What is the theory of quantum free electrons

Disgust for nothing

"Nothing is real", says the Beatles song "Strawberry Fields Forever". In his revolutionary drama “Danton's Death”, however, Georg Büchner had a protagonist ascertain: “Creation has spread so broadly, nothing is empty, everything is full of swarm.” What poetically collides with one another here was a controversial issue from the very beginning of Western philosophy - and it has remained so in physics to this day, with changed omens and changing triumphs. Is there somewhere - or was there at some point - a place in the universe or a state before it where absolutely nothing is or was?

"The question of empty space is probably the oldest scientific question that still occupies physics today," says Henning Genz from the University of Karlsruhe. The controversy began 2500 years ago among the pre-Socratics. At that time the plenists and the atomists were irreconcilable. The former, such as Empedocles, were convinced: "In space there is nowhere an empty space, nor one that is overfull." That was not a mere assertion, but could be justified empirically, as Empedocles' observation with the Klepshydra illustrated (see graphic " The experiment of Empedocles ”). The atomists, on the other hand, believed that a vacuum existed - though not everywhere. “In reality there are only atoms and empty space,” Democritus was convinced.

Until well beyond the Middle Ages, the plenists dominated with the view, particularly propagated by Aristotle and his students, that nature had a "horror vacui", a fear or disgust for emptiness. In 1644, the Italian physicist Evangelista Torricelli, encouraged by Galileo Galilei, showed that there is a vacuum: He invented the mercury barometer and recognized the space in the closed part above the mercury column as almost empty (see graphic "The Torricelli experiment"). This cavity is independent of the volume, shape, length and inclination of the mercury tube and must be a vacuum because air can neither penetrate through glass nor through mercury. Of course, not everyone was convinced of this - the French philosopher René Descartes mocked that a vacuum could only be found in Torricelli's head.

The Magdeburg natural scientist Otto von Guericke also became world famous, who a decade later sucked the air between two copper hemispheres (more precisely: almost 99 percent of the air) with the piston vacuum air pump he invented. The hemispheres could then no longer be separated by two teams of eight or ten horses on either side - but fell apart immediately when the air was let into the vacuum between them again. However, this is less a property of the vacuum than the pressure of the surrounding air. But the experiment showed that substances are not sucked in by the vacuum, but pressed into the vacuum by the ambient pressure.

Over the next two centuries the pumps were improved to the point where they achieved a residual pressure of less than a thousandth of a millibar. They were widespread around 1900 and were used, for example, in the manufacture of light bulbs. In the 20th century even more powerful pumps were invented, including turbo-molecular, cryogenic and sorption pumps. In the latter, remaining gas particles are bound to the vessel walls. With quite a bit of effort, up to 10–13 millibars can be achieved today. That corresponds to a density of a few hundred molecules per cubic centimeter.

But even the most sophisticated devices cannot yet come close to space conditions. Space is not free of particles - on average there is about one hydrogen atom in every cubic meter, in interstellar gas clouds there can be 10 or 100 - but it comes quite close to a “chemical vacuum”: a space free of atoms.

However, even areas of space without atomic nuclei and electrons are not empty. Because there are other types of matter - “ghost particles” such as neutrinos, for example, which hardly interact with the matter we are familiar with. "For them the earth is simply a ball, easy to penetrate on the way through space," rhymed the American writer John Updike. In fact, around 66 billion neutrinos shoot from the sun's interior every second through every square centimeter of the earth's surface - and through people at it - without leaving a trace. Even light-years-thick lead walls would not be able to stop them. Numerous astronomical measurements suggest that there are other types of so-called dark matter - elementary particles that, like neutrinos, do not make themselves noticeable by electromagnetic radiation.

Even if one disregards the dark matter, which many physicists around the world are currently trying to detect directly with sophisticated measuring devices, outer space is not a total empty space. Because it is filled with electromagnetic fields and the cosmic background radiation. It is the residual glow of the fireball stage from the Big Bang and has been greatly thinned and cooled by the expansion of the universe. However, around 400 photons still flow through every cubic centimeter, and the temperature of space is just under three degrees above absolute zero on the temperature scale (minus 273.15 degrees Celsius).

But electromagnetic fields can be shielded. And lower temperatures are possible: For example, astronomers have discovered a place, the Boomerang Nebula, 5000 light-years away in the constellation Centaurus, which is two degrees colder than the cosmic background radiation. An extremely rapid loss of gas from its central star - the speeds of the gas particles are up to 600,000 kilometers per hour - ensures the cooling effect. But the coldest point in the known universe, only 10–10 degrees above absolute zero, was a few years ago in the Low Temperature Lab of the Helsinki University of Technology: There atomic nuclei were almost brought to a standstill with magnetic fields (the temperature is also a measure of the particle movement).

