Quantum Mechanics, Miscellaneous

Quantum theory offers mathematical descriptions of measurable phenomena with great facility and accuracy, but it provides absolutely no understanding of why any particular quantum outcome is observed. It is the province of genuine explanations to tell us how things actually work—that is, why such descriptions hold and why such predictions are true. Quantum theory is long on the what, both mathematically and observationally, but almost completely silent on the how and the why. What is even more interesting is that, in (...) some sense, this state of affairs seems to be a necessary consequence of the empirical adequacy of quantum descriptions. One of the most noteworthy achievements of quantum theory is the accurate prediction of phenomena that, on pain of experimental contradiction, have no physical explanation. It is the purpose of this essay to make clear why quantum mechanics and quantum field theory are complete physical descriptions that describe the metaphysical incompleteness of the physical world, then to press the negative implications of this fact for naturalistic metaphysics. (shrink)

The many worlds interpretation of quantum mechanics (MWI) states that the world we live in is just one among many parallel worlds. It is widely believed that because of this commitment to parallel worlds, the MWI violates common sense. Some go so far as to reject the MWI on this basis. This is despite its myriad of advantages to physics (e.g. consistency with relativity theory, mathematical simplicity, realism, determinism, etc.). Here, we make the case that common sense in fact favors (...) the MWI. We argue that causal explanations are commonsensical only when they are local causal explanations. We present several quantum mechanical experiments that seem to exhibit nonlocal “action at a distance”. Under the assumption that only one world exists, these experiments seem immune to local causal explanation. However, we show that the MWI, by taking all worlds together, can provide local causal explanations of the experiments. The MWI therefore restores common sense to physical explanation. (shrink)

The measurement problem concerns an apparent conflict between the two fundamental principles of quantum mechanics, namely the Schrödinger equation and the measurement postulate. These principles describe inconsistent behavior for quantum systems in so-called "measurement contexts." Many theorists have thought that the measurement problem can only be resolved by proposing a mechanistic explanation of (genuine or apparent) wavefunction collapse that avoids explicit reference to "measurement." However, I argue here that the measurement problem dissolves if we accept Humeanism about laws of nature. (...) On a Humean metaphysics, there is no conflict between the two principles, nor is there any inherent problem with the concept of "measurement" figuring into the account of collapse. (shrink)

This is Part 2 of a four part paper, intended as an introduction to the key concepts and issues of time directionality for physicists and philosophers. It redresses some fundamental confusions in the subject. These need to be corrected in introductory courses for physics and philosophy of physics students. Here we analyze the quantum mechanical time reversal operator and the reversal of the deterministic Schrodinger equation. It is argued that quantum mechanics is anti-symmetric w.r.t. time reversal in its deterministic laws. (...) This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric (reversible), and that we must adopt the anti-unitary operator (T*) instead of the unitary time reversal operator (T) for time reversal in quantum mechanics. This is widely claimed as settled scientific fact, and large metaphysical conclusions about the symmetry of time are drawn from it. But it is an error. (shrink)

This is Part 1 of a four part paper, intended to redress some of the most fundamental confusions in the subject of physical time directionality, and represent the concepts accurately. There are widespread fallacies in the subject that need to be corrected in introductory courses for physics students and philosophers. We start in Part 1 by analysing the time reversal symmetry of quantum probability laws. Time reversal symmetry is defined as the property of invariance under the time reversal transformation, T: (...) t --> -t. It is shown that quantum mechanics (classical or relativistic) is strongly time asymmetric in its probability laws. This contradicts the orthodox analysis, found throughout the conventional literature on physical time, which claims that quantum mechanics is time symmetric or reversible. This is widely claimed as settled scientific fact, and large philosophical and scientific conclusions are drawn from it. But it is an error. The fact is that while quantum mechanics is widely claimed to be reversible on the basis of two formal mathematical properties (that it does have), these properties do not represent invariance under the time reversal transformation. A recent experiment (Batalhão at alia, 2015) showing irreversibility of quantum thermodynamics is discussed as an illustration of this result. Most physicists remain unaware of the errors, decades after they were first demonstrated. Orthodox specialists in the philosophy of time who are aware of the error continue to refer to the ‘time symmetry’ or ‘reversibility’ of quantum mechanics anyway – and exploit the ambiguity to claim false implications about physical time reversal symmetry in nature. The excuse for perpetrating the confusion is that, since it is has now become customary to refer to the formal properties of quantum mechanics as ‘reversibility’ or ‘time reversal symmetry’, we should just keep referring to them by this name, even though they are not time reversal symmetry. This causes endless confusion, in attempts to explain the physical irreversibility of our universe, and in philosophical discussions of implications of physics for the nature of time. The failure of genuine time reversal symmetry in quantum mechanics changes the interpretation of modern physics in a deep way. It changes the problem of explaining the real irreversibility found throughout nature. (shrink)

Eine Rezension des Buches "Every Thing Must Go - Metaphysics Naturalized" von James Ladyman und Don Ross.

