Vacuum takes up space


In principle, nothing speaks against the fact that all atoms - and thus also molecules - are removed from a macroscopic area of ​​space. Once that has been achieved, we want to speak of the ›vacuum of chemistry‹. Such a vacuum prevails in interstellar space in the disk of the Milky Way. There, each molecule is a macroscopic distance, on average around one centimeter, from its closest neighbor. In our macroscopic areas, with a few powers of ten, there are more or less always around

Molecules; they are on the ground

Molecules per cubic centimeter. No wonder, then, that it is extremely difficult to use technical means to create a space that is no more than

Molecules per cubic centimeter (pressure:

Millibars). But that has succeeded; and that's not what we care about.

So let all molecules be removed from one area of ​​space. Is it already empty for this reason, i.e. a physical vacuum instead of just a chemical vacuum? Of course not. Because it inevitably contains the Planckian thermal radiation that corresponds to its temperature. This radiation actually defines the temperature of the cavity, so that a space that is as empty as compatible with the laws of nature can only be spoken of in the borderline case in which the temperature

of the room area has been reduced to the (unreachable) temperature of absolute zero - minus 273 degrees Celsius. What remains at this temperature is the most empty space permitted by the laws of nature - and it is by no means empty in the literal sense of the word (see Fig. 5).

3.3 Cavity and Zero Point Radiation

The energy dE. the per volume dV and frequency range dν at the temperature T Radiation contained in a spatial area describes Planck's formula (Planck's radiation formula)

It says

for the speed of light and

for - as we know today - expected value

the energy of a harmonic oscillator with frequency

in thermal equilibrium at temperature

. In the formula means

the Planck constant and

Boltzmann's conversion factor from energy to temperature. As an expected value

the energy of a harmonic oscillator at temperature

we get its zero point energy

- as it has to be. We obtain

as the limit value of the energy of the electromagnetic radiation contained in a spatial area per volume dV and per frequency range dν at the transition from finite temperatures to temperature absolutely zero. Precisely this result is also provided by the observation by extrapolation when the temperature of a cavity is lowered more and more in the direction of the temperature absolutely zero.

There is also experimental evidence for residual or zero point radiation in a cavity. For example, the van der Waals attraction (van der Waals interaction) of atoms can be attributed to them. A second experimental proof is the Casimir effect; from him below. The electromagnetic zero-point radiation also forces the existence of charged particles in a vacuum, namely of particle-antiparticle pairs, which together carry the charge zero. More exotic contributions bring quarks and gluons as well as possibly ordered structures, among them the Higgs fields (Higgs mechanism).

3.4 Everything full of swarm

Our knowledge of space, which is as empty as it is compatible with the laws of nature, is based on special relativity and quantum mechanics. Quantum mechanics alone provides the uncertainty relations as the most important ingredients of our knowledge of empty space, the special theory of relativity the equivalence

of energy and mass, and from both together follows the theorem of antimatter: that for every particle there is an antiparticle. A particle and its antiparticle are oppositely charged in the same way, so that taken together they can have exactly the properties of empty space - except for the energy. Since, however, according to information from the uncertainty relation between energy and time, the energy fluctuates, particle-antiparticle pairs can emerge from space for a short time and then disappear again in it (see Fig. 6). The same applies to the necessary fluctuations in the momentum in limited areas. So that the momentum can fluctuate together with the energy, there must be 'something' as its carrier - be it pairs of massive electrons and positrons or massless photons and fields. For this reason alone, there cannot literally be an empty space.

In the emptiest space known to physics, not only electromagnetic rays cavort, but also virtual particles together with their antiparticles. The connections between these objects are established by Feynman graphs like the one in Fig. 7: A photon, as always represented in this essay by a wavy line, disappears and an electron and a positron are created instead. Physics knows the reverse process as well as this one. In addition, there is a generalization to gluons instead of photons and to quarks and antiquarks instead of electrons and positrons.

3.5 The spaces of general relativity

Ground state is the state of a physical system in which its energy is as low as possible. But what is a physical system? That can only be decided by the theory. Take two protons. According to both classical physics and non-relativistic quantum mechanics, they form a system that can assume different states. What they all have in common is that there are exactly two particles - the two protons. The basic state of this system is that in which the total energy of two protons is as low as possible. In quantum field theory, the two protons appear as states of a system described by a Lagrange function that can contain any number of protons and other elementary particles. The basic state of this system is one in which there are no real, but only virtual particles - the vacuum state in which all charges disappear.

Now to the attempt to transfer these conceptualizations to space, which is as empty as possible in harmony with the laws of nature. According to the general theory of relativity, masses bend space and the space acts back on masses by influencing their movements. If we disregard local effects of this kind, only the universe as a whole remains as the subject of our considerations. Let it be assumed that the universe is on average homogeneous and isotropic, so that it does not distinguish any place or direction from others. But whether universes of this kind are special states of a single system called the universe, or whether each of them represents a special system, can only be decided after a theoretical framework has been given, and remains open here. All universes of this kind can be described by the Robertson Walker metric (RWM). Except for one constant, which is usually

is called and the values

can assume and a positive function


the RWM is determined by the demands placed on it for homogeneity and isotropy. The value of

and the function

can only be determined by the properties of the observable universe as well as the Einstein equations - of course under the assumption that is included in the assumed homogeneity, that the observable universe is representative of the whole.

