Heisenberg, Cosmology, Lindau, 1968
Ladies and Gentlemen,
Cosmology is deemed to be the science of the spatial and temporal form of the universe, the cosmos.
Humans have thought about cosmology in philosophy and natural science since time began, but cosmology has only become a branch of modern
science through Einstein’s general theory of relativity.
I now have to make a remark which is semi-philosophical: cosmology’s task is not to study the laws for the cosmos, so to speak.
This is because the cosmos is unique.
A law, however, always takes the form: whenever this happens, that must also happen.
And this always presupposes the repetition, it presupposes that we can artificially create certain situations again and again,
and can then observe that this or that happens.
The cosmos is unique, however, there is only one cosmos, and therefore we cannot enquire about its laws.
Cosmology therefore involves a different issue, which can be phrased in the following way: we study the laws of nature in the finite areas
which are available for our daily experience and for our more complicated experiences in the experiments.
These laws do not allow any arbitrary form of the cosmos, and form is meant here in spatial and temporal terms, i.e. the question of whether
the cosmos is finite or infinite in terms of space, whether it began in terms of time, whether it will finish in terms of time and so on.
So the laws of nature only permit certain forms, these forms are the boundary conditions, as it were, with which the laws of nature must be
compatible or which have to be studied as possible boundary conditions to the very laws of nature.
Now, the decisive change that was brought about by Einstein’s general theory of relativity, was that geometry,
spatial as well as temporal geometry, was incorporated into physics by the statement that the gravitational field determines
the metrics of the world.
This means that the local gravitational field is also relevant for the metrics in the local region
of the cosmos where it is just being studied.
This caused, as I have already said, geometry to become a consequence of physics to a certain degree, or a part of physics, and this also
made topological conditions possible in the cosmos which prior to this would have been considered to be impossible.
For example the idea that the cosmos is spatially finite.
Now, you know that these cosmological problems in Einstein’s theory of relativity have been very carefully investigated, that there has been
a series of models for the cosmos, I think of de Sitter’s world, for example, Einstein’s idea, Friedmann’s cosmos etc.
Today I do not want to talk about these models, but about the question of whether this modern cosmology, which forms an important component
of the general theory of relativity, of course, whether this modern cosmology has anything at all to do with atomic physics and then also
with the physics of elementary particles.
Einstein himself understood the necessity of such a connection, and he initially attempted to extend his theory of gravitation to a unified
field theory which, he hoped, would include all of the world’s phenomena.
And since at the time, apart from gravitation, the most important field was first of all the electromagnetic field, Einstein and many other
researchers after him attempted to unify the theory of gravitation and the theory of the electromagnetic field.
From this imagination derived the hope that it could also be possible to derive the existence of the atoms,
i.e. of all atomic phenomena, from this unified field theory eventually.
Now, this hope ended in failure.
It has not been fulfilled, and various reasons can be given for this failure: First, an empirical one,
although this is not the most important one in my view.
During the past twenty years it has turned out that, in addition to the gravitational field and the electromagnetic field, there are many
other fields of similar structure, which of course all have to be taken into consideration in such a unified field theory, because we know:
every type of elementary particle has a field, and we have already observed more than a hundred different elementary particles in nature,
so such a unified field theory would necessarily have to include all these different fields of the elementary particles.
But this empirical reason, the fact that there are many fields, is not the decisive reason in my view.
The decisive reason for the failure of Einstein’s hope is the fact that there is a type of law in nature which does not fit in with the
causal ideas of a space-time causal field theory.
And this characteristic of nature was maybe phrased for the first time in this strict form by Niels Bohr as follows: the stability of matter
requires laws which have a different structure to those of classical physics.
Stability of matter here means that a piece of iron, for example, if you subject it to any changes you like, smelt it or have it form
compounds, if you then extract the iron again by chemical means, a piece of iron with similar physical properties will again be formed.
This, I would like to call it persistence of forms in nature, the stability which causes the same chemical elements to form again and again,
this requires a type of law which is just not compatible with classical physics.
