Janus Cosmological Model & FTL travel (and how to introduce negative mass in GR)

• Janus Cosmological Model & FTL travel (and how to introduce negative mass in GR) by flux_capacitor on 03 Aug, 2017 14:22
• In order to not hijack other threads dealing with the various theories regarding theoretical FTL travel, I have made this thread dedicated to present a particular framework:
  
  
  
  The Janus Cosmological Model (JCM) theoretically makes FTL interstellar travel possible, with limited energy source and journey duration compatible with human's lifespan. In order to understand how FTL travel is made possible in the model (superluminal speed being "apparent" and does not actually imply travelling over the speed of light, you'll see why) I have to first present its physical and mathematical foundations.
  
  Indeed, although the Janus model is based on Einstein's general relativity and does not make use of quantum mechanics, it represents a straight departure from current theories, in various aspects :
  
  Mainly, the JCM uses two coupled Einstein field equations instead of one:
  
  
  
  
  
  Giving several metrics to a single manifold is perfectly legit for mathematicians and geometers.
  This system of two coupled field equations introduces negative mass in cosmology with no paradox.
  
  The JCM described the universe as an M4 manifold with two conjugate Riemannian metrics, each one having its own family of geodesics, its own speed of light and where the length between two distant points can be measured as two different distances, according to the metric that is considered. A didactic 2D image:
  
  
                                              A 2D surface with two different scales
  
  Classically, when one wants to introduce negative mass in GR, the Newtonian approximation (which gives gravitational potentials and interaction laws between positive and negative mass species) gives rise to the unmanageable runaway paradox:
  
  
  1- Positive mass attracts positive mass
  2- Positive mass moves away from negative mass which chases it
  3- Negative mass repels negative mass
  
  The second interaction is called the runaway motion (first described by Hermann Bondi in 1957): the couple would then indefinitely accelerate, while its total kinetic energy would remain constant! This is why negative mass is not seriously considered in general relativity.
  
  This is because the single Einstein Field Equation only describes one side (one metric) for spacetime.
  
  The Janus cosmological model on the contrary implies two sides of the same coin. The motion of positive mass particles and the motion of negative mass particles do not occur in the same sector. Each species evolves along its own family of geodesics, in its own metric. It is as if spacetime had a recto and a verso. Negative mass is among us, but invisible to us, because negative mass emits negative energy photons that follow null geodesics of the metric g^(-) distinct from the family of geodesics of our metric g⁽⁺⁾. It is as if this negative mass was being located "on the other side of the sheet".
  
  Starting from the two coupled field equations of the Janus model, the Newtonian approximation gives new interaction laws that differ from the classical Newtonian approximation calculated after the single field equation of general relativity:
  
  
  1- Positive mass attracts positive mass
  2- Positive mass and negative mass repel each other (no runaway motion!)
  3- Negative mass attracts negative mass (negative mass is not self-repulsive!)
  
  The runaway paradox disappears.
  In the JCM, mass is not intrinsically positive or negative, as this concept becomes relative: it depends on which metric you are looking from.
  
  The two coupled field equations reduce to the Einstein field equation for regions of spacetime where positive mass density largely dominates, i.e. where almost all negative mass has been repelled away by the local concentration of positive mass matter (for example on Earth or in the solar system).
  
  Therefore the Janus model encompasses Einstein's general relativity, as general relativity encompassed Newtonian dynamics when considering low speeds v ≪ c and small curvatures.
  
  

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  The two "sheets" of this same universe have opposite arrows of time, like Sakharov's model where they both originate from the same Big Bang singularity:
  
  
  
  The origin where the arrow of time reverses is called the Janus Point (see also Julian Barbour's work on the same subject).
  
  The name of the model comes from this distinctive characteristic, as the Romanian god Janus "looks to the future and to the past at once":
  
  
  
  

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  The model also integrates a variable speed of light (VSL) framework, and more exactly a joint variation of all physical constants during the highest energy density state of the radiation-dominated era of the universe (just after the Big Bang) as a generalized gauge process, keeping all physical equations invariant.
  
  
  
     Excerpts of "Faster Than Light", JP Petit's science comics in the series of "The Adventures of Archibald Higgins"
  
  This primitive "variable constant regime" allows the arrow of time to reverse at the origin and connects the two sheets together at the Big Bang. It also explains the homogeneity of the primitive universe, without resorting to inflation.
  
  The model finally offers an alternative interpretation to the stellar black hole, i.e. when a neutron star reaches its critical mass. How physical constants behave at the Big Bang, what is going on in the center of a neutron star reaching criticality, and the possibility of FTL interstellar travel, are tightly related and will be explained further.
  
  The introduction of negative mass in cosmology, handled by two coupled field equations, could at first appear as lacking of "parsimony" according to Occam's razor. But take into account that the Janus model challenges the standard ΛCDM "concordance" model, which requires these additional tweaks:
  - The presence of invisible astroparticles of "dark matter" of unknown nature, to justify the anomalous galaxy rotation curves and gravitational lensing effects.
  - The presence of an invisible "dark energy" of unknown nature (resulting from the addition of a cosmological constant to the Einstein field equations) to justify the acceleration of the expansion of the universe.
  - The adjustment of six free parameters to fit with observational data.
  - The inflation hypothesis, with its inflaton field, invented to justify the homogeneity and isotropy of the primitive universe.
  
  The universe is no longer described as in the days of Einstein, Schwarzschild, Hilbert… who could elegantly explain the anomalous observations of that time (precession of the perihelion of Mercury, deflection of light by the Sun…) with exact solutions to general relativity. Nowadays the universe has become some kind of a recipe where 95% of its ingredients are of unknown nature:
  
  
  
  Well, the Janus model still uses plain-vanilla GR, but does not need such ingredients, although it naturally fits with observations. Unlike other alternative gravity theories like MOND, emergent gravity, MiHsC… the Janus model does not have to modify Newton's law according to some distance, nor rely on some unproved quantum phenomena. However it could be integrated in (is compatible with) other GR theories like the Gravitational Absorber Theory (modern version of the Hoyle-Narlikar theory of gravity), to cite only one example.
  
  See the wikipedia section about the Janus cosmological model for a summarized description of the theory and to download peer-reviewed papers cited in references, in particular the last four papers (published in 2014 and 2015).
  
  I attach two science comics below, made by Dr Petit in 2008 to popularize this 40-year-long work: the first presenting this bimetric approach (The Twin Universe) and the second one the VSL aspects of the model (Faster Than Light). Both comics include at the end a scientific appendix for physicists and mathematicians.
  
  Before reading the various peer-reviewed papers, these two documents are a good start to learn the basis of the theory, along the YouTube videos subtitled in English that Dr Petit is now making on YouTube, presented in the next post.
  
  

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  • For the problem of the introduction of negative mass in cosmology and how the Janus model resolves the Runaway paradox, and why T-symmetry reverses the mass of a particle, see this prior post I made in another thread.
  
  • For Sakharov's model about two mirror universes with opposite arrows of time as a solution to the baryon asymmetry of the universe, CPT symmetry, CP violation during baryogenesis and the missing primordial antimatter (theory included in the Janus model) see this prior post. It also describes the nature of the four types of matter (positive mass matter and positive mass antimatter, as well as negative mass matter and negative mass antimatter).
  
  • The negative pressure content of the universe drives the accelerating cosmic expansion. To learn why such a negative pressure is caused by the negative energy density of the universe's second sector, i.e. because of the global distribution of negative mass matter in the universe (and NOT because of some "repulsive power of the vacuum" of positive energy that classically results from the addition of a cosmological constant): see this post.
  
  • To see how the Janus model fits so well with latest observational data showing an accelerating expansion, the result being an exact solution with no had hoc parameter, see this post.
  
  If you have any comment on the theory (that would be welcomed!) please comment in this dedicated thread from now on.

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  The Twin Universe.pdf

  Faster Than Light.pdf
• #1 by flux_capacitor on 03 Aug, 2017 14:23
• NEW 2017 VIDEOS
  
  Astrophysicist Jean-Pierre Petit, 80 years old in 2017, is now making a series of Youtube videos to popularize the Janus cosmological model and explain the basic concepts.
  
  There are 27 videos to date but the 11 first ones rather talk about the history and evolution of astrophysics and cosmology through time, from antiquity to modern days. The foundations of the Janus model are broached from video #12.
  
  In order to share and expand the Janus model among scientists outside of France, where the climate is not favorable to the birth of novel ideas in cosmology, Dr Petit has decided to subtitle his videos in English. The difficulty is not to answer critics (critics are welcomed), but to be heard above the ambient noise, including the noise generated by trending theories backed up by the media. The difficulty is to be read, and most importantly to be understood. If Dr Petit manages to explains his model in various international conferences he plans to attend, and share his videos directly with the people interested, maybe an international collaboration with other scientists over the world could be triggered.
  
