do not know it. The future is not yet, the past not anymore, therefore they both are not being. There is nothing on earth, which is not bound to time. Everything has its time (Koh 3.1).
What is space and time? Do both exist out of discrete parts, as Newton^{26} has described it or do they form a continuum according to Leibniz^{22}? The Quantumtheory follows Newtons Idea. But the later one is only a description of the fact, which is valid for three or more dimensional bodies in space and time. The dimensions of space and time themself form rather a continuum, in which everything, which we want to describe in physics, chemistry and mechanics takes place.
Time can only be in the soul, only in there can past, present and future be kept apart and experienced. The soul is in the time. But the body of humans is in the three dimensional space.
Besides the physical time, which is measured today by the duration of even oscillations (clocks) (Augustin^{4} as orator used for it the duration of syllables of the human voice), there are other kinds of times. To emphasize is the individual, psychological time. It is from person to person and from opportunity to opportunity of different duration: Some feel themselves early old, others remain eternaly young or are early growing up. Sometimes the time passes fast sometimes it lasts endlessly. Time is in the human spirit; it is the condition of the soul.
The results, which were gained by the research in the areas of nuclear physics, quantum mechanics and cosmology, show that, besides the to us well known space dimensions point (zero dimensional), line (one dimensional), even (twodimensional) and room (threedimensional), still further space dimensions are existent. In the meantime, for the explanation of quantumcosmological phenomena, higherdimension areas are postulated, for example an elevendimensional spacetime for the explanation of the Big Bang at the beginning of our fourdimensional spacetime and the standardization of the three atomic forces (strong, weak and electromagnetic strength) with the force of gravity (Hawking^{16}). The same applies to the opinion, our threedimensional universe exists as diaphragm in a higherdimensional area (Arkani Hamed et al^{3}).
The extensive meaning of space and time becomes obvious, if one regards both in the spacetime continuum, which Hermann Minkowski^{25} had developed at the beginning of the 20. century. Therein space and time are regarded not as independent units, but in a fourdimensional union, which he called WORLD. In order to give due prominence to this relationship, however, the usual time coordinate t must be replaced by , an imaginary magnitude proportional to it, where c is the speed of light and t the time, so it has the dimension of a length. Than the time coordinate plays exactly the same role as the three space coordinates as Einstein^{11} explained:
The fourth dimension is naturally something real. However, it depends from where one regards the happening: In the fourdimensional WORLD (not accessible for us) the fourth dimension is real existing. With the three coordinates x, y, and z of the threedimensional space, associates as the fourth coordinate , which may be called “w”. , which has the dimension of a length, is freely exchangeable with the other three coordinates. In the threedimensional space however this fourth dimension w has an imaginary size, which develops for us with time and lets so develop the spacetime, for us the imaginary fourdimensional WORLD. The time is the tool, with which we notice and feel the fourth dimension as past and future (Bader^{6,7}1995).
One can clarify oneself experiencing the fourdimensional WORLD thereby, that one imagines a twodimensional creature, whose living space is the plane with the coordinates x and y. The towdimensional nature can experience our threedimensional space with the coordinates x, y and z only by the way, that it experiences the third dimension z of the space as an imaginary dimension with time. We will call this twodimensional organism an evennature. A threedimensional object is only then recognized by an evennature if it meets in its timeline this object. That is the temporal beginning of this object for the evennature. This object was before in the unknown future of the evennature. With the help of the time the evennature in its twodimensional plane wanders through this threedimensional object. The evennature recognizes this object not in its threedimensional expansion, but only in each case as a twodimensional cut through the object. If the timeline of the evennature leaves this object, it lies for the even nature in the past. For us spacenatures is this threedimensional object with its coordinates x, y and z present in its whole expansion, even if we are outside of the time of the evennature, thus in its past or its future or “elsewhere”, therefore outside of its liveline.
Insufficiently and roughly illustrated, the entire timebound human in spacetime (our life from the birth to death) can be compared with a loaf of bread, which is cut in slices and again built up from these slices (similarly as an imaginary twodimensional evennature would experience our threedimensional objects with the help of time). At each time we live only in a threedimensional layer of the spacetime (similar to a twodimensional slice of bread in our space). The individual layers (our threedimensional space) build themselves up with the time from beginning to end to an overall view, which we threedimensional natures (space natures) recognize as the fourdimensional WORLD. The time makes it thereby possible for us, to experience the four dimensions of spacetime, the WORLD, (similarly as the imaginary twodimensional evennature the third dimension of bread would witness) and thus to fulfill our life.
