DOCSLIB.ORG

The Potential of a Thick Present Through Undefined Causality and Non-Locality Alessandro Capurso# May 29, 2021 - Rome, Italy

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Potential of a Thick Present Through Undefined Causality and Non-Locality Alessandro Capurso# May 29, 2021 - Rome, Italy PREPRINT FOR PEER REVIEW - DOI: 10.31219/osf.io/52xyd (download the latest version) Contribution shared under a CC-BY Attribution license (creativecommons.org/licenses/by/4.0/) The potential of a thick present through undefined causality and non-locality Alessandro Capurso# May 29, 2021 - Rome, Italy Abstract: In the context of a spacetime described through information, we identify in a thick present the only quantum potential needed to describe evolution, differences and relations. The analysis of undefined causal orders through a Controlled-NOT quantum logic and the concept of superposed imaginary times (developing in a thick space-like foliation), allowed us to consider entanglement as the information related to the persistence of an open choice (in the time order or the spatial position). The superposed imaginary paths identified are then mapped to Closed Time-like Curves (CTC), which develop in the imaginary space-foliation and represent undefined causality and non-locality within each present instant. The proposal suggests the interpretation of CTC as memory-loops, considered the elementary structures for the persistence (in the thick present and along consecutive instants) of the information potential related to both the entanglement and the wave function. Keywords: time; causality; free will; thick present; entanglement; CTC; quantum potential; logic; information; quantum gravity; Introduction The nature of Time is often at the root of the debate in physics and possibly sits at the core of General Relativity (GR) and Quantum Mechanics (QM) incompatibility. In recent years, the search for a theory of Quantum Gravity (QG), able to include both the success of GR and QM, revived the study of time as a key ingredient for the understanding of a quantum description of spacetime. Beside time, the concept of entanglement has puzzled the physics community for decades, stimulating the discussion around causality and locality in physical laws. This paper investigates the possibility of a thick present as the only element of reality, intended as a quantum potential from which spacetime could emerge in a sequence of space-like foliations. In the context of an evolution occurring in discrete present instants, we investigate how undefined causal orders could be considered. Thanks to a parallel with a CNOT quantum gateway, the information of the undefined order is described through imaginary paths, developing as superposed imaginary times within each space-like foliation. We then describe the potential of the superposition of imaginary times through CTC withing the thick present. Following a Quantum Information Science (QIS) perspective, CTC are interpreted as logically consistent “memory-loops”, in which the still undefined potential of a possible “open choice” (temporal order or spatial position) could persist along the successions of present instants. The derived description promotes the connection of entanglement with non-locality, investigated in the final part of the contribution. Existence in a thick present The interpretation of the nature of time in physics has seen two opposite descriptions. The first, called Eternalism, is often related to the theory of Relativity and consider an ever-existing time, real in both the past and the future, and of which we perceive only limited cones of information. The opposite perspective, known as Presentism, is connected to the idea of evolution itself and pictures time as everchanging: a vanishing present compressed between past and future instants. The focus is on the difference between the past, already happened and irreversible, and the future, still undefined and open. The axis of time seems to become real only in the current instant and in the causal consequences of the past ones. Between these extremes, all the other meanings humans associate to time. # [email protected] - orcid.org/0000-0003-3277-3588 A. Capurso - The potential of a thick present through undefined causality and non-locality 2 of 9 Beside physics, the common experience sees a forward and causal progression of time, usually associated to thermodynamics and defined on average or macroscopically, as phenomena naturally tend to higher entropy states. In the context of the Free Will theorem (introduced by Conway in [1]), we should assume that the future is open and undetermined and pose a serious threat on the idea of a classical and ever-existing time in a “block-universe”. Moreover, from a QIS perspective, recent “gargantuan simulations” (reported in [2]) showed that time seems irreversible at the most fundamental level, beyond thermodynamic reasons. It has been shown that even a simple 3-bodies system “would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution”: what had been already can causally influence the present but cannot be changed and, beyond fundamental physical limits, cannot even be known with certainty. The irreversibility of events might seem in contradiction with a symmetric description of time, even if physical laws in a classical framework are time symmetric and there are several QM symmetric approaches too. The idea of an emerging causal reality connected to the superposition of both a forward and a backward propagating wave was proposed in the Two-State-Vector Formalism (TSVF) (introduced in [3]), and further elaborated recently in a more extensive description including elements of Energetic Causal Sets (in [4] and [5]). Even in a context of the irreversibility of events, we could still consider a QM time symmetric approach within a thick present, as a description of the spacelike foliation coming from a superposition of perspectives from a near past and a near future. If the future is open and yet to come, and the past is fixed and irreversible but might not be known beyond