  By the way, you can post here but also post questions in the comment section of YouTube under each video, as JP Petit read the posts there, and as he speaks and write English he could answer.
  
  Here is the Janus English YouTube playlist: https://goo.gl/MnGTHa
  
  And its description:
  
  

  Quote from: Jean-Pierre Petit

  In this series of videos, astrophysicist and cosmologist Jean-Pierre Petit explains the Janus Cosmological Model.
  
  JCM is a bimetric theory of gravity based on general relativity with a system of two coupled field equations, involving the presence of positive and negative masses in cosmology.
  
  It describes the universe as an M4 manifold with two metrics. The first metric g⁽⁺⁾ or "positive sector" refers to a family of geodesics with positive mass and positive energy particles, while the second metric g^(-) or "negative sector" refers to another family of geodesics with negative mass and negative energy particles. Negative mass particles emit negative energy photons that follow null geodesics of the metric g^(-) hence cannot be seen.
  
  The Newtonian approximation provides the interaction laws: particles whose masses own the same sign mutually attract through Newton's law, while particles whose masses have opposite signs mutually repel through anti-Newton's law. This solves the unmanageable Runaway paradox, which arises when one tries to include negative masses in Einstein's model.
  
  Like Andrei Sakharov's model, the second sector is a CPT symmetry of the first one, linked together by the Big Bang, and explains the apparent lack of primordial antimatter.
  
  Dynamical group theory demonstrates that the reversal of the arrow of time equals energy inversion, and provides the nature of negative species.
  
  The negative sector contributes to the gravitational field and negative pressure and replaces both dark matter and dark energy of the concordance model and its six free parameters, without ant ad hoc parameter.
  
  The model challenges dark matter as it explains the formation of galactic spiral structures, their confinement and their anomalous rotation curves. It also explains the formation of galaxy clusters and the large-scale structure of the universe, the giant voids and the Dipole Repeller effect. Mirage effects around galaxies and galaxy clusters are due to a negative gravitational lensing effect.
  
  The model challenges dark energy, giving an exact solution referring to the matter-dominated era, which exhibits an accelerating expansion process for positive species and fits very well with available observational data.
  
  During the radiation-dominated era, the universe undergoes a variable constants regime, with a variation of the speed of light (VSL) and of all the constants of physics, involved in a generalized gauge process. Then the horizon grows like the space scale factor. This explains the homogeneity and isotropy of the primitive universe with no need to resort to the inflation hypothesis and the inflaton field.
  
  The two sectors have different speeds of light and scale factors. If a space probe could achieve a mass inversion process and cruise at a relativistic velocity following geodesics of the negative sector, the travel duration could be three orders of magnitude shorter than a corresponding conventional relativistic trip in the positive sector. The model suggests that interstellar travel in a limited time inferior to human's lifespan becomes theoretically possible.
  
  The Janus model has been published in peer reviewed scientific journals.

  
  I will edit this post with more of the previous Janus videos once they are subtitled in English. Here they are (expand videos fullscreen to display subs correctly):
  
  • JANUS 13: Dynamical group theory. Time reversal equals energy inversion
  Time reversal goes with inversion of energy and mass. Consequence: there are two kinds of antimatter, of opposite mass. The invisible components of the universe are copies of classical particles, but with negative energy and mass.
  
  
  
  
  

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  • JANUS 14: A bit of geometry first. The negachip curvature
  The physical foundations of the Janus Cosmological Model involves familiarizing the audience first with the geometry aspects resulting from the introduction of negative masses in cosmology.
  
  
  
  
  

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  • JANUS 15: Two coupled field equations instead of one
  The two coupled field equations of the Janus Cosmological Model. Geometrical notion of positive and negative curvatures. Newtonian approximation and interaction laws of positive and negative masses.
  
  
  
  
  

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  • JANUS 16: Why the cosmic expansion is accelerating
  How the Janus Cosmological Model explains the accelerating cosmic expansion, challenging dark energy. The accelerating expansion is caused by the negative pressure of the invisible negative mass content of the universe. The nature of such negative energy constituents is described and incidentally identifies the nature of the mysterious dark matter and the missing primordial antimatter.
  
  
  
  
  

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  • JANUS 17: The only consistent interpretation of the Great Repeller
  The Janus Cosmological Model provides the only consistent interpretation of the Dipole Repeller. It also explains the flat rotation curves of galaxies, their confinement and their spiral structure, as well as the large-scale structure of the universe, challenging dark matter. Mirage effects around galaxies and galaxy clusters are due to a negative gravitational lensing effect.
  
  
  
  

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  • JANUS 18: Why the primitive universe is so homogeneous
  The current standard model justifies such homogeneity with a cosmic inflation due to an inflaton field. We present another explanation, already published in Modern Physics Letters A in 1988 and in 1995 in Astrophysics and Space Science. During the radiation-dominated era, the universe undergoes a variable constants regime, with a variation of the speed of light (VSL) and of all the constants of physics, involved in a generalized gauge process. Then the horizon grows like the space scale factor.
  
  
  
  
  

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  • JANUS 19: The speed of light had to be infinite at the Big Bang
  Sakharov's model can't be geometrized with a constant speed of light, which must be infinite at the Big Bang. The arrow of time becomes zero then reverses. The initial singularity is cancelled and replaced by a structure shown to have an elliptic geometry. The question of time near the Big Bang becomes meaningless and chronology is identified with entropy.
  
  
  
  
  

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  • JANUS 20: Falsifiability of the theory with negative weak lensing
  Any model should be "falsifiable" in the sense of Popper, i.e. it has to propose a test able to disprove or confirm the theory. Such a test of the Janus Cosmological Model, based on a negative weak gravitational lensing effect, is presented.
  
  
  
  
  

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  • JANUS 21: Dark matter, about time to break the deadlock
  A 30-year sterile quest after dark matter and supersymmetry. Pierre Salati, theoretical physicist at LAPTh, CNRS, says what others only think: they no longer believe. He concludes that we have to look in other directions.
  
  
  
  
  

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  The next video JANUS #22 is a big one as it is split into 5 parts. It deals with the Schwarzschild original solution, historically and mathematically, and exposes the problem with the classical black hole model, and offers a new interpretation. This mini video series will have its own dedicated post below once it has been subtitled in English.
• #2 by flux_capacitor on 14 Sep, 2018 17:52
• This has taken some time but Janus #22 "Black hole VS mass inversion" parts 1, 3, 4 and 5 are now available with English subtitles.
  
  Part 1- 2017 meetings. Negative energy states.
  
  
  
  
  
  

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  Part 2- Geometry, the part of the real and the imaginary
  (no English sub yet for this one)
  
  
  
  
  

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  Part 3- The Schwarzschild solutions.
  
  
  
  
  

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  Part 4- The Kerr metric. Finite time implosion with radial frame-dragging.
  
  
  
  
  

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  Part 5- Gravitational waves. The Leaking Neutron Star model.
  
  
• #3 by flux_capacitor on 14 Sep, 2018 18:09
• Dr Jean-Pierre Petit made a 20mn presentation through video-conference at the Estes Park Advanced Propulsion Workshop, 14 September 2018. Here is the recorded video explaining how negative energy and mass inversion can make apparent faster-than-light interstellar travel possible, as well as some speculative technical solutions for the spaceship.
  
  Various links under the video presentation on YouTube are available, to go further on the subject of mass inversion and FTL travel after this popularized introduction.
  
  
  
  During the short Q&A time following the video broadcast, some surprise has been shared about the peculiar saucer shape presented for the spaceship at 18mn50s
  Beside the rotation mandatory for the electrostatic charges to create a magnetic field, JP Petit answered that this saucer shape has actually something to do with MHD flow control during atmospheric flight, and he talked about peer-reviewed papers he published about shock wave cancellation by Lorenz force fields at supersonic speeds. As some of the attendees were interested in this research in magnetohydrodynamics, here are these papers:
  http://www.jp-petit.org/papers/MHD/
  
  [2019 UPDATE]: The link to the lengthy paper that was sent to Dr Fearn for the proceedings of the Estes Park workshop (more interesting than the short video): "Negative energy states and interstellar travel", attached below.

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  Negative energy states and interstellar travel.pdf
• #4 by colbourne on 16 Sep, 2018 13:30
• https://forum.nasaspaceflight.com/index.php?topic=13542.0
  
  http://alpha.web.cern.ch/
  
  
  The Alpha experiment at CERN is looking in to anti-matter an how it behaves relative to normal matter and might help in determining whether these theories  are possible.
  
  
  
  
• #5 by flux_capacitor on 16 Sep, 2018 14:22
• Quote from: colbourne on 16 Sep, 2018 13:30

  https://forum.nasaspaceflight.com/index.php?topic=13542.0
  
  http://alpha.web.cern.ch/
  
  
  The Alpha experiment at CERN is looking in to anti-matter an how it behaves relative to normal matter and might help in determining whether these theories  are possible.
  

