How are things defined in the 4th dimension

Of spaces and hidden dimensions

Wednesday, May 19, 2021

About the appropriation of Einstein's theories / 4

By Robert Brammer

On January 14, 1931, Albert Einstein writes an equation for the density of the Milky Way on a board at the Carnegie Institute in Pasadena, California (AP)

In the Einstein year, the use of the term "space-time" was booming: a space with three dimensions that we know from experience - height, width, depth - plus time. That is hardly imaginable and yet real - and yet not the whole reality of the Universe that today's physicists are exploring.

"The idea is then that at every point in our four-dimensional space-time there is still a small six-dimensional space attached. And if you had a very good microscope now, you could see that."

"The most beautiful and deepest thing that a person can experience is the feeling of the mysterious. It is the basis of religion, as well as all deeper striving in art and science. Whoever has not experienced this appears to me, if not like a dead person like a blind man. "

"The normal adult," Albert Einstein once admitted, "doesn't think about space-time problems. Children do that."

"We could be tied to a three-dimensional membrane for certain reasons. This means that the interactions that we experience in our daily life are limited to three dimensions and it is very difficult for us to enter the extra dimension or even signals who send the extra dimensions to the higher dimensions. "

Today physics is looking for unknown and hidden dimensions, for exotic spaces and for parallel worlds. In physics there is the idea that the world could exist in a higher dimensioned space.

"There is a nice example of this, that is the so-called" allegory of the cave "by Plato. It could be the same for us."

Scholars have always believed that space and time are absolute quantities, eternal and immutable. Because our entire existence, everything we do, think and experience - our entire perception - takes place in one space and within a time interval.

The concepts of space and time as we use them in our everyday ideas go back to the beginnings of science in antiquity. But science still doesn't know today: what is space? Is there a difference between space and matter? Is there such a thing as empty space? And is there space without material things in it?

For Newton, space and time were still the unchangeable stage of natural events. The English physicist declared space and time to be eternal and unchangeable components of the cosmos, primal givens that were withdrawn from all questions and explanations.

But Gottfried Wilhelm Leibnitz and others protested loudly against this point of view and declared that space and time were just accounting measures - a convenient method for summarizing the relationships between objects and events in the universe.

The Göttingen mathematician Bernhard Riemann then caused new irritations. In June 1854 he gave his famous inaugural lecture on theories of higher dimensions. With his hypotheses, he brought down the pillars of Greek geometry that had withstood all attacks for two thousand years. Riemann's geometry succeeded for the first time in defining a space with more than three dimensions.

Riemann's remarks were shocking at the time. Because, according to Hermann Nicolai, head of the Albert Einstein Institute for Gravitational Physics in Potsdam, they conveyed the knowledge that alternative geometries are also possible.

"The concept of a higher-dimensional space had long been known to mathematicians, and mathematicians have no difficulty operating with it. Imagining it concretely is a bit of a different question. We simply cannot visualize ourselves as a four-dimensional space looks like it really looks. Because we live in three dimensions of space and as biological beings we have arisen in three dimensions. We can only perceive three dimensions. But that doesn't mean that there isn't anything else beyond that. So if we do something Not being able to grasp it directly with the senses does not mean that we cannot understand it anyway. And it is similar with the higher dimensions. We cannot imagine them. But the rules of mathematics allow us or enable us to do so to operate with it and to draw conclusions from it, which one can then perhaps even verify experimentally k ann. "

It was 1905 when Einstein opened up a new worldview with his spectacular discoveries of the theory of relativity. But most people still orientate themselves more towards the traditional ideas of space and time. To this day we have not really internalized the theory of relativity - we have neither feeling nor intuition for its consequences. Because, according to the Potsdam physicist Stefan Theissen, we are unable to form a picture of the fourth dimension with our three-dimensional brains.

"You can't see four-dimensionally. In this respect, it's a limitation of our brain."

The painter Paul Klee wrote in 1905 - the year Einstein developed his special theory of relativity:

"" The law that supports space ", that should be the justified title of one of my images of the future!"

The interest in higher dimensions reached a peak between 1870 and 1920, when the "fourth dimension" - understood as a purely spatial dimension - occupied the public and gradually spread to all areas of art and science, to the philosophy and literature of Europe and The fourth dimension inspired the imagination of composers such as Scriabin, Varese and Antheil and appeared in the literary works of Wilde, Dostoevsky, Proust, Wells and Conrad.

