Theory Assessment and Final Theory Claim in String Theory

String theory has by now maintained a highly influential position in high energy physics for more than a quarter of a century. The present article analyses the reasons for the considerable trust exponents of string theory have in their theory even though it has neither found empirical confirmation nor a complete formulation up to this point. It is argued that this trust can be understood in terms of an emerging new conception of theory assessment that relies strongly on the identification of limitations to the underdetermination of scientific theory building. The second part of the paper makes the point that another conspicuous element of string theoretical reasoning, the prominent role of the notion of a final theory, can be understood in terms of this altered notion of theory assessment as well.     

Underdetermination,Realism, and Theory Appraisal: An Epistemological Reflection on Quantum Mechanics

This paper examines the epistemological significance of the present situation of underdetermination in quantum mechanics. After analyzing this underdetermination at three levels---formal, ontological, and methodological---the paper considers implications for a number of variants of the thesis of scientific realism in fundamental physics and reassesses Lakatos characterization of progress in physical theory in light of the present situation. Next, this paper considers the implications of underdetermination for Weinbergs dream of a final theory. Finally, the paper concludes by suggesting how one might still think of realism and progress in fundamental physics despite the possibility of persistent underdetermination in quantum mechanics.This paper draws from my Ph.D. dissertation, Ontological Commitments and Theory Appraisal in the Interpretation of Quantum Mechanics (University of Notre Dame, 1998). It was presented at the James T. Cushing Memorial Conference on Philosophical Issues in Physics, University of Notre Dame, November 2002. My thanks to the participants on that occasion for their comments and questions.     

The role of language in science

It is argued that language plays an active role in the development of scientific thought. A research project is outlined which will investigate this hypothesis and, in addition, focus on such questions as the role of mathematics in science and the status of the genetic code.

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Can von Neumann’s Theory Meet the Deutsch-Jozsa Algorithm?

The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on von Neumann’s theory. We try to investigate whether von Neumann’s theory meet our physical world. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1≤N<+∞). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of von Neumann’s projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. Therefore, von Neumann’s theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. Hence, von Neumann’s theory cannot meet the Deutsch-Jozsa algorithm. We propose the solution of the problem. Our solution is equivalent to changing Planck’s constant (?) to new constant (\(\hbar/\sqrt{2}\)). It may be that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does so.     

Non-local Effects of Conformal Anomaly

It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein’s equations. The fact that Einstein’s general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein’s theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in \(D=4\) for both the \(C^2\) invariant and the Euler (Gauss–Bonnet) invariant can only be achieved for N-extended supergravity multiplets with \(N \ge 5\).     

The joint measurement problem

According to orthodox quantum theory, the joint measurement of noncommuting observables is impossible. It has been claimed recently that such joint measurements are admitted in a generalized formalism for quantum theory developed by Ludwig and Davies, by means of so-called unsharp observables. It is argued in this paper that this claim has not been substantiated.     

Quantum cosmology and Eddington's large cosmic numbers

A theory that contains three fundamental constants from which one can build length, time, and mass (or force) etalons satisfies with that a necessary criterion of a universal unified field theory. In order to interpret such a theory physically, one has to translate it into the Galilei-Newtonian language. This leads to classical pictures whose compatibility is ensured by introducing appropriate measurement-theoretical principles which imply corresponding uncertainty relations. In this paper we compare different (mainly gravitational) theories from the point of view of the fundamental constants underlying each case, and of the respective uncertainty relations. Assuming Eddington's hypothesis of large cosmic numbers, it is argued in particular that in quantized general relativity one arrives at less stringent limitations on cosmology than in other conceivable approaches satisfying the principle of minimal coupling. These limitations, however, are in all cases strong enough to bar the way to quantum cosmology. Instead one is led to a Diophantean concept.     