Observations on why is there something rather than nothing, fine tuning, beauty, time, intelligent design, qualia, Zen, Bach, Jesus, poetry, consciousness.

Il existe trois problèmes majeurs dans la conception d'une théorie de la gravité quantique: la théorie quantique et la relativité générale présentent en elles-mêmes des problèmes conceptuels importants, les bases fondamentales disparates des deux théories génèrent de nouveaux problèmes majeurs en essayant de les combiner, et le contraste entre l'absence d'une théorie de la gravité quantique satisfaisante et des théories des ingrédients réussis soulèvent des questions sur la nature et la fonction de la discussion philosophique de la gravité quantique. DOI: (...) 10.13140/RG.2.2.31430.91203. (shrink)

We expect the laws of nature that describe the universe to be exact, but what if that isn't true? In this popular science article, I discuss the possibility that some candidate fundamental laws of nature, such as the Past Hypothesis, may be vague. This possibility is in conflict with the idea that the fundamental laws of nature can always and faithfully be described by classical mathematics. -/- [Bibliographic note: this article is featured on the magazine website under a different title (...) as "The fuzzy law that could break the idea of a mathematical universe" and on the magazine cover as "The Flaw at the Heart of Reality: Why precise mathematical laws can never fully explain the universe." It is a popular version of the article "Nomic Vagueness" that can be found on arXiv: 2006.05298.]. (shrink)

The paper portrays the influence of major philosophical ideas on the 1935 debates on quantum theory that reached their climax in the paper by Einstein, Podosky and Rosen, and describes the relevance of these ideas to the vast impact of the paper. I claim that the focus on realism in many common descriptions of the debate misses important aspects both of Einstein's and Bohr's thinking. I suggest an alternative understanding of Einstein's criticism of quantum mechanics as a manifestation of the (...) same methodological principles that served him in the construction of the special and the general theories of relativity. These principles address, in a very specific way, the relation of the theoretical mathematical representations to the represented physical systems. These ideas, I claim, played a key role in the influence of the paper on later works that changed our understanding of quantum theory despite the rejection of EPR's central conclusion. (shrink)

Quantum mechanics has recently indicated that, at the fundamental level, temporal order is not fixed. This phenomenon, termed Indefinite Causal Order, is yet to receive metaphysical or theological engagement. We examine Indefinite Causal Order, particularly as it emerges in a 2018 photonic experiment. In this experiment, two operations A and B were shown to be in a superposition with regard to their causal order. Essentially, time, intuitively understood as fixed, flowing, and fundamental, becomes fuzzy. We argue that if Indefinite Causal (...) Order is true, this is good evidence in favor of a B‐theory of time, though such a B‐theory requires modification. We then turn to theology, suggesting that a B‐theoretic temporal ontology invites serious reconsideration of the doctrine of salvation. This paper concludes that the best explanation for salvation given a B‐theory is mind‐dependent salvific becoming, a type of psychological soteriological change that occurs through downward causation. (shrink)

This opinion revolves around the discussion of matters that are beyond the realm of space-time. For instance, it discusses parallel universes, wormholes, and extrasensory perception or psi. Rationality is operationally defined. The opinion throws light on the manner in which the lines of rationality become unclear when it takes into consideration extrasensory phenomena. In addition, it contends that psychiatric disorders such as Schizophrenia are the result of contact from different parallel universes. Hence, Schizophrenia according to this paper is not a (...) disorder by itself but rather just a communication of messages from an alternate reality. Also, another psychological disorder called Dissociative Identity Disorder is also the result of different souls in one person or communication from different souls from parallel universes. Whether atoms are conscious or not is debatable but can be a possibility due to their eerie and unpredictable nature. The concept of parallel universes introduces a paradoxical manner of thinking, which is dealt with in the paper. The paper concerns itself with issues in quantum physics, clubbed with extrasensory perception in parapsychology. It subtly emphasizes rational thinking in the debate about space-time and beyond. Rationality as a concept is dealt with from different angles. Finally, quantum cognition is used to explain an all too familiar, pervasive yet inexplicable domain of knowledge, which is human behaviour. (shrink)

