How is E mc2 dimensionally consistent

The physical fundamentals of technology in the 21st century,

or today's physics is tomorrow's technology.


Today's understanding of the forces of nature, some of which are already used in modern technology, is based on the Quantum field theory and the general theory of relativity.
These theories were tested and confirmed with very high accuracy in the application areas of solid state physics, molecular physics, atomic physics, elementary particle physics and astrophysics / cosmology.
In the case of extremely high energy densities (such as directly after the Big Bang or in the center of black holes), as will be required for future highly developed technical civilizations to master advanced high technologies (e.g. hyperspace technology), we absolutely need a synthesis of the underlying principles of quantum field theory and general relativity , since here neither quantum effects nor space curvature effects can be neglected. This, of course, creates new conceptual problems since the application of the Heisenberg uncertainty relation on the force of gravity (gravitation) and thus directly on the space-time geometry means that classical geometrical ideas are no longer appropriate with "very small geometrical distances" (as with a future sub-nanotechnology). Without the unification of quantum theory and general relativity theory, fundamental questions about matter and the universe will remain unanswered.

The String theory is a hot candidate for a consistent quantum theory of gravitation (quantum gravity) and leads to a natural union of elementary particle forces. It makes it probable that in an intermediate area, before the concept of space-time-geometry becomes meaningless, the spatial dimension increases and gravitational forces do not exist as curvature effects in "invisible" higher dimensions. While the idea of ​​a very small fifth dimension as a geometric explanation for electricity and magnetism has existed since the 1920s, the quantum mechanical one shows duality different string theories that our observable space - time could only be a low dimensional component in a higher dimensional continuum. Energy that is needed to observe a fifth dimension can be derived from the energy balance of the supernova SN1987A. This is an example of how the physics of the smallest building blocks of matter (elementary particle physics) leads to relationships with the physics of stars (astrophysics) and with the structure of the universe on a large scale (cosmology).
According to string theory, the building blocks of matter occurring in the so-called standard model of elementary particles are no longer point-shaped (0-dimensional), but tiny oscillating threads (1-dimensional) or strings with a length of 10-33cm. In 1995, Edward Witten succeeded in mathematically uniting the various versions of string theory developed up to that point, i.e. largely demonstrating their mathematical equivalence. The resulting new theory is called "M-Theory", where "M" stands for membrane or mother of all theories. In M-theory there are not only 1-dimensional strings, but also multi-dimensional membranes, which are briefly referred to as branes. The M-theory can be formulated in 11 dimensions without any mathematical contradictions.

The Loop quantum gravity assumes that our world is made up of so-called loops that are linked to form networks. Changes over time arise from the fact that these networks are dynamically linked. The loop quantum gravity does away with our idea of ​​a structureless space-time, i.e. space and time are quantized. According to this, the measurement accuracy of these quantities would have a lower limit. The quanta of space and time can be calculated from the fundamental constants of the speed of light c, the gravitational constant G and the Plank constant h.
The so-called holographic principle establishes complete equivalence between two universes with different dimensions and different physical laws. Theoretical physicists have mathematically proven this principle for a special type of 5-dimensional space-time ("anti-de-sitter" space, a negatively curved space-time) and its 4-dimensional limit. According to this theory, the 5-dimensional universe is mapped onto a 4-dimensional boundary surface. In the 5-dimensional space-time, the superstring theory prevails, whereby a so-called conformal field theory with point particles applies to the 4-dimensional hologram. A black hole in 5-dimensional space-time is equivalent to the hot radiation on the hologram.

The universe has properties on its smallest physical scale (the Planck scale) that enable digital mathematical behavior. Quantum mechanics has intrinsic sources of randomness, which are gigantic Quantum computer can program. The laws of quantum mechanics are largely deterministic, but now and then random events (quantum fluctuations) are generated in the computer in such a way that its state is no longer strictly causal and different states arise with a certain probability at any later point in time. Information states (quantum bits) are generated by so-called decoherence, i.e. the irreversible disappearance of the superpositions of quantum mechanical states due to the inevitable interaction with the environment. The quantum bits program the universe and thus generate its evolutionary development. The number of quantum bit switchings since the existence of the universe is no greater than 10120 or 2400. In contrast to the conventional computer, the quantum computer can perform various different mathematical operations simultaneously.


