What are Physical Objects? ~~ Derivation in Japanese Articles

It has already been two years since this blog was launched. During that time, there has been some progress in the Japanese articles. This time, I would like to introduce the progress made and reconfirm the underlying theory.

[Contents]

▲Introduction of the main argument

The main argument begins by providing an answer to the fundamental question: "What exactly are all physical objects?" Furthermore, it naturally leads to the definition of the Big Bang. This Big Bang hypothesis constitutes one of the core elements of the main argument. However, the content also aims to go a bit further, exploring additional hypotheses. Since many of you may be reading this for the first time, I would like to start discussing the main argument from the beginning. Before we proceed, I would like to address the following two points before diving into the main topic.

[The importance of this theory]

The main theory is declared to be highly significant due to its potential to evolve into a groundbreaking and robust theory in physics, assuming it is correct and its connection to physics is established. Please enjoy the journey from simple ideas to startling conclusions.

［Structure of the Main Argument］

I have already published three articles in English, and among them, the first edition of the English version discusses many of the main claims of the main theory. Therefore, this time, I would like to incorporate the content of the first edition and add the developments in subsequent Japanese articles. There are two hypotheses: [Hypothesis 1] and [Hypothesis 2]. Hypothesis 1 serves to reaffirm the content of the first edition, while Hypothesis 2 was derived from subsequent discussions following the derivation of Hypothesis 1. However, there are also several hypotheses inferred during the process of article writing that I would like to introduce as well. Then, I would like to start by reflecting on the content of the first edition.

◆abbreviation introduction

MM theory = Mathematical Mapping theory (this theory)

ME = Mathematical Element

PE = Physical Element

The discovery of this theory (MM theory) dates back to 2014, ten years ago. Since my university days, I have vaguely believed that pursuing physics is equivalent to pursuing mathematics. While I didn't dwell on such thoughts much after entering society, there was a time in 2014 when I was flipping through my university math textbooks. I was reading theorems and such, but suddenly, it crossed my mind that the theorems written there might be the very elements of physics itself. At that moment, I experienced a sensation akin to shivers running down my spine. The sensation made me wonder what it could be, so I attempted to organize and reconsider the thoughts that had crossed my mind. I remember referencing Wikipedia or so on extensively, but ultimately, I came to the conclusion that each theorem in mathematics corresponds one-to-one with the subject matter of physics itself. I posted it as a 'question' on a physics discussion board that has now disappeared, desiring to ask someone about it. As a result, I received the following main criticisms:

1. Is there any difference between my claim and mathematical physics?
2. Not all meaningful theorems in mathematics necessarily have physical significance.

After receiving these criticisms, I became flustered and gave a nonsensical answer before leaving the scene. For my timid self, it was quite a frightening experience. I remember this happened around 2015, about a year after the discovery.

(Since then, I've been calling my research "MM Theory.") However, I didn't stop my research activities. This was because I believed that these criticisms did not contradict what I envisioned.

Now, I continued my research activities afterwards, but I remember there wasn't much progress, and my research became rather less frequent. However, at one point, not knowing much about logic, I thought I should gain some knowledge on the subject, so I read a book on logic. Although it was difficult to get through, I eventually finished reading it and came to understand that logic consists of logical formulas developed based on an axiomatic system. At the same time, a "major event" occurred. This happened in 2017. I considered the following two points.

1.  The mathematical element (ME) changes along with the "logical development."

2.  The physical element (PE) changes along with "time."

It could be concluded as described above.

Now, let us recall the fundamental concept of MM theory: the complete one-to-one correspondence between ME and PE. If ME equals PE, then the manner of their displacement is also equivalent. Incidentally, the displacement in ME is clearly (non-dense) countable. (A→B→C→・・・) Therefore, PE should also be of a similar countable type. Thus, I hypothesized that time must have a smallest unit, and upon investigation... there it was! Yes, there is indeed the smallest unit of time, called the Planck time!

This immediately leads to the following hypothesis.

[Hypothesis 1]

ME and PE are in a complete one-to-one correspondence.

The initial displacement corresponded to the origins of ME and PE, namely the onset of logical development and the Big Bang, respectively. (Logic development is governed by the axioms set forth initially.)

Both mathematical logic and PE have developed in parallel from the beginning.

This MP displacement is expected to occur every Planck time.

Now, what do you think? This hypothesis marks a milestone in the MM theory, but how does it resonate with you? Here, the truth of this universe is stated clearly. ME and PE have a one-to-one correspondence, where the smallest unit of change in ME corresponds to that in PE. Consequently, it is argued that one logical development corresponds to one Planck time. And thus a clear definition of the Big Bang is also provided...yes, indeed! The Big Bang was nothing but the onset of logical development! I believe it is not an overstatement to say that this is the most significant conclusion of the MM theory.

