4.1. Coincidences
Let us now ask the fundamental question about the position of a human in the Universe. The question is both of a physical and of a philosophical nature. Starting from the observation of masses and sizes of physical objects in our Universe, one notices that they are not arbitrary—it is rather that the mass is proportional to the size and so both quantities can be placed in linear dependence. In other words, the space of values of masses and sizes is not filled in randomly and only the structures which obey roughly the linear dependence can exist [
62]. This linear law shows some kind of coincidence which allows living organisms to evolve because they are subject to the same fundamental interactions (gravitational, electromagnetic, nuclear strong, and nuclear weak with appropriate dimensionless coupling constants
,
,
, and
). Bearing in mind physics, we know the reason—they exist due to stable equilibria between these fundamental interactions. For example, common objects of our every day life (a table, a spoon) exist due to a balance between an attractive force between the protons and electrons and a repulsive force (pressure) of degenerated electrons.
Actually, there are numerous facts both related to every day physics and to the universe’s physics which can be called coincidences. Let us enumerate some of them. Practical life shows us the benefit of the fact that water shrinks at 0–4 degrees Celsius which allows fish to survive the winter. The Earth is accompanied by a comparable mass natural satellite—the Moon—which prevents the Earth from wobbling chaotically. This does not happen for Mars, which has only tiny moons (presumably captured asteroids) and its chaotic change of obliquity can be as large as 45 degrees [
63], which can dramatically influence the climate and so prevents a possibility for the life to survive. The next example is the enormous variety of chemicals being the result of the fact that the electrons are light enough compared to the nuclei and so atoms do not form any kind of “binary” systems, allowing chemical bonds to develop. In fact, the ratio of the size of the nucleus and the size of an atom is about
Another issue is the influence of varying constants on chemical bonds. There are basically three types of inter-atomic bonds: ionic, covalent, and metallic [
62]. The ionic bonds are characterised by the strong electric interaction between the positive and negative ions of two different atoms which either take or donate electrons. Classic examples are the sodium chloride
, the sodium fluoride
, and the magnesium oxide
. In fact, the Coulomb electric force which makes the bond is different for each of these molecules because of difference in the charge and also in the distance between the ions. This results in different melting temperatures of these molecules in particular or in general in different physical characteristics of them. In our case of varying constants the strength of Coulomb force would also be varying with respect to a possible change of electric charge
e or alternatively the fine structure constant
and so would effect the chemical bonds resulting in different physical characteristics of the molecules destroying some coincidences such as the anomalous properties of water at 0–4 degrees. If one appealed to the relation (
9) defining the fine structure constant
one could perhaps also find a possibility that the varying speed of light
c would equally be influencing the ionic Coulomb force, so changing the chemical structures and physical properties of various molecules.
The covalent bonds are also due to the electric force though they are characteristic for the same atoms exchanging the electrons. The metallic bonds are due to positive ions of metal interacting with the free electron gas moving between these ions. Since they both are of the electric nature, they would be sensitive to a change of the values of e, , and c in the similar way as the ionic bonds.
The influence of varying G into the chemical bonds seems to be negligible since they are not gravitational in nature. However, once considering the bonds in gravitational field, their strength may be important in view of the macroscopic gravitational influence on larger structures in order to prevent them from being fractured. One should also mention possible influence of the quantum interactions on the molecular bonds which may also be the result of the change of the classical interactions.
Fine-tuned is also the nucleosynthesis (formation of atomic nuclei) in the early Universe which only takes place in a fixed period of time after big-bang (
) and is governed by the fine structure constant
and the ratio
leading to the condition
which is really the case in our universe. It is interesting to note that the nucleosynthesis would not be possible, if an electron was replaced by its heavier version—the muon.
On a more general level, one realises a very narrow range of physical parameters admissible in our universe—something we can acknowledge as the fine-tuning to fit the conditions for life to exist. Fine-tuned are the values of the fundamental constants
and
(cf.
Figure 2) [
64].
In fact, a slight change of would prevent the possibility of existence of life in the Universe. We can see that the “inhabitable” zone for life is set respectively to and . These values of and are fine-tuned for our existence, which is indicated by the white cross in the red striped region in the graph. In the orange region, deuteron is unstable and the main nuclear reaction in the star cannot proceed. For (dark blue region) carbon and higher elements are unstable. On the other hand, unless the electrons in atoms and molecules are unstable to pair creation (top-left part of green region). The requirement that the typical energy of chemical reactions is much smaller than the typical energy of nuclear reactions excludes bottom-right part of the green region. Besides, the light-blue region is excluded because there proton and diproton are not stable, affecting stellar burning and big bang nucleosynthesis. Finally, the electromagnetism is weaker than gravity in the region to the very left.
Last but not least, let us mention that the values of the fundamental interactions coupling constants
,
determine various “physical” conditions for life [
62]. For example, if gravitational energy on the surface of a planet is smaller than the energy required for fracture—any animal, including human, can exist—the condition involves the values of both electromagnetic and gravitational coupling constants
and
.
Such kind of argumentation reflected by the above mentioned coincidences leads physicists to create the notion of the anthropic principles, which expressed the fact that possibly the Universe is extremely “fine-tuned” to host humans!
