Hox gene collinearity (HGC) is a multiscalar property of many animal phyla particularly important in embryogenesis. It relates entities and events occurring in Hox clusters inside the chromosome DNA and in embryonic tissues. These two entities differ in linear size by more than four orders of magnitude. HGC is observed as spatial collinearity (SC) where the Hox genes are located in the order (Hox1, Hox2, Hox3 …) along the 3’ to 5’ direction of DNA in the genome and a corresponding sequence of ontogenetic units (E1, E2, E3, …) located along the Anterior – Posterior axis of the embyo. Expression of Hox1 occurs in E1. Hox2 in E2, Hox3 in E3… Besides SC, a temporal collinearity (TC) has been also observed in many vertebrates. According to TC first is Hox1 expressed in E1, later is Hox2 expressed in E2, followed by Hox3 in E3,… Lately doubt has been raised whether TC really exists. A biophysical model (BM) was formulated and tested during the last twenty years. According to BM, physical forces are created which pull the Hox genes one after the other driving them to a transcription factory domain where they are transcribed. The existing experiments support this BM description. Symmetry is a physical-mathematical property of Matter that was explored in depth by Noether who formulated a ground-breaking theory that applies to all sizes of Matter. This theory applied to Biology can explain the origin of HGC as applied not only to animals developing along the A/P axis but also to animals with circular symmetry.

This paper discovers that current variational principle and Noether theorem for different physics systems with (in)finite freedom systems have missed the double extremum processes of the general extremum functional that both is deduced by variational principle and is necessarily taken in deducing all the physics laws, but these have not been corrected for over a century since Noether's proposing her famous theorem, which result in the crisis deducing relevant mathematical laws and all physics laws. This paper discovers there is the hidden logic cycle that one assumes Euler-Lagrange equations, and then he finally deduces Euler-Lagrange equations via the equivalent relation in the whole processes in all relevant current references. This paper corrects the current key mistakes that when physics systems choose the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current articles, reviews and (text)books. The real physics should be after choosing the variational extreme values of physics systems, the general extremum functional of the physics systems needs to further choose the minimum absolute extremum zero of the general extremum functional, otherwise, the appearing processes of physics systems are still virtual processes. Using the double extremum processes of the general extremum functionals, the crisis and the hidden logic cycle in current variational principle and current Noether theorem are solved. Furthermore, the new mathematical and physical double extremum processes and their new mathematical pictures and physics for (in)finite freedom systems are discovered. This paper gives both general variational principle and general Noether theorem as well as their classical and quantum new physics, which would rewrite all relevant current different branches of science, as key tools of studying and processing them.

Chronology unprotected mechanisms are considered with a very low gravitational polarization to make the wormhole traversal with positive energy density everywhere. No need of exotic matter has been considered with the assumption of the Einstein-Dirac-Maxwell Fields, encountering above the non-zero stress-energy-momentum tensor through spacelike hypersurfaces by a hyperbolic coordinate shift.

The time interval description is a natural way to introduce finite intervals, like finite time intervals. This approach depends on results for radiation propagation from star sources, where properties relate to a propagation surface, which is finite for every realistic event and measurement. In contrast the usual vector approach like for Newton’s laws depends on introducing an infinite coordinate system. A time interval only approach necessarily has to start from scratch. Properties for time intervals have to be defined with time intervals. Where the first parts of this paper are devoted to time interval set properties, in the discussion part these are applied to quantities and measurements within astronomy. The introduction provides a survey of results.

Abstract: Hox gene clusters are crucial in Embryogenesis. It was observed that some Hox genes were located in order along the telomeric to centromeric direction of the DNA sequence: Hox1, Hox2, Hox3…. These genes were expressed in the same order in the ontogenetic units of the Drosophila embryo along the Anterior-Posterior axis. The two entities (genome and embryo) differ significantly in linear size and in-between distance. This strange phenomenon was named Spatial Collinearity (SP). Later, it was observed that, particularly in the Vertebrates, a Temporal Collinearity (TC) coexists: first is Hox1 expressed, later Hox2 and even later Hox3,…,. Hox clusters are irreversibly elongated along the force direction. According to a Biophysical Model (BM), pulling forces act at the anterior end of the cluster while a cluster fastening applies at the posterior end. During Evolution, the elongated Hox clusters are broken at variable lengths thus split clusters may be created. An Empirical Rule was formulated distinguishing development due to a complete Hox cluster from development due to split Hox clusters. BM can explain this Empirical Rule. In an accidental mutation where the cluster fastening is dismantled, a minimal pulling force can automatically shift the cluster inside the Hox activation domain. This cluster translocation can probably explain the absence of temporal collinearity in Drosophila.

Hox gene clusters are crucial in Embryogenesis. It was observed that some Hox genes are located in order along the telomeric to centromeric direction of the DNA sequence: Hox1, Hox2, Hox3…. These genes are expressed in the same order in the ontogenetic units of the Drosophila embryo along the Anterior-Posterior axis. The two entities (genome and embryo) differ significantly in linear size and in-between distance. This strange phenomenon was named Spatial Collinearity (SP). Later, it was observed that, particularly in the Vertebrates, a Temporal Collinearity (TC) coexists: first is Hox1 expressed, later Hox2 and even later Hox3,…,. According to a Biophysical Model (BM), pulling forces act at the anterior end of the cluster while a cluster fastening applies at the posterior end. Hox clusters are irreversibly elongated along the force direction. During Evolution, the elongated Hox clusters are broken at variable lengths thus split clusters may be created. An Empirical Rule was formulated distinguishing development due to a complete Hox cluster from development due to split Hox clusters. BM can ‘explain’ this Empirical Rule. In a spontaneous mutation where the cluster fastening is dismantled, a minimal pulling force can automatically shift the cluster inside the Hox activation domain. This cluster translocation can probably explain the absence of Temporal Collinearity in Drosophila.

This paper discovers that current canonical variational principle and canonical Noether theorem of (in)finite freedom systems for different physics systems have neglected doublet extreme value processes of the general extreme value functional that both is derived by variational principle and is necessarily be taken in deriving all ( quantum ) physics laws in phase space, but which have not been done for over one century since Noether's showing her distinguished theorem, which lead to the crisis deriving all (quantum) physics laws (necessary) in phase space. We discover there is the hidden logic cycle that people assume canonical equations, and then they finally deduce canonical equations by the equivalent relation in the whole processes in all current references. We correct the current key mistake concepts that when physics systems take the variational extreme values, the appearing processes of the physics systems are real physics processes, otherwise, are virtual processes in all current references. The real physics should be what after taking the physics systems' variational extreme values, the physics systems' general extremum functional needs to further take the general extremum functional's minimum absolute extremum zero, otherwise, the appearing processes of physics systems still are virtual processes. Conservation current equations and conservation currents, in phase space, of general canonical variational principle and general canonical Noether theorem are, respectively, deduced for the first time. Using the general extremum functionals' doublet extreme value processes, the hidden logic cycle and the crisis in current canonical variational principle and current canonical Noether theorem are solved. Consequently, the new mathematical pictures, classical and quantum new physics in phase space and the new mathematical and physical doublet extremum processes for (in)finite freedom systems are discovered. General canonical variational principle and general canonical Noether theorem naturally are given, which would rewrite all the different sciences in phase space, as key tools of studying and dealing with them.