Pablo Picasso, too, was inspired by the idea of ​​the idea of ​​higher-dimensioned rooms, for example when he portrayed the faces of women from different perspectives at the same time. Instead of choosing a single point of view, he shows several perspectives in his cubist paintings, as if someone had painted from the fourth dimension who is able to see all perspectives at the same time. He tried to see reality through the eyes of a four-dimensional creature. Such a being would see all angles at the same time when looking at a human face. Cubism emerged not least from a new understanding of the perception of form and space.

And Paul Klee, who also dealt with the theory of relativity in his writings, implemented this preoccupation in his pictures by drawing a horizontally structured system of stripes that expands or tapers like an elastic band. He was able to give the impression of limitless flow. These parallel structures, which are often spread out over the entire picture, never seem to begin and never to stop, thus suggesting the infinity of space.

The renowned physicist and gravitational researcher Jürgen Ehlers, who co-founded the Albert Einstein Institute in Potsdam in 1995, puzzles, however, whether the artists actually understand these highly complex theories.


"I feel like this when I hear artists talking about the fourth dimension or black holes, it seems to me that these words arouse associations in the artist that mean something to him, which he can then possibly translate into pictures, whether However, these words, which evoke ideas in his mind as to whether the content of these words has anything to do with the meaning of these words in physics, that remains completely open.I could even well imagine that an artist is not interested in which one These expressions have meaning in physics. For him it is sufficient and also essential that it gives him inspiration for new performing arts - just as there are ballet artists who dance according to the formula E = mc square. "

In the spring of 1905 Albert Einstein found out that Newton's static conceptions of space and time - until then the main pillars of classical physics - could not be correct. He turned Newton's cosmos upside down, as it were. Einstein recognized that space and time are not independent and absolute, as Newton had assumed, but are intimately connected with one another. He relativized space and time and at the same time saw them as parts of a unified whole.

"It used to be believed that if all things disappear from the world, space and time would still be left; according to the theory of relativity, however, time and space disappear with things. (Albert Einstein)"

Einstein realized that space and time are inextricably linked because the movement of an object through space affects its movement through time. And in his general theory of relativity ten years later he showed that space and time also have an effect on cosmic development through their curvatures.

Einstein's general theory of relativity predicted that the sun bends space and time in its environment - similar to the imprint of a bowling ball placed on a rubber blanket - and that this distortion affects the path that starlight takes. So space is constantly curved and can be deformed by matter.

Or to put it another way: When large masses move somewhere in the universe or when stars explode, space is stretched or squeezed. Every body changes the space-time of its environment. And every disturbance of spacetime manifests itself on earth as a gentle tremor, as the tiny rush of a wave.

Einstein revolutionized our ideas of space and time - but the material world, it has also become less vivid since then.

Einstein described the gravitational force of matter in his general theory of relativity as the curvature of space-time in a fourth dimension. But since we are in a three-dimensional world, four dimensions, according to the gravitational physicist Jürgen Ehlers, can only be imagined as a theoretical, as a mathematical model.

"We can't really visualize a curved three-dimensional space, let alone a curved four-dimensional spacetime. You have to study mathematics for that. And when you work in the field, you make something like pseudo-illustrations. I can do that This allows an architect to compare: based on two-dimensional representations of a house - namely by having a floor plan and an elevation, he can get used to imagining something three-dimensional in his head, even though he only has two-dimensional representations in front of him As a relativity theorist, one can make pseudo-illustrations in two and three dimensions and then gradually get a certain picture of four-dimensional space-time in addition to the formulas. "

The German physicist Theodor Kaluza was the first to bring the existence of additional dimensions into the discussion. In April 1919 Albert Einstein received a letter from the mathematician at the University of Königsberg. In it Kaluza suggested not starting from three spatial dimensions, but from four, so that together with time there were five spacetime dimensions. Only: at that time there was not the slightest hint of these additional spatial dimensions. Until the Swedish physicist Oskar Klein presented a plausible and coherent theory in 1926: just as, for example, a rope, if you look at it more closely, has an additional, small, coiled and circular dimension, the spatial structure could possibly also have a small, have a wound and circular dimension, which is so tiny that it cannot be detected by any measuring instrument and therefore remains hidden from us, according to Stefan Theissen from the Albert Einstein Institute in Potsdam.

