Pieter Thyssen

The aim of this doctoral dissertation is to closely explore the nature of Einstein’s block universe and to tease out its implications for the nature of time and human freedom. Four questions, in particular, are central to this dissertation, and set out the four dimensions of this philosophical investigation: (1) Does the block universe view of time follow inevitably from the theory of special relativity? (2) Is there room for the passage of time in the block universe? (3) Can we distinguish past from future in the block universe? (4) Is there room for human freedom in the block universe? Although the answer of most philosophers would be yes, triple no, my own answer, controversially, is no, triple yes. I thereby challenge the status quo with respect to each of these metaphysical questions, and argue that none of these questions can be answered from looking at physics alone. Physics may constrain our metaphysics, but it certainly does not settle it. What is needed in order to answer these questions, are additional metaphysical assumptions that fall outside the scope of modern physics. My primary goal in this dissertation, therefore, is not to settle the debates on the nature of time and human freedom, but to clarify them by expliciting the metaphysical assumptions that are otherwise left implicit.

To this day, a hundred and fifty years after Mendeleev's discovery, the overal structure of the periodic system remains unaccounted for in quantum-mechanical terms. Given this dire situation, a handful of scientists in the 1970s embarked on a quest for the symmetries that lie hidden in the periodic table. Their goal was to explain the table's structure in group-theoretical terms. We argue that this symmetry program required an important paradigm shift in the understanding of the nature of chemical elements. The idea, in essence, consisted of treating the chemical elements, not as particles, but as states of a superparticle. We show that the inspiration for this came from elementary particle physics, and in particular from Heisenberg's suggestion to treat the proton and neutron as different states of the nucleon. We provide a careful study of Heisenberg's last paper on the nature of elementary particles, and explain why the Democritean picture of matter no longer applied in modern physics and a Platonic symmetry-based picture was called for instead. We show how Heisenberg's Platonic philosophy came to dominate the field of elementary particle physics, and how it found its culmination point in Gell-Mann's classification of the hadrons in the eightfold way. We argue that it was the success of Heisenberg's approach in elementary particle physics that sparked the group-theoretical approach to the periodic table. We explain how it was applied to the set of chemical elements via a critical examination of the work of the Russian mathematician Abram Ilyich Fet the Turkish-American physicist Asim Orhan Barut, before giving some final reflections.

This review paper provides a detailed overview and critical analysis of the philosophical literature on the Rietdijk–Putnam–Maxwell argument for the four-dimensionality of the world. After briefly introducing the debate on the dimensionality of the world, I present the arguments by Rietdijk, Putnam and Maxwell, and highlight the differences between them. I subsequently raise a total of eleven objections against the Rietdijk–Putnam–Maxwell argument, and conclude that its validity is underdetermined by the formalism of special relativity.

The debate on the conventionality of simultaneity and the debate on the dimensionality of the world have been central in the philosophy of special relativity. The link between both debates however has rarely been explored. The purpose of this paper is to gauge what implications the former debate has for the latter. I show the situation to be much more subtle than was previously argued, and explain how the ontic versus epistemic distinction in the former debate impacts the latter. Despite claims to the contrary, I conclude that special relativity leaves the debate on the dimensionality of the world underdetermined.

This chapter gives an overview of the evolution of the position of the rare-earth elements in the periodic system, from Mendeleev’s time to the present. Three fundamentally different accommodation methodologies have been proposed over the years. Mendeleev considered the rare-earth elements as homologues of the other elements. Other chemists looked upon the rare earths as forming a special intraperiodic group and therefore clustered the rare-earth elements in one of the groups of the periodic table. Still others adhered to the intergroup accommodation of the rare earths, according to which the rare-earth elements do not show any relationship with the other elements, so that they had to be placed within the periodic table as a separate family of elements. The intergroup accommodation became the preferred one in the twentieth century. The advantages and disadvantages of the different representations of the modern periodic table are discussed.

Human freedom is in tension with nomological determinism and with statistical determinism. The goal of this paper is to answer both challenges. Four contributions are made to the free-will debate. First, we propose a classification of scientific theories based on how much freedom they allow. We take into account that indeterminism comes in different degrees and that both the laws and the auxiliary conditions can place constraints. A scientific worldview pulls towards one end of this classification, while libertarianism pulls towards the other end of the spectrum. Second, inspired by Hoefer, we argue that an interval of auxiliary conditions corresponds to a region in phase space, and to a bundle of possible block universes. We thus make room for a form of non-nomological indeterminism. Third, we combine crucial elements from the works of Hoefer and List; we attempt to give a libertarian reading of this combination. On our proposal, throughout spacetime, there is a certain amount of freedom that can be interpreted as the result of agential choices. Fourth, we focus on the principle of alternative possibilities throughout and propose three ways of strengthening it.

