ToE; New Physics explaining our world by Quantum Gravity E-Book

Claus Birkholz

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2016

Beschreibung

     Space, time, matter - what really is all that? What are charges, what flavours? What is preventing time from running backwards? Quantum Gravity is describing all that - consisely, comprehensively, to the point. The Grand Unified Theory (GUT = ToE = "Theory of Everything"), finally, is caring for the rest by relating all forces of nature to each other.

     Parities are the peep-holes into strange worlds before the Big Bang and beyond the event horizon. Everything is calculable, even the transitions there. By working out the value of the fine-structure constant, theory opens to recognizing Dark Matter as the cradle of visible matter; the GUT is demonstrating birth and properties of ordinary matter out of Dark Matter and by what its creation process is stopped again.

     A totally novel assessment is arising with respect to neutrino oscillations. Pauli's principle explains physically. Einstein's cosmological constant is demystified. Dark Energy, cosmic inflation, the number of dimensions we are living in are not any more dully accepted from outside - theory is deriving all that.

     As a matter of fact, the gateway to developing Quantum Gravity has been widely open since Einstein, Planck, and Dirac. Only, nobody has passed its threshold; nuclear fission had changed priorities. Then, Gell-Mann had knocked at the door of the GUT. This time, however, it was the "Standard" model to crash the door back into its frame, and the string model sealed the lock.

     - Meanwhile, the model succeeded in smuggling into the open underneath the feet of its jailers, ready for being applied more extensively.

Leseprobe

Claus Birkholz

ToE; New Physics explaining our world by Quantum Gravity

World's first Textbook on QG

BookRix GmbH & Co. KG81371 Munich

Documentation

The basic text on Quantum Gravity and New Physics had been edited in 2010 still as a print-book in German language („Weltbild … nach Vereinigung aller Kräfte der Natur …”, ISBN 978-3-00-030847-6).

Extracts including consequent onward developments, then, had been presented at various universities from 2011 to 2015 in the course of the annual spring conferences held by the German Physical Society (DPG), sections T (particle physics), GR (Gravity and Relativity), MP (Mathematical foundations of physics), and AGPhil (working group on the philosophy of physics). Their numerous manuscripts, predominantly in English, can be looked up in the internet (see www.q-grav.com / Lecture Notes). Their “Abstracts” are published, in addition, under “Verhandl. DPG (VI)”, starting with volume 46 (2011), see www.dpg-physik.de.

These research reports on the common base of particle physics and cosmology, including their confluence giving “Quantum Gravity” and a “Grand Unified Theory” (GUT), had been put forward to formulate a preliminary expert survey in 2013 (“The World Formula, …”, see www.q-grav.com).

Still further actualized, it took shape as a coherent top-down view of our world. In characteristic parts, however, where these reports would have asked too much of the rapid reader, they are more paying tribute to the requirements of a popular-science presentation. The respective e-books are (English versions): 1st edition: “New Physics, Dawn of Cognition” (2013), 2nd edition: “Flow of Time, Quantum Gravity giving New Physics”(2014).

All the same, the author’s endeavour had been not to drop the technical context completely – at least, it survived in terms of commentary headwords and special boxes. This procedure proved good by the striking success of more than 20.000 e-books sold within just 2 years.

Meanwhile, the interior of a Black Hole and its connecting relations across the event horizon are calculated. By indicating ways of experimental verifications of predictions made by Quantum Gravity, the state of the art has reached such a degree of maturity that this 3rd e-book edition may risk the step towards supplementing it to a veritable textbook on Quantum Gravity – the first in the world – embedded in a Grand Unification of all forces of nature. The picture is rounded by deriving the fine-structure constant at its correct value.

The substantial extension of this pioneering work far beyond its precursory editions will be turning upside down considerably deeper cognitions on the nature of things. This is not surprising because Quantum Gravity, the first time in history, is unifying Einstein’s General Relativity with Planck’ quanta. And the Grand Unification, by still including Gell-Mann’s quark model, is showing up as the “Theory of Everything” (ToE) string fans had been looking for in vain so long.

For the rapid reader just interested in a survey, the main body of mathematics is banned into extra boxes, with the respective background knowledge shifted into 12 specialized appendices. By that segregation, this “3rd edition” is satisfying the requirements of an elementary self-instruction manual (when including the appendix) as well as some survey representation for the interested layman (when omitting the appendix).

The original title in German reads “ToE; Neue Physik; Unsere Welt erklärt durch die Quantengravitation. Weltweit 1. Lehrbuch zur QG” (2016).

Special attention is directed to ensure that statements made here are not based on the ivory-towered fantasticalities “beyond” whatsoever as they are customary in this branch. The statements met here are fully in accordance with solid (present-day) experiments and based on consistent mathematics!

The Old Physics at Its End

This is a story deeply splitting the community of physicists into opponent camps. With his “World Formula”, Einstein once had coined a notion which now stands for failed trials to include electromagnetism into his 1915 concept of General Relativity, which is the geometrization of gravity.