Newton’s Metaphysics of Space as God’s Emanative Effect

In several of his writings, Isaac Newton proposed that physical space is God’s “emanative effect” or “sensorium,” revealing something interesting about the metaphysics underlying his mathematical physics. Newton’s conjectures depart from Plato and Aristotle’s metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophical concepts of supervenience clarify Newton’s ideas about space and offer a portrait of Newton not only as a mathematical physicist but an independent-minded rationalist philosopher.     

A model of classical thermodynamics based on the partition theory of integers,Earth gravitation,and semiclassical asymptotics. I

In the paper, a new construction of the theory of partitions of integers is proposed. The author defines entropy as the natural logarithm of the number of partitions of a number M into natural summands with repetitions allowed p(M) and repetitions forbidden q(M). The passage from ln p(M) to lnq(M) through the mesoscopic values M → 0 is studied. The topological transition from the mesoscopic lower levels of the Bohr–Kalckar construction to the macroscopic levels corresponding to the critical number of neutrons according to the consequence of Einstein’s inequality M ≤ c N _c , where c is determined for the particles of the given atomic nucleus. The role of quantum mechanics in establishing the new world outlook in physics is analyzed. It is pointed out that the main equations of thermodynamics in the volume “Statistical Physics” of the Landau–Lifshits treatise are obtained without appealing to the so-called “three main principles of thermodynamics”. It is also pointed out that Niels Bohr’s liquid model of the nucleus does not involve any interaction of particles in the form of attraction and is based on the presence of a common potential trough for all elements of the nucleus. The author constructs a new approach to thermodynamics, using quantum mechanics and the Earth’s gravitational attraction as a common potential trough.     

Tunable microwave generation based on frequency quadrupling

Kennedy (Philos. Sci. 62, 4 (1995)) has argued that the various quantum mechanical no-signalling proofs formulated thus far share a common mathematical framework, are circular in nature, and do not preclude the construction of empirically testable schemes wherein superluminal exchange of information can occur. In light of this thesis, we present a potentially feasible quantum-optical scheme that purports to enable superluminal signalling.     

Comment on “Non-representative Quantum Mechanical Weak Values”

Svensson (Found Phys 45: 1645, 2015) argued that the concept of the weak value of an observable of a pre- and post-selected quantum system cannot be applied when the expectation value of the observable in the initial state vanishes. Svensson’s argument is analyzed and shown to be inconsistent using several examples.     

About Maxwell’s equations on fractal subsets of ℝ3

In this paper we have generalized $F^{\bar \xi }$ -calculus for fractals embedding in ?³. $F^{\bar \xi }$ -calculus is a fractional local derivative on fractals. It is an algorithm which may be used for computer programs and is more applicable than using measure theory. In this Calculus staircase functions for fractals has important role. $F^{\bar \xi }$ -fractional differential form is introduced such that it can help us to derive the physical equation. Furthermore, using the $F^{\bar \xi }$ -fractional differential form of Maxwell’s equations on fractals has been suggested.     

A Lower Bound for the Lyapounov Exponents of the Random Schrödinger Operator on a Strip

We consider the random Schrödinger operator on a strip of width W, assuming the site distribution of bounded density. It is shown that the positive Lyapounov exponents satisfy a lower bound roughly exponential in ?W for W→∞. The argument proceeds directly by establishing Green’s function decay, but does not appeal to Furstenberg’s random matrix theory on the strip. One ingredient involved is the construction of ‘barriers’ using the random Schrödinger operator theory on $\mathbb{Z}$ .     