This experience happens with a certain speed, for which Minkowski^{25} used the term c, the speed of light. A conception of the fourdimensional spacetime gave already Galileo^{13} in his dialogue (1st day, 117), where he describes the acquisition of knowledge: These transitions, for which our spirit uses time, which it carries out gradually, passages the divine intellect equal to one instant or, which means the same, they are him always present. The yesterday and the morning of our threedimensional space are in the fourdimensional WORLD part of the today, they are simultaneous (Bader^{6}). This world is the place, in which everything takes place, in what Husserl^{20} was engaged in his “Logic investigations” and what Heidegger^{18} expressed in “sense and time”.
In the remembrance we can recall the way, which we covered in time (the fourth dimension), in our memory, for instance the years during our school time. In the future we mark out goals so we can reach them. The way there is the fourth dimension, which we will experience with help of time as tool. In a certain sense humans do not have a problem to convert the time in a length dimension for the sake of descriptiveness. This happens, if they want to plot an event graphicaly, for example the share quotation, There, in a Diagram (a twodimensional plane), the respective share quotation is laid on the ordinate (a onedimensional line) and the pertinent time in the abscissa (likewise a onedimensional line). From such graphics, in which the time is represented as a linear dimension, the course of the share quotation is evident in the past. From it one can now imply the share quotation in the near future. This will lead hopefully to a positive conclusion of a deal. Since we do not know however the future reliably, but can only suspect it, we cannot be safe over the suspected future from the past (in this case of the share quotations). A further example results in the case of filming: If the father shoots his children with a movie camera while playing, he transfers the temporal happening of threedimensional playing in the two dimensions of pictures on a filmstrip. The time is stored thereby as a linear line (the length of the filmstrip). When playing this strip the time appears again as a time dimension on the screen. The past is gotten into the present so to speak.
According to the theory postulated by George Gamov^{14} and confirmed of by Steven Weinberg^{33}, time and space resulted approximately 15 billion years ago from the socalled Big Bang. According to the usual view of the cosmology there was no time and no space (Stephen Hawking^{16,17}) before the Big Bang. That applies reliably to our fourdimensional spacetime, the WORLD, because before the Big Bang this WORLD was outside of our time coordinate and therefore, their was no space and time in this WORLD. This World, and according to that, space and time, are thought to have started by the explosion (Big Bang) of an infinitely small core, in which the entire energy of our universe was infinitely pressed together and developed by expansion like an explosion to its current size (Guth^{15}). However, are therefore space and time inventions of the Big Bang? Are they not rather conditions of the infinity? Has not the time ignited in the Big Bang our presence with its threedimensional space and leads from there on our threedimensional space through our fourdimensional WORLD? Couldn't it be the fact that the entire energy of our fourdimensional spacetime was always distributed over this WORLD but became only present for us at our time zero, at which point time stepped into our WORLD? The fourdimensional WORLD would then exist like in a Steady State  as Bond, Gold and Hoyle had suggested (Hawking^{16,17}) , which the threedimensional space experiences with time (Bader^{6,7}). That means, our universe did not develop from nothing, but from elemental powers, which were called in ageold creation stories of mankind darkness, Deluge, chaos, Tohuwabohu and other ones.
One could imagine then the development and change of our threedimensional space with time from the Big Bang up to now and further into the future formally like a twodimensional plane, which moves with time through a threedimensional ball or a threedimensional hyperboloid. At the beginning of our time (the Big Bang, approximately 15 billion years ago) our threedimensional space would have begun by the entrance of the time as a point on the surface of the fourdimensional WORLD and is moved from this point as a threedimensional spaceslice (brane, Randall^{28}) continuously with the help of time like a cut through the fourdimensional WORLD. Because of its spherical shape our space did experience at the beginning a sudden expansion out of nothing, the Big Bang. With time the expansion became ever slower when wandering through the fourdimensional WORLD. If the fourdimensional WORLD possesses actually ballsimilar shape, finally a contraction of the threedimensional space would take place up to the nothing. The reverse Big Bang, the collapse, would happen by leaving the fourdimensional WORLD. If the fourdimensional WORLD possesses however a shape similar to a hyperboloid, an always larger expansion up to the final dilution would take place. This would come the present knowledge nearest (Freedman^{12}).
