QUANTUM SPACE IN THE CONTEXT OF PHILOSOPHY.

The wave function, as the hardcore of quantum mechanics, consists in the quantum space. Consequently, the investigation for quantum space becomes an important part in both physics and philosophy, as well as the core problem in the philosophy of quantum mechanics. The speciality of quantum space is also the logical foundation of quantum mechanics and plays a determinant role. In this paper, we consider the quantum space as the primary entity and discuss its properties in the context of philosophy. Finally, we discuss the necessity of road to gravitation from the quantum space.


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conceptual system and structure, we have different description and knowledge about the quantum entity. Therefore, the quantum space, as a fundamental entity, displays relative uncertainty.
We resort to physical language and clarify our knowledge about the quantum space, which naturally get in the linguistic problems of significance, referent, and presupposition, when illustrating the formal system of quantum mechanics. In addition, the intentional action of observers is also involved. The way of correlation of the intentionality problem and physical language to the quantum space depends on the context of given conceptual system. For example, whether the quantum space is described by wave function or both wave function and particles depends on the intention of the interpreter. Consequently, the quantum space presents the intentional characteristic.
In this paper, we use the philosophical context and analyze the structure and dimensions of the quantum space. Finally, we demonstrate its relations to gravitation and its road to quantum gravity.
Structure of Quantum Space:-Regardless of one-particle or multi-particles, the wave function itself, as the unity of entity and structure, reflects the potential reality with entity structure. The reason why the one-particle wave function has the fruitful and latent structures is that it can be expanded as different and complete sub-wave functions, i.e. the one-particle wave function is divisible and can be decomposed according to the complete basis. The multi-particle wave function can manifest as entangled quantum entities by the causal interactions, and the sub-states in the entangling state forms the entangled structure. Therefore, the complexity of quantum system causes the complex structures of the quantum space. Confined in the context of quantum mechanics, the limitation of structure of quantum space is also the limitation of complexity of quantum system itself. The wave function, describing the quantum world, particles, and the interactions, obeys the Schr ̈dinger equation, which is the foundation of linguistic form of quantum mechanics.
Because of the wave-particle duality of the quantum objects and Bohr"s principle of complementarity, the quantum space and classical space should be complementary. The classical concept can just describe part of the physical picture and different levels of objects. The characteristic of underdeterminism of quantum phenomena is described by classical concept, and the quantum state is the symbolic representation for the quantum phenomena consisting of complementary classical pictures. Both the 3-dimensional observed space and the quantum space are fundamental spaces, the equality becomes the reality in the context of decoherence [1].
Because the measured state of quantum objects depends on the consciousness of observers, the structure of quantum space actually depends on how to interpret it, which describes the characteristics of the quantum system. However, the interpreting subjects have no any freedom both to choose the state vector basis and to measure the corresponding objects. The Hamiltonian, describing the interactions in quantum space that must have corresponding one in the 3dimensional ordinary space, can be independent of the measuring environment and context. As a result, the structure of 3-dimensional space reflects the structure of quantum space [2].
The structure of quantum space relates closely to itself and the interactions between the embedded presupposition bodies. Different interactions between either the particles or particle and wave function result in different symmetries, which thus bring about the structures of quantum space. In this sense, the choice of structure of quantum space depends on the intentions of the subjects. Once choosing the given context to describe and interpret the quantum space, different structure is just the mathematical description for the corresponding physical reality. Therefore, they are the same in observations.

Dimension of Quantum Space:-
The dimension of quantum space, as part of the quantum space, has obviously semantic multidimensionality, i.e. 3dimension or 3N-dimension. According to the complementary principle, the quantum mechanics just can describe the results of experiments, instead of the real world. However, the experimental results just can present and describe the phenomena in the 3-dimensional ordinary space [3]. According to Erwin Schr ̈dinger, the wave function evolves in the 3N-dimensional configuration space for a N-particles system [4], which just represents the quantum state of the N-particles system and gives us to the knowledge of the eigen-state of observables describing the system [5]. Therefore, the wave function is just the mathematical tool used to describe the quantum characteristics of particles 948 on the configuration space. However, It subsequently claimed, according to the wave function substantialism, that the wave function is the wave field in 3N-dimensional configuration space, which locates in the 3N-dimensional space, instead of the 3-dimensional ordinary space [6]. We cannot observe the realistic level of the 3N-dimensional configuration space [7], and it is the intrinsic dynamics that leads us to the understanding for the fundamental properties of the quantum world, which subsequently determine the quantum space and its structure [8,9].
It can be found that the different understanding for dimension of quantum space depends on how to understand the quantum theory. If we stand on the point of scientific experiment, the 3-dimensional ordinary space keeps the local causality and thus is appropriate and logical. If we treat the quantum space as a container, it is the secondary concept and the emergent result of some more fundamental objects. The dimension of quantum space with multidimensionality, which reflects the overall structure of the quantum space, as the trinity of "object-relationproperty", has complexity in the aspect of epistemology. The complexity results from four pairs of contradiction, i.e. the contradiction between certainty and uncertainty, the contradiction between entity and tool, the contradiction between locality and non-locality, and the contradiction between logic and intuition.
It is the unobservability of the structure of quantum space that leads to the contextual dependence for the interpretation of dimension of quantum space. For all kinds of the interpretations, we should understand and analyze them according to given boundary condition and presuppose the boundary condition, i.e. correlated context. Different interpretations for quantum space and the structural relation determine the different semantic borders. In order to avoid the complexity, we should remove the complexity and multidimensionality on the level of epistemology.

Road to Quantum Gravity:-
When we discuss the structure of quantum space, it naturally involves the geometry of space-time and thus the effects of gravitation, which is described by Einstein"s general relativity. Whether we consider the wave function as particles or fields, it carries energy and momentum, which will cause the space-time bending. While the curved space-time, in turn, has influence on the motion of the particles and fields in it, and then the evolution of wave function. Consequently, we cannot neglect the interaction between the structures of quantum space and their gravitation and should seek for the unification between quantum theory and gravitation.
In order to unify the standard quantum mechanics and gravitation, i.e. general relativity, we need to apply the canonical quantization, i.e. Hamiltonian form, to general relativity and then quantize the gravitation by usual method, which creates the canonical quantum gravity. In quantum gravity, the wave function describes the 3-dimensional geometry on the 3-dimensional Riemann configuration space, instead of the physical state. In the standard quantum mechanics, the interactions between particles are local interactions, and the superposition of different states of each quantum object can independently represent the superposition state. However, the interactions between the structures of quantum space realize by the gravitational quanta, which is long rang. Accordingly, the quantum space is a non-local concept and physical entity. Owing to the principle of complementarity, we cannot determine some dynamical variable and its variance rate with respect to time. As a result, the uncertainty principle doesn"t allow us to give the determinism of evolution of space with respect to time to any physical significance, in the framework of canonical quantum gravity. The time related Schr ̈dinger equation is not appropriate in such framework, because the state vector is buried in the Hamiltonian. The Hamiltonian, describing the interactions of the structures, doesn"t evolve with time. Consequently, the formed quantum theory is independent of the background and becomes the theory of default time, which has significant influence on the development of space-time realism.