This paper proposes an evidence-based definition for what is “statistically impossible” relative to an appropriate set of domains, including the universe of all quantum events, all possible earthly events, the history of all human events, and a human lifetime. For example, any event which has less than one chance of occurring in the total number of all quantum vibrations in the history of the universe (10120) should, according to this proposed convention, be confidently declared as “statistically impossible.” Moreover, sequences of events that are less likely than the square of all quantum events in the universe (10240) (which is equal to all quantum events in 10120 multiverses) are properly described as “absurdly impossible.”According to this convention, if such a "statistically impossible" event is ever observed then one must conclude either: (A) the observed event is non-random, or (B) the universe of all possible events is larger than previously assumed. This convention is therefore useful for testing a priori assumptions and distinguishing random from non-random events. Also discussed is the need for a new ratio, similar to an effect size calculation, for describing the likelihood of a series of events within a given domain of possible events as either “certain”, “likely”, “possible”, “improbable”, and “impossible.”
This paper proposes an evidence-based definition for what is “statistically impossible” relative to an appropriate set of domains, including the universe of all quantum events, all possible earthly events, the history of all human events, and a human lifetime. For example, any event which has less than one chance of occurring in the total number of all quantum vibrations in the history of the universe (10120) should, according to this proposed convention, be confidently declared as “statistically impossible.” Moreover, sequences of events that are less likely than the square of all quantum events in the universe (10240) (which is equal to all quantum events in 10120 multiverses) are properly described as “absurdly impossible.”According to this convention, if such a "statistically impossible" event is ever observed then one must conclude either: (A) the observed event is non-random, or (B) the universe of all possible events is larger than previously assumed. This convention is therefore useful for testing a priori assumptions and distinguishing random from non-random events. Also discussed is the need for a new ratio, similar to an effect size calculation, for describing the likelihood of a series of events within a given domain of possible events as either “certain”, “likely”, “possible”, “improbable”, and “impossible.”
Solid experimental evidence has now been obtained that confirms the violation of Bell's inequality in tests of maximally entangled qubit pairs. This violation is widely interpreted as definitive proof of the impossibility of describing quantum phenomena in terms of locally defined elements of reality. In a series of recent papers, we have noticed, however, that this conclusion inadvertently, yet crucially, relies on the assumed existence of an absolute frame of reference, with respect to which it would be possible to describe independently of each other the hypothetical elements of reality and the measurement devices that test them. Otherwise, a non-zero geometric phase may appear in the description of the former with respect to a closed sequence of settings of the latter, leading to the violation of the inequality. Following this observation, we discuss an explicit statistical model, which fully reproduces the predictions of Quantum Mechanics for the Bell experiment.
We argue that the many worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics. Decoherence---the modern version of wave-function collapse---is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the environment. In fact decoherence is absent in the complete description of any region larger than the future light cone of a measurement event. However, if one restricts to the causal diamond---the largest region that can be causally probed---then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment. We argue that the global multiverse is a representation of the many worlds (all possible decoherent causal diamond histories) in a single geometry. We propose that it must be possible in principle to verify quantum-mechanical predictions exactly. This requires not only the existence of exact observables but two additional postulates: a single observer within the Universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite. In causal diamonds with a finite surface area, holographic entropy bounds imply that no exact observables exist, and both postulates fail: experiments cannot be repeated infinitely many times; and decoherence is not completely irreversible, so outcomes are not definite. We argue that our postulates can be satisfied in hats (supersymmetric multiverse regions with vanishing cosmological constant). We propose a complementarity principle that relates the approximate observables associated with finite causal diamonds to exact observables in the hat.
This essay is a two-step reflection on the question 'Which events (can be said to) occur in quantum phenomena?' The first step regiments the ontological category of "statistical phenomena" and studies the adequacy of "probabilistic event models" as descriptions thereof. Guided by the conviction that quantum phenomena are to be circumscribed within this same ontological category, the second step highlights the peculiarities of probabilistic event models of some non-relativistic quantum phenomena, and thereby of what appear to be some plausible answers to our initial question. The reflection ends in an aporetic state, as it is by now usual in encounters between ontology and the quantum.
