量子物理学に今､革命が起ころうとしている
｢神の粒子｣を超えた探索が始まった
レーダーマンは傑出した実験家であるのみならず、ウィルソンの志を継いで、研究所と周辺の環境との融和や地域住民との交流にも努めた。また、本文中にもそれとなく触れられているように、飛行機に飛び乗ってワシントンDCに乗り込んでは、基礎科学研究への助成を精力的に訴えてきた。
さらに、次世代への科学教育のためのプロジェクトにも多大なエネルギーを注ぎ、この方面ではレーダーマンその人に捧げられた本もあるほどだ。（『Science Literacy for the Twenty-First Century』［邦訳『科学力のためにできること科学教育の危機を救ったレオン・レーダーマン』渡辺政隆監訳、野中香方子訳、近代科学社］）。
テバトロンを完成させるためには、テクノロジーの壁をいくつも乗り越える必要があった。とくに重要だったのが、本書にも折に触れて登場する超伝導磁石である。フェルミ研究所は、このタイプの強大な磁石を作るためにユニークな設計思想を打ち立て、その後世界中で作られたほとんどの加速器はそれを継承している。さらに、そうして開発されたテクノロジーは、加速器のみならず、さまざまな分野での応用を生み出すことになった。レーダーマンは、純粋な基礎科学研究のために開発されたテクノロジーや概念が、医療や情報通信をはじめとする多くの分野で、現実の社会に大きく貢献できるということを、最先端の現場でまのあたりにしてきたのである。
とかく世間では、科学のビッグプロジェクトというと、「どうして理系オタクの知的好奇心なんかに、われわれの税金を使わなきゃいけないのか」という反応が起こりがちだ。しかし、それは間違いだ、とレーダーマンは本書の中で訴える。そう思い込んでいる社会の未来は暗い。科学には正真正銘、社会を活気づけ、豊かにする力があるのだ、と。
古典物理学から量子物理学への転換に匹敵する革命とは
20世紀の後半には、次々と大きな粒子加速器が作られ、どんどん高いエネルギー領域に手が届くようになった。加速器でビーム粒子のエネルギーを上げるということは、その粒子の量子波長を短くすることだ（木材伐採用のナタを、手術用のメスにするようなもの）。ビーム粒子をきりきりと絞りあげて、小さな世界を見ようとするわけだ。
また、粒子と反粒子のビームを逆向きに加速して正面衝突させれば、両者は打ち消しあって、あとには純粋なエネルギーだけが残される。これは無駄をなくして大きなエネルギーを得る方法である。エネルギーを元手に、身の回りの世界には姿を見せない、質量の非常に大きな（それゆえ、作るためには大きなエネルギーを要する）、新粒子を作り出すこともできる。そうして作られた不思議な粒子たちがダイナミックに相互作用をする、驚くべき量子物理学の世界が、われわれの目の前に着々と広がっていった。
こうして、次々と高いエネルギー領域を目指すアプローチのことを、「高エネルギーフロンティア」という。このアプローチを一般向けに説明するときは、しばしば、「宇宙の始まりに迫る」とか、「未知の（重い）粒子を作る」といったキャッチフレーズが使われる。
20世紀には、このアプローチからめざましい成果が上がった。実験と理論とが、あたかも車の両輪のようにうまく噛み合って回り出し、こんにちの量子物理学の基礎となる「標準理論」が作られた。しかし大きな成果が上がったがゆえの副作用もあった。素粒子物理学の実験というのは、次々と大きな加速器を使って高エネルギーフロンティアを切り開くことだ、というイメージが固まってしまったのである。
しかし、そのイメージは間違いだ、とレーダーマンは力説する。レーダーマンは、高エネルギーフロンティアを先頭に立って開拓してきた人物である。しかし第一人者であればこそ、そのアプローチだけがすべてではないことも知っている。そもそも、こんにち量子物理学で記述される、素粒子たちの不思議な世界が、どうやって発見されたのかを考えてみればいい。19世紀の末に古典物理学が完成すると、あとは細部をこつこつ詰めていくだけだ、という見方が支配的になった。物理学にはもうやるべきことは残されていない、物理学は終わったのだ、という気分がはびこった。http://toyokeizai.net/articles/-/137270?page=3
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\title{\bf Announcement 300: New challenges on the division by zero z/0=0\\
(2016.05.22)}
\author{{\it Institute of Reproducing Kernels}\\
Kawauchi-cho, 5-1648-16,\\
Kiryu 376-0041, Japan\\
%\date{\today}
\maketitle
{\bf Abstract: } In this announcement, for its importance we would like to state the
situation on the division by zero and propose basic new challenges.
