### Author Topic: Theoretical FTL  (Read 39124 times)

#### gospacex

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##### Re: Theoretical FTL
« Reply #80 on: 07/13/2017 11:51 AM »
But this axiom was stated before the discovery of the accelerating expansion of the universe. [8] We are even now in a "dark-energy-dominated era". Since such an acceleration implies the action of a negative pressure, and since a pressure is a density of energy (per unit of volume), this question should be reconsidered.

This is wrong. Pressure is not a density of energy. Energy is the T00 component of stress-energy tensor; pressure is components T11, T22 and T33. Accelerating expansion must have _positive_ energy density of vacuum (then it has negative pressure).

I just usde the international System of Units (SI). We are in the habit of calculating a pressure in pascals, which are newtons per squared meter. But this is also similar to joules per cubic meter, a "volumetric" (i.e. per unit volume) energy density.

A pressure can be expressed as a force per unit surface, or an energy per unit volume, i.e. an energy density. They share the same physical units.

Of course all components of stress-energy tensor have the same units. This is not the issue.

The issue is that pressure is a flux of *momentum* through *spatial* coordinates x,y,z. Whereas energy is a flux through *time* coordinate. Different things. Negative pressure does not cause negative energy.
« Last Edit: 07/13/2017 11:51 AM by gospacex »

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #81 on: 07/14/2017 12:30 AM »
Of course all components of stress-energy tensor have the same units. This is not the issue.

The issue is that pressure is a flux of *momentum* through *spatial* coordinates x,y,z. Whereas energy is a flux through *time* coordinate. Different things.

You are referring to the stress-energy tensor:

We can express the energy density in the stress energy-tensor as ρc2

What is it? n is the "density number" (number of particles per cubic meter) multiplied by mc2, an energy. Thus this is an energy per unit volume, in joules (or newton-meter) per cubic meter.

The other terms of the stress-energy tensor are three times the pressure and they have exactly the same dimension.

So p is also expressed in joules per cubic meter: an energy density. All the terms of the tensor expressed here share the same dimension.

If this is not a demonstration that p is also an energy per unit volume?!

As a whole, the stress-energy tensor Tµv is expressed in J/m3

Force   ×   Length             Energy
Pressure  =   –––––––     ––––––––   =   ––––––––  =  Energy density
Area    ×   Length             Volume

and with respect to time, as the work done is basically Force × Length, it is a change in Energy.

Then:

dE = F dx = P dV

One must consider how the physics behaves in various aspects of reality.

Pressure and energy density are the same thing. In physics, the choice of joules per cubic meter even comes first, with respect to the more usual daily form in newtons per square meter.

- Pneumatic pressure as in a cylinder with a compressing piston is the work done over a volume of gas.

- Pressure as strain σ in a material expresses the elastic deformation in the volume of the material.

- Magnetic pressure is also an energy density associated with a magnetic field.

- Coulomb pressure and electrostatic pressure are stresses defined in terms of energy density, as already detailed by Dr Rodal on theses NSF forums.

- Radiation pressure of electromagnetic fields on a conductive surface has been similarly detailed by Rodal, as the cyclic time-average of the energy density.

etc.

Pressure is an energy density and vice versa, in all aspects of physics.
« Last Edit: 07/14/2017 12:37 AM by flux_capacitor »

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #82 on: 07/14/2017 01:21 AM »
Negative pressure does not cause negative energy.

It is true dark energy has a positive energy density associated to a negative pressure in the concordance model.

Conversely, does negative energy have to cause positive pressure?

As for negative energy density states, an example is the Casimir effect. In between the attracted plates there is indeed a negative pressure. But it has been shown that the negative energy density can also be either positive or negative in that region of limited spatial extension, with respect to the ground state energy of the vacuum. [13]

So both a negative pressure and a negative energy density at the same time…

In a more general form the pressure components in the stress-energy tensor can be written in terms of mass density:

p = α ρ

with α > -1

α being a scalar quantity. [14]

This opens the possibility of negative pressures, but this has not to be the case for any scenarii, including positive or negative energies.

Except the particular case of the Casimir effect, the physical behavior of negative energy states is rather unknown, so no conclusions, based solely on the extrapolation after effects due to positive energy, can be made certain.

Especially as the two coupled field equations of the Janus cosmological model generate a different Newtonian approximation for the gravitational interaction of positive vs negative mass matter, when compared to the Newtonian approximation for those two species from a single metric in general relativity.

In the model, when the negative element dominates, both ρ and p are negative. Because the detected pressure in this case is not a "pressure of the quantum vacuum" but the effect of the invisible presence of negative matter of mass density ρ located in the negative sector, and acting on our positive sector.

As for the three minus signs in the stress-energy tensor, they come from the metric tensor because the metric signature is written as time-positive ( + - - - )

Not intuitive at all.

