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There is a magical bottle with unlimited capacity, which is too big for the whole Pacific Ocean to hold!

Some scientists even say that even the water in the world can't fill the Pacific Ocean.

My first feeling is: Is this bottle leaking? !

However, one truth is universal. The bottle doesn't leak, but your brain capacity limits your imagination! But this is not your fault, because the world we live in is a three-dimensional space. Strictly speaking, this bottle is something that exists in four dimensions.

It's normal that you can't understand things in four dimensions in three dimensions.

This bottle has a romantic name: Klein bottle.

Just looking at this foreign-style and beautiful name makes me feel unusual. In order to find out, I found this bottle specially and successfully moved it to my laboratory. I can't make the Pacific Ocean, but I made an oversized syringe to hold water. Although the result is naked, I just want to see:

How I was defeated by a small bottle!

Today's experiment is a bit brain-burning, please pay attention to replenish your brain in time!

Experimental purpose

Understand the characteristics of Klein bottle as a non-directional plane

experimental materials

Clear water, large-capacity syringe and Klein bottle model

operation sequence/order

1. To facilitate filling, put the plastic hose into the bottle.

2. Inject water with a large-capacity syringe. In order to facilitate observation, you can drop the pigment into the water (unnecessary).

3. The plastic hose is connected with the syringe, and the water in the syringe is continuously pushed into the bottle (note: the capacity of the bottle is about 400ml, and the capacity of the syringe is 550ml).

Phenomena and principles

Through the above experiments, we found that the water level in Klein bottle model gradually increased by continuously injecting water from the entrance of the bottle model. When the water in the bottle is "filled", the water does not cross the surface of the bottle and is discharged directly from the entrance. In other words, the surface of this bottle is endless and can never be filled.

Water will not cross the surface.

The following animation may be more intuitive. Let's have a look. (There is a complete experimental video at the end of the article)

What is a Klein bottle?

Klein bottle, in the field of mathematics, refers to a plane without orientation. This object has no "edge", the inside is the outside, and the outside is the inside. It is different from a sphere. If you put a fly in it, the fly can fly directly from the bottle to the outside without crossing the water surface, and the water can also flow. Klein bottle is an undirected topological space in topology.

The origin of the name Klein bottle

Klein bottle was originally proposed by German geometrician Felix Klein, hence its name.

However, its name is a self-defeating result.

Its real name is "Crane Plane". When it was first named in German, its name was "Kleinsche Fl? Che means Klein plane. Because of translation problems, it was written as Flasche, which means bottle. However, this plane looks like a bottle, so the name "Klein bottle" has been used ever since.

How do we understand Klein bottles?

The structure of Klein bottle we see can be expressed as: there is a hole in the bottom of the bottle. Now, put the bottleneck out and screw it into the bottle, and then connect it with the hole at the bottom. Unlike the cup we usually use to drink water, this object has no "edge" and its surface will not end.

Flies may know better than I do:

The picture originated from the network and has been deleted.

This is inferred from the four-dimensional space, but because we are in a three-dimensional world, we can't really make Klein bottles. Because in the four-dimensional space, the twisted bottleneck does not need to intersect with the bottle and enter the bottle, but the technology of human society is limited and cannot be truly realized.

So the "Klein bottle" we see now is actually a three-dimensional Klein bottle model.

Scientists believe that it can only hold water in four dimensions, which means that this bottle does not belong to the human world. It comes from the high-dimensional space of the universe, and it is a mysterious field for human beings. Everything is possible.

Einstein once said that when there is only one you in the world, there is also a person outside the door and inside the door, because inside the door is outside the door.

This is probably the most popular understanding of Klein bottle.

What is a four-dimensional space?

There are various multidimensional spaces in mathematics, but so far, the physical world we know is only four-dimensional, that is, three-dimensional space (the real world we live in) plus one-dimensional time. The high-dimensional space mentioned in modern microphysics is another meaning, which only has mathematical significance.

According to Einstein's theory of relativity, the three-dimensional space we face in life and time constitutes the so-called four-dimensional space. Because the time we feel on the earth is very slow, we will not obviously feel the existence of four-dimensional space.

If there is a chance to board a spaceship or reach the universe, and the speed of our reference system starts to get faster or close to the speed of light, we can find the change of time:

At that time, your life expectancy was much longer than that on earth. ...

Scientists have described that in four-dimensional space, we can take out the yolk directly without breaking the eggshell.

Feeling is something that a monkey can do.

However, four-dimensional space is still difficult for us to understand. In the three-dimensional world, it is better to live every day truly than anything else, isn't it?

Ok, that's enough for today. One more thing: four-dimensional things are a bit brain-burning. Let's do some serious work in the three-dimensional world, such as clicking a like. See you next time.

For more exciting original scientific experiments, please click:

In the magic science experiment, learn these two tricks and open cans gracefully and effortlessly.

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I am a nanny with a master's degree in science and technology. I love life and science, and I have done more than 400 "magic science experiments" with my baby. Pay attention to subscribe to me, do a small experiment at home with your child for 3 minutes every day, and cultivate your child's scientific literacy!

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