\bigskip
\section{Introduction}
%\label{sect1}
By a {\bf natural extension} of the fractions
\begin{equation}
\frac{b}{a}
\end{equation}
for any complex numbers $a$ and $b$, we found the simple and beautiful result, for any complex number $b$
\begin{equation}
\frac{b}{0}=0,
\end{equation}
incidentally in \cite{s} by the Tikhonov regularization for the Hadamard product inversions for matrices and we discussed their properties and gave several physical interpretations on the general fractions in \cite{kmsy} for the case of real numbers.
The division by zero has a long and mysterious story over the world (see, for example, Google site with the division by zero) with its physical viewpoints since the document of zero in India on AD 628, however,
Sin-Ei Takahasi (\cite{kmsy}) established a simple and decisive interpretation (1.2) by analyzing the extensions of fractions and by showing the complete characterization for the property (1.2):
\bigskip
{\bf Proposition 1. }{\it Let F be a function from ${\bf C }\times {\bf C }$ to ${\bf C }$ satisfying
$$
F (b, a)F (c, d)= F (bc, ad)
$$
for all
$$
a, b, c, d \in {\bf C }
$$
and
$$
F (b, a) = \frac {b}{a }, \quad a, b \in {\bf C }, a \ne 0.
$$
Then, we obtain, for any $b \in {\bf C } $
$$
F (b, 0) = 0.
$$
}
Note that the complete proof of this proposition is simply given by 2 or 3 lines.
\medskip
We thus should consider, for any complex number $b$, as (1.2);
that is, for the mapping
\begin{equation}
w = \frac{1}{z},
\end{equation}
the image of $z=0$ is $w=0$ ({\bf should be defined}). This fact seems to be a curious one in connection with our well-established popular image for the point at infinity on the Riemann sphere. Therefore, the division by zero will give great impacts to complex analysis and to our ideas for the space and universe.
However, the division by zero (1.2) is now clear, indeed, for the introduction of (1.2), we have several independent approaches as in:
\medskip
1) by the generalization of the fractions by the Tikhonov regularization or by the Moore-Penrose generalized inverse,
\medskip
2) by the intuitive meaning of the fractions (division) by H. Michiwaki,
\medskip
3) by the unique extension of the fractions by S. Takahasi, as in the above,
\medskip
4) by the extension of the fundamental function $W = 1/z$ from ${\bf C} \setminus \{0\}$ into ${\bf C}$ such that $W =1/z$ is a one to one and onto mapping from $ {\bf C} \setminus \{0\} $ onto ${\bf C} \setminus \{0\}$ and the division by zero $1/0=0$ is a one to one and onto mapping extension of the function $W =1/z $ from ${\bf C}$ onto ${\bf C}$,
\medskip
and
\medskip
5) by considering the values of functions with the mean values of functions.
\medskip
Furthermore, in (\cite{msy}) we gave the results in order to show the reality of the division by zero in our world:
\medskip
\medskip
A) a field structure containing the division by zero --- the Yamada field ${\bf Y}$,
\medskip
B) by the gradient of the $y$ axis on the $(x,y)$ plane --- $\tan \frac{\pi}{2} =0$,
\medskip
C) by the reflection $W =1/\overline{z}$ of $W= z$ with respect to the unit circle with center at the origin on the complex $z$ plane --- the reflection point of zero is zero,
\medskip
and
\medskip
D) by considering rotation of a right circular cone having some very interesting
phenomenon from some practical and physical problem.
