The Eternal Flame is a hard science-fiction novel by Australian author Greg Egan and the second part of the Orthogonal trilogy. The novel was published by Night Shade Books on 26 August 2012 with a cover art by Cody Tilson and by Gollancz on 8 August 2013 with a cover art by Greg Egan. [1] [2] [3] The novel describes the journey of the generation ship Peerless, which has departed in The Clockwork Rocket , [4] [5] [6] and the development of new technology as well as changes of the society on board. An essential task is the construction of an engine not needing any fuel to generate thrust, but instead perfectly balancing out the radiation it emits with the energy this generates. To make such a process work, the universe of the novel is based on a Riemannian instead of a Lorentzian manifold (which describes our own universe, where emitting radiation instead consumes energy), changing the rules of physics. The details are described by Greg Egan on his website. [7] The story is continued in The Arrows of Time. [8] [9] [10]
Three generations after the departure of the Peerless from the home world, the ever increasing population (which can't be controlled due to spontaneous reproduction) overstreches its limited capacities. For a drastic solution, newborns are euthanized. The long mission of research is continued in the meantime: Tamara, an astronomer, studies an object on a course close to the Peerless and plans to dispatch the spacecraft Gnat to it. Carla, a physicist, studies light and finds a seemingly perfect ratio of five to four in one of her experiments. It has already been discovered that Nereo's equation (corresponding to the Maxwell equations) makes wrong predictions. She conducts further experiments with her students to gather more data. Patrizia, one of these students, later goes over the mathematics of collisions and comes up with the hypothesis of quantization for particles of light, later known as Patrizia's principle (corresponding to the Planck relation). She proposes luxites as names for the quanta after the luxagens causing them and an already proposed idea by an ancient philiosopher without evidence. Carla renames them into photons to avoid confusion. First surprised by the ingenius idea, which explains the data and in which an integer number of photons is necessary to give the luxagens enough energy to leave an energy valley, she soon notices some problems. She had studied wavelengths for which four or five photons carry enough energy and now wants to conduct new experiments for which six are necessary.
Carlo, a biologist, measures signals used by animals and himself to shapeshift their bodies. Previously it has been discovered through coloring, how their flesh can end up in different parts of their limbs during this process, giving rise to the question about how the ever changing communication with the brain works. Special attention is given to the signals by males to initiate reproduction. There are two kinds of species, where the females either divide in two or four children (biparteous and quadruparteous, latter of which is their own species). Carlo intends to measures those signals and swap them, potentially transferring the division into only two children artificially to their own species, solving the population crisis. Their way of reproduction also poses a problem to Tamaro, the co of Tamara and therefore supposed to trigger hers, who doesn't want her to go on board the Gnat and hence risk the lives of their children. Together with their father Erminio, he imprisons Tamara and spreads news about her having given birth on the Peerless. Tamara can persuade Tamaro with a deal to let her go free and later joins the mission on the Gnat with Carla and Ivo. They cause an almost fatal detonation for them near the Object, pushing it on an almost parallel course with the Peerless, It turns out, that the thermodynamic arrow and the arrow of entropy decrease of the Object point in the opposite directions and hence contact of any matter from the Peerless with the Object would again result in a detonation.
Carlo travels through the forest section inside the Peerless to catch the four arborines (two pairs of cos) for experiments. He then records the light signal of Zosimo when triggering the splitting of Zosima in two children and then sends it into one half of Benigna to mimick Benigno triggering her splitting. Benigna sheds a single female child and survives the birth injured. A successful experiment on their own species could turn the next election around, but time is running out. When this achievement is made public on the Peerless some males, fearing their upcoming extinction, set the entire forest on fire. Tamara, not wanting them to have the last word with violence, but knowing about the fatal consequences of Carlo's last experiment, agrees to have the arborine signal transmitted into a part of her body. She also sheds a single female child, who she named Erminia after her mother, and survives injured. Message of the birth is made public and swings the vote around, making the new technology available for every female choosing it and hence solving the population crisis.
