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| Tags: breakdown, interpretation, schwingers, vacuum |
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#1
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(New thread as the original one was bifurcated).
Schwinger (1951) (& see arXiv:hep-ph/9805507, Melissinos) hypothesized that vacuum would break down if, in a field with intensity Es, an electron would amass the energy mc^2 over a path of the (rationalized) CWL hbar/mc. Thus Es*el*Lrcw = mc^2 with Es given as 1.3x10^18 V/m with hbar/mc or, Ess would be 2.1x10^17 V/m with h/mc (regular) (1c) being a statement of force time distance, with the two interpretations of CWL of being either h/mc or hbar/mc. (Schwinger paper not to hand). I developed my own version (unknowingly) of the Schwinger effect While trying to deduce the content of the vacuum for my Dual Space theory. It can be seen in SI units (overly detailed), in my paper #1, "Permittivity", on my website http://www.dualspace.net I deduced that the vacuum consists of a matrix of elastically-bound pairs of electrons and positrons centered in a cubic domain of L = 3.514e-14m. Fig. 2 op cit Each charge has the range of a half-cell: L' = L/2 = CWL*FSC The half-cell range L' of each charge exactly equals the Compton wavelength scaled down by the FSC = 1/137. The FSC is really the scale factor between pair-space and our universe, as amplified below. These polarizable charge pairs are what make the permitivity of space equal to eps = 8.8e-12 F/m (or Coul/volt-meter) The dimension L was derived by assuming the cell or cube was a capacitor which, with Vc = 1.022MV (from Vce = 2mc^2 of pair production) across it, would produce 2e. This is pair-production, that is, Vc was required to push them out of the cell, and it is a reproduction of Schwinger's effect (to cause vacuum breakdown with issuance of pairs). Permittivity eps was used in computing the capacity C = eps*L^2/L = eps*L so that, fully "charged" C*Vc = 2e In other words as we gradually raise the voltage up to Vc the pair will approach the boundary and exit. We get the critical field intensity Ec as Ec = Vc/L = 2.88x10^19 V/m Eq. 8a (It is impossible to impose a step voltage on a capacitor or on the 'primal cell' as this would require a singular delta function of current). It will be seen that Ec = Ess/FSC or Ec = Ess* 137 times that is, the ratio is nicely alpha, when using 'regular' CWL (1c above). We can calculate a maximum force Fmax: Fmax = Ec*e = 4.6N Eq. 8b Thus there is a linear spring constant K K = Fmax/L' = 2.6x10^14 N/m Eq. 11a Then the work done over L' (where F = Kx) is (both) W = .5 Fmax * L' x 2 = mc^2 Eq. 8c for both electron and positron. Therefore we push for the use of h/mc in Ess above, and conclude that Schwinger's idea justifies the logic of dual space theory. Many other parameters of the vacuum follow immediately, the mass and charge density, resonant frequency, modulus of elasticity, transmission at the speed of light as shown in Eq. 9-13 op cit. But the most important conclusion is that our stars came from electrons out of pair space, shored up by the fact that the electrons expand by 1/FSC^3 or 2.5 million to become the density of iron, the flagship element of our universe. The expansion energy is sufficient to accelerate iron to the speed of light. (Eq. 13-19) of the DS book. Briefly the energy density of pairspace times alpha^3 = rho-Fe* c^2. The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. John Polasek http:www.dualspace.net |
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#2
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"jpolasek" wrote in message
ups.com... (New thread as the original one was bifurcated). Schwinger (1951) (& see arXiv:hep-ph/9805507, Melissinos) hypothesized that vacuum would break down if, in a field with intensity Es, an electron would amass the energy mc^2 over a path of the (rationalized) CWL hbar/mc. Thus Es*el*Lrcw = mc^2 with Es given as 1.3x10^18 V/m with hbar/mc or, Ess would be 2.1x10^17 V/m with h/mc (regular) (1c) being a statement of force time distance, with the two interpretations of CWL of being either h/mc or hbar/mc. (Schwinger paper not to hand). I developed my own version (unknowingly) of the Schwinger effect While trying to deduce the content of the vacuum for my Dual Space theory. It can be seen in SI units (overly detailed), in my paper #1, "Permittivity", on my website http://www.dualspace.net I deduced that the vacuum consists of a matrix of elastically-bound pairs of electrons and positrons centered in a cubic domain of L = 3.514e-14m. Fig. 2 op cit Each charge has the range of a half-cell: L' = L/2 = CWL*FSC The half-cell range L' of each charge exactly equals the Compton wavelength scaled down by the FSC = 1/137. The FSC is really the scale factor between pair-space and our universe, as amplified below. Not exactly. The real factor is the sqrt(alpha) which is about 1/11.706. And this is simply the ratio between electronic charge and quantum "vacuum" charge (QVC) = +,- sqrt(hbar*c). With QVC being charge associated with gauge bosons -- most notably photons. And this is just taking vacuum polarization to tree level. The scale factor between our spacetime and pair spacetime is most likely much greater than this if we take into consideration a Randall-Sundrum RS1-like "warped geometry" scenario. Most likely on the order of 10^18. But from our perspective it looks like on the order of alpha. These polarizable charge pairs are what make the permitivity of space equal to eps = 8.8e-12 F/m (or Coul/volt-meter) The dimension L was derived by assuming the cell or cube was a capacitor which, with Vc = 1.022MV (from Vce = 2mc^2 of pair production) across it, would produce 2e. This is pair-production, that is, Vc was required to push them out of the cell, and it is a reproduction of Schwinger's effect (to cause vacuum breakdown with issuance of pairs). Permittivity eps was used in computing the capacity C = eps*L^2/L = eps*L so that, fully "charged" C*Vc = 2e In other words as we gradually raise the voltage up to Vc the pair will approach the boundary and exit. We get the critical field intensity Ec as Ec = Vc/L = 2.88x10^19 V/m Eq. 8a (It is impossible to impose a step voltage on a capacitor or on the 'primal cell' as this would require a singular delta function of current). It will be seen that Ec = Ess/FSC or Ec = Ess* 137 times that is, the ratio is nicely alpha, when using 'regular' CWL (1c above). We can calculate a maximum force Fmax: Fmax = Ec*e = 4.6N Eq. 8b Thus there is a linear spring constant K K = Fmax/L' = 2.6x10^14 N/m Eq. 11a Then the work done over L' (where F = Kx) is (both) W = .5 Fmax * L' x 2 = mc^2 Eq. 8c for both electron and positron. Therefore we push