  
  Thanks for this input. There is also the GBAR experiment to weight antimatter:
  https://home.cern/about/updates/2017/03/raising-gbar-antimatter-exploration
  
  The Janus model makes a prediction regarding all these experiments: such antimatter created in the lab, which has a positive energy hence positive mass, will simply fall down in the Earth gravitational field.
  
  According to Sakharov's theory, then the Janus cosmological model, there are not one but two kinds of antimatter:
  - C-symmetry antimatter (predicted by Paul Dirac): the antimatter created in lab. It has a positive energy and positive mass. It falls down in a gravity well.
  - PT-symmetry antimatter (predicted by Richard Feynman and Andrei Sakharov): this is the missing cosmological antimatter, which is invisible and populates the negative, antichronous sector of the universe. It has a negative energy and negative mass due to T-symmetry. I would "fall up" in the Earth gravitational field.
  
  PT-symmetry antimatter is invisible to us because it has a negative energy, thus it emits negative energy photons, which follow their dedicated null-geodesics of the negative metric of the universe. Our eyes and optical instruments are not equipped to see these negative energy photons.
  
  To better understand how negative energy particles are created and populates the negative sector, the following picture is an explanation of Sakharov's theory about CP violation and the matter–antimatter imbalance in the universe (see the Sakharov part in the Wikipedia article about CP violation):
  
  
  
  If we apply an orthochronous (positively-directed time) lecture of events to the whole diagram, we can consider that:
  
  Dominant particles at t < 0, made of an excess of antiquarks of negative energy, pass "one through the other" at the instant t = 0 when the density is infinite (classically considered as the Big Bang), and decay with an excess of quarks of positive energy when t > 0, realizing total CPT symmetry of the universe.
  
  All the phenomena at t < 0 are assumed in this hypothesis to be CPT reflections of the phenomena at t > 0.
  
  In other words:
  
  • Positive energy antimatter (blue) made of a minority of antiquarks of positive energy at t > 0 has been annihilated with positive energy matter in excess (red), which is the only species remaining in our sector.
  
  • Opposite CP violation at t < 0 where negative energy matter (green, CPT-symmetry wrt our matter), made of a minority of quarks of negative energy, is annihilated with negative energy antimatter in excess (purple, C×CPT = PT symmetry wrt our matter), which is the only species remaining in the negative sector.
  
  Arrow of times are opposite in the two sectors.
  Time flows always with increasing entropy away from the instant t = 0.
  
  The antimatter recreated in the lab is the blue species, of positive energy and mass.
  However, if a mass inversion process was discovered and tested in a laboratory, we could invert the energy of particles. Upon energy inversion, such negative mass particles would immediately be repulsed by the Earth gravitational field and "fall up". But having become invisible due to T-symmetry, they would seem to have completely disappeared in front of us and our instruments, being transferred in the negative sector. They would still interact through gravitation, though. And the mass inversion process would be accompanied by the emission of gravitational waves that could be detected with some sensitive instruments nearby, LIGO-like.
• #6 by colbourne on 17 Sep, 2018 03:16
• I will be looking forward to hearing the results from the AEGIS and GBAR experiments. It could answer lots of questions when we find out how gravity effects antimatter. It is possible that not all antimatter particles will respond the same way, and it may also be the case that there are some normal matter particles that will also behave differently.
• #7 by flux_capacitor on 04 Oct, 2018 23:39
• New website under construction, gathering information and bibliography about the Janus model:
  
  http://www.januscosmologicalmodel.com
• #8 by Baadlyy on 17 Oct, 2018 10:04
• A quick question,
  what about time dilatation for particle or objects travelling close to the speed of c(-) in the "negative" sector ? 
  Thanks
  Alex
• #9 by flux_capacitor on 17 Oct, 2018 13:01
• Quote from: Baadlyy on 17 Oct, 2018 10:04

  A quick question,
  what about time dilatation for particle or objects travelling close to the speed of c(-) in the "negative" sector ? 
  Thanks
  Alex
  

  
  Excellent question. Considering that the ratio of the two space scale factors (warp factor) a^(-)/a⁽⁺⁾ = 100, this gives a Lorentz factor α = 100 to calculate the velocity at which the ship has to appear to conserve energy. This velocity would be:
  
  v = (1-1/α²)^(1/2)×c = 99.995% of c
  
  c is here c^(-), which is 10× c⁽⁺⁾. So the speed of the ship would be about 2,997,775 km/s.
  
  Don't forget that distances to cover at such speed are divided by 100 according to the metric g_μν^(-) of the negative sector.
  
  If we consider there would be no special "time gauge effect" between the two sectors, so the traveler would take his proper time τ with him and this proper time would slow down for an earthly observer when the traveler moves at such a relativistic speed with the same magnitude with respect to the local speed of light c^(-), as it would slow down with the same percentage with respect to c⁽⁺⁾ (maybe this is not a valid hypothesis, but it seems fair a priori).
  
  As the velocity of the ship would be 99.995% of c^(-), and c^(-) = 10× c⁽⁺⁾, time dilatation for a one-way trip of 10 light-years (LYs) would give 1 year "lost" on Earth. As for the traveler's journey duration, it would be negligible (3.7 days). The fact that distances between two faraway points in the universe are shorter by a factor of 100 when they are measured in the negative sector is a game changer.
  
  So if we limit, in the beginning of our interstellar exploration, the majority of trips to distances within a radius of say, 20 light-years around the Earth, the "temporal cost" would be very acceptable (4 years max for each probe for a two-way trip). An acceptable exploration plan implying returns to Earth and steady exchanges between new worlds and our mother planet, compatible with human lifetime, could be considered up to a 100-lightyear radius, IMHO.
  
  Such interstellar express subway through the universe would not however allow the exploration of the whole galaxy (about 100,000 LYs across), which would take 100 years for a traveler to cross, and 10,000 years passed on Earth. Let alone trips to other galaxies…
  
  But to put things in perspective, when we take the number of stars around us, (taken as observations + probabilities using the average star density per cubic parsec according to the Gliese Catalogue of Nearby Stars), there are about:
  
  • 10 stars within 10 light-years from the Earth
  • 60 stars within 15 LYs
  • 200 stars within 25 LYs
  • 1,800 stars within 50 LYs
  • 15,000 stars within 100 LYs
  • 1.8 million stars within 500 LYs
  
  Even if we target only G-type (like the Sun) and K-type (orange dwarfs) star systems, which represents 20% of the list above, this seems enough to me
  
  Attached: table comparing time dilatation for travelers moving at 99.995% of c^(-) vs people on Earth. Distances are given in light-years according to our own metric g_μν⁽⁺⁾. Feel free to verify my calculus (I don't guarantee I made no mistake).

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• #10 by Baadlyy on 17 Oct, 2018 14:56
• Oh thanks ! didn't expect such precise answer but it was exactly what I was looking for !
  thanks again
   
• #11 by flux_capacitor on 27 Apr, 2019 10:32
• A sixth video in English has just been added to the Janus 22 series (which toped at 5 videos initially) dedicated to the black hole model, due to the first composite image of a "supermassive black hole" at the center of the galaxy M87 being released. This picture is presented in all media as a definitive proof of black holes. Dr Petit thinks it is a massive yet subcritical object made of a low-density plasma, remnant of a past active galactic nucleus, which is explained in the Janus cosmological model (first ever model of the quasar phenomenon).
  
  Such a subcritical object would emit photons (contrary to the event horizon of a black hole which should stay perfectly black) even if such radiation is considerably weaker than the one emitted by the relativistic accretion disk, which appears very bright in the composite image.
  
  This giant plasma ball does not collapse under its own gravitational weight, not because of its thermal counter-pressure within (it would be not enough) but due to the gigantic magnetic pressure B²/2µ₀ at its core, and the radial gradient of such pressure. Magnetic fields in these objects indeed defy imagination.
  
  If the object reaches criticity at some point (R > 0.94 Rs) then a mass inversion occurs at its center and the mass in excess is expelled away in the antichronous sector through the center surface throat acting as a one-way membrane, which quickly closes. Like a flapper-flush valve preventing water overflow in a toilet tank. Same mechanism as in the "leaking neutron star" model presented in the Janus video #22 Part 5 above.
  
  
• #12 by meberbs on 27 Apr, 2019 23:29
• I watched a bit of the latest video, but it did not seem worth the time to sit through the whole thing. (For example a bunch of time was wasted talking about how the first theoretical visualization (and some later ones) of a black whole used the simpler Schwarzschild metric rather than the more general Kerr metric, with wording making it sound like there is something wrong with this before dropping it saying "this is a minor detail" (which it is.))
  
