Extremely many worlds would exist mathematically where the results of quantum processes happen to occur from now on outside earth always according to completely other probability distributions then the known ones. At first glance it seems to be extremely improbable to perceive ourselves in a world where the probability distributions will remain those according to the simple rules of quantum theory. This is called a probability paradox, and further similar paradoxes are presented. A strategy is described to search for solutions, an information theoretic approach. In that approach infinitely many worlds are considered in parallel.
Extremely many worlds would exist mathematically where the results of quantum processes happen to occur from now on outside earth always according to completely other probability distributions then the known ones. At first glance it seems to be extremely improbable to perceive ourselves in a world where the probability distributions will remain those according to the simple rules of quantum theory. This is called a probability paradox, and further similar paradoxes are presented. A strategy is described to search for solutions, an information theoretic approach. In that approach infinitely many worlds are considered in parallel.
In classical physics there is, in accordance with common sense, an objective world ‘out there’. That world evolves in a clear and deterministic way, being governed by precisely formulated mathematical equations. This is as true for the theories of Maxwell and Einstein as it is for the original Newtonian scheme. Physical reality is taken to exist independently of ourselves; and exactly how the classical world ‘is’ is not affected by how we might choose to look at it. Moreover, our bodies and our brains are themselves to be part of that world. They, also, are viewed as evolving according to the same precise and deterministic classical equations. All our actions are to be fixed by these equations - no matter how we might feel that our conscious wills may be influencing how we behave. Such a picture appears to lie at the background of most serious 1 philosophical arguments concerned with the nature of reality, of our conscious perceptions, and of our apparent free will. Some people might have an uncomfortable feeling that there should also be a role for quantum theory - that fundamental but disturbing scheme of things which, in the first quarter of this century, arose out of observations of subtle discrepancies between the actual behaviour of the world and the descriptions of classical physics. To many, the term ‘quantum theory’ evokes merely some vague concept of an ‘uncertainty principle’, which, at the level of particles, atoms or molecules, forbids precision in our descriptions and yields merely probabilistic behaviour. Actually, quantum descriptions are very precise, as we shall see, although radically different from the familiar classical ones. Moreover, we shall find, despite a common view to the contrary, that probabilities do not arise at the minute quantum level of particles, atoms, or molecules - those evolve deterministically - but, seemingly, via some mysterious larger-scale action connected with the emergence of a classical world that we can consciously perceive. We must try to understand this, and how quantum theory forces us to change our view of physical reality.
In a previous study a spiritual difficulty for public health was considered, that many people say that there would be definitely no afterlife with Judgment Day, and that some such persons might sometimes try to harm innocent others secretly to obtain advantages, e.g., financial, with negative impact on public health. Considering additional knowledge, new thought experiments are conducted, including arbitrary infinite bitstrings as programs, run, e.g., on theoretical Turing machines, and mathematical structures providing generalized findings, including results for questions of quantum probabilities, e.g., the Born rule - which is experimentally confirmed. In quantum processes, randomness instead of pseudorandomness is more probable than within the less general structures of the previous study. This is achieved designing generalized structures, e.g., programs, which do not function when they are “alone”. Additional structures show that pseudorandomness remains relevant. A paradox of the extreme variety of incomprehensible universes is described. It could be solved here considering further structures, e.g., the extremely large number of, e.g., world part copies simulated by various short programs, providing a large probability for comprehensible worlds. In all these mathematical structures, aliens’ pains emerge naturally.
The nature of the electron, a point particle according to the Standard Model, presents a paradox that challenges our ability to comprehend the physical reality. This paradox lies in the apparent contradiction between the complexity represented according to mathematical models that fully describe experimental results and the world around us perceived as a representation of an intuitive process. For example, how come all electrons are the same? As we shall see in this chapter, a seemingly simple question stimulated original reflections that later led to significant theoretical developments. Stern and Gerlach’s experiments demonstrated that the electron possesses an intrinsic property, the spin, whose generalization led to the distinction between fermions and bosons. The spin property, however, is apparently not reconcilable with the point properties of the electron. It has, in fact, not any analogue in classical physics. This incongruence also applies to the electron’s magnetic dipole moment. The key to everything is perhaps the spin property, which has Pauli’s Exclusion Principle as its consequence, to which we owe the existence of matter as we perceive it.
In this note we discuss a few simple classical (as opposed to quantum) prediction problems. The thrust of this work is to examine the predictive role of probability theory and we shall see that some situations are not re-ally paradoxical. In particular we want to separate the role of probability as a predictive tool from one of the basic sources of strangeness in quan-tum mechanics, namely the principle of superposition of states. For that we shall re-examine some of the quantum paradoxes, recast as a problem about making a prediction about the result of a random experiment in classical physics when some information is known. 1
Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a straightforward implication of how Bayes's rule works). Relatedly, hypotheses with a very low prior cannot be updated to have a very high posterior without a tremendous amount of new evidence to support them (or to make other possibilities highly improbable). Cromwell's rule appears at odds with our intuition of how humans update probabilities. In this work, we report two simple decision making experiments, which seem to be inconsistent with Cromwell's rule. Quantum probability theory, the rules for how to assign probabilities from the mathematical formalism of quantum mechanics, provides an alternative framework for probabilistic inference. An advantage of quantum probability theory is that it is not subject to Cromwell's rule and it can accommodate changes from zero or very small priors to significant posteriors. We outline a model of decision making, based on quantum theory, which can accommodate the changes from priors to posteriors, observed in our experiments.