The main claim of this study is that, contrary to Latour’s view about the need to leave aside epistemology to deal with anything valuable about science, Mario Bunge has consistently built up a detailed and thorough epistemology. The argumentative strategy will be to show that (a) it is not true that we have never been modern (b) epistemology is here to stay, and (c) Mario Bunge endorses a strong scientific realism, a brand of materialism, systemism and emergentism, including a moral (...) dimension (there are objective values like, truth, peace and justice that deserve to be respected). Then, Bunge’s realism rejects axiological neutrality making scientists responsible for their actions. Bunge has always been modern and keeps enriching his own views. (shrink)

Tous les chercheurs intéressés aux fondements de la théorie quantique s’entendent sur le fait que celle-ci a profondément modifié notre conception de la réalité. Là s’arrête, toutefois, le consensus. Le formalisme de la théorie, non problématique, donne lieu à plusieurs interprétations très différentes, qui ont chacune des conséquences sur la notion de réalité. Cet article analyse comment l’interprétation de Copenhague, l’effondrement du vecteur d’état de von Neumann, l’onde pilote de Bohm et de Broglie et les mondes multiples d’Everett modifient, chacun (...) à sa manière, la conception classique de la réalité, dont le caractère local, en particulier, requiert une révision. (shrink)

Cette étude défend l’idée que, contrairement à l’opinion de Latour sur la nécessité de laisser de côté l’épistémologie pour traiter de tout ce qui a de la valeur pour la science, Mario Bunge a systématiquement construit une épistémologie détaillée et approfondie. La stratégie argumentative consistera à montrer (a) qu’il est faux que nous n’avons jamais été modernes (b) que l’épistémologie est là pour de bon et (c) que Mario Bunge soutient un réalisme scientifique fort, une version du matérialisme, du systémisme (...) et de l’émergentisme, comportant une dimension morale (il existe des valeurs objectives comme la vérité, la paix et la justice qui méritent d’être étudiées). Ensuite, le réalisme de Bunge rejette la neutralité axiologique rendant les scientifiques responsables de leurs actions. Bunge a toujours été moderne et continue à enrichir ses propres positions. (shrink)

We live in a world full of mysteries. How do our brains create consciousness? Which animals are conscious, and which are not? How can we have free-will in a deterministic universe? What are the fundamental Laws of Nature? What caused the Big Bang? How can we make sense of Quantum Mechanics? Why is the universe so finely-tuned for Life? And how did Life begin? Despite investigating such mysteries for decades or more, scientists and philosophers are no closer to finding clear (...) and convincing answers that everyone can agree upon. The big question is: why do such mysteries exist, and can they ever be solved? -/- In Life, the Universe and Consciousness, A. T. Bollands introduces us to twelve so-called intractable problems, demonstrating how each one arises from a conflict between beliefs. And yet, beliefs that are in conflict cannot all be true, which means that one or more of them must be false. To solve each problem, therefore, all we need to do is work out which of our beliefs are false and correct them. This may sound easy, but these beliefs include the most fundamental assumptions of modern science. If that wasn’t enough, it turns out that these twelve intractable problems are related, such that we cannot solve any one of them satisfactorily until we have solved all twelve within the same coherent worldview. -/- Examining each of these problems in turn, we finally arrive at our twelfth intractable problem: What is Life? A. T. Bollands proposes a new definition for Life, and with it a new way of understanding the physical world – a scientific worldview he calls Universal Life. Armed with this new worldview, he proceeds to solve all twelve intractable problems one by one, thereby developing the Theory of Universal Life and the solution to the “Big Problem of 20th Century Science”. By successfully solving each problem, he shows that Universal Life offers us a simpler, more natural, more coherent and hence more credible explanation for ourselves and the world we live in than our current scientific worldview ever can. (shrink)

We define and develop a notion of spacetime that incorporates both McTaggart's A-series and his B-series that is consistent with special relativity. This 'McTaggartian spacetime' or 'AB-spacetime' requires *five* not *4* variables. The interface of two AB-spacetimes from different *ontological perspectives* is quantum mechanical. This note concentrates on the physics and not the philosophy. This is an invitation to contribute to a theory that is a work in progress.

We motivate and develop a new theory of time and apply it to a few thought experiments in physics.

