Widdekind

The Type II SN, ~4.6 GYA, which triggered the formation of our star system, surely triggered the formation of other star systems, "nearby", in the "neighborhood" of the Sun at that time. In principal, it is possible to (perhaps partially) reconstruct the Sun's "stellar sibko" — to wit, that group of stars w/ which the Sun first formed. For, the Sun's "stellar siblings" would all have highly similar properties — the same age (~4.6 GY), the same "metallcity mix", and similar galactic orbital parameters (radius ~8.5 kpc, period ~220 MY). Indeed, such "stellar families" could be tracked much as Astronomers today track "asteroid families" in our Solar System's Main Asteroid Belt (eg. the Baptistina group, responsible for the impactor(s) that killed off the Dinosaurs ~65 MYA). http://www.astronomyforum.net/planetary-forums/84613-how-find-suns-sibling-stars-exo-planets.html However, such "stellar sibkos" — to wit, Open Clusters — typically disperse over hundreds of millions of years. Today, after roughly 4.6 GY, the Sun's "stellar sibko" is surely smeared out over a vast stretch of the Galactic disk. So, as previously pointed out above, our nearby neighboring star systems today are not necessarily our "stellar siblings", from roughly 4.6 GYA. But, apparently, after restricting attention to all known stars, in our Galactic disk, that have similar Galactic orbital parameters, and similar stellar ages, the Sun seems to be about 40% richer in metals, as compared to that limited sub-sample of stars. That gives us a "window to the past", and allows us to conclude, that, ~4.6 GYA, the Sun was a comparatively metal-rich star (surely along w/ all its "stellar siblings").

Apparent Magnitude (m): [math]m = M_{\odot} - \frac{5}{2} log_{10} \left( \frac{F}{F_{\odot, 10pc}} \right)[/math] [math]M_{\odot} = 4.76[/math] [math]F_{\odot, 10pc} = \frac{L_{\odot}}{4 \pi \; 10pc^{2}}[/math] Received Flux (F), across cosmological distances: [math]F = \frac{L}{4 \pi \left( w \left( 1 + z \right) \right)^{2}}[/math] Present distance (w), equivalent to the comoving coordinate, of an observed object, at a given Redshift (z), in a Flat universe ([math]\Omega_{0} = 1[/math]): [math]w = \frac{2 \; c}{H_{0}} \left( 1 - \frac{1}{\sqrt{1+z}} \right)[/math] [math]H_{0} \approx 75 \; km \; s^{-1} \; Mpc^{-1}[/math] From these relations, we can calculate the Apparent Magnitude (m), of quasars of fixed Luminosity (L), at varying Redshifts (z). On the following figure, lines of constant Luminosity have been overlain atop the plot of Redshift vs. Apparent Magnitude for known quasars. Beginning with the upper left line, Luminosities displayed are [math]10^{14} \; L_{\odot}[/math], [math]10^{13} \; L_{\odot}[/math], ..., [math]10^{8} \; L_{\odot}[/math]: CONCLUSIONS: At any given epoch, quasars' intrinsic Luminosities vary over roughly three orders-of-magnitude. And, quasars appear to brighten from z=3 to z=2, before steadily dimming, by about three orders-of-magnitude, from z=2 to z=0.03, after which quasars have faded from view. Quasar numbers also follow a similar evolution, rapidly increasing in comoving density, before fading from view: Thus, as quasars "powered up" across the cosmos, they became both (1) more numerous; and (2) more Luminous. Likewise, as quasars faded from view, they became both (1) rarer; and (2) dimmer. Note that no quasars were ever brighter than about [math]10^{14} L_{\odot}[/math], nor were any ever dimmer than about [math]10^{9} L_{\odot}[/math]. And, in the quasars' Redshift vs. Apparent Magnitude plot, their appears to be the hint of a linear feature running nearly parallel to the [math]10^{11} L_{\odot}[/math] contour — perhaps representing the stablest, and longest-lived, sub-population of quasars ?? SOURCES: Carroll & Ostlie. Introduction to Modern Astrophysics, pp. 89,1289-ff. Jayant V. Narlikar. Seven Wonders of the Cosmos, pg. 307. Martin Rees. New Perspectives in Astrophysical Cosmology, pg. ~100.

Thanks for the link, but I think I accurately quoted the program: http://www.msnbc.msn.com/id/5023748/

I think it requires accretion from a companion, until it exceeds the Chandrasekhar Mass Limit of roughly [math]1.4 M_{\odot}[/math].