Meanwhile, the number of forces has increased by still adding nuclear forces. It turned out that the dynamics of all those “internal” forces in addition to gravity can be roughly described by Schrödinger’s wave mechanics, which is a particular aspect of quantum theory.

The (”chiral”) interactions of those “internal” nuclear forces seem to follow comparable (“gauge”) structures, too – although, in terms of the “Standard Model”, those (gauge) structures, as far as their abstract origins are concerned, are not well understood until to-day.

And quantum theory – the other component of modern physics – is based on Planck’s discovery in 1900 that nature does not behave in a continuous way but is showing up in discrete steps. This, however, is a stringent consequence of a physical statement in order to be verifiable by measurement. For, a living organism like a human, due to its limited span of life, cannot count up to infinity. Hence, infinities are unphysical, i.e., not measurable; everything must stay finite in physics. Even an elementary particle cannot be accelerated beyond all bounds – its energy must remain delimited.

As a non-rational, “continuous” number only can be reproduced by an infinite series of rational numbers (decimal digits, e.g.), non-rational numbers are not denumerable, either. Rational numbers, however, are countable. Hence, fundamental physics will have to deal with finite sets of rational numbers only, and not with their limiting values, either.

In consideration of its continuous treatment of space and time, classical physics (Einstein’s General Relativity included) in this sense is “unphysical”, too. Thus, it necessarily will have to be “discreticised”, or “quantized”, which is the modern way of formulating it.

Only, since one century, gravity, i.e., Einstein’s General Relativity, stubbornly refused to “cooperate” with Planck’s quantum theory – and, v.v.: those “internal” forces denied any cooperation with General Relativity, likewise.

The action of General Relativity is best visualized by the well-known, familiar model of a flat rubber membrane stretching itself horizontally. An object deposited on its surface, by its weight and by the elasticity of the membrane will give rise to some downward depression, there. By this depression, a small marble, then, kicked (in a non-centric way) towards that object will be deviated from its straight run such as if that object and the marble are attracting each other.

The reason for this strange behaviour is traced back to geometry, i.e., to that depression in the membrane. The formerly flat plane, now, is not any more flat but bent downwards in the region where the object is located. Mathematicians are attributing such a surface curvature to some “non-linear” condition, as they call it. (For, “linear” equations are exclusively describing straight lines and flat planes.)

Special Relativity is a subset of General Relativity, acting in flat space-time only. Physically, it is neglecting the acceleration created by mass attraction. This acceleration, however, just is the crucial result of a (here: gravitational) force. Thus, Special Relativity is dropping forces.

On the other hand, the current theories of elementary particles – i.e., the “quantum field theories” – are exclusively working with Special Relativity only. And no successful trial is officially known to prove that they are tolerating their extension to General Relativity, while, equally, the (official) theory of gravity does not show up to tolerate wave mechanics, i.e., the superposition principle of waves.

This is another indication of Einstein’s General Relativity apparently not to be “consistent” with Planck’s quantization concept Schrödinger’s wave mechanics is a derivation of. Briefly, nobody yet is (officially) acknowledged to have combined Planck’s quantum theory with Einstein’s General Relativity in a consistent way.

By interpreting a linear superposition as a contradiction to a non-linear surface, small-minded contemporaries even are trying to persuade us that a unification of Einstein with Planck should be principally impossible. (However, they are comparing “apples with oranges”.)

This (false) conclusion is symptomatic. For, we just realized that Special Relativity is cancelling forces. And particle physicists, instead of letting themselves be guided by General-Relativistic ideas, are continuously inventing a wealth of substituting strategies in order to describe interaction forces by circumventing General Relativity.

V.v., a much more promising access would be to extend General Relativity in order to include the “internal” forces, in addition. This, however, is Einstein’s old idea of a “World Formula” which, then, should be excavated – although, due to its well documented failures in the past, this access has had to bear a heavy loss of reputation, since.

After the detection of nuclear forces, Einstein’s notion of a “World Formula” even had become somewhat ambiguous. On the one hand, it would have to include the consistent combination of Planck’s quantum theory with Einstein’s General Relativity. This, actually, is attributed to a “Quantum Gravity” still to be constructed.

On the other hand, it would have to include the unification of all “internal” forces with each other and with gravity to a “Grand Unification (Theory)” (GUT) of all forces of nature. (String models are calling it a “Theory of Everything (ToE)”.)Our so called “Standard Models”, however, (that of particles and that of cosmology) are far from covering any of those targets.

“String/brane“ models are digging even deeper into that dead end of physics because they uncritically have taken over crucial parts of those bad features of the aged quantum field theories – for the expert let me just mention the “variation principle” (Leibnitz, Bernouilli, 400 years ago) with its arbitrariness of parameters in their “path integrals” and “Lagrangians”, e.g., once designed for point mechanics. But is it wise to apply great-great-grandpa’s magic cooking formulas to a world of quanta?

