scholarly journals What If Quantum Theory Violates All Mathematics?

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 598-602
Author(s):  
Elemér Elad Rosinger
Keyword(s):  
Mathematical Logic ◽  
Quantum Theory ◽  
Bell Inequalities ◽  
List Type ◽  
Elementary Argument ◽  
And Mathematics

Abstract It is shown by using a rather elementary argument in Mathematical Logic that if indeed, quantum theory does violate the famous Bell Inequalities, then quantum theory must inevitably also violate all valid mathematical statements, and in particular, such basic algebraic relations like 0 = 0, 1 = 1, 2 = 2, 3 = 3, … and so on … An interest in that result is due to the following three alternatives which it imposes upon both Physics and Mathematics: Quantum Theory is inconsistent. Quantum Theory together with Mathematics are inconsistent. Mathematics is inconsistent. In this regard one should recall that, up until now, it is not known whether Mathematics is indeed consistent.

Bell’s theorem

2018 ◽  
Author(s):  
Arthur Fine
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Experimental Tests ◽  
Bell Inequalities ◽  
Bell’S Theorem ◽  
Bell's Theorem ◽  
Bell Theorem ◽  
System Of Inequalities ◽  
Action At A Distance ◽  
High Degree

Bell’s theorem is concerned with the outcomes of a special type of ‘correlation experiment’ in quantum mechanics. It shows that under certain conditions these outcomes would be restricted by a system of inequalities (the ‘Bell inequalities’) that contradict the predictions of quantum mechanics. Various experimental tests confirm the quantum predictions to a high degree and hence violate the Bell inequalities. Although these tests contain loopholes due to experimental inefficiencies, they do suggest that the assumptions behind the Bell inequalities are incompatible not only with quantum theory but also with nature. A central assumption used to derive the Bell inequalities is a species of no-action-at-a-distance, called ‘locality’: roughly, that the outcomes in one wing of the experiment cannot immediately be affected by measurements performed in another wing (spatially distant from the first). For this reason the Bell theorem is sometimes cited as showing that locality is incompatible with the quantum theory, and the experimental tests as demonstrating that nature is nonlocal. These claims have been contested.

How Effective is Tutorial Assistance for Aboriginal Students?

1983 ◽  
Vol 11 (1) ◽  
pp. 43-53
Author(s):  
P. Rendall
Keyword(s):  
Secondary Students ◽  
Superior Performance ◽  
List Type ◽  
Three Solutions ◽  
Assistance Program ◽  
Aboriginal Students ◽  
Tutorial Program ◽  
And Mathematics ◽  
State Schools ◽  
Type Of School

AbstractThis report is a limited evaluation of the Tutorial Assistance program within the Aboriginal Secondary Grants Scheme.Achievement of Aboriginal secondary students receiving tuition was analysed according to several criteria, including sex and the type of school attended. The major findings were: Tutored Aboriginal students had significantly higher achievement than untutored students, in both English and Mathematics.Aboriginal students in boarding schools had significantly higher achievement than those in state schools, regardless of tutoring.There were no significant differences between male and female students.It could not be concluded that tutorial assistance caused the superior performance of tutored students. Student motivation was a highly possible intervening factor, and there are probably many others.In addition, various solutions to the problem of underachievement by Aboriginal students were ranked according to their effectiveness as perceived by people in the tutorial program. Three solutions were judged equally preferable and viable: Employing more Aboriginal teachers, aides and counsellors.Providing tutorial assistance to Aboriginal students.Sensitising non-Aboriginal teachers to the problems faced by Aboriginal students.

scholarly journals Extended Boole-Bell Inequalities Applicable to Quantum Theory

2011 ◽  
Vol 8 (6) ◽  
pp. 1011-1039 ◽  
Author(s):  
Hans De Raedt ◽  
Karl Hess ◽  
Kristel Michielsen
Keyword(s):  
Quantum Theory ◽  
Bell Inequalities

scholarly journals Is a time symmetric interpretation of quantum theory possible without retrocausality?