the causal consequences, we could consider a thick present as the elementary quanta in the passage of time and the only element of reality along an emerging thermodynamic arrow of time (idea also elaborated in [6], following an intuitionist mathematical language, and [7] from an QM ontological perspective). A thick present could be described as a thick space-like foliation of the universe, bounded between -T and +T. Within a thick present we could consider both a quantum information potential (connected to a QM probabilistic description and an open future in the coming cycles) as well as the information of the irreversible events (as causal fixed points from which the present emerges, and the future opens), efficiently discarding the information of the far past states that is not needed to reconstruct the current spacetime. A thick present could be intended as well as the realization of the idea of a “discreteness of time”. The possibility of a minimum interval in the passage of time has been recently investigated in [8], where an experimental proof of a discrete time is proposed though the relation with the Planck mass and a minimum corresponding phase difference. A thick present has also been recently considered in the description of human perception of time and it is often related in QIS to a discrete elaboration cycle of the information. There are several theories that consider evolution in discrete cycles. To mention a few, Finite State Classical Mechanics (proposed in [9]) is based on Lattice Dynamics, where the information is described through discrete positions and the evolution rules are often referred as “cellular automata” models. Signal-State Quantum Mechanics, further developed in a theory of Quantized Detector Networks (presented in [10]), describes particles as storing entangled phase information and focus on observers and their apparatus, as a realization of the Heisenberg’s “instrumentalist approach” to quantum physics. To describe a thick present in a cyclic evolution, we could consider a minimum time interval T like a π rotation, as to see things from a different perspective and as if 2T (equivalent to 2π) were needed for a full cycle. We could consider these discrete 2T steps, from -T to +T, as the elaboration cycle of the quantum information potential from which spacetime could emerge. As Freeman Dyson wrote (in [11]), the only role of a local observer seems becoming the distinction between a classical past and a still open and probabilistic future. The relation between the observation of a variable at a given instant (identifying an event) and the derived difference between past and future has also been elaborated in [12] as a “dynamics of difference”. A. Capurso - The potential of a thick present through undefined causality and non-locality 3 of 9 Observers, events or potential ones, all exist in a thick present able to account for a superposition of perspectives from a near past and a near future, resulting time symmetric within its thickness, and assuring consistency between “what it was” (causally happened) and “what it could be” in the current cycle. Information could persist as a potential in case no events occurred in the present elaboration cycle, while events of collapse or “measurements” should be interpreted as irreversible, also in line with the QIS and computational perspective. From the irreversibility of events (in the succession of the thick present instants), a thermodynamic oriented arrow of time could also be considered as emerging in the memory of the observers, from lower to higher entropy states at different scales of observation. It is worth to clarify that the “present” is not intended as a global “perceived now”. The passage of time for local observers within spacetime follows relativity and time intervals measured by local quantum clocks are lengthen according to the equations of GR. The thick present represents the potential of the current space of events and possibilities. In a QIS description, its duration could be related to a “spacetime sampling rate”. It could represent a global reference for a minimum time interval, allowing relative confrontation of local quantum clocks with respect to one another in a discrete passage of time.
Load more

Recommended publications
  • Accommodating Retrocausality with Free Will Yakir Aharonov Chapman University, [email protected]
    Chapman University Chapman University Digital Commons Mathematics, Physics, and Computer Science Science and Technology Faculty Articles and Faculty Articles and Research Research 2016 Accommodating Retrocausality with Free Will Yakir Aharonov Chapman University, [email protected] Eliahu Cohen Tel Aviv University Tomer Shushi University of Haifa Follow this and additional works at: http://digitalcommons.chapman.edu/scs_articles Part of the Quantum Physics Commons Recommended Citation Aharonov, Y., Cohen, E., & Shushi, T. (2016). Accommodating Retrocausality with Free Will. Quanta, 5(1), 53-60. doi:http://dx.doi.org/10.12743/quanta.v5i1.44 This Article is brought to you for free and open access by the Science and Technology Faculty Articles and Research at Chapman University Digital Commons. It has been accepted for inclusion in Mathematics, Physics, and Computer Science Faculty Articles and Research by an authorized administrator of Chapman University Digital Commons. For more information, please contact [email protected]. Accommodating Retrocausality with Free Will Comments This article was originally published in Quanta, volume 5, issue 1, in 2016. DOI: 10.12743/quanta.v5i1.44 Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 License. This article is available at Chapman University Digital Commons: http://digitalcommons.chapman.edu/scs_articles/334 Accommodating Retrocausality with Free Will Yakir Aharonov 1;2, Eliahu Cohen 1;3 & Tomer Shushi 4 1 School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. E-mail: [email protected] 2 Schmid College of Science, Chapman University, Orange, California, USA. E-mail: [email protected] 3 H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK.