for the use of h/mc in Ess above, and conclude that Schwinger's idea justifies the logic of dual space theory. Some of the logic. The "dual space" part IMHO, is a natural follow thru to explain a necessary "hidden sector". "Higgs-field Portal into Hidden Sectors" -- Brian Patt and Frank Wilczek http://www.arxiv.org/abs/hep-ph/0605188 We can see here that even Wilczek is getting on the bandwagon of dual spacetime scenarios with talk of "hidden sectors" and "phantom matter". ;-) Yeah, baby! Many other parameters of the vacuum follow immediately, the mass and charge density, resonant frequency, modulus of elasticity, transmission at the speed of light as shown in Eq. 9-13 op cit. But the most important conclusion is that our stars came from electrons out of pair space, shored up by the fact that the electrons expand by 1/FSC^3 or 2.5 million to become the density of iron, the flagship element of our universe. The expansion energy is sufficient to accelerate iron to the speed of light. (Eq. 13-19) of the DS book. Briefly the energy density of pairspace times alpha^3 = rho-Fe* c^2. The above paragraph is messed up. Pions can be produced in the same way as e+e- pairs theoretically. The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. As Melissinos points out, this hypothesis has somewhat been shown to be true by the SLAC e144 experiment. There are some planned experiments using the new X-Ray Free Electron Lasers to further test the hypothesis but I don't know what the current status is. The effect also means that in the vincinity of an electron to order hbar/mc, the field strength of an electron is enough to spontaneously create pairs from the quantum "vacuum". This is all covered quite nicely in Milonni's "The Quantum Vacuum: An Introduction to QED". But the quantum "vacuum" is more than just John's pair-space. It includes a dynamical intersection "distance" between the dual spacetimes. FrediFizzx Quantum Vacuum Charge papers; http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps http://www.arxiv.org/abs/physics/0601110 http://www.vacuum-physics.com |
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On Sun, 3 Sep 2006 18:02:10 -0700, "FrediFizzx"
wrote: "jpolasek" wrote in message oups.com... (New thread as the original one was bifurcated). Schwinger (1951) (& see arXiv:hep-ph/9805507, Melissinos) hypothesized that vacuum would break down if, in a field with intensity Es, an electron would amass the energy mc^2 over a path of the (rationalized) CWL hbar/mc. Thus Es*el*Lrcw = mc^2 with Es given as 1.3x10^18 V/m with hbar/mc or, Ess would be 2.1x10^17 V/m with h/mc (regular) (1c) being a statement of force time distance, with the two interpretations of CWL of being either h/mc or hbar/mc. (Schwinger paper not to hand). I developed my own version (unknowingly) of the Schwinger effect While trying to deduce the content of the vacuum for my Dual Space theory. It can be seen in SI units (overly detailed), in my paper #1, "Permittivity", on my website http://www.dualspace.net I deduced that the vacuum consists of a matrix of elastically-bound pairs of electrons and positrons centered in a cubic domain of L = 3.514e-14m. Fig. 2 op cit Each charge has the range of a half-cell: L' = L/2 = CWL*FSC The half-cell range L' of each charge exactly equals the Compton wavelength scaled down by the FSC = 1/137. The FSC is really the scale factor between pair-space and our universe, as amplified below. Not exactly. The real factor is the sqrt(alpha) which is about 1/11.706. And this is simply the ratio between electronic charge and quantum "vacuum" charge (QVC) = +,- sqrt(hbar*c). Fredi you need eps0 in sqrt(hbar*c*eps0) to make it coulombs and then it's about 3.3 electrons or 1/sqrt(4pi*alpha) electrons. With QVC being charge associated with gauge bosons -- most notably photons. And this is just taking vacuum polarization to tree level. The scale factor between our spacetime and pair spacetime is most likely much greater than this if we take into consideration a Randall-Sundrum RS1-like "warped geometry" scenario. Most likely on the order of 10^18. But from our perspective it looks like on the order of alpha. Fredi, what does your theory say about the Schwinger effect? What features would cause the vacuum to emit pairs? These polarizable charge pairs are what make the permitivity of space equal to eps = 8.8e-12 F/m (or Coul/volt-meter) The dimension L was derived by assuming the cell or cube was a capacitor which, with Vc = 1.022MV (from Vce = 2mc^2 of pair production) across it, would produce 2e. This is pair-production, that is, Vc was required to push them out of the cell, and it is a reproduction of Schwinger's effect (to cause vacuum breakdown with issuance of pairs). Permittivity eps was used in computing the capacity C = eps*L^2/L = eps*L so that, fully "charged" C*Vc = 2e In other words as we gradually raise the voltage up to Vc the pair will approach the boundary and exit. We get the critical field intensity Ec as Ec = Vc/L = 2.88x10^19 V/m Eq. 8a (It is impossible to impose a step voltage on a capacitor or on the 'primal cell' as this would require a singular delta function of current). It will be seen that Ec = Ess/FSC or Ec = Ess* 137 times that is, the ratio is nicely alpha, when using 'regular' CWL (1c above). We can calculate a maximum force Fmax: Fmax = Ec*e = 4.6N Eq. 8b Thus there is a linear spring constant K K = Fmax/L' = 2.6x10^14 N/m Eq. 11a Then the work done over L' (where F = Kx) is (both) W = .5 Fmax * L' x 2 = mc^2 Eq. 8c for both electron and positron. Therefore we push for the use of h/mc in Ess above, and conclude that Schwinger's idea justifies the logic of dual space theory. Some of the logic. The "dual space" part IMHO, is a natural follow thru to explain a necessary "hidden sector". "Higgs-field Portal into Hidden Sectors" -- Brian Patt and Frank Wilczek http://www.arxiv.org/abs/hep-ph/0605188 We can see here that even Wilczek is getting on the bandwagon of dual spacetime scenarios with talk of "hidden sectors" and "phantom matter". ;-) Yeah, baby! Many other parameters of the vacuum follow immediately, the mass and charge density, resonant frequency, modulus of elasticity, transmission at the speed of light as shown in Eq. 9-13 op cit. But the most important conclusion is that our stars came from electrons out of pair space, shored up by the fact that the electrons expand by 1/FSC^3 or 2.5 million to become the density of iron, the flagship element of our universe. The expansion energy is sufficient to accelerate iron to the speed of light. (Eq. 13-19) of the DS book. Briefly the energy density of pairspace times alpha^3 = rho-Fe* c^2. The above paragraph is messed up. Pions can be produced in the same way as e+e- pairs theoretically. Fred I am