Carla revisits some of the newly discovered physics and is saddened by the fact, that her legacy will ultimately only be to have taught Patrizia, whose name will go down in history with Patrizia's principle. She does some sketches involving an atom with three different orbitals as well as the emission and absorption of photons, one of which is reflected by a moving mirror to change its frequency, and finally realizes to just have come up with a process to make the eternal flame possible. Some time later, the space probe Eternal Flame is dispatched into space to demonstrate the engine indeed working, solving the fuel crisis. Some others, including Tamara and her daughter Erminia, are also watching. Carlo tells Carla to be delighted to have saved her life with his new technology, but she refuses to immediately make use of it, as she rather wants to wait what the new day will bring.
Due to Greg Egan begin very popular in Japan, the novel was released by Hayakawa Publishing in Japanese as エターナル・フレイム (etānaru fureimu, direct transcription of the original English title into Katakana) in 2016. [11] The translation was done by Makoto Yamagishi (山岸真) and Toru Nakamura (中村融). [12] [13]
The novel was a Locus Award Nominee for Best SF Novel in 2013 and reached the 20th place. [14]
The consequences of the sign change in the metric on the laws of physics are explained in detail (with illustrations and calculations) on Greg Egan's website. [15] The correspondence of the principles presented in the novel with those in our universe are explained in the afterword of the novel.
One insight about the Riemannian universe described in the novel is the description of Dirac spinors, the solutions of the Dirac equation, by quaternions. A similar mathematical description is not possible in a Lorentzian universe like ours. Dirac matrices are defined using the underlying metric in their anticommutator relation . [16] Switching a sign in the metric results in the corresponding Dirac matrix to be multiplied with the imaginary number . This is known as the Wick rotation relating Riemannian with Lorentzian geometry through the concept of imaginary time. Dirac matrices (and hence Dirac spinors) in a four-dimensional spacetime are four-dimensional, but there is no connection between the numbers. In a five-dimensional spacetime, they would also be four-dimensional. Quaternions are composed out of four real numbers and therefore also four-dimensional. This makes it possible to formulate the Dirac equation in a Riemannian universe entirely with quaternions. The calculations are described by Greg Egan on his website. [17]
The Dirac equation also provides another important concept for the novel. As it is constructed as a square root of the Klein–Gordon equation (a relativistic generalization of the Schrödinger equation), the energies of its solutions are affected by the same problem as the square roots of positive numbers, which is the ambiguity of the sign. [18] This led to the theoretical discovery of antimatter in 1928 [16] before the first observation of a positron (the antiparticle of the electron) in 1932. [19] But as negative energy poses certain problems in further calculations, the negative sign is often shifted to time using the uncertainty principle of energy and time. [18] This interpretation in quantum field theory of antimatter traveling backward through time is known as the Feynman–Stückelberg interpretation. [20] [21] Ordinary matter and antimatter colliding results in their total annihilation, [22] [23] which happens in the novel and explained with the opposite arrows of time. [24] A different situation arises in the sequel The Arrows of Time after the Peerless has turned around and inverted its own arrow of time.
David Brin, Hugo and Nebula Award-winning author of Earth and Existence, claims that „Greg Egan is a master of 'what-if' science fiction". His „characters work out the implications and outcomes as they struggle to survive and prevail″ and he presents „the most original alien race since Vernor Vinge's Tines“. [25]
Jerry Oltion, Nebula Award-winning author of Abandon in Place, claims that „when most people switch a minus sign for a plus, they re-do the math. Egan re-does the entire universe.“ [25]
Karen Burnham, writing in Strange Horizons , says that „the physics is mind-blowing“ and that „Egan develops almost all of the ideas in the story through dialogue. Some people may say that when the dialogue occurs the action grinds to a halt. However, it's clear that in these novels, the dialogue is the action.“ Concerning the struggles with reproduction, she writes that „more than any Egan story to date, the books of the Orthogonal trilogy place science in a broader social context“. [26] In a review of the sequel The Arrows of Time , she adds that „in order to get there, we tour through a huge amount of speculative world building, physics, biology, and sociology.“ [27]
A french review by Éric Jentile was published in print in Bifrost, #88 in October 2017. [28]
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.