"What Kaluza introduced was an additional dimension to the topology of a circle. Kaluza's idea was that at every point in three-dimensional space there is an additional circle in the fourth dimension, so to speak. One can easily imagine if you first reduce the three-dimensional space to two dimensions, where a circle is attached to each point. You can imagine that. "

Even so, this theory makes you feel dizzy. Because this is about extra dimensions, says Hermann Nicolai, which are so small that they have not yet been able to be detected even with the most modern measuring devices.

"According to Kaluza Klein, the extra dimensions are rolled up, rolled up, compacted, as they say. And rolled up so that you can no longer see them. You can imagine it as a garden hose that looks like a one-dimensional line from a distance. But if you take a closer look, it becomes clear that the garden hose does have expansion. And that's how you can imagine it with the extra dimensions. "

The twentieth century gave birth to two great physical theories: Einstein's theory of relativity for long distances, for stars and galaxies, and quantum mechanics for the nanoscale, for molecules, for atoms and subatomic parts. But as conclusive as these two theoretical structures are, they do not fit together, they are even mutually exclusive.

Albert Einstein tried to resolve this contradiction. Today physicists believe that with string theory they have finally found a system with which they can combine the discoveries and insights of relativity and quantum theory into a seamless whole - into a single theory that is supposed to be able to describe all physical phenomena.

The ten-dimensional string theory, according to the Munich scientist Dieter Lüst, is considered by many physicists to be the strangest - but also the most powerful theory that has ever existed.

"The special thing, and this now results from the mathematics of string theory, is that string theory by itself, quite automatically, cannot live in three dimensions, but must be automatically embedded in a higher-dimensional world. That is, the String can only execute its oscillations in a mathematically consistent manner in a higher-dimensional world. "

String theory leads us into worlds that know 10 or even 26 dimensions. String theory holds that the particles we know are not the fundamental building block of the universe and that the atomic matter that constitutes us is not the essential substance of our universe.

The fundamental building blocks - these are the strings - long threads made of energy, of pure energy. And that vibrate differently like the sides of a cello. And depending on the vibration of the string, instead of a certain tone, for example an electron or a quark is created. Every particle in our universe is characterized by a swaying, oscillating, dancing, one-dimensional thread. Tiny filaments of energy, defined as the smallest unit in our cosmos - around a hundred billion billion times smaller than a single atomic nucleus, as it were, infinitely thin rubber bands that swing back and forth. The higher their vibration frequency, the greater their energy and thus their mass. Strings are the ultra-microscopic components of the elementary particles that make up atoms. String theory explains all matter and all forces from these vibrating strings.

And just as there is an infinite number of sounds that can be composed for a violin, there could also be an infinite number of forms of matter that can be constructed from vibrating strings. On the ultramicroscopic level, the universe becomes the epitome of a gigantic concert, a cosmic symphony. Physicist and mathematician Brian Green enthuses that matter is nothing more than the sounds created by these vibrating strings.

The cosmos - a gigantic concert? Music has long served as a favorite metaphor for philosophers and naturalists thinking about the cosmos.

And the possible existence of six or seven additional dimensions gives us cause for the craziest dreams. What is behind these dimensions? And how do you explore the world behind that is hidden behind these dimensions?

From a mathematical point of view, the strings must exist in nine spatial dimensions in order to be able to carry out their vibrations. But what determines these nine spatial dimensions? Why are three dimensions large today and six reduced to a minimum? What has shrunk these six dimensions? Then why were they swallowed?

"Yes, that's a very good question. This is probably a very complicated dynamic process that we admittedly do not yet fully understand in string theory. First, let's try to be descriptive. We take an approach that our world consists of three large dimensions and six small dimensions and check whether this is at least a solution to the so-called string equation, and that is indeed the case.But there are other options as well. It could also be that the world is actually higher dimensional. That not only expanded three dimensions, but also several. We don't really have this dynamic under control yet, although there are certain signs of it going in certain directions. But that is still the subject of modern research. Why there are three large and six small dimensions. "

This poetic image has only one flaw: so far it has been based on pure theory. The experiments are calculated on the computer. None of this has been proven experimentally. The strings are so tiny that a particle accelerator the size of the Milky Way would be required to detect them.

String theory is above all a theory of the tiny. If one were to inflate an atom to the size of our solar system, then a string would be the size of a tree.

The fact that we are unable to measure distances smaller than a billionth of a billionth of a meter also includes the possibility of tiny additional dimensions.

