Does light really travel at the ultimate speed limit in interstellar and intergalactic space? Perhaps we can more thoughtfully answer this question than by giving the simple response, “Yes”. Consider the index of refraction of Earth’s atmosphere for visible light at optical frequencies. The value is almost equal to one differing from one by only one part in about 10,000. As we go to lower and lower densities, the refraction index draws more closely to unity. Now, the gas in the depths of interstellar space is generally far more rarefied than the partial vacuums we can produce in a laboratory environment here on Earth. The density within intergalactic space is even less that that within intragalactic space. Within the space outside of galactic superclusters, the medium of space is even more rarefied. We would expect that an absolutely pure vacuum has a refractive index of precisely and exactly one. However, a pure vacuum not taking into account zero point field energy and virtual particles does not exist. The intragalactic, and extra-galactic medium does indeed include atomic and molecular gases, as well as high energy atomic nuclei and electrons. The medium of space is also suffuse with starlight, quasar light, supernova light, brown dwarf light, CMBR non-CMBR radiofrequency radiation, and other photonic sources in addition to Cold Dark Matter, and the recently discovered Dark Energy. As a result of all of these sources, the refractive index of deep space is likely to be variably ever so slightly greater than one. The reasons for a non-unitary refractive index are subtle. First, the extension of a photon at any frequency or energy is not precisely defined. The probability of finding a given photon anywhere in the universe cosmos is technically not zero, even for a universe of infinite extent. It would seem that for a universe of Ω light-years in linear extent, the probability of measuring the photon at a maximum possible linear distance from its classically predicted position would be a function of P[1/Ω EXP 3]. For a universe of Aleph 0 light-years in linear extent, the probability of measuring the photon at a maximum possible linear distance from its classically predicted position would be a function of P[1/(Aleph 0) Ω EXP 3]. For a universe of Aleph 1 light-years in linear extent, the probability of measuring the photon at a maximum possible linear distance from its classically predicted position would be a function of P[1/(Aleph 1) Ω EXP 3]. For a universe of Aleph 2 light-years in linear extent, the probability of measuring the photon at a maximum possible linear distance from its classically predicted position would be a function of P[1/(Aleph 2) Ω EXP 3]. For a universe of Aleph 3 light-years in linear extent, the probability of measuring the photon at a maximum possible linear distance from its classically predicted position would be a function of P[1/(Aleph 3) Ω EXP 3]. More generally, for a universe of Aleph n light-years in linear extent, the probability of measuring the photon at a maximum possible linear distance from its classically predicted position would be a function of P[1/(Aleph n) Ω EXP 3]. where n = 1, 2, 3, …, Ω, …, Aleph 0, .., Aleph 1, …, Aleph 2, … Aleph Ω, …, Aleph (Aleph 0), …, Aleph (Aleph 1), …, Aleph (Aleph 2), …, Aleph (Aleph Ω), …, Aleph (Aleph (Aleph 0), .., Aleph (Aleph (Aleph 1), …, Aleph (Aleph (Aleph 2), …, Aleph (Aleph (Aleph Ω), .. and so on ad infinitum. The use of the transfinite ordinals is only ad hoc in intention since we really do not know whether our universe is finite or infinite in spatial extent, and if infinite, how large the infinite value is. Perhaps the much greater probability of a photon interacting with a gas atom one meter off to the side of the photon’s classical travel path such as would be the norm in deep intergalactic space for ever cubic meter of photon propagation can enhance the refractive index of intergalactic space to a value of 1 + E where E is the inverse of a suitable sub-ensemble number. Second, since the universe is suffuse with CMBR and starlight, even though photons obey Bose-Einstein statistics, such photons may none-the-less undergo ever so light non-linear superpositions about crossing paths of travel. Perhaps such non-linear effects can induce a greater than non-zero but very small increase in the refractive index of deep space. Third, Dark Matter may perhaps interact ever so slightly with the photonic background to provide a very small greater than zero increase in