    [Show full text]
  • On the Emergence of Time in Quantum Gravity
    Imperial/TP/98–99/23 On the Emergence of Time in Quantum Gravity1 J. Butterfield2 All Souls College Oxford OX1 4AL and C.J. Isham3 The Blackett Laboratory Imperial College of Science, Technology & Medicine South Kensington London SW7 2BZ 13 December 1998 Abstract We discuss from a philosophical perspective the way in which the normal concept of time might be said to ‘emerge’ in a quantum the- ory of gravity. After an introduction, we briefly discuss the notion of arXiv:gr-qc/9901024v1 8 Jan 1999 emergence, without regard to time (Section 2). We then introduce the search for a quantum theory of gravity (Section 3); and review some general interpretative issues about space, time and matter (Section 4). We then discuss the emergence of time in simple quantum ge- ometrodynamics, and in the Euclidean approach (Section 5). Section 6 concludes. 1To appear in The Arguments of Time, ed. J. Butterfield, Oxford University Press, 1999. 2email: [email protected]; jeremy.butterfi[email protected] 3email: [email protected] 1 Introduction The discovery of a satisfactory quantum theory of gravity has been widely regarded as the Holy Grail of theoretical physics for some forty years. In this essay, we will discuss a philosophical aspect of the search for such a theory that bears on our understanding of time: namely, the senses in which our standard ideas of time, and more generally spacetime, might be not fundamental to reality, but instead ‘emergent’ as an approximately valid concept on sufficiently large scales. In taking up this topic, our aim in part is to advertise to philosophers of time an unexplored area that promises to be fruitful.
    [Show full text]
  • A More Direct Representation for Complex Relativity
    A more direct representation for complex relativity D.H. Delphenich ∗∗∗ Physics Department, Bethany College, Lindsborg, KS 67456, USA Received 22 Nov 2006, revised 5 July 2007, accepted 5 July 2007 by F. W. Hehl Key words Complex relativity, pre-metric electromagnetism, almost-complex structures, 3- spinors. PACS 02.10.Xm, 02.40.Dr, 03.50.De, 04.50.+h An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that the bundle of real 2-forms is given an almost- complex structure. From this, one can define a complex orthogonal structure on the bundle of 2- forms, which results in a more direct representation of the complex orthogonal group in three complex dimensions. The geometrical foundations of general relativity are then presented in terms of the bundle of oriented complex orthogonal 3-frames on the bundle of 2-forms in a manner that essentially parallels their construction in terms of self-dual complex 2-forms. It is shown that one can still discuss the Debever-Penrose classification of the Riemannian curvature tensor in terms of the representation presented here. Contents 1 Introduction …………………………………………………………………………. 1 2 The complex orthogonal group …………………………………………………….. 3 3 The geometry of bivectors ………………………………………………………….. 4 3.1 Real vector space structure on A 2……………………………………………….. 5 3.2 Complex vector space structure on A 2…………………………………………... 8 3.3 Relationship to the formalism of self-dual bivectors……………………………. 12 4 Associated principal bundles for the vector bundle of 2-forms ………………….. 16 5 Levi-Civita connection on the bundle SO (3, 1)( M)………………………………… 19 6 Levi-Civita connection on the bundle SO (3; C)( M)……………………………….
    [Show full text]
  • On the Rational Relationship Between Heisenberg Principle and General
    CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server On the Rational Relationship between Heisenberg Principle and General Relativity Xiao Jianhua Henan Polytechnic University, Jiaozuo City, Henan, P.R.C. 454000 Abstract: The research shows that the Heisenberg principle is the logic results of general relativity principle. If inertia coordinator system is used, the general relativity will logically be derived from the Heisenberg principle. The intrinsic relation between the quantum mechanics and general relativity is broken by introducing pure-imaginary time to explain the Lorentz transformation. Therefore, this research shows a way to establish an unified field theory of physics. PACS: 01.55.+b, 03.65.-w, 04.20.-q, 04.20.Ky Keywords: Heisenberg principle, general relativity, commoving coordinator, Riemannian geometry, gauge field 1. Introduction There are many documents to treat the relationship between the Newton mechanics and general relativity. There are also many documents to treat the relationship between the quantum mechanics and general relativity. For some researchers, the related research shows that an unified field theory be possible. For others, the actual efforts to establish an unified field theory for physics have shown that such an unified field theory is totally non-possible. The physics world is divided into three kingdoms. Hence, the title of this paper may make the reader think: See! Another nut! However, the unification of matter motion is the basic relieves for science researchers. The real problem is to find the way. This is the topic of this paper. The paper will firstly derive the Heisenberg principle from general relativity principle.