The purpose of this note is to show how an 'AB-series' interpretation of time leads, surprisingly, apparently, to AdS_5 geometry. This is not a theory of 2 time dimensions. Rather, it is a theory of 1 time dimension that has both A-series and B-series characteristics. To summarize the result, a spacetime in terms of (1) the earlier-to-later aspect of time, and (2) the (related) future-present-past aspect of time, and (3) 3-d space, it would seem, gives us the AdS_5 geometry.

Since 2015, incredible many have published UNBELIEVABLE similar ideas to my ideas published between 2002-2008!!! There were others who published UNBELIEVABLE similar ideas to my ideas even earlier (since 2008, in general), but the number has an incredible jump after 2014. Why? In 2014, I have sent emails to thousands of people (many countries, many domains (Physics, Philosophy, and Cognitive Science)) regarding the UNBELIEVABLE similarities between my ideas (2002-2008) and Markus Gabriel’s ideas (his book from 2013). Is it this a (...) coincidence? I don’t believe so… Why so many people from so many countries from so many domains on so many topics have published UNBELIEVALBE similar ideas to my ideas (2002-2008 and later)? Because I have changed EVERYTHING! (shrink)

I investigate the UNBELIEVABLE similarities between the ideas of Oreshkov et al. and my ideas. In fact, their framework (the ontological background) is UNBELIEVABLE similar to my EDWs perspective!

In this paper, I investigate the UNBELIEVABLE similarities between Chiribella et al.’ ideas and my ideas. My main question is: “How was it possible these authors to elaborate their thought experiments without having an ontological background? The answer would be: there are geniuses, of course….

(March 2019) UNBELIEVALBE similar ideas, UNBELIEVABLE similar framework of the article on “quantum mechanics” written by Proietti et al (2019) with my EDWs (2002-2008) -/- Gabriel Vacariu -/- The article that I investigate in this section is -/- (2019) Experimental rejection of observer-independence in the quantum world -/- Massimiliano Proietti,1 Alexander Pickston,1 Francesco Graffitti,1 Peter Barrow,1 Dmytro Kundys,1 Cyril Branciard,2 Martin Ringbauer,1, 3 and Alessandro Fedrizzi1 at arXiv:1902.05080v1 [quant-ph] 13 Feb 2019 -/- In the article written by Proietti et al. (...) (2019), there are UNBLELIEVABLE similar ideas to my ideas (2002-2008); in fact, the framework of this article seems UNBELIEVABLE similar to my framework, the EDWs perspective!!!! I applied my EDWs to quantum mechanics (getting micro-EW, wave-EW), to Einstein’s special relativity getting EDWs for those two observers (one in the train and one on the pavement), to microparticles and macro-objects (EDWs), etc. -/- The authors of this article work in an UNBELIEVABLE similar framework (see below details), and applied this framework to quantum mechanics referring to the relationship between two observers and the microparticle. In this way, they get EDWs for the same microparticle. However, I have done exactly the same application to Einstein’s special relativity. I emphasize that it would be necessary my EDWs to apply this framework to the same particle. In my book 2014, if the reader replaces the macro-objects with the microparticle, there would obtain exactly the EDWs for the microparticle that can be found in this article! Amazing it is the fact that the authors, having no background in philosophy and having no new theory on quantum mechanics, have discovered the existence of observer-independent “facts of the world” (that are exactly my EDWs!!!). Obviously, the authors are geniuses like sean carroll, markus Gabriel, carolo rovelli, and so many from my manuscript referring to UNBELIEVABLE similarities (see the bibliography at the end of this article!) . (shrink)

Traditionally Ψ is used to stand in for both the mathematical wavefunction (the representation) and the quantum state (the thing in the world). This elision has been elevated to a metaphysical thesis by advocates of the view known as wavefunction realism. My aim in this paper is to challenge the hegemony of the wavefunction by calling attention to a little-known formulation of quantum theory that does not make use of the wavefunction in representing the quantum state. This approach, called Lagrangian (...) quantum hydrodynamics (LQH), is not an approximation scheme, but rather a full alternative formulation of quantum theory. I argue that a careful consideration of alternative formalisms is an essential part of any realist project that attempts to read the ontology of a theory off of the mathematical formalism. In particular, I show that LQH undercuts the central presumption of wavefunction realism and falsifies the claim that one must represent the many-body quantum state as living in a 3n-dimensional configuration space. I conclude by briefly sketching three different realist approaches one could take toward LQH, and argue that both models of the quantum state should be admitted. When exploring quantum realism, regaining sight of the proverbial forest of quantum representations beyond the Ψ is just the first step. (shrink)

This is a review of Peter J. Lewis' book "Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics.".