Especially since Rutherford’s model of the atom became known, it was clear that such a planetary system in miniature would never have the
degree of stability which is actually observed in nature for the elements, for the atoms.
And you know that this type of stability was then eventually formulated in quantum theory, which began with Planck’s great discovery,
and which then in the 1920s found its final mathematical form.
This is the reason why attempts to include the problem of atomic physics from Einstein’s theory, from his unified field theory as well, and
to make a connection between cosmological problems and issues of atomic physics or elementary particle physics have been unsuccessful.
Now, atomic physics and elementary particle physics have made such progress during the last decades, from hundreds or thousands of
experiments we know so much more about elementary particles, that we can now pose the question the other way round, is it maybe possible to
make the connection from the known laws of elementary particle physics to Einstein’s ideas of the theory of gravitation,
the unified field theory and finally cosmology.
In order to prepare this connection I now have tell you a little bit about the development of atomic physics or elementary particle physics
during the last decades.
And I would like to emphasise that the most important, most crucial discovery in this development by far has been the discovery of
antimatter or the antiparticles by Dirac; this discovery is now almost 40 years old to the day,
and so we are possibly celebrating a certain anniversary now.
I feel it is important that it is only in the course of the decades that the full significance of this discovery back then has become clear,
and become clear due to the later experiments and later theories.
Forty years ago, as you know, Dirac found that there exist anti-electrons or positrons in addition to electrons, and we now know that there
are antiparticles for every type of elementary particle, and it is therefore possible to say in general that matter always has antimatter
which differs from the matter by the electric charge, for example.
And this discovery initially meant that the whole concept of elementary particles had to be revised.
The original idea, even in the quantum mechanics of the 1920s, for example, was that the elementary particles, which make up an atom, that
they are eternally unchangeable entities, which nature simply created at the beginning, so to speak, and which exist, and for which it was
possible only to make empirical statements, but for which there were really no laws of nature which exceeded these statements.
In those days, the atomic nucleus and the electrons were the elementary particles which made up the atom more or less.
After Dirac’s discovery, this concept was no longer possible, because from this moment on, one had to say, for example, that a hydrogen atom
did not necessarily consist of one proton and one electron, but one could say with the same justification that the hydrogen atom consists of
one proton, two electrons and one positron.
And as is usual in quantum mechanics, one can at least say that the hydrogen atom also consists virtually of such states.
After all, we have learned from quantum mechanics that an atomic system is determined by its symmetry properties and that everything which
is possible within these symmetry properties also virtually belongs to this atom.
As an example: today we can no longer say that a, let us say, oxygen molecule, for example, necessarily consists of two neutral oxygen
atoms, we can also say it consists of a negative oxygen ion and a positive oxygen ion.
This means all entities which are consistent with symmetry are also virtually present in the relevant stationary state.
Now, from this follows initially that the elementary particle is not elementary, but an entity with a complicated composition, and this
applies to every elementary particle.
This statement must have been a great disappointment to all the physicists who were working in atomic physics at that time,
because it was hoped, of course, that at least the elementary particles were slightly simpler,
and over the years one had to force oneself to the idea, brought about by Dirac’s discovery, that the elementary particles themselves
are complicated dynamic entities.
The first experimental consequence of this rethink was the finding that when two elementary particles collide, if the energy is high enough,
a great many new elementary particles can be generated.
It was therefore possible to understand that the whole process of the division of matter
comes to a completely different conclusion than the earlier philosophy had assumed.
In the earlier philosophy one would have asked: yes, there are two options, either matter can be subdivided further and further,
i.e. if I simply use sufficiently high forces, I can divide an atom into nucleus and electron,
the nucleus into proton and neutron, can subdivide the proton into something smaller and so on.
Or, if this infinite divisibility does not exist, a belief that atomic physics naturally would suggest,
then there are some smallest units which cannot be subdivided at all.
And for some time, most physicists believed that proton and electron were such smallest units.