Looking back on all this, it can be said that there is nothing but the logic of mathematics in this world, and from certain axioms, logical developments have proceeded rigorously in sequence (*01)*1, meanwhile, the early universe expanded at an exponential rate. And this point of onset corresponds to what is commonly referred to as the Big Bang. I imagine that the explosive expansion eventually subsided, forming the current three-dimensional universe. Furthermore, as explained by [Hypothesis 2], we are also no exception; we are forms of ME in the shape of "logical sentences" (*02)*2. While we recognize various MEs through our interactions with the surrounding logic(*03)*3, we perceive them as PEs (physical objects), defined as distinct from MEs. If this logical system is a model in which logical numbers do not decrease, it can also be considered as a reason for the expansion of the current universe. An example of such a model is provided by the tree model at the end of this paper.

Reference)

(*01)There is an issue regarding the order of developments, which is explained in the tree model at the end of this paper.

(*02) While other forms of ME besides logical sentences are conceivable, when considering what constitutes a tangible ME, it is in the form of 'sentences'. This is clarified in [Hypothesis 2].

(*03) "Interacting with the surrounding logic" is a geometric concept, but it can be conceptualized in logical terms through the tree model provided at the end of this paper. Furthermore, the geometric imagery will be explained later in a one-dimensional model presented.

The progression from the initial inspiration of MM to the derivation of Hypothesis 1, which posits the Big Bang mechanism, is described above.

I would like to write down the subsequent flow as well.

The striking conclusion led me to submit it for publication in the scientific journal Nature by the end of 2018. The argument was dismissed as lacking solid evidence, even though it might have been stimulating for researchers engaging in such discussions. However, it failed to meet the criteria for publication. I considered submitting it to other publishers as well, but after some thought, I decided to abandon the idea as I concluded that it didn't reach the level of a research paper. Afterward, I changed my plans to publish a Kindle book, but still feeling unsettled and unable to focus, I ended up not writing it. Despite various attempts afterward, I eventually hit a dead end, and in January 2022, I published my first blog post.

The above is the sequence of events following the derivation of Hypothesis 1.

How was it? I found the transition from a very simple idea to an extremely significant conclusion to be quite striking. I'm curious about the thoughts of the readers, but I'd like to proceed to the next step. Let's take a look at the progress of the MM theory.

During the process of writing the blog, there were moments when my thoughts progressed. One example of this is the following hypothesis. However, since there were quite similar descriptions to the content of this hypothesis in the materials from 2020 before I started writing the blog, it's highly likely that I had already reached this conclusion before the writing process. Now, let me explain how I arrived at the hypothesis through the following process.

I speculated the existence of Planck volumes from the concept of the Planck length, and upon investigation, I found that they indeed exist (*04)*4. So I imagined that there would be one PE occupying each Plank volume. This means that each Plank cube contains one tangible PE (*05)*5. Conversely, it can be readily inferred that one tangible ME (*05) corresponds to one logical sentence. Therefore, one tangible PE corresponds to one logical sentence within one Plank volume. And now, from the standpoint of mathematical logical elements, the ME that characterizes these logical sentences is the coefficient of the logical sentence. On the other hand, from the standpoint of PE, the PE that characterizes the physical entity occupying the volume is inferred to be state variables such as temperature and pressure. Therefore, it is inferred that the coefficients of ME correspond to the state variables of PE.

Additionally, when considering the temporal displacement of PE, operators such as gravity and electromagnetic fields come to mind. Conversely, when considering the developmental displacement of ME, "solution methods" can be thought of as operators. Therefore, it is hypothesized that the operators such as "forces" in PE correspond to the operators, specifically "solution methods" in ME.

Reference)

(*04) I later learned about the existence of the Planck unit system, which is present in all unit systems.

(*05) "Having tangibility" means that the presence or absence of it corresponds directly to the existence or nonexistence of the PE or ME itself. For example, without volume, a physical entity cannot exist. Similarly, without a logical sentence, a logical space cannot exist. Conversely, if there is volume or a logical sentence, there is some form of PE or ME. These represent the minimal and indispensable units of PE and ME.

Summarizing these points leads to the following [Hypothesis 2].

[Hypothesis 2]

Each PE in one Planck volume corresponds one-to-one with each ME composed of one logical sentence.

If we make further inferences, the state variables such as temperature and pressure that characterize each PE within a Planck volume correspond to the coefficient values of the corresponding ME sentence.

