Quote from: gospacex on 07/13/2017 11:19 AMQuote from: flux_capacitor on 07/12/2017 10:40 PMBut 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.

Quote from: flux_capacitor on 07/12/2017 10:40 PMBut 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).

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.

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.

Quote from: gospacex on 07/13/2017 11:51 AMNegative 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 ρwith α > -1α 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.

Pressures and Energies in Magnetized Vacuum and in Casimir effectCERN Document ServerRojas, H P2004-01-01We 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.

Quote from: gospacex on 07/13/2017 11:51 AMOf 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 ρc^{2}What is it? n is the "density number" (number of particles per cubic meter) multiplied by mc^{2}, 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?!

Quote from: https://worldwidescience.org/topicpages/c/casimir+energy+density.htmlhttp://cds.cern.ch/record/726991/files/0402213.pdfPressures and Energies in Magnetized Vacuum and in Casimir effectCERN Document ServerRojas, H P2004-01-01We 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.

Quote from: flux_capacitor on 07/14/2017 12:30 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.

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

Quote from: gospacex on 07/14/2017 03:58 PMQuote from: flux_capacitor on 07/14/2017 12:30 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

Quote from: flux_capacitor on 07/14/2017 01:21 AMQuote from: gospacex on 07/13/2017 11:51 AMNegative 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 ρwith α > -1α 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_energySome 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,Quote from: https://worldwidescience.org/topicpages/c/casimir+energy+density.htmlhttp://cds.cern.ch/record/726991/files/0402213.pdfPressures and Energies in Magnetized Vacuum and in Casimir effectCERN Document ServerRojas, H P2004-01-01We 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.

Negative bare mass of the electron[edit]The mass of the electron is positive according to the massenergy 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...

Quote from: dustinthewind on 07/14/2017 02:16 AMQuote from: flux_capacitor on 07/14/2017 01:21 AMQuote from: gospacex on 07/13/2017 11:51 AMNegative 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 ρwith α > -1α 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_energySome 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,Quote from: https://worldwidescience.org/topicpages/c/casimir+energy+density.htmlhttp://cds.cern.ch/record/726991/files/0402213.pdfPressures and Energies in Magnetized Vacuum and in Casimir effectCERN Document ServerRojas, H P2004-01-01We 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 QuoteNegative bare mass of the electron[edit]The mass of the electron is positive according to the massenergy 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.

Accelerating expansion must have _positive_ energy density of vacuum (then it has negative pressure).

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

Quote from: flux_capacitor on 07/16/2017 04:56 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 gravitationThis 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 from: flux_capacitor on 07/16/2017 04:56 PMThis negative mass matter is nothing but antimatter (PT-symmetry) as suggested by Richard Feynman in 1949This 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.

Quote from: gospacex on 07/17/2017 12:52 PMQuote from: flux_capacitor on 07/16/2017 04:56 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 gravitationThis 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.

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.

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.

4.3. p=0, Λ=0This 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 S̈ must be nonnegative, and then from (26) that k = -1. Integrating (25) with p = 0 and k = -1 we findS = α^{2} cosh^{2} ut + t_{o} = α^{2} (1/2 sinh 2u + u)where α and t_{o} are constants.