Appendix F - Extra

 
          Fleegello's fictitious critique of octan physics represents an attempt to examine human physics from a speculative ideobasic perspective (developed in Part I and Part II of Appendix E). According to ideobasism, our physical universe is one self-contained subset of a larger, complete set of abstract mathematical objects that both define spatial-temporal relationships and are compatible with consistency logic. This idea is similar to the mathematical universe hypothesis proposed by the cosmologist Max Tegmart. [1]
          The discussion addresses in particular two paradigm shifts that revolutionized twentieth century science here on Earth — quantum physics [2] and relativity theory [3][4]. Much of the standard quantum mechanics content can be found in modern textbooks. [5][6]  Further discussion and references concerning both quantum and relativity theory, including interpretations of the probabilistic character of quantum physics, and how human ideas connect with octan thought, are provided in the commentary section on octan philosophy.
          In Jopian culture, non-relativistic quantum theory is also known as Shrodiik physics, in honor of the fictional physicist Shrodo. This name was inspired by Erwin Schrödinger, an important contributor to the development of human quantum mechanics. [7]  Relativity theory on Jopitar was pioneered by the fictitious Niestu. This name evokes Albert Einstein, who introduced both the special theory and the general theory of relativity on our own planet. [8]  Einstein did not actually coin the term relativity theory, and was supposedly not entirely happy with it, as the label was often misinterpreted to suggest "everything is relative." Yet even though it overturned the absolute space and time of Newtonian physics, the new theory was itself based on absolutes – in particular, the invariance of the laws of physics and the speed of light for all inertial observers. Einstein is thought to have originally preferred the term invariance theory. [9]  While this did not catch on in human society, on Jopitar Niestu's theories are known as the theories of inertial invariance and general invariance. Einstein's thinking was strongly influenced by the physicist Ernst Mach, in particular by his conjecture that inertial frames are not absolute in a Newtonian sense, but ultimately tied to and determined by the large-scale distribution of matter in the universe.[10] Mach is the namesake of the Jopian physicist Machi, who argued that spacetime itself is ultimately defined by matter.
          The multi-time (MT) formulation of quantum mechanics (attributed in the text to the octan physicist Draci) dates back at least to a paper published in 1932 by Paul Dirac, [11] in an attempt to incorporate special relativity into quantum physics. He and others soon argued (within certain assumptions) that relativistic quantum field theory (QFT) was a mathematically equivalent but simpler solution to this problem. [12]
          There has recently been renewed interest in overtly MT theories. [13]  Inclusion of multiple time coordinates is still, however, generally considered merely a way to deal with the effect of relativistic velocity transformations on individual particle spatial coordinates (space and time coordinates become mixed). The MT wavefunction thus includes a separate space and time variable for each particle (all measured with respect to a 4D observer frame), and is defined only on spacelike configurations of a multiparticle system. The traditional single-time wavefunction is recovered by setting all time coordinates to a common observer time.
          A more radical Jopian notion is presented in the text – that MT coordinates are also required to account for limits on the synchronization of distinct proper time lines. The MT wavefunction now explicitly includes a separate time variable for the observer, in addition to individual particle space and time variables. This function is interpreted as a joint probability amplitude that, at a given observer time, the observer sees each particle not only at a specified location, but also synchronized with the observer at a specified particle time (corresponding to a particle proper time). The wavefunction is defined over the entire range of particle spacetime coordinates, and a distinct normalization condition (involving invariant 4D integrals) applies. Because relativistic invariance demands that the observer time variable be paired with a spatial variable, the wavefunction must even incorporate a quantum state for the observer!
          QFT is currently the most widely accepted fundamental quantum theory on Earth. [14]  Besides special relativity, the Standard Model incorporates all known interactions except gravity. Attempts to include gravity, which is still separately described by non-quantized general relativity, have not yet succeeded. This failure is one of the outstanding challenges to physics today. A multi-time version of QFT may ultimately be required to address this and other problems with the Standard Model. [13]
          The traditional method for computing interaction probabilities for elementary particles in standard QFT involves drawing Feynman diagrams of all the ways an interaction can occur (including the creation and destruction of intermediary virtual particles), and then summing the likelihoods of the drawings. Because QFT at present does not properly handle events at very short distances and high energies, infinities are encountered in this process. For most forces (but not gravity), these can be removed by a renormalization procedure, resulting in an effective field theory. [15]