Quantum field theory


In the sub-nuclear area, matter and forces are described by quantum fields. A field is generally a form of energy that fills the space. Quantum fields are clearly spoken, force fields composed of energy packets. The energy packets have both wave and particle character and elude our macroscopic view. They can therefore only be grasped with appropriate mathematical concepts, the beginnings of which date back to the beginning of the 20th century and which are in part still the subject of intensive research.

Quantum field theory on curved spacetime can be viewed as a preliminary stage for theories of quantum gravity, in which matter fields are described as quantized on the background of classical gravitational fields.

The quantum field theory forms the theoretical basis for understanding the elementary particles and, based on the assumption of local (point-like) interactions, enables the forces between matter particles to be calculated. The, in a classical approximation, imagined point-like interaction areas lead to infinities, which make a direct field quantization of gravity inconsistent. The only known way out at the moment is a string theory in which the elementary degrees of freedom are no longer punctiform.


General theory of relativity (gravity / gravitation)


Based on the mass independence of movement in the gravitational field, A. Einstein succeeded in interpreting the effect of gravitation as the curvature of space and time on the basis of the four-dimensional space-time continuum of the special theory of relativity. The variability of space-time geometry, the source of which is the distribution of matter, has important consequences. Their most spectacular is the existence of causally separate space-time regions, the black holes. If quantum effects are neglected, matter can penetrate a black hole, but cannot leave it again. This is associated with an enlargement of the decoupled region and thus its delimitation (the horizon). The physical laws that describe the behavior of stationary black holes are very similar to the laws of thermodynamics. That these laws are actually of thermodynamic origin can only be seen by including quantum effects: Due to the Hawking process, a black hole emits radiation with a defined temperature. A microscopic understanding of the entropy associated with it, but also of other effects, however, requires a real quantum theory of gravity that goes beyond a simple quantization of the matter fields.
A mysterious "dark energy" was introduced to explain the metrologically proven increase in the expansion speed, which should not exist according to current cosmology. The physical nature of dark energy is not yet known today (2011), only its property to accelerate the expansion of the universe. Since the general theory of relativity (GTR) does not exactly predict this effect, one could speculate that it has to be adapted for very large distances in the universe. It could also be possible that a superordinate theory has to be developed in order to describe the expansion acceleration effect or to be able to predict it freely. This superordinate theory would then contain the GTR for small distances, just as the Newton theory is contained in the special theory of relativity (SRT) for small speeds related to the speed of light.
Perhaps this "super general theory of relativity (SART)" has the mathematical properties to elegantly quantize the gravitational field in order to combine it with field quantum theory (FQT).


Uncertainty relation, space and time


Quantum theory teaches that the energy or the momentum of "matter waves" can only occur in integer multiples of a basic quantity that is proportional to the frequency. Since the possible test objects themselves have to obey these laws, it follows that energy and time (or momentum and place) due to the Heisenberg uncertainty relation can never be measured exactly at the same time. Based on the rest energy E = mc2 of an elementary particle results in a time uncertainty and as a path the "Compton wavelength", which the light travels in this time. The Compton wavelength is the natural unit of magnitude for the positional uncertainty of a point particle with mass m. If we include gravity in our considerations, a point-like elementary particle (e.g. an electron) forms a black hole whose Schwarzschild radius corresponds to Mass increases as the Compton wavelength decreases. With the so-called Planck mass of approx. 1019GeV / c2 (that's about 1019 times the mass of a proton, or 1016 times the highest energy achieved in particle accelerators) the Compton wavelength of a point particle reaches its own horizon (10-33cm, i.e. the 10th20-most part of the size of an atom!), so that here the difference between elementary particles and black hole is blurred and the space-time geometry can in principle no longer be recorded. The "shortest moment" would then be the time that the light needs to cover this so-called Planck length (10-33cm). Because of the fundamental uncertainty, the question of the "smallest" building blocks of matter in its original form no longer makes sense and has to be replaced by new concepts. The extremely high energy per particle (approx. 1019GeV) can also be converted into a temperature (approx. 10-32K), which only prevailed in the universe immediately after the Big Bang, i.e. approx. 10-40 Seconds. From the quantum fluctuations, the density fluctuations presumably also arose in the following epoch, which then led to the formation of galaxies and galaxy clusters in the course of cosmic development.
These limits cannot yet be reached experimentally. The Planckenergie (1019 GeV) exceeds the energies of (103 GeV) by 16 orders of magnitude. That means what happens on the Planck scale can only be derived theoretically or indirectly from experiments.