References

[13] Sopova, V.; Ford, L. H. (2002). "The Energy Density in the Casimir Effect". Physical Review D. 66: 045026. arXiv:quant-ph/0204125. doi:10.1103/PhysRevD.66.045026.

[14] Stress-energy tensor: negative pressure revisited, from Moore, T. A. (2013). "A General Relativity Workbook", Chapter 20 "The Stress-Energy Tensor". University Science Books. ISBN 978-1-891389-82-5.
« Last Edit: 07/14/2017 11:36 AM by flux_capacitor »

#### dustinthewind

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##### Re: Theoretical FTL
« Reply #83 on: 07/14/2017 02:16 AM »
Negative pressure does not cause negative energy.

It is true dark energy has a positive energy density associated to a negative pressure in the concordance model.

Conversely, does negative energy always have to cause positive pressure?

As for negative energy density states, an example is the Casimir effect. In between the attracted plates there is indeed a negative pressure. But it has been shown that the negative energy density can also be either positive or negative in that region of limited spatial extension, with respect to the ground state energy of the vacuum. [13]

So both a negative pressure and a negative energy density at the same time…

In a more general form the pressure components in the stress-energy tensor can be written in terms of mass density:

p = α ρ

with α > -1

α being a scalar quantity. [14]

This opens the possibility of negative pressures, but this has not to be the case for any scenarii, including positive or negative energies.

Except the particular case of the Casimir effect, the physical behavior of negative energy states is still unknown, so no conclusions, based solely on the extrapolation after effects due to positive energy, can be made certain. Especially as the two coupled field equations of the Janus cosmological model generate a different Newtonian approximation for the gravitational interaction of positive vs negative mass matter, when compared to the Newtonian approximation for those two species from a single metric in general relativity.

References

[13] Sopova, V.; Ford, L. H. (2002). "The Energy Density in the Casimir Effect". Physical Review D. 66: 045026. arXiv:quant-ph/0204125. doi:10.1103/PhysRevD.66.045026.

[14] Stress-energy tensor: negative pressure revisited, from Moore, T. A. (2013). "A General Relativity Workbook", Chapter 20 "The Stress-Energy Tensor". University Science Books. ISBN 978-1-891389-82-5.
https://en.wikipedia.org/wiki/Negative_energy
Some other forms of negative energy exist.  One is gravitational energy which pulls things together.  I was suspecting queezed light might be a way of helping push against the vacuum and seems integral to detecting gravitational waves.  Squeezed light is also connected to negative energy.

There are the virtual particles that seem to pop in and out of existence that also have connections to negative energy.

also found this which may possibly be of relation or maybe not,

Pressures and Energies in Magnetized Vacuum and in Casimir effect

CERN Document Server

Rojas, H P

2004-01-01

We study vacuum pressures and energies for electron-positron vacuum zero point energy in a strong magnetic field $B$ and for photon vacuum in Casimir effect, by a common method. Vacuum becomes magnetized, and due to it, the pressure transversal to $B$ is negative, whereas along $B$ an usual positive pressure arises. Similarly, in addition to the usual negative Casimir pressure perpendicular to the plates, the existence of a positive pressure along the plates is predicted. Both vacua bear the property of leading to a negative energy-momentum tensor trace ${\\cal T}_{\\mu}^{\\mu}<0$, which may lead to a repulsive gravity typical of dark energy. By assuming a space distribution of magnetic and/or Casimir domains, cosmological implications are also discussed.
« Last Edit: 07/14/2017 02:18 AM by dustinthewind »

#### gospacex

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##### Re: Theoretical FTL
« Reply #84 on: 07/14/2017 03:58 PM »
Of course all components of stress-energy tensor have the same units. This is not the issue.

The issue is that pressure is a flux of *momentum* through *spatial* coordinates x,y,z. Whereas energy is a flux through *time* coordinate. Different things.

You are referring to the stress-energy tensor:

We can express the energy density in the stress energy-tensor as ρc2

What is it? n is the "density number" (number of particles per cubic meter) multiplied by mc2, an energy. Thus this is an energy per unit volume, in joules (or newton-meter) per cubic meter.

The other terms of the stress-energy tensor are three times the pressure and they have exactly the same dimension.

So p is also expressed in joules per cubic meter: an energy density. All the terms of the tensor expressed here share the same dimension.

If this is not a demonstration that p is also an energy per unit volume?!

No, it is not.
Energy is linked to *time*, and momentum to *space*. Pressure (say, of gas) on a surface is caused by momentum of gas particles crossing this spatial surface.