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160607 ◽  
Author(s):  
Matthew S. Leifer ◽  
Matthew F. Pusey
Keyword(s):  
Quantum Theory ◽  
Quantum State ◽  
General Framework ◽  
Bell Inequalities ◽  
Time Symmetry ◽  
Causality Criterion ◽  
The Status ◽  
Interpretation Of Quantum Theory ◽  
Huw Price ◽  
New Interpretation

Huw Price has proposed an argument that suggests a time symmetric ontology for quantum theory must necessarily be retrocausal, i.e. it must involve influences that travel backwards in time. One of Price's assumptions is that the quantum state is a state of reality. However, one of the reasons for exploring retrocausality is that it offers the potential for evading the consequences of no-go theorems, including recent proofs of the reality of the quantum state. Here, we show that this assumption can be replaced by a different assumption, called λ -mediation, that plausibly holds independently of the status of the quantum state. We also reformulate the other assumptions behind the argument to place them in a more general framework and pin down the notion of time symmetry involved more precisely. We show that our assumptions imply a timelike analogue of Bell's local causality criterion and, in doing so, give a new interpretation of timelike violations of Bell inequalities. Namely, they show the impossibility of a (non-retrocausal) time symmetric ontology.

Formenanalyse bei Marx und ihr Verhältnis zur Systemwissenschaft / Analysis of forms by Marx and its relation to systems research

1975 ◽  
Vol 4 (3) ◽  
Author(s):  
Werner Loh
Keyword(s):  
Mathematical Logic ◽  
Empirical Analysis ◽  
The Other ◽  
Systems Research ◽  
Other Hand ◽  
Empirical Logic ◽  
Formal Concepts ◽  
And Mathematics ◽  
Different Levels

AbstractMARX’s analysis of forms and modern systems research have in common the problem of form. MARX analyzed forms by functionally relating elements to each other on different levels. Contrary to modern systems theories and Marxism-Leninism elements are for MARX forms themselves and not non-formal elementary qualities. The analysis of forms, therefore, is able to characterize its objects only relationally-functionally. On the other hand modern systems theories integrate concepts like ‚action‘ or ‚goal‘ in an elementaristic manner. The analysis of forms must be controlled by systematic concretization and totalization adequate to the problem. The formal concepts of systems research are often interpreted as logical-mathematical. Logic and mathematics are usually understood as non-empirical. Empirical analysis of forms is in need of an empirical logic and mathematics.

scholarly journals Symmetries in Foundation of Quantum Theory and Mathematics

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 409 ◽  
Author(s):  
Felix M. Lev
Keyword(s):  
Quantum Theory ◽  
Dark Energy ◽  
Lie Algebra ◽  
De Sitter ◽  
Classical Level ◽  
Standard Quantum ◽  
Background Space ◽  
Classical Mathematics ◽  
Formal Limit ◽  
And Mathematics

In standard quantum theory, symmetry is defined in the spirit of Klein’s Erlangen Program—the background space has a symmetry group, and the basic operators should commute according to the Lie algebra of that group. We argue that the definition should be the opposite—background space has a direct physical meaning only on classical level while on quantum level symmetry should be defined by a Lie algebra of basic operators. Then the fact that de Sitter symmetry is more general than Poincare symmetry can be proved mathematically. The problem of explaining cosmological acceleration is very difficult but, as follows from our results, there exists a scenario in which the phenomenon of cosmological acceleration can be explained by proceeding from basic principles of quantum theory. The explanation has nothing to do with existence or nonexistence of dark energy and therefore the cosmological constant problem and the dark energy problem do not arise. We consider finite quantum theory (FQT) where states are elements of a space over a finite ring or field with characteristic p and operators of physical quantities act in this space. We prove that, with the same approach to symmetry, FQT and finite mathematics are more general than standard quantum theory and classical mathematics, respectively: the latter theories are special degenerated cases of the former ones in the formal limit p → ∞ .

scholarly journals Does mathematics look certain in the front, but fallible in the back?