String theory


The elementary degrees of freedom in string theory are 1-dimensional objects, the so-called strings (strings = strings = threads with tension). Like a tensioned string, they have fundamental and harmonics. Their quantized vibration modes can be identified with the elementary particles. These one-dimensional objects can interact with each other in that the surfaces swept over by their time development in the space-time continuum, the so-called world surfaces, unite and split up again in a continuous process. String theory thus unifies the various types of elementary particles as oscillation states of a fundamental object on the one hand, and their various interactions through the dynamics on the 2-dimensional world surface in the space-time continuum on the other. An extension of the points of interaction in particle physics to so-called smooth areas of interaction is based on the consistency of string theory at very small distances. Consistency at large distances always requires supersymmetry (i.e. superstrings) and thus also explains the existence of fermions. In a somewhat simplified way, we can identify the fermions with matter and the bosons with the force fields. If the tension is very high, the "threads" become very short, you can approach the Planck length (10-33 cm), although the length scales in string theory can also be much larger. When observing from a distance (as is usual in everyday life) we only see the point-like interaction of point-like elementary particles.
In addition to strings, string theory also describes so-called Dirichlet branes (D-branes for short). The word branes is a short form of the word of membranes. The D-branes resemble solid, expansive surfaces drifting through space. They are "sticky" and "slippery" at the same time. The ends of the open strings adhere to a D-Bran, but can move around freely on its surface. Elementary particles (e.g. electrons) are open strings and therefore adhere to a D-Bran. In addition to the open strings, there are also closed strings or loops. Since they have no free ends, they do not stick to a D-brane, but can move freely between the extra dimensions, i.e. also between branes. The graviton (transmits the gravitational force) is e.g. such a closed string.