  Some basic questions I would liketo see answered include:
  -Are there any actual testable and falsifiable predictions made? (for example a calculation of how bright the radiation from the "black" part of the image would be and whether that would be distinguishable from the noise in this measurement.)
  -What form of matter is the object supposedly made out of?
  -Where exactly does this supposed extremely large magnetic field come from, since the object as a whole is almost certainly neutral overall?
  -How does such a magnetic field produce the pressure needed to cancel the force of gravity, saying "big magnetic field" isn't enough. The object is less dense than air at sea level, by a factor of around 3 so it really doesn't make sense that such a large radius could be maintained by "magnetic pressure"
  
  -Finally, it seems important to him to claim that it might not be a black hole, why? Does the Janus model fail if it is shown that black holes exist?
• #13 by flux_capacitor on 28 Apr, 2019 19:18
• Quote from: meberbs on 27 Apr, 2019 23:29

  -Are there any actual testable and falsifiable predictions made? (for example a calculation of how bright the radiation from the "black" part of the image would be and whether that would be distinguishable from the noise in this measurement.)

  
  Not to my knowledge for now. If someday some radiation is indeed detected as being emitted in this place, although it shouldn't, one could argue it is due to some excited interstellar gas located not in the center of the object, but between the object and us. So more objects of this type should be studied, and obviously this is only the very beginning.
  
  

  Quote

  -What form of matter is the object supposedly made out of?

  
  This is a low-density ball of plasma, ionized interstellar gas and dust, the same type of matter found in all galaxies. Not a particular type of exotic matter if this is the sense of your question.
  
  

  Quote

  -Where exactly does this supposed extremely large magnetic field come from, since the object as a whole is almost certainly neutral overall?

  
  The fact is that scientists do not know exactly the origin of such magnetic field in (around) these object, they just acknowledge that there are magnetic fields there. see for example this recent (October 2018) NASA statement:
  "Magnetic Fields May Be the Key to Black Hole Activity" https://www.nasa.gov/feature/magnetic-fields-may-be-the-key-to-black-hole-activity
  
  Observations show very long and very thin plasma filaments there, that are arranged along poloidal formations (magnetic field lines generally perpendicular to the plane of the galaxy):
  
  
  
  I agree that a black hole should be neutral and I don't think that the ionized accretion disc, although rotating at relativistic speeds around, would produce such an axial magnetic field, as all charges within spin in the same direction, and the plasma is also neutral overall. But due to the extreme velocity, perhaps electrons radially separate from protons and the plasma becomes non-Maxwellian, I don't know. Researchers rather think the other way around, i.e. that the donut shape of the accretion disk is dictated by such magnetic field. But the origin of the magnetic field? They don't know.
  
  Kollatschny et al. (University of Göttingen, Germany) showed in 2015 that the quasar PG0043+039 has been measured to produce a magnetic field of 200 million gauss. That's quite strong. arXiv:1504.04271
  
  According to Petit, all non-active galaxies may have arisen from Seyfert galaxies having an active nucleus in the past, that would have calmed down. I don't know if you saw that Petit offers an explanation for the origin of such giant magnetic field at the center of active galaxies, from 17mn15s in the video Janus #22-6 you are talking about? Joint fluctuations of the two conjugate metrics in the Janus model produce density fluctuations which trigger radial density waves converging from the periphery of a galaxy toward its center. Such density waves ionize the intragalactic interstellar gas in their path, the plasma then radiates and becomes visible (as rings in Hoag's galaxies). A magnetohydrodynamic effect, when the magnetic Reynolds numbers is high, makes the magnetic field lines frozen-in: each plasma ring radially converging toward the center of the galaxy drags these magnetic field lines with it, focusing them at the center. As the magnetic flux is conserved, and although the galactic magnetic field is quite weak overall (a few microgauss only), it becomes enormous once completely focused. Then, if the phenomenon is powerful enough, it triggers fusion reactions at the core and the magnetic pressure ejects two plasma lobes at relativistic speeds, acting as a supersize particle accelerator (which would explain the quasar phenomenon, relatively small objects that yet radiate 1,000× more than the whole galaxy they lay in).
  
  
  
  Such metric fluctuations may calm down over time, eventually giving rise to intermittently active galaxies (like Cygnus A) then non-active galactic nuclei (like in our Milky Way). But all these objects have this strong magnetic field, its energy having being gathered from the whole galaxy and some of it having being converted into heat at the center. This magnetic flux compression mechanism and the radial plasma waves focusing at the center of galaxies are then what feed and trigger the birth of their central object.
  
  For a numerical estimation, take the Kollatschny et al. paper. For a numerical prediction for any galaxy, take the average value of the (low) magnetic field of that galaxy, and multiply by the ratio of the two surfaces (the surface area of the galaxy, the other one being the size of the object, e.g. π (3× Pluto orbit)²  in the case of M87. Either way, that is a lot of teslas.
  
  

  Quote

  -How does such a magnetic field produce the pressure needed to cancel the force of gravity, saying "big magnetic field" isn't enough. The object is less dense than air at sea level, by a factor of around 3 so it really doesn't make sense that such a large radius could be maintained by "magnetic pressure"

  
  I do not have calculations for the gravitational force pulling such an object inward so can't really answer your question.
  But as I said, magnetic pressure is equal to B²/2µ₀. Taking a magnetic field of 2×10⁴ teslas such as in the example above, the outward pressure at the center of the object is equal to almost 4×10¹³ pascals, i.e. nearly 400 millions times the standard atmospheric pressure at sea level.
  There is also a gradient of this magnetic pressure, as it is stronger at the center and weaker at the periphery of the object, so there is a radial force pushing the plasma outward, against its gravitational pull that tends to make it collapse. I agree precise calculations should be done.
  
  

  Quote

  -Finally, it seems important to him to claim that it might not be a black hole, why? Does the Janus model fail if it is shown that black holes exist?
  

  
  Quick answer is "no", but a longer answer would be "maybe yes"
  
  Quick answer: No, the Janus model could still be on track if black holes did actually exist. Afterall, it is a bimetric theory of gravity with two coupled field equations, so one could imagine it could produce black holes (stellar-size ones from critical neutron stars and supermassive ones in the center of galaxies) exactly like single-metric theories such as general relativity do.
  
  Long answer: The Janus model has two hypotheses departing from the mainstream lambda-CDM model based on GR (besides offering a different origin and identification for dark matter and dark energy):
  1- it has two CPT-symmetric spacetimes (obviously, as it is a bimetric theory) instead of a single one, as imagined first by Andrei Sakharov in 1967 to explain the baryon asymmetry of the universe.
  2- it considers a variable constant regime in the early universe as an alternative to cosmic inflation and its inflaton field, a mechanism allowing the cosmic horizon of the primitive universe to vary like R, hence accounting for its great homogeneity. This mechanism is triggered only during the high energy density state of the radiation-dominated era, at the very beginning of the universe, instead of the inflation moment in the concordance model. But this is not the only thing the variable constant regime does, as it is tightly related to the first point above, about the matter-antimatter imbalance.
  
  Andrei Sakharov considered a universe in perfect symmetry with no violation, in which the anomalous excess of quarks over antiquarks in our universe, that produced more matter than antimatter (CP violation) was offset symmetrically with an opposite CP violation in a second spacetime emerging from the same Big Bang origin (which Sakharov calls "the initial singularity Φ"), but with an opposite arrow of time (hence a second universe in complete CPT symmetry):
  
  "We can visualize that neutral spinless maximons (or photons) are produced at t < 0 from contracting matter having an excess of antiquarks, that they pass "one through the other" at the instant t = 0 when the density is infinite, and decay with an excess of quarks when t > 0, realizing total CPT symmetry of the universe. All the phenomena at t < 0 are assumed in this hypothesis to be CPT reflections of the phenomena at t > 0."
  
  Hence there is a remnant of matter in our positive (orthochronous) sector; and a remnant of (PT-symmetric) antimatter in the negative (antichronous) sector. The latter is the apparently lacking primordial antimatter.
  
  It is worth noting that such opposite arrow of time in this "second universe" does not make the local events run backward in time (consequences do not precede their cause). Indeed entropy is increasing away from t = 0, on both "sides" of the initial singularity Φ. Sakharov:
  
  "One may consider in cosmology not only later times than Φ, but also earlier times, but then the statistical properties of the state of the Universe at the instant Φ are such that the entropy increases not only going forward in time from this instant, but also going backward in time:
  dS/dt > 0,    S_(t) > S₍₀₎   for t > 0
  dS/dt < 0,    S_(t) > S₍₀₎   for t < 0
  The author has named this sort of situation the reversal of time's arrow."
  
  At this point you could ask yourself why the hell I am talking about Sakharov and the Big Bang, the radiation-dominated era and baryogenesis… as the subject is about Petit's idea on black holes in our contemporary matter-dominated era. This is because the two things are tightly related.
  
  Sakharov advocated that the reversal of time's arrow, and the associated "bridge" linking the two universe sheets at t = 0, could only be triggered in a state of minimal entropy. By the way, Sakharov was a proponent of a "cold Big Bang".
  