Now, Dirac’s discovery has shown that in addition to this alternative, which would appear to the philosophy as a clearly positioned
alternative which has no other option, that nature has thought of something new in addition to this alternative.
This means, when matter is subdivided, if I want to divide with sufficiently large forces, i.e. if I let two elementary particles collide
with sufficiently high energy, then a great many particles are being generated by this process.
These particles are by no means smaller than the elementary particles which are split up, however, but they are again entities of the same
type, again elementary particles of roughly the same size.
Now this had been foreseen, around the year 1936, as a theoretical possibility,
and had only been experimentally corroborated after the 1950s by the large accelerators.
We therefore now know that the elementary particles are indeed complex dynamic entities in this sense, that there is a spectrum of
elementary particles, just like there is a spectrum of stationary states of the iron atom,
for example, which had already existed in the older atomic physics.
One can therefore say: in the collision of two elementary particles the energy of the collision becomes matter
by turning into the form of elementary particles.
We have known this to be the case experimentally since the large accelerators which were first built around the beginning of the 1950s.
Now the crudest way to express this fundamental change in the idea of the concept of elementary particle is maybe to say:
Dirac’s discovery forced us to take the path away from, or the deviation from, Democritus’ philosophy to Plato’s philosophy.
Democritus’ philosophy is of course based on the idea that there are atoms, smallest indivisible entities, and it is possible to say the
philosophy of Democritus is based on the phrase, in the beginning was the particle.
The philosophy of Plato is based on the phrase, in the beginning was the symmetry.
And we have learned from Dirac’s discovery that in the beginning was the symmetry.
Now, the theory of elementary particles has made it clear that, in order to come to an understanding of these many elementary particles and
their laws, we have to start to talk about symmetry, i.e. in some form, in a mathematical form, one has to specify those symmetries which we
have to assume to be valid as a result of our empirical observations.
We know that in our experience the so-called Lorentz group applies,
i.e. the symmetry property of nature which has formed the subject of the Special Theory of Relativity.
We also know that there is a group which has been known for 35 years under the name isospin group, and which relates to the electric charge.
I naturally do not want to discuss details here.
There are further symmetry properties, which have turned out empirically, and it is obviously the task of theoretical physics in this field
to summarise these symmetry properties in a useful mathematical form, and in such a way that the elementary particles which are observed
empirically then follow from the law so formulated.
The issue is therefore, regardless of how one sees the success of the previous attempts, quite certainly: what is the fundamental law from
which the spectrum of elementary particles follows, i.e. a unified theory of the elementary particles is required.
Whether this has to be a unified field theory, as I myself would like to believe, or whether this unified theory has a different form,
this must remain unsettled at the moment, it is not very important for what I want to say later.
Only: if there is such a unified theory, then of course the question immediately arises as to whether it is not possible to automatically
find the way from this unified theory to the electromagnetic phenomena, to gravitation and finally also to cosmology.
Well, this way is not really conclusive.
Mr. von Weizsäcker, in particular, has emphasised in philosophical talks recently that this way is really forced upon us, i.e. that a
unified theory of elementary particles, if it can be correct at all, that it then also necessarily contains gravitation and cosmology.
Before I now go into the details of how this connection can be made, I would like to emphasise that the two fields that Einstein studied,
i.e. the electromagnetic fields and the gravitational fields, that these fields differ slightly, and very characteristically, from the other
fields which we have discovered in the last decades.
Most fields, the electron waves, for example, or the waves corresponding to a proton,
or corresponding to the pi-meson etc., most fields are short-range fields.
This means forces which are exerted by these fields have only a very short range, at greater separations the forces disappear,
an example are the forces which act in chemistry, and which bond atoms to form molecules.
These forces obviously have a short range.
They are sufficient to keep molecules, these small entities, together, but they are no longer effective if the atoms have large separations.
Only the electromagnetic and the gravitational forces, those are long-range fields and so it is only these fields which have really been
known and studied in classical physics.