Furthermore, the operators between PEs, such as electromagnetic fields and gravity, correspond to the displacement operators between MEs, namely "solution methods."

This Hypothesis 2 states the relationship between various forms of PE in the present universe and various forms of ME in the logical space, implying that almost all types of PE and ME can be accounted for by these. It can be seen as enhancing the specificity of the MM theory.

Now, considering the differences between conventional research and MM research, I believe there are differences in the following two aspects. Here, we introduce 'CR' as the abbreviation for Conventional Research.

1)[MM]: Specific ME analysis.

   [CR]: Idealized ME analysis.

2) [MM]: A complete deductive analysis starting from the primordial ME expansion.

    [CR]: A non-complete deductive analysis starting from the current concept of the universe.

▼Examples

The following are examples at the high school level of mathematics.

Example1）

［MＭ］If 

then the ratio of the solutions is   

［CR］When the ratio of the solutions of is ,

then     

Therefore, because of we can express the equation as

         

Example２）

［MＭ］

If and

     ⇒  

［CR］

If and ,

then if also  

    ⇒ 

In Example 1, MM expresses the properties of equations satisfied by specific coefficients while conventional research focuses on equations in general that possess specific properties. Along with this generalization, coefficient terms are considered.

Additionally, in Example 2, MM deals with specific relationships of coefficients, whereas conventional research typically uses symbolic coefficients to generalize the state further. Additionally, when considering conditions for symbolic coefficients, such as the underlined 'a > b', as conditions for the establishment of the state, these conditions can be regarded in the PE space as conditions related to state values such as temperature and pressure.

I hoped to come up with a good example, but I could only think of clumsy ones. However, I believe this example somewhat clarifies the difference (1) between MM and the conventional approach. In the conventional case, analysis involves the use of coefficient terms as a result of idealizing ME. Just getting a sense of the general direction is fine by me.

▼Conclusion from the theory of relativity

As I mentioned earlier, PE in one Planck volume equals one logical sentence. Here, I'd like to consider the consequence in the theory of relativity, which states that the maximum speed of movement is the speed of light. That is, since the speed of light is defined as the speed of one Planck length in one Planck time unit, considering that one Planck time unit corresponds to one logical development and that there exists one physical entity (PE) equivalent to one logical sentence at the end of a movement of one Planck length, the following conclusion can be drawn.

[Conclusion] Anything moving at the speed of light interacts with the logic of its 'neighbor' one Planck length away in a single logical step.

This consequence can be considered as providing the relationship between the logical space and the geometric space of the current universe.

I attempted to explore the connection with the theory of relativity in a Japanese article, but it ended in failure. However, I believe that the following one-dimensional model discussed in the article is valid in approximated terms.

▲One-Dimensional Model

[Explanation of the One-Dimensional Model]

1) Each P represents a position, and each horizontal line indicates the same moment in time.

2) Stationary logic displaces. The number increases by one, the position remains the same, and it interacts with the neighboring logic.

3) The moving logic does not displace. The number remains the same, and it moves to the adjacent position, interacting with the neighboring logic.

Proceeding according to this rule.

Now, this model provides a guideline for the nature of the logical expansion space within this geometric space. There are interactions with both moving logic and stationary logic, and in doing so, it qualitatively demonstrates the requirements of the theory of relativity：

1) After n Planck times, it can interact with logic n Planck lengths away.

2) Logic that has moved at the speed of light and returned will interact with stationary logic, with a difference in their logical displacement.

I believe this direction is correct, but how does it seem to you, the readers? I would like to leave it to each individual's consideration.

Now, I would like to shift the discussion to the previously mentioned order of developments and related matters. I believe that the following tree model is suitable for explaining the pure logical expansion space. This tree model is the simplest model, and therefore, it could be said that it is the only model that my analytical capabilities can handle.

▲[Tree Model]

Axiom:  A

Logical displacement rule:  The original logic T can combine with any logic S along its transformation path to derive T∧S. Furthermore, it is also possible to derive T as it is, without combining with any other logic.

Here, let's introduce the rule for combining with other logics, as mentioned in the Japanese article. Though the 'combination (∧)' mentioned above was related to self-displacement, as demonstrated in the 1-dimensional model as increasing numbers, we also consider the way of combining with other logics. Therefore, we establish the following combination rule.

Logical combination rule>

The logical combination occurs only between logics with the same past logical paths and logical shapes.

Now, according to this rule, C₁ and C₂ in the diagram are isomorphic and will combine since they have past logics on the same paths. The same applies to B₂ and B₃. However, concerning B₁, the past logic used is B₀ and it is not present on the paths of B₂ and B₃. Therefore, B₁ will not combine with B₂ and B₃, although they are isomorphic.