  But a second possibility to reverse the arrow of time at the beginning is to make the speed of light vary, so it reaches infinity at the Big Bang. When the speed of light increases more and more, the light cone becomes flatter and flatter. Going backward in time toward the Big Bang, when c = ∞ at t = 0, the light cone and the arrow of time reverse for t < 0. BTW, this was shown in the video Janus #19 from 3mn19s, subtitled in English, the main popularized drawing is this one:
  
  
  
  In this regime, all constant vary jointly (and not only c) so all laws of physics remain unchanged, because when one tries of vary the speed of light only, this has serious drawbacks like breaking the Lorentz invariance, breaking the fine-structure constant (hence preventing the formation fo atoms)…
  
  
  
  Out of this variable constant regime, a symmetry breaking occurs (i.e. matter becomes "frozen space" like ice cubes floating in a glass of water).
   
  The original idea to make all constants of physics vary together accordingly started from something laying inside Einstein's coupling constant χ:
  
  "The Einstein field equations have zero divergence. The zero divergence of the stress–energy tensor is the geometrical expression of the conservation law. So it appears that constants in the Einstein equations cannot vary, otherwise this postulate would be violated. However, since Einstein's coupling constant is evaluated by a calculation based on a time-independent metric, this by no mean requires that G and c must be unvarying constants themselves, the only postulate derived from conservation of energy is that the ratio G/c² must be constant."
  
  This is Petit's interpretation of Sakharov's initial singularity triggering complete CPT reflections while a particle is crossing its throat, except that in Petit's model, there is no central singularity. A hypertoric bridge opens before all the universe is gathered within a point-like event. Such hypertoric bridge makes particles flow from one sector to the other. The excess of quarks here naturally transforms into an excess of antiquarks there, passing over the throat. BTW I already talked about this in this prior post (see the image there).
  
  "Topologically, such geometric object is not a manifold in the classical sense of the term, but an orbifold containing a singular region where the object is locally non-orientable. This is not a sphere, but a projective P2." → This is why I don't write "throat sphere" but "throat surface". In 2D, you can assimilate it to Boy's surface. But as the two most opposite events of spacetime (Big Bang and Big Crunch for example) get in touch together through a hypertoric bridge, the object (the universe at this stage) is rather topologically assimilable (still in 2D as a surface embedded in a 3D space) to a Klein bottle.
  
  Now, back to the black hole. (finally!)
  
  Karl Schwarzschild himself noted a few months before his death a peculiar thing in his second 1916 paper about the "interior solution" (every details of this paper are not well known even among specialists who only studied parts of it along the whole 20th century, as the original paper has been translated from German to English for the first time only in late 1999… so 83 years after its publication! See arXiv:physics/9912033): at the center of a "Schwarzschild body" as it was called afterwards (now called a black hole), the speed of light and pressure at the center of the object both quickly increase to infinity BEFORE the Schwarzschild radius R_s  is reached. An infinite pressure that has later been "rediscovered" by Richard C. Tolman then J. Robert Oppenheimer and George Volkoff, which led to their famous "TOV equation" according to the initials of their names. So a physical criticality is reached before the geometric criticality Ř (which transforms the object into a black hole) can be ever reached:
  
  
  
  [UPDATES ADDED IN RED]: this TOV graphic above, published in a previous version of the paper, is wrong, as meberbs trivially showed it in the following messages afterward. The pressure is not according to the ratio Rn/Rs (which is variable and inconsistent) but the critical ratio Ř = √(3c² / 8πGρ ) which is fixed for any mass varying with a contant mass density. The correct graph is:
  
  
  
  According to Petit, any physicist should wonder about the physical meaning of an "infinite pressure" arising inside an object. Petit's answer is to claim that this triggers a joint variation of all the constants of physics, exactly like at the beginning of the universe. When the objects reaches 0.94 Ř, the speed of light as well as the pressure (which is also dimensionally an energy density) both increase up to infinity at the center. Before going up to such unphysical value, some energy density threshold is reached (according to Petit, this should occur when neutrons go toe-to-toe and cannot accommodate their wave function anymore) their mass is "inverted" as it flows from one spacetime to the other through an ephemeral hypertoric bridge, then the cosmic plughole quickly closes again.
  
  For scientific details and equations that you may ask, I attach a two-part paper recently presented at the COSMO-17 international conference in Paris (Late August 2017). First part is a lengthy historical and mathematical analysis of the exterior Schwarzschild solution and the geometry of the described object. Second part is more in line with the current subject as it tackles the interior Schwarzschild solution and proposes an alternative to the black hole model: the "leaking neutron star" (same occasional mass inversion mechanism as at the center of supermassive subcritical objects in the center of galaxies).
  
  Under this point of view, the Big Bang, destabilized neutron stars, quasars and supermassive black holes all experience the same mass inversion process through a hypertoric bridge. The Big Bang could even be considered as "the mother of all black holes" if you put aside the fact that no baryon existed yet at this time.
  
  As a side note, there is no more "freeze-frame" effect (test-particle "paused" before the event horizon of a black hole during an infinite time for a distant observer), which is classically:
  
  
               proper time of a falling test-particle VS
          coordinate time according to a distant observer
  
  On the contrary, mass inversion occurs in a finite time (during a very brief event). Black holes (destabilized neutron stars) are very massive objects spinning very fast (cf. the Kerr metric). They induce an azimuthal frame-dragging effect in the ergosphere, which was by the way well rendered for the black hole "Gargantua" in the movie Interstellar (2014), thanks to Kip Thorne's involvement on the movie. Moreover, according to Petit, a neutron star reaching criticality is so massive and it collapses so fast that it radially drags space with it, like when you push with your finger on a garden tablecloth just over the table parasol hole, literally. Therefore, there is necessarily also a radial frame-dragging that is usually never considered. Such radial frame-dragging effect should be associated to Eddington's time coordinate, so the black hole is no more eternal. It is shown that the throat acts as a one-way membrane. See at the end of the second paper attached.
  
  Let's recap:
  • Considering frame-dragging and Eddington's time: no more freeze-frame like in the black hole. The throat surface acts as a one-way membrane.
  • Considering Schwarzschild's original solution using Einstein's original metric signature, i.e. with a real line element (and not an element of pure imaginary length like Hilbert did^* as well as everyone after him) then the geometry of the 4D hypersurface is necessarily non-contractible and is like a 2D torus (hypertoric in 3D) with no center.
  • Considering Sakharov and bimetry, the two Minkowski spacetimes linked by the throat surface are CPT-symmetric. The throat acts like a bridge between the orthochronous and the antichronous sectors.
  • Considering Souriau's work in dynamical systems theory as well as taking a T operator linear and unitary in quantum mechanics, T-symmetry means energy inversion, hence mass inversion as -m = -E/c². Therefore, PT-symmetric antimatter populating the antichronous sector has a negative mass.
  Thus, crossing the throat surface (assimilable to the event horizon in the black hole model) triggers a hyperspace transfer from one sector to the other, accompanied by a mass inversion, in a finite and brief time.
  
  
  
  The classical black hole model introduces geodesic incompleteness and singularities in spacetime. Saving the geodesic completeness of spacetime the way Petit does in the Janus model framework is consistent with the black hole being exposed as a wormhole mouth, as described for example in Alex Flournoy's recent course at the Colorado School of Mines, from about 46mn44s in this video:
  
  
  
  Except that in the Janus model, the "wormhole" is not steady-state (hence one doesn't have to prop the wormhole up with some "exotic matter" or some "negative energy density"): its mouth opens then closes almost immediately, as soon as R_n  < 0.94 Ř again.
  
  According to the red bullet list above, mass inversion at the Big Bang in particular and in every critical object in the universe afterward (neutron stars, supermassive subcritical objects in galactic centers, quasars…) i.e. when R_n  = 0.94 Ř, is tightly related to the Janus cosmological model. This is a natural consequence of it. Also, this is the mechanism that could make mass inversion artificially reproductible, enabling interstellar travel with apparent FTL speeds. None of these bullet points work in a single metric theory.
  
  So the Janus model could still work if black holes were definitely proven to exist, but it would be a bit less plausible and coherent.
  
  

  ---

  
  * As explained in the two papers below: For David Hilbert (and everyone after him) the metric signature of general relativity, as introduces by Einstein as ( + – – – ) and used as is by Schwarzschild, Droste, Weyl… had to change to ( – + + + ). You will find physicists stating that both signatures are equivalent. But they are not, especially for the case of the black hole. Indeed for Hilbert, spacetime is a fiber bundle, built from a real space { x, y, z } but the fiber, i.e. his fourth coordinate, time (as well as proper time), is purely imaginary. However, the length element s, hence the proper time, is the only thing independent of the choice of coordinates on the 4D hypersurface of general relativity. If one decides to stick to the real world, when one explores parts of the (numerical) space related to variables, and comes across an element of pure imaginary length, or when the signature of the metric becomes altered (which is the same thing) then one is then simply… outside of the hypersurface. Therefore, people trying to make analytic continuations beyond the "event horizon" of the black hole, down to its "central singularity" are like a Mad Mechanic trying to glue a patch on a flat tire, precisely in a place located near the axis center of the inner tube, where the tire… doesn't even exist.
  