    [Show full text]
  • The Philosophy and Physics of Time Travel: the Possibility of Time Travel
    University of Minnesota Morris Digital Well University of Minnesota Morris Digital Well Honors Capstone Projects Student Scholarship 2017 The Philosophy and Physics of Time Travel: The Possibility of Time Travel Ramitha Rupasinghe University of Minnesota, Morris, [email protected] Follow this and additional works at: https://digitalcommons.morris.umn.edu/honors Part of the Philosophy Commons, and the Physics Commons Recommended Citation Rupasinghe, Ramitha, "The Philosophy and Physics of Time Travel: The Possibility of Time Travel" (2017). Honors Capstone Projects. 1. https://digitalcommons.morris.umn.edu/honors/1 This Paper is brought to you for free and open access by the Student Scholarship at University of Minnesota Morris Digital Well. It has been accepted for inclusion in Honors Capstone Projects by an authorized administrator of University of Minnesota Morris Digital Well. For more information, please contact [email protected]. The Philosophy and Physics of Time Travel: The possibility of time travel Ramitha Rupasinghe IS 4994H - Honors Capstone Project Defense Panel – Pieranna Garavaso, Michael Korth, James Togeas University of Minnesota, Morris Spring 2017 1. Introduction Time is mysterious. Philosophers and scientists have pondered the question of what time might be for centuries and yet till this day, we don’t know what it is. Everyone talks about time, in fact, it’s the most common noun per the Oxford Dictionary. It’s in everything from history to music to culture. Despite time’s mysterious nature there are a lot of things that we can discuss in a logical manner. Time travel on the other hand is even more mysterious.
    [Show full text]
  • Retrocausality in Energetic Causal Sets Arxiv:1902.05082V3 [Gr-Qc]
    Realism and Causality II: Retrocausality in Energetic Causal Sets Eliahu Cohen1, Marina Cortesˆ 2;3, Avshalom C. Elitzur4;5 and Lee Smolin3 1 Faculty of Engineering, Bar Ilan University, Ramat Gan 5290002, Israel 2 Instituto de Astrof´ısica e Cienciasˆ do Espac¸o Faculdade de Ciencias,ˆ 1769-016 Lisboa, Portugal 3 Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2J 2Y5, Canada 4 Iyar, The Israeli Institute for Advanced Research, POB 651, Zichron Ya’akov 3095303, Israel 5 Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA November 3, 2020 Abstract We describe a new form of retrocausality, which is found in the behaviour of a class of causal set theories, called energetic causal sets (ECS). These are discrete sets of events, connected by causal relations. They have three orders: (1) a birth order, which is the order in which events are generated; this is a total order which is the true causal order, (2) a dynamical partial order, which prescribes the flows of energy and momen- tum amongst events, (3) an emergent causal order, which is defined by the geometry of an emergent Minkowski spacetime, in which the events of the causal sets are em- arXiv:1902.05082v3 [gr-qc] 1 Nov 2020 bedded. However, the embedding of the events in the emergent Minkowski spacetime may preserve neither the true causal order in (1), nor correspond completely with the microscopic partial order in (2). We call this disordered causality, and we here demon- strate its occurrence in specific ECS models. This is the second in a series of papers centered around the question: Should we accept violations of causality as a lesser price to pay in order to keep realist formula- tions of quantum theory? We begin to address this in the first paper [1] and continue here by giving an explicit example of an ECS model in the classical regime, in which causality is disordered.
