Linear independence of field operators at different space-time points

1976 ◽  
Vol 1 (3) ◽  
pp. 171-174
Author(s):  
K. Just ◽  
K. Kraus
Keyword(s):  
Linear Independence ◽  
Space Time ◽  
Time Points

scholarly journals S-money: virtual tokens for a relativistic economy

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190170 ◽  
Author(s):  
Adrian Kent
Keyword(s):  
Data Storage ◽  
Relevant Information ◽  
Space Time ◽  
User Privacy ◽  
Standard Quantum ◽  
Bit Commitment ◽  
Time Points ◽  
Security Questions ◽  
Time Point

We propose definitions and implementations of ‘S-money’—virtual tokens designed for high-value fast transactions on networks with relativistic or other trusted signalling constraints, defined by inputs that in general are made at many network points, some or all of which may be space-like separated. We argue that one significant way of characterizing types of money in space–time is via the ‘summoning’ tasks they can solve: that is, how flexibly the money can be propagated to a desired space–time point in response to relevant information received at various space–time points. We show that S-money is more flexible than standard quantum or classical money in the sense that it can solve deterministic summoning tasks that they cannot. It requires the issuer and user to have networks of agents with classical data storage and communication, but no long-term quantum state storage, and is feasible with current technology. User privacy can be incorporated by secure bit commitment and zero-knowledge proof protocols. The level of privacy feasible in given scenarios depends on efficiency and composable security questions that remain to be systematically addressed.

Cross-view action matching using a novel projective invariant on non-coplanar space-time points

2015 ◽  
Vol 75 (19) ◽  
pp. 11661-11682 ◽  
Author(s):  
Qi Jia ◽  
Xin Fan ◽  
Zhongxuan Luo ◽  
Haojie Li ◽  
Kang Huyan ◽  
...  
Keyword(s):  
Space Time ◽  
Time Points ◽  
Projective Invariant

Relative Locations

2018 ◽  
Author(s):  
Andrew Bacon
Keyword(s):  
Space Time ◽  
Pivotal Role ◽  
Abstract Objects ◽  
Time Points ◽  
The Cost ◽  
Physical Laws

The fact that physical laws often admit certain kinds of space-time symmetries is often thought to be problematic for substantivalism—the view that space-time is as real as the objects it contains. The most prominent alternative, relationism, avoids these problems but at the cost of giving abstract objects (rather than space-time points) a pivotal role in the fundamental metaphysics. This incurs related problems concerning the relation of the physical to the mathematical. This paper presents a version of substantivalism that respects Leibnizian theses about space-time symmetries, and argues that it is superior to both relationism and the more orthodox form of substantivalism.

scholarly journals Lorentz-invariant quantum fields in the space-time tangent bundle

2003 ◽  
Vol 2003 (24) ◽  
pp. 1529-1546 ◽  
Author(s):  
Howard E. Brandt
Keyword(s):  
Tangent Bundle ◽  
Planck Scale ◽  
Beltrami Operator ◽  
Space Time ◽  
Quantum Field ◽  
Time Points ◽  
High Energies ◽  
Maximal Acceleration ◽  
Particle Spectra ◽  
Invariant Quantum

A maximal-acceleration invariant quantum field is defined on the space-time tangent bundle with vanishing eigenvalue when acted on by the Laplace-Beltrami operator of the bundle, and the case is addressed in which the space-time is Minkowskian, and the field is Lorentz invariant. In this case, the field is shown to be automatically regularized at the Planck scale, and particle spectra are cut off at extremely high energies. The microcausality is addressed by calculating the appropriate field commutators; and it is shown that provided the adjoint field is consistently generalized, the necessary commutators are vanishing and the field is microcausal, but that there are Planck-scale modifications of the boundary of the causal domain that are significant for extremely large relative four-velocities between the separated space-time points. For vanishing relative four-velocity, the causal domain is canonical. The geometry of the causal domain indicates that near the Planck scale, causal connectivity may occur between spacelike separated points, and also at larger scales for extremely large relative four-velocities.

scholarly journals Dispositional Essentialism and the Nature of Powerful Properties

Disputatio ◽  
2013 ◽  
Vol 5 (35) ◽  
pp. 1-19 ◽  
Author(s):  
William A. Bauer
Keyword(s):  
Point Theory ◽  
Space Time ◽  
Time Points ◽  
Dispositional Essentialism ◽  
Powerful Qualities

Abstract Dispositional essentialism maintains that all sparse properties are essentially powerful. Two conceptions of sparse properties appear compatible with dispositional essentialism: sparse properties as pure powers or as powerful qualities. This paper compares the two views, criticizes the powerful qualities view, and then develops a new theory of pure powers, termed Point Theory. This theory neutralizes the main advantage powerful qualities appear to possess over pure powers—explaining the existence of powers during latency periods. The paper discusses the relation between powers and space-time points, whether pure powers need to occupy space, and how to account for the movement of pure powers through space-time. Given Point Theory, dispositional essentialists should maintain that sparse properties are pure powers.

scholarly journals Visit Probability in Space–Time Prisms Based on Binomial Random Walk

