New Discovery on Planck Units and Physical Dimension in Cosmic Continuum Theory

In 1899, Max Planck integrated the Planck constant h with the gravitational constant G and the speed of light c, discovered a set of physical constants, and created Planck Units System. Since 20th century, the development of physics made the gravitational constant, the speed of light, and the Planck constant the most important fundamental constants of physics representing classical theory, relativity, and quantum theory, respectively. Now, the Planck Units have been given new physical meanings, revealing the mysteries of many physical boundaries. However, more than 100 years have passed, Planck Units System not only failed to get rid of the incompatibility between the basic theories of physics, but also cannot surpass the limitations of existing physics theories. In Cosmic Continuum Theory, physical dimensions can be transformed under the principle of equivalence. Planck units system not only integrates into the axiom system of Cosmic Continuum Theory, but also establishes a benchmark for the unity of physical dimensions. The introduction of the abstract physical dimensions “JX” and “XJ” makes the physical dimension of existence quantity and dimension quantity unified respectively.


Introduction
The fundamental constants of physics are the passwords of the universe and important scientific discoveries. Among all the physical constants, the well-known gravitational constant G, speed of light c, and Planck constant h are the three most fundamental constants of physics. These three fundamental con-stants of physics represent the different epoch-making basic theory of physics respectively. The gravitational constant G represents classical theory, the speed of light c represents relativity, and the Planck constant h represents quantum theory.
However, because these three basic theories of physics have different logical preconditions, they are regarded as three different cosmologies. There are disputes between high speed and low speed, macroscopic and microscopic, continuous and discrete between the three parties, and no consensus has been reached so far.
Cosmic Continuum Theory is an axiomatized physics system built on the mathematical continuum model. In Cosmic Continuum Theory, the universe is a continuum consisting of an existence continuum and an existing dimension continuum. The existence continuum is composed of mass bodies, energy bodies and dark mass bodies. The existing dimension continuum is composed of space, time and dark space. Mass, energy and dark mass are collectively called the existence quantity, and the quantity of space, time and dark space is called the dimension quantity [1] [2] [3].
This theory holds that a fundamental constant of physics should not only serve a certain physical basic theory. As cosmic codes of physics that gradually discovering in the course of continuous advancement, they are human's basic understanding of the natural world and should be an important basis for the unity of physics.
It was Max Planck himself who tried to unify fundamental constants of physics and achieved remarkable success. In 1899, he combined the Planck constant h with the gravitational constant G and the speed of light c, and found a series of physical constants. These physical constants are the so-called Planck units, and the following four constants are related to the existence quantity and the dimension quantity [4].

The Physical Boundaries and Their Conversion of Planck Units System
In the following, we include the Planck units in the axiom system of Cosmic Continuum Theory for discussion.

Fundamental Concepts and Lemmas
This article uses the fundamental concepts and axioms system in [1]. The following lemmas are cited in [1], these lemmas will be used in later proofs.
Lemma 1: The existence quantity has its elementary unit min e (Proof see [1]).
This lemma is equivalent to the quantification hypothesis.
Lemma 2: The interaction force between the initial fields of the existences 1 Z and 2 Z is: f Z Z r , and the action direction is along the line connecting 1 Z and 2 Z , where, r is the distance between 1 Z and 2 Z (Proof see [1]).
This lemma contains the law of universal gravitation. When the existence is a mass body, the theorem is the law of universal gravitation.
Lemma 3: An existence has a maximum speed and the speed of an energy body is the maximum speed (Proof see [1]).
This lemma includes the speed of light postulate.
Lemma 5: When the particle reaches its maximum speed, it will be converted to a quantum; when the particle or quantum reaches its maximum frequency, it will be transformed into dark particle (Proof see [1]).
Lemma 6: The existence quantities of mass m and energy 2 E mc = are equivalent: m E ≡ . "≡" is the "equivalent" symbol (Proof see [1]).
This lemmas contain mass-energy relation 2 E mc = .
Lemma 7: The dimension quantity of 1-second of time is equivalent to that of c-kilometer space: 1 second ≡ c km, where, c indicates the speed of light (Proof see [1]). and dark particle (Axiom in [1]).
Lemma 12: The interaction force between the initial fields of the existences 1 Z and 2 Z is: f Z Z r , and the action direction is along the line connecting 1 Z and 2 Z , where, r is the distance between 1 Z and 2 Z (Proof see [1]).