#### gospacex

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##### Re: Theoretical FTL
« Reply #85 on: 07/14/2017 04:09 PM »

Pressures and Energies in Magnetized Vacuum and in Casimir effect

CERN Document Server

Rojas, H P

2004-01-01

We study vacuum pressures and energies for electron-positron vacuum zero point energy in a strong magnetic field $B$ and for photon vacuum in Casimir effect, by a common method. Vacuum becomes magnetized, and due to it, the pressure transversal to $B$ is negative, whereas along $B$ an usual positive pressure arises. Similarly, in addition to the usual negative Casimir pressure perpendicular to the plates, the existence of a positive pressure along the plates is predicted. Both vacua bear the property of leading to a negative energy-momentum tensor trace ${\\cal T}_{\\mu}^{\\mu}<0$, which may lead to a repulsive gravity typical of dark energy. By assuming a space distribution of magnetic and/or Casimir domains, cosmological implications are also discussed.

"Both vacua bear the property of leading to a negative energy-momentum tensor trace" means that tensor looks like T = diag(ρ, -ρ, -ρ, -ρ) and therefore its trace is -2ρ.

Any vacuum state must have energy-momentum tensor proportional to the metric, since vacuum is invariant under boosts. (This is markedly different from states with particles (i.e. "not vacuums"), which are not invariant under boost - if observer is moving with a different velocity, it sees all particles having different velocity too).

For the usual case of flat Minkovski space this means that vacuum's energy-momentum tensor must be proportional to diag(1, -1, -1, -1).

If it is diag(ρ, -ρ, -ρ, -ρ), then it has positive energy density and negative pressure.
If it is diag(-ρ, ρ, ρ, ρ), then it has negative energy density and positive pressure.

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #86 on: 07/14/2017 11:57 PM »
{snip}
If this is not a demonstration that p is also an energy per unit volume?!

No, it is not.
Energy is linked to *time*, and momentum to *space*. Pressure (say, of gas) on a surface is caused by momentum of gas particles crossing this spatial surface.

You dont' articulate your sentence with the rest of my post that you didn't quote. Please explain to all readers here how pressures we experience in physics, aka the pneumatic pressure, the strain in materials, the magnetic pressure, the coulomb pressure, the electrostatic pressure, the radiation pressure, etc… cannot, according to you, be expressed in terms of energy densities, whereas this is how every engineer and physicist do it since time immemorial.

The relationship between radiation PRESSURE, ENERGY DENSITY and LAGRANGIAN DENSITY
and
The relationship between radiation PRESSURE and the POYNTING VECTOR
both posts by Dr Rodal in the EmDrive threads.
« Last Edit: 07/23/2017 11:57 PM by flux_capacitor »

#### gospacex

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##### Re: Theoretical FTL
« Reply #87 on: 07/15/2017 12:40 AM »
{snip}
If this is not a demonstration that p is also an energy per unit volume?!

No, it is not.
Energy is linked to *time*, and momentum to *space*. Pressure (say, of gas) on a surface is caused by momentum of gas particles crossing this spatial surface.

You dont' articulate your sentence with the rest of my post that you didn't quote. Please explain to all readers here how pressures we experience in physics, aka the pneumatic pressure, the strain in materials, the magnetic pressure, the coulomb pressure, the electrostatic pressure, the radiation pressure, etc… cannot, according to you, be expressed in terms of energy densities

No, that's not "according to me". I'm not saying that, it's you not understanding what I'm saying.

#### dustinthewind

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##### Re: Theoretical FTL
« Reply #88 on: 07/16/2017 05:40 AM »
Negative pressure does not cause negative energy.

It is true dark energy has a positive energy density associated to a negative pressure in the concordance model.

Conversely, does negative energy always have to cause positive pressure?

As for negative energy density states, an example is the Casimir effect. In between the attracted plates there is indeed a negative pressure. But it has been shown that the negative energy density can also be either positive or negative in that region of limited spatial extension, with respect to the ground state energy of the vacuum. [13]

So both a negative pressure and a negative energy density at the same time…

In a more general form the pressure components in the stress-energy tensor can be written in terms of mass density:

p = α ρ

with α > -1

α being a scalar quantity. [14]

This opens the possibility of negative pressures, but this has not to be the case for any scenarii, including positive or negative energies.

Except the particular case of the Casimir effect, the physical behavior of negative energy states is still unknown, so no conclusions, based solely on the extrapolation after effects due to positive energy, can be made certain. Especially as the two coupled field equations of the Janus cosmological model generate a different Newtonian approximation for the gravitational interaction of positive vs negative mass matter, when compared to the Newtonian approximation for those two species from a single metric in general relativity.

References

[13] Sopova, V.; Ford, L. H. (2002). "The Energy Density in the Casimir Effect". Physical Review D. 66: 045026. arXiv:quant-ph/0204125. doi:10.1103/PhysRevD.66.045026.

[14] Stress-energy tensor: negative pressure revisited, from Moore, T. A. (2013). "A General Relativity Workbook", Chapter 20 "The Stress-Energy Tensor". University Science Books. ISBN 978-1-891389-82-5.
https://en.wikipedia.org/wiki/Negative_energy
Some other forms of negative energy exist.  One is gravitational energy which pulls things together.  I was suspecting queezed light might be a way of helping push against the vacuum and seems integral to detecting gravitational waves.  Squeezed light is also connected to negative energy.