T. Kaluza and O. Klein proposed in 1919 and 1926 to understand electromagnetism within the framework of the general theory of relativity (ART) as a curvature effect in a very small fifth dimension.
In 1919 the physicist T. Kaluza made the following discovery:
In generalizing A.Einstein's theory of gravity for a world with four dimensions of space and one dimension of time, i.e. a total of five dimensions, one obtains Einstein's field equations of gravitation theory plus Maxwell's field equations of electromagnetism.
So the electromagnetism arises simply from the effect of the gravitation in an additional fifth space dimension. However, since we can practically not see this additional dimension of space, the mathematician O. Klein developed the idea in 1926 that the fifth dimension should be 8 x 1031 cm. Unfortunately, this idea received little attention for half a century because an experimental verification of its consequences was not possible. Only with a construction of the supersymmetric extension of the theory of gravity (SUGRA = super gravity) and the question of whether extended and / or higher-dimensional supersymmetry can resolve the inconsistency of quantum gravity, these considerations became topical again. In the meantime, the core forces had been discovered and formulated as a gauge theory (quantum chromodynamics) analogous to electromagnetism (quantum electrodynamics), so that a geometric unification of the natural forces now requires at least an 11-dimensional space-time continuum. The 11th dimension is at the same time the maximum possible dimension in which a SUGRA exists. This theoretical agreement raised high hopes, which were not fulfilled for the time being, because the 11-dimensional SUGRA still has some divergences.
In this situation, a work by M. Green and J. Schwarz triggered the first string revolution in 1984:
It turned out that superstrings automatically lead to a consistent 10-dimensional SUGRA with parity violation (i.e., as observed in nature, there are only left-handed neutrinos, but no right-handed ones). The superstring theory is the only known theory today that provides a prediction for the space-time dimension; i.e. the prediction of a 10-dimensional space. Many decades later, a plausible scenario was created from the idea of ​​T. Kaluza and O. Klein: We live in a 10-dimensional world.
In the meantime, however, the range of possibilities has expanded, as advances in the understanding of quantum phenomena in string theories triggered the second string revolution in 1995. It turned out that the type II A string theory generates an additional dimension in the area of ​​strong coupling so that the 11th spatial dimension has now been given new honors under the name "M theory". The letter M stands for "membrane". According to string theory, numerous "membrane-shaped" parallel universes move through a higher-dimensional space.
Not only about the number of dimensions, but also about their size, the very last word has not yet been spoken. From the dualities between 5 different 10-dimensional consistent string theories we have learned that the dimensions do not necessarily have to be small, but that the space-time physics observable for us on charged "3-dimensional membranes" (Dirichlet branes, named after the German mathematician Dirichlet) is located in a higher-dimensional continuum. The objects are solutions of 10- or 11-dimensional string motion equations and lead to large quantum effects, which can greatly modify the earlier predictions of string phenomenology. Every point in our 4-dimensional space-time could then possibly in reality be a multi-dimensional hypersurface.
Black holes can in the M-theory as oscillation states of a "D3 Bran " represented and thus understood as elementary particles with mass, charge and spin. According to the theory, there are point-like (0-dimensional) D0 branes, thread-like (1-dimensional) D1-branes, flat (2-dimensional) D2-branes, spatial (3-dimensional) D3-branes up to 9-dimensional ones D9 branes. A whole universe can "stick" to a spatial D3 brane. Black holes and Elementary particles appear in the M-theory as the same physical objects, but each in a different so-called "Calabi Yau Room ". A Calabi-Yau room is a geometry to describe the additional 6 dimensions of the room. named after the mathematicians Eugenio Calabi and Sing-Tung Yau.
Only a fraction of a millimeter next to our universe could exist on their own branes parallel universes invisible to us. But they could also be different "bran leaves" of our own multiply folded universe. The so-called dark matter can then be explained by the gravitational effect of stars and galaxies made of ordinary matter from neighboring branes or bran leaves of our own universe. Your gravity (gravitons) can reach us via "shortcuts" through the extra dimensions. Electrons, protons, photons and all other particles of the standard model cannot move in the extra dimensions. Electric and magnetic field lines do not spread into the higher-dimensional space. Only the field lines of gravity spread into the higher-dimensional space, i.e. extra dimensions are only noticeable through gravity.
Branes move effortlessly through the extra dimensions. So many other Bran worlds can move somewhere in the higher-dimensional space. Each Bran world is a whole universe for the observer trapped in it. In some respects, branes behave physically like elementary particles, i.e. they can collide, destroy one another and form systems in which branes orbit one another. According to this theory, we could live on a D3 brane embedded in a 5-dimensional hyperspace, which in turn is embedded in even higher-dimensional spaces.
If our universe is a D3 brane floating through a higher dimensional space, the big bang could have been the collision of our brane with another. Such collisions could recur cyclically and each time trigger another big bang.
In one examined scenario, e.g. B. the physics in an energetic intermediate area first 5-dimensional, before then later all 10 or 11 dimensions come into play. As a mechanical analogy, one can imagine a narrow valley from which one can only escape by using a minimum amount of energy. Correspondingly, the 5th dimension could become noticeable in high-energy processes in elementary particle physics in accelerator experiments, or in the radiation of gravitational waves in the energy balance of supernova explosions.


