No Preferred Reference Frame at the Foundation of Quantum Mechanics

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance and Continuity, at the foundation of those axiomatic reconstructions, maps to “no preferred reference frame” (NPRF, aka “the relativity principle”) as it pertains to the invariant measurement of Planck’s constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein’s use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance and Continuity. Consequently, the “mystery” of the Bell states is understood to result from conservation per Information Invariance and Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.

Commitment Without Consequences. A Carnapian Approach to Fictional Objects and Negative Existence Statements

<p>The overall aim of this thesis is to present a fresh perspective on three closely related areas of enquiry: Descriptivist theories of reference, Direct Reference theories and the Carnapian approach to questions of existence and identity. This perspective is developed and tested by a critical analysis of the work of a leading Carnapian theorist, Amie Thomasson, and by looking at some of the central problems associated with our talk of fictional objects. It concludes in an account of negative existence statements and fictional objects as possibly existing objects. In Chapter one I set out the key elements of Carnap’s approach, as that approach was developed over time and in dialogue with his colleague Quine. In Chapter two I explore the relation between the previously mentioned three areas of enquiry through an examination of Amie Thomasson’s brand of Carnapian meta-ontology. In Chapters four and five I develop the view that fictional objects are objects that meet the criteria of existence and identity of at least one linguistic framework but fail to meet the criteria of another, preferred framework. This provides the basis for a neo-Carnapian account of fictional objects in terms of the relations between linguistic frameworks, a novel approach to the questions surrounding such objects. In chapter five, the concluding chapter of the thesis, I further develop my explanation of how there can be truths about fictional and non-existent objects by giving an ontological version of John MacFarlane’s relativity principle. This paves the way for a neo-Carnapian analysis of true negative existence statements. Here I integrate the story I have told about fictional objects and the relations between linguistic frameworks with theories of reference and meaning. In particular, I incorporate a satisfactory concept of the rigid designation of ordinary proper names (and, potentially, of natural and artefactual kind terms). This then leads on to an explanation of how fictional objects, contra Kripke and many others, may reasonably said to be possible objects that, though they don’t exist, might exist under different circumstances.</p>

Commitment Without Consequences. A Carnapian Approach to Fictional Objects and Negative Existence Statements

<p>The overall aim of this thesis is to present a fresh perspective on three closely related areas of enquiry: Descriptivist theories of reference, Direct Reference theories and the Carnapian approach to questions of existence and identity. This perspective is developed and tested by a critical analysis of the work of a leading Carnapian theorist, Amie Thomasson, and by looking at some of the central problems associated with our talk of fictional objects. It concludes in an account of negative existence statements and fictional objects as possibly existing objects. In Chapter one I set out the key elements of Carnap’s approach, as that approach was developed over time and in dialogue with his colleague Quine. In Chapter two I explore the relation between the previously mentioned three areas of enquiry through an examination of Amie Thomasson’s brand of Carnapian meta-ontology. In Chapters four and five I develop the view that fictional objects are objects that meet the criteria of existence and identity of at least one linguistic framework but fail to meet the criteria of another, preferred framework. This provides the basis for a neo-Carnapian account of fictional objects in terms of the relations between linguistic frameworks, a novel approach to the questions surrounding such objects. In chapter five, the concluding chapter of the thesis, I further develop my explanation of how there can be truths about fictional and non-existent objects by giving an ontological version of John MacFarlane’s relativity principle. This paves the way for a neo-Carnapian analysis of true negative existence statements. Here I integrate the story I have told about fictional objects and the relations between linguistic frameworks with theories of reference and meaning. In particular, I incorporate a satisfactory concept of the rigid designation of ordinary proper names (and, potentially, of natural and artefactual kind terms). This then leads on to an explanation of how fictional objects, contra Kripke and many others, may reasonably said to be possible objects that, though they don’t exist, might exist under different circumstances.</p>

Theoretical and Practical Aspects Regarding Third Parties in the Light of Contracts’ Effects Relativity Principle

The contract is the subject of civil law that creates the basic entity of the national and international economy, and the contracting process is the most important stage in economic affairs in general. Naturally producing effects between the parties, we can say that vis-à-vis the parties, the contract is binding, or, in other words, the signatory parties must comply with the provisions of the contract. On the other hand, compared to third parties, the effects of the contract being only an exception, we can say that the production of the effects towards them is relative. This study represents an exemplary synthesis of the theoretical and practical dimension of the issue of the third party notion in the light of the new regulations of the Civil Code, norms that created new ways of economic development of the Republic of Moldova.

