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!!