          The proposed origin of our world's three extended spatial dimensions (ascribed to the octan physicist Wittuu) is speculative, and not grounded in any substantiated theory. Over the past century, physicists have proposed various explanations for the dimensionality of nature. Much modern theoretical work involves some variant of (super)string theory, or more recently M-theory, that seeks to unify all consistent versions of superstring theory. [16]  Elementary particles are no longer regarded as points, but are instead treated as extended objects – originally tiny vibrating strings (either open-ended or closed loops), or more recently miniscule higher-dimensional surfaces. Particle world lines are replaced by world sheets. These formulations naturally require either six (superstrings) or seven (M-theory) extra dimensions, in addition to the standard four (3+1) spacetime dimensions, for mathematical consistency. The extra dimensions are either compactified to very small scales, or our world inhabits a 3+1 dimensional subspace, known as a brane, of a larger macroscopic system. In the latter case, all particle interactions (except gravity) and motions would be restricted to the brane. It is also possible that separate physical universes exist with macroscopic branes of dimensionality smaller or larger than 3+1, but intelligent life cannot evolve in such worlds, due to inhospitable laws of physics. In this case, by a weak anthropic argument, we can only find ourselves in a universe with three large spatial dimensions and one time dimension. [17]
          Though string theory is still in its infancy, it can in principle be formulated as a QFT, but without the need for renormalization. Quantum gravity is itself a natural feature of string theory, without the intractable infinities generated by standard quantum field theoretic approaches. While other avenues are also being actively pursued to develop a viable quantum theory of gravity (most notably, loop quantum gravity), string theory offers a grand unification of all known interactions. [18]  Yet novel predictions may be untestable for the foreseeable future, as the relevant distance scales are so small (~10^-33 cm).
          There have been various other attempts to reformulate QFT, both to simplify and to extend the range of computations. Traditional QFT calculations using Feynman diagrams can be extremely arduous, involving a huge number of terms even for simple processes. One attempt to facilitate the mathematics suggests that a scattering amplitude – a basic quantity defining the probability that a given set of particles will transform into another set upon colliding – may be equivalent to the volume of a new type of geometric object in higher dimensions. One version of this polyhedron analogue, that does not incorporate gravity, has been called an amplituhedron. [19]  Important features of the physical universe, such as unitarity (the sum of the probabilities of competing processes must equal one) and locality (a particle is directly affected only by its immediate environs), appear to be emergent properties of the amplituhedron, rather than innate. The traditional view of particles moving through spacetime may even be illusory. Alternatively, the amplituhedron may simply be a convenient calculation tool, and reflect the underlying mathematical structure of our world in part because it is compatible with unitarity and other fundamental principles.
          Fleegello's account of quantum time is highly speculative, and not based on conventional human physics. Spacetime is still assumed to be continuous both in conventional QFT and in current versions of string theory. While many theorists feel that spacetime must be quantized in any ultimate theory, it is not yet clear how this may be accomplished, and still preserve sacrosanct symmetry principles. It should be noted that no serious attempt to date suggests that gravity is a natural consequence of time quantization (though in loop quantum gravity, quantization of general relativity gives spacetime a discrete structure). Of course, a fictional character like Fleegello is free to playfully speculate on such matters to his heart's content!
          A highly technical review of discrete time mechanics has been published by George Jaroszkiewicz. [20]  Farias and Recami have also published a paper on various attempts to quantize time. [21]  They note that time discretization can be achieved either by attributing a discrete structure to time – the approach followed by Fleegello (for proper time scales along particle world lines) – or by considering time as a continuum in which events occur only at discrete instants. The authors discuss an extension of a proposed theory by P. Caldirola that follows the second approach. Here the chronon, or quantum of time, has a value much larger than the Planck time. This value is further not universal, but dependent on the system under examination.
          Quantization of spacetime should reduce the information content of the physical world. Whether or not spacetime is quantized is thus related to the unresolved question of whether the physical (pan)universe contains a finite or an infinite amount of information. An ideobasic argument has been advanced that, if the physical universe is a subset of a unified conscious field (the Consistency Idea Field), then it must be possible to definitively locate every bit of information within it. Any elusive content would not meaningfully exist. This in turn may require that the information content be finite (though outrageously vast). Alternatively, infinite information content may be permissible, so long as the infinity is countable (the elements can be put in one-to-one correspondence with the set of natural numbers). The author personally finds the thought of a truly infinite consciousness particularly alien, and even frightening. While humans can conceptualize continuous dimensions and infinity, human consciousness appears finite in extent. Yet this in itself does not preclude the existence of an infinite awareness.