Thanks for the clarifications about the non-linearities of GR. Would you please posit some speculations, about such "Hyperspace" (aka "The Bulk") ?? In particular, is there any likelihood, that light travels faster in Hyperspace — to wit, even if you could "jump out" of the "3-Brane" of standard Spacetime (and if you could "jump back in" some place else), could you use such "Hyperspace travel" to voyage faster than light ?? And, also, if you could "jump out" of the "3-Brane"... what force keeps particles back inside it ?? To make a crude QM analogy, could there be some sort of "energy barrier", acting along the "Hyperspace dimension / axis" (the "W" direction on a Flamm Paraboloid), that "squeezes" particles "back into" the 3-Brane ?? Could such an "energy barrier skin" around the 3-Brane explain the tiny sizes of String Theory's extra dimensions (they're not "curled up", but "energy bounded") ???

REVISED UPDATE (1) Circumstellar Disk Analogy — Magnetic Field Lines transfer Angular Momentum outwards According to Jayant V. Narlikar (From Black Clouds to Black Holes, pp. 61-64), magnetic field-lines, threading through circumstellar disks, can spin up outer disk regions, while spinning down inner disk regions: In Figure 5.9, a magnetic pole at A will be forced by the magnetic field in the cloud to move to B along the line of force. Now, these lines of force have a tendency to stick on to cloud particles all the time. So, as A & B rotate about a common axis, the line of force moves w/ them. But, since A & B do not rotate at the same rate, w/ A rotating faster than B, the line of force gets twisted. And, when twisted, it tends to straighten itself. In this process, it pulls A back, while making B go faster, this reversing the tendency of the cloud as a whole to rotate faster in the center & slower in the outskirts. This resistance offered by the line of force serves the two required needs: 1) it slows the central part down, 2) it pushes the outer parts further out by making them rotate faster. (2) Similarly structured Magnetic Fields, in Galactic Disks, strongly influence dynamics According to Carroll & Ostlie (Introduction to Modern Astrophysics, pg. 935), Galactic magnetic fields resemble those depicted above, for forming star systems: Within the [Galactic] disk, the field tends to follow the Galaxy' spiral arms, and has a typical strength of 4 [math]\mu G[/math]... Although the global Galactic magnetic field is quite weak, relative to terrestrial fields, it likely plays a significant role in the structure & evolution of the Milky Way. This can be seen by considering its energy density, which appears to be comparable (perhaps equal) to the thermal energy density of gas within the disk. (3) Estimation of Magnitude of Magnetic Tension Force in Galactic Disk The Magnetic Tension Force: [math]\frac{1}{\mu}\left( \vec{B} \cdot \vec{\nabla} \right) \vec{B} = \frac{1}{\mu} \; B \frac{d}{ds}[/math] can be decomposed, into the component tangential to the Magnetic Field Lines, and the component normal to them: [math]\vec{B_{t}} = \frac{\partial}{\partial S} \left (\frac{B^{2}}{2 \; \mu} \right) \hat{t}[/math] [math]\vec{B_{n}} = \frac{B^{2}}{\mu \; R_{c}} \hat{n}[/math] where Rc is the Radius of Curvature of the Magnetic Field Line, [math]\hat{t}[/math] is the outward-pointing unit tangent vector, [math]\hat{n}[/math] is the inward-pointing unit normal vector, and the derivative [math]\frac{\partial}{\partial S}[/math] is taken along the field line, in the direction of [math]\hat{t}[/math]*. * http://www-solar.mcs.st-and.ac.uk/~alan/sun_course/Chapter2/node15.html#fig13 Now, to lowest order, we