FOUNDATIONS FOR A NEW BASIC
COSMOS-MODEL. EINSTEIN – ONLY PART OF A WHOLE GERD HELMECKE
E-mail: dok-helmecke@t-online.de
Lotharstr. 65, D-47057 Duisburg, Germany E-mail: herkenrath@math.uni-duisburg.de
1. INTRODUCTION If the universe as a whole is modeled and studied, the principal problem arises that it cannot be included into a larger model or system, about which something as for structure, laws or evolution is known. The various limitations of perception of mankind and individual human beings reinforce the difficulties of creating such a model. One has to extrapolate models and laws which are appropriate and valid for “subsystems” to design a maximal model for the universe as a whole. The first question is which models and laws are appropriate for such an extrapolation, the next one is how the extrapolation should be performed. In science the extrapolation of models and laws from a domain, in which their validity can be assured either by experience or by experiments, to a much larger domain, generally leads to delicate questions as to its admissibility. Since mathematics offers the keys to deal with science and to explain natural reality, extrapolations are performed via or by means of mathematical models. In general these models can be extrapolated to any extent or “up to infinity” according to the rules of mathematics. But if one wants to learn about natural reality, the question remains, whether an extrapolated mathematical model corresponds to a phenomenon existing in natural reality or not, i.e. whether a mathematical extrapolation is valid or admissible with regard to natural reality. Especially in the context of “infinity”, i.e. “infinitely large or small” (infinitesimal magnitudes e.g.), the problems of extrapolation reach their peak. With respect to the problem of admissible extrapolations or of limited admissibility of theoretical or mathematical models and laws, we point out three basic reasons for inadmissible extrapolation: First, the validity of a model may be restricted with respect to various aspects of the phenomenon to be modeled, i.e. some aspects are modeled appropriately, others not. As a classical example we mention the models for light, wave or particle. Another example is induced by the stochastic process of Brownian motion which represents the usual mathematical model for the motion of a small particle in a liquid. As is well-known, all paths of this process are almost everywhere non-differentiable, hence a velocity of the particle cannot be derived from this model. Of course, the velocity of the particle can be explained by means of a different model. Second, the right, true model respectively law can perhaps not be determined by observation or experiment because of the natural restrictions in the perception of human beings. The restrictions are either caused by the lack of appropriate technical instruments for observation or experimentation, or they are brought about by the observable range of the corresponding phenomena. Starting from a smaller range of observation, which is under control, and going to a larger one, there may be a change in the structure of the model or law. Up to some time in the past mankind had not been able to find out the laws of relativistic mechanics, but only those of “classical” mechanics. As further examples we mention some physicists’ doubt in our days that the well-known law of gravitation is correct over any wide range in the universe and Newton's second law is correct under any circumstances, cf. Milgrom (2002). Maybe the true laws applicable to the whole universe have not been found up to now, because of our limited capacity of observation. Third, necessary parameters for the evaluation or application of a certain law of nature possibly are not measured correctly. For example the law of gravitation in its known form may induce misleadings, because distances are not measured correctly. If inadmissible extrapolations are performed, they will provoke misleadings, contradictions, bizarre phenomena. On the level of mathematical models there appear so-called singularities, which in some sense represent the concentrated rest of unaccountable or contradictory facts and insufficiencies. Again, we mention some examples demonstrating these effects: The seeming possibility of time travelling (in the strict sense); a statement like “The effect precedes the cause”; the phenomenon of Dark Matter which is possibly caused by applying incorrectly the known law of gravitation or a false law; a statement like “There is a multitude of universes parallel to ours” without providing any empirical hint to that. With respect to the last statement the term “a multitude of universes” seems to be contradictory in itself already from the linguistic point of view. If one wants to build a model for the universe
as a whole, in spite of the problems described, we propose to look out for
general or basic principles, which are universally valid in nature. Therefore
we are going to speak of foundations for a basic cosmos-model (abbreviated to
BCM). We propose three principles or - first, a universally observable law for structuring and restructuring natural reality; - second, a principle for ordering events in natural reality, a procedure that is necessary, if one wants to do and develop science claiming reliability; - third, an extension of the existing dimensionality, a mean that is necessary because of the insufficiencies and incompleteness of the existing models. The 2. FIRST COSMIC LAW: CRITICAL STABILITY Every system, as for example any accumulation or
condensation of masses, is subject to the natural law of “critical stability”
respectively instability. This phenomenon of nature appears because of the
following reason: At least one influence factor associated to the system is always
active, modeled by a metric variable Therefore instability represents a mechanism of
a permanent remodelling of natural reality including the universe as a whole.
