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Dialogo

New considerations on a spiritual difficulty for public health, including questions about quantum probabilities and comprehensibility of worlds

Richard Woesler

Published Dec 5, 2022• 1 citation
Publisher

Abstract

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.

DOI
10.51917/dialogo.2022.9.1.14

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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.
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.
As we saw in the previous chapter, the Everett interpretation seems to dispense with probabilities in quantum mechanics. Instead of describing a world for which many things are possible, but only some of those possibilities are actualised, it suggests a world in which all possibilities actually happen . Moreover, this is something of which we can be absolutely certain . Obviously, this does not straightforwardly fit our experience. We do not see multiple possibilities becoming actual. Whenever we measure a superposed particle, we observe only one property or another. Moreover, we have a very useful probabilistic rule to help us to predict what we will see. How can the success of this probabilistic rule be explained, if an Everett world does not involve any uncertainty? There are two main moves that are employed in response to this challenge. The first – what I call Stage A – is to show that there is a relevant sort of uncertainty, even in a universe where we are certain that everything will happen. The second move – Stage B – is to try to vindicate the probability of the Born rule in particular. That is, to show that we should not merely be uncertain about the future, but that we have good reason to attach the particular probabilities dictated by the Born rule to the possible outcomes of a quantum experiment. We will consider these two stages in turn.
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.
I interpreted the repeated measurement experiments of the previous chapter by saying that quantum mechanics can find probabilities only, not certainties (that is, that quantum mechanics is “probabilistic”, not “deterministic”). You may object, maintaining that the world is deterministic, but that my particular deterministic scheme (the “magnetic arrow”) is incorrect. The next chapter presents an ingenious argument, invented by Einstein, which shows that no local deterministic scheme could give the results observed by experiment. In order to understand that argument you need some background in probability. But in fact, a knowledge of probability is generally useful in day-to-day life as well as in physics. You walk across a street — what is the probability of your being hit by a car? You are advised to undergo elective surgery — what is the probability that the surgery will extend your life, and what is the probability that the surgery will go wrong and injure you? You breath some asbestos or smoke a cigarette — what is the probability of contracting cancer? Misconceptions about probability abound and can lead to disastrous public policy decisions. A knowledge of quantum mechanics is good for your soul, but it is of practical importance only to the designers of lasers, transistors, and superconductors. A knowledge of probability is of practical importance to everyone.
When metaphysicians pay attention to theories in fundamental physics, they are usually interested in their implications for fundamental metaphysics: they want to know what the theories imply or suggest concerning the ultimate structure of reality. This essay, by contrast, is concerned with the “derivative metaphysics” of quantum mechanics. I will be considering a certain hypothesis about the fundamental structure of reality, which I will call H. I am interested in H because it strikes me as embodying the most obvious, flat-footed way to read an account of the fundamental structure of reality off the mathematical apparatus of elementary quantum mechanics. But I won’t be defending this claim here, or trying to argue that the members of H are more plausible than other accounts of the fundamental structure of reality inspired by quantum mechanics. Instead, my question is: if H were true, could there be (non-fundamentally speaking, of course) such ordinary objects as plants, planets and people? More specifically: could there be such ordinary objects as ourselves and the things we are familiar with, having more or less the ordinary properties we take them to have? And more generally: given that the fundamental structure of a possible world is such as to make H true, what is its correct description in ordinary terms? Of course, I care about these questions in part because I want to explore the extent to which we might have good reason to believe H, or something akin to it. But even if H turned out to be consistent with our ordinary knowledge about the world of ordinary objects, it would obviously take a lot more work to show that it has any serious claim on our credence. At a minimum, one would have to say something about how likely we should regard our evidence as being, given H; one would want to make some sort of survey of alternative hypotheses; and one would want to take into account our specialised scientific knowledge as well as our ordinary knowledge, including the facts that make trouble for elementary quantum mechanics and force us to look beyond it to quantum field theory and ultimately towards some kind of theory of quantum gravity.
Ultimately, any explanation of quantum measurement must be extendable to relativistic quantum mechanics (RQM), since many precisely confirmed experimental results follow from quantum field theory (QFT), which is based on RQM. Certainly, the traditional "collapse" postulate for quantum measurement is problematic in a relativistic context, at the very least because, as usually formulated, it violates the relativity of simultaneity. The present paper addresses this with a relativistic model of measurement in which the state of the universe is decomposed into decoherent histories of measurements recorded within it. The approach is essentially Everettian, in the sense that it uses the unmodified, unitary quantum formalism of RQM. But it addresses the difficulty with typical "many worlds" interpretations on how to even define probabilities over different possible ``worlds''. To do this, Zurek's concept of envariance is generalized to the context of relativistic spacetime, giving an objective definition of the probability of any one of the quantum histories, consistent with Born's rule. It is then shown that the statistics of any repeated experiment within the universe also tend to follow the Born rule as the number of repetitions increases. The wave functions that we actually use for such experiments are local reductions of very coarse-grained superpositions of universal eigenstates, and their "collapse" can be re-interpreted as simply an update based on additional incremental knowledge gained from a measurement about the "real" eigenstate of our universe.