# How is gravity contained in empty space?

## Einstein and the power of empty space

**Over the course of history, worldviews have changed, and theologians and philosophers, physicists and astronomers have given very different answers. Modern cosmology emerged at the beginning of the 20th century - and Albert Einstein was one of its creators. Rudolf Kippenhahn describes how much the “engineer of the universe” shaped our ideas of space and time.**

Albert Einstein launched his major attack on space in the war winter of 1916/17, which was given the name "turnip winter" because of the food shortage. In the autumn of 1916 Einstein had once again visited his friends and colleagues in the Dutch university city of Leiden. There he also met the astronomer Willem de Sitter. It was probably this encounter that prompted him to apply his new theory of gravity - general relativity - to the universe as a whole.

On February 1, 1917, the German army command declared unrestricted submarine warfare; Little did she suspect that she thus sealed America's entry into the war and thus its ultimate defeat. A week later Albert Einstein gave a lecture at the Prussian Academy of Sciences on the application of his new theory to the entire universe. Physicists and astronomers had tried this before as part of the classical Newtonian theory of gravity, but without success.

Infrared - Hubble Deep Field

In principle, it turned out to be impossible to determine the gravitational field of a universe that was uniformly filled with stars to infinity. It was possible to calculate the force of gravity in a cosmos that fills with stars up to great distances, but the space further outside is empty. But such an accumulation of matter would ultimately collapse due to gravity. But they were looking for a universe that has existed forever and should last for all eternity.

Actually, a universe filled with matter uniformly to infinity should be easy to understand: Since there is no specific direction in it, there should also be no force of gravity, because the forces pulling in different directions cancel each other out. The resulting gravity is zero. But this simple consideration turns out to be wrong. The physicists and astronomers, especially Hugo von Seeliger, who worked in Munich, noticed this as early as the end of the 19th century.

### Space without gravity

Out of necessity, the researchers changed Newton's law of gravity by introducing an additional repulsive force. In the solar system, even up to hundreds of light years, it does not play a role; but in the great distances of cosmology it can even overcome the force of attraction. This modified law of gravity made it possible to determine the gravitational field of a universe that was uniformly filled with matter to infinity.

And indeed: the forces of attraction in different directions cancel each other out; In this universe, gravity is zero everywhere, it is weight-free. But that was only possible through the modified law of gravity: Newton's gravity, supplemented by an additional repulsion, for the existence of which there was otherwise no evidence.

When Einstein applied his new theory of gravity to matter throughout the universe, he encountered the same difficulty. No wonder, because in the case of weak gravitational fields his theory changes into Newtonian - with all its problems. But without seriously violating the principles that he had applied in deriving general relativity, Einstein was able to supplement his equations in such a way that they also provided additional repulsion. In general relativity, too, this repulsion only becomes important at great distances. Einstein called the addition in his equations the "cosmological link". With this he succeeded in finding a solution for a universe uniformly filled with matter.

Curved space

In contrast to the cosmos described by Newton's theory, this space has an additional property: It is curved. This means that the normal geometry no longer applies. The sum of the angles in the triangle is no longer 180 degrees. But that was not surprising, because in Einstein's theory gravity fields bend space. Einstein's cosmos is unlimited, but it has a finite volume. Such spatial shapes are nothing new to mathematicians. The simplest space with this property is the surface of a sphere. It too is finite. But if you always hike in one direction on it, you never come to a limit, but you get back to the starting point. The two-dimensional space of the spherical surface is unlimited, but not infinitely large.

### World models

The world was all right for Einstein. He had a cosmos uniformly filled with matter, which remained in equilibrium. Of course, matter does not fill the real universe uniformly. It is in stars that accumulate in star systems. In between the space is empty. But over great distances the star systems are evenly distributed, and a space of constant density is a good approximation of reality. In Einstein's cosmos the density has been the same for ages - and it will not change in the future either. That went well with the fact that the speeds of the stars and star systems Einstein knew were slow.

But in the same year Willem de Sitter published a work in Holland in which he showed that Einstein's equations also allow temporally variable world models. De Sitter had found a particularly curious solution. The density of matter in his cosmos was zero, so there was no attraction. But the equations did contain the cosmological term with its repulsive effect, and that is why de Sitter's cosmos expands. That this world model contains no matter is no reason to reject it, because it describes a world in which the density of matter is so low that its gravity is small compared to the repulsive force caused by the cosmological limb.

In 1921, the Russian meteorologist Alexander Friedman showed that Einstein's equations - with and without a cosmological term - provide models of the world that can expand or collapse. Albert Einstein was not enthusiastic about the time-changing world models. He also believed he had found a mistake in Friedman's calculations, but later had to admit that he was wrong. Einstein was convinced that only a static model correctly describes the real world. He considered the cosmological link to be necessary in order “to enable a distribution of matter as it corresponds to the fact of the small star velocities”. To understand this, we have to imagine the picture of space that prevailed in 1917.

the Milky Way

By the time Einstein was writing his cosmological work, astronomers had long since recognized that our sun and billions of other suns are standing in a flat area of space, the shape of which is reminiscent of a disk. Today we know that it takes about 100,000 years for a ray of light to travel from one point on the edge across the middle to the opposite point on this disk. The stars of the system move around the center. The speeds are around a hundred kilometers per second. The system as a whole does not change its size. These were the "small star speeds" to which Einstein referred in his work. Obviously he had no idea about the clouds of fog that fly through space at great speeds.