 
The names of the fictional Jopian researchers found in Fleegello's critique are derived from humans who investigated related topics, as listed below.

Planko – German physicist Max Planck (1858–1947)
Planck (reluctantly) helped beginthe human quantum revolution in 1900, when he postulated that electromagnetic energy could only be emitted in quantized form. He further proposed that the energy of each quantum is proportional to both the frequency of the radiation, and the so-called Planck constant h. Planck won the 1918 Noble Prize in physics for this daring conjecture. Planck also introduced the system of natural units (including the Planck length and Planck time) mentioned in the text. [22][23]

Niestu – German-born theoretical physicist Albert Einstein (1879-1955)
Einstein introduced both the special theory and the general theory of relativity that so revolutionized physics. He also contributed greatly to the new quantum theory (though he had an uneasy relation with it), and won the 1921 Noble Prize in physics for related work on the photoelectric effect. [8]

Machi – Austrian-Czech physicist and philosopher Ernst Mach (1838–1916)
Mach made important contributions to 19th century physics, in particular concerning the study of shock waves. Philosophically, Mach was a logical positivist who espoused a phenomenalistic philosophy of science. n particular, he believed that while we can order our obervations using mathematics, all we can ultimately know is sensory experience. His criticisms of Newtonian notions of space and time helped inspire Einstein's work in relativity theory. [10]

Noethra – German mathematician Emmy Noether (1882–1935)
Noether helped explain the connection between physical symmetries and conservation laws. Her work showed, for example, that if the equations of physics are unaffected by displacements in time and space, then it is possible to define quantities energy and momentum that are constants of motion. [24]

Shrodo – Austrian physicist Erwin Schrödinger (1887–1961)
In addition to other significant contributions to the new quantum physics and to physics in general, Schrödinger formulated the differential wave equation describing the time development of a quantum system. He shared the 1933 Nobel Prize in physics for this work, and is sometimes referred to as the "father of quantum mechanics." [7]

Draci – English theoretical physicist Paul Dirac (1902–1984)
Among many important contributions that furthered the development of quantum theory, Dirac proposed the Dirac equation, which describes the time development of fermions (elementary particles with half-integral spin), and predicted the existence of antimatter. He shared the 1933 Nobel Prize in Physics. [25]

Vigno – Hungarian-American physicist and mathematician Eugene Wigner (1902–1995)
Wigner made many cross-disciplinary contributions to physics. He shared the 1962 Noble Prize in physics, in recognition of his work on nuclear structure, and the application of symmetry principles to quantum mechanics. [26]

Evette – American physicist Hugh Everett III (1930–1982)
Everett proposed the first version of what is now commonly known as the many-worlds interpretation of quantum physics in 1957 (see the commentary section on octan philosophy). This viewpoint challenged the orthodox Copenhagen interpretation, which maintains that our universe has a single history, and that a measurement of some observable causes the system wavefunction to collapse in a discontinuous manner into a single eigenstate of that observable. The many-world interpretation was originally dismissed by most physicists, and did not begin to receive significant attention until the 1970's. [27]

Wittuu – American theoretical physicist Edward Witten (born 1951)
Witten has made important contributions to research in string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics. He is the only physicist to have been awarded a Fields Medal by the International Mathematical Union. [28]