4.2. Anthropic Principles (AP)
What are the anthropic principles? Opponents say that they are just tautologies or some self-explanatory statements with no practical meaning. Some physicists take them into account seriously. Others consider trivial statements with no meaning for the contemporary scientific method of physics. We take a position that they should be explored as kind of “boundary” options for the evolution of the physical universe. In fact, these principles were first presented by Brandon Carter [
66,
67] on the occasion of 500th anniversary of the birth of Copernicus during the IAU meeting in Kraków, Poland in 1974 and further developed by Barrow and Tipler in their book about the topic [
62].
A fundamental problem raised by AP refers to the question about the reason that out of many possible ways of the evolution of the Universe just one specific way was chosen—that one which led to formation of galaxies, stars, planetary systems, and finally both the unconscious and the conscious life. Of course, while using the term “many possible ways” we immediately touch the problem of “other” worlds (at least hypothetically) potentially and in that sense we refer to the notion of the multiverse. Let us then discuss some formulations of the anthropic principles in order to insight their relation to the multiverse concept.
4.2.1. Weak Anthropic Principle (WAP)
The statement is as follows [
62]: “the observed values of all physical and cosmological quantities are not equally probable, but that they take on values restricted by the requirement that there exist sites where carbon-based life can evolve and by the requirement that the Universe be old enough for it to have already done so”. In other words, life may have evolved in the Universe. In terms of statistics, WAP is usually expressed by the application of the famous Bayes theorem [
68].
The Bayes theorem is based on the notion of the conditional probability
, i.e., the probability of proposition
B assuming that proposition
A is true. The conditional probability fulfils the multiplication rule
which due to symmetry leads to the formulation of the theorem
where
is the probability of proposition
A assuming that proposition
B is true. In Bayesian inference one considers set of models
,
and using (
37) one constructs the so-called posterior probability in view of some data set
D [
69]:
The best model based on set
D is the one with the largest value of posterior probability. Before applying the data set
D the so-called prior probability for each model
is usually assumed to be equal, i.e., that
. The probability
is called the evidence of model likelihood
.
The relative plausibility of any model
compared to some base model
, also called the posterior odds is
In view of the equality of prior probabilities
, one gets the so-called Bayes factor
which for
says that both models are equally good in view of the data, while for
model
is preferred.
An example of the application of the Bayes theorem is when one considers the large size of the Universe as related to the origin of life on Earth [
70]. If
is the model which says that the large size of the Universe is superfluous for life, then
, while for
saying that the large size is necessary for life to appear, then
, while
, so
and it prefers model
.
4.2.2. Strong Anthropic Principle (SAP)
It says that “the Universe must have the properties which allow life to develop within it at some stage of its history” [
62]. In other words (or more physically) it says that the constants of Nature (e.g., gravitational constant) and laws of Nature (e.g., Newton’s law of gravity) must be such that life has to appear. It is interesting to look into various interpretations of the SAP because some of them are quite extreme.
Interpretation A says that “there exists only one possible Universe designed with the goal of generating and sustaining observers” [
62]. In fact, it is very teleological, and this is why it sometimes is also called “An Intelligent Project” interpretation.
Interpretation B is very radical and says that “observers are necessary to bring the Universe into being” [
62]. Such a statement is based on the philosophical ideas of Berkeley and developed by John Archibald Wheeler as the
Participatory Anthropic Principle [
62].
Interpretation C says that “the whole ensemble of other and different universes is necessary for the existence of our Universe” [
62]. The best-known, though most controversial version of this interpretation is the many-worlds theory of Everett [
71,
72] having recently some strong support from superstring theory [
73].
4.2.3. Final Anthropic Principle (FAP)
It says that “the intelligent information-processing must come into existence in the Universe, and, once it comes into existence, it will never die out” with an alternative statement that “no moral values of any sort can exist in a lifeless cosmology” [
62]. As it is easily noticed, it has some broader than physical meaning.
4.2.4. Minimalistic Anthropic Principle (MAP)
This is the most reserved of anthropic principles saying that “ignoring selection effects while testing fundamental theories of physics using observational data may lead to incorrect conclusions” [
67].
4.2.5. Going Beyond
The most challenging for the Author is the interpretation C, since it has some strong support from the most advanced and avant-garde theories of contemporary physics such as the many-world interpretation [
71] and the superstring theory [
73]. The former says that each time one makes a measurement of a physical observable in the quantum world in one of the universes, one also has infinitely many other universes which are equally real and instantaneous in which the result of the measurement is different. In other words, we have a completely different world history in all the other universes (e.g., in one of them, one is married, and in another one, one is single)—called parallel universes.
As for the latter concept, there is the so-called superstring landscape [
74] (nowadays even extended into the so-called swampland [
75]) which allows to generate
different vacua (being the properties of individual universes) which determine different sets of physical laws governing the evolution. It is worth noticing that this number is much larger then even the Eddington number
.
The number
comes because in superstring theory there are many ways of the symmetry breaking and the choices of quantum mechanical vacua. Since the basic space-time of the superstring theory is 10-dimensional, then a 9-dimensional space (plus time) is compactified into a 3-dimensional world in a couple of hundreds (500) ways (called topological cycles). There are about 10 fluxes which can wrap on these topological cycles giving
options [
74,
76] (see also the discussion of M. Douglas in this volume [
77]).
It is worth emphasizing that the Interpretation C somehow moves back SAP to WAP because in some rough interpretation both suggest that our Universe is one of many other options and the other options do not necessarily show any (specific to our Universe) coincidences and fine-tuning.