In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles, called "Dirac particles", such as electrons and quarks for which parity is a symmetry. It is consistent with both the principles of quantum mechanics and the theory of special relativity, and was the first theory to account fully for special relativity in the context of quantum mechanics. It was validated by accounting for the fine structure of the hydrogen spectrum in a completely rigorous way. It has become vital in the building of the Standard Model.
In physics, charge conjugation is a transformation that switches all particles with their corresponding antiparticles, thus changing the sign of all charges: not only electric charge but also the charges relevant to other forces. The term C-symmetry is an abbreviation of the phrase "charge conjugation symmetry", and is used in discussions of the symmetry of physical laws under charge-conjugation. Other important discrete symmetries are P-symmetry (parity) and T-symmetry.
In quantum field theory, the Dirac spinor is the spinor that describes all known fundamental particles that are fermions, with the possible exception of neutrinos. It appears in the plane-wave solution to the Dirac equation, and is a certain combination of two Weyl spinors, specifically, a bispinor that transforms "spinorially" under the action of the Lorentz group.
In theoretical physics, a chiral anomaly is the anomalous nonconservation of a chiral current. In everyday terms, it is equivalent to a sealed box that contained equal numbers of left and right-handed bolts, but when opened was found to have more left than right, or vice versa.
In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magnetic moment is −9.2847646917(29)×10−24 J⋅T−1. In units of the Bohr magneton (μB), it is −1.00115965218059(13) μB, a value that was measured with a relative accuracy of 1.3×10−13.
In mathematical physics, the gamma matrices, also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts. This in turn makes it possible to represent infinitesimal spatial rotations and Lorentz boosts. Spinors facilitate spacetime computations in general, and in particular are fundamental to the Dirac equation for relativistic spin particles. Gamma matrices were introduced by Paul Dirac in 1928.
In differential geometry and mathematical physics, a spin connection is a connection on a spinor bundle. It is induced, in a canonical manner, from the affine connection. It can also be regarded as the gauge field generated by local Lorentz transformations. In some canonical formulations of general relativity, a spin connection is defined on spatial slices and can also be regarded as the gauge field generated by local rotations.
In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity. It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic theory was outlined by Bryce DeWitt in a seminal 1967 paper, and based on earlier work by Peter G. Bergmann using the so-called canonical quantization techniques for constrained Hamiltonian systems invented by Paul Dirac. Dirac's approach allows the quantization of systems that include gauge symmetries using Hamiltonian techniques in a fixed gauge choice. Newer approaches based in part on the work of DeWitt and Dirac include the Hartle–Hawking state, Regge calculus, the Wheeler–DeWitt equation and loop quantum gravity.
In the theory of general relativity, a stress–energy–momentum pseudotensor, such as the Landau–Lifshitz pseudotensor, is an extension of the non-gravitational stress–energy tensor that incorporates the energy–momentum of gravity. It allows the energy–momentum of a system of gravitating matter to be defined. In particular it allows the total of matter plus the gravitating energy–momentum to form a conserved current within the framework of general relativity, so that the total energy–momentum crossing the hypersurface of any compact space–time hypervolume vanishes.
The harmonic coordinate condition is one of several coordinate conditions in general relativity, which make it possible to solve the Einstein field equations. A coordinate system is said to satisfy the harmonic coordinate condition if each of the coordinate functions xα satisfies d'Alembert's equation. The parallel notion of a harmonic coordinate system in Riemannian geometry is a coordinate system whose coordinate functions satisfy Laplace's equation. Since d'Alembert's equation is the generalization of Laplace's equation to space-time, its solutions are also called "harmonic".