Quantum mechanics is usually defined in terms of some loosely connected axioms and rules. Such a foundation is far from the beauty of, e.g., the `principles' underlying classical mechanics. Motivated, in addition, by notorious interpretation problems, there have been numerous attempts to modify or `complete' quantum mechanics. A first attempt was based on so-called hidden variables; its proponents essentially tried to expel the non-classical nature of quantum mechanics. More recent proposals intend to complete quantum mechanics not within mechanics proper but on a `higher (synthetic) level'; by means of a combination with gravitation theory (R Penrose), with quantum information theory (C M Caves, C A Fuchs) or with psychology and brain science (H P Stapp). I think it is fair to say that in each case the combination is with a subject that, per se , suffers from a very limited understanding that is even more severe than that of quantum mechanics. This was acceptable, though, if it could convincingly be argued that scientific progress desperately needs to join forces. Quantum mechanics of a closed system was a beautiful and well understood theory with its respective state being presented as a point on a deterministic trajectory in Liouville space---not unlike the motion of a classical N -particle system in its 6N -dimensional phase-space. Unfortunately, we need an inside and an outside view, we need an external reference frame, we need an observer. This unavoidable partition is the origin of most of the troubles we have with quantum mechanics. A pragmatic solution is introduced in the form of so-called measurement postulates: one of the various incompatible properties of the system under consideration is supposed to be realized (i.e. to become a fact, to be defined without fundamental dispersion) based on `instantaneous' projections within some externally selected measurement basis. As a result, the theory becomes essentially statistical rather than deterministic; furthermore there is an asymmetry between the observed and the observing. This is the point where consciousness may come in. Complemented by an introduction and several appendices, Henry Stapp's book consists essentially of three parts: theory, implications, and new developments. The theory part gives a very readable account of the Copenhagen interpretation, some aspects of a psychophysical theory, and, eventually, hints towards a quantum foundation of the brain--mind connection. The next part, `implications', summarizes some previous attempts to bridge the gap between the working rules of quantum mechanics and their possible consequences for our understanding of this world (Pauli, Everett, Bohm, Heisenberg). The last section, `new developments', dwells on some ideas about the conscious brain and its possible foundation on quantum mechanics. The book is an interesting and, in part, fascinating contribution to a field that continues to be a companion to `practical' quantum mechanics since its very beginning. It is doubtful whether such types of `quantum ontologies' will ever become (empirically) testable; right now one can hardly expect more than to be offered some consistent `grand picture', which the reader may find more or less acceptable or even rewarding. Many practicing quantum physicists, though, will remain unimpressed. The shift from synthetic ontology to analytic ontology is the foundation of the present work. This means that fundamental wholes are being partitioned into their ontologically subordinate components by means of `events'. The actual event, in turn, is an abrupt change in the Heisenberg state describing the quantum universe. The new state then defines the tendencies associated with the next actual event. To avoid infinite regression in terms of going from one state of tendencies to the next, consciousness is there to give these events a special `feel', to provide a status of `intrinsic actuality'. The brain of an alert human observer is similar in an important way to a quantum detection device: it can amplify small signals to large macroscopic effects. On the other hand, actual events are not postulated to occur exclusively in brains. They are more generally associated with the formation of records. Records are necessarily part of the total state of the universe: it is obvious that the state of the universe cannot undergo a Schrödinger dynamics and at the same time record its own history. `The full universe consists therefore of an exceedingly thin veneer of relatively sluggish, directly observable properties resting on a vast ocean or rapidly fluctuating unobservable ones.' The present ideas also bear on how the world should be seen to develop. While conventional cosmology encounters problems as to how to define the intial conditions, which would enter the governing equations of motion, here `the boundary conditions are set not at some initial time, but gradually by a sequence of acts that imposes a sequence of constraints. After any sequence of acts there remains a collection of possible worlds, some of which will be eliminated by the next act.' Connected with those acts is `meaning': there has always been some speculation about the special significance of local properties in our understanding of the world. One could argue that correlations (even the quantum correlations found, e.g., in the EPR-experiments) were as real as anything else. But also Stapp stresses the special role of locality: the `local observable properties, or properties similar to them are the natural, and perhaps exclusive, carriers of meaning in the quantum universe. From this point of view the quantum universe tends to create meaning.' This sounds like an absolute concept: meaning not with respect to something else, but defined intrinsically---not easy to digest. The role of consciousness in the developing quantum universe requires more attention. `The causal irrelevance of our thoughts within classical physics constitutes a serious deficiency of that theory, construed as a description of reality.' This is taken to be entirely different within quantum mechanics. `The core idea of quantum mechanics is to describe our activities as knowledge-seeking and knowledge-using agents.' `21st century science does not reduce human beings to mechanical automata. Rather