The threedimensional timeslice, in which we live, is by the speed of the light not even, but bend into the past. The further we look with a telescope, the further the event lays back in the past. Because of the final speed of the light we will never see the presents, thus things as the are simultaneously, but always as the were in the past.
The fourdimensional WORLD is already for a long time familiar to us as Period. We speak of a period, if we mean for example a certain time in past history, like the time of baroque. This period covers roughly the development of the threedimensional space in the years of the 18th century with all events and space changes during this time. This period is thus fourdimensional. Also, the period, which we name for example midday of 12 o'clock to 13 o'clock and in which we have threedimensionally lunch, is fourdimensionally. And like that the whole period of our life is fourdimensional. The term period is called in German “Zeitraum”, which is, translated into English word by word: “Timespace”. And this term describes exactly what it means: The fourdimensional space, in which we accomplish our life, the WORLD, as we know it, began through the time. We experience the development of our WORLD from the beginning to today and into the future with time (Augustine^{5}, God state, XI, 6). We humans however live in this WORLD in the time. Here the question emerges whether with traversing of such a fourdimensional WORLD everything that happens in the threedimensional space is already predetermined or whether humans possess by strength of their soul, given by God, the possibility of forming the WORLD. Maimonides^{23} means to that: The answer to this question is longer as the measure of the earth and more broadly than the sea. Is the fourdimensional WORLD the place, at which the dark mass and the dark energy (which constitute the larger part of our universe) is situated and which influences from there our three dimensional space?
God gave humans with their will the possibility to arrange (to change) the process of their life and concomitantly the future of the WORLD. Similarly as the farmer ploughs into his field furrows and thereby changes by his work the field according to his will to his favour, humans are created by God to administer the WORLD. Times form us, while we form the world. Freely moving, the will is nevertheless at the same time moved by another: it resembles a passenger of a ship, who can spend its days freely in hundred fold changing resolutions and actions, whereas he moves nevertheless in the course of the ship. Freely hustle humans themselves at board of the necessity (Bernhart^{8}). From the possibilities of the present the reality of the future develops through us with the help of time. But then however this future is already again the past (similar to the wave particle dualism of the quantum theory, Peter Pasic^{27}.
Time itself is a yardstick, which does not disappear simply when one experiences the fourdimensional spacetime, but will exist further on in the fourdimensional WORLD. It serves as tool, with which the experience of a higherdimension of space is made possible. The fourth dimension of the WORLD, which is a length dimension as the remaining already existing three dimensions of the space, does not develop from the time, but by the time. As one can imagine a fourdimensional space, in which the threedimensional space gains through the time the fourth space dimension (Minkowskis^{25} WORLD), one can imagine that the fourdimensional timespace experiences the fifth dimension again with the help of the time and ever higher dimensions, until one comes finally to the infinitely dimensional space (figure). One can call this infinitely dimensional space ALL.
There cannot be a further space dimension, thus also no movement and no time to experience. One can express the disappearing of the time in the infinitely dimensional space mathematically by introducing a factor, which divides the time by the number of given space dimensions. So the time disappears in the infinitedimensional space.
Likewise one can imagine a space with fewer dimensions than our threedimensional space. In a twodimensional space (evenspace) the third dimension of our space becomes time (Abbott^{1} and Stewart^{29}). This resembles the tomography in medicine, by which the physican divides the threedimensional body (like the body of humans) with the time into twodimensional layers. One can build these twodimensional layers up again with time by computer treatment to a threedimensional form, so, if arranged with correct selection, the organs of humans (for example the heart or the brain), can be looked at in their threedimensional form and examined, without hurting the body of the human. In contrast to the tomography of the physician, which runs discontinuously, timing takes place continuously. The time of yesterday does not move towards today and further towards tomorrow. Rather the time moves us with the threedimensional space through the fourdimensional world.
The time is the basis of physics and concomitantly of technology. Mathematics uses the time for the description of phenomena, philosophy strives around the meaning of the time for humans and theology tries finally to understand the origin of the time and thus its Creator (God).