It was 31-year-old Immanuel Kant who had drawn attention 150 years earlier to elliptical nebulae that can be seen in the telescope between the stars. He suspected they were disk-shaped clusters of stars - similar to our star system, only far out in space. If we look at them vertically from above, they appear to us as circular disks; if we look at an angle, they appear to us to be elliptical. Were these nebulae islands of the world made up of billions of stars? Or were they maybe just glowing clouds of gas in our star system, of which there are many in the space between the stars?

When Albert Einstein wrote his cosmological paper, the question had not yet been decided. However, there were nebulae at high speeds that did not match the image of gas plumes between the stars. There is, for example, the nebula in the constellation Andromeda, which is already visible to the naked eye. It comes flying towards us at 300 kilometers per second. But elliptical nebulae were also known, which fly away from us at more than a thousand kilometers per second. Such and much higher velocities, as American astronomers found more and more frequently in elliptical nebulae, suggested that these nebulae are not in our star system.

### Galaxies on the run

The next step came in 1924, when the American astronomer Edwin P. Hubble recognized individual stars in the Andromeda Nebula with what was then the largest telescope in the world, the 2.5-meter mirror of the Mount Wilson Observatory north of Los Angeles. That enabled him to determine the distance: a million light years. The Andromeda Nebula is another star system, similar to ours - a world island in space, so far out that the light from its stars merges into a nebula even in large telescopes. Today we know that this galaxy is twice as far away as Hubble suspected at the time.

Andromeda Galaxy

Now Hubble tried to determine the speeds of other galaxies. It was not an easy task, since exposure times of fifty to one hundred hours were required for these faint objects. The telescope therefore had to be aimed at the same object for several consecutive nights. In 1929, Hubble knew that all distant star systems were moving away from us, and the faster they were moving away from us. The following applies: double the distance - double the speed; Speed and distance are therefore proportional to each other. The expansion began a finite time ago, which can be determined from the expansion rate. The Andromeda Nebula itself is an exception. It is so close that its escape speed is disturbed by the gravitational pull of its neighboring star systems. That's why he's moving towards us.

In 1931 Albert Einstein visited the observatory on Mount Wilson on a trip to America. It was there that Edwin Hubble made his discovery, and Einstein was convinced that the real universe behaves differently from his temporally unchanging cosmos. The force of gravity and the repulsive force it additionally introduces do not keep each other in equilibrium. Rather, the universe is expanding, driven by a momentum initially given to it, which gravity counteracts, but which it has not been able to slow down to this day. The reason why Einstein had introduced the additional repulsive force - namely to maintain a cosmos that did not change over time - had suddenly disappeared. Now he didn't want to have anything more to do with this power. In 1946 he wrote: "If Hubble's expansion had already been known at the time the general theory of relativity was developed, the cosmological term would never have been introduced."

Nonetheless, he faced a problem because, like Hubble himself, he was using a now obsolete value for the rate of expansion, which provided a world age of 1.5 billion years. This was countered by the theory of the evolution of the stars over time, which indicated a much higher age of the world. The reason for this discrepancy: The astronomical distance determinations were wrong at the time, and the theory of stellar evolution overestimated the age of the oldest stars. Today astronomers estimate their age at 13.6 billion years and the world age derived from the expansion at 13.7 billion years. Einstein was right, the universe can be described with his equations without using the repulsive force caused by the cosmological term.

For a number of years now, astronomers have had a new tool at hand to determine the distance to star systems far out in space. Certain types of exploding stars called Type Ia supernovae are excellent milestones in space. Since they are at a great distance and since light rushes through space with great but finite speed, we see the distant objects not as they move today, but as they moved when the light was sent out, that reaches us today from them.

Albert Einstein at the telescope

Because exploding stars are accompanied by large bursts of light, they can also be observed from a great distance. And since the view into the distance is also a glimpse into the past, these supernovae make it possible to determine the rate of expansion during different epochs of the evolution of the universe. The result: At first, the mutual attraction of the gravitational force of the star systems slowed the expansion, but then the expansion began to accelerate and this acceleration continues today. Obviously, in addition to the attractive force of gravity, an additional repulsive force acts at large distances between the bodies. The universe behaves exactly as Einstein's equations with a cosmological term demand!

But where does that come from? It is probably not a matter of a new force demanded by the theory of relativity, but of a kind of new matter that exerts different forces than those previously known. Physicists came up with them regardless of the question of the structure of the universe. Its cause lies in quantum mechanics, which does not allow absolutely empty space. It is populated by virtual, otherwise unnoticeable particles and their antiparticles. Only occasionally does one of them come into reality for a short time together with a corresponding particle of antimatter. This ghostly particle world exerts a pressure, so it causes a repulsive force.

In the equations of general relativity, empty space creates a force just like the cosmological term. We do not yet know the strength of the forces in empty space. Can you explain the observed acceleration in expansion? Albert Einstein would probably not have been enthusiastic if he had experienced that the cosmology, the cornerstone of which he laid in 1917, should one day be rounded off by the effects of quantum mechanics - because he could not get used to it all his life.

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