\medskip
In (\cite{mos}), many division by zero results in Euclidean spaces are given and the basic idea at the point at infinity should be changed. In (\cite{ms}), we gave beautiful geometrical interpretations of determinants from the viewpoint of the division by zero. The results show that the division by zero is our basic and elementary mathematics in our world.
\medskip
See J. A. Bergstra, Y. Hirshfeld and J. V. Tucker \cite{bht} for the relationship between fields and the division by zero, and the importance of the division by zero for computer science. It seems that the relationship of the division by zero and field structures are abstract in their paper.
Meanwhile, J. P. Barukcic and I. Barukcic (\cite{bb}) discussed recently the relation between the divisions $0/0$, $1/0$ and special relative theory of Einstein. However, their logic seems to be curious and their results contradict with ours.
Furthermore, T. S. Reis and J.A.D.W. Anderson (\cite{ra,ra2}) extend the system of the real numbers by introducing an ideal number for the division by zero $0/0$.
Meanwhile, we should refer to up-to-date information:
{\it Riemann Hypothesis Addendum - Breakthrough
Kurt Arbenz
https://www.researchgate.net/publication/272022137 Riemann Hypothesis Addendum - Breakthrough.}
\medskip
Here, we recall Albert Einstein's words on mathematics:
Blackholes are where God divided by zero.
I don't believe in mathematics.
George Gamow (1904-1968) Russian-born American nuclear physicist and cosmologist remarked that "it is well known to students of high school algebra" that division by zero is not valid; and Einstein admitted it as {\bf the biggest blunder of his life} [1]：
1. Gamow, G., My World Line (Viking, New York). p 44, 1970.
For our ideas on the division by zero, see the survey style announcements 179,185,237,246,247,250 and 252 of the Institute of Reproducing Kernels (\cite{ann179,ann185,ann237,ann246,ann247,ann250,ann252,ann293}).
\section{On mathematics}
Apparently, the division by zero is a great missing in our mathematics and the result (1.2) is definitely determined as our basic mathematics, as we see from Proposition 1. Note its very general assumptions and many fundamental evidences in our world in (\cite{kmsy,msy,mos}). The results will give great impacts on Euclidean spaces, analytic geometry, calculus, differential equations, complex analysis and physical problems. See our announcements for the details.
The mysterious history of the division by zero over one thousand years is a great shame of mathematicians and human race on the world history, like the Ptolemaic system (geocentric theory). The division by zero will become a typical symbol of foolish human race with long and unceasing struggles. Future people will realize this fact as a definite common sense.
We should check and fill our mathematics, globally and beautifully, from the viewpoint of the division by zero. Our mathematics will be more perfect and beautiful, and will give great impacts to our basic ideas on the universe.
\section{Albert Einstein's biggest blunder}
The division by zero is directly related to the Einstein's theory and various
physical problems
containing the division by zero. Now we should check the theory and the problems by the concept of the RIGHT and DEFINITE division by zero. Now is the best time since 100 years from Albert Einstein. It seems that the background knowledge is timely fruitful.
\section{Computer systems}
The above Professors listed are wishing the contributions in order to avoid the zero division trouble in computers. Now, we should arrange new computer systems in order not to meet the division by zero trouble in computer systems.
\section{General ideas on the universe}
The division by zero may be related to religion, philosophy and the ideas on the universe, and it will creat a new world. Look the new world.
\bigskip
We are standing on a new generation and in front of the new world, as in the discovery of the Americas.
\bigskip
\bibliographystyle{plain}
\begin{thebibliography}{10}
\bibitem{bb}
J. P. Barukcic and I. Barukcic, Anti Aristotle—The Division of Zero by Zero. Journal of Applied Mathematics and Physics, {\bf 4}(2016), 749-761.
doi: 10.4236/jamp.2016.44085.