In mathematical physics, spacetime algebra (STA) is the application of Clifford algebra Cl1,3(R), or equivalently the geometric algebra G(M4) to physics. Spacetime algebra provides a "unified, coordinate-free formulation for all of relativistic physics, including the Dirac equation, Maxwell equation and General Relativity" and "reduces the mathematical divide between classical, quantum and relativistic physics."
Orthogonal is a science fiction trilogy by Australian author Greg Egan taking place in a universe where, rather than three dimensions of space and one of time, there are four fundamentally identical dimensions. While the characters in the novels always perceive three of the dimensions as space and one as time, this classification depends entirely on their state of motion, and the dimension that one observer considers to be time can be seen as a purely spatial dimension by another observer.
The Clockwork Rocket is a hard science-fiction novel by Australian author Greg Egan and the first part of the Orthogonal trilogy. The novel was published by Night Shade Books on 1 July 2011 with a cover art by Cody Tilson and by Gollancz on 15 September 2011 with a cover art by Greg Egan. The novel describes an alien civilization being threatened by the appearance of hurtling meteors entering their planetary system with an unprecedented speed and the implementation of an unusual plan: All the technology needed for an effective defense shall be developed on board of a generation ship launched into the void while only a few years pass back on the home world in the meantime due to time dilation. This is possible due to different laws for space and time in this universe, in which they have the same signature instead of different ones, or which is alternatively described by a Riemannian instead of a Lorentzian manifold. The consequences on some of the physical concepts needed in the novel including time dilation and radiation, are described by Greg Egan with diagrams in the novel and also his website. The story is continued in The Eternal Flame and The Arrows of Time.
In quantum field theory, the nonlinear Dirac equation is a model of self-interacting Dirac fermions. This model is widely considered in quantum physics as a toy model of self-interacting electrons.
In mathematical physics, the Dirac equation in curved spacetime is a generalization of the Dirac equation from flat spacetime to curved spacetime, a general Lorentzian manifold.
In comparison with General Relativity, dynamic variables of metric-affine gravitation theory are both a pseudo-Riemannian metric and a general linear connection on a world manifold . Metric-affine gravitation theory has been suggested as a natural generalization of Einstein–Cartan theory of gravity with torsion where a linear connection obeys the condition that a covariant derivative of a metric equals zero.
In mathematical physics, the Gordon decomposition of the Dirac current is a splitting of the charge or particle-number current into a part that arises from the motion of the center of mass of the particles and a part that arises from gradients of the spin density. It makes explicit use of the Dirac equation and so it applies only to "on-shell" solutions of the Dirac equation.
The Arrows of Time is a hard science-fiction novel by Australian author Greg Egan and the third part of the Orthogonal trilogy. The novel was published by Gollancz on 21 November 2013 with a cover art by Greg Egan and by Night Shade Books on 5 August 2014 with a cover art by Cody Tilson. The novel describes the return journey of the generation ship Peerless, which has been launched in The Clockwork Rocket and traveled into the void in The Eternal Flame, and the reverse enabling the construction of a device to receive messages from the own future as well as the journey to a world where time runs in reverse. The universe of the novel is therefore based on a Riemannian instead of a Lorentzian manifold, changing the rules of physics. The details are described by Greg Egan on his website.
Dichronauts is a hard science-fiction novel by Australian author Greg Egan. The novel was published by Night Shade Books on 11 July 2017. It describes a universe with two time dimensions, one of which corresponds to the time perception of the characters while the other influences their space perception, for example by rotations in this directions to be impossible. Hence a symbiosis of two life forms is necessary, so that they can even see in all directions. Furthermore, many fundamental laws of physics are altered crucially: Objects can roll uphill or not fall over any more when oriented suitably. There is negative kinetic energy and a fourth state of matter. Planets are no longer spherical, but hyperbolic and therefore have three separate surfaces. Egan describes these details on his website.