may estimate the tangential derivative by using a Single Zone Approximation: [math]\frac{\partial}{\partial S} \left (\frac{B^{2}}{2 \; \mu} \right) \approx \frac{\Delta (B^{2})}{2 \; \mu \; S} = \frac{B^{2} - B_{0}^{2}}{2 \; \mu \; S}[/math] where S is the integrated Arc Length from the pole to the point in question, B0 is the magnetic field strength at the pole, and B is the field strength at the point in question. This is depicted below. Note that, b/c the field strength decreases along Galactic field lines [math]\left( \frac{\partial}{\partial S} < 0 \right)[/math], the tangential component of the Magnetic Tension Force actually points along the inward-pointing tangent vector. To make a mechanical analogy, this is akin to keeping an axe-head on an axe-handle by virtue of the flaring, of the latter, outwards towards its tip: Now, Spiral Galaxy Arms typically take the shape of a Logarithmic Spiral, with Pitch Angles typically between 10-40 degrees. For the Milky Way, that angle is about 12 degrees*. And, for Logarithmic Spirals, we have the following relations for the Radius of Curvature and the integrated Arc Length**: [math]R_{c} = R \; \sqrt{1 + b^{2}}[/math] [math]S = R \frac{\sqrt{1 + b^{2}}}{b}[/math] where b is the reciprocal, of the tangent, of the compliment, of the Pitch Angle***. * http://en.wikipedia.org/wiki/Logarithmic_spiral ** http://www.2dcurves.com/spiral/spirallo.html *** http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/KURSATgeometrypro/golden%20spiral/logspiral-history.html Thus, we wish to compare the total (radial) force, acting on a parcel of fluid in the ISM [math]\left( \rho \frac{V^{2}}{R} \right)[/math], with the (radial) force from Magnetic Tension. For sake of simplicity, we shall presume a pretty plausible Pitch Angle of 45 degrees, for which case, b = 1, Rc = S = 21/2 R, and [math]\hat{-t} \cdot (-\hat{r}) = \hat{n} \cdot (-\hat{r}) = 2^{-1/2}[/math]. Then, the estimated inward-radial component, of the Magnetic Tension Force, is: [math]\vec{F_{MT}} \cdot (-\hat{r}) = \left( \vec{B_{t}} + \vec{B_{n}} \right) \cdot (-\hat{r})[/math] [math] = \frac{\partial}{\partial S} \left (\frac{B^{2}}{2 \; \mu} \right) \left( \hat{t} \cdot (-\hat{r}) \right) + \frac{B^{2}}{\mu \; R_{c}} \left( \hat{n} \cdot (-\hat{r}) \right)[/math] [math]\approx \frac{B_{0}^{2} - B^{2}}{2 \; \mu \; 2^{1/2} \; R} 2^{1/2} + \frac{B^{2}}{\mu \; 2^{1/2} \; R} 2^{1/2}[/math] [math] = \frac{B_{0}^{2} + B^{2}}{2 \; \mu \; R}[/math] So, we define the ratio: [math]\beta \equiv \frac{ \frac{B_{0}^{2} + B^{2}}{ 2 \; \mu \; R} }{\rho \frac{V^{2}}{R}} = \frac{1}{2 \; \mu \; \rho}\frac{B_{0}^{2} + B^{2}}{V^{2}}[/math] For the Sun, and using values for the Warm Ionized Medium, we have that: [math]B_{0} = 40 \; \mu G[/math] [math]B = 4 \; \mu G[/math] [math]V = 220 \; km \; s^{-1}[/math] [math]\rho = (0.4 - 1) \times 8.4 \times 10^{-25} \; g \; cm^{-3}[/math] so that: [math]\beta \approx 0.16 - 0.39[/math] And, these values could be up to 3 orders of magnitude greater, for the Hot Ionized Medium, which "makes up most of the ISM"*. Thus, Magnetic Tension could, quite conceivably, play an important (perhaps pivotal ?) role, in Spiral Galaxy Disk dynamics. * http://en.wikipedia.org/wiki/Interstellar_medium (4) Predicted correlation, between Galactic Magnetic Field Strengths, and Spiral Arm Pitch Angles If Galactic magnetic fields dominate disk dynamics, and if said fields thread through spiral arms, then since magnetic tension tries to straighten field lines, therefore Galaxies possessing more powerful magnetic fields should show straighter spiral arms, having higher Pitch Angles.