Quantum mechanics without the projection postulate and its realistic interpretation

It is widely held that quantum mechanics is the first scientific theory to present scientifically internal, fundamental difficulties for a realistic interpretation (in the philosophical sense). The standard (Copenhagen) interpretation of the quantum theory is often described as the inevitable instrumentalistic response. It is the purpose of the present article to argue that quantum theory doesnot present fundamental new problems to a realistic interpretation. The formalism of quantum theory has the same states—it will be argued—as the formalisms of older physical theories and is capable of the same kinds of philosophical interpretation. This result is reached via an analysis of what it means to give a realistic interpretation to a theory. The main point of difference between quantum mechanics and other theories—as far as the possibilities of interpretation are concerned—is the special treatment given tomeasurement by the projection postulate. But it is possible to do without this postulate. Moreover, rejection of the projection postulate does not, in spite of what is often maintained in the literature, automatically lead to the many-worlds interpretation of quantum mechanics. A realistic interpretation is possible in which only the reality ofone (our) world is recognized. It is argued that the Copenhagen interpretation as expounded by Bohr is not in conflict with the here proposed realistic interpretation of quantum theory.     

13-Moment System with Global Hyperbolicity for Quantum Gas

We point out that the quantum Grad’s 13-moment system (Yano in Physica A 416:231–241, 2014) is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad’s expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new hyperbolic regularization theory developed in Cai et al. (SIAM J Appl Math 75(5):2001–2023, 2015) and Fan et al. (J Stat Phys 162(2):457–486, 2016). This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the hyperbolic regularization theory.     

Proper time synchronization

A clock-transport method of synchronization employing proper time is described that yields in any given inertial system the same result as slow transport, but that imposes no limit on transport proper speed. It is argued that because the method involves only the empirically validated kinematic invariant proper time, on which all observers must agree, there exists an option to synchronize clocks in such a way that thesimultaneity of spatially separated events is agreed upon by all observers, hence is absolute. Such agreement refers only to phase equality of members (present at the events judged simultaneous) of comoving clock sets, not to clock rates or clock phase numerical values in different inertial systems. The demonstration employs only the on-worldline assertions of Einstein's kinematics. It thus depends on a limited subset of his ideas and allows a different identification of the spacelike invariant.     

What is Quantum Mechanics? A Minimal Formulation

This paper presents a minimal formulation of nonrelativistic quantum mechanics, by which is meant a formulation which describes the theory in a succinct, self-contained, clear, unambiguous and of course correct manner. The bulk of the presentation is the so-called “microscopic theory”, applicable to any closed system S of arbitrary size N, using concepts referring to S alone, without resort to external apparatus or external agents. An example of a similar minimal microscopic theory is the standard formulation of classical mechanics, which serves as the template for a minimal quantum theory. The only substantive assumption required is the replacement of the classical Euclidean phase space by Hilbert space in the quantum case, with the attendant all-important phenomenon of quantum incompatibility. Two fundamental theorems of Hilbert space, the Kochen–Specker–Bell theorem and Gleason’s theorem, then lead inevitably to the well-known Born probability rule. For both classical and quantum mechanics, questions of physical implementation and experimental verification of the predictions of the theories are the domain of the macroscopic theory, which is argued to be a special case or application of the more general microscopic theory.     

On the theory of temperature distribution over the Earth’s atmosphere

The steady-state temperature distribution over the Earth’s atmosphere is described in terms of the law of degradation of energy (or the principle of entropy increase). The distribution is in satisfactory agreement with meteorological measurements. Using constructed dissipative function \(\dot Q\), a nonlinear differential equation is rigorously derived that describes the synergetics of the steady-state temperature distribution over the atmosphere, from troposphere to exosphere. A detailed analysis of solutions of this equation makes it possible to qualitatively explain nontrivial dependence T(z) over an atmospheric area inhomogeneous in chemical composition. This fact substantiates the correctness of formal introduction and necessity to consider interaction between blackbody radiation and convective stream. It is argued that hard gamma quanta far from the violet part of the spectrum are responsible for heat radiation coming from the Sun.     

The Failure to Perform a Loophole-Free Test of Bell’s Inequality Supports Local Realism

It is argued that the long standing failure to show an uncontroversial, loophole-free, empirical violation of a Bell inequality should be interpreted as a support to local realism. After defining realism and locality, this as relativistic causality, the performed experimental tests of Bells inequalities are commented. It is pointed out that, without any essential modification of quantum mechanics, the theory might be compatible with local realism.