\bibitem{bht}
J. A. Bergstra, Y. Hirshfeld and J. V. Tucker,
Meadows and the equational specification of division (arXiv:0901.0823v1[math.RA] 7 Jan 2009).
\bibitem{cs}
L. P. Castro and S. Saitoh, Fractional functions and their representations, Complex Anal. Oper. Theory {\bf7} (2013), no. 4, 1049-1063.
\bibitem{kmsy}
M. Kuroda, H. Michiwaki, S. Saitoh, and M. Yamane,
New meanings of the division by zero and interpretations on $100/0=0$ and on $0/0=0$,
Int. J. Appl. Math. {\bf 27} (2014), no 2, pp. 191-198, DOI: 10.12732/ijam.v27i2.9.
\bibitem{ms}
T. Matsuura and S. Saitoh,
Matrices and division by zero $z/0=0$,
Linear Algebra \& Matrix Theory (ALAMT)(to appear).
\bibitem{msy}
H. Michiwaki, S. Saitoh, and M.Yamada,
Reality of the division by zero $z/0=0$. IJAPM International J. of Applied Physics and Math. {\bf 6}(2015), 1--8. http://www.ijapm.org/show-63-504-1.html
\bibitem{mos}
H. Michiwaki, H. Okumura, and S. Saitoh,
Division by Zero $z/0 = 0$ in Euclidean Spaces.
International Journal of Mathematics and Computation
(in press).
\bibitem{ra}
T. S. Reis and J.A.D.W. Anderson,
Transdifferential and Transintegral Calculus,
Proceedings of the World Congress on Engineering and Computer Science 2014 Vol I
WCECS 2014, 22-24 October, 2014, San Francisco, USA
\bibitem{ra2}
T. S. Reis and J.A.D.W. Anderson,
Transreal Calculus,
IAENG International J. of Applied Math., {\bf 45}(2015): IJAM 45 1 06.
\bibitem{s}
S. Saitoh, Generalized inversions of Hadamard and tensor products for matrices, Advances in Linear Algebra \& Matrix Theory. {\bf 4} (2014), no. 2, 87--95. http://www.scirp.org/journal/ALAMT/
\bibitem{ttk}
S.-E. Takahasi, M. Tsukada and Y. Kobayashi, Classification of continuous fractional binary operations on the real and complex fields, Tokyo Journal of Mathematics, {\bf 38}(2015), no. 2, 369-380.
\bibitem{ann179}
Announcement 179 (2014.8.30): Division by zero is clear as z/0=0 and it is fundamental in mathematics.
\bibitem{ann185}
Announcement 185 (2014.10.22): The importance of the division by zero $z/0=0$.
\bibitem{ann237}
Announcement 237 (2015.6.18): A reality of the division by zero $z/0=0$ by geometrical optics.
\bibitem{ann246}
Announcement 246 (2015.9.17): An interpretation of the division by zero $1/0=0$ by the gradients of lines.
\bibitem{ann247}
Announcement 247 (2015.9.22): The gradient of y-axis is zero and $\tan (\pi/2) =0$ by the division by zero $1/0=0$.
\bibitem{ann250}
Announcement 250 (2015.10.20): What are numbers? - the Yamada field containing the division by zero $z/0=0$.
\bibitem{ann252}
Announcement 252 (2015.11.1): Circles and
curvature - an interpretation by Mr.
Hiroshi Michiwaki of the division by
zero $r/0 = 0$.
\bibitem{ann281}
Announcement 281(2016.2.1): The importance of the division by zero $z/0=0$.
\bibitem{ann282}
Announcement 282(2016.2.2): The Division by Zero $z/0=0$ on the Second Birthday.
\bibitem{ann293}
Announcement 293(2016.3.27): Parallel lines on the Euclidean plane from the viewpoint of division by zero 1/0=0.
\end{thebibliography}
\end{document}
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