Are acids natural kinds? Or are they merely relevant kinds? Although acidity has been one of the oldest and most important concepts in chemistry, surprisingly little ink has been spilled on the natural kind question. I approach the question from the perspective of microstructural essentialism. After explaining why both Brønsted acids and Lewis acids are considered functional kinds, I address the challenges of multiple realization and multiple determination. Contra Manafu and Hendry, I argue that the stereotypical properties of acids are not multiply realized. Instead, given the equivalence between the proton-donating and electron-accepting mechanisms of Brønsted and Lewis, respectively, I show that acidity as a property type can be identified with a unique microstructural property, namely the presence of a LUMO or other low energy empty orbital. In doing so, I defend the view that the Lewis theory encompasses Brønsted--Lowry, and that all Brønsted acids are also Lewis acids. Contra Hacking and Chang, I thus maintain that the different concepts of acidity do not crosscut, and that the hierarchy requirement is met. Finally, by characterizing natural kinds as powerful objects and by adopting a dispositional view of functions, I illustrate how the microessentialist can make sense of the latent and relational character of most acids. In sum, I contend that acids are genuine natural kinds, even for the microstructural essentialist.

The block universe theory of time is commonly said to be incompatible with temporal becoming. This confuses Maudlin who upholds both eternalism and passage. The aim of this paper is to answer Maudlin’s plea for clarification by distinguishing four degrees of temporal becoming. After discussing their respective compatibility with the block universe, I show that Maudlin asks much less from temporal becoming than most philosophers of time. Consequently, his form of becoming is compatible with the block universe, whereas the stronger forms of becoming are not.

At the heart of chemistry lies the periodic system of chemical elements. Despite being the cornerstone of modern chemistry, the overall structure of the periodic system has never been fully understood from an atomic physics point of view. Group-theoretical models have been proposed instead, but they suffer from several limitations. Among others, the identification of the correct symmetry group and its decomposition into subgroups has remained a problem to this day. In an effort to deepen our limited understanding of the periodic law, we have extended the traditional Lie algebraic framework to account for the peculiar degeneracy structure of the periodic system. Starting from the four-dimensional hidden symmetry and accidental degeneracy of the hydrogen atom, as first revealed by Fock in 1935, our research has mainly focussed on the way this SO(4) symmetry of the Coulomb potential gets broken in the periodic system as a consequence of the transformation of the hydrogenic (n, l) filling order to the Madelung (n+l, n) order due to electronic repulsions, relativistic effects and spin-orbit couplings. In this PhD dissertation, a new left-step format of the periodic table is first proposed on the basis of the Madelung rule. Following the particle physics tradition, the chemical elements are then considered as various states of some 'atomic matter', which is described by a non-compact spectrum-generating dynamical Lie group. The chemical elements are shown to form a basis for a single infinite-dimensional degeneracy space of the SO(4,2) ⊗ SU(2) group. An explanation for the period doubling is then proposed in terms of a particular symmetry breaking of the SO(4,2) group to the anti de Sitter SO(3,2) group. The Madelung rule is rationalised on the basis of nonlinear Lie algebras which reflect the screening of the Coulomb hole. This opens new perspectives for a symmetry-based understanding of how the periodic law emerges from its quantum mechanical foundations, and holds the future promise of complementing our current phenomenological approach by a direct atomic physics approach.

According to Leininger, presentists and growing blockers cannot explain why past and present regularities persist in the future. In order to do so, they would have to appeal to enforcers, such as causation, laws or dispositions. But in a world with no future, these enforcers are powerless and cannot guarantee future regularity. I disagree and argue that Leininger’s coordination problem can be met by distinguishing type- from token-level necessitation. Whereas token-level necessitation is cross-temporal and subject to Leininger’s coordination problem, type-level necessitation is atemporal and immune to the coordination problem. For this solution to work, though, type-level necessitation must be ontologically prior to token-level necessitation. This forces us to adopt a Platonist position according to which universals are transcendent, and not immanent.