talking about creation ab initio; no lab in the world can extract just the electron. The Milossimos paper is about banging two laser beams together just to produce pairs which are temporary sparks and then they're short by 3 orders of magnitude. I am talking about the electronbeams as currents that suck together (Faraday) rather than repel and cook for 10Byrs to become our stars full of elements. I'm saying the most they could be initially would be iron; heavier atoms are by nuclear accretion. The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. As Melissinos points out, this hypothesis has somewhat been shown to be true by the SLAC e144 experiment. There are some planned experiments using the new X-Ray Free Electron Lasers to further test the hypothesis but I don't know what the current status is. The effect also means that in the vincinity of an electron to order hbar/mc, the field strength of an electron is enough to spontaneously create pairs from the quantum "vacuum". Fred, to get my field Ec from an electron it would have to penetrate down to .39 of L', the cell radius. It is probably a forbidden operation. This is all covered quite nicely in Milonni's "The Quantum Vacuum: An Introduction to QED". But the quantum "vacuum" is more than just John's pair-space. It includes a dynamical intersection "distance" between the dual spacetimes. Fred I think you can see that I insist on working from first principles and I have put up a lot of numbers that you can take a shot at. So have at it. I don't believe in all the arcane, the RS warped geometry, or spacetime either for that matter. None of that mumbo jumbo is necessary. FrediFizzx Quantum Vacuum Charge papers; http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps http://www.arxiv.org/abs/physics/0601110 http://www.vacuum-physics.com John Polasek |
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"John C. Polasek" wrote in message
... On Sun, 3 Sep 2006 18:02:10 -0700, "FrediFizzx" wrote: "jpolasek" wrote in message oups.com... (New thread as the original one was bifurcated). Schwinger (1951) (& see arXiv:hep-ph/9805507, Melissinos) hypothesized that vacuum would break down if, in a field with intensity Es, an electron would amass the energy mc^2 over a path of the (rationalized) CWL hbar/mc. Thus Es*el*Lrcw = mc^2 with Es given as 1.3x10^18 V/m with hbar/mc or, Ess would be 2.1x10^17 V/m with h/mc (regular) (1c) being a statement of force time distance, with the two interpretations of CWL of being either h/mc or hbar/mc. (Schwinger paper not to hand). I developed my own version (unknowingly) of the Schwinger effect While trying to deduce the content of the vacuum for my Dual Space theory. It can be seen in SI units (overly detailed), in my paper #1, "Permittivity", on my website http://www.dualspace.net I deduced that the vacuum consists of a matrix of elastically-bound pairs of electrons and positrons centered in a cubic domain of L = 3.514e-14m. Fig. 2 op cit Each charge has the range of a half-cell: L' = L/2 = CWL*FSC The half-cell range L' of each charge exactly equals the Compton wavelength scaled down by the FSC = 1/137. The FSC is really the scale factor between pair-space and our universe, as amplified below. Not exactly. The real factor is the sqrt(alpha) which is about 1/11.706. And this is simply the ratio between electronic charge and quantum "vacuum" charge (QVC) = +,- sqrt(hbar*c). Fredi you need eps0 in sqrt(hbar*c*eps0) to make it coulombs and then it's about 3.3 electrons or 1/sqrt(4pi*alpha) electrons. Well, in SI units it is actually sqrt(4pi*eps0*hbar*c) since in SI Units the relationship is, alpha = e^2/(4pi*eps0*hbar*c) In cgs units or Heaviside-Lorentz units, I don't need eps0. 1/4pi works just fine for eps0. Anywise, the ratio for electronic charge to QVC is always about 1/11.706 no matter what units you are using. With QVC being charge associated with gauge bosons -- most notably photons. And this is just taking vacuum polarization to tree level. The scale factor between our spacetime and pair spacetime is most likely much greater than this if we take into consideration a Randall-Sundrum RS1-like "warped geometry" scenario. Most likely on the order of 10^18. But from our perspective it looks like on the order of alpha. Fredi, what does your theory say about the Schwinger effect? What features would cause the vacuum to emit pairs? Exactly the same as what Melissinos is talking about. Any slowly varying critical field strength electric or magnetic field should produce pairs from the quantum "vacuum". You should be able to jack up the field strength even more to spontaneously produce pions also. However, we suspect and predict that neutrino pairs should be produced also by critical field strength related to 15 MeV. Difficult to detect though. These polarizable charge pairs are what make the permitivity of space equal to eps = 8.8e-12 F/m (or Coul/volt-meter) The dimension L was derived by assuming the cell or cube was a capacitor which, with Vc = 1.022MV (from Vce = 2mc^2 of pair production) across it, would produce 2e. This is pair-production, that is, Vc was required to push them out of the cell, and it is a reproduction of Schwinger's effect (to cause vacuum breakdown with issuance of pairs). Permittivity eps was used in computing the capacity C = eps*L^2/L = eps*L so that, fully "charged" C*Vc = 2e In other words as we gradually raise the voltage up to Vc the pair will approach the boundary and exit. We get the critical field intensity Ec as Ec = Vc/L = 2.88x10^19 V/m Eq. 8a (It is impossible to impose a step voltage on a capacitor or on the 'primal cell' as this would require a singular delta function of current). It will be seen that Ec = Ess/FSC or Ec = Ess* 137 times that is, the ratio is nicely alpha, when using 'regular' CWL (1c above). We can calculate a maximum force Fmax: Fmax = Ec*e = 4.6N Eq. 8b Thus there is a linear spring constant K K = Fmax/L' = 2.6x10^14 N/m Eq. 11a Then the work done over L' (where F = Kx) is (both) W = .5 Fmax * L' x 2 = mc^2 Eq. 8c for both electron and positron. Therefore we push for the use of h/mc in Ess above, and conclude that Schwinger's idea justifies the logic of dual space theory. Some of the logic. The "dual space" part IMHO, is a natural follow thru to explain a necessary "hidden sector". "Higgs-field Portal into Hidden Sectors" -- Brian Patt and Frank Wilczek http://www.arxiv.org/abs/hep-ph/0605188 We can see here that even Wilczek is getting on the bandwagon of dual spacetime scenarios with talk of "hidden sectors" and "phantom matter". ;-) Yeah, baby! Many other parameters of the vacuum follow immediately, the mass and charge density, resonant frequency, modulus of elasticity, transmission at the speed of light as shown in Eq. 9-13 op