yuanxue60616

the speed of phase wave is real number, the phase wave itself is not real.

Irrationality and logical paradox 1: Rational thinking and the self of rational thinking If and only if we know the definition of self in human thinking, can we know the structure of human thinking. I will start by discussing the basis of rational thinking-formal logic and use logical paradox as testing. There are three basic laws of formal logic. 1: The law of identity 2: The law of non-contradiction 3: The law of excluded middle The law of identity states that something is what it is. Expressed as symbols: A = A. The law of non-contradiction says that a statement cannot be both true or false at the same time and in the same way. Expressed as symbols: A ≠ -A. The law of excluded middle says that a statement is either true or false. Expressed as symbols: = A or = -A. When thinking rationally, there must be a "self" existing in the process of thinking. The three laws of formal logic only use opposing concepts A and -A. To define the self of rational thinking, in addition to A and -A, we must introduce a third presence. This is in conflict with formal logic. Formal logic proves that the self of rational thinking cannot exist outside of A and –A. As it is not A or -A, the self of rational thinking can be defined as below. 1: ≠ A and ≠ -A. 2: inseparable with both A and -A. 2: Irrational thinking and the self of irrational thinking By putting all three laws of formal logic through reversion, I derive the laws of anti-logic. The way to achieve reversion is to reverse the signs into their opposites: the “=” is now “≠”; the “≠” is now “=”; the “A” is now “-A” and the “or” is now “and”. Here I only do the odd-numbered transformation because the even-numbered transformation does not produce results of anti-logic. The law of identity becomes two laws of difference. 1: A ≠ A; 2: A = -A. The law of non-contradiction becomes two laws of contradiction. 1: A = -A; 2: A ≠ A. The law of excluded middle is more complex, it can offer a variety of results. It produces two laws of middle. 1: ≠ A and ≠ -A; 2: = A and = -A. The law of excluded middle can also derive: ≠ A or = -A, = A or ≠ -A, etc. These are not anti-logic, therefore not required. It is easy to tell that the law of difference 1 and the law of contradiction 2 are the same; the law of difference 2, the law of contradiction 1 and the law of middle 2 are same. Removing duplicates, we get three laws of anti-logic. The law of difference: A ≠ A; The law of contradiction: A = -A; The law of middle: ≠ A and ≠ -A. The law of contradiction and the law of middle are in conflict. We separate these three anti-logic laws into two groups. Group 1: The law of different: A ≠ A; the law of contradiction: A = -A. Group 2: The law of different: A ≠ A; the law of middle: ≠ A and ≠ -A. Each group represents one type of irrational thinking. Group 1 is the feature of Chinese philosophy. Group 2 is the feature of Indian philosophy. Rationality, as everyone knows, is the feature of Greek philosophy. The laws of anti-logic also only use opposing concepts A and -A, therefore the self of irrational thinking has same definition as the self of rational thinking. This guarantees that the self of thinking could freely switch between rational and irrational thinking. It’s easy to find that the self of thinking's definition include the law of middle. Below I will discuss the relationship between the two types of irrational thinking. This is related with logical paradox. 3: Conversion between two type of irrational thinking and Logical paradox Conversion 1: When the law of contradiction exists, applying the law of non-contradiction (cannot be both true), Any of A and -A is denied, it will result in the law of middle. Because A = -A. Denying A will also deny -A, denying -A will also deny A. Conversion 2: When the law of middle exists, applying the law of excluded middle (cannot be both false), Any of A or -A is affirmed, it will result in the law of contradiction. Because the law of middle logically requires that "A is affirmed" will result in "-A is affirmed", "-A is affirmed" will result in "A is affirmed". If a self-referential proposition "I am A" is -A. The symbol is expressed as: "I = A" = -A, can infer A = -A. This proposition contains contradictory laws. If "I am A" is a self-denying judgment, then at least one of A and -A is denied. According to the conversion 1, this "I" logically satisfies the intermediate law, and this "I" is the same as the self of thinking. According to the conversion 2, the intermediate law leads to the law of contradiction. That’s the reason we have logical paradox. According to the above discussion, a proposition leading to paradox must satisfy two conditions, and 1) is a direct or indirect self-referential judgment. 2) This judgment is actually self-denying and introduces a set of contradictory propositions.