 The concept of duality in mathematics means that there is a close relationship between the most important variants of supergravity and string theory. In quantum field theory, the term duality means that physical models with different classical degrees of freedom and / or coupling strengths lead to equivalent quantum theories and thus a certain physical model can be realized using different classical starting points, which then no longer differ after quantization. For a long time, ignorance of the exact quantum corrections, it was assumed that there are five different consistent superstring theories (in 10 dimensions): Type I corresponds to open strings ("relativistic strings with free ends"), Type II A and II B correspond to closed strings ( "supersymmetrical rubber rings"). As classic theories, they can all be clearly distinguished. As exact quantum theories, however, they are presumably continuously connected to one another by varying certain parameters (vacuum expectation values ​​of massless scalar fields, called moduli). String dualities lead to the idea of ​​a continuum of string theories (called modulus space), the analysis of which is currently only possible in certain borderline cases, in which the exact quantum theory can be approximated well enough by a classical description. Such borderline cases are, besides the five classic superstring theories and the M theory, a multitude of lower dimensional models.
The duality shows that possibly all developed physical theories are only part of a superordinate theory. With that none of the developed theories would be really wrong but only different interpretations of one and the same world.
The practical value of the duality hypothesis is that it can be used to determine exact quantum corrections in one of the string theories mentioned by a classical calculation, which, however, is based on other "elementary objects" (with different dimensions of the underlying space-time continuum). With such calculations, the hypothesis of the duality of all consistent string theories has been extensively tested and confirmed in recent years.


This theory (called loop theory for short) or quantum geometry is an alternative to the string theory of quantum gravity. It combines the basic principles of quantum mechanics and general relativity.
The term loop theory or quantum geometry follows from the assumption that loop-shaped structures in spacetime play an essential role in this theory. Space is described as a dynamic quantum mechanical spin network, i.e. the geometry of space-time is dynamic on a microscopic level. The network consists of lines and nodes. One consequence is the quantization of space and time in the area of ​​the Planck length (10-33 cm) or Planck time (10-43 s). The node distances correspond to the Planck length. The flow of time is a constant structural change in the spin network. A quantum state of space is described by a network of nodes that are connected by lines, with the nodes being assigned certain physical properties that are mathematically similar to those of the spin of elementary particles. In a certain sense, an elementary volume (Planck volume = 10-99 cm3) assign. Matter exists as a node of the spin network. Time advances in discrete jumps from Planck's time (10-43 s) continue. However, there is no time in between. The movement of particles corresponds to a displacement of the corresponding node types in the network or a union of nodes or the emergence of several nodes from a single one. The network (spin network) is not embedded in the space but is the space itself, a fabric made of tiny thread-like loops. As with space, these temporal changes in the network are not embedded in time, but rather represent the flow of time itself. In this point, loop quantum gravity differs from string theory, whose equations are formulated in a classical, ie non-quantum mechanical, space-time are.

By adding time as the fourth dimension, nodes become lines and lines become surfaces in space-time. One speaks of a so-called spin foam of quantum space-time. As already described, structural changes in the network correspond to the course of time. In the spin foam model, this means that the foam patches are roughly the same size in all directions and end at the contact edges with their neighbors.

The spin nets, also called graphs, are subject to structural rules and have certain similarities with the Feynman diagrams with which the interactions between particles are described, but they are fundamentally structurally completely different.

The loop quantum gravity is able to correctly describe some already known or suspected physical phenomena:

  • Long wave gravitational waves on a flat background spacetime.

  • Jacob D. Bekenstein's formula, according to which the entropy of a black hole is proportional to its surface area.

  • The Hawking radiation that black holes emit.

  • A positive cosmological constant, for the existence of which astronomical observations have provided urgent evidence, follows relatively easily from loop quantum gravity.

From the loop quantum gravity it follows that the speed of light depends on the wavelength of the light. The deviations are particularly noticeable when the wavelengths are comparable to the node distances and thus the Planck length, so that the photons feel the quantum structure of space-time, so to speak.