According to the National Geographic Channel documentary Direct from the Moon (TV), Dr. Fumi Yoshida et al. have shown, that the size distribution of Main Belt Asteroids precisely matches the size distribution of craters on Moon, dating to the Late Heavy Bombardment period (4.0 to 3.8 billion years ago). This "fingerprint" establishes the Main Belt — and not comets — as the source of the LHB of the Inner Solar System. These results are described in detail here. Planet Formation Times could conceivably play some part in said analysis — for example, the Ice Giants apparently finally formed after hundreds of millions of years... about the same time as the LHB.

In the Milky Way Galaxy, Star Formation Rates apparently peak at about 5 kpc from the Galactic Core: Observations of supernovae remnants indicate that supernovae peak at about 60% of the Sun's distance from the galactic center [~8.5 kpc], where they are about 1.6 times more frequent than at our location*. And, as indicated upon National Geographic's amazing Milky Way Galaxy poster**, this coincides w/ the Scutum & Norma spiral arms. Indeed: The region where the Scutum-Crux arm meets the central bulge of the galaxy is rich in star-forming regions. In 2006 a large cluster of new stars containing 14 red supergiant stars was discovered there and named RSGC1. In 2007 a cluster of approximately 50,000 newly formed stars named RSGC2 was located only a few hundred light years from RSGC1; it is thought to be less than 20 million years old and contains 26 red supergiant stars, the largest grouping of such stars known***. Apparently, the region within the Scutum & Norma arms is basically considered the Galactic Core: Intriguingly, it is precisely at this point, that the density of [Thin?] Disk gas becomes exceeded, by the density of [Thin?] Disk stars#: This strongly suggests some sort of connection, between Star Formation Rates, and the relative Disk densities of Gas vs. Stars. And, there are no Spiral Arm structures in the central region, where the Star Formation Rates begin to drop off. * Guillermo Gonzalez, Donald Brownlee, & Peter D. Ward. Refuges for Life in a Hostile Universe. Printed in: [scientific American] Majestic Universe, pg. 10. ** http://shop.nationalgeographic.com/product/307/359/173.html *** http://en.wikipedia.org/wiki/Scutum-Crux_Arm # Guillermo Gonzalez, et al, ibid. Merged post follows: Consecutive posts mergedFrom the data depicted in the attached charts (see OP above), it is clear that, at a distance of only 5 kpc from the Galactic Core: Metallicity is some 60% higher Disk Gas Density is some 60% higher And, according to the quoted text from the same source: Supernovae Rate is some 60% higher This strongly suggests, that — at least outside the Galactic Core regions — Disk Gas Density ([math]\rho_{ISM}[/math]), Supernovae Rates ([math]\Gamma_{SN}[/math]), and Metallicity (Z) are all comparatively closely correlated: [math]\rho_{ISM} \propto \Gamma_{SN} \propto Z[/math] Moreover, the Supernovae Rate roughly tracks the Star Formation Rate ([math]\Gamma_{SF}[/math]) (especially so for Type II Supernovae): Type II Supernovae involve short-lived, massive stars, so their rate closely tracks the Star-Formation Rate. The rate of Type I Supernovae, on the other hand, depends upon the production of longer-lived, intermediate mass stars, so it responds more slowly to changes in the Star Formation Rate. (ibid., pg. 8) Thus, as a rough rule: [math]\rho_{ISM} \propto \Gamma_{SF} \propto \Gamma_{SN} \propto Z[/math] This chain of cause & effect explains the observations, that denser Disk regions are also much more "Metallicitous". Merged post follows: Consecutive posts mergedCosmologists essentially say that the densest regions of the early Cosmos collapsed to create the biggest Galaxies. And, those biggest Galaxy-regions will tend to have had the most Star Formation, and, hence, have made the most Metals. This corroborates the above conclusion, on the "grand scale". Indeed, And, the Luminosity of Galaxies tracks their Masses (citation pending)... so, even on the Galactic scale, "Metals track mass" — which is essentially saying the same thing as "denser Disk regions are much more 'Metallicitious'" (where there's more mass, there's more Metals). ADDENDUM: In the Local Group of Galaxies, apparently, only the Milky Way & Andromeda Galaxies are likely to harbor (in)habited worlds.

According to McBride & Hughes (pg. 7): However, this ignores the sudden increase in solids at the Snow Line, in the Sun's Proto-Planetary Disk: My original analysis (OP) did not account for the Snow Line's effects on the density of solids in the Proto-Planetary Disk. Perhaps all of the Outer Planets' formation times should be divided by some factor — such as 2.2.

