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引言。
我们的目标是介绍一些关于天体物理学、宇宙学和基本粒子理论的新观点。
基本思想相对简单。它们可以用三种不同的形式表达：
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用专业术语。
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用图表形式。
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用普通语言。
可以用不同的方法来撰写关于科学的普通文本。
...一般来说，撰写科学类普通书籍的作者会提供一些漂亮的图像，以激发读者的想象力。但到了书的末尾，读者并没有真正学到多少东西。
使用图像，我的意思是几何学，自从一个世纪前几何学极大地渗透到物理学中以来，它能为大脑提供更好的营养。
...适当的类比转换可以唤起理论的主要目标和路径。顺便说一句，读者最终将获得扎实的二维几何知识。
牛顿与反牛顿。
...宇宙结构是由一种基本力：引力组织起来的。如果宇宙中的物体不相互吸引，那里就不会发生任何事情。星系、恒星和行星都不会形成，我们也不会在这里谈论它们。例如，如果引力是排斥力，它会阻止物体接近。宇宙将保持无定形、松散，这将是致命的无聊。
吸引力的定律是牛顿定律：
(1)
G 是引力常数。m 和 m' 是两个质量，d 是它们之间的距离。
...正如稍后将展示的那样，我们的模型涉及“正常质量 m”和我们称之为“幽灵质量 m”的东西。星系、恒星、行星、人类、猫都是由正常质量构成的。没有人知道幽灵猫是否存在。
...主要问题是物质和幽灵物质仅通过引力相互作用。除此之外，它们彼此无视。例如，它们不能交换光子，因此幽灵物体在我们宇宙的这一分支中是不可见的。相反，如果存在一个“幽灵观察者”，他无法看到我们，也无法看到我们的星系、恒星等...
相互作用的图示如下：
(2)
两个普通质量相互吸引，根据经典的牛顿定律。
同样适用于两个幽灵质量。
但一个普通质量和一个幽灵质量相互排斥，根据某种“反牛顿”定律：
(3)
...我们可以将对应于普通质量和幽灵质量的两组质量点放入计算机中，让它们相互作用，并观察发生了什么。但物理学家会立即提出异议：
- 你的幽灵物质具有负质量 m* < 0！
确实，如果我们反转牛顿定律中一个质量的符号：
(5)
力的符号就会改变。
...但如果我们改变两个质量的符号，力保持不变。因此，人们会倾向于得出结论，在这个模型中，我们只是有两种质量：一种是正的，另一种是负的，因为它考虑了所提出的力的图示。
...但负质量 m* < 0 对应于 m*c² < 0 的能量，这首先由法国数学家 Jean-Marie Souriau 在他的著作中研究过：
《动态系统结构》（法国第一版，1973年，第197至200页）：Birkhäuser出版社，1997年。
...具有负能量的物体会带来严重的问题。事实上，当它们与具有正能量（正质量）的物体相撞时会发生什么？
...这并不对应于物质与反物质的湮灭。正如将在《几何物理学 B, 4》中展示的那样，位于我们宇宙中的反物质具有正质量和正能量。它们的相遇会产生光子。所产生的两个光子携带了物质和反物质粒子在碰撞前的总能量。如果具有相反能量的两个物体能够相遇并碰撞，结果将完全不同。那将……什么都没有。
...在宇宙的最初阶段，根据标准模型，物质和反物质频繁碰撞，产生高能光子。但相反，这些高能光子又会产生物质-反物质粒子对。这两种过程在早期宇宙中达到平衡。但如果宇宙中同时存在正质量和负质量、正能量粒子和负能量粒子，这两个子集将相互抵消。如果初始比例是各占一半，整个宇宙都将消失。
这就是为什么物理学家对负质量粒子如此怀疑的原因。
...因此，有必要以图表形式介绍这个模型。正如稍后将展示的那样，“它就像幽灵物质具有负质量一样运作”。为了处理这个看似矛盾的问题，我们必须学习一些几何学知识。
原文版本（英文）
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Introduction.
Our purpose is to present some new insights on astrophysics, cosmology and elementary particles theory.
The underlying ideas are relatively simple. They can be expressed into three different forms :
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In a specialist's language.
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Schematically.
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In an ordinary way.
One can write ordinary texts on science following different methods.
...In general the writer of ordinary books, devoted to science, offers pretty images, in order to stimulate the reader's imagination. But, by the end of the book, he has not gained very much.
Using images, I mean, geometry, which greatly invaded physics since one century ago, one can offer better food for brains.
...An adequate analogical conversion makes possible to evoke the main goals and paths of a theory. By the way, the reader gainS, at the end, solid knowledge in 2d geometry.
Newton and anti-Newton.
...Cosmic structures are organised by a fundamental force : gravitation. If the objects of the cosmos did not mutually attract, nothing would happen over there. The galaxies would not have formed, neither stars, or planets. We wouldn't be here to talk about it all. For an example, if the gravitational force was a repulsive force, it would keep the objects far away one from another. The cosmos would stay amorphous, flabby, which would be deadly boring.
The attraction's law is the Newton's law :
(1)
G is the constant of gravitation. m and m' are two masses and d is the distance between them.
...As will be shown further, our model involves "normal masses m " and something we call "ghost mass m ". Galaxies, stars, planets, human beings, cats, are made of normal mass. Nobody knows if ghost cats exist.
...The main point is that matter and ghost matter interact only through the gravitational force. Out of this, they ignore each other. For example they cannot exchange photons, so that the ghost objects are invisible from our fold of the Universe. Conversely if a "ghost observer" exists, he cannot see us, nor our galaxies, stars, etc...
The interaction scheme is the following :
(2)
Two ordinary masses attract each other, following the classical Newton's law.
Same thing for two ghost masses.
But an ordinary mass and a ghost mass repel each other, according to some sort of "Anti-Newton's" law :
(3)
...We could pu two sets of mass points, corresponding to ordinary and ghost masses, in a computer, let them interact, and see what happens. But the physicist will immediately argue :
- Your ghost matter has a negative mass m* < 0 !
In effect, if we reverse the sign of one mass in the Newton's law :
(5)
the sign of the force changes.
...But if we change the sign of the two masses, the force is unchanged. Then one would tend to conclude that in this model we have simply two kinds of masses : one positive and the other negative, for it takes into account the suggested force's schema.
...But negative masses m* < 0 goes with m*c2 < 0 energies, which was investigated first by the french mathematician Jean-Marie Souriau in his book :
Structure of Dynamic Systems ( first edition in France, 1973, pages 197 to 200 ) : Birkhauser Ed. 1997.
...Negative energy objects arise a serious problem. In effect, what happens when they collide with positive energy ( positive mass ) object ?
...This does not correspond to matter anti-matter annihilation. As will be shown in Geometrical Physics B, 4 , anti-matter located in our universe owns a positive mass and positive energy. Their meeting gives photons. The two produced photons carry the total amount of energy of the matter and anti-matter particles, before their collision. If two objects with opposite energies could meet, collide, the result should be totally different. That would give .... nothing.
...In the very begining of the universe, according to the Standard Model, matter and anti-matter collide frequently, producing high energy photons. But, conversely, these high energy photons give pairs of matter anti-matter particles. The two processes balance each other, in the early universe. But if the Universe would have contained positive and negative masses, positive energy particles and negative energy particles, the two sub-sets would have simply cancelled each other. If the initial proportion would have been fifty-fifty, the whole universe would have disappeared.
That's for the physicists are so skeptical about negative mass particles.
...That's why there is a need for a schematic presentation of the model. As will be show further "it works as if the ghost matter own a negative mass". To approach this apparent paradox we have to learn some geometry.