"We shouldn't imagine that this microcosm is now inhabited by micro-civilizations or micro-people. We have explored these distances up to a certain range, but not further to about 10 to the minus 15 or 10 to the power of minus 16 centimeters. And if we do If you want to penetrate even deeper into the structure of matter, then we need even better, even more powerful accelerator facilities, and these are, so to speak, our experimental tools to penetrate even further into the structure of space there are still very, very small extra dimensions. But I wouldn't go so far as to speak of very, very small civilizations. "

For the first time in the history of physics, there is now a system that can be used to explain every fundamental property of the universe. And maybe string theory can also provide a plausible theory of creation.

The Big Bang possibly came about when the originally ten-dimensional cosmos collapsed into a four- and a six-dimensional universe.

Because according to string theory, our cosmos before the Big Bang was a perfect ten-dimensional universe. But the ten-dimensional world was unstable and eventually "shattered" into a four- and a six-dimensional world. This cosmic catastrophe created the universe in which we live. Our four-dimensional universe expanded explosively, while the six-dimensional twin universe contracted violently, until it had shrunk to infinitely tiny. Thus, only its four-dimensional images remain of the once ten-dimensional string. According to this theory, according to Hermann Theissen, our cosmos still has an accompanying universe that has wound itself into a small six-dimensional ball - so tiny that it cannot be observed.

"One assumes in cosmology that the universe was very small and that the universe has expanded. And then one could ask: perhaps the universe was very small in all ten directions: why did only four directions expand. Yes that is a good question, and there is no good answer to it. So why the universe has four large spacetime dimensions and six small ones in this geometrical picture, that is not understood. That is a large, an important, an open question. "

But it is also conceivable, according to the Munich string theorist Dieter Lüst, that other universes also have a different number of extended universes, for example narrow universes with no or only one large spatial dimension and other, expansive universes with eight, nine or ten extended dimensions. Much is hard to grasp even at the second thought.

“There are indeed very, very many possibilities in string theory. And there are very, very many possibilities, a number of about ten to the power of a hundred or even ten to the power of a thousand possibilities. That is practically unimaginable be that in other universes that there can be, there are not just three, but four, five, six, seven or eight great dimensions - or none at all. "

Perhaps our universe is also a so-called hypersurface, a flat universe, a 'bran' in a higher-dimensional universe. Because string theorists have calculated with the help of complicated mathematical models that the string threads expand into two or more dimensional bodies - and these "membranes" can then reach the size of a universe. So it could be, according to the American string researcher Brian Green, that we live on a three-dimensional membrane that floats in a higher-dimensional space. The space in which we exist is perhaps just a splinter floating in a larger cosmos. This membrane theory, according to Hermann Nicolai, plays an important role in string theory today Role.

"Lately there have been other scenarios where the extra dimensions remain large. And then the idea is more that our universe, our four-dimensional universe, is a kind of hypersurface in an even higher-dimensional hyperuniverse and that only matter is trapped on this hypersurface. So you have to imagine it like those old flycatchers that used to exist. That you hung in the kitchen and then when the fly came on it, it stuck firmly on it and the fly can then only crawl around on this tape. And That's how you have to imagine it with these industry scenarios. So our universe is a kind of fly catcher. We are the flies that crawl around on it. But there are other dimensions into which we cannot enter. "

Hermann Nicolai's office is dominated by a blackboard full of formulas. But the formula that is being sought at the Albert Einstein Institute for Gravitational Physics in Potsdam should be simpler, perhaps even fit on a single sheet of paper. One is looking for a unified picture, just as the universe was in a symmetrical phase at the beginning. But, according to Hermann Nicolai, it would be an enormous achievement if our human race were to succeed in finding out the laws on which the entire universe is based.

"We are by no means certain that we have the right theory. We have some indications that we are going in the right direction. And on the other hand, we have to reckon with the fact that there will be spectacular new data over the next ten or twenty years will come from astrophysics. Here, for example, we very much hope that not only will gravitational waves be detected, but that gravitational waves may even be used to look into space, to look back almost to the beginning. "

The research results of the string theorists are spectacular, they demand a lot from our intellect and often exceed the most adventurous science fiction fantasies.

If the ten-dimensional theory is correct, then that would be tantamount to recognizing that the traditional "three-dimensional world" is too small to, according to Hermann Nicolai, accommodate all the known forces of our world in it.

"In my opinion that would be a spectacular insight if we found out that the universe is not four-dimensional, but actually has other dimensions. That would be an insight that would certainly be as important as the insight of Copernicus, for example, that Copernican Revolution. "

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