In this way, in the third stage, there will be three types, totaling four ME sentences generated. The logical development proceeds in a rigorously ordered manner, as evident from this. By the way, when writing the logical expressions for the fourth stage, six types are derived: C∧B, C∧A, B∧B, C, B, and A. Within these, several isomorphic logics combine with each other.

I will refrain from further analysis. Also, in reality, there may be many axioms or complex displacement rules, but I find it difficult to delve further into these considerations, so I will also refrain from further analysis here.

Let's provide a more specific example in response to this analysis. It may be trivial, but I hope it brings some enjoyment.

Here, the symbol '∧' is not necessarily read as 'and', but rather can be interpreted as other symbols like 'implies'.

From (3) and (4), we reach the conclusion that x = -1 and y = 2, but this conclusion cannot be directly inferred in this model. However, since we have (1) and (2) as past logics, we can reach this conclusion.

Here, I will explain the descriptions of (*01) and (*03) that I have not yet answered.

(*01) This tree model determines the order of logical development precisely, resulting in a unique way of logical reactions. It may seem that there is a certain arbitrariness in the way logical developments unfold, but in reality, they are considered to be unique. This aligns with the empirical perception that there is only one universe. This is also one of the conclusions of MM theory.

(*03) As a result of logical development, it is generally recognized that logic 'neighboring' tends to combine, and it is also generally recognized that the distance between logical entities reacting after n developments is n times the Planck length. The important point is not so much that they react because they are neighbors, but rather that the logics reacting are recognized to be neighbors in this current universe. In a developed space where sufficient time has elapsed, it is recognized that logical states emerge such that they "interact with surrounding logics." The discussion may be somewhat shallow, but I believe an understanding of the MP development space has been obtained from a logical perspective.

▲Summary

I will conclude the main discussion here.

There were a few other topics to discuss, but I'd like to conclude here for now. What impressions do you all have? The assertion that everything in the world is equivalent to each individual logical sentence seems to be unique within the scope of my research. When repeatedly asking the question "What is a physical object?" I believe MM brilliantly answers the ultimate question of how it should be defined. My understanding of physics and mathematics is limited, so this is not a thoroughly scrutinized theory. However, based on my knowledge, I do not see any significant flaws. From this point on, I would like to leave the further examination to the readers. Thank you for reading this far.

*1:(*01)There is an issue regarding the order of developments, which is explained in the tree model at the end of this paper.

*2:(*02) While other forms of ME besides logical sentences are conceivable, when considering what constitutes a tangible ME, it is in the form of 'sentences'. This is clarified in [Hypothesis 2].

*3:(*03) "Interacting with the surrounding logic" is a geometric concept, but it can be conceptualized in logical terms through the tree model provided at the end of this paper. Furthermore, the geometric imagery will be explained later in a one-dimensional model presented.

*4:(*04) I later learned about the existence of the Planck unit system, which is present in all unit systems.

*5:(*05) "Having tangibility" means that the presence or absence of it corresponds directly to the existence or nonexistence of the PE or ME itself. For example, without volume, a physical entity cannot exist. Similarly, without a logical sentence, a logical space cannot exist. Conversely, if there is volume or a logical sentence, there is some form of PE or ME. These represent the minimal and indispensable units of PE and ME.

MM Theory ~In Comparison with Ordinary Physics~

△[Preface]

In my previous article, I wrote the first half of the Japanese version No. 5 and would write the second half next time. But after that, my thoughts and what I wanted to write changed. So, I changed my plan and decided to write small excerpts from previous Japanese articles and what I thought back and reconsidered.

I wrote the original version of this issue, but in terms of its quantity, there was a possibility that it could be difficult to understand the main points, so I decided to drastically reduce the volume of the article. Still, I have some more things to write, but I would like to look forward to it later.

Although this theory is in the category of philosophy, it is a very grand theory. I would be happy if you were interested in this thesis.

Galaxy01

Abbreviations

ME＝Mathematical Element　　PE＝Physical Element

MM theory=Mathematical Mapping theory (this theory)

OP=Ordinary Physics

◆In some parts, abbreviations may be used frequently, so please be patient.

Link to Japanese articles

物理哲学！

▲<Review>

In MM theory, the physical object = PE and the mathematical element = ME are equivalent in principle, and they are in perfect one-to-one correspondence. In fact, there is nothing other than MEs in this “world”, and we are no exception and interact with other MEs. Through that, we perceive the MEs in the form of “PE” and distinguish them from ME.