cit. But the most important conclusion is that our stars came from electrons out of pair space, shored up by the fact that the electrons expand by 1/FSC^3 or 2.5 million to become the density of iron, the flagship element of our universe. The expansion energy is sufficient to accelerate iron to the speed of light. (Eq. 13-19) of the DS book. Briefly the energy density of pairspace times alpha^3 = rho-Fe* c^2. The above paragraph is messed up. Pions can be produced in the same way as e+e- pairs theoretically. Fred I am talking about creation ab initio; no lab in the world can extract just the electron. The Milossimos paper is about banging two laser beams together just to produce pairs which are temporary sparks and then they're short by 3 orders of magnitude. I am talking about the electronbeams as currents that suck together (Faraday) rather than repel and cook for 10Byrs to become our stars full of elements. I'm saying the most they could be initially would be iron; heavier atoms are by nuclear accretion. How exactly does a group of electrons make protons and neutrons? The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. As Melissinos points out, this hypothesis has somewhat been shown to be true by the SLAC e144 experiment. There are some planned experiments using the new X-Ray Free Electron Lasers to further test the hypothesis but I don't know what the current status is. The effect also means that in the vincinity of an electron to order hbar/mc, the field strength of an electron is enough to spontaneously create pairs from the quantum "vacuum". Fred, to get my field Ec from an electron it would have to penetrate down to .39 of L', the cell radius. It is probably a forbidden operation. John, calculate the electric field strength of an electron at a distance of hbar/mc from it. It is equal to Schwinger's Ec. What about closer to the electron? Field strength is even higher so how do we even find the original electron from all the electrons in the pairs that are being produced at a distance of less than hbar/mc? LOL! This is all covered quite nicely in Milonni's "The Quantum Vacuum: An Introduction to QED". But the quantum "vacuum" is more than just John's pair-space. It includes a dynamical intersection "distance" between the dual spacetimes. Fred I think you can see that I insist on working from first principles and I have put up a lot of numbers that you can take a shot at. So have at it. I don't believe in all the arcane, the RS warped geometry, or spacetime either for that matter. None of that mumbo jumbo is necessary. Well, I already have told you many times that you are way off on your "pair-space" density figures. FrediFizzx Quantum Vacuum Charge papers; http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps http://www.arxiv.org/abs/physics/0601110 http://www.vacuum-physics.com |
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On Sun, 3 Sep 2006 20:47:55 -0700, "FrediFizzx"
wrote: "John C. Polasek" wrote in message .. . On Sun, 3 Sep 2006 18:02:10 -0700, "FrediFizzx" wrote: "jpolasek" wrote in message oups.com... (New thread as the original one was bifurcated). Schwinger (1951) (& see arXiv:hep-ph/9805507, Melissinos) hypothesized that vacuum would break down if, in a field with intensity Es, an electron would amass the energy mc^2 over a path of the (rationalized) CWL hbar/mc. Thus Es*el*Lrcw = mc^2 with Es given as 1.3x10^18 V/m with hbar/mc or, Ess would be 2.1x10^17 V/m with h/mc (regular) (1c) being a statement of force time distance, with the two interpretations of CWL of being either h/mc or hbar/mc. (Schwinger paper not to hand). I developed my own version (unknowingly) of the Schwinger effect While trying to deduce the content of the vacuum for my Dual Space theory. It can be seen in SI units (overly detailed), in my paper #1, "Permittivity", on my website http://www.dualspace.net I deduced that the vacuum consists of a matrix of elastically-bound pairs of electrons and positrons centered in a cubic domain of L = 3.514e-14m. Fig. 2 op cit Each charge has the range of a half-cell: L' = L/2 = CWL*FSC The half-cell range L' of each charge exactly equals the Compton wavelength scaled down by the FSC = 1/137. The FSC is really the scale factor between pair-space and our universe, as amplified below. Not exactly. The real factor is the sqrt(alpha) which is about 1/11.706. And this is simply the ratio between electronic charge and quantum "vacuum" charge (QVC) = +,- sqrt(hbar*c). You need to stick to ratios because neither charge has coulombs any more. If 1/4pi = eps0 you are losing the coulombs/volt-meter coefficient which reveals that space can store energy at all. Fredi you need eps0 in sqrt(hbar*c*eps0) to make it coulombs and then it's about 3.3 electrons or 1/sqrt(4pi*alpha) electrons. Well, in SI units it is actually sqrt(4pi*eps0*hbar*c) since in SI Units the relationship is, alpha = e^2/(4pi*eps0*hbar*c) In cgs units or Heaviside-Lorentz units, I don't need eps0. 1/4pi works just fine for eps0. Anywise, the ratio for electronic charge to QVC is always about 1/11.706 no matter what units you are using. OK 4pi and 11.7. But what is alpha the square of, that it should be valuable in comparing two charge units? With QVC being charge associated with gauge bosons -- most notably photons. And this is just taking vacuum polarization to tree level. The scale factor between our spacetime and pair spacetime is most likely much greater than this if we take into consideration a Randall-Sundrum RS1-like "warped geometry" scenario. Most likely on the order of 10^18. But from our perspective it looks like on the order of alpha. Fredi, what does your theory say about the Schwinger effect? What features would cause the vacuum to emit pairs? Exactly the same as what Melissinos is talking about. Any slowly varying critical field strength electric or magnetic field should produce pairs from the quantum "vacuum". You should be able to jack up the field strength even more to spontaneously produce pions also. However, we suspect and predict that neutrino pairs should be produced also by critical field strength related to 15 MeV. Difficult to detect though. 