1) Planck mass m p
According to Lemma 2, the gravitational potential energy of two existing bodies with a distance of r and a mass of m is Let the vibration period of mass body m be t, then its frequency is: Also set its speed to V, then its movement distance in a period t is: The search for Planck unit is to define the boundaries of physical events. According to Lemma 3, the velocity boundary of the microscopic particles is the speed of light c, so the change in the gravitational potential energy between the two bodies of Planck mass p m in one cycle t should be: According to Lemma 1, the quantification hypothesis, we get: Substituting (1) into (4) yields: From the formula (5), we can get the Planck mass p m : 2) Planck energy E p Planck energy p E can be obtained from Lemma 6: Substituting (6) into (7)) gives Planck energy p E :

3) Planck time t p
According to Lemma 1, the Planck time p t can be found by: where p υ is the frequency of the Planck time p t period: Substituting (10)  Obtain p t from (12): 4) Planck length l p Planck length p l can be obtained from Lemma 7: Substituting formula (13) into formula (14) yields:

Corollary
Conversion is one of the core ideas of Cosmic Continuum Theory. The mutual transformation of mass, energy, and dark mass makes the universe colorful.
However, these transformations are not arbitrary, but are determined by the existence boundaries of particles, quantum, and dark particles. With the mutual conversion between particles, quantum, and dark particles, space, time, and dark space also follow.
Corollary 1: When the mass of particles reaches Planck mass p m , the particles are converted into quantum and the mass is converted into energy.
Proof: From (3), we can see that Planck mass p m is obtained by taking the speed as a variable to obtain the limit. According to Lemma 5, when the particle reaches the limit velocity c, it will turn into a quantum. According to the concept in [1], the energy body is a body composed of quantum, so when Planck mass is p m , the mass has been transformed into energy. Q.E.D. According to corollary 2, the quantum is transformed into dark particles and the energy is converted into dark mass. According to the concept in [1], dark space is the existence dimension of dark masses. Therefore, when the amount of time is less than or equal to Planck time p t , the time will be converted into a dark space. Q.E.D.
Corollary 5: When the amount of space is less than or equal to Planck length p l , the space is converted to a dark space.
Proof: From (14), Planck length p l is the distance traveled at the speed of light in Planck time p t . According to corollary 4, when time is less than or equal to Planck time p t , time has been converted to dark space. Therefore, when the amount of space is less than or equal to Planck length p l , the space will also be converted into a dark space. Q.E.D.

Unity of Physical Dimensions
The Planck unit system cleverly integrates the three fundamental constants of physics of Planck constant h, gravitational constant G, and speed of light c, and realized their dimensionless processing. Unfortunately, the physical significance of Planck units system is far from being fully reflected due to the inconsistency between the existing physical basic theories.

New Understanding of the Benchmark Value of Planck Units
The establishment of any physical dimension must be based on a certain benchmark. There are two kinds of benchmarks, one is the maximum, such as the speed of light c; the other is the minimum, such as the Planck constant h.
There are many such benchmarks in the Planck units. Q.E.D. Corollary 7-13 allows us to obtain the elementary unit of energy, the elementary unit of mass, the elementary unit of time, the elementary unit of space, the maximum of frequency, the maximum of quantum energy, and the maximum of particle mass 7 limit constants, this shows that the Cosmic Continuum Theory further develops the benchmark value of the Planck units.

Equivalent Abstract Physical Dimension
In Due to the fact that there is no international standard unit for the amount of dark mass, it is temporarily replaced by "Unit". According to Lemma 11, there are only particle, quantum, and dark particle three basic forms, thus we have unified the physical dimension of existence quantity to an abstract physical dimension "JX": Similarly, there is currently no international standard unit for the amount of dark space, it is temporarily replaced by "Unit". According to Lemma 11,there are only three basic forms of particle, quantum, and dark particle. According to Concept 4, Concept 5, and Concept 6, there are also only three basic dimensional forms: space, time, and dark space. Therefore, we have unified the physical dimension of dimension quantity to an abstract physical dimension "XJ": Obviously, this physical dimensions system is exactly the same as the Planck Units System. However, the two physical dimensions "JX" and "XJ" are essentially different from our existing physical dimensions. Existing physical dimensions are specific physical dimensions, including Planck units. There is no connection between different specific physical dimensions. But the "JX" and "XJ" are abstract physical dimensions. The function of an abstract physical dimension is to achieve the unity of specific physical dimensions.

A New Interpretation of Gravitational Redshift
The following is an attempt to solve the gravitational redshift problem by applying the equivalent unified scheme of physical dimensions proposed in this paper.
We know that the energy of a photon E is:

Conclusion
The new fundamental constants of physics often represent a new basic theory of physics, and the logical unity of basic physical constants is essentially the unity of physics. The Planck system of units profoundly reveals the physical boundary problem, but it has always been constrained by inconsistencies between the basic theories of physics. In Cosmic Continuum Theory, Planck Units System completely escapes the incompatibility of the physical basis. The axiomatization of Planck Units System enables the logical unity of fundamental constants of physics that represent different physical foundations to be realized. In particular, based on Planck unit, 7 limit constants were deduced, giving a unified benchmark for physical dimensions. The introduction of abstract physical dimensions "JX" and "XJ" to achieve unity of physical dimensions will sweep away another barrier for the unification of physics.

Conflicts of Interest
I declare that there is no competing Interest.