There are the virtual particles that seem to pop in and out of existence that also have connections to negative energy.

also found this which may possibly be of relation or maybe not,

Pressures and Energies in Magnetized Vacuum and in Casimir effect

CERN Document Server

Rojas, H P

2004-01-01

We study vacuum pressures and energies for electron-positron vacuum zero point energy in a strong magnetic field $B$ and for photon vacuum in Casimir effect, by a common method. Vacuum becomes magnetized, and due to it, the pressure transversal to $B$ is negative, whereas along $B$ an usual positive pressure arises. Similarly, in addition to the usual negative Casimir pressure perpendicular to the plates, the existence of a positive pressure along the plates is predicted. Both vacua bear the property of leading to a negative energy-momentum tensor trace ${\\cal T}_{\\mu}^{\\mu}<0$, which may lead to a repulsive gravity typical of dark energy. By assuming a space distribution of magnetic and/or Casimir domains, cosmological implications are also discussed.

This quote from https://en.wikipedia.org/wiki/Woodward_effect
Quote
Negative bare mass of the electron
The mass of the electron is positive according to the mass–energy equivalence E = mc2 but this invariant mass is made from the bare mass of the electron "clothed" by a virtual photon cloud. According to quantum field theory, as those virtual particles have an energy more than twice the bare mass of the electron, mandatory for pair production in renormalization, the nonelectromagnetic bare mass of the "unclothed" electron has to be negative.[45]

Using the ADM formalism, Woodward proposes that the physical interpretation...

This rings a bell for me.  I was suspecting the anti-matter as having some means of cloaking its negative mass so as to appear positive till annihilation.  Now we see the electron surrounded by the vacuum negative energy seemingly polarized by its presence.  Probably the only thing holding it back would be other annihilated and repelled electrons bonded to their counter parts.

If the electron has its mass effectively reduced by this effect then a bare proton may have its mass effectively increased if its attracting annihilated electrons from the vacuum.

I suspect inertia is a property of the vacuum as do some others.  The reverse time retarded waves would be the anti-matter positron fluctuations and the forward time waves are the vacuum annihilated electron waves.  These waves appear as photons or polarization of the vacuum (forward and reverse time simultaneously) such that an electric field can travel through space.  Its the local metric of this vacuum that determines what appears to be the constant speed of light while non-locally allowing it to change and why when annihilating a charge pair, light is made, while when reversing that light such that it converges in reverse time, we can get back those same two annihilated pairs.

Gravity would be some gradient induced in the vacuum, initially by some unknown method of matters attraction of anti-matter out of the vacuum - particularly positrons - maybe by the outer electron cloud particularly.  This initial polarization of the vacuum is not caused by the gradient in time however, this cloud of negative energy or polarization of the vacuum (e-p phantom pairs) slows time time in a gravity well.  This gradient in time then causes attraction of other matter.  Well maybe, its just a hypothesis.
« Last Edit: 07/16/2017 05:45 AM by dustinthewind »

#### ChrisWilson68

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##### Re: Theoretical FTL
« Reply #89 on: 07/16/2017 06:44 AM »
Negative pressure does not cause negative energy.

It is true dark energy has a positive energy density associated to a negative pressure in the concordance model.

Conversely, does negative energy always have to cause positive pressure?

As for negative energy density states, an example is the Casimir effect. In between the attracted plates there is indeed a negative pressure. But it has been shown that the negative energy density can also be either positive or negative in that region of limited spatial extension, with respect to the ground state energy of the vacuum. [13]

So both a negative pressure and a negative energy density at the same time…

In a more general form the pressure components in the stress-energy tensor can be written in terms of mass density:

p = α ρ

with α > -1

α being a scalar quantity. [14]

This opens the possibility of negative pressures, but this has not to be the case for any scenarii, including positive or negative energies.

Except the particular case of the Casimir effect, the physical behavior of negative energy states is still unknown, so no conclusions, based solely on the extrapolation after effects due to positive energy, can be made certain. Especially as the two coupled field equations of the Janus cosmological model generate a different Newtonian approximation for the gravitational interaction of positive vs negative mass matter, when compared to the Newtonian approximation for those two species from a single metric in general relativity.

References

[13] Sopova, V.; Ford, L. H. (2002). "The Energy Density in the Casimir Effect". Physical Review D. 66: 045026. arXiv:quant-ph/0204125. doi:10.1103/PhysRevD.66.045026.

[14] Stress-energy tensor: negative pressure revisited, from Moore, T. A. (2013). "A General Relativity Workbook", Chapter 20 "The Stress-Energy Tensor". University Science Books. ISBN 978-1-891389-82-5.
https://en.wikipedia.org/wiki/Negative_energy
Some other forms of negative energy exist.  One is gravitational energy which pulls things together.  I was suspecting queezed light might be a way of helping push against the vacuum and seems integral to detecting gravitational waves.  Squeezed light is also connected to negative energy.