15MeV? Over what distance, CWL? If vacuum breaks down at 1.022MeV, how are you going to get to 15? These polarizable charge pairs are what make the permitivity of space equal to eps = 8.8e-12 F/m (or Coul/volt-meter) The dimension L was derived by assuming the cell or cube was a capacitor which, with Vc = 1.022MV (from Vce = 2mc^2 of pair production) across it, would produce 2e. This is pair-production, that is, Vc was required to push them out of the cell, and it is a reproduction of Schwinger's effect (to cause vacuum breakdown with issuance of pairs). Permittivity eps was used in computing the capacity C = eps*L^2/L = eps*L so that, fully "charged" C*Vc = 2e In other words as we gradually raise the voltage up to Vc the pair will approach the boundary and exit. We get the critical field intensity Ec as Ec = Vc/L = 2.88x10^19 V/m Eq. 8a (It is impossible to impose a step voltage on a capacitor or on the 'primal cell' as this would require a singular delta function of current). It will be seen that Ec = Ess/FSC or Ec = Ess* 137 times that is, the ratio is nicely alpha, when using 'regular' CWL (1c above). We can calculate a maximum force Fmax: Fmax = Ec*e = 4.6N Eq. 8b Thus there is a linear spring constant K K = Fmax/L' = 2.6x10^14 N/m Eq. 11a Then the work done over L' (where F = Kx) is (both) W = .5 Fmax * L' x 2 = mc^2 Eq. 8c for both electron and positron. Therefore we push for the use of h/mc in Ess above, and conclude that Schwinger's idea justifies the logic of dual space theory. Some of the logic. The "dual space" part IMHO, is a natural follow thru to explain a necessary "hidden sector". "Higgs-field Portal into Hidden Sectors" -- Brian Patt and Frank Wilczek http://www.arxiv.org/abs/hep-ph/0605188 We can see here that even Wilczek is getting on the bandwagon of dual spacetime scenarios with talk of "hidden sectors" and "phantom matter". ;-) Yeah, baby! Many other parameters of the vacuum follow immediately, the mass and charge density, resonant frequency, modulus of elasticity, transmission at the speed of light as shown in Eq. 9-13 op cit. But the most important conclusion is that our stars came from electrons out of pair space, shored up by the fact that the electrons expand by 1/FSC^3 or 2.5 million to become the density of iron, the flagship element of our universe. The expansion energy is sufficient to accelerate iron to the speed of light. (Eq. 13-19) of the DS book. Briefly the energy density of pairspace times alpha^3 = rho-Fe* c^2. The above paragraph is messed up. Pions can be produced in the same way as e+e- pairs theoretically. Fred I am talking about creation ab initio; no lab in the world can extract just the electron. The Milossimos paper is about banging two laser beams together just to produce pairs which are temporary sparks and then they're short by 3 orders of magnitude. I am talking about the electronbeams as currents that suck together (Faraday) rather than repel and cook for 10Byrs to become our stars full of elements. I'm saying the most they could be initially would be iron; heavier atoms are by nuclear accretion. How exactly does a group of electrons make protons and neutrons? Just the same way it makes subdivisions after 10 billion years. The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. As Melissinos points out, this hypothesis has somewhat been shown to be true by the SLAC e144 experiment. There are some planned experiments using the new X-Ray Free Electron Lasers to further test the hypothesis but I don't know what the current status is. The effect also means that in the vincinity of an electron to order hbar/mc, the field strength of an electron is enough to spontaneously create pairs from the quantum "vacuum". Fred, to get my field Ec from an electron it would have to penetrate down to .39 of L', the cell radius. It is probably a forbidden operation. John, calculate the electric field strength of an electron at a distance of hbar/mc from it. It is equal to Schwinger's Ec. What about closer to the electron? Field strength is even higher so how do we even find the original electron from all the electrons in the pairs that are being produced at a distance of less than hbar/mc? LOL! No Fred, it's 137x lower than Schwingers; it's 9.6e15 V/m vs 1.3e18 V/m. This is all covered quite nicely in Milonni's "The Quantum Vacuum: An Introduction to QED". But the quantum "vacuum" is more than just John's pair-space. It includes a dynamical intersection "distance" between the dual spacetimes. Fred I think you can see that I insist on working from first principles and I have put up a lot of numbers that you can take a shot at. So have at it. I don't believe in all the arcane, the RS warped geometry, or spacetime either for that matter. None of that mumbo jumbo is necessary. Well, I already have told you many times that you are way off on your "pair-space" density figures. Fred: I tried to make you see that thepairspace electron density of 1me/L^3 or 2.05e10 kg/m^3 is 2.5 million or 1/alpha^3 that of iron. (Eq. 10 of paper). The uncreated electrons from pairspace, when freed up (created, but not by electric field), expand by 1/alpha, reaching the density of iron and the speed of light and become the raw material for all the stars. I had a whole book written on Dual Space in 2001 in which cell size was twice as small, L = alpha x CWL which seemed so natural, till after I pondered the 8:1 density ratio, that I saw that I needed to double L to 3.514e-14m. As a result, the density turned to iron. FrediFizzx Quantum Vacuum Charge papers; http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps http://www.arxiv.org/abs/physics/0601110 http://www.vacuum-physics.com John Polasek http:www.dualspace.net |
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"John C. Polasek" wrote in message
... On Sun, 3 Sep 2006 20:47:55 -0700, "FrediFizzx" wrote: "John C. Polasek" wrote in message .. . On Sun, 3 Sep 2006 18:02:10 -0700, "FrediFizzx" wrote: "jpolasek" wrote in message oups.com... (New thread as the original one was bifurcated). Schwinger (1951) (& see arXiv:hep-ph/9805507, Melissinos) hypothesized that vacuum would break down if, in a field with intensity Es, an electron would amass the energy mc^2 over a path of the (rationalized) CWL hbar/mc. Thus Es*el*Lrcw = mc^2 with Es given as 1.3x10^18 V/m with hbar/mc or, Ess would be 2.1x10^17 V/m with h/mc (regular) (1c) being a statement of force time distance, with the two interpretations of CWL of being either h/mc or hbar/mc. (Schwinger paper not to hand). I developed my own version (unknowingly) of the Schwinger effect While trying to deduce the content of the vacuum for my Dual Space theory. It can be seen in SI units (overly detailed), in my paper #1, "Permittivity", on my website http://www.dualspace.net I deduced that the vacuum consists of a matrix of elastically-bound pairs of electrons and positrons centered in a cubic domain of L = 3.514e-14m. Fig. 2 op cit Each charge has the range of a half-cell: L' = L/2 = CWL*FSC The half-cell range L' of each charge exactly equals the Compton wavelength scaled down by the FSC = 1/137. The FSC is really the scale factor between pair-space and our universe, as amplified below. Not exactly. The real factor is the sqrt(alpha) which is about 1/11.706. And this is simply the ratio between electronic charge and quantum "vacuum" charge (QVC) = +,- sqrt(hbar*c). You need to stick to ratios because neither charge has coulombs any more. If 1/4pi = eps0 you are losing the coulombs/volt-meter coefficient which reveals that space can store energy at all. I wish I could figure out a way to convince you that nothing is "lost" no matter what unit system you are using. I will readily admit that the process is more clear in SI units. Especially if that is the unit system you are used to. However, most of the advanced literature is written in gaussian cgs or Heaviside-Lorentz units with hbar = c = 1 so one must also be able to understand the process in those unit systems also. Fredi you need eps0 in sqrt(hbar*c*eps0) to make it coulombs and then it's about 3.3 electrons or 1/sqrt(4pi*alpha) electrons. Well, in SI units it is actually sqrt(4pi*eps0*hbar*c) since in SI Units the relationship is, alpha = e^2/(4pi*eps0*hbar*c) In cgs units or Heaviside-Lorentz units, I don't need eps0. 