  

  ---

  Leaking Neutron Star Part 1.pdf

  Leaking Neutron Star Part 2.pdf
• #14 by flux_capacitor on 29 Apr, 2019 18:37
• Quote from: Slangny on 29 Apr, 2019 15:55

  I'm extremely sceptical of J. P. Petit's work. He is not a cosmologist, but worked on magnetohydrodynamics.

  
  Jean-Pierre Petit's 1972 Ph.d thesis "Applications of the kinetic theory of gases to plasma physics and galactic dynamics" is, as its name suggests, about plasma physics and indeed magnetohydrodynamics (MHD). If you had some real scientific background you would know that MHD is not only an engineering (water and plasma propulsion) discipline, but also applies to astrophysics (hint: "galactic dynamics" at the end of the title of the thesis). Petit publishes as an astrophysicist from 1974 (about galactic dynamics), then cosmology since 1977 (about the twin universes theory), first in the Proceedings of the French Academy of Sciences, then in Modern Physics Letters A for his VLS theory from 1988, then in Il Nuovo Cimento B, and mainly Astrophysics and Space Science. For decades, most part of his career up to his retirement, he worked as a senior researcher at the Marseille Observatory, France.
  
  He attended many international conferences on cosmology and continues to do so. Recently for example, COSMO-17 in Paris, France, as well as the 3rd Karl Schwarzschild meeting on gravitational physics and the gauge/gravity correspondence, Frankfurt, Germany, in 2017. in June 2019 he is even invited by Russians and will give a talk entitled "Mass inversion through the Schwarzschild sphere" at the 10th Alexander Friedmann international seminar on gravitation and cosmology, St Petersburg.
  
  But he is not a cosmologist…
  
  

  Quote

  Years ago he stated that he was in direct contact with "UMMO" aliens. I guess this means that he must have been smoking some good stuff!
  {troll flooding of unsubtitled, non-dubbed old French TV videos series that have nothing to do with science and the current thread}

  
  This forum is not the place to troll about other's views and hobbies of unrelated personal interests. Isaac Newton believed in astrology and alchemy, which he was a representative. As for Jean-Marie Souriau talked to trees! Does anybody invoke these personal hobbies to make fun of them "therefore" invalidate their work? No, because these eccentric ideas are unrelated to the universal law of gravitation, or to symplectic geometry. You registered especially today to post such low-quality biased comment on this forum, what an achievement (what an agenda, rather).
  
  

  Quote

  On top of that, the equations he is using are not his, but are plagiarised from Sabine Hossenfelder (an established cosmologist in Germany).
  https://arxiv.org/abs/0807.2838v1
  https://arxiv.org/abs/0908.3384v1
  https://arxiv.org/abs/0909.2094

  
  Is it some kind of joke? Petit started working on his bimetric theory from 1977, more than thirty years before Sabine Hossenfelder's own model. It was a newtonian model at that time. From 1994, his model becomes relativistic, with a field equation integrating the effect of negative mass from a "twin fold". From this 1994 equation, he then doubles it and he publishes for the first time his system of two coupled field equations in 2001, that is to say, seven years before Sabine Hossenfelder's very similar equations (2008). She was the first to give a Lagrangian derivation of her system, though. Talking of "plagiarism" in a way or another for two similar coupled equations that doesn't emerge from the same process rather looks like insanity. On the contrary, two unrelated authors concluding to very similar equations independently is the sign that this idea may be good stuff.
  
  All references I cited are listed (and downloadable) at the bottom of the page:
  https://januscosmologicalmodel.com/#refs
  
  

  Quote

  I wouldn't take anything he says too seriously!

  
  Again some sophism and an appeal to ignorance.
  
  

  Quote

  The journals he is publishing in are not peer-reviewed journals within the cosmology community, but predatory journals for cranks and crackpots. I don't want to be unkind, but this is really not science, just insane narcissism.
  

  
  What? Astrophysics and Space Science is not a peer-reviewed journal? Modern Physics Letters A? You are now definitively proving that you simply don't know at all what your are talking about. Do you even think by yourself, try to source gossips you hear and you are about to spread, or do you just report fake news like without verifying the validity of the information first?
  
  What your are doing is not only called logical fallacies, but also blatant lies (moreover using grotesque tricks). They are usually the sign of jealous people that are also not very smart. Especially when one uses several of them in a single post, like ad hominem attacks ("crank", "crackpot", "insane narcissist"), the straw man ("contact with aliens", "smoking some good stuff"), red herring ("look at this UFO stuff") and so on.
  
  You sir, are a Master Troll. You are proving to everyone here that you are actually the kind of person in this world who's purpose is to prevent things to be built or even destroy what you cannot achieve yourself, instead of trying to help build new things. I pity you…
  
  Be advised that this kind of low-quality comment, attacks and mockery are usually not tolerated on this well-managed forum. Hence your post has been reported to as such to administrators.
• #15 by flux_capacitor on 30 Apr, 2019 13:13
• The Janus model is the work of almost one man for more than 40 years (and his small team, more recently) but reading the (now erased) previous biased comment (same trolling goes on and on in the YouTube comments), I should emphasis that this model is not some "lone crackpot theory" as it is somewhat confirmed on its theoretical grounds (i.e. general relativity extended to a bigravity context where repulsive negative mass is at the same time self-attractive) by the work of various researchers around the world that find again same field equations, or develop these ideas independently on the exact same grounds.
  
  So let's cite independent yet very similar work:
  
  • S. Hossenfelder, "Anti-gravitation", Physics Letters B, 636: 119-125 (May 2006). arXiv:gr-qc/0508013. Open Access.
  + an appendix "attached" to the paper as an ArXiv preprint:
  • S. Hossenfelder, "Cosmological Consequences of Anti-gravitation" (May 2006). arXiv:gr-qc/0605083.
  
  • Johan Noldus, Patrick Van Esch, "Rebuttal on “anti-gravitation” by S. Hossenfelder", Physics Letters B, 636: 119-125 (July 2006). Open Access.
  
  This work is not so recent (2006) but I cite it as an introduction to show that one cannot introduce negative mass in general relativity while at the same time preventing the runaway motion paradox. Sabine Hossenfelder, a quite famous German physicist, failed to do so in 2006. She tried at that time to introduce the very same interaction laws promoted in the Janus model, i.e. like masses attract while opposite masses repel (that prevent the runaway motion and other inconsistencies of negative masses) in the single-metric framework of general relativity, with sophisticated mathematics. Alas, as shown by Noldus and Van Esch two months only after its publication, Hossenfelder's 2006 model is plagued with inconsistencies. They demonstrate that the line-worlds of her positive masses are necessarily dependent on the a particular frame of the observer, breaking general covariance.
  
  Afterward, Hossenfelder solved this problem, reconsidering the situation as a bimetric framework:
  
  • S. Hossenfelder, "Bimetric theory with exchange symmetry", Physical Review D, 78: 044015 (August 2008). arXiv:0807.2838. doi:10.1103/physrevd.78.044015.
  
  • S. Hossenfelder, "Antigravitation", 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions, Boston (June 2009). arXiv:0909.3456. doi:10.1063/1.3327545.
  
  In these newer paper, Hossenfelder introduces two metrics, one set for positive masses, the other for negative masses. Therefore she get a system of two field equations, coupled. This system is very similar to the Janus one, except she introduces additional pull-overs. Newtonian approximation gives the same geodesics and interaction laws as in the Janus model (like masses attract and unlike masses repel). She was the first to propose a Lagrangian derivation in the 2018 paper (so before Petit) from where she finds the metric determinant ratios. So this make some people question the real anteriority of such bimetric model. Petit publishes the twin universes theory in 1977 originally as a Newtonian model, publishes the first field equation referring to the positive sector in 1994, and the second, symmetric one from the negative sector in a conference paper in 2001, giving the first system of two coupled field equations. He also presents this work in 2007 as a bimetric theory of gravity at the CITV, the French workshop annually organized by late mathematician and geometer Jean-Marie Souriau, see arXiv:0712.0067, uploaded 1 Dec 2007. This definitely proves that such idiotic anteriority controversy has no place in this forum nor everywhere else.
  