However, since there is a general equation of PE = ME, PE has a hidden mathematical property, and we figured it out in the form of "mathematics". And we use that mathematics to analyze back this physical space. This is just "physics".

And there is also another significantly important conclusion derived from above MP equivalence.

That is, the Big Bang, which is the beginning of the PE space, coincides with the initial logical expansion from certain axiom system, which is the beginning of the ME space.

This is the exact definition of the Big Bang!!

Also, one logical expansion, which is the minimum unit of displacement in logical space, corresponds to one Plank time, which is the minimum unit of displacement in physical space. That is, one logical displacement occurs every one Plank time.

▲<6 major differences >

I mentioned in my last article of English version that 3) of the 3 major differences has broken down. However, as I wrote in a subsequent Japanese article, I have shown that 3) is still intact.

In addition, while thinking about various things in writing articles of the Japanese version, some other differences surfaced between ordinary physics and MM theory. The number of them is six in total, including the previous three, and can be cited as the "six major differences". I will briefly describe the contents of each.

Before that, I would like to list the six major differences.

1)Current PE criterion or initial ME criterion

2) Idealized ME or concrete ME

3) Whether PE≠ME or PE=ME

4) Inside or outside of the system

5)Inductive or deductive

6) Integration or discretization

The former refers to the nature of OP and the latter refers to the nature of MM.

Here, the most essential difference among them is the idealized ME in 2), I think. I would like you to pay attention to that point as you read.

▽1) Current PE criterion or initial ME criterion

[OP] OP is based on physical objects in our current universe. Although various quantities of physics have been expressed in mathematical formulas, they are derived from the current concept of physics. We gain its physical meaning only from the present universe, and theories start from that physical meaning.

[MM] On the other hand, in MM, the PE is considered to be the virtual image of ME. Unlike physics, which has many unclear points, mathematics is more essential in that it can be completely elucidated by complete deduction, except for undecidable propositions. Also, we begin our consideration with the initial development of mathematical logic corresponding to the Big Bang.

▽2) Idealized ME or concrete ME

[OP] In theorizing PE we must idealize the ME. After idealization, we will categorize and analyze originally individual ME=PE. We will make considerations such as ``PEs of the kind α_i have the mathematical properties ω_i''. This will be effective in states of large number of logics.

[MM] In principle, there is a perfect one-to-one correspondence between ME and PE. We must do strict research because we consider each concrete ME according to that principle. This will be effective immediately after the Big Bang.

▽3)Whether PE≠ME or PE＝ME

[OP] At present, OP may have a composition of "each PE corresponds to an ME", but, we have just arrived ”consequently” at the truth of ME=PE. Based on PE in the current universe, it is not a complete one-to-one correspondence like MM, but incomplete. Therefore, ME≠PE.

[MM]In principle, ME-PE perfect one-to-one correspondence. PE is exactly what ME is.

▽4) Inside or outside of the system

[OP] We are inside this system of logical development, and there, we interact with other ME around us. We regard such surrounding MEs as "PEs". In other words, we regard what "we perceive" from the inside of the system as "PE".

[MM] Under MP equivalence, perform ME expansion and derive the PE state. It objectively analyzes the state of the system in ME expansion, so we can say that this is an analysis from the outside of the system.

▽5)Inductive or deductive

[OP] We begin consideration from the current state of logical equilibrium, which is the terminal state of the expansion, and pursue the essence of ME deployment. This analysis is the opposite order of the logical expansion, so can be said to be exactly inductive.

[MM] Analysis of ME (and thus PE) is performed under complete deductive approach from the axiomatic system. This analysis goes in the same order as the logical expansion, going from the essence of the expansion to its end, so can be said to be exactly deductive.

▽6)Integration or discretization

[OP] We have theorized PE and derived its mathematical properties. At this time, we aim to make multiple general PEs correspond to one ME and aim for a unified treatment of physical objects. The attitude of this research can be considered as the integration of PEs into MEs.

[MM] MM theory aims to decompose the idealized physical objects into individual PEs (=MEs). The attitude of this research can be considered as the discretization of PEs into individual MEs.

△[Afterword]

Compared to the first manuscript of this article, the quantity was reduced considerably, so this time, I don't think I could mention much about new things. On the contrary, I think that the main points of this article became easier to grasp.

Well, has there been any change in your perception of physical objects?

I feel excited because I think it will have explosive power if the MM theory is true and the "ME-PE correspondence" is gained.

I would be happy if you were interested in this MM theory and I think it would be pleasure if you could think MM theory or beyond.

See you again!!

