Observer Dependent Biases of Quantum Randomness

Quantum mechanics (QM) proposes that a quantum system measurement does not register a pre-existing reality but rather establishes reality from the superposition of potential states. Measurement reduces the quantum state according to a probability function, the Born rule, realizing one of the potential states. Consequently, a classical reality is observed. The strict randomness of the measurement outcome is well-documented (and theoretically predicted) and implies a strict indeterminacy in the physical world’s fundamental constituents. Wolfgang Pauli, with Carl Gustav Jung, extended the QM framework to measurement outcomes that are meaningfully related to human observers, providing a psychophysical theory of quantum state reductions. The Pauli-Jung model (PJM) proposes the existence of observer influences on quantum measurement outcomes rooted in the observer’s unconscious mind. The correlations between quantum state reductions and (un)conscious states of observers derived from the PJM and its mathematical reformulation within the model of pragmatic information (MPI) were empirically tested. In all studies, a subliminal priming paradigm was used to induce a biased likelihood for specific quantum measurement outcomes (i.e., a higher probability of positive picture presentations; Studies 1 and 2) or more pronounced oscillations of the evidence than expected by chance for such an effect (Studies 3 and 4). The replicability of these effects was also tested. Although Study 1 found strong initial evidence for such effects, later replications (Studies 2 to 4) showed no deviations from the Born rule. The results thus align with standard QM, arguing against the incompleteness of standard QM in psychophysical settings like those established in the studies. However, although no positive evidence exists for the PJM and the MPI, the data do not entirely falsify the model’s validity.

Johannes Kepler and Twenty-First-Century Science

Johannes Kepler’s little book on the snowflake anticipates one direction of twenty-first-century science. Why do snowflakes all have six corners? Kepler searches for a geometry inscribed in nature, a “formative faculty” that shapes the dynamic patterns of both inorganic and organic forms. A similar search drives modern biotechnology. Twentieth-century science, exemplified by Wolfgang Pauli, had built on principles in tune with those of Kepler’s rival, the hermeticist Robert Fludd. Quantum physics is invested in archetypal numbers (such as 137, the fine-structure constant), in unobjectifiability (the impossibility of viewing a world unaffected by the observer), and in action-at-a-distance (effects that can be calculated but whose cause remains unknown). Kepler scorns such principles. Instead he looks for patterns of organization that account for the real world, whether in snowflakes, the heavens, or living bodies. Today that project has been revived in the life sciences, in ecology and ecosystems, in fractal geometry, in nanotech and biotech. Perhaps Kepler’s vision of science has come into its own.

4. Enthusiastic resignation

‘Enthusiastic resignation’ describes Bohr’s work with Wolfgang Pauli and Werner Heisenberg. ‘Resignation’ refers to their realization that the electron orbits that had served as the basis of Bohr’s theory had only ‘symbolic’ value. They took the correspondence principle as a guide to translating symbols describing the orbits, like position and momentum, into symbols specifying the values of observable products of atoms, like the frequency and intensity of spectral lines. Heisenberg’s breakthrough in the summer of 1925, based on a particulate view of matter, provided a basis for a coherent description of the phenomena to which atomic electrons give rise. Almost simultaneously, Erwin Schrödinger found another route to the same mathematical solution, based on a wave picture of matter, which avoided discontinuity and made calculations easier. In answering Schrödinger’s challenge, Heisenberg invented the Uncertainty Principle and Bohr worked out a more general reconciliation of the quantum puzzles, which he called ‘complementarity’.

Born’s Interpretation of the Wavefunction

Schrödinger hoped that his wave mechanics would help to re-establish some sense of ‘visualizability’ of the physics going on inside the atom. In searching for a suitable interpretation of the wavefunction, he focused on the density of electrical charge, which he associated with the wavefunction ψ‎ multiplied by its complex conjugate. Hidden in his words is the interpretation that would eventually come to dominate our understanding of the wavefunction. Max Born had no hesitation in concluding that the only way to reconcile wave mechanics with the particle description is to interpret the modulus-square of the wavefunction as a probability density. It was Wolfgang Pauli who proposed to interpret this not only as a transition probability or as the probability for the system to be in a specific state, as Born had done, but as the probability of ‘finding’ the electron at a specific position in its orbit inside an atom.