This natural phenomenon of instability may be formulated positively as the
phenomenon of limited or critical stability. At the critical upper bound The ability of abstract thinking allows man to
deal with the term “infinity” in mathematics and physics, although our world of
experience is finite. As conclusion we formalize the first The function where Taking into account this normed scale, we take
the exponential function to represent the instability With regard to (in)stability each system depends
on its internal state and external conditions which influence the system. The
internal state may be characterized by the sort of matter and the structure of
the system; external conditions may be for example pressure, temperature or
gravitational effects. The dependence of instability on internal and external
conditions refers to the critical bounds With regard to the above considerations the
natural law of instability or the first if if the instability Stability Instability as a term should be considered analogously to terms like (mathematical) entropy or probability. Within corresponding contexts terms like health or explosivity have a similar nature like instability. According to the above formula instability is a dimensionless term like those cited before. The natural phenomenon of instability manifests in different effects. In a concrete context instability therefore must
be represented by an associated and apt measurable characteristic A rule of measuring As an example one may consider the measurable
characteristic Of course the constants In microcosmos the law of instability is active
for example in the accumulation of nuclear substances in an atom. Here the atom
represents the system; the influence factors which cause the instability are
the mass of the nucleus in combination with the constellation of the charge
distribution in the atom. For instable elements exist already below the
critical nuclear mass because of their constellation of the charge
distribution. Whether 238 or 266 is taken as critical upper bound for the
nuclear mass depends on the context, that is, whether only natural elements are
considered or synthetic elements as well. It is obvious that an arbitrary
accumulation of the nuclear mass is impossible. The finding and definition of
one single valid metric influence variable Next we show that the law of decay of
radioactive matter presents an example of the law of instability, respectively
the measuring of instability according to that law. Any radioactive element has
a characteristic constant Therefore the
instability of this element is Under normed conditions the constants where Also in mesocosmos, i.e. within the range of nature which is directly perceptible by man we find the validity of the law of instability everywhere: - The size of buildings and technical constructions as systems in the above sense, is limited owing to the laws of statics as to internal conditions, and because of interactions of the system with its environment as to the laws of mechanics. - Similarly, the growth of plants and living beings as systems in the above sense is limited, where the internal conditions are determined by the potential and abilities of the “system” with respect to constitution and structure; the external conditions are determined by their environment in form of light, air, water, etc. - Phenomena like the turning over of water in a lake caused by a lack of oxygene, the collapse of the circulation in a human being caused by increasing stress factors could be modeled, comprehended and finally measured by applying the law of instability. In a quite general context the failure
probability of a technical system up to time Here the measured instability is a probability and therefore without dimension. We mention the size of stars as example in
macrocosmos, i.e. the system is represented by a star, its instability is
caused by the accumulation of matter and perhaps measured by means of its
reciprocal life-time. In this case the critical upper bounds With respect to astrophysics and cosmology the
consequences of the first - Also Black Holes have a limited stability and cannot absorb any amount of mass. -- The whole mass of the universe itself is not stable. Since the physics of condensed matter in Black
Holes, even more in the range of the total mass of the universe is not
developed enough, one is not capable of knowing the critical upper bound This law can be found everywhere in natural reality, therefore it is an actual principle for the structuring of masses, respectively their interaction, and one of its consequences is that any accumulation of masses is limited. 3. SECOND COSMIC LAW: THE PRINCIPLE OF EVOLUTIONARY CAUSALITY Regarding the universe under conventional scientific aspects, one has to deal with the ideas of space and time. Due to Einstein we know that time depends on the velocity of a reference system and therefore is a relative term. If man, in searching for perception, wants to establish a concept of order within the totality of happenings in nature, if he claims for an absolute lawfulness or a universal principle of order, such a principle cannot be based on time, as a relative term cannot be used to represent an absolute principle. In this context Kronheimer and Penrose (1967) for example introduce causal spaces endowed with causal relations to distinguish between causal and chronological order. The essential physical components of the