One can continue now to the linear space (linespace) and finally to the zerodimensional space (pointspace). In the pointspace no space dimension exist but only time, spaceless ONLYTIME. At both ends of our spacetime we have thus the infinity, either the condition with infinite space dimensions without time, the ALL (“their is the time in a present now”, Meister Eckhart^{24}), or the condition with infinite ONLYTIME without space dimensions. One can call it according to the ageold designation of beginning and end of the life alpha (ONLYTIME) and omega (ALL). That leads finally to the realization that space and time are inseparable parts of eternity.
One can further cut our threedimensional space into infinitely many levels (smooth or curved). However, this means, as the threedimensional space has infinitely many levels (twodimensional spaces), the fourdimensional WORLD Minkowskis^{25} has infinitely many threedimensional spaces. Hence it follows that the infinitedimensional UNIVERSE must have infinitely many WORLDS.
The additional space dimensions up to the infinitedimensional ALL, described here, are not, as with the string theory of the cosmology (Hawking^{16,17}), in threads rolled up dimensions (socalled strings) (Randall^{28}), which are attached to the fourdimensional timespace. They are rather dimensions, which are equal to the three dimensions of our threedimensional space and exchangeable with them. We cannot recognize them however, since they are for us in the past or the future. Minkowskis^{25} fourth dimension is characterized by an imaginary number. Therefore we cannot notice them with our senses, which are part of our threedimensional body, but we can separate them only with our understanding, which is part of the soul. This is called usually the sixth sense. Here one could ask, if the dark matter and the dark energy (David B. Cline^{9}), which contain obviously a multiple of the known mass of the protons, but are only detectable by their gravity, may be part of Minkowskis^{25} fourdimensional WORLD or further moredimensional spaces.
One could call the point, line, even, room, world and all, which result through the time and which are perceptible with our senses and recognizable with our understanding, according to their initial letters: PLERWA. This expression sounds similar to the oldGreek word Pleroma (plerwma), which means abundance or perfection and which Theilhard de Chardin^{30,31} called: the mysterious result of the fulfillment and completion for the absolute being, God, the eternal being himself. These considerations at space and time raise reliably more questions than they can solve. What lies between fourdimensional timespace and the infinite dimensional eternity? Is that the space, in which exists, what we call purgatory (1 Kor 3.1315) or hell (Mt 25.41)? Is that the space, in which the angels (Luk 20.36) or the extraterrestrials live? Where do we find the prince of the darkness (the devil, John 14.30)? Where is the haven (Mt 5.16) to be arranged? Are the revelation of John, the visions of Hildegard of Bingen^{19}, or the divine comedy of Dante^{10} to assign to the timespace between our habitat and the eternity? Should there be natures in the fourdimensional WORLD, nothing would speak against it that these natures have a free will at least comparably to that of us humans.
These questions are naturally insignificant, if one denies the existence of God from the beginning. What, however, do then the moredimensional spaces, which result from the advancement of the fourdimensional timespace and which are inaccessible for humans during their life, stand for? Who is where? Do the events in the Big Bang, the cosmology or the quantum theory run off from the multidimensional spacetimes described here? The solution of the mystery of the life in space and time lies outside from space and time (Wittgenstein^{34}). Humans control the space, the time however prevail over humans. There are time and space, which unite organically, in order to weave the worldmaterial with one another (Teilhard de Chardin^{28}).
The ideas over the PLERWA (the fourdimensional world and the infinitedimensional universe resulting from it) developed here naturally do not claim, to explain any physical, chemical or biological problems, which run off in the threedimensional space and the fourdimensional spacetime and which we can experience and investigate consciously. Rather the framework shall be pointed out, within which all these things occur and happen, just so the realm of God.
The PLERWA is what humans call according to their religion or their customs heaven, paradise, eternity, Brahman, Pantheon, the other world, all (infinitely dimensional UNIVERSE) or nothing (zerodimensional ONLYTIME). Our threedimensional real universe is the nutshell in the fourdimensional, for us imaginary WORLD, of which Stephen Hawking^{17} speaks, if he quotes Shakespeare (Hamlet): God, I could be bound in a nutshell and count myself a king of infinite space.
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