2011 ◽  
Vol 41 (6) ◽  
pp. 839-866 ◽  
Author(s):  
Christian Greiffenhagen ◽  
Wes Sharrock
Keyword(s):  
Mathematical Logic ◽  
Doctoral Students ◽  
Research Articles ◽  
And Mathematics ◽  
Writing Science ◽  
The Way

In this paper we re-examine the implications of the differences between ‘doing’ and ‘writing’ science and mathematics, questioning whether the way that science and mathematics are presented in textbooks or research articles creates a misleading picture of these differences. We focus our discussion on mathematics, in particular on Reuben Hersh’s formulation of the contrast in terms of Goffman’s dramaturgical frontstage–backstage analogy and his claim that various myths about mathematics only fit with how mathematics is presented in the ‘front’, but not with how it is practised in the ‘back’. By investigating examples of both the ‘front’ (graduate lectures in mathematical logic) and the ‘back’ (meetings between supervisor and doctoral students) we examine, first, whether the ‘front’ of mathematics presents a misleading picture of mathematics, and, second, whether the ‘front’ and ‘back’ of mathematics are so discrepant that mathematics really does look certain in the ‘front’, but fallible in the ‘back’.

scholarly journals The Platonic solids and fundamental tests of quantum mechanics

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 293 ◽  
Author(s):  
Armin Tavakoli ◽  
Nicolas Gisin
Keyword(s):  
Quantum Mechanics ◽  
Natural Philosophy ◽  
Bell Inequality ◽  
Bell Inequalities ◽  
Convex Polyhedra ◽  
Classical Antiquity ◽  
Platonic Solids ◽  
Mathematical Beauty ◽  
Regular Convex ◽  
And Mathematics

The Platonic solids is the name traditionally given to the five regular convex polyhedra, namely the tetrahedron, the octahedron, the cube, the icosahedron and the dodecahedron. Perhaps strongly boosted by the towering historical influence of their namesake, these beautiful solids have, in well over two millennia, transcended traditional boundaries and entered the stage in a range of disciplines. Examples include natural philosophy and mathematics from classical antiquity, scientific modeling during the days of the European scientific revolution and visual arts ranging from the renaissance to modernity. Motivated by mathematical beauty and a rich history, we consider the Platonic solids in the context of modern quantum mechanics. Specifically, we construct Bell inequalities whose maximal violations are achieved with measurements pointing to the vertices of the Platonic solids. These Platonic Bell inequalities are constructed only by inspecting the visible symmetries of the Platonic solids. We also construct Bell inequalities for more general polyhedra and find a Bell inequality that is more robust to noise than the celebrated Clauser-Horne-Shimony-Holt Bell inequality. Finally, we elaborate on the tension between mathematical beauty, which was our initial motivation, and experimental friendliness, which is necessary in all empirical sciences.

Simplified foundations for mathematical logic

1955 ◽  
Vol 20 (2) ◽  
pp. 123-139 ◽  
Author(s):  
Robert L. Stanley
Keyword(s):  
Mathematical Logic ◽  
Set Theory ◽  
Natural Deduction ◽  
Small Body ◽  
The Other ◽  
Consistency Proof ◽  
Basic Notion ◽  
Relative Consistency ◽  
And Mathematics

A system SF, closely related to NF, is outlined here. SF has several novel points of simplicity and interest, (a) It uses only one basic notion, from which all the other concepts of logic and mathematics may be built definitionally. Three-notion systems are common, but Quine's two-notion IA has for some time represented the extreme in conceptual economy, (b) The theorems of SF are generated under just three rules of analysis, which unify into a single postulational principle, (c) SF is built solely in terms of what is commonly, known as the “natural deduction” method, under which each theorem is attacked primarily as it stands, by means of a very small body of rules, rather than less directly, through a very large, potentially infinite backlog of theorems. Although natural deduction is by no means new as a method, its exclusive applications have previously been relatively limited, not even reaching principles of identity, much less set theory, relations, or mathematics proper, (d) SF is at least as strong as NF, yielding all of its theorems, which are expressed here in forms analogous to those of the metatheorems in ML. If NF is consistent, so is SF. The main points in the relative consistency proof are set forth below in section seven.

Sign in / Sign up

Export Citation Format

Share Document