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Limited Validity Of The Space-Time Concept
The following article is not up-to-date anymore. But many aspects still valid are considered to be worth mentioning,
All attempts to find a theory of everything seem to be doomed to failure. [1]  Many essentials in the three important areas, i.e. the galaxies, life on Earth, and the elementary particles, are not accessible to a reductionist analysis. Especially the widely accepted big bang model does not give any indication about how the initial conditions came about.

Extrapolation of the expansion of the universe backwards in time using general relativity yields a singularity for the density and temperature at a finite time in the past implicating the breakdown of general relativity. [2]

Following the ideas of emergence [3] the universe can be considered kind of a living organism, for which a basic pattern for self-organization has to be found. In such an unknown area, icono­clastic speculation may be an allowed heuristic principle although generally it should be rejected. This can be seen as equivalent to the technique of selecting survivors from a strongly mutated and mostly damaged specimen (e.g. of bacteria). It has been checked which basic laws and assumptions are really essentials and valid everywhere.
The main assumption in doubt seems to be the primary existence of space and time. According to the relativity theory of Einstein space and time are bent close to big masses which means they are not an allowed linear reference system there. In addition, the values, which both these parameter can take, are different in the three areas mentioned above by so many orders of magnitude that it is hardly possible to say those have the same space and time. Of course, these areas are not separate. But statements about space and time cannot refer to extreme areas like within supernovae or within elementary parti­cles. Elementary particles make up supernovae, and super­novae are the birthplace of elementary particles. But space and time cannot be attributed any relev­ance within supernovae, and equally not for the genuine inner process of generation of elementary parti­cles usually described as quantum leaps by delta functions. Measurements of space need a reference, which cannot be given there. Time can only be measured for separate intervals of stepwise transformations. We should accept that space and time are generated in the respective areas by the prevailing masses and energies. Especially in very extreme areas these can be assumed to be in a rough equilibrium according to the generally valid Einstein formula. It should be noted that by speaking about a ?respective area? and using the words ?here? and ?there? thereby is not meant again a not defined space, but only a set in the sense of a set theory which still has to be defined.
If such a set is conceived to be a preferable axiomatic concept to a space-time coordi­nate system, then the question has to be asked what are the elements of such sets. There is hardly other choice than to accept that quantum numbers will do this job. This is equivalent to taking numbers as basic elements in a mathematical set theory.
The ground state of a basic set can most simply be assumed to be without any quantum number. The most likely candidate for it is the dark energy [4] which may be considered as equivalent with a prim­ary matter. As no space-time is to be taken into account yet, the conflict between the two possibilities to understand dark energy either as constant (the fundamental con­stant) or as a variable quintessence is avoided.
A next axiomatic step has to be the requirement of a perturbation leading to the coming up of quantum numbers. A hint of what kind of perturbation this could be are the experiments about Bose­novae [5] although initially no specified bosonic matter might be involved. Stirring up the dark energy by such a perturbation means creating different compression and vortices, mathema­tically spoken divergence and rotation. These notions do not necessarily require the existence of space and time, but can be accounted for by quantum numbers different from zero. Compression means coming up of momentum, and vortices mean the introduction of spin (angular momentum), both to be described only by quantum numbers.
This, however, brings us into difficulties concerning the classical conservation laws for energy, momen­tum and angular momentum, because they are formulated for a space-time coordinate system only and seem to depend on it. But concerning a more general validity of these laws no major doubt is existing. It has to be asked whether these laws can be formulated in a new different way just starting from quantum numbers. Although this clearly seems necessary and possible, the task will not be tackled here.
More important seems to point out that the Pauli principle as a matter of fact means not only just for­bidding two identical fermionic states, but a separation between penetrable and not penetrable matter implicating conservation of mass-energy and for energy and particle mass separately in non-relativistic situations. The principle can only be formulated starting from quantum numbers, because space-time would not be defined at this point, but it can be grouped together with the clas­sical conservation laws. This means that basically all those four conservation laws are assumed to be of the same kind and should be formul­ated in a similar way by using quantum numbers and thereby making them indepen­dent of space-time and allowing for a unified system.
Anywhere in the world only transformations are observed, but not creation. This means conserva­tion of mass-energy. This term is used in the same way like space-time showing the parallel concept. Not a single experiment in all sciences has ever shown a genuine creation of anything. This argument is in striking contrast to the assumption of an initial hyper-dense state possibly implicating kind of creation. Something has to have existed initially, either kind of a super­galactic ocean or at least one collapsed universe.
A first quantum number being either 0 or 1 would bring the differentiation between bosonic and fermio­nic matter (though fermions usually are attributed a half integer quantum number). Bosonic matter without having space-time can be considered as a Bose-Einstein condensate (accepted as dark matter).  Neutralinos as in models of supersymmetry and Kaluza?Klein dark matter as in models of universal extra dimensions [6] would at the first glance be excluded, because both kinds of models are based on space-time. Nevertheless neutrino-like matter remains a candidate. For fermionic matter the validity of a Pauli principle has to be assumed leading to not penetrable matter. Particle mass could be understood as coming about by allowed superposition of spin wave functions leading to a sink (negative divergence) of energy, if without space-time there is no reflection. Over­lapping fermions have to stick together. Thus by assuming the Pauli principle, the formation of not penetrable particle mass could be understood as condensing fermionic matter.
Ongoing perturbation may lead to further quantized states of both bosonic and fermionic matter. This would mean interaction of fermionic matter with bosonic matter and of bosonic matter with fermionic matter, which can be interpreted as coming up of free energy and as coming up of excited particles.
Further quantum numbers can lead to further differentiation in the same way as assumed either in the standard model or in the inflation theory. First part of this differentiation has to be the generation of space-time, possibly with own quantum numbers. The explan­ation of the particle zoo and of all forces is not seen as a first rank goal in the elaboration of this hypothesis, because space-time now being available allows delegating the task to the standard model as before.
Genetic genes may be seen as the natural continuation of quantum numbers in areas like on Earth where energies or temperatures are too low to allow for switching of quantum numbers. The coming up of additional quantum numbers as well as of additional genes can be seen as characteristics of new generations. Essentially giving up space-time as a basic reference frame is equivalent to a fundamental change of paradigm leading to a kind of minimal physics.
The above arguments at the first glance may seem too speculative, as no experiments, mathematical formula and direct new proofs will be given. But it should be pointed out that essentially the assump­tion of a primordial space-time system, which in addition should be linear, was even more speculative, as all experiments using and evidently proving it are done here on Earth or at least within usual dimen­sions in the solar system, which means under very restricted conditions. All likelihood says that the validity of our usual space-time system is limited and not usable for a generalized view of the world. To ask for mathematical formulations often means to force people into accepting beforehand a general space-time system. This is avoided here for the time being in putting up this concept.
Probably it is not possible to select an axiomatic system without any speculation. Initially every choice of an axiomatic system has kind of a religious or at least philosophical aspect. These notions should however be taken in a very modern sense, meaning independence from any kind of authority, but com­prising the existential facts of Nature and the laws governing them. The deciding points should be con­sistence and simplicity, probably also beauty most likely meaning symmetry laws.
Of course, the space-time coordinate system is correct and very valuable for technical applications in a very wide sense as even for exploration of not very remote star systems. As shown for instance by the well known application of the GPS system applying the relativity theory it can been used, of course, outside of the Earth. This wide sense also includes the astonishingly exact standard model. But the more the basic assump­tions of linear space and time are violated, the more the describing theories need additional correcting para­meters, as for instance the cosmological constant. As a consequence these theories become compli­cated, maybe in an unnecessary way, as for instance the standard model with even more constants. Such concepts are valuable only for highly trained special­ists while we foster a general belief that basically Nature is simple.
This comes close to ancient ideas of the Chinese Taoism (modern form: Daoism), which sees the uni­verse as being in a constant process of re-creating itself. According to those ancient concepts every­thing that exists is a mere aspect of qi, which is said to be a diluted, indefi­nite potential, but condensed, it becomes life. [7]  Qi is seen as a perpetual trans­formation between its diluted and condensed state and thus has essential properties of a hypothe­ti­cal primary matter. The two diff­erent states of qi can nowadays be understood as bosons and fermions or energy and mass. In Tao­ism they are embodiments of the abstract entities of yin and yang, understood as two complimen­tary extremes that constantly play against and with each other and can not exist without the other one.
The assumption of quantum numbers as essential primary elements is in agreement with fractal cosmo­logy. Each coming up of a new quantum number means a new branching of a fractal generation into fractal ?children?, -  a process continuing in life processes with the evolution of new genes. Mathema­tically fractals are not differentiable, which means that they cannot be measured by space-time.
Historically at the beginning the similarity of planet movements with the shell structure of atoms was compared. Then similar statements about stars and nuclei were brought up. Now we are even able to state a similar correspondence between supernovae and elementary particles, hoping to come closer to a unified con­cept of the world.

[1]  Laughlin, Robert B. (2005). A Different Universe: Reinventing Physics from the Bottom Down. Basic Books. ISBN 978-0-465-03828-2.
[2]  Hawking, S.W.; Ellis, G.F.R. (1973). The Large-Scale Structure of Space-Time. Cambridge University Press. ISBN 0-521-20016-4.
[3]  Goldstein, Jeffrey (1999), Emergence as a Construct: History and Issues, Emergence: Complexity and Organization 1 (1): 49?72.
[4]  Trimble, V. (1987), Existence and nature of dark matter in the universe. Annual Review of Astronomy and Astrophysics 25: 425-472, Bibcode 1987ARA&A..25..42ST. doi:10.1146/ annurev.aa.25. 090187.002233.
[5]  van Putten, Maurice H. P. M., Pair condensates produced in bosenovae. Physics Letters A, 374, Issue 33, p. 3346-3347  doi: 10.1016/j.physleta.2010.06.020.
[6]  Bertone, G, Hooper, D., Silk, J. (2005), Particle dark matter: Evidence, candidates and constraints, Physics Reports 405 (5?6): 279?390. arXiv:hep-ph/0404175. Bibcode 2005PhR...405..279B. doi:10.1016/j.physrep.2004.08.031.
[7]  Robinet, Isabelle, Taoism: Growth of a Religion. (Stanford University Press, 1997; original French edition 1992). ISBN 0-8047-2839-9.   

Version dated  Oct. 26, 2012