There are the virtual particles that seem to pop in and out of existence that also have connections to negative energy.

also found this which may possibly be of relation or maybe not,

Pressures and Energies in Magnetized Vacuum and in Casimir effect

CERN Document Server

Rojas, H P

2004-01-01

We study vacuum pressures and energies for electron-positron vacuum zero point energy in a strong magnetic field $B$ and for photon vacuum in Casimir effect, by a common method. Vacuum becomes magnetized, and due to it, the pressure transversal to $B$ is negative, whereas along $B$ an usual positive pressure arises. Similarly, in addition to the usual negative Casimir pressure perpendicular to the plates, the existence of a positive pressure along the plates is predicted. Both vacua bear the property of leading to a negative energy-momentum tensor trace ${\\cal T}_{\\mu}^{\\mu}<0$, which may lead to a repulsive gravity typical of dark energy. By assuming a space distribution of magnetic and/or Casimir domains, cosmological implications are also discussed.

This quote from https://en.wikipedia.org/wiki/Woodward_effect
Quote
Negative bare mass of the electron
The mass of the electron is positive according to the mass–energy equivalence E = mc2 but this invariant mass is made from the bare mass of the electron "clothed" by a virtual photon cloud. According to quantum field theory, as those virtual particles have an energy more than twice the bare mass of the electron, mandatory for pair production in renormalization, the nonelectromagnetic bare mass of the "unclothed" electron has to be negative.[45]

Using the ADM formalism, Woodward proposes that the physical interpretation...

This rings a bell for me.  I was suspecting the anti-matter as having some means of cloaking its negative mass so as to appear positive till annihilation.  Now we see the electron surrounded by the vacuum negative energy seemingly polarized by its presence.  Probably the only thing holding it back would be other annihilated and repelled electrons bonded to their counter parts.

If the electron has its mass effectively reduced by this effect then a bare proton may have its mass effectively increased if its attracting annihilated electrons from the vacuum.

I suspect inertia is a property of the vacuum as do some others.  The reverse time retarded waves would be the anti-matter positron fluctuations and the forward time waves are the vacuum annihilated electron waves.  These waves appear as photons or polarization of the vacuum (forward and reverse time simultaneously) such that an electric field can travel through space.  Its the local metric of this vacuum that determines what appears to be the constant speed of light while non-locally allowing it to change and why when annihilating a charge pair, light is made, while when reversing that light such that it converges in reverse time, we can get back those same two annihilated pairs.

Gravity would be some gradient induced in the vacuum, initially by some unknown method of matters attraction of anti-matter out of the vacuum - particularly positrons - maybe by the outer electron cloud particularly.  This initial polarization of the vacuum is not caused by the gradient in time however, this cloud of negative energy or polarization of the vacuum (e-p phantom pairs) slows time time in a gravity well.  This gradient in time then causes attraction of other matter.  Well maybe, its just a hypothesis.

It's actually not even a hypothesis.  Statements like "inertia is a property of the vacuum" are incoherent.  They're logically equivalent to "two is a property of green".

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #90 on: 07/16/2017 04:56 PM »
WHY NEGATIVE MASS GOES WITH NEGATIVE PRESSURE

In the standard ΛCDM model, the vacuum has a positive energy density and exerts a negative pressure, which drives the cosmic expansion.
Conversely, if the vacuum had a negative energy density, il would exert a positive pressure.
That's why when a model involving negative energies is presented, typical answers like this arise:

Accelerating expansion must have _positive_ energy density of vacuum (then it has negative pressure).
Negative pressure does not cause negative energy.

This puzzled me enough to email Dr Jean-Pierre Petit about his Janus model and how he relates a negative mass density to a negative pressure driving the cosmic expansion process.

Dr Petit was kind enough to write an answer, attached below as a PDF.

The misunderstanding comes from the vacuum being responsible for the accelerating expansion of the universe in the concordance model, whereas in the Janus cosmological model the acceleration of the cosmic expansion does not come from such "vacuum".

This document summarizes the basic relation, with general relativity and the standard equations of physics, between mass energy density and pressure, and it demonstrates why negative mass densities go with a negative pressure.

The main difference with the standard ΛCDM model, besides the two coupled field equations of the Janus model, is that:

• According to the ΛCDM model, the vacuum is "empty" (from a matter point of view: there are almost no real particles in a hard vacuum) but is "non-empty" from an energy point of view. It has a positive energy state. Invisible dark matter (of positive mass) may be there in space, but has nothing to do with the accelerating cosmic expansion, unlike the so-called "dark energy" and its associated negative pressure driving the expansion process. Two different things.