it elevates human beings to agents whose free choices can, according to the known laws, actually influence their behaviour.' An example with respect to perception is discussed: `Why, when we look at a triangle, do we experience three lines joined at three points and not some pattern of neuron firings?' The brain `does not convert an actual whole triangle into some jumbled set of particle motions; rather it converts a concatenation of separate external events into the actualization of some single integrated pattern of neural activity that is congruent to the perceived whole triangle.' How convincing is this proposal? It is hard to tell. I think Henry Stapp did a good job, but there are tight limitations to any such endeavour. Quantum mechanics is often strange indeed, but it also gives rise to our classical world around us. For the emergence of classicality jumps and measurement projections (the basic phenomena connected with those fundamental events of choice) are not needed. Therefore, I doubt whether the explanation of the evolution of our world really allows (or requires) that much free choice. On the other hand, most scientist will agree that empirical science was not possible without free will: we could not ask independent questions if this asking was part of a deterministic trajectory. The fact that the result of a quantum measurement is indeterminate (within given probabilities) does certainly not explain free will. How about the type of measurment? The experimentalist will have to assume that he can select the pertinent observable within some limits. But given a certain design the so-called pointer basis (producing stable measurement results) is no longer a matter of free choice. `The main theme of classical physics is that we live in a clocklike universe.' Today it is often assumed that the universe was a big (quantum-) computer or a cellular automaton. Many would be all too happy to leave that rather restrictive picture behind. But where to go? Stapp suggests giving consciousness a prominent role: `The most profound alteration of the fundamental principles was to bring consciousness of human beings into the basic structure of the physical theory.' How far we are able to go in this direction will depend on the amount of concrete research results becoming available to support this view.
A psychokinetic (PK) effect--a mental influence on the outcome of chance processes--was first reported by Louisa and J. B. Rhine (Rhine & Rhine, 1943) from experiments with dice. Through the introduction of electronic random number generators based on quantum randomness (Schmidt, 1971), the experiments became more easily accessible and even more challenging to physicists. Today, a large number of successful PK experiments with random number generators have been reported (Radin & Nelson, 1989). It has not yet been possible, however, to stabilize and strengthen the statistically weak effects so that they can be easily demonstrated on demand. The discovery of PK effects on prerecorded random events (Schmidt, 1976) did not make the gathering of data less arduous, but it permitted the inclusion of independent observers who, with little investment of time and effort, could obtain first-hand evidence for any PK effects that might occur. All five experiments to be discussed here included such independent observers. PK Tests with Prerecorded Events and Independent Observers In a typical PK experiment, a random number generator produces a binary random sequence that the subject tries to bias in a certain manner. Let us take, for example, the case where the random generator produces in each test run a sequence of 100 binary events displayed as a sequence of 100 red (for a 0-bit) and green (for a 1-bit) light flashes, while the subject is instructed to mentally enforce the appearance of more red than green flashes. The sequence of red and green signals is stored on floppy disk, and a score that is measured by the difference between the numbers of red and green signals is displayed and recorded at the end of the run. The arrangement for an experiment with prerecorded random events is similar, but there is a time delay between the generation of the random events and their display to the subject. First, the random signals for a large number of test runs are generated and recorded on floppy disk. Days or months later, the stored signals are translated by the computer into a corresponding sequence of red and green light flashes while the subject tries to mentally enforce the appearance of more red than green signals. Experiments have shown that selected subjects can succeed in this arrangement (Schmidt, 1976, 1987), provided that the prerecorded events have not been inspected by anybody before the subject makes the PK effort. To let an independent observer participate in the experiment, we prerecord the bit sequences for all test runs planned for the experiment, and we let a computer make a printout of the scores for all the test runs. Being careful that nobody can observe the scores, we send a sealed copy of the printout to the independent observer. Leaving the printout sealed, the independent observer randomly specifies for each test run whether the subject's PK effort should be aimed at a high score (excess of red signals in the example) or a low score (excess of green signals). In the subsequent PK test sessions, the subject follows for each test run the independent observer's assignments, aiming for an excess of red or green signals, respectively. At the end of the experiment, the independent observer opens the sealed printouts. If the subject's effort was successful, the independent observer can confirm this first-hand by a tendency of the scores to point in the directions (positive or negative) that he had randomly specified. Because the independent observer had randomly assigned the directions, he or she can be certain that no such systematic tendency should occur (in the absence of the claimed anomaly). Using an appropriate statistical method, the independent observer can assess the significance of such a tendency without having to consider the reliability of the experimenter and his procedures. Test Arrangement with Distant Subjects The five experiments under discussion followed this general outline with minor variations. …