the refractive index of deep space. Such a mechanism for interaction may include electroweak mixing parameters, electro-strong mixing parameters, electroweak-strong mixing parameter, and any supersymmetric analogues. Fourth, the presence of more or less static magnetic and electric fields may induce a greater than zero component to the refractive index of deep space by non-linear electromagnetic superposition effects. Fifth, the presence of gravitational fields throughout deep space may also provide a greater than zero component to the refractive index of deep space by non-linear energy densifying for which the sum of the gravitational and electromagnetic energy in a given volume of space is somehow greater than the two energy species separately added. Sixth, the presence of Dark Energy throughout deep space may also provide a greater than zero component to the refractive index of deep space by non-linear energy densifying for which the sum of the Dark Energy and electromagnetic energy in a given volume of space is somehow greater than the two energy species separately added. Because deep space may have a slightly greater than one variable and varying electromagnetic refractive index, perhaps the true cosmic speed limit as is actually practiced by Mother Nature is that for gravitation and gravitational waves. Since the electromagnetic refractive index is currently defined as n = C/v, where C is the velocity of light in vacuu, perhaps, the electromagnetic refractive index perhaps should alternatively be defined as Nem = [C + (Eatomic-gas) + (Eem-non-linear) + (Eem-dark-matter)+ (Estatic e-&-m-fields)+ (Egrav-non-linear)+ (Edark-energy-non-linear)]/v where C is the average velocity of light in the vacuum of space. Alternatively, the electromagnetic refractive index might be defined as Nem = [C – (Eatomic-gas) – (Eem-non-linear)- (Eem-dark-matter) – (Estatic e-&-m-fields)- (Egrav-non-linear) – (Edark-energy-non-linear)]/v, where C is the absolute maximum possible velocity of light in vacuu. The true refractive electromagnetic index might be defined as Nem = [Cgrav - (Eatomic-gas) – (Eem-non-linear)- (Eem-dark-matter) – (Estatic e-&-m-fields)- (Egrav-non-linear) – (Edark-energy-non-linear)]/v, where Cgrav is the velocity of gravitation in vacuu. Since gravitation is the weakest force and involves propagation topological deformities is space-time itself, perhaps gravitational waves are less slowed down as a result of the atomic gas, electromagnetic gas, Cold Dark Matter, and Dark Energy in deep intragalactic and deep extragalactic space. Regardless, since gravitational energy is real, perhaps the above six mechanisms for bosonic slowing are also operative on gravitational waves. Thus, perhaps the gravitational refractive index should be defined as Ngrav = Cgrav-max/v, where Cgrav-max is the maximum possible velocity of gravitational radiation in vacuu, or alternatively be defined as n = [Cgrav + (Eatomic-gas) – (Eem-non-linear)- (Eem-dark-matter) – (Estatic e-&-m-fields)- (Egrav-non-linear) – (Edark-energy-non-linear)]/v where Cgrav is the average velocity of gravitational radiation in the vacuum of space. Alternatively, the gravitational refractive index might be defined as Ngrav = [Cgrav-max - (Eatomic-gas) – (Eem-non-linear)- (Eem-dark-matter) – (Estatic e-&-m-fields)- (Egrav-non-linear) – (Edark-energy-non-linear)]/v, where Cgrav-max is the absolute maximum possible velocity of gravitation in vacuu. Regarding inertial bodies traveling as sub-ensemble gamma factors, perhaps the bodies would experience a non-Lorentz component increase or decrease in gamma factor. Alternatively, such bodies might in spirit travel faster than Mother Natures preferred velocity of light and thereby experience backward time travel. Another possible consequence is that the bodies might have a compounded superluminal travel resulting in the bodies already traveling slightly in excess of the preferred velocity arriving slightly earlier at a cosmic distant destination than they otherwise would. Traveling substantially faster than light may be a puzzle that we work on indefinitely but which may always prove elusive until perhaps we reach a technological Omega point in the ever so distant future. We might even experience exotic discontinuities in the propagation path as we achieve sub-ensemble gamma factors or discreet jumps in along the orientation of a spacecraft velocity vector.
Posted on: Tue, 18 Jun 2013 06:57:31 +0000
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