• According to the Janus model, where vacuum appears to be "empty" it is also really not. But don't be fooled, this is not according to some quantum notion of an "energy of the vacuum" and has all to do with the invisible presence of some mass. In our positive sector, the vacuum appears to be a rarefied medium full of photons with almost no mass particles. But in reality some mass, located in the negative sector, is "there" everywhere, especially in the voids of deep space, although being invisible. Such matter has a negative energy hence a negative mass. It interacts with positive mass matter in our positive sector through gravitation (challenging dark matter) and it also exerts a negative pressure (challenging dark energy) which drives the accelerating expansion of the universe. See the paper attached.

This negative mass matter is nothing but antimatter (PT-symmetry) as suggested by Richard Feynman in 1949; and later by Andrei Sakharov in 1967 (see 2nd part of this prior post) who identified it with the lacking primordial antimatter; and nowadays by some other physicists like Julian Barbour who identifies some "mirror matter" populating a "mirror universe having an opposite arrow of time". In the Janus cosmological model: same thing, except that moreover this invisible primordial antimatter interacts through gravitation with our normal matter, as being of negative mass -m = -E/c2 simply because T symmetry goes with E inversion (Souriau 1970, see this prior post).

EDIT — October 4, 2017: Broken links in the original attachement, updated version re-uploaded.
« Last Edit: 10/04/2017 10:10 AM by flux_capacitor »

#### gospacex

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##### Re: Theoretical FTL
« Reply #91 on: 07/17/2017 12:52 PM »
• According to the Janus model, where vacuum appears to be "empty" it is also really not. But don't be fooled, this is not according to some quantum notion of an "energy of the vacuum" and has all to do with the invisible presence of some mass. In our positive sector, the vacuum appears to be a rarefied medium full of photons with almost no mass particles. But in reality some mass, located in the negative sector, is "there" everywhere, especially in the voids of deep space, although being invisible. Such matter has a negative energy hence a negative mass. It interacts with positive mass matter in our positive sector through gravitation

This means that this model predicts that properties of the vacuum change for observers moving with different velocities relative to each other. For vacuum to look the same to all such observers, it has to have energy-momentum tensor proportional to metric.

Quote
This negative mass matter is nothing but antimatter (PT-symmetry) as suggested by Richard Feynman in 1949

This contradicts the previous paragraph, where negative matter was said to be "invisible", i.e. undetectable except via gravity. We experimentally know that antimatter is not undetectable.

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #92 on: 07/17/2017 04:06 PM »
• According to the Janus model, where vacuum appears to be "empty" it is also really not. But don't be fooled, this is not according to some quantum notion of an "energy of the vacuum" and has all to do with the invisible presence of some mass. In our positive sector, the vacuum appears to be a rarefied medium full of photons with almost no mass particles. But in reality some mass, located in the negative sector, is "there" everywhere, especially in the voids of deep space, although being invisible. Such matter has a negative energy hence a negative mass. It interacts with positive mass matter in our positive sector through gravitation

This means that this model predicts that properties of the vacuum change for observers moving with different velocities relative to each other. For vacuum to look the same to all such observers, it has to have energy-momentum tensor proportional to metric.

The nature of dark energy in the standard model cannot be explained otherwise as saying it is some peculiar attribute of the vacuum of space. Actually such "energy of the vacuum" profoundly involves a quantum notion and is a problem with quantum mechanics, not gravitational theories. The wedding between general relativity and quantum mechanics has not been done yet.

The Janus model does not use quantum notions. It stays carefully in a context of differential geometry, using plain-vanilla general relativity only. In the model, the "vacuum energy" does not exist. The space vacuum is just full of photons.

"Vacuum" would be a container. But there is only content.

As such modern "dark energy" of quantum origin is unmanageable in the ΛCDM model, for the lack of a grand unified theory or theory of everything, it is related to a "cosmological constant" as Einstein introduced in his field equations, originally for bad reasons (because he wanted his universe to be static); but such cosmological constant has again recently been took out of mothballs to explain the accelerating cosmic expansion. Thus the use of such cosmological constant which has a "negative pressure proportional to the metric".

The Repulsive Power of the Vacuum™ of the ΛCDM model simply becomes in the Janus model the repulsive power of the negative pressure due to the global negative mass density in the cosmos.

It seems it will take time before people understand that in the Janus model, there is no need for Λ gµν terms anymore in the EFE.

That said, the question about the spatial variation of mass densities due to the negative mass distribution in the Janus model is interesting.

If we're talking about the isotropy and homogeneity of the primitive universe at a very large scale, the Janus model is in accordance with such a cosmological principle.

As an aside: at smaller scales (< 250 million light-years) in the matter-dominated era, the universe is inhomogeneous. We have for example those giant voids with no matter within. By the way, how to explain classically the formation of such voids? As both matter and dark matter are of positive mass (attractive) in the concordance model, all the Jeans instability (the gravitational instability) can do is making lumps of matter, not giant void bubbles.