There are typical structures which even the “Standard Models” do not catch at all – not to mention their incompetence of explaining them. Among them, there are notions like “Big Bang”, “Black Hole”, “cosmological constant”, “cosmic inflation”, “Dark Energy”, “Dark Matter”, “parity violation”, “flavour physics”, “broken quantum numbers”, “non-valence part of an elementary particle”, “virtual state”, “quark confinement”, etc., etc. But even such every-day notions like “mass”, “length”, “time”, “dimension”, “charge” are among them.

Everybody is internally conscious of the disability of the “Standard Models” laboriously patched up since decades, which ought to be given to the garbage long since. However, nobody knows by what to replace them – the great helplessness everywhere.

The New Physics

Theoretical physics is the mapping of (parts of) nature into mathematics. Current “string theories” do not care about nature. Hence, string theories cannot any more be considered to belong to the category of “natural” sciences. Even to their protagonists it is unclear what at all they are mapping into mathematics.

String models do not try to reproduce nature, but, the other way round, they are hoping that, in nature, there are existing structures – still to be uncovered – which will correspond to their models. This cross-over method “beyond the Standard Model” of not asking theory to reproduce nature but of nature to follow theory, still up to the 1960s had been considered as the typical prototype of a confuse, unserious doctrine of incompetence, demonstrating what not is physics. – How times are changing; half a century of stagnation is giving rise to queer practices!

Let us, hence, follow another line of argumentation. As we cannot count up to infinity, a measurement can reproduce a result at most up to the accuracy of some rational number. The total of all our measuring results, then, must be some finite set of rational numbers.

This demands physical models of nature basicly to be of an atomistic structure, i.e., “quantized”, in order to stay a subject not only to falsification but also to verification; this is the key property of physics. Let us designate their “atoms”, here, as “quanta”. By the huge number of quanta available in our universe, most of their structure only can be covered by statistical methods.

In mathematics, an atomistic structure is dealt with by combinatorics, and statistics is dealt with by the theory of probability. The combination of combinatorics with probability is “group theory”. A typical example of group theory is the property of a “spin” – that “intrinsic angular momentum” where nothing is rotating.

For the majority of physicists, group theory has remained a complete mystery. Even Einstein did not care about it; his General Relativity does not take it into account, spin is foreign to General Relativity. Schrödinger scornfully renamed "group theory" to “group pestilence”, and Pauli jumped onto that trend.

“Learning during all one’s life” at those times, already, had been a unilateral postulate by the elder people directed towards the younger ones, but not towards senior graduates. In professional life, tired after the stress of a long education, it is all too human to face more progressive, novel demands with negative scepticism instead of enthusiastically trying to find out promising points of attachment with respect to some better, new physics – as it had been usual in more productive periods. Where only did the eager expectations of theoreticians ooze away?!

Instead, technically innocent freeloaders are setting hopes in profiting from boosting those instinctive defence mechanisms of their seniors by trying to act as a resonance box of their masters, trumpeting forth their most absurd statements. For the realization of veritably novel findings we, hence, are depending on the creative impulse of descendent generations who are not putting up with being deposited on a sooty steam-engine yard of a railway museum.

On the other hand, we shall observe that group theory, this underestimated discipline of mathematics widely swept under the carpet so long, just is representing the “missing link” between Planck and Einstein: Still during the course of the actual century, it might take over the leading position in fundamental physics.

This book especially addresses the younger students. Off with great-grandpa’s antiquated fug; the future is calling, let us shape it!

Now, What Really Is Space and Time?

There are subsets of the generators of Quantum Gravity which are identical in both channels – in the reaction and in the dynamic channel. These are their common generators, which the “Standard Model” would call “compact” if it would accept them as operators. A still smaller subset of them, up to some r-number factors (which also are defining the measuring units), even is leaving the state unchanged which they are acting on.

These r-numbers are their “measuring values”, and their generators are called “diagonal”. (This denotation offers if such a generator is written down as some matrix acting on a state vector.) Another word for these “measuring values” is “quantum numbers”.

Technically, such a (linear) “diagonal generator” just is counting the number of certain types of quanta the physical (product) state is consisting of, and the different (linear) quantum numbers of one and the same state are distinguishing themselves by the types of quanta they are adding up with a positive sign and those to be added up with a negative sign.

Hence, up to some arbitrary unit factor like “1 cm times 1 gram” or similar constructs arising from some arbitrary normalization, these “quantum numbers” should be multiples of some integer numbers. (In the case of a “spin” value, that normalization, usually, is arbitrarily separating another factor 1/2 off that value, and, in the case of a particle number or of a charge, people often like to split off a factor 1/3, instead.)

As a result, the statement is: Up to (arbitrarily chosen) normalization factors and up to relative signs, there are 4 “diagonal” linear quantum numbers: