Nature – limited concepts
Nature – limited concepts
Attempts to find a theory of everything seem to be doomed to failure.
Many essentials in the three main 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. 
Following ideas of emergence  the universe can be considered kind of a living organism, for which a basic pattern for self-organization has to be found. Heuristic principles like any kind of thinking may be allowed or even iconoclastic speculation, which could 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 at any point.
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 putting doubt on any linear reference system. In addition, the values, which both these parameter can take, are be 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 can not refer with certainty to extreme areas like within super- or even kilonovae or within elementary particles or even further substructures. Elementary particles make up all kinds of novae, which can be considered as birthplaces of elementary particles. But space and time cannot be attributed any relevance within those novae, and equally not for the genuine inner process of generation of elementary particles often described as quantum leaps.
We could accept that space and time are generated in respective areas by the prevailing masses and energies. For any preferable axiomatic concept to a space-time coordinate system, quantum numbers will have to do a share of this job. This is equivalent to taking numbers as basic elements in purely mathematical set theories.
A next axiomatic step has to be the requirement of a perturbation leading to the coming up of quantum numbers. Compression means coming up of momentum, and vortices mean the introduction of angular momentum, spin or transformations needing quantum numbers for description.
This, however, brings us into difficulties concerning the classical conservation laws for energy, momentum and angular momentum, because they are mostly formulated for a space-time coordinate system only and seem to depend on it. Concerning a more general validity of these laws doubts are justified. It could be asked whether these laws can be formulated in a new different way just starting from quantum numbers. 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 assumption like 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.
Ongoing perturbation may lead to further quantized states. 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 such a hypothesis, because space-time then being available allows delegating the task to the quite well accepted 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, may be 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. To ask for mathematical formulations often means to force people into accepting beforehand a general space-time system.
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 
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 making difficult measurements by space-time.
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© Copyright ans all rights Hans J. Unsoeld, Bangkok 2012 and Berlin 2018
Updated April 21, 2018