 
REFERENCES__________________________ 
1. Max Tegmark, "The Mathematical Universe," Foundations of Physics 38 (2008):101-150.
2. For a popular introduction to quantum mechanics, see John Gribbin, In Search of Schrödinger's Cat: Quantum Physics and Reality (New York: Bantam, 1984).
3. For an introduction to relativity theory, see N. David Mermin, It's About Time: Understanding Einstein's Relativity (Princeton: Princeton Univ. Press, 2009).
4. For an alternative, semipopular introduction to relativity, see Robert M. Wald, Space, Time, and Gravity: The Theory of the Big Bang and Black Holes (Chicago: Univ. of Chicago Press, 1992).
5. For an introductory textbook on quantum mechanics, see David J. Griffiths, Introduction to Quantum Mechanics, 2nd ed. (London: Pearson Education, 2005).
6. For a more advanced textbook on quantum mechanics, see R. Shankar, Principles of Quantum Mechanics (New York: Springer Science, 1994).
7. John Gribbin, Erwin Schrödinger and the Quantum Revolution (London: Bantam, 2012).
8. Abraham Pais, Subtle is the Lord: The Science and life of Albert Einstein (Oxford: Oxford Univ. Press, 1982).
9. Walter Isaacson, "Special Relativity, 1905," in Einstein: His Life and Universe (New York: Simon & Schuster, 2008), 107-139.
10. John T. Blackmore, Ernst Mach: His Work, Life, and Influence (Berkeley and Los Angeles: University of California Press, 1972).
11.P. A. M. Dirac, "Relativistic quantum mechanics," Proc. R. Soc. A 136/829 (1932): 453-464.
12.Sin-Itiro Tomonaga, "Development of Quantum Electrodynamics,” in Nobel Lectures in Physics (1963-1970), ed. Stig Lundqvist (Singapore: World Scientific, 1998), 126-139.
13. Matthias Lienert, Sören Petrat and Roderich Tumulka, Multi-time Wave Functions - An Introduction (SpringerBriefs in Physics, 2020).
14. A. Zee, Quantum Field Theory in a Nutshell, 2nd ed. (Princeton: Princeton Univ. Press, 2010).
15. Richard P. Feynman, QED: The Strange Theory of Light and Matter, intro. by A. Zee (Princeton: Princeton University Press, 2006).
16. Brian R. Greene, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory (New York: Norton, 2003).
17. Max Tegmark, "On the dimensionality of spacetime," Classical and Quantum Gravity 14 (1997): L69–L75.
18. Lee Smolin, Three Roads to Quantum Gravity (New York: Basic Books, 2001).
19. Natalie Wolchover, "A Jewel at the Heart of Quantum Physics," Quanta Magazine, September, 2013.
20. George Jaroszkiewicz, Principles of Discrete Time Mechanics (New York: Cambridge Univ. Press, 2014).
21. Ruy A. H. Farias and Erasmo Recami, "Introduction of a Quantum of Time ('chronon') and its Consequences for Quantum Mechanics," Advances in Imaging and Electron Physics 163 (2010): 33–115.
22. Helge Kragh, "Max Planck: The Reluctant Revolutionary," Physics World, December, 2000, 31–35.
23. Brandon R. Brown, Planck: Driven by Vision, Broken by War (New York: Oxford University Press, 2015).
24. Dwight E. Neuenschwander, Emmy Noether's Wonderful Theorem (Baltimore: John Hopkins Univ. Press, 2010).
25. Graham Farmelo, The Strangest Man: The Hidden Life of Paul Dirac, Mystic of the Atom (New York: Basic Books, 2009).
26. Eugene Wigner and Andrew Szanton, The Recollections of Eugene P. Wigner: As Told to Andrew Szanton (New York: Plenum, 1992).
27. Peter Byrne, "The Many Worlds of Hugh Everett," Scientific American, December, 2007, 98–105.
28. John Horgan, "The Pied Piper of Superstrings," Scientific American, November, 1991, 42-47 .