In the language of quantum theory it is said that those elementary particles which correspond to such fields have rest mass zero.
Light quanta, for example, which correspond to the electromagnetic fields, have rest mass zero, and if gravitons exist, i.e. particles which
correspond to the gravitational field, and we must believe this according to quantum theory, these gravitons will also have rest mass zero.
So these classical fields, which Einstein also studied, they have indeed a special position as part of the whole spectrum of elementary
particles, and therefore one supposes that these particles also play a special role in the overall workings of the theory of elementary
particles, and that a special intellectual step is required in order to get from the general spectrum of elementary particles with the many
individual symmetries that exist there to the special fields which have a long range or whose particles have zero rest mass.
Now, I believe that we can already say, regardless of the special form which one wants to assign
to this unified theory of elementary particles, where the connections to these special fields must be made.
And this is again a crucial consequence from Dirac’s discovery of antimatter.
Until Dirac’s discovery, i.e. in the old idea of elementary particles, one could assume that the ground state of the physics of the
elementary particles was simply the vacuum, or let us say ‘nothingness’.
The state of lowest energy was, one would have said then, precisely the state in which there is no matter at all, nothing at all, and the
nothing at all has of course the highest possible symmetry, i.e. any possible transformation transforms it back into nothing again.
The moment that antimatter was discovered, however, this idea could no longer be maintained, because even the pure nothing at all can
virtually transform into a number of pairs of electron-positron, or proton and anti-proton etc.
This means that this ground state also suddenly becomes, due to the discovery of antimatter,
a composite system, if you like, or maybe better, a dynamic problem.
So the ground state must also be a solution to the equations with which the unified theory of the elementary particles is formulated.
This now suddenly creates a situation in the theory of elementary particles as we know it from the usual quantum mechanics,
from solid state physics, for example.
A crystal is itself the solution of these complex quantum mechanical equations which can be formulated in the form of the Schrödinger
equation, for example, or a matrix equation, and it is a mathematical problem to determine which form the crystal has.
It is therefore possible to say: with Dirac’s discovery the ground state of elementary particle physics is no longer nothingness,
but precisely the cosmos.
And the cosmos itself has to be a solution of that unified theory of elementary particles.
Now we can, in order to think about what can happen with this problem, remember the parallels from the theory of solid bodies.
We know, for example, we start in the theory of the crystals with a Schrödinger equation, for example, or a Hamilton function of quantum
mechanics, which is of course invariant with respect to rotations in space.
There is no preferred direction in space, of course.
Nevertheless we will then find that the ground state of the crystal is not rotationally symmetric, but that the crystal has an axis.
The fundamental equation, which is itself rotationally symmetric or symmetric with respect to rotation, gives rise to a ground state of the
crystal which is not rotationally symmetric, but asymmetric, which has an axis,
which therefore transforms into another possible ground state under rotation.
We also know that one and the same fundamental equation, i.e. one and the same Schrödinger equation for the crystal,
can possibly have different ground states as solutions.
After all, there are chemical substances which can exist in different crystal structures at absolute zero.
From this comparison it now follows that, in the world of the large scales as well, the cosmos does not have to have the symmetry which the
laws of nature themselves possess; that we therefore may have a lesser symmetry in the cosmos, if the cosmos is the solution to this unified
fundamental equation, and that such a lesser symmetry must then of course also have important consequences
for the details of elementary particle theory as well.
Now, one of the most important consequences of the break in symmetry by the ground state is precisely the existence of forces with long
range, or of particles with zero rest mass.
I would like to make this statement, which in mathematical form is often also given in the form of the so-called Goldstone theorem, meaning
the theorem is from Goldstone, and was drawn up around ten years ago,
I would like to make this theorem plausible again using solid state theory.
It is possible to visualise this fact without any mathematics whatsoever if one takes an example from solid state physics,
and I would like to think specially of the theory of crystals.
We therefore again assume that the fundamental equation of the crystal is invariant with respect to rotations in space, this is almost
natural at the moment where no external electric or magnetic forces are assumed, and we will assume that a crystal which has an axis,
has a preferred direction, results as the solution of this Hamilton function.