I examine the epistemological debate on scientific realism in the context of quantum physics, focusing on the empirical underdetermin- ation of different formulations and interpretations of QM. I will argue that much of the interpretational, metaphysical work on QM tran- scends the kinds of realist commitments that are well-motivated in the light of the history of science. I sketch a way of demarcating empirically well-confirmed aspects of QM from speculative quantum metaphysics in a way that coheres with anti-realist evidence from (...) the history of science. The minimal realist attitude sketched withholds realist com- mitment to what quantum state |Ψ⟩ represents. I argue that such commitment is not required for fulfilling the ultimate realist motiva- tion: accounting for the empirical success of quantum mechanics in a way that is in tune with a broader understanding of how theoretical science progresses and latches onto reality. (shrink)

Concepts, Experiments, History and Philosophy Daniel Greenberger, Klaus Hentschel, Friedel Weinert. 5. W. Hittorf, Ueber die Elektricit ̈atsleitung der Gase , Annalen der Physik 136, 1–31, 197–234 (1869); Engl. transl. On the Conduction of ...

Heisenberg, in constructing quantum mechanics, explicitly followed certain principles exemplified, as he believed, in Einstein's construction of the special theory of relativity which for him was the paradigm for radical theoretic change in physics. These were the principles of scientific realism, stability of background knowledge, E-observability, contextual re-interpretation, pragmatic continuity, model continuity, simplicity. Fifty years later, in retrospect, Heisenberg added the following two: a principle of non-proliferation of competing theories - scientific revolutions are not a legitimate goal of physics - (...) and a principle of tenacity - existing theories are to be conserved as far as possible. The conservative as well as the revolutionary potential of these principles is then discussed. A more penetrating philosophical criticism of these principles is postponed. (shrink)

We clarify the significance of quasiprobability in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov’s weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We (...) also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality. (shrink)

We investigate the Peres–Horodecki positive partial transpose criterion in the context of conserved quantities and derive a condition of inseparability for a composite bipartite system depending only on the dimensions of its subsystems, which leads to a bi-linear entanglement witness for the two qubit system. A separability inequality using generalized Schrodinger–Robertson uncertainty relation taking suitable operators, has been derived, which proves to be stronger than the bi-linear entanglement witness operator. In the case of mixed density matrices, it identically distinguishes the (...) separable and non separable Werner states. (shrink)

A quantum state represents neither properties of a physical system nor anyone’s knowledge of its properties. The important question is not what quantum states represent but how they are used—as informational bridges. Knowing about some physical situations, an agent may assign a quantum state to form expectations about other possible physical situations. Quantum states are objective: only expectations based on correct state assignments are generally reliable. If a quantum state represents anything, it is the objective probabilistic relations between its backing (...) conditions and its advice conditions. This paper offers an account of quantum states and their function as informational bridges, in quantum teleportation and elsewhere. (shrink)

One implication of Bell’s theorem is that there cannot in general be hidden variable models for quantum mechanics that both are noncontextual and retain the structure of a classical probability space. Thus, some hidden variable programs aim to retain noncontextuality at the cost of using a generalization of the Kolmogorov probability axioms. We generalize a theorem of Feintzeig to show that such programs are committed to the existence of a finite null cover for some quantum mechanical experiments, i.e., a finite (...) collection of probability zero events whose disjunction exhausts the space of experimental possibilities. (shrink)

The rigorous equivalence of the Schrödinger and Heisenberg pictures requires that one uses Born–Jordan quantization in place of Weyl quantization. We confirm this by showing that the much discussed “ angular momentum dilemma” disappears if one uses Born–Jordan quantization. We argue that the latter is the only physically correct quantization procedure. We also briefly discuss a possible redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution associated with Born–Jordan quantization, and (...) which has proven to be successful in time-frequency analysis. (shrink)