Of course, there is neither a complete vacuum in the boomerang fog nor in Helsinki. There seems to be absolutely no place, not even in the intergalactic space between the galaxy clusters, where there is nothing. But in thought experiments, physicists can get closer to emptiness and explore a space free of matter and radiation at absolute zero temperature. According to the laws of nature, even it is not completely empty. A “horror vacui” does indeed seem to exist in nature.

As early as 1948, the Dutch physicist and later Nobel laureate Hendrik Casimir and Dik Polder, who both worked at the Philips laboratory in Eindhoven, predicted the existence of so-called zero-point radiation, which has now been confirmed experimentally. The two researchers realized that even a seemingly perfect vacuum is filled with inevitable tiny quantum fluctuations. This follows from Heisenberg's uncertainty relation of energy and time. Virtual photons and particle-antiparticle pairs are constantly wafting through space. They appear suddenly and immediately disappear again without ever being caught - a spontaneous couple formation and annihilation. Physicists refer to them as “virtual” in contrast to the “real” particles, which can be directly detected and manipulated.

“What at first glance appears to be a total void is actually a beehive of fluctuating spirits that appear and disappear in an unpredictable, exuberant dance,” describes the British physicist Paul Davies, professor of natural philosophy at the University of Sydney.

This is not a daring speculation, but has been proven experimentally. For example, virtual photons collide with electrons on atomic orbits, which causes small but measurable differences in the respective energy levels. This energy shift in atomic spectra, known as the Lamb shift, was discovered in 1947 by the American physicist Willis Eugene Lamb (Nobel Prize 1955) and his doctoral student Robert C. Retherford and can only be explained in terms of quantum physics.

The zero-point radiation is also noticeable in the form of the so-called Casimir effect (see graphic "The Casimir effect"): If two plates that are impermeable to electromagnetic radiation are aligned in parallel in a vacuum so that there is only a fraction of a millimeter between them, then they experience a weak electromagnetic force which causes the plates to attract a little. The effect is tiny: with two parallel, completely reflective surfaces one square meter in size at a distance of one hundredth of a millimeter, the force of attraction corresponds to that of a particle with a mass of one millionth of a gram. But: This extremely weak effect is measurable. The best confirmation of Casimir's prediction to date - with an accuracy of plus / minus 15 percent - was achieved by Gianni Carugno, Roberto Onofrio and their colleagues from the University of Padua in 2002 with a plate distance of 0.5 to 3 thousandths of a millimeter.

The cause of the Casimir effect is the "boiling" of the vacuum. Because in quantum physics particles are also waves, the space between two plates can only contain those photons whose wavelength is an integral fraction of the distance between the plates. Outside the plates there are all possible wavelengths and thus many more virtual particles. This excess exerts a tiny force that compresses the plates together. An analogous effect is well known among seafarers: two ships lying next to each other are driven towards each other because the sea between them does not participate in the waves around them. However, the ships do not simply reflect the wave trains, they also move with them.

With the Casimir effect, the energy density between the plates is negative relative to the environment. Thus, if you define “nothing” as a perfect vacuum without particles and radiation, nothing is still “something” on the one hand. On the other hand, there is even less than nothing, because there is less virtual zero point radiation in the vacuum between the metal plates than outside.

“The empty space of quantum physics is the net equivalent of the empty space of our imagination, but not gross,” concludes Henning Genz. The retired professor for theoretical physics chooses a clear comparison: “Let's take a poor swallower who owns nothing gross or net because all his accounts are always empty, and a pumping genius, whose accounts total and always also total zero, individually but sometimes here and sometimes there have large positive or negative amounts. The empty space of our imagination is empty like the poor swallower's accounts. The empty space of physics, on the other hand, resembles the accounts of the pump genius. "

But the zero point radiation is not the only ingredient of the vacuum. There must be other fields, say physicists and cosmologists. One is the Higgs field, which Peter Ward Higgs of the University of Edinburgh postulated as early as 1964 in order to explain the masses of elementary particles. These interact with him and only thereby gain the difficulty of existence, according to the widely accepted idea. When the Large Hadron Collider at the European Nuclear Research Center CERN near Geneva goes into operation the year after next, the Higgs field should be proven quickly - that would be another Nobel Prize-worthy triumph for theoretical physics.

Other fields are also under discussion. In recent years it has become clear that a mysterious dark energy has been accelerating the expansion of the universe for at least five billion years. What is hidden behind it - Albert Einstein's ominous "cosmological constant" is still the most conservative assumption - is one of the greatest puzzles in current physics.

In any case, it is certain that the vacuum is not “nothing”, but only the lowest-energy physical ground state. And even that is not forever. It could be different in other, far-flung areas of space - or in other universes. Here, too, it could change in the future - which would result in the destruction of all the matter that we know and of which we are ourselves. And it seems to have been different in the past: cosmologists speak of a “false vacuum” which, shortly after the Big Bang, made space large in the first place thanks to its exponential expansion. This cosmic inflation is also based on one field - or even several - called an inflaton.

