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.

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.

This paper gives both a general canonical quantum gravity theory and the general canonical quantum gravity theories of the Universe and general black hole, and discovers the relations reflecting symmetric properties of the standard nonlinear gravitational Lagrangian, which are not relevant to any concrete metric models. This paper concretely shows the general commutation relations of the general gravitational field operators and their zeroth, first, second and third style, respectively, of high order canonical momentum operators for the general nonlinear system of the standard gravitational Lagrangian, and then has finished all the four styles of the canonical quantization of the standard gravity.

This paper gives solutions to puzzles of double Wheeler’s delayed choice experiments, a photon’s passing two paths simultaneously and wave collapse velocity measure, and shows new quantum control, new quantum oscillation and new controlling photon oscillator (that can be arranged in quantum computer and quantum network as their classical correspondences) in experiments. Furthermore, this paper obtains the measured attractive state and the new useful key technology of altering state’s evolving paths for quantum systems. We discover the reason and the technological way for the present changes the past, further show their feasible experiments of new quantum control, new quantum oscillation and new quantum oscillator. Finally, this paper achieves the collapse response time t of wave, further concretely deduces the measured collapse velocity of quantum system. In the past, the collapse velocity cannot be objectively deduced and experimentally measured.

This paper derives measurement and identical principles, then makes the two principles into measurement and identical theorems of quantum mechanics, plus the three theorems derived earlier, we deduce the axiom system of current quantum mechanics, the general quantum theory no axiom presumptions not only solves the crisis to understand in current quantum mechanics, but also obtains new discoveries, e.g., discovers the velocities of quantum collapse and entanglement are instantaneously infinitely large. We deduce the general Schrȍdinger equation of any n particles from two aspects, and the wave function not only has particle properties of the complex square root state vector of the classical probability density of any n particles, but also has the plane wave properties of any n particles. Thus, the current crisis of the dispute about the origin of wave- particle duality of any n microscopic particles is solved. We display the classical locality and quantum non-locality for any n particle system, show entanglement origins, and discover not only any n-particle wave function system has the original, superposition and across entanglements, but also the entanglements are of interactions preserving conservation or correlation, three kinds of entanglements directly give lots of entanglement sources. This paper discovers, one of two pillars of modern physics, quantum mechanics of any n particle system is a generalization ( mechanics ) theory of the complex square root ( of real density function ) of classical statistical mechanics, any n particle system’s quantum mechanics of being just a generalization theory of the complex square root of classical statistical mechanics is both a revolutionary discovery and key new physics, which are influencing people’s philosophical thinking for modern physics, solve all the crisises in current quantum theories, quantum information and so on, and make quantum theory have scientific solid foundations checked, no basic axiom presumption and no all quantum strange incomprehensible properties, because classical statistical mechanics and its complex square root have scientific solid foundations checked. Thus, all current studies on various entanglements and their uses to quantum computer, quantum information and so on must be further updated and classified by the new entanglements. This and our early papers derive quantum physics, solve all crisises of basses of quantum mechanics, e.g., wave-particle duality & the first quantization origins, quantum nonlocality, entanglement origins & classifications, wave collapse and so on.Key words: quantum mechanics, operator, basic presumptions, wave-particle duality, principle of measurement, identical principle, superposition principle of states, entanglement origin, quantum communication, wave collapse, classical statistical mechanics, classical mechanics

Density distribution function of classical statistical mechanics is generally generalized as a product of a general complex function and its complex Hermitian conjugate function, and the average of classical statistical mechanics is generalized as the average of the quantum mechanics. Furthermore, this paper derives three ones of the five axiom presumptions of quantum mechanics, e.g., deduces Schrȍdinger equation by two general ways, makes the three axiom presumptions into three theorems of quantum mechanics, not only solves the crisis to hard understand, but also gets new theories and new discoveries, e.g., this paper solves the crisis of the origin of the wave-particle duality, derives operators, eigenvalues and eigenstates, deduces commutation relations for coordinate and momentum as well as the time and energy, and discovers quantum mechanics is just a generalization ( mechanics ) theory of the complex square root of ( real density function of ) classical statistical mechanics. Quantum mechanics being just a generalization theory of the complex square root of classical statistical mechanics is both new physics and revolutionary discovery, which are affecting people’s deep philosophical thinking for modern physics development, solve all the crisises of quantum mechanics, quantum information and so on, and make quantum mechanics have scientific solid bases being checked and both no basic axiom presumption and no all the quantum strange incomprehensible properties, because classical statistical mechanics and the complex square root of classical statistical mechanics have the scientific solid bases being checked. In addition, this paper discovers the reason no taking the time derivative of space coordinates in Schrȍdinger equation. Therefore, this paper gives solution to the crisis of the first quantization origin, and mainly deduces quantum physics no all the quantum current strange incomprehensible properties.

This paper uncovers that quantum uncertain principle makes the single particle with global property have no certain path, and then wave of quantum particle can simultaneously do pass the double slits. The two subwaves after passing Young’s double slits are entanglement, they may form interference of subwaves. Consequently, we find a kind of quantum probabilistic entanglements with Wheeler's delayed choice. Quantum particles such as photons, electrons, neutrons, protons etc mean that wave of the quantum particle can simultaneously do pass through Young's double slits, rather than individual quantum particle may pass through Young's double slits at the same time. When considering wave property, we cannot consider particle property (Just as in the photoelectric effect, considering the particle nature of the system, people cannot consider wave property, otherwise the photoelectric effect cannot appear). Therefore, this paper discovers that the ability of single photon to hit electrons out in photoelectric effect is complementarily equivalent to the ability of wave of the single photon to simultaneously pass through Young's double slits in wave-particle duality. Objective criteria for distinguishing classical and quantum particles are discovered and objectively give the applicable realm of quantum mechanics for the first time. The crisis of the single particle’s simultaneously passing through Young's double slits, which has been plaguing physicists in the whole world up to now for decades, is solved, in which the studies are classified as classical and quantum particles, the classical particle and quantum particle wave cannot and can pass the Young’s slits, respectively. This paper discovers both the new physics mechanism of passing the double slits of the wave with the amplitude of 4-dimensional momentum representation wave function reflecting particle nature and the principle of self-adaptive emergence of wave-particle duality, and then using the principle, this paper gives both direct explanations to the current experiments and new predictions of new some experiments for wave-particle duality. All the deduced results here are consistent with all relevant physics experiments.