2. Motion and inertia

This chapter explores the question of what it means for something to move, and why physics cannot be done without an answer to that question. It does so mostly in the context of Newtonian physics, leaving considerations of the theory of relativity to the next chapter. We cannot simply define motion of one body as relative to another body if we want to do physics—we have to introduce the idea of a ‘rest frame’ that defines which bodies are at rest (Newton called this rest frame ‘absolute space’). But physics also satisfies the relativity principle—it is impossible to distinguish the rest frame from another frame moving at constant speed in that frame. So what physics really requires is not a preferred rest frame, but a family of inertial frames, all moving at uniform speeds relative to one another. The notion of ‘spacetime’ has been introduced as a way of understanding this family of inertial frames, but philosophers of physics disagree as to whether spacetime explains the nature of motion in physics, or merely codifies it. The chapter concludes by explaining how gravity can be thought of as a change in the structure of the inertial frames: though it was Einstein who first saw this clearly, it has nothing to do with relativity and makes sense even in Newtonian physics.

Unit-Lapse Forms of Various Spacetimes

<p><b>Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate systems, however, are better than others. In this text, we begin with a brief introduction into general relativity, Einstein's masterpiece theory of gravity. We then discuss some physically interesting spacetimes and the coordinate systems that the metrics of these spacetimes can be expressed in. More specifically, we discuss the existence of the rather useful unit-lapse forms of these spacetimes. Using the metric written in this form then allows us to conduct further analysis of these spacetimes, which we discuss. </b></p><p>Overall, the work given in this text has many interesting mathematical and physical applications. Firstly, unit-lapse spacetimes are quite common and occur rather naturally for many specific analogue spacetimes. In an astrophysical context, unit-lapse forms of stationary spacetimes are rather useful since they allow for very simple and immediate calculation of a large class of timelike geodesics, the rain geodesics. Physically these geodesics represent zero angular momentum observers (ZAMOs), with zero initial velocity that are dropped from spatial infinity and are a rather tractable probe of the physics occurring in the spacetime. Mathematically, improved coordinate systems of the Kerr spacetime are rather important since they give a better understanding of the rather complicated and challenging Kerr spacetime. These improved coordinate systems, for example, can be applied to the attempts at finding a "Gordon form" of the Kerr spacetime and can also be applied to attempts at upgrading the "Newman-Janis trick" from an ansatz to a full algorithm. Also, these new forms of the Kerr metric allows for a greater observational ability to differentiate exact Kerr black holes from "black hole mimickers".</p>

Unit-Lapse Forms of Various Spacetimes

<p><b>Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate systems, however, are better than others. In this text, we begin with a brief introduction into general relativity, Einstein's masterpiece theory of gravity. We then discuss some physically interesting spacetimes and the coordinate systems that the metrics of these spacetimes can be expressed in. More specifically, we discuss the existence of the rather useful unit-lapse forms of these spacetimes. Using the metric written in this form then allows us to conduct further analysis of these spacetimes, which we discuss. </b></p><p>Overall, the work given in this text has many interesting mathematical and physical applications. Firstly, unit-lapse spacetimes are quite common and occur rather naturally for many specific analogue spacetimes. In an astrophysical context, unit-lapse forms of stationary spacetimes are rather useful since they allow for very simple and immediate calculation of a large class of timelike geodesics, the rain geodesics. Physically these geodesics represent zero angular momentum observers (ZAMOs), with zero initial velocity that are dropped from spatial infinity and are a rather tractable probe of the physics occurring in the spacetime. Mathematically, improved coordinate systems of the Kerr spacetime are rather important since they give a better understanding of the rather complicated and challenging Kerr spacetime. These improved coordinate systems, for example, can be applied to the attempts at finding a "Gordon form" of the Kerr spacetime and can also be applied to attempts at upgrading the "Newman-Janis trick" from an ansatz to a full algorithm. Also, these new forms of the Kerr metric allows for a greater observational ability to differentiate exact Kerr black holes from "black hole mimickers".</p>

On Group Property of Hassani Transforms and Relativity Principle in Hassani Kinematics

In the present paper, based on the ideas of Algerian physicist M.E. Hassani, the generalized Hassani spatio-temporal transformations in real Hilbert space are introduced. The original transformations, introduced by M.E. Hassani, are the particular cases of the transformations, introduced in this paper. It is proven that the classes of generalized Hassani transforms do not form a group of operators in the general case. Further, using these generalized Hassani transformations as well as the theory of changeable sets and universal kinematics, the mathematically strict models of Hassani kinematics are constructed and the performance of the relativity principle in these models is discussed.