1/4pi works just fine for eps0. Anywise, the ratio for electronic charge to QVC is always about 1/11.706 no matter what units you are using. OK 4pi and 11.7. But what is alpha the square of, that it should be valuable in comparing two charge units? It takes at least "two to tango" and with the e^2 in the expression we have the two. So the sqrt(alpha) is the expression for one e. Very simple. With QVC being charge associated with gauge bosons -- most notably photons. And this is just taking vacuum polarization to tree level. The scale factor between our spacetime and pair spacetime is most likely much greater than this if we take into consideration a Randall-Sundrum RS1-like "warped geometry" scenario. Most likely on the order of 10^18. But from our perspective it looks like on the order of alpha. Fredi, what does your theory say about the Schwinger effect? What features would cause the vacuum to emit pairs? Exactly the same as what Melissinos is talking about. Any slowly varying critical field strength electric or magnetic field should produce pairs from the quantum "vacuum". You should be able to jack up the field strength even more to spontaneously produce pions also. However, we suspect and predict that neutrino pairs should be produced also by critical field strength related to 15 MeV. Difficult to detect though. 15MeV? Over what distance, CWL? If vacuum breaks down at 1.022MeV, how are you going to get to 15? The distance is hbar*c/(15 MeV) ~= 1.3E-14 meters. Our "pair-space" has more than just e+e- pairs in it. Muons and pions should also be able to be produced spontaneously from the quantum "vacuum" with high enough electric or magnetic field strength. [snip uncommented text] The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. As Melissinos points out, this hypothesis has somewhat been shown to be true by the SLAC e144 experiment. There are some planned experiments using the new X-Ray Free Electron Lasers to further test the hypothesis but I don't know what the current status is. The effect also means that in the vincinity of an electron to order hbar/mc, the field strength of an electron is enough to spontaneously create pairs from the quantum "vacuum". Fred, to get my field Ec from an electron it would have to penetrate down to .39 of L', the cell radius. It is probably a forbidden operation. John, calculate the electric field strength of an electron at a distance of hbar/mc from it. It is equal to Schwinger's Ec. What about closer to the electron? Field strength is even higher so how do we even find the original electron from all the electrons in the pairs that are being produced at a distance of less than hbar/mc? LOL! No Fred, it's 137x lower than Schwingers; it's 9.6e15 V/m vs 1.3e18 V/m. At the distance of hbar/mc? You didn't answer my question. This is all covered quite nicely in Milonni's "The Quantum Vacuum: An Introduction to QED". But the quantum "vacuum" is more than just John's pair-space. It includes a dynamical intersection "distance" between the dual spacetimes. Fred I think you can see that I insist on working from first principles and I have put up a lot of numbers that you can take a shot at. So have at it. I don't believe in all the arcane, the RS warped geometry, or spacetime either for that matter. None of that mumbo jumbo is necessary. Well, I already have told you many times that you are way off on your "pair-space" density figures. Fred: I tried to make you see that thepairspace electron density of 1me/L^3 or 2.05e10 kg/m^3 is 2.5 million or 1/alpha^3 that of iron. (Eq. 10 of paper). The uncreated electrons from pairspace, when freed up (created, but not by electric field), expand by 1/alpha, reaching the density of iron and the speed of light and become the raw material for all the stars. You didn't answer my previous question on how a bunch of electrons can make protons and neutrons. I had a whole book written on Dual Space in 2001 in which cell size was twice as small, L = alpha x CWL which seemed so natural, till after I pondered the 8:1 density ratio, that I saw that I needed to double L to 3.514e-14m. As a result, the density turned to iron. That might be OK for e+e- density but if you take into consideration qqbar density, it is way way higher than iron. Probably about 18 to 20 orders of magnitude higher. FrediFizzx Quantum Vacuum Charge papers; http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps http://www.arxiv.org/abs/physics/0601110 http://www.vacuum-physics.com |
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On Mon, 4 Sep 2006 12:15:28 -0700, "FrediFizzx"
wrote: "John C. Polasek" wrote in message .. . On Sun, 3 Sep 2006 20:47:55 -0700, "FrediFizzx" wrote: "John C. Polasek" wrote in message .. . On Sun, 3 Sep 2006 18:02:10 -0700, "FrediFizzx" wrote: "jpolasek" wrote in message oups.com... (New thread as the original one was bifurcated). Schwinger (1951) (& see arXiv:hep-ph/9805507, Melissinos) hypothesized that vacuum would break down if, in a field with intensity Es, an electron would amass the energy mc^2 over a path of the (rationalized) CWL hbar/mc. Thus Es*el*Lrcw = mc^2 with Es given as 1.3x10^18 V/m with hbar/mc or, Ess would be 2.1x10^17 V/m with h/mc (regular) (1c) being a statement of force time distance, with the two interpretations of CWL of being either h/mc or hbar/mc. (Schwinger paper not to hand). I developed my own version (unknowingly) of the Schwinger effect While trying to deduce the content of the vacuum for my Dual Space theory. It can be seen in SI units (overly detailed), in my paper #1, "Permittivity", on my website http://www.dualspace.net I deduced that the vacuum consists of a matrix of elastically-bound pairs of electrons and positrons centered in a cubic domain of L = 3.514e-14m. Fig. 2 op cit Each charge has the range of a half-cell: L' = L/2 = CWL*FSC The half-cell