Symmetry is at the heart of our understanding of matter. This book tells the fascinating story of the constituents of matter from a common symmetry perspective. The standard model of elementary particles and the periodic table of chemical elements have the common goal to bring order in the bewildering chaos of the constituents of matter. Their success relies on the presence of fundamental symmetries in their core. The purpose of Shattered Symmetry is to share the admiration for the power and the beauty of these symmetries. The reader is taken on a journey from the basic geometric symmetry group of a circle to the sublime dynamic symmetries that govern the motions of the particles. Along the way the theory of symmetry groups is gradually introduced with special emphasis on its use as a classification tool and its graphical representations. This is applied to the unitary symmetry of the eightfold way of quarks, and to the four-dimensional symmetry of the hydrogen atom. The final challenge is to open up the structure of Mendeleev's table which goes beyond the symmetry of the hydrogen atom. Breaking this symmetry to accommodate the multi-electron atoms requires us to leave the common ground of linear algebras and explore the potential of non-linearity.

Since its inception in 1869, the periodic system — icon of modern chemistry — has suffered from the problematic accommodation of the rare-earth elements. The substance of this paper intends to retrace Mendeleev’s shifting attitudes with regard to the rare-earth crisis during the period 1869–1871. Based on a detailed examination of Mendeleev's research papers from that period, it will be argued that the rare-earth crisis played a key role in inducing a number of important changes in Mendeleev’s philosophical viewpoints with regard to the epistemological concept of a chemical element and the nature of elementary groups. Many of Mendeleev's most cherished beliefs got endangered by the nature of these elements. Their mystifying properties forced him to revise his ideas about primary and secondary groups, the elements as basic and simple substances, and the use of short and long form tables. They made him question the validity and universality of the periodic law, and led him into hypothesizing about the internal structure of matter and constitution of atoms.

Are acids natural kinds? Or are they merely relevant kinds? Although acidity has been one of the oldest and most important concepts in chemistry, surprisingly little ink has been spilled on the natural kind question. I approach the question from the perspective of microstructural essentialism. After explaining why both Brønsted acids and Lewis acids are considered functional kinds, I address the challenges of multiple realization and multiple determination. Contra Manafu and Hendry, I argue that the stereotypical properties of acids are not multiply realized. Instead, given the equivalence between the proton-donating and electron-accepting mechanisms of Brønsted and Lewis, respectively, I show that acidity as a property type can be identified with a unique microstructural property, namely the presence of a LUMO or other low energy empty orbital. In doing so, I defend the view that the Lewis theory encompasses Brønsted–Lowry, and that all Brønsted acids are also Lewis acids. Contra Hacking and Chang, I thus maintain that the different concepts of acidity do not crosscut, and that the hierarchy requirement is met. Finally, by characterizing natural kinds as powerful objects and by adopting a dispositional view of functions, I illustrate how the microessentialist can make sense of the latent and relational character of most acids. In sum, I contend that acids are genuine natural kinds, even for the microstructural essentialist.

Since Mendeleev’s discovery in 1869, the periodic table has figured as the ultimate paper tool in chemical research. It has proved to be a vital research instrument in the arsenal of the chemical community. No chemistry textbook, lecture theatre or scientific laboratory is complete without a copy of the periodic table of the elements. This however, should not necessarily imply that the periodic table has never had to contend with problems. In this thesis, the history of the accommodation of the rare-earth elements in the periodic table will be addressed. When Mendeleev published his periodic table in 1869, the rare earths already constituted a major obstacle. Mendeleev was able to include only four members of the rare earths and he experienced great difficulties in positioning these elements. Question marks and wrong atomic weights reigned in the last rows of Mendeleev’s system. This problematic accommodation quickly grew into one of the most serious threats for the periodic law. For over fifty years, chemists continually struggled with the placement of these maddeningly similar elements. As a consequence, a lot of chemists started to question the validity of the periodic law, but others took it as a sign that the concept of a chemical element had to be reconsidered. As a result, this work intends to retrace the mutual influence of the philosophical ideas about the nature of chemical elements and the development of the periodic table from its inception in 1869 to the discovery of Moseley’s law in 1913 and Bohr’s publication of his landmark paper On the Constitution of Atoms and Molecules. The aim of this thesis is to show how, on the one hand, the periodic table (as a research instrument) helped in reformulating the contemporary ideas about chemical elements, and how it aided in developing a new research program in order to resolve the rare earth crisis. On the other hand, the question will be taken up to what extent Crookes’ evolutionary ideas about meta elements helped in saving the periodic table from a severe downfall by solving the gnawing problem of the rare-earth elements. In particular, this work will also focus on the investigations of the Czech chemist, Bohuslav Brauner. It will be shown how Brauner, under the influence of Crookes’ ideas, was led to his formulation of the Asteroid Hypothesis, according to which all the rare-earth elements should be placed in a single case of the periodic table.