  Alas, in 2008 Hossenfelder only considered a perfect symmetry of her two metrics, noticing such model does not explain observations very well… therefore she gave up, never pursued the route of bigravity after these two papers published ten years ago. She never considered on the contrary a profound asymmetry between the two mass densities, that is the key of all observations according to Petit, especially the missing mass effect (dark matter) and the cosmic acceleration (dark energy). A density asymmetry that is explained not because there would be more negative mass than positive mass in the universe (these values are equal) but because there are two space scale factors depending of the metric considered, i.e. we could say that one of the two "universe radius" is considerably smaller than the other. Then, negative mass drives the positive mass matter distribution in the universe as well as its rate of expansion, as shown in the Janus papers.
  
  
  • G. Manfredi, J.-L. Rouet, B. Miller, G. Chardin, "Cosmological structure formation with negative mass", Physical Review D, 98: 023514 (July 2018). arXiv:1804.03067. doi:10.1103/PhysRevD.98.023514.
  
  Gabriel Chardin is not the lead author, but is the one appearing in the media, as he is responsible for an experiment aimed to weigh antimatter. He cites Hossenfelder, but never Petit, following the motto given in all French labs. But in 2018 he considers the Janus model (still without citing the name nor their authors) and christens the negative mass PT-symmetric antimatter with the name "antiplasma" in this paper (because the expressed gravitational interaction, i.e. "like masses attract while unlike masses repel" is opposed to the electrodynamic interaction of charged particles) and presents himself and his team in the French media as the proponent of such ideas.
  
  
  • S. A. Rahman, "On the existence of exotic matter in classical Newtonian mechanics", Modern Physics Letters A, 34: (February 2019). doi:10.1142/S0217732319500494. Available on ResearchGate.
  
  Sabbir Rahman focuses on computer simulations. He notes the similarity of Petit's model with Hossenfelder's, but in fact he does not consider yet the great asymmetry of the two mass densities in the Janus model vs the exact density symmetry in Hossenfelder's theory. Rahman has also a more complete preprint on ResearchGate, with a similar title.
  
  
  • S. Bondarenko, "Negative mass scenario and Schwarzschild spacetime in general relativity", Modern Physics Letters A, 34: 1950084 (March 2019). arXiv:1807.07412. doi:10.1142/S0217732319500846.
  
  Sergey Bondarenko is a Russian researcher working at the Ariel University, Israel. In this paper he considers PT transformation according to Sakharov, Souriau and Petit, to infer that PT-symmetric antimatter has a negative mass and interacts with normal matter from a second dark sector, like the one used in the Janus model, cited. The paper focuses on the Schwarzschild metric according to these hypotheses.
  
  
  • P. Marquet, "Twin Universes: a New Approach", Progress in Physics, 15: 64–67 (July 2019). Published online in Open Access.
  
  This is an interesting theoretical paper as the author finds the system of two coupled field equations of the Janus model using a completely different approach (Elie Cartan's equivalence method and the Hodge star operator).
  
  
  N.B.: In this recent bibliography about negative mass in cosmology, I didn't list the "dark fluid" approach of Jamie Farnes that was recently published with a lot of media coverage, as Farnes stays in the single metric framework of general relativity and the lambda-CDM model, thus decides to deal with the paradoxical runaway motion phenomenon and the fact that negative masses repel everything, including themselves. Moreover, Farnes uses a continuous "Creation Field" for his negative mass fluid, like in older disproved steady-state models of gravity, to keep up with and account for the accelerating expansion of the universe. Indeed, without such C-field, his "dark fluid" quickly dilutes over time and cannot account for observations, especially the cosmic acceleration. Such density dilution due to the expansion is also predicted in the Janus model, but as the space scale factor of the second metric is 100× more contracted than the one of the positive sector, and the cosmic expansion is actually decelerating in the negative one, such change in the rate of expansion recedes in the far future of the universe. Since we can observe past and present only, all we can do about future states of the universe is making predictions based on these observations coupled to consistent theories.
  
  Nonetheless, a critical paper of Farnes' model has just been published (April 2019) which also lists other approaches about negative mass in cosmology:
  
  • H. Socas-Navarro, "Can a negative-mass cosmology explain dark matter and dark energy?", Astronomy & Astrophysics (April 2019). arXiv:1902.08287. doi:10.1051/0004-6361/201935317.
• #16 by Ricvil on 02 May, 2019 12:42
• Quote from: flux_capacitor on 30 Apr, 2019 13:13

  The Janus model is the work of almost one man for more than 40 years (and his small team, more recently) but reading the (now erased) previous biased comment (same trolling goes on and on in the YouTube comments), I should emphasis that this model is not some "lone crackpot theory" as it is somewhat confirmed on its theoretical grounds (i.e. general relativity extended to a bigravity context where repulsive negative mass is at the same time self-attractive) by the work of various researchers around the world that find again same field equations, or develop these ideas independently on the exact same grounds.
  
  So let's cite independent yet very similar work:
  
  • S. Hossenfelder, "Anti-gravitation", Physics Letters B, 636: 119-125 (May 2006). arXiv:gr-qc/0508013. Open Access.
  + an appendix "attached" to the paper as an ArXiv preprint:
  • S. Hossenfelder, "Cosmological Consequences of Anti-gravitation" (May 2006). arXiv:gr-qc/0605083.
  
  • Johan Noldus, Patrick Van Esch, "Rebuttal on “anti-gravitation” by S. Hossenfelder", Physics Letters B, 636: 119-125 (July 2006). Open Access.
  
  This work is not so recent (2006) but I cite it as an introduction to show that one cannot introduce negative mass in general relativity while at the same time preventing the runaway motion paradox. Sabine Hossenfelder, a quite famous German physicist, failed to do so in 2006. She tried at that time to introduce the very same interaction laws promoted in the Janus model, i.e. like masses attract while opposite masses repel (that prevent the runaway motion and other inconsistencies of negative masses) in the single-metric framework of general relativity, with sophisticated mathematics. Alas, as shown by Noldus and Van Esch two months only after its publication, Hossenfelder's 2006 model is plagued with inconsistencies. They demonstrate that the line-worlds of her positive masses are necessarily dependent on the a particular frame of the observer, breaking general covariance.
  
  Afterward, Hossenfelder solved this problem, reconsidering the situation as a bimetric framework:
  
  • S. Hossenfelder, "Bimetric theory with exchange symmetry", Physical Review D, 78: 044015 (August 2008). arXiv:0807.2838. doi:10.1103/physrevd.78.044015.
  
  • S. Hossenfelder, "Antigravitation", 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions, Boston (June 2009). arXiv:0909.3456. doi:10.1063/1.3327545.
  
  In these newer paper, Hossenfelder introduces two metrics, one set for positive masses, the other for negative masses. Therefore she get a system of two field equations, coupled. This system is very similar to the Janus one, except she introduces additional pull-overs. Newtonian approximation gives the same geodesics and interaction laws as in the Janus model (like masses attract and unlike masses repel). She was the first to propose a Lagrangian derivation in the 2018 paper (so before Petit) from where she finds the metric determinant ratios. So this make some people question the real anteriority of such bimetric model. Petit publishes the twin universes theory in 1977 originally as a Newtonian model, publishes the first field equation referring to the positive sector in 1994, and the second, symmetric one from the negative sector in a conference paper in 2001, giving the first system of two coupled field equations. He also presents this work in 2007 as a bimetric theory of gravity at the CITV, the French workshop annually organized by late mathematician and geometer Jean-Marie Souriau, see arXiv:0712.0067, uploaded 1 Dec 2007. This definitely proves that such idiotic anteriority controversy has no place in this forum nor everywhere else.
  
  Alas, in 2008 Hossenfelder only considered a perfect symmetry of her two metrics, noticing such model does not explain observations very well… therefore she gave up, never pursued the route of bigravity after these two papers published ten years ago. She never considered on the contrary a profound asymmetry between the two mass densities, that is the key of all observations according to Petit, especially the missing mass effect (dark matter) and the cosmic acceleration (dark energy). A density asymmetry that is explained not because there would be more negative mass than positive mass in the universe (these values are equal) but because there are two space scale factors depending of the metric considered, i.e. we could say that one of the two "universe radius" is considerably smaller than the other. Then, negative mass drives the positive mass matter distribution in the universe as well as its rate of expansion, as shown in the Janus papers.
  
  
  • G. Manfredi, J.-L. Rouet, B. Miller, G. Chardin, "Cosmological structure formation with negative mass", Physical Review D, 98: 023514 (July 2018). arXiv:1804.03067. doi:10.1103/PhysRevD.98.023514.
  
  Gabriel Chardin is not the lead author, but is the one appearing in the media, as he is responsible for an experiment aimed to weigh antimatter. He cites Hossenfelder, but never Petit, following the motto given in all French labs. But in 2018 he considers the Janus model (still without citing the name nor their authors) and christens the negative mass PT-symmetric antimatter with the name "antiplasma" in this paper (because the expressed gravitational interaction, i.e. "like masses attract while unlike masses repel" is opposed to the electrodynamic interaction of charged particles) and presents himself and his team in the French media as the proponent of such ideas.
  
