ビッグバンの前にはもうひとつの「古い宇宙」があった：研究結果
宇宙はビッグバンから始まった…という通説は間違っていたのかもしれない。現在の宇宙は、収縮状態にあった「古い宇宙」が膨張し始めたことで生まれたということを、量子力学を用いて示す研究が発表された。
TEXT BY VICTORIA WOOLLASTON
WIRED (UK)
1172570 - fractal - wormhole
PHOTO: JAN CARBOL / 123RF
宇宙は常に膨張状態にあり、それは「ビッグバン」──無限大の密度をもつ高温の1点からの爆発によって始まった、と一般的に考えられている。
しかし、初期の宇宙に関する研究によって、宇宙はまったく新しいものから始まったのではなく、古い壊れかけの宇宙から形成されたのかもしれないということが示された。
物理学者たちは、このアイデアについて長い間議論してきた。ビッグバン理論では、われわれが理解している物理法則に反する状態から宇宙が始まったことになるからだ。その代わりに、宇宙には「収縮」と「膨張」の2つの時期があり、それがビッグバンのタイミングで切り替わったのだと考える科学者もいる。
このいわゆる「ビッグバウンス」理論は、1922年に発表されたものである。しかし、宇宙がどのようにして収縮状態から膨張状態に移行したのか（あるいは逆に膨張から収縮に移行するのか）を物理学者たちは説明できずに議論は保留されていた。いままでずっと。
宇宙を助けたクオンタム
インペリアル・カレッジ・ロンドンのステフェン・ギーレン博士とカナダのペリメーター理論物理学研究所の所長であるニール・トゥロク博士は、どのようにビッグバウンスが起こりうるかを発表した。
研究によれば初期の宇宙は、宇宙全体の構造から原子レヴェルにまで同じように物理法則が働いて、すべてのスケールにおいて同じ挙動を示していたという。この考えは「コンフォーマルシンメトリー」として知られている。
現代の宇宙では、原子より小さい粒子は大きい物質とは異なる挙動を示すので、このシンメトリーは崩れている。素粒子は、いわゆる量子力学の支配下にあるからだ。
しかし初期の宇宙では、すべてのものが信じられないほど小さかったので、わたしたちが現在目にする大きなスケールでの物理学ではなく、量子力学の原理だけが適用されていたという。
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まだ見ぬ宇宙の「リアル」な想像図：太陽系の外で観測された惑星たち
宇宙の130億年を、2分半で体験する（動画あり）
宇宙が始まったころはコンフォーマルシンメトリーの状態にあり、それが量子力学のルールに則るという考えを用いて、ギーレン博士とトゥロク博士はどのように宇宙が進化したかを説明する数理モデルを構築した。量子力学を使うことで、現在の宇宙は1点から始まったのではなく、収縮する古い宇宙から始まったと説明するものだ。
2人は特に、量子力学が働いていたからこそ、収縮段階の終盤に宇宙の崩壊や破壊（ビッグクランチやビッグリップとして知られる）が起こらなかったのだろうと考えている。その代わり、宇宙は完全に崩壊することなく収縮状態から膨張状態へ変遷したのだと。
ギーレン博士は言う。「量子力学は、物事が破壊するときにわたしたちを助けてくれます。それは電子の落下を防ぎ、原子が壊れないようにしてくれるのです。だからおそらく、量子力学が、ビッグバンとビッグクランチが起こりうるような激しい終わりと始まりの時期に宇宙を救ったのでしょう」
「わたしたちの研究の驚くべき点は、ビッグバンのいちばん最初の瞬間を量子力学に基いて説明したということです。合理的に、最小限の仮定を使ってね」とトゥロク博士はつけ加える。「この仮説によれば、ビッグバンは収縮を膨張に転換する『バウンス』だったのです」
2人はいま、このモデルを使って「ゆらぎ」として知られる宇宙の摂動の起源を説明できないか調査しているという。この研究は『Physical Review Letters』で発表された。
［7月29日 本文の一部を訂正いたしました。］
TAGS
#Physics #Science #Space
http://wired.jp/2016/07/29/big-bounce-universe/
興味あります：
\documentclass[12pt]{article}
\usepackage{latexsym,amsmath,amssymb,amsfonts,amstext,amsthm}
\numberwithin{equation}{section}
\begin{document}
\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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