## The Rigakubu News

Disclaimer: machine translated by DeepL which may contain errors.

### ~ Message from a graduate studentWhat if the world were scale invariant?

 Yoshitaka Okuyama Department of Physics, 1st Year Doctoral Student Birthplace Kanagawa, Japan High School Kaisei High School Faculty Department of Physics, Faculty of Science, The University of Tokyo

The human body is made up of molecules. When these molecules are enlarged, we can see that they are made up of atoms. These atoms also have finer structures such as electrons, neutrons, and protons.

We have all seen this description in physics textbooks. According to the Standard Model of particle theory, we know at this stage that the smallest constituent units of matter are quarks and leptons. Nature generally has such a hierarchical structure and changes its shape according to the scale at which we view it.

However, there are some things in nature that do not depend on scale, that is, they do not change even when scaled up or down. Figure a is a plant called romanesco, which shows the same structure even if it is scaled up or down. Figure b is a schematic representation of a phenomenon that occurs when a model of a magnet called the Ising model is placed at a special temperature called the critical temperature. Fluctuations (blurring) of all sizes are visible, indicating that this phenomenon does not have a typical scale. I am studying what is called conformal field theory, which describes such scale-independent phenomena.

What would be the basic elements in a scale-invariant world? Let's look again at Figure b. The fluctuations in Figure b can be thought of as a superposition of various "tones," so to speak. Just as "sound" can be decomposed into "scales," fluctuations can be decomposed into reference modes of fluctuation, which can be regarded as the basic elements.

The reference mode of fluctuation has properties that cannot be captured by a simple analogy with sound. See Figure c. For example, suppose we place a piano at point x and play a Do note. If a microphone is placed at point y, naturally, the sound of "Do" will be detected. This is the same for both fluctuation and sound. In the case of a fluctuation, think of the meter at point y as detecting the reference mode φD of the fluctuation caused by striking point x with a hammer or the like, as it is. Next, suppose that a "Do" is sounded at point x and a "So" at point y. Then, at point z, both "Do" and "So" are sounded. Then, at point z, we should hear a chord of Do and So. This is because sound has the superposition property of linearity. However, this is not the case in conformal field theory. At point z, instead of a simple superposition of the fluctuations φDo andφSo played at points x and y, we hear a jumble of all "pitches". Fluctuations emanating from points x and y fuse together by the time they reach point z, and change into something not unlike it! Note: I am studying how the propagation of fluctuations with such a nonlinear structure is affected by the causality law of space-time.

My research is not directly useful for life. This can be seen from the fact that while our universe is scale-dependent, my research is concerned with an extreme world that is not scale-dependent. However, the joy of pursuing one's own interests, forgetting all about applications, is incomparable to anything else. I believe that the freedom to think outside the box that I have cultivated in this way will give me the power to change something.

(Note) In other words, "some fluctuations can be created from other fluctuations," which is incompatible with reductionist thinking. All fluctuations are equally fundamental.

The Rigaku-bu News, January 2022

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