The very formal structure of quantum mechanics implies the loss of individuality of physical systems and it requires to look at the Universe as an unbroken whole. The main reason for which, within such a theory, one must renounce to a clear identification of the parts and the whole is the superposition principle which stays at the basis of the theory. It implies, as well known, the phenomenon of entanglement which, in the most extreme case, entails that the constituents of (...) a composite system do not possess any objective property; only the system as a whole, when it is isolated, has some properties. Another source of difficulties derives from the symmetry requests that the theory imposes in the case of systems containing identical constituents. We discuss these points in detail and we outline recent proposals yielding a consistent solution to the problems arising from the entanglement between a microsystem and a macrosystem which unavoidably occurs in a measurement process. In particular we take into account the so called “collapse” theories which embody a mechanism forbidding, at an appropriate level, the persistence of superpositions and, as a consequence, lead, in general, to the emergence of precise individual properties for macroscopic systems. We then pass to a critical analysis of the difficulties related to the identity of the constituents. We stress that various misunderstandings characterize the treatment of this problem and we make fully clear how one has to deal with the very concept of entangled systems when identical constituents are involved. The ensuing picture should make clear to which extent one can still consistently ground the distinction between the parts and the whole in a genuinely quantum context. (shrink)

In recent papers, Zurek [(2005). Probabilities from entanglement, Born's rule pk=|ψk|2 from entanglement. Physical Review A, 71, 052105] has objected to the decision-theoretic approach of Deutsch [(1999) Quantum theory of probability and decisions. Proceedings of the Royal Society of London A, 455, 3129–3137] and Wallace [(2003). Everettian rationality: defending Deutsch's approach to probability in the Everett interpretation. Studies in History and Philosophy of Modern Physics, 34, 415–438] to deriving the Born rule for quantum probabilities on the grounds that it courts (...) circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born rule for its validity. Using the Heisenberg picture and quantum Darwinism—the notion that classical information is quantum information that can proliferate in the environment pioneered in Ollivier et al. [(2004). Objective properties from subjective quantum states: Environment as a witness. Physical Review Letters, 93, 220401 and (2005). Environment as a witness: Selective proliferation of information and emergence of objectivity in a quantum universe. Physical Review A, 72, 042113]—I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability. (shrink)

A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.

The idea that, in the microscopic world, particles are indistinguishable, interchangeable and without identity has been central in quantum physics. The same idea has been enrolled in statistical thermodynamics even in a classical framework of analysis to make theoretical results agree with experience. In thermodynamics of gases, this hypothesis is associated with several problems, logical and technical. For this case, an alternative theoretical framework is provided, replacing the indistinguishability hypothesis with standard probability and statistics. In this framework, entropy is a (...) probabilistic notion applied to thermodynamic systems and is not extensive per se. Rather, the extensive entropy used in thermodynamics is the difference of two probabilistic entropies. According to this simple view, no paradoxical behaviors, such as the Gibbs paradox, appear. Such a simple probabilistic view within a classical physical framework, in which entropy is none other than uncertainty applicable irrespective of particle size, enables generalization of mathematical descriptions of processes across any type and scale of systems ruled by uncertainty. (shrink)

This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the set of observables of a physical system, be it classical or quantum, is described by a Jordan-Lie algebra. From the geometric point of view, the space of states of any system is described by a uniform Poisson space with transition probability. Both these structures (...) are here perceived as formal translations of the fundamental twofold role of properties in Mechanics: they are at the same time quantities and transformations. The question becomes then to understand the precise articulation between these two roles. The analysis will show that Quantum Mechanics can be thought as distinguishing itself from Classical Mechanics by a compatibility condition between properties-as-quantities and properties-as-transformations. -/- Moreover, this dissertation shows the existence of a tension between a certain "abstract way" of conceiving mathematical structures, used in the practice of mathematical physics, and the necessary capacity to specify particular states or observables. It then becomes important to understand how, within the formalism, one can construct a labelling scheme. The “Chase for Individuation” is the analysis of different mathematical techniques which attempt to overcome this tension. In particular, we discuss how group theory furnishes a partial solution. (shrink)

What sort of entities are electrons, photons and atoms given their wave-like and particle-like properties? Is nature fundamentally deterministic or probabilistic? Orthodox quantum theory evades answering these two basic questions by being a theory about the results of performing measurements on quantum systems. But this evasion results in OQT being a seriously defective theory. A rival, somewhat ignored strategy is to conjecture that the quantum domain is fundamentally probabilistic. This means quantum entities, interacting with one another probabilistically, must differ radically (...) from the entities of deterministic classical physics, the classical wave or particle. It becomes possible to conceive of quantum entities as a new kind of fundamentally probabilistic entity, the “propensiton”, neither wave nor particle. A fully micro realistic, testable rival to OQT results. (shrink)