We can then imagine that we take out any finite region from this crystal which initially was assumed to be infinite,
and now attempt to make a small rotation in this finite region.
External forces will then act on this part which is rotated, of course, and we ask: which oscillation frequencies will occur if this rotated
part now so-to-speak springs back and starts to oscillate, can we say anything about the oscillation frequencies?
We can do this in the following way, if all forces occurring have a short range.
If the restoring forces which try to turn this rotated part of the crystal back, if they act only on the surface, then if this rotated part
is sufficiently large, the restoring forces will be proportional to the surface of this rotated entity,
of course, but the inertial forces are clearly proportional to the volume.
This means that the bigger this rotated part, the slower will be the oscillation frequency, because if the rotated part becomes bigger and
bigger, the surface to volume ratio as it were becomes smaller and smaller.
An oscillation will be produced, therefore, a collective oscillation,
which has the property that the frequency approaches zero for an infinitely large wavelength.
Now these are precisely oscillations of the type which in a relativistic theory can only be caused by particles of zero rest mass.
The oscillation frequency approaches zero if the wavelength approaches infinity.
And this means, if I now translate this into particle language,
that the particles corresponding to this oscillation frequency have zero rest mass.
Now, this conclusion, which immediately makes sense from the illustration, is mathematically not absolutely imperative in only one case, it
is not absolutely imperative if the forces which try to turn this rotated part back,
if these forces do not have a short, but a very long range.
Because then the forces can also become proportional to the volume, and there are indeed cases like this in elementary particle physics, the
phenomenon of superconductivity, for example, this is based on electromagnetic forces, i.e. Coulomb forces, becoming effective, and
superconductivity does not have these types of oscillations whose frequency approaches zero when the wavelength approaches infinity.
But you see, in any case, no matter how the thoughts on these two channels go, the consequence will always be that if the ground state has
the degeneracy stated just now, if it has a directional property, then either particles of zero rest mass or long-range forces must occur.
Now this fact, which was first expressed mathematically by Goldstone, but which was discovered earlier by others, Dürr for example, and
which was emphasised for the first time in elementary particle physics by Pauli, I would also like to say this, in work that Pauli and I
jointly attempted ten years ago, this fact now means that it is precisely the existence of long-range forces and particles of zero rest mass
which can be a consequence of the degeneracy of the ground state.
This Goldstone theorem is one of the key components of the connection which leads from elementary particle physics to cosmology and
Einstein’s field theory, gravitation theory.
A second component has been established by important work by Thirring, Weinberg, Yang and Mills and others in recent years.
Thirring and Weinberg have posed the questions quite differently.
Initially they said, what would happen if we completely forget about Einstein’s general theory of relativity and the theory of gravitation
for a while, and pretend all this does not exist, and if we were to conduct pure elementary particle theory.
We also want to make the additional assumption that in this elementary particle theory, for reasons which we will not yet discuss,
long-range fields exist or particles of zero rest mass exist.
And they ask what does it look like, which fields do we then get, and what can be said about the physical consequences of these fields.
And Thirring started by stating the following: if we assume that tensor fields exist, i.e. in quantum theoretical language, fields
corresponding to particles with spin two, then these fields must belong to a field equation which in first approximation corresponds to
Einstein’s gravitational equations.
And it turns out furthermore that, although one started with Euclidean metric and a Lagrange function which is invariant with respect to the
special relativity group, that afterwards via the scales and clocks Einstein’s metric results after all.
This means it is possible to prove that if such a field exists, if there is such a tensorial interaction, then scales and clocks change such
that if one defines the metric by the scales and clocks one returns to Einstein’s metric, i.e. returns to the world with curvature.
It is therefore possible to state that Einstein’s theory of relativity, general theory of relativity, can here be taken to be a consequence
of field theory, of elementary particle theory, without us now already having to commit ourselves
to a quite specific form of elementary particle theory.
