四维时空与数学宇宙

题图：Cheva 用AI生成

前天的帖子试着讲了一下宇宙的本源是数学这个让人费解又烧脑的假说。但是感觉还是没讲清楚。首先为什么数学定律是永恒不变的，甚至比物理定律还要厉害，如现在我们所知的物理定律，在大爆炸起始和黑洞的中心奇点都会完全失效，但似乎没有谁会认为数学会失效，就像三角形的内角和永远是180度，平行线永远不会相交，1加1也永远等于2。但是我们自身和我们周围的世界却在不断变化，我们从婴儿长到成人，从成人变成老人，最后又死亡，身体又分解为基本的原子，不再存在。即便是宇宙星辰这样宏大的物体，它也只是寿命更长一点，本身也有它的演化会和生命周期。而数学结构却不会，比如一个正十二面体，你给它再长的时间，它也不会多长出一个面来变成十三面体。

这个问题要换一个角度来思考，爱因斯坦为我们初步的提供了答案。在上一个帖子中说到，我们所感知的现实，其实是我们人类在大脑中构建出的一个模型，它和现实有联系，但并不是现实本身，而我们大脑构建模型的方式就是牛顿的世界观，空间是三维的,时间是独立于空间存在，永恒流逝的。但爱因斯坦的相对论告诉我们并不是这样的，时间和空间是交织在一起的整体，叫时空，是四维的。四维的东西我们无法想象，那我们就把空间减去一维，变成一个二维的平面，然后把时间想象成垂直于这个平面的第三个维度。然后我们再想象月球围绕地球旋转这样一个场景，当然二维的星球自然也从球形变成了圆，地球在中心位置不动，但是随着时间它会不断地向上运动，就形成了一个圆柱体，而月球围绕着地球做圆周运动，同时也随着时间流逝，在垂直方向上运动，那么月球就会形成一个像弹簧一样的螺旋形，那么在四维的时空中，这个圆柱和螺旋形，就是地球和月球的形状。而且可以认为这个形状是永恒的，就像数学结构一样。同样的，我们自己所经历的人生，也可以理解为在四维时空中的一个形状，当然这个形状比圆柱和螺旋形要复杂得多。这也就是爱因斯坦说，“过去现在和未来之间的差别，只是人类的幻觉”的原因之一。

这样一来万事万物只不过是摆放在四维时空中的一个个形状各异的雕塑，突然觉得这种理解似乎是一种宿命论，过去永远存在，而未来也早已确定，而我们的意识只是这个雕塑的一部分，只能随着时间的流逝，直到生命的尽头，才能知道雕塑的全貌而已。不过用这种观点看待宇宙和世界本身，确实让人有点脑袋爆炸，如果真的是这样的话，我们也就没有必要去追求什么永生了，因为我们本身就是永生的，只是是在四维的时空中永生。那些逝去的事物，其实也没有逝去，而那些未来还未发生的事情，其实也早就发生了，这真是一个很怪异的宇宙。

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The post the day before yesterday tried to talk about the puzzling and brain-burning hypothesis that the origin of the universe is mathematics. But it still doesn't feel clear. First of all, why the laws of mathematics are eternal, even more powerful than the laws of physics. As we know the laws of physics, they will completely fail at the beginning of the big bang and the central singularity of the black hole, but no one seems to think that mathematics will Invalid, just like the sum of the interior angles of a triangle is always 180 degrees, parallel lines never intersect, and 1 plus 1 is always equal to 2. But we ourselves and the world around us are constantly changing. We grow from babies to adults, from adults to old people, and finally die, and the body breaks down into basic atoms and ceases to exist. Even for such a magnificent object as the stars in the universe, it only has a longer lifespan, and it also has its own evolution and life cycle. However, mathematical structures do not. For example, a regular dodecahedron, no matter how long you give it, it will not grow one more face to become a tridecahedron.

This question needs to be considered from another angle, and Einstein provided us with a preliminary answer. As mentioned in the previous post, the reality we perceive is actually a model built by our human beings in our brains. It is related to reality, but it is not reality itself, and the way our brains build models is Newton’s world view , space is three-dimensional, time exists independently of space, and eternity passes. But Einstein's theory of relativity tells us that this is not the case. Time and space are intertwined as a whole, called space-time, which is four-dimensional. We can't imagine four-dimensional things, so we subtract one dimension from space to become a two-dimensional plane, and then imagine time as the third dimension perpendicular to this plane. Then we imagine a scene where the moon revolves around the earth. Of course, the two-dimensional planet naturally changes from a spherical shape to a circle. The earth does not move in the center, but it will continue to move upwards over time, forming a cylinder. , and the moon moves in a circle around the earth, and at the same time, moves in the vertical direction as time goes by, then the moon will form a spiral shape like a spring, then in the four-dimensional space-time, the cylinder and spiral shape are Shapes of the Earth and the Moon. And this shape can be thought of as eternal, like a mathematical structure. Similarly, the life we ​​experience ourselves can also be understood as a shape in four-dimensional space-time. Of course, this shape is much more complicated than cylinders and spirals. This is one of the reasons why Einstein said, "The difference between the past, the present, and the future is only a human illusion."

In this way, everything is just sculptures of different shapes placed in the four-dimensional space-time. Suddenly, this understanding seems to be a kind of fatalism. The past exists forever, and the future has already been determined, and our consciousness is just this. A part of the sculpture can only be seen as a whole with the passage of time until the end of life. However, looking at the universe and the world itself from this point of view really makes people's heads explode. If this is the case, there is no need for us to pursue immortality, because we are immortal, but only in the four-dimensional space-time eternal life. Those things that have passed away have not actually passed away, and those things that have not yet happened in the future have actually happened long ago. This is really a very weird universe.