EXPANDED EDITION (eBook): -/- Infinity Is Not What It Seems...Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes (...) in a divine Creator infinite in knowledge, power, and benevolence. -/- According to this treatise, such assumptions are mistaken. In reality, to be is to be finite. The implications of this assessment are profound: the Universe and even God must necessarily be finite. -/- The author makes a compelling case against infinity, refuting its most prominent advocates. Any defense of the infinite will find it challenging to answer the arguments laid out in this book. But regardless of the reader’s position, FOREVER FINITE offers plenty of thought-provoking material for anyone interested in the subject of infinity from the perspectives of philosophy, mathematics, science, and theology. -/- This electronic edition of FOREVER FINITE is offered free online for all and is expanded with content that does not appear in the published edition due to print production page limitations. From the Introduction to the Conclusion, Chapters 1–27 are identical to the published print edition, including the page numbering for the chapters. This electronic edition adds an appendix and associated content—specifically, updates to the book’s back matter (68 new endnotes, 17 new bibliographic references, 3 new figure credits, 14 new glossary terms) and front matter (an updated table of contents and this preface note). (shrink)

Abstract: In a 1999 book entitled 'The Cosmic Sphere', the author proposed an unconventional model of the Universe intended to solve conceptual and empirical problems facing the Big Bang theory. The author has since had second thoughts, however, and has concluded that his proposed Cosmic Sphere Model (CSM) of the Universe is flawed and cannot be accurate. In this article, the author provides an overview of 'The Cosmic Sphere' and CSM, points out the errors of both, analyzes the implications of (...) the errors, and closes with a few words about a future philosophical publication on cosmology. (shrink)

Although many find it hard to believe that every physical thing—no matter how simple or small—involves some form of consciousness, panpsychists offer the reassurance that their claims are perfectly compatible with everything physics has to say about the physical world. This is because although physics has a lot to say about causal and structural properties it has nothing to say about the intrinsic natures of physical things, and if physics is silent in this regard it is perfectly possible that everything (...) physical has an experiential intrinsic nature. Following in Thomas Nagel’s footsteps, panpsychists have also argued that by revealing that everything is composed of the same fundamental ingredients, physics provides grounds for holding that if any physical things (e.g. our neural processes) have an experiential intrinsic nature then all must. My main contention in this paper is that the relationship between physics and panpsychism is considerably more complex than panpsychists have tended to assume. Nagel’s reasoning may be sound in the context of simplistic atomic theories which posit just one kind of fundamental particle. However, it begins to look distinctly dubious in the context of the diverse range of primitive entities that are to be found in the Standard Model of particle physics. Galen Strawson has suggested that mass-energy interconvertibility should be regarded as evidence that everything physical has the same intrinsic nature. I suggest Strawson’s claim relies on a dubious construal of the nature of energy. Special relativity is another of the cornerstones of contemporary physics, and it too makes life difficult for panpsychists, a fact which emerges when we consider what it would like to be a ray of light. However in this case I suggest that there is an interesting—if radical—move open to the panpsychist: they can simply deny that light exists. To conclude I briefly consider whether what QCD has revealed about the nature of mass poses a problem for panpsychism. (shrink)

Exposed in 1948, within his masterpiece on the scope and limits of human knowledge, the epistemological tenets that Bertrand Russell regarded as fundamental elements in the construction of scientific knowledge, are still worthy of a detailed discussion today. Given the excellence of the author, it will not be surprising to see that Russell's gnoseologic postulates, even for the present scientific view, address some of the most controversial questions still to be solved in the theory of knowledge.

In view of a resurgence of concern about the measurement problem, it is pointed out that the Relativistic Transactional Interpretation remedies issues previously considered as drawbacks or refutations of the original TI. Specifically, once one takes into account relativistic processes that are not representable at the non-relativistic level, absorption is quantitatively defined in unambiguous physical terms. RTI therefore provides a well-defined terminus to what appears to be a necessary infinite regress concerning ‘absorption’ when only the non-relativistic level is considered. In (...) addition, specifics of the relativistic transactional model demonstrate that the Maudlin ‘contingent absorber’ challenge to the original TI cannot even be mounted: basic features of established relativistic field theories dictate that the ‘slow-moving offer wave’ required for the challenge scenario cannot exist. It is concluded that issues previously considered obstacles for TI are no longer legitimately viewed as such, and that reconsideration of the transactional picture is warranted in connection with solving the measurement problem. (shrink)

Cramer's Transactional Interpretation (TI) is applied to the ``Quantum Liar Experiment'' (QLE). It is shown how some apparently paradoxical features can be explained naturally, albeit nonlocally (since TI is an explicitly nonlocal interpretation). At the same time, it is proposed that in order to preserve the elegance and economy of the interpretation, it may be necessary to consider offer and confirmation waves as propagating in a ``higher space'' of possibilities.

