Unique Root Approach

A working Alternative to String/M-Theory with some Applications

Jürgen Kässer

EnglischSince nearly half a century physicist try developing a comprehensive theory unifying particle and gravity physics. All approaches stuck in a quagmire of mathematical problem and are unable to achieve solid results. It is time to start with a new strategy.
The Unique Root (UR) approach takes a new way to unification. It is based on local isomorphism between internal and external symmetry groups generating force and geometry. It results that the basic symmetries of the universe are SO(6) and SU(4). These symmetries allow formulating physics in a timeless six dimensional space and a Lagrangian describing interaction between four entities.
Assuming this physics to hold also in our universe - a subspace of the complex expansion of the six dimensional one- four dimensional physics is deducted.
The conflict between background dependent and independent theories can be resolved. So the Standard model of particle physics and a pendant to a GUT as well as a quantum theory of gravitation, giving inter alia the results of General Relativity, are found.
UR allows a better understanding of the basic physical quantities, makes interpreting of experiments as the double-slit one much easier, eliminates paradoxes as Schrödinger’s cat and is able to explain Dark Matter.
Don’t expect a theory worked down to the last detail but a book demonstrating how the basic physical aspects of the universe are deducted from very few assumptions.

DeutschSeit bald einem halben Jahrhundert versuchen Physiker, eine geschlossene Theorie für Teilchen- und Schwerkraftphysik zu finden. Alle bisherigen Versuche stecken in einem Morast mathematischer Probleme und sind nicht in der Lage, handfeste Ergebnisse zu liefern. Es ist Zeit für eine neue Herangehensweise.
Der Unique Root (UR)-Ansatz geht davon aus, dass die Gruppen der inneren und äußeren Symmetrien, die für die Kräfte und die Geometrie zuständig sind, lokal isomorph sind. Daraus folgen für das Universum SO(6) und SU(4) als grundlegende Symmetriegruppen. Dies ermöglicht die Formulierung der Physik in einem sechsdimensionalen, zeitlosen Raum und einer Lagrange Dichte zur Beschreibung der Wechselwirkung zwischen vier Entitäten.
Unter der Annahme, dass diese Physik auch in unserer Welt – einem Unterraum der komplexen Erweiterung des sechsdimensionalen – gilt , lässt sich daraus die vierdimensionale Physik herleiten.
Der Konflikt zwischen hintergrundabhängigen und -unabhängigen Theorien löst sich auf und es lässt sich sowohl das Standardmodel der Teilchenphysik oder das Pendant zur GUT herleiten als auch eine Quantentheorie der Gravitation, die u.a. die Ergebnisse der Allgemeinen Relativitätstheorie liefert.
UR ermöglicht ein besseres Verständnis der elementaren physikalischen Größen, macht die Interpretation von Messungen wie etwa beim Doppelspaltexperiment sehr viel einfacher, beseitigt Paradoxa wie Schrödingers Katze und ist in der Lage, Dunkle Materie zu erklären.
Erwarten Sie keine bis in alle Einzelheiten ausgearbeitete Theorie, sondern ein Buch, das zeigt, wie aus wenigen Grundannahmen die Grundzüge unserer Physik abgeleitet werden können.

Genre: Fachbuch

Sprache: englisch

Erschienen: 2019


128 Seiten

ISBN: 978-3-938721-08-7

Preis: 19,80 €

Ebook in Planung


Chapter 2

Concepts of unification

Considering unification from a very general standpoint there are three problems to be overcome.
One of them is expressed by the Coleman-Mandula theorem.[6] It states that it is impossible to combine the compact internal (unitary) symmetry groups of particle physics with the external symmetries of space-time as e.g. the Poincaré group other than in a trivial manner. This prevents all generators combining these symmetries. Theories trying to unify particle physics and gravitation in the formalism of gauge theories however just want to do this.

They have to use an alternative offered by the Haag-Lopuszaski-Sohnius-theorem.[7] Generalizing symmetry to supersymmetry i.e. introducing generators complying not only as in symmetry groups with eommutators but also with anticommutators allows such nontrivial combinations (see e.g. [8]). It doubles the number of particles, to each known fermion there exists a partner boson and vice versa. By symmetry breaking effects the additional particles can have other masses than the original ones. [9]

The intensive search for the additional particles proposed by the Constrained Minimal Supersymmetric Standard Model up to now is not successful. Only a small part of the parameter space where they are assumed to exist remains to be tested.[10, 11] But there exist other supersymmetric models in which the masses of the lightest particles are so high that only future expansion stages of the LHC will be able to detect them or even much higher. This makes a falsification of the approach difficult, if not even impossible.

Any alternative means using the trivial combination of the symmetry groups. This demands formulating a relation between particle physics and gravity in its decisive parts not based on gauge invariance. A way pursued with the new approach is presented in this book.

The next problem arises by Newton’s understanding of space and time as a given stage on which physical events happen. This meaning of the structure of our environment also holds for Special Relativity, particle physics and the original formulations of M-theory. Such theories are called background dependent to distinguish them from the background independent theories like General Relativity. There the structure of space and time is not fixed but changes with the constellation of massive particles nearby.[12] Modern formulations are based on general covariance i.e. invariance of the form of a physical law under arbitrary differentiable coordinate transformations.