range L' of each charge exactly equals the Compton wavelength scaled down by the FSC = 1/137. The FSC is really the scale factor between pair-space and our universe, as amplified below. Not exactly. The real factor is the sqrt(alpha) which is about 1/11.706. And this is simply the ratio between electronic charge and quantum "vacuum" charge (QVC) = +,- sqrt(hbar*c). So I guess the CWL divided by 11.706 would be an important metric in your space. I have not heard you mention it. Certainly as a scale factor between two worlds there must be important consequences other than regarding your synthetic QVC. You need to stick to ratios because neither charge has coulombs any more. If 1/4pi = eps0 you are losing the coulombs/volt-meter coefficient which reveals that space can store energy at all. I wish I could figure out a way to convince you that nothing is "lost" no matter what unit system you are using. I will readily admit that the process is more clear in SI units. Especially if that is the unit system you are used to. However, most of the advanced literature is written in gaussian cgs or Heaviside-Lorentz units with hbar = c = 1 so one must also be able to understand the process in those unit systems also. Fredi you need eps0 in sqrt(hbar*c*eps0) to make it coulombs and then it's about 3.3 electrons or 1/sqrt(4pi*alpha) electrons. Well, in SI units it is actually sqrt(4pi*eps0*hbar*c) since in SI Units the relationship is, alpha = e^2/(4pi*eps0*hbar*c) In cgs units or Heaviside-Lorentz units, I don't need eps0. 1/4pi works just fine for eps0. Anywise, the ratio for electronic charge to QVC is always about 1/11.706 no matter what units you are using. OK 4pi and 11.7. But what is alpha the square of, that it should be valuable in comparing two charge units? It takes at least "two to tango" and with the e^2 in the expression we have the two. So the sqrt(alpha) is the expression for one e. Very simple. With QVC being charge associated with gauge bosons -- most notably photons. And this is just taking vacuum polarization to tree level. The scale factor between our spacetime and pair spacetime is most likely much greater than this if we take into consideration a Randall-Sundrum RS1-like "warped geometry" scenario. Most likely on the order of 10^18. But from our perspective it looks like on the order of alpha. Fredi, what does your theory say about the Schwinger effect? What features would cause the vacuum to emit pairs? Exactly the same as what Melissinos is talking about. Any slowly varying critical field strength electric or magnetic field should produce pairs from the quantum "vacuum". You should be able to jack up the field strength even more to spontaneously produce pions also. However, we suspect and predict that neutrino pairs should be produced also by critical field strength related to 15 MeV. Difficult to detect though. 15MeV? Over what distance, CWL? If vacuum breaks down at 1.022MeV, how are you going to get to 15? 15 MeV = 15 mc^2 and with 15MV the field strength is 1.15x10^21 V/m. These are not believable numbers. Compare Schwinger 10^18 and he regards his as a limit. JP The distance is hbar*c/(15 MeV) ~= 1.3E-14 meters. Our "pair-space" has more than just e+e- pairs in it. Muons and pions should also be able to be produced spontaneously from the quantum "vacuum" with high enough electric or magnetic field strength. Muons and pions, yeah. They can't even blast out electron pairs with the hottest lasers. What do you mean by "our pair-space" white man? I would be glad to hear about muons etc. if you can be specific, as their polarizability would enhance permittivity (and change my numbers). Tell me about it. [snip uncommented text] The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. As Melissinos points out, this hypothesis has somewhat been shown to be true by the SLAC e144 experiment. There are some planned experiments using the new X-Ray Free Electron Lasers to further test the hypothesis but I don't know what the current status is. The effect also means that in the vincinity of an electron to order hbar/mc, the field strength of an electron is enough to spontaneously create pairs from the quantum "vacuum". Fred, to get my field Ec from an electron it would have to penetrate down to .39 of L', the cell radius. It is probably a forbidden operation. John, calculate the electric field strength of an electron at a distance of hbar/mc from it. It is equal to Schwinger's Ec. What about closer to the electron? Field strength is even higher so how do we even find the original electron from all the electrons in the pairs that are being produced at a distance of less than hbar/mc? LOL! No Fred, it's 137x lower than Schwingers; it's 9.6e15 V/m vs 1.3e18 V/m. At the distance of hbar/mc? You didn't answer my question. Hbar/mc = 3.8e-13m and the electron field is 9.6e15V/m. Schwingers is 1.3e18V/m. You're alpha down from Schwinger. What did I do wrong? This is all covered quite nicely in Milonni's "The Quantum Vacuum: An Introduction to QED". But the quantum "vacuum" is more than just John's pair-space. It includes a dynamical intersection "distance" between the dual spacetimes. Fred I think you can see that I insist on working from first principles and I have put up a lot of numbers that you can take a shot at. So have at it. I don't believe in all the arcane, the RS warped geometry, or spacetime either for that matter. None of that mumbo jumbo is necessary. Well, I already have told you many times that you are way off on your "pair-space" density figures. Then tell me now what the pair-space density should be. I need numbers. Fred: I tried to make you see that thepairspace electron density of 1me/L^3 or 2.05e10 kg/m^3 is 2.5 million or 1/alpha^3 that of iron. (Eq. 10 of paper). The uncreated electrons from pairspace, when freed up (created, but not by electric field), expand by 1/alpha, reaching the density of iron and the speed of light and become the raw material for all the stars. You didn't answer my previous question on how a bunch of electrons can make protons and neutrons. A whole lot easier than re-condensing from gases after the Big Bang. I had a whole book written on Dual Space in 2001 in which cell size was twice as small, L = alpha x CWL which seemed so natural, till after I pondered the 8:1 density ratio, that I saw that I needed to double L to 3.514e-14m. As a result, the density turned to iron. That might be OK for e+e- density but if you take into consideration qqbar density, it is way way higher than iron. Probably about 18 to 20 orders of magnitude higher. I have not seen this term "qqbar density ". I have already said the electron density in pairspace begins at 2.5 million times the density of iron and you are telling me that qqbar density is lots greater than iron. There is a failure here to communicate. FrediFizzx Quantum Vacuum Charge papers; http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps http://www.arxiv.org/abs/physics/0601110 http://www.vacuum-physics.com This thread is getting hard to manage, to reply to. In Agent it's all the same color John Polasek |