At the beginning of the 1970s, Roger Penrose proposed spin networks for a theory of the loop - quantum gravity, the idea was taken up again in the early 1990s and successfully further developed by Lee Smolin and Carlo Rovelli, among others.


Holographic model of space-time


From the theory of quantum gravity and the theory of black holes, it can be concluded that the universe could resemble a gigantic hologram. The holographic model requires a negatively curved space, the so-called anti-de-Sitter space (named after the Dutch physicist Willem de Sitter, 1917). The holographic model developed from this establishes complete equivalence between two universes that have different dimensions and different physical laws. Mathematically this is a special type of a 5-dimensional space-time and its 4-dimensional limit. The 5-dimensional universe is mapped onto its 4-dimensional interface like a hologram. In the 5-dimensional space-time the superstring theory prevails and on the 4-dimensional hologram a so-called "conformal field theory with 1-dimensional point particles. A black hole in the 5-dimensional space-time is equivalent to hot radiation on the hologram.
According to the holographic model, our spatially 3-dimensional universe with gravity corresponds physically to a 2-dimensional universe without gravity. The 3-dimensional universe emerges from the 2-dimensional universe like a spatial holographic image from a flat holographic image. The 2-dimensional universe therefore exists on the interface of the 3-dimensional universe.
A field, such as the electromagnetic one, now varies continuously from point to point and thus has an infinite number of degrees of freedom. In superstring theory, the number of degrees of freedom is infinite. However, holography limits the degrees of freedom within an interface to a finite number. The holographic principle says that the universe is like a hologram, i.e. a 3-three-dimensional image that is stored on a 2-dimensional surface. The extremely high mass density of black holes indicates that this principle could apply. From the theory of black holes it can be deduced that the maximum entropy content or the maximum amount of information of any spatial area does not depend on the volume but on the surface of the spatial area. There is therefore another physical theory, only defined on a 2-dimensional interface, which describes 3-dimensional physics completely. With this, our 3-dimensional cosmos could be completely equivalent to all quantum fields and all physical laws that run on a vast, distant area. The particles on the edge behave similarly to quarks and gluons. Whereby gluons can form chains that behave similarly to strings, but that have a higher-dimensional space than the gluons. Mathematically, this theory has not yet been fully proven, but more recent high-energy particle experiments seem to support this theory.
But if our universe resembles a gigantic hologram, then the world we are so familiar with would in "truth" be totally different from how we perceive it with our physiological senses. Our innate perception makes us believe that we live in a 3-dimensional universe. However, if we take the holographic model seriously, our sensory perception is just an illusion.In reality we then live in a two-dimensional universe.
Perhaps holography will tell us the way to the fundamental theory we are looking for. This would then be the final victory of the idea that our universe is made up of pure information.


The quantum computing paradigm of the universe


The universe constantly processes information on the level of atoms and elementary particles. So it is a physical system that can be programmed on its lowest level to carry out universal digital arithmetic operations. The universe can therefore also be understood as a huge quantum computer that creates complexity and order in the universe. At the level of quantum mechanics, quantum fluctuations permanently generate random quantum bits in the universe. The universe constantly processes and interprets the randomly created quantum bits due to its computer properties. Then the reality of the universe is the sequence of a gigantic, self-creating gigantic computer program. Some subroutines are only written when the program is running. From this, the diverse complex physical orders and structures arise in a completely natural way. Some sub-programs may develop life and even consciousness.
The theoretical foundations of quantum theory enable the universe to be reduced to quantum bits as the smallest logically simple basic building blocks. The reason for all being is thus quantum information.


The universe's quantum simulator paradigm


How do we know that the universe we live in is naturally real? Do we live in a computer simulation, programmed on a higher-dimensional (e.g. 6-dimensional) quantum computer? In a 6-dimensional quantum computer, a 4-dimensional space-time can be programmed well, just as we can program a 2-dimensional virtual world in our 3-dimensional computers. But who are the (6-dimensional) programmers? Do you exist in the 6-dimensional quantum vacuum? For what purpose was the universe and thus we programmed? Is there perhaps only one responsible programmer?