    [Show full text]
  • Disentangling the Quantum World
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Apollo Entropy 2015, 17, 7752-7767; doi:10.3390/e17117752 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Disentangling the Quantum World Huw Price 1;y;* and Ken Wharton 2;y 1 Trinity College, Cambridge CB2 1TQ, UK 2 San José State University, San José, CA 95192-0106, USA; E-Mail: [email protected] y These authors contributed equally to this work. * Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +44-12-2333-2987. Academic Editors: Gregg Jaeger and Andrei Khrennikov Received: 22 September 2015 / Accepted: 6 November 2015 / Published: 16 November 2015 Abstract: Correlations related to quantum entanglement have convinced many physicists that there must be some at-a-distance connection between separated events, at the quantum level. In the late 1940s, however, O. Costa de Beauregard proposed that such correlations can be explained without action at a distance, so long as the influence takes a zigzag path, via the intersecting past lightcones of the events in question. Costa de Beauregard’s proposal is related to what has come to be called the retrocausal loophole in Bell’s Theorem, but—like that loophole—it receives little attention, and remains poorly understood. Here we propose a new way to explain and motivate the idea. We exploit some simple symmetries to show how Costa de Beauregard’s zigzag needs to work, to explain the correlations at the core of Bell’s Theorem. As a bonus, the explanation shows how entanglement might be a much simpler matter than the orthodox view assumes—not a puzzling feature of quantum reality itself, but an entirely unpuzzling feature of our knowledge of reality, once zigzags are in play.
    [Show full text]
  • The No-Boundary Proposal Via the Five-Dimensional Friedmann
    The no-boundary proposal via the five-dimensional Friedmann-Lemaˆıtre-Robertson-Walker model Peter K.F. Kuhfittig* and Vance D. Gladney* ∗Department of Mathematics, Milwaukee School of Engineering, Milwaukee, Wisconsin 53202-3109, USA Abstract Hawking’s proposal that the Universe has no temporal boundary and hence no be- ginning depends on the notion of imaginary time and is usually referred to as the no-boundary proposal. This paper discusses a simple alternative approach by means of the five-dimensional Friedmann-Lemaˆıtre-Robertson-Walker model. PAC numbers: 04.20.-q, 04.50.+h Keywords: no-boundary proposal, FLRW model 1 Introduction It is well known that Stephen Hawking introduced the no-boundary proposal using the concept of imaginary time, making up what is called Euclidean spacetime [1]. While ordi- nary time would still have a big-bang singularity, imaginary time avoids this singularity, implying that the Universe has no temporal boundary and hence no beginning. By elim- inating the singularity, the Universe becomes self-contained in the sense that one would arXiv:1510.07311v2 [gr-qc] 7 Jan 2016 not have to appeal to something outside the Universe to determine how the Universe began. Given that imaginary time is orthogonal to ordinary time, one could view imaginary time as an extra dimension. The existence of an extra dimension suggests a different start- ing point, the five-dimensional Friedmann-Lemaˆıtre-Robertson-Walker model (FLRW) [2]. This model produces a simple alternative version of the no-boundary proposal. 2 The FLRW model Let us recall the FLRW model in the usual four dimensions [3]: dr2 ds2 = dt2 + a2(t) + r2(dθ2 + sin2θdφ2) , (1) − 1 Kr2 − ∗kuhfi[email protected] 1 where a2(t) is a scale factor.
    [Show full text]
  • THE PHYSICS of TIMLESSNESS Dr
    Cosmos and History: The Journal of Natural and Social Philosophy, vol. 14, no. 2, 2018 THE PHYSICS OF TIMLESSNESS Dr. Varanasi Ramabrahmam ABSTRACT: The nature of time is yet to be fully grasped and finally agreed upon among physicists, philosophers, psychologists and scholars from various disciplines. Present paper takes clue from the known assumptions of time as - movement, change, becoming - and the nature of time will be thoroughly discussed. The real and unreal existences of time will be pointed out and presented. The complex number notation of nature of time will be put forward. Natural scientific systems and various cosmic processes will be identified as constructing physical form of time and the physical existence of time will be designed. The finite and infinite forms of physical time and classical, quantum and cosmic times will be delineated and their mathematical constructions and loci will be narrated. Thus the physics behind time-construction, time creation and time-measurement will be given. Based on these developments the physics of Timelessness will be developed and presented. KEYWORDS: physical time, psychological time, finite and infinite times, scalar and vector times, Classical, quantum and cosmic times, timelessness, movement, change, becoming INTRODUCTION: “Our present picture of physical reality, particularly in relation to the nature of time, is due for a grand shake-up—even greater, perhaps, than that which has already been provided by present-day relativity and quantum mechanics” [1]. Time is considered as www.cosmosandhistory.org 1 COSMOS AND HISTORY 2 one of the fundamental quantities in physics. Second, which is the duration of 9,192,631,770 cesium-133 atomic oscillations, is the unit.