Non-real relational values and simultaneity: the relationship between special relativity, matter wave and uncertainty principle 1: For any two associated physical quantities present in physics, such as time and space or a pair of conjugate variables, the relational value reflecting the two associated physical quantities changes, such as the velocity or the product of conjugate variables, is the real relational value. It corresponds to a non-real relational value. The non-real relational value also reflects the changes of the associated physical quantities. The real relational value is defined by the relevant physical quantities, so it cannot alone prove the correlation of the associated physical quantities. The non-real relational value and the real relational value both have extreme values. Their extreme values are equal in magnitude and opposite in polarity. That is, if a real relational value has a maximum value, the non-real relational value has a minimum value; if a real relational value has a minimum value, the non-real relational value has a maximum value. When a real relational value reaches the extreme value, the non-real relational value also reaches the extreme value at the same time. The real relational value, the non-real relational value and their extreme value satisfy a certain mathematical relationship. 2: The velocity of material movement is the real velocity, which corresponds to a non-real velocity. We discuss the existence of this non-real velocity from Einstein's analysis of simultaneity. The two points in space in different inertial frames have different simultaneity, this is the relativity of simultaneity. Einstein's conceptual analysis is a qualitative analysis. To derive the spatiotemporal transformation in the special relativity, qualitative analysis is not enough, quantitative analysis is needed. The relativity of simultaneity is the time difference between the two points of the relative motion inertial system in the direction of moving, which is a length of time. If the ratio of this length of time and the length of space between two points is linear, then we have a velocity (this linear relationship) to quantify this length of time. From the Einstein's analysis of simultaneity, this velocity is related to both the velocity of light and the real velocity and it is neither velocity of light nor real velocity. This velocity is the third velocity other than real velocity and velocity of light: a non-real velocity. In this case, the Lorentz transformation of the special relativity naturally implies this non-real velocity. So logically we can restore this non-real velocity from the Lorentz transformation. This is very simple, we only need use the molecular part of the time coordinate transformation formula in the special relativity:. quantifies the relativity of simultaneity. x is the spatial coordinate. It is easy to deduce that the non-real velocity is equal to . The maximum value of the real velocity is the speed of light. The minimum value of the non-real velocity is the velocity of light also. Their product is equal to the square of the speed of light. It is easy to see that this non-real velocity is the phase velocity of matter wave. Any object moving at velocity v is accompanied by a matter wave of velocity . There is indeed a non-real velocity of . It is an integral part of time and space unity and an integral part of the material movement. If we believe that this is not a mathematical coincidence, we finally know the physical meaning of the phase velocity of matter wave, it is the measure of the relativity of simultaneity. 3: The product of a pair of conjugate variables is a real relational value. I use the symbol x represent this product. This product will correspond to a non-real relational value, which is also the product of the pair of conjugate variables. I use the symbol y represent it. What is the physical meaning of y? Take a pair of conjugate variables: energy and time. The physical meaning of x is the product of the amount of change of energy and time. y is the non-real relational value accompanying to x. It is the measure of simultaneity relative to different energies. According to the uncertainty principle, we already know that x has a minimum value: h/4π. Then y has a maximum value, which is also h/4π. We think about the circumstances under which x and y will have extreme values . Still use the pair of conjugate variables, energy and time. Because x contains the change of energy, when a substance is not exchanged with external energy, if x still exists, then at this time, the x should be at the minimum value. At the same time, its corresponding non-real relational value y is at the maximum value. This is the same for all substances, no matter what the energy of the substance is. Therefore, De Broglie's theory of matter waves is the case when y is at the extreme value. The frequency formula of the matter wave actually gives a time period of simultaneous. Since the amount of y divided by the energy of the substance is the time period of simultaneous, and y is at the extreme value h/4π, the length of this maximum time period of simultaneous is equal to h/4πE. It multiplied by the non-real velocity is the length of the space with simultaneity, easy to get the value h/4πP. For a moving matter, the frequency formula of the matter wave can derive the wavelength formula. The two formulas of matter waves are not independent of each other. Simultaneity will cause interference. And impossible to observe a presence without changing simultaneity. 4: The relation of non-real relational values and superposition principle, please see my article “Superposition principle and irrationality”. Superposition principle and irrationality.docx

there is no wave, just act like wave. I have one article to prove superposition is equal to the law of middle or included the middle. another one is tell how a thing satisfy the law of middle exist. Superposition principle and irrationality.docx Non-real relational values and simultaneity.docx