If the cosmological constant introduced by Einstein and soon rejected

disappears, the numerical value of decides

both about the future fate of the universe - whether it will expand forever (k = -1 or 0), or whether it will ultimately collapse - as well as its curvature: At

the curvature of the universe is negative like that of a saddle in two dimensions, at

it is Euclidean and flat, and at

it has a positive curvature like the surface of a sphere in two dimensions. What ever

be describes

the dimensions of the universe, for example by the distance between two selected galaxies (clusters) as a function of cosmic time


At this point we want to state that ›the space‹ of the general theory of relativity is by no means an attributeless nothing, which can be introduced into or removed from the body without changing it. He himself has qualities; and even to describe one homogeneous and isotropic space at one time - the present

- are at least two Numbers required, namely the values ​​of

and from

. But they are not enough to determine the future (and previous!) Fate of the universe. The pressure

and the matter density

as functions of time, the cosmological constant

as well as the current relative rate of expansion - the Hubble number

- have to be added.

Under the assumptions of the RWM apply to


the Einstein equations in the form


Choice of the present

as time in the first equation results with the definition of critical matter density

the relationship

In the equations it says

for the gravitational constant and

for the speed of light. Inspection shows that a non-vanishing

works just like an additional density of matter

along with an additional print

. The pressure

and the matter density

themselves stand for the pressure and the energy density of 'ordinary' matter such as galaxies, dust, neutrinos and radiation fields - everything that can be removed from areas of space, at least in principle. Not included in the off

resulting energy density

is the contribution of gravity itself - the, classically speaking, negative potential energy of matter. Exactly if, with vanishing cosmological constant, the current energy density

the special value

owns, the total energy of the universe is - well With the negative contribution of gravitation - zero, and it can therefore have developed from a long-lived quantum fluctuation and continue to develop in accordance with the quantum mechanical uncertainty relation between energy and time. The third of the above equations shows that - continues at

- exactly in the case the universe is flat as a whole, that is

applies. Is

greater than or equal to

, the universe will expand forever; if not, it will eventually collapse. That the cosmological constant will remain the same in the future is one of them requirements of these inferences.

The cosmological constant describes the contribution of the ›empty‹ space to the pressure and energy density of the universe. Regardless of their origin, it encompasses all of them to form a metric

proportional contributions to the energy-momentum tensor

of the universe together. One contribution to it is Einstein's original cosmological constant, which, without giving any information about its origin, appears in his equations as a parameter to be determined empirically. But also the elementary particles, which are recorded in the Lagrange function of the universe, make contributions to the energy density of the vacuum and thus to

. Mind you, this is not about the elementary particles that make up the universe such as the photons of the background radiation, the neutrinos from the sun or the quarks of the galaxies - they get through


described - but about those Types of elementary particles, which, according to the laws of nature, can exist.



are naturally positive quantities, they have to

equivalent additional contributions


different signs (or disappear). Which contribution is positive depends on the sign of

from. In the history of the universe only non-negatives appear

to have occurred, so we limit ourselves to this case. Now it is not acceptable to unseen one of the variables appearing in Einstein's equations and to leave the others unchanged, because they only solve the equations together. Therefore, although we can make contributions to an effective energy density

and an effective pressure

speak, but not of what would remain, for example, if all matter were taken out of the universe - this would result in a different universe with a generally different value of

. If you look at the whole, in the parameter space of


Areas are delineated in which universes with certain values ​​of

, so curvatures, as well as certain behavior of their

are located (e.g. [23]). If

does not go away, we get a flat universe with his

at any

apparently for


With the expansion of the universe its material content is diluted, so that for sufficiently large

and sustained expansion in both equations for the time dependence of

the to

proportional terms will dominate on the right-hand sides of the equations. Also applies

or is

large enough, we get from the above as effective equations for the evolution of the universe


whereby the second is also obtained from the first by differentiating according to time. The general solution is


is a parameter. So if the assumed approximations can be made, the universe will expand at an exponential rate for growing


The solution is physically interesting in two cases. First, the currently (February 2000) most probable solution [23] of Einstein's equations for the evolution of the universe has a

that on

leads - so

-, and that contains a vacuum component that is by the factor

greater is than the matter fraction. Indeed, under these conditions, the universe will expand forever, and accelerated.