    [Show full text]
  • Swinging in Imaginary Time More on the Not-So-Simple Pendulum
    GENERAL ARTICLE Swinging in Imaginary Time More on the Not-So-Simple Pendulum Cihan Saclioglu When the small angle approximation is not made, the exact solution of the simple pendulum is a Jacobian elliptic function with one real and one imaginary period. Far from being a physically meaningless mathematical curiosity, the second period represents the imaginary time the pendu- lum takes to swing upwards and tunnel through Cihan Saclioglu teaches the potential barrier in the semi-classical WKB physics at Sabanci approximation1 in quantum mechanics. The tun- University, Istanbul, neling here provides a simple illustration of simi- Turkey. His research lar phenomena in Yang{Mills theories describing interests include solutions of Yang–Mills, Einstein weak and strong interactions. and Seiberg–Witten equations and group 1. Introduction theoretical aspects of string theory. Consider a point mass m at the end of a rigid massless stick of length l. The acceleration due to gravity is g and the oscillatory motion is con¯ned to a vertical plane. Denoting the angular displacement of the stick from the 1When the exact quantum me- vertical by Á and taking the gravitational potential to chanical calculation of the tun- be zero at the bottom, the constant total energy E is neling probability for an arbitrary given by potential U(x) is impracticable, the Wentzel–Kramers–Brillouin 1 dÁ 2 approach, invented indepen- E = ml2 + mgl(1 cos Á) dently by all three authors in the 2 dt ¡ µ ¶ same year as the Schrödinger = mgl(1 cos Á0); (1) equation, provides an approxi- ¡ mate answer. 2 where Á0 is the maximum angle.
    [Show full text]
  • Retrocausality and TGD
    Retrocausality and TGD M. Pitk¨anen Email: [email protected]. http://tgdtheory.com/. June 20, 2019 Abstract This article was inspired by the preprint \Is a time symmetric interpretation of quan- tum theory possible without retrocausality?" of Leifer and Pusey related to the notion of retrocausality. Retrocausality means the possibility of causal influences propagating in non- standard time direction. The conjecture is that retrocausality could allow wave functions to be real and allow to get rid of the problematic notion of state function reduction. The work is interesting from TGD view point for several reasons. 1. TGD leads to a new view about reality of wave function solving the basic problem of quantum measurement theory. In ZEO quantum states are replaced by zero energy states analogous to pairs of initial and final states in ordinary positive energy ontology and can be regarded as superpositions of classical deterministic time evolutions. The sequence of state function reductions means a sequence of re-creations of the superpositions of classical realities identified as space-time surfaces. The TGD based view about scattering amplitudes has rather concrete connection with the view of Cramer as I interpret it. There is however no attempt to reduce quantum theory to a purely classical theory. The notion of the \world of classical worlds" (WCW) consisting of classical realities identified as space-time surfaces replaces space-time as a fixed observer independent reality in TGD. 2. Retrocausality is basic aspect of TGD. Zero Energy Ontology (ZEO) predicts that both arrows of time are possible. In this sense TGD is time symmetric.
    [Show full text]
  • On Stability of Physical Systems in a Complex Plane
    ON STABILITY OF PHYSICAL SYSTEMS IN A COMPLEX PLANE V.V. Lyahov, V.M. Neshchadim 1. Introduction Complex numbers have fully come into common use in mathematics from the very moment of their discovery. Let's mention only one their property – the property of algebraic closedness of the field of complex numbers. The physics even now is in the stage of half-recognizing of complex numbers. On the one hand, the physics, using mathematical means, manipulates imaginaries; on the other hand, common sense says that all observable quantities should be associated with real numbers. Complex calculus should be only an auxiliary, mathematically formal tool. The line of reasoning of a modern physicist is as follows: “We live in the real world; therefore, all quantities should be featured by real numbers”. This statement seems to be completely natural without any additional argumentation. Such situation is an example of paradigm and is taken for granted by scientists. It may be said that the advancement of science confirms this thesis. But it seems that there are also opposite examples. Imaginary timeτ=i⋅ct is introduced into the relativity theory, and only in this form together with three spatial coordinates it forms a four-dimensional space-time. The fourth axis of space-time is an imaginary quantity. In the theory of relativity, on the one hand, it is always underlined that imaginary time is of conditional nature, but, on the other hand, it is also always noted that a deeply essential linkage between space and time was discovered for the first time. The basic object of the quantum mechanics - a complex-valued wave function is referred to as not being of any physical sense, but the square of this function has physical sense.
    [Show full text]