Infinite Freedom of Space-Time for Zero-Energy-Entity in Quantum Mechanics

Zero-energy state is investigated by taking infinitesimal energy and observing its uncertainty in space-time, adopting quantum mechanics. In this paper, the uncertainty in conventional quantum mechanics is found to be interpreted as freedom in space-time, which results in possibility of time travel and space transition of the zero-energy state, which could be information or mind. The wave function of a physical system composed of multiple particles or wave-packets is examined and found that it can be arbitrarily changed by grouping by observers. It leads to an idea that even infinitesimal energy or wave-packets in a heavy physical system may separately exist and it has the infinite freedom of space-time.


Introduction
In non-relativistic quantum mechanics, the state of a physical system in space and time is represented by the wave function ( ) ,t ψ x , which is governed by the Schrödinger equation [1]: where,  is the reduced Planck's constant are not a function of C. T. Rim mentary variables of a particle such as momentum p and position x as well as energy E and time t, which is governed by Heisenberg's uncertainty principle [2]: where, p σ , x σ , E σ , and t σ are the standard deviation of momentum, position, energy, and time, respectively. Though there are a few disputes on Equation (2) in literatures [3], the validity of Equation (2) is basically unchanged. Heisenberg uncertainty principle is so general that it can be applicable to a particle (or the wave-packet of a particle) of arbitrary mass m, arbitrary velocity v ( v c  ), and arbitrary size.
So far, conventional quantum mechanics only have dealt with the physical system of non-zero mass or energy, as evidently identified from Equations (1) and (2). It is inevitable for the modern physics to deal with such a case because only measurable quantities are allowed to enter the scope of scientific research.
We are living, however, in the world of information and mind consists of bits and neurons. The universe is not necessarily composed of physical entities with non-zero energy only, but also composed of information entities with zero-or near-zero-energy, which cannot be measured experimentally, but can only be logically proven with quantum information conservation.
An idea of dealing with zero-energy-entity was proposed, where zero-energy bipolar quantum entanglement can be non-local [4] [5] [6] [7]. Schrödinger equation was linked to the idea to explain that zero energy information can travel instantly [8]. Though not easy to demonstrate the bipolar quantum entanglement experimentally, this idea provides us the possibility of dealing with zero-energy entity not as artificial one but as physical one.
The speed of quantum information was measured by a Bell experiment [9], where nonlocal correlations were observed and Einstein's spooky action at a distance propagates much faster than at speeds of light by at least four orders of magnitude.
The above ideas confirmed the non-locality of nature in general and have stimulated the possibility of infinite freedom in space and time for the zero-energy-entity.
In this paper, the characteristics of entities with zero energy are explored in general form as an extension of quantum mechanics without the engagement of bipolar quantum entanglement. The zero-energy properties are gained from a physical system, which is composed of non-zero mass or energy. The multi-layered wave function is first introduced to explain the proposed idea. It is identified that infinite "freedom" of space and time is one of the characteristics of the zero-energy-entity.

Multi-Layered Wave Functions
The wave function of a physical system composed of multiple particles, which are also represented by wave-packets, can be arbitrarily changed by grouping of observers. As shown in Figure 1, a physical system, represented as the dotted square box, contains n particles of different momentum and energy ( ) In Equation (3), the wave function is determined by the following generalized Schrödinger equation, which is applicable even to the non-linear case where the particles interact each other and the potential An example case of the non-linear Schrödinger equation is the free electrons in a metal lattice, where each electron interacts not only with each other but also with positrons in nuclei. In Equation (4), the energy of the k-th particle E k is introduced instead of the mass m k for the general expression purpose as follows: In the case that the wave function of each particle ( ) is independent each other, e.g., the ideal gas where no interaction exists between each particle, Equation (4) becomes as follows: Note from Equation (3) that the selection of particles, i.e., grouping, can be This grouping idea can be extended to a layered physical system consists of different physical properties, e.g., a group of light particles (such as free electrons) and a group of heavy particles (such as neutrons), as shown in Figure 2. If there is no interaction between two groups A and B as well as between each particle in a group, there is no doubt that the group wave function of Equation (3) is determined by the superposition of individual wave function of Equation (6).
In the case that there is any interaction between each particle or each sub-system, as depicted by arrows in Figure 2, the superposition is still valid if the generalized Schrödinger equation of Equation (4) is used to obtain the non-linear individual wave functions. In other words, the group wave function is simply the sum of individual wave functions, which could be obtained from either linear or non-linear Schrödinger equations. This apparently strange statement can be understood from a similar case that the total energy of a particle can be obtained by the sum of potential energy and kinetic energy, which may be non-linear with respect to the velocity or position of the particle. The energy is linear with respect to each energy, but each energy can be non-linear with respect to other variables.
It can be still argued that the wave function may not be linear each other under some extreme conditions; however, it is not likely happen to conventional wave packets, and it will beyond the scope of this paper if it is the unusual case.

Space-Time Uncertainty of Infinitesimal Energy
Now the multi-layered wave function concept is extended to the zero-energy-entity. As shown in Figure 3, the "bit" of information can be understood as the energy-entity of zero value. The value of information "0" or "1" is not directly related to the energy state of the information hardware. The information itself may have zero energy whereas the information hardware should have non-zero energy as identified from Shannon's Theorem in conventional  communication systems [10]. As evidently identified from Equations (4) or (6), the Schrödinger equations cannot be directly applied to the characterization of the zero-energy-entity because the denominator of energy term becomes zero.
It is remarkable that the Schrödinger equations of Equation (1)  Still a remaining question is that "what is the nature of information?". The information, defined as a group of wave functions in this paper, may be either a truly zero-energy-entity or an asymptotically zero-energy-entity. Because we have neither a theory nor a measurement method to deal with the truly zero-energy-entity in quantum mechanics, it is beyond the scope of this paper. Instead, it is postulated in this paper that the information is an asymptotically ze-  (7), the uncertainties of information in position and time are infinity. As the wave function represents the probability of existence, information can be measured everywhere and anytime in universe. Therefore, it can be said that the asymptotically zero-energy-entity such as information and mind has infinite "freedom" of space and time in quantum mechanics. Zero mass or zero energy gives rise to the freedom of going everywhere and anytime. In theory, information and mind may reach to any place and time in universe at once. In other words, a time machine or a teleporter can be realized by information machines (computers or artificial intelligence) or living things including human being, which can think and therefore has mind. This result is consistent to the bipolar atom theory, which is applicable to not only physical worlds but also logical, mental, social, and biological worlds [4] [5] [6] [7] [8].
Note that the zero-energy-entity (Group A) is based on and correlated with the non-zero-energy-entity (Group B), as shown in Figure 3. Therefore, the non-zero-energy-entity such as a computer and human body cannot be a time machine or teleporter but information and mind can be.