MM Theory ~Deductive Analysis of the Truth of the Universe~

▽[Preface]

This text is an English translation of the first half of No.5, the last article in the Japanese edition of Philosophy of Physics. This article involves changes of what was stated in the first edition, and it partially withdraws the claim of conversion from ordinary physics. However, despite the change, since the withdrawal is partial, the elements of the claim remain sufficient.

Now let's discuss the MM theory with you.

Galaxy02

Just in case, I put the abbreviation here.

ME = Mathematical Elements　　PE = Physical Elements

MM theory = Mathematical Mapping theory (This theory)

The first article is so important that I recommend reading it first also for your enjoyment.

From MP equivalence to Big Bang mechanism - Philosophy of Physics !! (hatenablog.com)

▲[Ordinary research is also ME=PE]

In classical mechanics, PE is considered to be given by position, velocity, charge density, mass density (including rot and div), etc., and the amount of information is finite.

On the other hand, in quantum mechanics, each PE corresponds to such as a function on space, including a wave function. Then we obtain physical information by applying (external) logical operators. For example, in a certain range of space, if the wave function Φ is given as

　Φ(x, y, z) = xy + z

then the function after the operation will be such as

　Φx=∂Φ/∂x=y

　Γ = Φ (x, y, z) - Φ (z, x, y) = (y - z) (x - 1)

By integrating these within the range, physical information is obtained as the expected value etc.

The basic idea of the wave function is probably like this. (Please forgive any mistakes.) However, while thinking like this, I came to think that it was necessary to correct my previous thinking.

I mentioned the following three major differences before, but now I have doubts about (3).

(1) Initial ME criteria or current PE criteria

(2) Concrete ME or idealized ME

(3) Whether PE = ME or PE ≠ ME

In classical mechanics, PE≠ME, but as I mentioned above, I have come to think that each PE is treated in the same way as the ME such as the wave function in quantum mechanics. Regarding this, we can see one of the differences between the classical mechanics and quantum mechanics in the amount of the information: each classical PE has only several information whereas each quantum PE has huge amount of information. We can assume that this is because quantum mechanics represents a huge amount of information each ME has come to have through the logical development for so long time.[corrected]

To reiterate, out of the three major differences, (3) will no longer hold. This is something I argued a lot in my previous article of Japanese version, so it's a little troublesome. However, the other two differences are not denied.

The reason why I insisted that PE ≠ ME in ordinary research is that in my image, I regarded ordinary physics as classical mechanics. (I have only a superficial understanding of the fundamentals of quantum mechanics, so I can't go into too much detail...) Yet it is probably correct that modern physics has reached the extent of (3).

Also, as I mentioned in my previous Japanese article, ordinary physics is an analysis "from the inside of the system" in the "present", I think, therefore, we will focus on "PEs" from the "current point" of view, and furthermore, we will consider statistical logic because of the huge number of MEs at present. This will also guarantee (1) and (2). By the way, please remember that MM is an analysis from outside the system.

From the above discussion, even in ordinary research, ME = PE, so (3) is likely to collapse, but as the nature of ordinary research, (1) the current PE criteria and (2) the idealized ME are concluded still correct.

▲[Inductiveness of ordinary research]

By the way, in MM, the analysis of PE is deductive, whereas that of ordinary physics has an inductive aspect. The difference between the two methods of research arises from (1) and (2) above. Let's explore this in a little more detail.

Ordinary research is based on the present state of equilibrium, and pursues properties between logical groups. The analysis there will be statistical logic different from the MM that considers initial and concrete ME. Therefore, we start ordinary research from ''the present'' of the developed state, with the opposite direction of time, also, we start ordinary research proceeding from idealized ME analysis to essential ME information, in the opposite of deductive analysis. Ultimately, we can say that ordinary research is to estimate the axiom system that gives the basis of the developed state. It is exactly inductive.

In contrast, MM is completely deductive in principle, which demonstrates the inductiveness of ordinary research and the deductiveness of MM. Now, we can see clearly the difference between the two research.

Now the topic changes a little, I want to note here that though PE = ME, logical sentences other than theorems may be displaced immediately, so statistical logic will mainly deal with theorems. In other words, the various quantities in modern physics are considered to be these theorems. This is an important matter, so I want you to hold it firmly. Conversely, please note that MM theory deals with all logical sentences.

Now, back to the topic, of course, deductive research is desirable because it is more accurate and the process of obtaining results is often simpler, however, as the number of logical expansions increases, the number of logics becomes enormous, resulting in difficulty in execution. To repeat frequently, the research then shifts to ordinary research, statistical logic; as I said before, ordinary research also has one advantage. However, modern physics is becoming so complex and difficult that some say it has already come to an end. Such now, I think that MM research, which proceeds from the exact opposite position, has an advantage.