The consequences of these different views is shown impressively by Godel’s proof. that in General Relativity there only can exist spatial and no temporal coordinates. To show this he created an exact solution of the Einstein field equations with a special energy-momentum tensor and showed that in this universe time travelling would be possible. Analyzing the consequences he came to his conclusion.[13] There are other solutions e.g. the Kerr metric that under special conditions produce structures (”naked singularities”) in which causality is breached. To avoid such phenomena destroying our understanding of the world based on time and causality additional conditions as the Chronology Protection Conjecture of Hawking or the Cosmic Censorship hypotheses of Penrose must be introduced.

A unified theory should conciliate the two world sights and make the additional conditions unnecessary.

Finally by a seemingly unimposing question dramatic consequences are generated. Newton’s postulate of separability under some circumstances gets lost in quantum physics. Two entangled particles constitute a unit that cannot be described completely by the features of the two single particles.[14]

1935 Einstein, Podolski and Rosen proposed a thought experiment, today called EPR experiment, in which entanglement occurs. In the experimentally verifiable version formulated by Bohm a molecule with zero spin emits two particles with spin 1/2. As the spin of the molecule is unaltered the state of the two particles in quantum mechanics is described by an antisymmetric two particle wave function, forming a new entity with zero spin. This type of a wave function is not expressible as a product of individual wave functions but is instead a superposition of product states that cannot be separated in two single particle wave functions. Measuring now the spin of one particle in an arbitrary direction the wave function is reduced and the other particle is described by a one particle wave function with spin in opposite direction to the measured one. So measuring the second particle the result is predictable.

The question arises how the second particle that can be arbitrary far away from the first one is able to realize that a measurement has taken place.

Einstein and his colleagues conclude from this behaviour, that quantum physics does not give a complete description for the system, that it is incomplete. They take the view that there exist hidden variables that determine the spin of both particles already before a measurement, so that the above formulated question does not occur. This view means that they do not accept the entirety of the entangled wave function but demand instead a sometimes local realism called description based on separability and individuation.

Bohr’s answer on the (original) EPR experiment denies incompleteness of quantum mechanics and attributes its results to the specifics of measurement and as another prove of the novelty of the theory. (For a deeper insight of the implications of EPR and of Bohr’s answer see e.g. [15].)

How important for Einstein his view was can be learned from two of his letters written in 1948 to Born. Born and Heisenberg together had formulated the matrix mechanics representation of quantum physics. The Einsteins and Borns were friends. In one Einstein writes (translation by the author): ”...that, what we think to be existing (>is real<) in some way should be localized temporal and spatial. I.e. the real in a part A of space should (in theory) >exist< somehow independent of that what is thought real in another part B of space. If a physical system covers A and B then what is existing in B should have an existence somehow independent of what is existing in A. What is real existing in B so should not depend on which type of measurement in the part A of space is executed; it should also be independent of whether in A at all a measurement was done or not. Renouncing however the assumption that what is real in different parts of space has an independent existence I see not at all what physics is to describe.”

In his next letter he articulates his reservations against some interpretations of quantum physics and a lack of separability even more distinct: "Asking what independent of quantum-theory is characteristic for the physical way of thinking at first the following attracts attention: the notations of physics are related to a real outside world, i.e. there are set ideas of objects (bodies, fields etc.) that claim a >real existence< independent of the recognizing subjects... . For this classification of the entities introduced by physics it further seems to be essential that to a specific time things can claim an existence independent of each other, as far as these things >are located in different parts of the space<. Physical thinking in the sense familiar to us would not be possible without the assumption of such an independence of existence ...that originates from everyday thinking. Without such a clean probing one also does not see how physical laws can be formulated and tested. The field theory has carried out this principle to the extreme in localizing the underlying elementary entities existing independent of each other ... in the infinitely small elements (four-dimensional) of space. Characteristic for the relative independence of spatially distant entities (A and B) is the idea: external influence on A has no immediate influence on B . The complete cancellation of this principle would make the idea of the existence of (quasi)- closed systems impossible and with that make it impossible to devise an empirically testable law in the sense familiar to us.” [16]

A decision whether hidden variables as supposed by Einstein are acting or whether the antisymmetric two particle wave function is giving a correct description became possible when in 1963 Bell devised its inequality saying that in a slightly modified EPR experiment the different approaches should show distinguishable results. As found in various experiments, the latest given in [17] the result is unambiguous, quantum mechanics gives the right description.

This result brings us back to the question: how does the second particle know that the first one has been measured and what is the meaning of Einstein’s arguments?

Howard analyses the problems. He finds that because of the shown non-separability none of the actual theories all based on Newton’s postulate of separability and individuation can be used to generate a fundamental theory, even quantum mechanics is not appropriate:

”Strictly speaking, the quantum theory of interactions implies that we should write down one grand nonfactorizable state function for the whole of the forward light cone of every event. Of course we do not do this, but we have no fundamental principle that justifies our ignoring this radical nonseparability of quantum states.” [18]

As separation in space and time no longer can be used as an argument for separability and individuation a unified theory must find a new justification, it must reconcile the view of Bohr and Einstein.