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"John C. Polasek" wrote in message
... On Mon, 4 Sep 2006 12:15:28 -0700, "FrediFizzx" wrote: "John C. Polasek" wrote in message .. . On Sun, 3 Sep 2006 20:47:55 -0700, "FrediFizzx" wrote: "John C. Polasek" wrote in message .. . On Sun, 3 Sep 2006 18:02:10 -0700, "FrediFizzx" wrote: [snip] 15MeV? Over what distance, CWL? If vacuum breaks down at 1.022MeV, how are you going to get to 15? 15 MeV = 15 mc^2 and with 15MV the field strength is 1.15x10^21 V/m. These are not believable numbers. Compare Schwinger 10^18 and he regards his as a limit. JP The distance is hbar*c/(15 MeV) ~= 1.3E-14 meters. Our "pair-space" has more than just e+e- pairs in it. Muons and pions should also be able to be produced spontaneously from the quantum "vacuum" with high enough electric or magnetic field strength. Muons and pions, yeah. They can't even blast out electron pairs with the hottest lasers. What do you mean by "our pair-space" white man? I would be glad to hear about muons etc. if you can be specific, as their polarizability would enhance permittivity (and change my numbers). Tell me about it. Don't need lasers. Crash electrons and positrons into each other to produce the field high enough to produce muons and pions. You really need to get yourself a good particle physics textbook. However, I never seen one done up using SI units so you are going to be in trouble. The closest is Griffiths' "Introduction to Elementary Particles" that uses gaussian cgs and leaves in hbar and c almost everywhere. So easy to convert to SI. I mean by "our pair-space" the one in QVC and the Spin Matrix. Not yours. You have the start of the right concept but are ignoring all the other content except for e+e- pairs. Our Spin Matrix also gives a naive view of what the geometrical configuration of the pair-space matrix might be like. And generates a first generation fermion mass spectrum and more with only m_e*c^2 as input. Plus we get two centers of symmetry; one centered on the e+e- LTV pairs and one centered on uubar quark pairs. U(1) and SU(3)? A geometrical math wizard is needed. ;-) [snip uncommented text] The Schwinger effect is a valuable and accurate (and reassuring) hypothesis against which to test the conclusions of dual space theory. As Melissinos points out, this hypothesis has somewhat been shown to be true by the SLAC e144 experiment. There are some planned experiments using the new X-Ray Free Electron Lasers to further test the hypothesis but I don't know what the current status is. The effect also means that in the vincinity of an electron to order hbar/mc, the field strength of an electron is enough to spontaneously create pairs from the quantum "vacuum". Fred, to get my field Ec from an electron it would have to penetrate down to .39 of L', the cell radius. It is probably a forbidden operation. John, calculate the electric field strength of an electron at a distance of hbar/mc from it. It is equal to Schwinger's Ec. What about closer to the electron? Field strength is even higher so how do we even find the original electron from all the electrons in the pairs that are being produced at a distance of less than hbar/mc? LOL! No Fred, it's 137x lower than Schwingers; it's 9.6e15 V/m vs 1.3e18 V/m. At the distance of hbar/mc? You didn't answer my question. Hbar/mc = 3.8e-13m and the electron field is 9.6e15V/m. Schwingers is 1.3e18V/m. You're alpha down from Schwinger. What did I do wrong? Answer my question first. How do we tell the original electron from the electrons in the pairs being produced at a distance of less than hbar/mc to the original electron. QFT is a bitch, ain't it? ;-) This is all covered quite nicely in Milonni's "The Quantum Vacuum: An Introduction to QED". But the quantum "vacuum" is more than just John's pair-space. It includes a dynamical intersection "distance" between the dual spacetimes. Fred I think you can see that I insist on working from first principles and I have put up a lot of numbers that you can take a shot at. So have at it. I don't believe in all the arcane, the RS warped geometry, or spacetime either for that matter. None of that mumbo jumbo is necessary. Well, I already have told you many times that you are way off on your "pair-space" density figures. Then tell me now what the pair-space density should be. I need numbers. See below. Fred: I tried to make you see that thepairspace electron density of 1me/L^3 or 2.05e10 kg/m^3 is 2.5 million or 1/alpha^3 that of iron. (Eq. 10 of paper). The uncreated electrons from pairspace, when freed up (created, but not by electric field), expand by 1/alpha, reaching the density of iron and the speed of light and become the raw material for all the stars. You didn't answer my previous question on how a bunch of electrons can make protons and neutrons. A whole lot easier than re-condensing from gases after the Big Bang. Well, how exactly? I had a whole book written on Dual Space in 2001 in which cell size was twice as small, L = alpha x CWL which seemed so natural, till after I pondered the 8:1 density ratio, that I saw that I needed to double L to 3.514e-14m. As a result, the density turned to iron. That might be OK for e+e- density but if you take into consideration qqbar density, it is way way higher than iron. Probably about 18 to 20 orders of magnitude higher. I have not seen this term "qqbar density ". I have already said the electron density in pairspace begins at 2.5 million times the density of iron and you are telling me that qqbar density is lots greater than iron. There is a failure here to communicate. It is quark pair density. Here is "average density" number you asked for the fermionic pair content of the quantum "vacuum". Using the vacuum expectation value of vev = 246 GeV as a rough starting point for max energy content of the "vacuum", I get about 8.5e29 kg/m^3 or about 19 orders of magnitude greater than your 2.05e10 kg/m^3. Why the huge difference? Simple; you haven't accounted for *all* the content of pair-space. There is one spot in your book that I think you get this close to right indirectly but I am too lazy to look it up right now. ;-) vev = 246 GeV corresponds to a length of about 8.02e-19 meters. FrediFizzx Quantum Vacuum Charge papers; http://www.vacuum-physics.com/QVC/qu...uum_charge.pdf or postscript http://www.vacuum-physics.com/QVC/qu...cuum_charge.ps http://www.arxiv.org/abs/physics/0601110 http://www.vacuum-physics.com |