So far, we have discussed the MM theory especially in the present universe, but the emphasis of MM lies in the Big Bang, and I even think that MM research should be limited to the Big Bang. This has been consistently stated since the first article. However, since the idea of MM should exist also in the current universe, I think we should definitely consider applying it to the present.

▲[Summary and Caution]

In the previous Japanese article No.5, we came to the understanding that ME = PE in ordinary research as well. However, the idea that ME = PE in ordinary research is different from that in MM. In the MM principle, ME = PE, and logical development from the initial ME corresponds to evolution from the Big Bang. And the one-to-one correspondence between ME and PE is the origin of MM research. That is, my claim is that this universe is nothing other than ME. This looks quite different from ordinary physics. On the other hand, ordinary research is based on (1) current PE criteria and (2) idealized ME. As for (3), we may have reached the same result as MM while researching, but it is not based on clear principles like MM. Also, ordinary research does not arise from perfect deductiveness, instead from a kind of inductive ME=PE analysis. Ordinary research and MM have completely different properties.

▽[Conclusion]

Well, how was your journey of intellectual exploration?

I hope that this article was stimulating because it is an excerpt from an article with relatively deep content. I would like to excerpt the second half if I have time.

If this theory is correct and the methodology is established, I think that this will lead to tremendous results, so I have great expectations in my heart. If anyone is interested, I would be happy and hope you to think about MM theory or beyond.

Thank you for reading this far.

See you again!!

From MP equivalence to Big Bang mechanism

About this article

This article is an English translation of a Japanese article published on January 10, 2022. With some arrangements, they are not exactly the same, but the claims are the same. Well, this article is a discussion about the question of what physical objects are. What do you think of physical object? Let's think together what the truth is. Though I'm worried if I can make you understand well in my English, I hope you can get along with my poor English.

At first, I notify that this theory is written as MM theory (=Mathematical Mapping theory), named after the original discovery.

Immediately, what do you think of physical objects?

Many will think of the earth as a celestial body that orbits the sun due to universal gravitation or the electron as a mathematical entity that satisfies the wave function in quantum mechanics. My challenge here is to try a major shift in these ideas.

I called my thesis MP equivalence, but now I will clarify the meanings of it first. This MP means that

M = Mathematics

P = Physics

In other words, it is Mathematics-Physics equivalence, but I would like to discuss later how this is related to the Big Bang mechanism. This is by no means difficult to explain and can be easily achieved, but the reason is that if I write it first, this story may become boring. I would like to ask you to read it patiently a little.

＜Background to writing this article＞

Well, I would like to move on the main subject, but first of all, I think it is the best way for understanding what my idea is to tell the background behind my writing this article, so I would like to write about that process. In fact, not all the records are available, so I'll just give you approximate years below.

The first event dates back to 2014. I have believed that pursuing Physics is equal to pursuing Mathematics since college and one day I was flipping through college math textbooks. At that time, I suddenly came up with the idea that the theorems written there had a one-to-one correspondence with each object of physics. Then, a creepy sensation ran all over my body because I felt that such a thinking way is clearly different from the conventional way about physical objects.

I wondered what this feeling was, and considered it deeply, and researched it on Wikipedia and so on, but the conclusion at that stage was such as written above: that is, each logical element of mathematics (=Mathematical Element = ME) has a one-to-one correspondence with each physical element (=PE). With this idea, I posted it on a physics bulletin board that is now gone in the form of a "question", desiring someone to know it. There were two main criticisms returned to me: they are

1.   Is there any difference from mathematical physics?

2.   Not all the important mathematical theorems are necessarily meaningful in physics.

Having received these criticisms, I was impatient, so I could not investigate or scrutinize them in detail, instead gave a sloppy answer and withdrew once.

(However, even if I had taken quite a time, I would not have been able to withstand these criticisms at that time.) I was very scared. This was certainly in 2015.

However, I was not disappointed with these criticisms. I believed that these criticisms were not inconsistent with what I had in my mind (what I imagined), and that my thoughts were not denied, therefore, I continued my research activities albeit little by little.

After that, there was still not much progress and I did research only occasionally. But, it was 2017. I came to the recognition that logic is a formula that develops one after another based on the axiomatic system after a little study of "logic". Soon after, a "major incident" occurred. I wrote it as a "major incident" on the assumption that no one has noticed it yet. I would feel "shame" if someone had been aware of it ... I considered 1,2 below.

１．The state of logic(=ME) is displaced by logical expansion.