Texte zur Quantentheorie

Die in diesem Band zusammengestellten Texte Schlicks aus den Zwanziger- und Dreißigerjahren vermitteln vor dem Hintergrund der Einstein’schen Relativitätsrevolution das Bild einer Zeit des radikalen Umbruchs und der Entstehung des Neuen in der Physik. Als Protagonist einer Epoche intensiver Wechselwirkung zwischen naturwissenschaftlicher Forschung und philosophischer Reflexion stand Schlick, der bei Max Planck promoviert wurde, in einem intensiven Gedankenaustausch mit der Gemeinschaft der Quantenphysiker, wozu u. a. Max Born, Werner Heisenberg, Erwin Schrödinger, Pascual Jordan und Wolfgang Pauli zählten. Während sie der noch jungen Theorie der Quanten zum Durchbruch verhalfen, lieferte Schlick vor allem in Auseinandersetzung mit Hans Reichenbach und unter dem Einfluss der sprachphilosophischen Wende Ludwig Wittgensteins stehend zentrale Beiträge zum neuen Verständnis der physikalischen Realität, zu den Begriffen von Kausalität und Wahrscheinlichkeit, aber auch zum Problem der Messung und zum Verhältnis zwischen Physik und Biologie.

Fine-structure constant from Sommerfeld to Feynman

The fine-structure constant, which determines the strength of the electromagnetic interaction, is briefly reviewed beginning with its introduction by Arnold Sommerfeld and also includes the interest of Wolfgang Pauli, Paul Dirac, Richard Feynman and others. Sommerfeld was very much a Pythagorean and sometimes compared to Johannes Kepler. The archetypal Pythagorean triangle has long been known as a hiding place for the golden ratio. More recently, the quartic polynomial has also been found as a hiding place for the golden ratio. The Kepler triangle, with its golden ratio proportions, is also a Pythagorean triangle. Combining classical harmonic proportions derived from Kepler’s triangle with quartic equations determine an approximate value for the fine-structure constant that is the same as that found in our previous work with the golden ratio geometry of the hydrogen atom. These results make further progress toward an understanding of the golden ratio as the basis for the fine-structure constant.

Nuclear Electrons and Nuclear Structure

Serious contradictions to the existence of electrons in nuclei impinged in one way or another on the theory of beta decay and became acute when Charles Ellis and William Wooster proved, in an experimental tour de force in 1927, that beta particles are emitted from a radioactive nucleus with a continuous distribution of energies. Bohr concluded that energy is not conserved in the nucleus, an idea that Wolfgang Pauli vigorously opposed. Another puzzle arose in alpha-particle experiments. Walther Bothe and his co-workers used his coincidence method in 1928–30 and concluded that energetic gamma rays are produced when polonium alpha particles bombard beryllium and other light nuclei. That stimulated Frédéric Joliot and Irène Curie to carry out related experiments. These experimental results were thoroughly discussed at a conference that Enrico Fermi organized in Rome in October 1931, whose proceedings included the first publication of Pauli’s neutrino hypothesis.

Move Over, God

In the last two hundred years, physics, biology, and linguistics have markedly increased our understanding of three mysteries that continue to pique human curiosity: How did the universe begin? What is the origin of life? What accounts for language, a capacity we share with no other creature? For helping us answer these questions, we have to thank linguists like Steven Pinker, evolutionary biologists like Richard Dawkins, and theoretical physicists like Steven Weinberg. They each have a gift for translating important technical arguments in their respective disciplines into the ordinary English we all can understand. Accompanying this extraordinary achievement in popularization, however, there is an odd fellow traveler, a campaign against religion, against God, a concerted attack extraordinary in its persistence and its vehemence. In this final chapter, I would like to investigate the extent, source, and nature of this attack, this insistence on the part of so many scientists that they are not agnostics, properly skeptical of God’s existence, but atheists, firm believers in his nonexistence, that science, not God, is the only wellspring of the sublime. It is the firmness of their belief that is in question. When Wolfgang Pauli purportedly said of another scientist’s work that “it is not right; it is not even wrong,” he meant that this work violated the boundaries of the discipline Pauli so successfully inhabited, that the offending scientist was deluded when he thought he was doing physics. Of course, such professional judgments are far from perfect. Two eminent English mathematicians had already dismissed the work of Ramanujan when G. H. Hardy, having received it unsolicited in the morning mail, judged its author as on a par with Euler or Gauss. Still, this reversal of fortune is the exception, not the rule. When, however, even world-renowned scientists cross the border into a neighboring discipline in the humanities, say theology or biblical study, the exception is the rule: they dismiss what they do not trouble to understand.