We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is not a (...) new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof. (shrink)

This paper explains the delayed choice quantum eraser of Kim et al. in terms of the transactional interpretation of quantum mechanics by Cramer. It is kept deliberately mathematically simple to help explain the transactional technique. The emphasis is on a clear understanding of how the instantaneous “collapse” of the wave function due to a measurement at a specific time and place may be reinterpreted as a relativistically well-defined collapse over the entire path of the photon and over the entire transit (...) time from slit to detector. This is made possible by the use of a retarded offer wave, which is thought to travel from the slits to the detector and an advanced counter wave traveling backward in time from the detector to the slits. The point here is to make clear how simple the transactional picture is and how much more intuitive the collapse of the wave function becomes if viewed in this way. Also, any confusion about possible retro-causal signaling is put to rest. A delayed choice quantum eraser does not require any sort of backward in time communication. This paper makes the point that it is preferable to use the TI over the usual Copenhagen interpretation for a more intuitive understanding of the quantum eraser delayed choice experiment. Both methods give exactly the same end results and can be used interchangeably. (shrink)

In 1994, Maudlin proposed an objection to retrocausal approaches to quantum mechanics in general, and to the transactional interpretation in particular, involving an absorber that changes location depending on the trajectory of the particle. Maudlin considered this objection fatal. However, the TI did not die; rather, a number of responses were developed, some attempting to accommodate Maudlin's example within the existing TI, and others modifying the TI. I argue that none of these responses is fully adequate. The reason, I submit, (...) is that there are two aspects to Maudlin's objection; the more readily soluble aspect has received all the attention, but the more problematic aspect has gone unnoticed. I consider the prospects for developing a successful retrocausal quantum theory in light of this second aspect of the objection. (shrink)

The transactional interpretation of quantum mechanics, following the time-symmetric formulation of electrodynamics, uses retarded and advanced solutions of the Schrödinger equation and its complex conjugate to understand quantum phenomena by means of transactions. A transaction occurs between an emitter and a specific absorber when the emitter has received advanced waves from all possible absorbers. Advanced causation always raises the specter of paradoxes, and it must be addressed carefully. In particular, different devices involving contingent absorbers or various types of interaction-free measurements (...) have been proposed as threatening the original version of the transactional interpretation. These proposals will be analyzed by examining in each case the configuration of absorbers and, in the special case of the so-called quantum liar experiment, by carefully following the development of retarded and advanced waves through the Mach-Zehnder interferometer. We will show that there is no need to resort to the hierarchy of transactions that some have proposed, and will argue that the transactional interpretation is consistent with the block-universe picture of time. (shrink)

The attractive feature of the Everett approach is its admirable spirit of approaching the quantum puzzle with a Zen-like "beginner’s mind" in order to try to envision what the pure formalism might be saying about quantum reality, even if that journey leads to a strange place. It is argued that the transactional interpretation of quantum mechanics (TI), appropriately interpreted, shares the same motivation and achieves much more, with far fewer conceptual perplexities, by taking into account heretofore overlooked features of the (...) quantum formalism itself (i.e. advanced states). In particular, TI does not need to talk about brain states, consciousness, or observers (rational or otherwise). In its possibilist variant (“PTI”), it shares the realist virtues of treating state vector branches as genuine dynamical entities, without having to explain how or why all of their associated outcomes actually happen (they don’t), how to account for a plenitude of counterpart observers in some coherent notion of trans-temporal identity of the bifurcating observers (observers don’t bifurcate in TI), nor how the certainty of all outcomes could be consistent with any coherent theory of probability, let alone the Born probability (the Born probability emerges naturally in TI). In short, TI is precisely the one-world interpretation Kent is looking for in his (2010). (shrink)

If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and final boundary conditions in non-relativistic quantum mechanics leads to the idea that the properties of macroscopic quantum systems, relevantly measuring instruments, are uniquely determined by the boundary conditions. An important element in reaching that conclusion is that preparations and measurements belong in a (...) special class because they involve many subsystems, at least some of which do not form superpositions of their physical properties before the boundary conditions are imposed. It is suggested that the primary role of the formalism of standard quantum mechanics is to provide the consistency condition on the boundary conditions rather than the properties of quantum systems. Expressions are proposed for assigning a set of (unmeasured) physical properties to a quantum system at all times. The physical properties avoid the logical inconsistencies implied by the no-go theorems because they are assigned differently from standard quantum mechanics. Since measurement outcomes are determined by the boundary conditions, they help determine, rather than are determined by, the physical properties of quantum systems. (shrink)

This essay provides a historical, philosophical, and critical overview of the development of the transactional interpretation of quantum mechanics. It is separated into two parts. Part I presents the history and development of TI from 1986 up to 2016. Part II lays out current areas of divergence among researchers in TI.