universe are space, energy and matter which are linked by interactions. We
state as universal law for all happenings in the cosmos, i.e. as second
This is not the classical strong principle of causality of philosophy and physics. Randomness is admitted as cause, chaotic phenomena are explained by uncertainty because of inobservability or by random effects. In particular determinism of the happenings is not implied. The principle of Evolutionary Causality, however, implies: What has happened cannot be made reversible as event nor altered. An event remains forever with all its consequences and interactions. Therefore, in particular, time travelling (in the strict sense), i.e. with influence on and change of former events, is not possible. This principle suits all laws of nature which have the structure “if-then”, i.e. such laws which describe a certain effect provided a certain condition in form of an active cause is fulfilled. We regard some scientists’ statements that in the range of microcosmos the principle of causality should be questioned in the sense that the cause precedes the effect (cf. Delbrück 1986) as misinterpretation. The reason for their interpretation is that not all causes are taken into account in the design of the experiment or by the technique of measurement or that randomness is not admitted as cause. Particularly, in such a context the principle of Evolutionary Causality should be applied as directrix for a consistent modelling and explanation of the phenomena. We design the ordered scale of causality to formalize the above principle. With respect to this scale one is able to state “The cause precedes its effect”. All events of the structure “cause-effect” are “mapped” on this scale. The causality-scale is modeled by a set The elements or points on the scale In principle all events can be located on The causality-scale models the principle of
Evolutionary Causality in the sense that for all events of the type
“cause-effect” the point The location of events on We explain a time measurement as a function Since to man causalities and effects are not
always perceivable, for practical purposes an established order for chains of
events with respect to a time-scale is installed. For a wide range of the
reality that we are able to perceive, the time-scale is equivalent with the
causality-scale. But since time is a relative magnitude, its scale may be
biased with respect to the causality-scale, because of an inadequate The principle of Evolutionary Causality is absolute. It is neither conditioned by a medium like light, nor is it conditioned by the velocity of light at all. Should higher velocities than the one of light ever be detected in the future, this principle requires no alternation nor correction, whereas in Einstein’s model with velocities exceeding the one of light, phenomena may appear, for which the effect seems to precede the cause. 4. THIRD COSMIC LAW: THE NUMBER OF DIMENSIONS OF THE UNIVERSE IS LARGER THAN 4 The universe is the complete totality of natural reality, that means the whole where this reality is located and takes place. It presents the space for matter and energy, and the scenery on which events may take place. A BCM should offer the facility to describe and analyze the universe with regard to its state and evolution within sciences, such as physics, astrophysics or cosmology. Such a model must have an absolute “nature” and not a relative one. That means it must be separated from reference systems and any restricting subsystems of the universe in order not to narrow, shorten or condition perception, facilities of measurement, knowledge and understanding. For this purpose up to now spacetime models have been designed like the four-dimensional spacetime continuum of relativistic physics, which is widely regarded and accepted as a “standard model”. We think that this model is not sufficient as a BCM as explained above, because of the following reasons: - time is a relative term, it lacks the absolute nature as principle of order for processes, - 3 dimensions of space are too few to make room for all items which exist in natural reality. This idea itself is not new. Kaluza (1921) and
Klein (1926) dealt with a higher-dimensional model. In the context of cosmology
Liebscher (1994, chapter 9) takes into consideration a model with more than 3
dimensions for representing space. For more than 20 years a group of physicists
has been working with higher-dimensional models aiming at explaining the
different physical interactions within a unified theory (GUT, Grand Unified
Theory), see Breuer (1993). Since the eighties the champions of the so-called
string-theory have been assuming more than 3 space-dimensions for their theory,
for instance a 10-dimensional spacetime. In his remarkable book and approaches to models with more than 3
space-dimensions. How many space-dimensions should be considered, remains an
open question to him, too. That depends on the phenomena to be studied. The
totality of those has not been known up to now. We want to draw the important