Furthermore, Weinberg showed that if one poses the question even more generally and wants to know what fields of zero rest mass or
long-range fields could exist at all, if we make certain general assumptions for elementary particle theory which are generally accepted.
If we assume, for example, that in elementary particle theory there must be a unitary scattering matrix or S-matrix from which the
asymptotic behaviour of some experiments, i.e. the outgoing and incoming particles and waves, can be calculated.
Weinberg found out that under very general assumptions, which I naturally do not want to go into at the moment, that under such general
assumptions only two types of fields are in fact possible: firstly, fields of spin one, or expressed in the old form, vector fields which
have precisely the shape of the electromagnetic fields, and secondly fields of spin two, or tensorial fields,
which have precisely the shape of Einstein’s gravitational fields.
Fields of spin zero or three or four can be excluded according to Weinberg for reasons which I do not want to discuss here in detail.
And you see that this really already makes the complete connection.
Because, on the one hand, we now know that from the degeneracy of the ground state, i.e. from the fact that the ground state is a dynamic
problem and so solutions of the elementary particle equations can exist which are less symmetric than these equations, which results in the
fact that particles of zero rest mass or long-range forces must exist.
From Thirring and Weinberg we know that, if these forces exist, then there can only be fields of spin one and spin two, and these are
precisely the electromagnetic and gravitational fields.
On the other hand, if these fields exist, if the symmetry of the ground state is degenerate, then you see that we have come full circle.
We can say on the one hand: the asymmetric ground state ensures that particles with zero rest mass exist.
They have the form of gravitation and electromagnetism.
But these fields ensure in turn that asymmetric solutions exist.
Because we know already that the electromagnetic fields, for example, break the isospin symmetry precisely at the elementary particles,
that in terms of their size and form they are responsible for breaking the isospin group.
In a final theory of elementary particles there is therefore no need to decide whether the breaking of the symmetry is primary and the
generation of the electromagnetic and gravitational fields secondary, or whether it is the other way round, whether nature first thought of
producing particles of zero rest mass and thus electromagnetic and gravitational fields, as it were,
and then produced the asymmetric cosmos from this.
So this is the general line of thought for this connection which leads from atomic physics or elementary particle physics to cosmology.
And now I would like to provide more details about this connection, as far as they are known.
If one wants to know the details, then one naturally needs to know first what the symmetries are,
the exact symmetries, of the law of nature on which they are based.
You know that I myself believe that these symmetries can be represented in a simple equation.
But I especially do not want to start from this special form of the elementary particles,
but would rather begin with the experiment for the moment.
I believe that, experimentally, one can say with almost certainty that the Lorentz group
and the isospin group belong to the fundamental symmetries.
Not, for example, the SU(3) group or higher groups.
I do not want to say anything about the discrete groups which have also been discussed.
Now there is no doubt that the cosmos is not symmetric with respect to the isospin group, and I believe there is also no doubt that the
existence of the electromagnetic field follows precisely from this asymmetry.
If we believe that the electromagnetic field can be explained in this way, then we now have a tool available in the properties of the
electromagnetic particles and the electromagnetic field to enable us to state something about the cosmos.
We will then have to say that the cosmos is not symmetric with respect to the isospin group, but it should be symmetric with respect to the
particle/antiparticle group, i.e. with respect to the so-called C parity, if I may speak in this special language here.
Now this is a quite concrete statement for cosmology as well.
It means initially that the world we observe does not transform into itself if we exchange proton and neutron,
if we turn a proton into a neutron, so to speak.
And this is an empirically trivial fact, very many stars consist mainly of hydrogen, but it would be impossible to build a star from
neutrons, at any rate not stars of this size.
Nature overall is therefore not symmetric with respect to the isospin group, but it should, in order for us to understand electromagnetism,
it should be symmetric with respect to C-parity, and that would mean that on average there must be
just as much matter as antimatter in the cosmos.