  
  • S. A. Rahman, "On the existence of exotic matter in classical Newtonian mechanics", Modern Physics Letters A, 34: (February 2019). doi:10.1142/S0217732319500494. Available on ResearchGate.
  
  Sabbir Rahman focuses on computer simulations. He notes the similarity of Petit's model with Hossenfelder's, but in fact he does not consider yet the great asymmetry of the two mass densities in the Janus model vs the exact density symmetry in Hossenfelder's theory. Rahman has also a more complete preprint on ResearchGate, with a similar title.
  
  
  • S. Bondarenko, "Negative mass scenario and Schwarzschild spacetime in general relativity", Modern Physics Letters A, 34: 1950084 (March 2019). arXiv:1807.07412. doi:10.1142/S0217732319500846.
  
  Sergey Bondarenko is a Russian researcher working at the Ariel University, Israel. In this paper he considers PT transformation according to Sakharov, Souriau and Petit, to infer that PT-symmetric antimatter has a negative mass and interacts with normal matter from a second dark sector, like the one used in the Janus model, cited. The paper focuses on the Schwarzschild metric according to these hypotheses.
  
  
  • P. Marquet, "Twin Universes: a New Approach", Progress in Physics, 15: 64–67 (July 2019). Published online in Open Access.
  
  This is an interesting theoretical paper as the author finds the system of two coupled field equations of the Janus model using a completely different approach (Elie Cartan's equivalence method and the Hodge star operator).
  
  
  N.B.: In this recent bibliography about negative mass in cosmology, I didn't list the "dark fluid" approach of Jamie Farnes that was recently published with a lot of media coverage, as Farnes stays in the single metric framework of general relativity and the lambda-CDM model, thus decides to deal with the paradoxical runaway motion phenomenon and the fact that negative masses repel everything, including themselves. Moreover, Farnes uses a continuous "Creation Field" for his negative mass fluid, like in older disproved steady-state models of gravity, to keep up with and account for the accelerating expansion of the universe. Indeed, without such C-field, his "dark fluid" quickly dilutes over time and cannot account for observations, especially the cosmic acceleration. Such density dilution due to the expansion is also predicted in the Janus model, but as the space scale factor of the second metric is 100× more contracted than the one of the positive sector, and the cosmic expansion is actually decelerating in the negative one, such change in the rate of expansion recedes in the far future of the universe. Since we can observe past and present only, all we can do about future states of the universe is making predictions based on these observations coupled to consistent theories.
  
  Nonetheless, a critical paper of Farnes' model has just been published (April 2019) which also lists other approaches about negative mass in cosmology:
  
  • H. Socas-Navarro, "Can a negative-mass cosmology explain dark matter and dark energy?", Astronomy & Astrophysics (April 2019). arXiv:1902.08287. doi:10.1051/0004-6361/201935317.
  

  
  This article is very interesting.
  
  • P. Marquet, "Twin Universes: a New Approach", Progress in Physics, 15: 64–67 (July 2019). Published online in Open Access.
  
  I'm interested on the effects of "inversion" on the electromagnetic fields.
  
  I've found what can be a "group" where a "inversion at a spherical surface" , together with a "duality inversion" ( wich may be associated with hodge duality) and other transformation, wich preserves the flat spacetime metric.
  This "inversion at a spherical surface" appears to be a Mobius transformation.
  As a electromagnetic "toy model", the fields inside a cavity with non zero intrinsic curvature boundary conditions, appears model a "Janus point" as a very narrow electromagnetic "bound state" induced by the curvature.
  
  Just look  carefully the fields inside the cavity on anexed file ( see it in black and white if necessary). You can see a very narrow bright mode "linking" the antinodes of field at bottom.

  ---

  
• #17 by Ricvil on 02 May, 2019 14:03
• The cavity below is the version of "bell cavity" with only impulsive boundary conditions  intrinsic curvature at the junctions, been zero ( boundary conditions intrinsic curvature) at walls.
  Theorically, it will presents the same narrows modes pointed on previous quote.

  ---

  
• #18 by flux_capacitor on 02 May, 2019 14:14
• Quote from: Ricvil on 02 May, 2019 12:42

  This article is very interesting.
  
  • P. Marquet, "Twin Universes: a New Approach", Progress in Physics, 15: 64–67 (July 2019). Published online in Open Access.
  
  I'm interested on the effects of "inversion" on the electromagnetic fields.
  
  I've found what can be a "group" where a "inversion at a spherical surface" , together with a "duality inversion" ( wich may be associated with hodge duality) and other transformation, wich preserves the flat spacetime metric.
  This "inversion at a spherical surface" appears to be a Mobius transformation.
  As a electromagnetic "toy model", the fields inside a cavity with non zero intrinsic curvature boundary conditions, appears model a "Janus point" as a very narrow electromagnetic "bound state" induced by the curvature.
  
  Just look  carefully the fields inside the cavity on anexed file ( see it in black and white if necessary). You can see a very narrow bright mode "linking" the antinodes of field at bottom.
  

  Quote from: Ricvil on 02 May, 2019 14:03

  The cavity below is the version of "bell cavity" with only impulsive boundary conditions  intrinsic curvature at the junctions, been zero at walls.
  Theorically, it will presents the same narrows modes pointed on previous quote.
  

  
  Ricvil, I don't really understand the concepts you handle and do not know if they are valid or not. I don't know if the bottom bright mode (which I do see in the picture provided) is real or is instead an artifact of the simulation. I can't tell for sure. Honestly, I don't see the connection of RF resonant cavities with cosmology in general and the Janus model in particular, especially as any artificial mass inversion would make particles seem to have disappeared from our spacetime, having been transferred to the negative dark sector. Perhaps I don't see the connection that may be be there because I fail to understand your concepts.
  
  Nonetheless, if you are interested in such C/PT/CPT transformations, time reversal and energy inversion, Lie algebra especially the coadjoint action of a Lie group, ie. the action of a group on the dual vector space to its Lie algebra (its lie coalgebra), you should have a serious look at Souriau's work in symplectic geometry in general, and dynamical group theory in particular.
  
  PM me for Souriau's work translated in English if you're interested.
  
  For example: Souriau's non-trivial extension of the Poincaré group to a 5D-spacetime, the 5th dimension being a compact (Planck length) fiber-bundle handing the electric charge. As well as Petit's extension of the full Poincaré group to two 5D-spacetimes (handling matters and antimatters of positive and negative energies) which he now calls the Janus group. See for example the preprint arXiv:math-ph/0502042.
  
  The work done in dynamical systems theory above has recently been transposed to quantum mechanics (and published) with a T operator linear and unitary, handing mass-energy inversion. See Debergh et al. 2018: arXiv:1809.05046.
  This is still 4D with no handling of the electric (quantum) charges yet, so PT-symmetries only, not CPT-symmetries. But I undestand this may be extended in a future work, quite innovative in the field if they manage to publish it.
  
  I see you are interested in topology, about the Möbius thing. For the cosmic explanation in fewer dimensions using a 2D sphere embedded in a 3D space, folded as a double cover of a projective space P2 aka Boy's surface, see Part 5: "Topological Structure" in "Five Dimensional bigravity. New topological description of the Universe", preprint here: arXiv:0805.1423.
  Be aware that the second dimension of the 2-sphere is in fact time, so it is actually embedded in a 3D space-time (not only space). Big Bang, the point-origin, is its North pole, and Big Crunch, its South pole. The equator of the sphere is a state of the universe of minimal entropy, in a far future when all particles of matter in the whole universe have decayed into radiation, and their wavelengths will tend to infinity due to the cosmic expansion. Temperature will tend to the absolute zero and Petit's VSL theory predicts that the speed of light will again vary and decrease toward zero also. The universe will then be made of only cold photons (the "cosmos death"). Then, at this state of minimal entropy, the arrow of time will reverse again. Following events correspond to the South hemisphere. When the sphere is folded as Boy's surface (each small strip portion of the sphere is then a Möbius strip) every point of our spacetime is "locally connected" with its antipodal point, i.e. with an opposite location in the universe, spatially, but also in its far future with an opposite time arrow, temporally. T-symmetry triggers apparent mass inversion, and folding space according to Möbius/Boy makes space coordinates appear chirally inverted too (P-symmetry). That is to say, our positive mass matter gravitationally interacts with the antipodal negative mass, aka PT-symmetric antimatter. In particular, the Big Crunch in the far future enters is conjunction with the Big Bang in the far past, in the very same event. If you cancel these point-like singularities and make a small tubular bridge linking the two events instead (like a wormhole throat), Boy's surface becomes topologically like a Klein bottle. Hence, our universe is a Klein hyperbottle
• #19 by Ricvil on 02 May, 2019 15:42
• Thank you for the answers, explanations and references.
  What I've found is a 4D discrete cyclic group, and involves a totally spatial spherical surface of inversion.