But any serious cosmological model considers the isotropy and homogeneity of the universe at a very large scale, and so does the Janus model. Although, like matter distribution in the universe at smaller scales, there are similarly local inhomogeneities in the negative mass distribution, there is also a statistical density of negative mass taken globally, at a very large scale. To my knowledge, such a very large scale statistical mass density has not been calculated yet in the model. Will suggest the author to do it
« Last Edit: 07/17/2017 04:16 PM by flux_capacitor »

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #93 on: 07/17/2017 04:06 PM »
This negative mass matter is nothing but antimatter (PT-symmetry) as suggested by Richard Feynman in 1949

This contradicts the previous paragraph, where negative matter was said to be "invisible", i.e. undetectable except via gravity. We experimentally know that antimatter is not undetectable.

You didn't carefully read the diagram "baryon asymmetry of the universe after Sakharov" and the explanation underneath about the nature of particles in the model (the 2nd part of this prior post of mine). So here it is again with more explanation about antimatter:

BARYON ASYMMETRY OF THE UNIVERSE AFTER SAKHAROV
LEFT: positive energy species | RIGHT: negative energy species
A: Primitive universe, 4 components: positive energy quarks and antiquarks; and negative energy quarks and antiquarks.
B: They combine to give more positive mass matter (red) than positive mass antimatter (blue) due to CP violation in the 1st sector; and more negative mass antimatter (purple) than negative mass matter (green) due to opposite CP violation in the 2nd sector.
C: Positive energy quarks and antiquarks stop combining and positive mass matter and antimatter annihilate each other in the first sector. Same thing in the 2nd sector for negative mass matter and antimatter.
D: In the 1st sector, positive energy photons remain from positive mass matter-antimatter annihilation, leaving a remnant of positive mass matter and positive energy antiquarks. In the 2nd sector, negative energy photons remain from negative mass matter-antimatter annihilation, leaving a remnant of negative mass antimatter and negative mass quarks.

So there are two kinds of matter:

positive energy matter : the normal matter we are made of.

negative energy matter : invisible matter located in the negative sector. CPT-symmetry with respect to our matter. T-symmetry is responsible for its invisibility and its opposite mass, from our point of view.

Then both have their own kind of antimatter (this addresses your question):

positive energy antimatter: C-symmetry wrt our matter (this is the antimatter after Dirac, in blue in the diagram). It has a positive mass and falls down in Earth's gravitational field. It has a positive arrow of time, hence is located in our positive sector and is visible to observational instruments. This is the antimatter created in lab.

negative energy antimatter: negative mass matter with a charge conjugation: C×CPT = PT-symmetry wrt our matter (this is the antimatter after Feynman, in violet in the diagram). It has a negative mass and "falls up" in Earth's gravitational field. It has an opposite arrow of time, hence is located in the negative sector and is invisible (T-symmetry is also why it appears as having a negative energy, and a negative mass, from our point of view).

NB: Positive mass antimatter is now absent from our universe due to CP violation during baryogenesis, and matter remains. Conversely in the negative sector, an opposite CP violation occurred and lead to a lack of negative mass matter, so the negative sector has been populated by negative mass antimatter. Taken globally, no violation occurred (Sakharov 1967).

There are also two kinds of photons (the photon is its own antiparticle):

positive energy photons: those photons follow null-geodesics of the metric g(+) (positive sector) and are seen by our eyes and instruments.

negative energy photons: those photons follow null-geodesics of the metric g(-) (negative sector) and cannot be seen by our eyes nor our instruments. This is why we can't optically detect negative mass antimatter (which is a candidate for dark matter) since it emits negative energy photons.

In fact this has been entirely geometrized with dynamical groups 20 years ago. If you like matrices you may read the four references below, which explain C, P, T, and E symmetries and relations. Please be aware those articles may content a few typos and some dated terminology sometimes ("momentum space" instead of "momentum map"; the "twin/shadow/ghost fold" now called the "negative sector" identified to the metric g(-), etc.) but the concepts presented there still hold and are at the heart of the Janus model:

Geometrization of matter and antimatter through coadjoint action of a group on its momentum map:

1: Charges as additional scalar components of the momentum of a group acting on a 10D-space. Geometrical definition of antimatter.

2: Geometrical description of Dirac's antimatter.

3: Geometrical description of Dirac's antimatter. A first geometrical interpretation of antimatter after Feynmann and so-called CPT-theorem.

4: The twin group. Geometrical description of Dirac's antimatter. Geometrical interpretation of antimatter after Feynmann and so-called CPT-theorem.