I therefore believe that from elementary particle theory one can risk the hypothesis that on average there is as much matter as antimatter
in the cosmos, and probably this assumption would only be thinkable in the form that in the cosmos there are just as many galactic systems
made of matter as are made of antimatter.
The astrophysicists have to decide whether this is correct.
There are theories which state, they were presented to us in Munich a few years ago by Edward Teller, which state that certain,
very peculiar objects in the firmament of the so-called quasar, that they with their incredible brightness, an enormous emission of energy,
are caused by galaxies, for example, by matter and antimatter colliding and annihilating there and converting the energy into radiation.
Now, I do not know whether these theories are correct.
This is a matter for astrophysicists to decide, and I know there are counterarguments, but I believe that one should take from elementary
particle theory an argument for those views in any case, that one has to say that the symmetries of the electromagnetic field indicate there
should be as much matter as antimatter on average in the world.
You therefore see that such symmetry considerations then come to quite specific statements
which can be confirmed or rejected by empirical means.
The second group which certainly plays a decisive role in elementary particle physics is the Lorentz group, and I believe that one has to
make a connection between it and gravitation, that the universe is not symmetric with respect to the translation group in the Lorentz group,
i.e. with respect to the inhomogeneous part of the Lorentz group.
If one assumes that this asymmetry exists, then, as I said a while ago, according to Thirring and Weinberg, the gravitational fields follow,
and conversely the gravitational fields bring about the disturbance of the translation group.
It could be the case, for example, that due to the gravitational fields the true model of the world or the cosmos corresponds to de Sitter’s
model, where the translation cannot be carried out as simply as in a Euclidean world.
If the translation group is disturbed, on the detour via Thirring’s and Weinberg’s considerations, a curved space will therefore result,
and thus all these world models which had already been in discussion in Einstein’s theory of relativity are put up for discussion again.
Now, this part of physics is by no means concluded yet, and maybe I should say this especially with a view to the young physicists present
here, there are still many problems to be solved here, because while one can more or less already see how the electromagnetic field follows
from elementary particle physics, this is still at the very beginning for gravitational physics,
and many details still need to be worked on here.
And what the consequences will be for the model of the cosmos, i.e. de Sitter’s, Friedmann’s, Einstein’s world etc.,
there is no information at all on this for the time being.
Now, in elementary particle physics there are fields in addition to these two classical fields, the gravitational and electromagnetic
fields, which do not have a long range, but particles of zero rest mass or almost zero nevertheless, this is not known,
these are the neutrinos, and assigned to them or somehow connected to them is the so-called weak interaction.
Now in the weak interaction the lack of clarity is very much greater than in gravitational theory or even electromagnetic theory.
Despite this, there are some indications that the weak interactions are also somehow connected to the breaking of symmetry.
Firstly, in the so-called weak interactions the parity, for example, the left/right symmetry is broken, one can therefore assume that the
existence of the weak interaction is connected with the fact that in the cosmos this left/right symmetry is not maintained, the disturbances
seem to be extraordinarily weak, however, and finally in recent years the symmetry in relation to time reversal has also been questioned,
i.e. with the decay of the K-mesons the PC-group or, what corresponds to it, the T-group seems to be broken.
I do not want to speak about this weak interaction here, simply because as good as nothing is known about it yet.
It is not yet possible to see as clearly as with gravitation that a symmetry break, of the parity or PC-invariance, for example,
is related directly to these weak interactions, that the weak interactions follow from this symmetry break, as it were.
And here there is still completely unknown territory which I hope will inspire many of the young generation to turn their minds to it.
Whatever one may think about these problems, I believe that we are already seeing where the connection must be made between atomic and
elementary particle physics and cosmology, and I believe that the development in the next years, maybe in the near future, will be that
cosmology becomes a part of elementary particle physics in a similar way to that
which Einstein had hoped for earlier as part of his unified field theory.
But this, as I have just said, is still a long way off for the most part, but I nevertheless believe that here in Lindau it is acceptable to
sometimes talk about things for the future, and on this note I would like to conclude.