In quantum mechanics physical processes procede by two different mechanisms. John von Neumann enumerated them as 1, the "discontinuous ... arbitrary changes by measurement," and 2, continuous evolution via the Schroedinger Equation. That the physical world does not obey a single overriding law - unitary evolution by the Schroedinger Equation - is philosophically disturbing to some. Others face it with equanimity. One narrative that preserves the findings of quantum mechanics yet does produce pure unitary evolution is that of the multiverse. Given below is the narrative by which Born's Rule emerges without pre-assigning to it the notion of probability. It requires that the number of universes in the multiverse not be enumerable!
In quantum mechanics physical processes procede by two different mechanisms. John von Neumann enumerated them as 1, the "discontinuous ... arbitrary changes by measurement," and 2, continuous evolution via the Schroedinger Equation. That the physical world does not obey a single overriding law - unitary evolution by the Schroedinger Equation - is philosophically disturbing to some. Others face it with equanimity. One narrative that preserves the findings of quantum mechanics yet does produce pure unitary evolution is that of the multiverse. Given below is the narrative by which Born's Rule emerges without pre-assigning to it the notion of probability. It requires that the number of universes in the multiverse not be enumerable!
Quantum Mechanics notoriously faces a measurement problem, the problem that the unitary time evolution, encoded in its dynamical equations, together with the kinematical structure of the theory generally implies the non-existence \nof definite measurement outcomes. There have been multiple suggestions to solve this problem, among them the so called many worlds interpretation that originated with the work of Hugh Everett III. According to it, the quantum state and time evolution fully and accurately describe nature as it is, implying that under certain conditions multiple measurement outcomes that are seemingly mutually exclusive can be realized at the same time – but as different 'worlds' contained in a global, quantum mechanical structure, sometimes referred to as 'the multiverse'. The many worlds interpretation has, however, been confronted with serious difficulties over the course of its development, some of which were solved by the advent of decoherence theory. The present thesis critically investi- \ngates the state of play on a key remaining problem of the many worlds interpretation, the problem of the meaning and quantification of probabilities in a quantum multiverse. Recent attempts of deriving the pivotal statistical ingredient of quantum mechanics, Born’s rule, from either principles of decision theory or from quantum mechanics alone, supplemented with a few general premises about \nprobability are analyzed and their premises are scrutinized. It will be argued that, though both approaches yield promising results, they both ultimately fail \nto clearly establish the validity of Born’s rule in the context of the many worlds interpretation. It is hence suggested that further research on this problem is indicated.
The modern version of the wave-function collapse in quantum mechanics is based on decoherence and leads to the multiverse interpretation of quantum mechanics. The decoherence causes the universe to develop an emergent branching structure. One can interpret the branching structure either as a tree structure or as parallel different histories. Time is not continuous since there are no measurable continuous in quantum physics. Notion of continuous range of possible values of time is just an idealization. The same goes with the direction of time that is a prior assumption based on the branching structure of the multiverse. The multiverse does not exist in external space nor time since there is nothing more beside it. The observer's mind should be not in a superposition with himself. Because of this, in the Many-minds interpretations it is argued that the distinction between worlds should be made at the level of the individual observer. The human bodies are in a superposition, but the minds have definite states that are never in superposition. All possible lives, personalities that do not violate the laws of physics are facts since they represent a valid history in the multiverse. We are one of this possible personalities. Our choices are defined by our personality explained to us by our mind, our consciousness is the unchangeable part of us. It is nonphysical and it senses the world. It does not interact with the brain in the other way beside it.
Hugh Everett thought it was preposterous to accept the Schrodinger equation as a fundamental law of quantum physics, but then assert that it is usually violated in any observation of quantum phenomena. Demanding that the Schrodinger equation always holds led him to the 'many worlds' interpretation. To avoid this conclusion, I propose that the Schrodinger equation is not fundamental, but that one should instead regard as primary a von Neumann version of the equation which lets the density matric evolve unitarily, but where conclusions reached concerning measurements always involve the non-unitary step of tracing out environmental degrees of freedom which always exist even if the system in question is the entire observable universe.
Quantum mechanics is our most successful physical theory. It predicts the behavior of atoms, molecules, and light to ten decimal places. No experiment has ever contradicted it. It also contains a crack at its foundation. The theory’s central equation—the Schrodinger equation—describes a smooth, continuous, perfectly predictable evolution of the quantum state. But whenever anyone performs a measurement, they get a single, definite result. Which result they get appears to be random. The transition from smooth evolution to random outcome is called the “collapse of the wavefunction,” and after nearly a century of analysis, there is no agreed-upon explanation for what causes it, when it occurs, or whether it occurs at all. This is the measurement problem. The measurement problem is not a minor puzzle at the margins of the theory. It is a failure to explain the most basic operation in science: looking at the result of an experiment. Around it cluster other puzzles. Light behaves like a wave in some experiments and like a particle in others—two contradictory descriptions. Two particles that have interacted remain correlated across arbitrary distances, as though communicating faster than light. The probabilities that govern measurement outcomes appear as a postulate—the Born rule—inserted by hand with no deeper justification. And the theory offers no unified picture of reality: quantum mechanics, general relativity, and the standard model of particle physics speak incompatible mathematical languages. A century of effort has produced many interpretations of quantum mechanics. Copenhagen. Many-worlds. De Broglie-Bohm. Objective collapse. Quantum Bayesianism. None has achieved consensus. The measurement problem remains. This document proposes that the source of these puzzles is not quantum mechanics itself. It is a single, invisible assumption made at the very beginning of the theory in 1900—an assumption so deeply embedded that nobody noticed they were making it. Change that assumption, and the puzzles do not get solved. They dissolve. They stop being puzzles. They become predictable consequences of geometry.
How does it come about then, that great scientists such as Einstein, Schrödinger and De Broglie are nevertheless dissatisfied with the situation? Of course, all these objections are levelled not against the correctness of the formulae, but against their interpretation. […] The lesson to be learned from what I have told of the origin of quantum mechanics is that probable refinements of mathematical methods will not suffice to produce a satisfactory theory, but that somewhere in our doctrine is hidden a concept, unjustified by experience, which we must eliminate to open up the road. (Born [1954], pp. 8, 11) It is truly surprising how little difference all this makes. Most physicists use quantum mechanics every day in their working lives without needing to worry about the fundamental problem of its interpretation. (Weinberg [1992], p. 66) I endorse the view that it may be of no relevance to the acceptability of the Everett interpretation of quantum mechanics as a physical theory whether or not an informed observer can be uncertain about the outcome of a quantum measurement prior to its having occurred. However, I suggest that the very possibility of post-measurement, pre-observation uncertainty has an essential role to play in both confirmation theory and decision theory in a branching universe. This is supported by arguments which do not appeal to van Fraassen’s Reflection Principle. 1. Dendritic Unitary Evolution 2. The Born–Vaidman Rule 3. Greaves on Uncertainty 4. Retroactive Counterfactual Uncertainty 5. Odds and Ends
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules of probability theory apply to it when it interacts with a quantum system. Under mild assumptions, we recover the unitary dynamics, collapse and Born rule postulates from quantum theory. Nonetheless, there is no decoherence, because the quantum state remains pure conditioned on the classical trajectory. This results in one world, rather than many-worlds. Our main technical tool is to exploit a change of measure on the space of classical paths, the functional form of which is shown to characterise the quantum dynamics and Born rules of a class of quantum-like theories.