Documents attached below.
« Last Edit: 07/17/2017 06:07 PM by flux_capacitor »

#### gospacex

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##### Re: Theoretical FTL
« Reply #94 on: 07/18/2017 06:22 AM »
• According to the Janus model, where vacuum appears to be "empty" it is also really not. But don't be fooled, this is not according to some quantum notion of an "energy of the vacuum" and has all to do with the invisible presence of some mass. In our positive sector, the vacuum appears to be a rarefied medium full of photons with almost no mass particles. But in reality some mass, located in the negative sector, is "there" everywhere, especially in the voids of deep space, although being invisible. Such matter has a negative energy hence a negative mass. It interacts with positive mass matter in our positive sector through gravitation

This means that this model predicts that properties of the vacuum change for observers moving with different velocities relative to each other. For vacuum to look the same to all such observers, it has to have energy-momentum tensor proportional to metric.

The nature of dark energy in the standard model cannot be explained otherwise as saying it is some peculiar attribute of the vacuum of space. Actually such "energy of the vacuum" profoundly involves a quantum notion and is a problem with quantum mechanics, not gravitational theories. The wedding between general relativity and quantum mechanics has not been done yet.

The Janus model does not use quantum notions. It stays carefully in a context of differential geometry, using plain-vanilla general relativity only. In the model, the "vacuum energy" does not exist.

A model may postulate that expansion is done by fairies. By itself, this is not a crime.

What's important is that (a) a model should be mathematically consistent, and (b) its predictions should match experiments. If a model fails (a) or (b), it is in trouble.

By the looks of it, Janus model predicts that properties of the vacuum change for observers moving with different velocities relative to each other. This contradicts experiments.
« Last Edit: 07/18/2017 06:22 AM by gospacex »

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #95 on: 07/19/2017 10:47 AM »
By the looks of it, Janus model predicts that properties of the vacuum change for observers moving with different velocities relative to each other. This contradicts experiments.

I'm not quite sure what you are referring to. Can you please expand further with maths what does represent "isotropic properties of the vacuum" and point to some of the experiments your referred to, whose results showed such isotropic "properties of the vacuum"?
« Last Edit: 07/21/2017 11:04 AM by flux_capacitor »

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #96 on: 07/21/2017 12:53 AM »
What's important is that (a) a model should be mathematically consistent, and (b) its predictions should match experiments. If a model fails (a) or (b), it is in trouble.
I agree with you. You forgot (c) a model should also explain observations.
This is not exactly like point (b) which states a model can predict some physical behavior that can later be confirmed/disproved with experimental setups; while explaining observational data is the other way: popper falsifiability showing if a model can naturally fit, or if a model needs some tweaks to fit, or if a model can't fit at all new peculiar observations.

About this question of the cosmic expansion vs observations, here is the work done by Gilles d'Agostini (coworker of Dr Petit) about the Janus model and the acceleration of the cosmic expansion:

A new interpretation of the cosmic acceleration (paper attached below)

The work is structured on the comparison to the largest observational data available to date (740 high-z supernovae). The Janus bimetric model model (pink curve) challenges the ΛCDM concordance model (dotted black curve) quite well:
- in order for the concordance model to fit the curve, it has to include dark energy (non-zero cosmological constant added to the Einstein field equations) and adjust no less than 6 free parameters.
- Conversely, the exact solution of the Janus model fits naturally without resorting to a "vacuum dark energy": negative acceleration (i.e. deceleration) coefficient:
q0 = -0.087 ±0.015
is rather small, with no need to introduce a non-zero cosmological constant to fit the available data.

The exact solution of the Janus cosmological model for the evolution of the positive mass spacetime in the matter-dominated era is the same as Bonnor's parametric equation of the scale function S of a universe with negative mass and without a cosmological constant, given in the section 4.3 of ref. [6] in this prior post:

Quote from: William Bonnor

4.3. p=0, Λ=0

This case is actually included in the foregoing, but I mention it explicitly because it corresponds to the simplest Friedmann models of traditional cosmology. It follows from (27) that must be nonnegative, and then from (26) that k = -1. Integrating (25) with p = 0 and k = -1 we find

S = α2 cosh2 u
t + to = α2 (1/2 sinh 2u + u)

where α and to are constants.

It is worth noting that while the expansion of the positive mass universe is accelerating, conversely, the negative mass universe undergoes a decelerating expansion and follows one of the classical Friedmann models.
« Last Edit: 07/21/2017 11:21 AM by flux_capacitor »

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #97 on: 07/21/2017 01:18 AM »
Dr Petit, 80 years old, is making a series of Youtube videos to popularize the Janus cosmological model and explain the basic concepts. There are 19 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.

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.
« Last Edit: 08/03/2017 05:53 PM by flux_capacitor »

#### flux_capacitor

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##### Re: Theoretical FTL
« Reply #98 on: 07/28/2017 11:09 AM »
Explaining the Janus model takes too much posts and I do not want to "hijack" a general thread like this one. So I created a dedicated topic about the model instead:
Janus Cosmological Model & FTL travel