2020 ◽  
Vol 9 (9) ◽  
pp. 555
Author(s):  
Deepak Elias ◽  
Bart Kuijpers
Keyword(s):  
Random Walk ◽  
Moving Objects ◽  
Formal Model ◽  
Dimensional Space ◽  
Space Time ◽  
Mathematical Framework ◽  
Two Dimensional ◽  
Time Points ◽  
Dimensional Space Time ◽  
Measured Sample

Space–time prisms are used to model the uncertainty of space–time locations of moving objects between (for instance, GPS-measured) sample points. However, not all space–time points in a prism are equally likely and we propose a simple, formal model for the so-called “visit probability” of space–time points within prisms. The proposed mathematical framework is based on a binomial random walk within one- and two-dimensional space–time prisms. Without making any assumptions on the random walks (we do not impose any distribution nor introduce any bias towards the second anchor point), we arrive at the conclusion that binomial random walk-based visit probability in space–time prisms corresponds to a hypergeometric distribution.

scholarly journals APIE „KLAIDINGĄ IMPLIKACINĘ PRIELAIDĄ“

Problemos ◽  
2006 ◽  
Vol 70 ◽  
Author(s):  
Jonas Dagys ◽  
Mindaugas Briedis
Keyword(s):  
Space Time ◽  
Formal Logic ◽  
Quantitative Interpretation ◽  
Conditional Statement ◽  
Time Points ◽  
Qualitative Interpretation ◽  
Empirical Fact ◽  
Truth Value ◽  
False Premise

Straipsnyje kritikuojamas 68-ame „Problemų“ numeryje skelbtas J. Čiurlionio teiginys, kad matematiniai Zenono Elėjiečio aporijos sprendimai „remiasi klaidinga implikacine prielaida“. Pirma, logikos dėsniai nedraudžia iš klaidingų teiginių pagrįstai išvesti teisingus teiginius, todėl prielaidos klaidingumas neužtikrina išvados klaidingumo. Antra, minimos implikacijos antecedento loginę reikšmę lemia empirinis faktas, todėl net jei implikacijos konsekventas būtinai klaidingas, implikacija yra loginiu požiūriu atsitiktinė. Trečia, implikacijos konsekventas gali būti interpretuojamas dvejopai. Viena interpretacija padaro jį nomologiškai būtinai klaidingą, bet nerelevantišką Zenono aporijai; kita interpretacija padaro teiginį relevantišką, bet nebūtinai klaidingą. Taigi nėra jokio pagrindo manyti, kad implikacinė prielaida, kuria, Čiulionio teigimu, remiasi matematiniai Zenono Elėjiečio aporijos sprendimai, yra klaidinga.Pagrindiniai žodžiai: Achilo ir vėžlio aporija, tapatumo sąlygos, aporijų sprendimai. REGARDING THE “FALSE CONDITIONAL PREMISE”Jonas Dagys and Mindaugas Briedis Summary We criticize the claim made by Èiurlionis, namely that mathematical solutions to Zeno’s aporia are unsatisfactory, as they rely on “a false conditional premise”. First, the rules of formal logic do not forbid deriving true statements from false statements, so even if mathematical solutions rely on a false premise this does not guarantee the falsity of their conclusion. Second, the truth value of the antecedent of the conditional depends on an empirical fact, so even granted that the consequent is false, the conditional statement should be viewed as contingent. Third, and most important, the statement in the consequent admits of two interpretations: a strict qualitative interpretation of identity of space-time points, which makes the statement nomologically necessarily false but irrelevant to the Zeno’s aporia; and a looser mathematical quantitative interpretation of the identity of space-time points, which makes the statement relevant but not only contingently false. We conclude that there is no reason to accept the claim that this conditional statement is false and that Èiurlionis takes a wrong path in his attempt to resolve Zeno’s aporias.Keywords: Achilles and tortoise aporia, identity conditions, solutions of aporias.

EDGIS: a dynamic GIS based on space time points

2010 ◽  
Vol 24 (3) ◽  
pp. 329-346 ◽  
Author(s):  
Edward Pultar ◽  
Thomas J. Cova ◽  
May Yuan ◽  
Michael F. Goodchild
Keyword(s):  
Space Time ◽  
Time Points

scholarly journals FERMION SYSTEMS IN DISCRETE SPACE–TIME EXEMPLIFYING THE SPONTANEOUS GENERATION OF A CAUSAL STRUCTURE

2008 ◽  
Vol 23 (27n28) ◽  
pp. 4579-4620 ◽  
Author(s):  
A. DIETHERT ◽  
F. FINSTER ◽  
D. SCHIEFENEDER
Keyword(s):  
Variational Principle ◽  
Causal Structure ◽  
Planck Scale ◽  
Space Time ◽  
Discrete Space ◽  
The Self ◽  
Self Organization ◽  
Spontaneous Generation ◽  
Time Points ◽  
Fermion Systems

As toy models for space–time at the Planck scale, we consider examples of fermion systems in discrete space–time which are composed of one or two particles defined on two up to nine space–time points. We study the self-organization of the particles as described by a variational principle both analytically and numerically. We find an effect of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure.

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