２．The state of the physical object(=PE) is displaced with time passages.

Now remember the basic ME-PE one-to-one correspondence.

If ME = PE, the displacement method should be the same. By the way, the displacement type of ME should be countable. Therefore, the displacement of PE is also countable, so I guessed the time, what displaces PE, must be decomposed to the minimum unit. So, I looked it up ... and there was it!! Yes, there is a Planck time, minimum unit of time!

You can see that the following <Hypothesis> can be obtained immediately from here.

< Hypothesis >

There is a one-to-one correspondence between PE and ME.

First, the origin of PE, the Big Bang, and the origin of ME, the beginning of logical development (defined by the axiomatic system), corresponded.

With the development of ME, PE also has been developing from the Big Bang.

This MP displacement will occur every 1 Planck time.

Since ME = PE, it is not necessary to treat the PE space and the ME space separately but I wrote them separately because they are different in the form we recognize.

Well, how about? This < Hypothesis > is one of the arrival points, but how did you feel it? Here you will have a clear understanding of the Big Bang. The Big Bang is none other than the beginning of logical development.

The number of logics increases steadily over time, but I think this can explain the reason for the expanding universe. Also, since one Planck time (5.4 x 10-44 seconds) is extremely short, a huge number of logical expansions have been carried out up to now, so, in a sense, the logical expansion seems to be in equilibrium by now. Conversely, we can guess that the logical state was very dynamic immediately after the Big Bang. I suspect that this is the reason why the understanding immediately after the Big Bang does not go well.

However, I will make notification that this is not beyond speculation and has not produced any physical results. The suggestion of this article is one possibility about the truth of the universe and is not in the methodology. However, it is conscientious to show the direction of the solution, even if it is not a methodology. Therefore, I may write about the direction later if I hit upon any good ideas, but don't expect so much.

Now, I would like to talk about my subsequent process.

Having reached this daring conclusion, I planned to post it in the scientific journal Nature to publish it in a formal way. After asking a physicist for his opinion in late 2018, I tried to post to the magazine. But, as a result, my paper was rejected because the editor concluded that it did not have the firm rationale needed to publish it. Also, the physicist replied that my research might be in the field of philosophy of science, so, I also researched that field, but concluded that it does not suit my paper. After that, while I made various plans, I got stuck, so, I decided to launch this blog, though I was a little reluctant.

Further prospects

The above is the background from the discovery of MP equivalence to the present. This is the proposal for MP equivalence and the Big Bang mechanism, but many readers may not be convinced yet.

The reason is that we consider logic to be a component of theory, and think it is different from PE, which we usually think of as the " terminal element " of theory, even though they may have something in common. But what exactly is the terminal element of theory as PE or the component of theory as ME?

As a matter of fact, based on the above MM theory, every PE is nothing other than ME, furthermore each PE = ME is in a perfect one-to-one correspondence. Due to lack of physical and mathematical knowledge, I will avoid description how the logical expansion progressed after the Big Bang, but I would like to emphasize that each PE corresponds to each logical sentence generated from the axiomatic system.

However, the number of logics is enormous at present, and the detailed information of individual MEs loses its importance. Instead, it is the general nature of group ME that has become important. This does not refer to a concrete ME, but to the nature of "typed ME" and the interrelationship between types of MEs. This analysis of idealized MEs and ME groups has an aspect similar to statistical mechanics dealing with innumerable molecules. Now, let's call the analysis of this logical sentence "statistical logic". This statistical logic is a normally closed logical system, also called theory. This, I think, is the usual approach.

This PE = ME treated in statistical logic, theory, is not a concrete one but an idealized ME = PE. On the other hand, since MM deals with concrete ME = PE, you may feel that MM takes a more direct mathematical approach to PE than standard method. Conversely, normal analysis seems more indirect.

Once again, since the standard analysis deals with types of ME groups, the analysis classifies each ME by its type and describes the general theory of ME. The subject of consideration is not a concrete ME but an idealized ME. Because of this virtual ME analysis, we consider it an indirect analysis.

This statistical logic may be convenient and suitable for analysis when considering physics at present. However, since the information of individual concrete ME is important in the early universe, the approach by statistical logic becomes difficult. Therefore, I think that MM analysis will be necessary in the early universe. This is the reason why I think MM theory has significance in the Big Bang analysis.

In addition, since it is undeniable that there is an influence of concrete ME in the typed ME discussion, the scope of application of MM theory has a possibility to be wider.

Basically, that's all I want to say, but I think there may be some progress in the future. Also, I hope that this article will give you some kind of intellectual stimulation. Well then, I would like to conclude this description.

See you again!