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.

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":

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.

• 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.