Second, according to the theory of inflation, there was an epoch in the early history of the universe in which its development was dominated by a large positive cosmological constant based on the properties of the elementary particles. This was when the temperature of the expanding universe had become so low that a Higgs field could develop, but none had yet developed. If the Higgs field exists, it assumes an ordered state, and in it the total energy is smaller than it is without the Higgs field: the transition from nothing to something pays off energetically in this case. Everyone knows from the heat of crystallization that the transition from disorder to order can be accompanied by a release of energy. So if there is a Higgs field, but there is not, the lowest possible energy of the universe is smaller than the actual one, and this can therefore be interpreted as the energy of the vacuum, so that it leads to exponential expansion. The expansion ends when the Higgs field actually develops: With this and thereby the universe passes into a state of lower energy. In this process, which cannot be described by Einstein's equations, the positive vacuum energy is converted into manifest energy: The universe, which had become cold during the inflationary expansion against the resistance of gravity, heats up again, and its further fate can can be described by the picture of the hot big bang. When vacuum energy is converted into manifest energy, its influence on the development of the universe changes abruptly - the repulsion (caused by the negative pressure of the vacuum energy) becomes 'normal' pressure and normal gravitational attraction.

3.6 Fluctuations

In through

In spatial areas limited in one dimension, the momentum fluctuates at least as much

that the uncertainty relation

between place and impulse is fulfilled. The same applies to time spans

and the fluctuations in energy

, namely

. Larger fluctuations than those required by the uncertainty relation are possible, but their probability decreases with their size so that the uncertainty relations are in fact also called


can be written.

The uncertainty relation between energy and time is often appropriately described in such a way that the vacuum 'gives' energy - a lot for a long time, a little for a short time. The total value of the electric charge and other charges cannot change the fluctuations, so that particles (which, like the photon, are not identical with their antiparticle) can only appear as particle-antiparticle pairs in fluctuations. But they can and must. The greater the mass of a particle, the more energy its very existence requires, so the fluctuations it contains must be more short-lived.

The particles fluctuating in a vacuum lack nothing but energy, which they do not have to give back in order to become real particles. These are made available by the machines of elementary particle physics. In a simple case, a high-energy photon hits a ›virtual‹ electron-positron pair hidden in a vacuum, transfers its energy to it and thereby elevates it to a pair of actually existing particles (see Fig. 8).Accelerators, in which particles are shot at antiparticles, reverse the vacuum fluctuations. Particles and antiparticles initially destroy each other in a mess of pure energy, which then helps the particles fluctuating in the vacuum to real existence. The reaction products point the experimenters to accelerators like that Large electron positron ring (LEP) at CERN in Geneva in their detectors.

3.7 Casimir effect

The unlimited ›empty‹ space is also filled with the temperature

Fluctuations in the electromagnetic field with continuously many wavelengths between zero and infinity. Electromagnetic waves cannot penetrate electrical conductors, so they have nodes on conductor surfaces: They are reflected from the surfaces and therefore exert pressure on them. Let us now assume that two electrically neutral conductive walls - two metal plates, ie mirrors for electromagnetic waves that experience a recoil from them - face each other in the otherwise ›empty‹ space (see Fig. 9a). Then only those zero point oscillations can occur between the plates, the wavelengths of which are adapted to the gap. From the outside, however, zero-point vibrations with any wavelength burn up to the plates. Because they are more numerous, they exert more pressure on the plates than those from the inside: The plates are forced towards one another; in other words, they attract. Fig. 9b illustrates this effect by a vibrating string extending to the right into infinity, which is clamped at its starting point as well as at another point.

It should be noted that this illustrative argument must be used with caution because there are two infinite Deducting sizes from one another - the internal pressure from the external pressure, both of which diverge at short wavelengths. That the complications brought by the infinite must be taken seriously when electromagnetic waves are reflected on surfaces is already shown by the fact that in some more complicated geometries than that of two opposing plates the total pressure of the electromagnetic waves leads to repulsion rather than attraction. Actual calculations of the force between conductive bodies in the supposedly empty space use their energy densities instead of the impulses of the waves. Here, too, two opposing, individually infinite effects must be subtracted from one another. Firstly, when the distance between the plates is reduced, the energy is increased in that the interior is replaced by more energetic exterior. Second, the energy density in the interior drops because again fewer wavelengths fit into it. But the final formula for strength

with which two are at a distance

parallel, uncharged electrically conductive plates per cross-sectional area


is remarkably simple: besides pure numbers, it only contains the natural constants


. Their appearance shows that quantum mechanics and relativity are together responsible for attraction.

The Dutch theoretical physicist H.B.G. Casimir predicted in 1948; Experimentally proven, but with major errors, it was ten years later by M. J. Sparnaay. It was not until 1997 that convincing evidence with small errors was achieved (see [29]).

3.8 The oversized contributions of the vacuum energy of the elementary particles to the effective cosmological constant

Any system that works with a frequency

can vibrate, possesses the energy in its state of lowest energy

. So that the state of lowest energy is Lorentz-invariant, the following contributions to the energy-momentum tensor are

to the metric

proportional and therefore contribute to the cosmological constant

at. In fact, that delivers

of each elementary particle makes an assessable contribution

. The contribution of bosons is positive, that of fermions is negative, and it should be mentioned that in the unbroken supersymmetry in which bosons and fermions appear in pairs, the sum of the contributions of all particles to

Is zero. But because the unbroken supersymmetry does not hold in the real world, we are confronted with the fact that there are many contributions to