conclusion that As a consequence we state as third Essential for this statement are the comprehension of, respectively the requirements for the concept of dimension. As characteristics we state: - dimensions induce an ordering structure in our range of cognition, - they are necessary for localizing and measurement, - they do not depend on measurements in different reference systems, like e. g. on velocity, but are invariants given by nature. Considering the number of dimensions which is necessary for a BCM we claim: - The BCM must be endowed with enough dimensions to represent masses and physical interactions. It must be closed in the sense that masses cannot disappear from the model “into some nothing”, neither can they coming “from the nothing” enter the model. The BCM shall include the whole natural reality. - If one or more of the dimensions given by nature are omitted when designing a BCM, possibilities of comprehending, representing and investigating natural reality are lost, the view is narrowed. One might encounter contradictions in a narrowed model. Based on this comprehension of the concept of dimension, we need more than 4 dimensions for the equipment of the BCM. We are going to explain this approach in detail, as follows: First, there is no doubt about the 3 dimensions of the space, which we can directly see. But time does not satisfy the requirements of a dimension. Time is not apt as an ordering principle, since it is relative, i.e. time differs depending on a velocity in space. Moreover time is bound by space, as already Augustinus stated. Instead of time we integrate the causality-scale as dimension into the BCM. As explained above, time is a map of this scale which depends on a reference system. Therefore time can appear as dimension in a “relative" model, which represents a section of natural reality like in the 4-dimensional spacetime continuum, however not in a BCM, that means in a model of absolute nature. The relativistic 4-dimensional spacetime continuum represents a “projection” of the BCM, which is appropriate for modelling efficiently an important, large section of natural reality. But it is possible that 3-dimensional objects are transformed by a physical interaction in such a way, that they “lose” their dimensionality. As an example we mention the transformation of matter into energy. According to our requirements for the concept of dimension, respectively the number of dimensions, the question arises about how to conceive such a phenomenon with respect to dimensionality. In a system with 3 dimensions for space and 1 for time energy does not have a dimension, since one cannot represent or locate it within those dimensions. As energies undoubtedly exist in nature, they must be conceived in one or more additional dimensions according to our requirements to dimensionality, otherwise the BCM would not be complete. If one does not admit an additional new dimension for energies, 3-dimensional energy would disappear into nothing, as it cannot be represented in the 4-dimensional spacetime either. 5. CONCLUSIONS As has already been indicated, we consider these
three The first The second The third The question of the dimensionality of the universe as reality in itself is of eminent importance, as measurements of distances for instance or of volumes always depend on the dimension of the space in which the process of measuring takes place. So the 3-dimensional unit cube has the 4-dimensional volume zero. The shortest distance between two points depends on the space structure, which is available for the process of measuring, and thus it particularly depends on the dimensions of this space. The shortest distance between two points on a 3-dimensional sphere for example is shorter than the shortest distance between these points on the 2-dimensional surface of the sphere. The true distances between two masses may differ from the actually measurable distances in a 3-dimensional space-structure because of a higher dimensionality of natural reality. This fact can cause misleadings when applying the law of gravitation in so far, as masses are measured incorrectly on the basis of measured forces of attraction. Based upon this, a new aspect of the phenomenon of Dark Matter might be revealed. A higher-dimensional universe with corresponding higher-dimensional masses offers interesting perspectives for the use of 3-dimensional infinitesimal masses as a model, the same applies to argumentations in the physics of elementary particles or in cosmology in the context of the big-bang. An “infinitesimal something” with respect to 3 dimensions may be a 4-dimensional object. Provided that the big-bang takes place in a reality of a higher dimension than the conventional one, the extension of events is not subject to the conventional space-time-structure. This leads to the conclusion that masses and energies which exist in reality do not have to be detectable in the 3 space-dimensions which we are able to ascertain. Based upon this a new aspect of the phenomenon of Dark Matter is revealed too. The expansion of the matter which was produced by the big-bang may also take place inhomogeneously or incontinuously through the visible space, since deviations through additional dimensions might be possible. The additional dimensions of an Of course, it is true that one only finds what one is looking for. We hope that our study will encourage physicists, astronomers, cosmologists to venture into unknown areas. REFERENCES Breuer, R. (Ed.): 1993, Delbrück, M.: 1986, Fahr, H. J.: 1992, Fahr, H. J.: 1995, Kaku, M.: 1995, Kaler, J. B.: 2000, Kaluza, T.: 1921, Klein, O.: 1926, Kronheimer, E. H., Penrose, R.: 1967, Proc.
Cambridge Philosoph. Soc., Liebscher, D. E.: 1994, Milgrom, M.: 2002, |