All these more or less hypothetical fields, from the Higgs field to the Inflaton, are not rigid, but fluctuate according to quantum physics. And even more: “Quantum physics cannot be a ruler without a country because fluctuations are part of its essence. If it reigns, 'something' necessarily appears in the most insignificant nothing that it allows and disappears again, "summarizes Henning Genz and asks:" Is it one of the preconditions of quantum mechanics that there is time and space in which fluctuations exist of something can occur? Or does she rather create the stage herself from space and time, which then populate her swaying figures? "

Even a space that is completely free of matter, radiation and quantum - in which we do not live but can describe the physicist - would therefore still have properties and therefore would not be nothing. This follows from the general theory of relativity. It also makes it possible to characterize “empty universes”. As Albert Einstein and the Dutch mathematician and astronomer Willem de Sitter recognized as early as 1917, such empty universes would be negatively curved like a saddle, positively curved like a spherical surface or flat like a tabletop - and under certain circumstances they would even have a dynamic, that is, they could expand or contract.

Henning Genz sums up all the findings on the physics of the vacuum in a nutshell: “Can the room be compared to a stage on which things can, but do not have to, appear? And can the space always be the same, unaffected by the things that occur in it? The answer from physics to both questions is a resounding no. ”But that's not all. Despite all the advances, the original controversy over nothing is still pending. Genz: “The final answer to the question of the nature of a space that is as empty as compatible with the laws of nature is still pending. Because this answer can only be given by a theory that unites quantum physics with general relativity. "

Such a theory of quantum gravity, which Einstein sought in vain in the last decades of his life, could, according to the horizon of expectations, shed light on the nature of space-time itself. In fact, there are already some promising candidates, including quantum geometry or loop quantum gravity (bild der Wissenschaft 12/2003, “Beyond Space and Time” and 4/2004, “Strings Against Loops”). According to her, space and time are not fundamental at all, but are made up of a thread-like network of tiny one-dimensional structures, between which there is literally “nothing”. They are not in space, they create space in the first place. Whether this “space-time dust”, known in technical jargon as the spin network, is eternal and everywhere is currently being meticulously investigated by Abhay Ashtekar's quantum geometry researchers at Pennsylvania State University. According to the first promising calculations, the Big Bang is only a transition in the state of this spin network (Bild der Wissenschaft 6/2006, “What was before the Big Bang?”).

Other quantum cosmologists, on the other hand, have been postulating the emergence of the universe out of nothing since the early 1980s. This does not mean an act of creation in the theological sense. Because that presupposes at least a creator who would not be nothing, even if he did not need anything else - that is, no chaotic primordial material that he would "put in order", that is, form a cosmos. Rather, according to Alexander Vilenkin of Tufts University in Medford, Massachusetts, “everything” really came from nothing (Bild der Wissenschaft 5/2002, “Hawking & Co”). Not only matter and energy, but also space and time would thus have a beginning. Stephen Hawking of Cambridge University developed a very similar hypothesis shortly after and independently of Vilenkin.

“I found a mathematical description of a universe that is zero in size - nothing! - tunneled into a finite radius, ”recalls Vilenkin in his popular science book“ Many Worlds In One ”, published a few weeks ago. According to the hypothesis of the Ukrainian cosmologist, the universe emerged “suddenly from nowhere and immediately began to expand in an inflationary manner. The radius of the newborn universe is determined by its vacuum energy density.The higher it is, the smaller the radius. ”Vilenkin assumes values ​​on the order of a trillionth (10–12) meter.

Vilenkin throws off the obvious question of causality: “It is a quantum process and does not require a cause.” Likewise, the question of what was before: “Before the tunneling process there was neither space nor time, so the question of what happened before it is meaningless. Nothing - a state without matter, space and time - seems to be the only satisfactory starting point for the creation of the world. "

But even if this were so, and this is by far not all quantum cosmologists are convinced, one would have no final explanation, but an even more difficult problem. Because Vilenkin did not answer the philosophical question why something is and not nothing, but rather elegantly circumvented it. And at a high price, as he himself admits: “Of course, the state of 'nothing' is not to be equated with an absolute nothing. Tunneling is described using the laws of quantum physics, so 'nothing' has to obey these laws. The laws of physics must have existed even if there was no universe. ”Rüdiger Vaas ■


• The physical nothingness, the vacuum, is very difficult to create - and has exotic properties.

• Even a space free of matter and radiation is not empty, but filled with quantum processes and various fields.

• Nevertheless, the cosmos could have arisen from “nothing”.

November 21, 2006

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