Conceptual barriers to a unified theory of physics Dennis Crossley∗ Dept. of Physics, University of Wisconsin-Sheboygan, Sheboygan, WI 53081 August 31, 2012 Abstract The twin pillars of twentieth-century physics, quantum theory and general relativity, have conceptual errors in their foundations, which are at the heart of the repeated failures to combine these into a single unified theory of physics. The problem with quantum theory is related to the use of the point-particle model, and the problem with general relativity follows from a misinterpretation of the significance of the equivalence principle. Correcting these conceptual errors leads to a new model of matter called the space wave model which is outlined here. The new perspective gained by space wave theory also makes it clear that there are conceptual errors in the two main thrusts of twenty-first- century theoretical physics, string theory and loop quantum gravity. The string model is no more satisfactory than the point-particle model and the notion that space must be quantized is, frankly, nonsensical. In this paper I examine all of these conceptual errors and suggest how to correct them so that we can once again make progress toward a unified theory of physics. 1 Introduction { the challenge of the unification program The goal of theoretical physics is to construct a single unified description of fundamental particles and their interactions, but flaws in the foundations of physics have prevented physi- cists from achieving this goal. In this essay I examine conceptual errors that have led to this impasse and propose alternatives which break this impasse and let us once again move forward toward the goal of a unified theory of physics. The history of theoretical physics in the twentieth century is characterized by two suc- cesses and one frustrating failure. The successes are, of course, relativity theory[1] and quantum theory[2]. The failure is the inability to combine these two theories into a single unified theory of physics. Built upon the foundations of quantum theory, the standard model of particle physics gives us a model of the elementary particles and their interactions (ex- cluding gravity)[3]. Built upon the foundations of special relativity, Einstein's general theory of relativity gives us a model of the gravitational interaction but says nothing about ele- mentary particles[4]. These two theories use profoundly different concepts and methods and all attempts to construct a unified theory by forming a direct link between them have been unsuccessful. As we will see below, the difficulty lies deeper than merely an incompatibility of the methods of these two theories; the fundamental concepts on which these theories are constructed contain inconsistencies which preclude their successful unification. ∗[email protected] 1 Early efforts, by Einstein and others, to construct a unified theory of physics involved attempts to incorporate the electromagnetic field into the formalism of general relativity[5]. The goal of this early work was a unified field theory, built on the foundation of general relativity, describing the gravitational and electromagnetic interactions of matter in a unified mathematical formalism. With the discovery of the nuclear interactions, it became acknowl- edged that the goal of the unified field theory program was too limited. With no apparent way of incorporating the nuclear interactions into the geometric approach of general relativity, this approach was abandoned. Subsequent efforts have, instead, taken quantum field theory as the foundation. With the successes of gauge theories to describe both the electromagnetic and the nuclear interactions[6], some efforts have been made to incorporate gravity into this formalism by expanding the gauge group to include the gauge group of general relativity[7]. As we enter the twenty-first century, these unification efforts have morphed into the programs of string theory[8] and loop quantum gravity[9]. String theory attempts to adapt quantum field theory using one-dimensional strings instead of point particles, while loop quantum gravity attempts to incorporate quantum concepts directly into general relativity. But neither of these programs addresses the conceptual problems underlying quantum theory and relativity theory upon which they are built, and therefore have little more chance of success than their twentieth-century predecessors. Thus, all efforts to date to construct a unified theory of physics have taken general rela- tivity and quantum field theory, and the conceptual foundations upon which they are built, and have attempted to combine them in some way, using one or the other as a foundation. But a critical examination of the conceptual foundations of these theories exposes a funda- mental error in the conceptual foundations of each of them, and it becomes clear that neither general relativity nor quantum field theory nor their extensions in the form of string theory and loop quantum gravity are adequate foundations upon which to build a unified theory of all interactions. Both general relativity and quantum field theory appear to be \correct" theories in the sense that they both give correct predictions for the behavior of matter, but correct predic- tions, though necessary, is not a sufficient criterion for choosing a final theory. In the context of the unification program, we must also consider the generalizability of a theory, and on this criterion both general relativity and quantum field theory fail. We begin our search for a new foundation for fundamental physics with a critical analysis of the fundamental concepts upon which our current theories are built. 2 Barrier #1: the particle model The particle concept[10] has proven to be extremely useful in virtually all areas of classical physics, regardless of the intrinsic size of the object being modeled. For example, objects as large as the Sun and the Earth are adequately modeled as point particles in Newtonian 2 gravity theory, and elementary particles can be modeled as point particles in Maxwell's elec- tromagnetic theory (as long as the interaction distances are not too small). The point particle concept reaches beyond its range of applicability, however, when it is applied to the micro- scopic domain to describe fundamental particles. It is the adherence to the particle model which has necessitated the introduction of probability into quantum mechanics. Likewise, the Heisenberg uncertainty principle, which makes sense in the wave context in terms of Fourier transforms, becomes probabilistic nonsense in the particle context. The point-particle con- cept cannot account for the existence of intrinsic properties like spin and gauge degrees of freedom, both of which require internal structure, nor can it account for the existence of particle interactions (forces)[11]. The wave nature of fundamental particles becomes apparent when interaction distances become small. Quantum theory accounts for the wave nature of fundamental particles by simply tacking it onto the particle concept, resulting in a rather schizophrenic juxtaposition known as wave/particle duality. While wave/particle duality has brought us closer to a complete understanding of fundamental particles, it has brought us only half-way. Quantum theorists, building upon the legacy of classical physics, kept the point particle concept central and attempted to graft the newly discovered wave properties of matter onto it. They were naturally led to ask the wrong question: How can a particle have wave-like properties? The answer is, of course, that it can't, so elementary particles must be strange objects, they concluded, which sometimes behave like particles and sometimes like waves. This dominance of the particle concept on our thinking has been a subtle but insurmountable barrier to the unification of theoretical physics. To get beyond barrier #1, we need to abandon the notion that the particle concept is fundamental and instead embrace the wave nature. There are strong reasons for believing that the wave properties of matter are more fundamental than the particle properties. This leads to a reversal of our logic. If we say that waves exist and that somehow (not so mysteriously) they have particle properties associated with them, the whole situation becomes much clearer. In the language of wave-particle duality we are then led to ask the right question: How can a wave have particle-like properties? This rephrasing may seem simple, but the consequences of it are profound since the question now has an answer: Waves can have particle-like properties by being localized in space. Such localized waves are commonly referred to as solitons and are familiar in a variety of contexts. This soliton model contains the key to a new approach to understanding fundamental particles and their interactions, but by itself is not the complete answer. Many questions present themselves, perhaps the most important of which is: What is the \medium" in which these localized waves propagate? I offer a surprisingly simple answer to this question in section 4, but first we must adjust our approach to gravitation theory so that it can be made compatible with the wave model of fundamental particles. 3 3 Barrier #2: the equivalence principle What's wrong with curved space? The weak equivalence principle of general relativity states that gravity can be described either by a nonzero gravitational interaction in Euclidean space or by curved (Riemannian) space with the gravitational interaction identically zero. Gen- eral relativity is based on the second formulation. The first formulation, which I will refer to as “flat gravity" is, unfortunately, a theory that does not exist. I am not referring to Newtonian gravity, which is a quasi-static theory comparable to Coulomb's law in electro- magnetic theory, but rather to a theory which includes the finite propagation velocity of the gravitational interaction, comparable to Maxwell's theory. Some work in this direction was being done around the same time that Einstein developed general relativity but was put aside with Einstein's \successful" formulation of gravity in terms of geometry.