"Hyperspace Directionality" to mass-induced Curvature of Spacetime Basic geometric arguments seemingly suggest, that there is a "directionality" to the Curvature of Spacetime, "through Hyperspace", caused by mass. Consider the Flamm Paraboloids of two nearby masses — the two "dimples" in the "rubber sheet" of Spacetime. Mathematically, it makes no differenece, whether you visualize those Flamm Paraboloids as "pointing upwards" — looking like "mountains" jutting up above Flatland — or as "pointing downwards" — looking like "valleys" sinking down below Flatland. Equivalently, you can look at Flatland from above, or below, seeing mountains, or valleys (respectively), but you'll always see the same motions. But — imagine that, on the "rubber sheet" of Flatland, one mass produced a "mountain", but the other mass produced a "valley". That is, imagine that two equal masses (say) produced "equal but opposite pointing" dimples on the rubber sheet. Locally, their Gravitational effects work out fine. But, now, imagine those masses move towards each other, and collide & combine. The "mountain" from the first mass will — purely Geometrically speaking — exactly cancel out the "valley" from the second mass... leaving a perfectly flat "rubber sheet"... w/ no more Gravity (!!). ____/\____ + _____..._____ = ______________ ............................\/ But, this is clearly unphysical — two equal masses cannot collide & combine to produce perfectly flat Space(time). (More generally, two masses cannot collide & combine to amount to less mass (but what about Matter vs. Anti-Matter ??).) CONCLUSION: The "Hyperspace directions" of the Flamm Paraboloids produced by masses — their "dimples" in the "rubber sheet" — are not arbitrary: they all point in the same sense "through Hyperspace" (they all create "valleys", or they all create "mountains", but not a random mix of both). Whether you look at Spacetime "from above", or "from below" — to see either "mountains" or "valleys" — may be arbitrary. But every mass "dimples" Spacetime in the same "Hyperspace direction". QUESTION: How does mass know "which way to go" ?? How does mass know to "dimple down", or "mountain up" ?? How is it, that every mass "pushes into" Spacetime in the same Hyperspace direction ?? (What about Matter vs. Anti-Matter — would their "dimples" in Space "point in opposite directions" ??) Merged post follows: Consecutive posts merged Thanks for this succinct summary !! Merged post follows: Consecutive posts merged Rudolf v.B. Rucker (Geometry, Relativity, and the Fourth Dimension, pg. 107) depicts a (1+0)D slice through the curved space of a (vaguely (Hyper-)Spherical) Closed Universe. Note that all of the masses "bulge outwards", away from the Center of Curvature. This satisfies our requirement of "directionality", for the Hyperspace curvature, caused by mass, in Space(time). Returning to the rubber sheet analogy, we now have a big "rubber balloon" — and whenever we put masses onto said rubber balloon, the balloon bulges outwards. Confining ourselves strictly to the analogy, this situation requires that there be some sort of "expansion pressure" inside the balloon, that "pushes out" masses placed onto the rubber balloon... as if there was some "reverse radial gravity field". (For (1+0)D, you could create this effect by rapidly rotating a rubber band upon a Carousel. Then, whenever you put masses up against that rubber band, Centrifugal Forces would push them outwards, precisely as in R.v.B.Rucker's picture.) Could such an "expansion Pressure", originating from the "interior Hyperspace" inside of a curved, Closed, Cosmos, cause, perhaps, both the expansion of that Space, as well as pushing all masses "outwards", towards "exterior Hyperspace", away from the Center of Curvature ??? Could this explain, perhaps, the Cosmological Constant [math]\Lambda[/math] ???

Rudolf v.B. Rucker (The Fourth Dimension, pg. 211) depicts a (2+0)D visualization of Spacetime, in an isotropic Universe "marred" (my word) by one mega-massive object: Thus, 2D Flatland Space is curved, "through Hyperspace", into a shape like a lightbulb. Now, if you imagine concentrating more & more mass into that mega-massive "central mass", perhaps that lightbulb-shaped Space would "shrink into itself" something like this: And, running time in reverse, perhaps you could explain the Big Bang ??? Note that the radius of the "throat" stretching down towards the mega-mass approaches the Schwarzschild Radius of the primordial "reverse Black Hole"; whereas, the radius of the ballooning Space beyond that "throat" would be the Radius of Curvature of the Universe.

(1) According to the National Geographic Channel documentary Naked Science -- Birth of the Solar System (TV), scientists have detected Iron-60 isotopes in meteorites. Iron-60 comes exclusively from Supernovae events, and has a relatively short Half-Life. Therefore, Iron-60 typically decays before traveling very far from its source. Thus, this strongly suggests, that the nascent Solar System was w/in about 20 light-years of some Supernovae event. (2) About 4.6 billion years ago, when our star system was born, it was comparatively metal-rich, for its time & place: In the Galaxy as a whole, the Star Formation Rate peaked about 8 to 10 billion years ago, and has been declining ever since. Today, the Metallicity in the solar neighborhood is increasing by about 8% every billion years... The Thin Disk is the Sun's home. The Metallicity of its gas declines w/ distance from the Galactic Center. At the Sun's location, about 8.5 kiloparsecs (28,000 light-years) out, it is decreasing at 17% per kiloparsec... The Sun itself is about 40% richer in metal than other stars formed at the same time [~4.6 billion years ago] & location in the [Thin] Disk. This increased metal content may have given life on Earth a head start*. Moreover, Iron-Peak compounds — presumably including Iron-60 — are produced mainly by Type I Supernovae events, "most of which result from the detonation of a White Dwarf star"**. * Guillermo Gonzalez, Donald Brownlee, & Peter D. Ward. Refuges for Life in a Hostile Universe. Printed in: [scientific American] Majestic Universe, pg. 8. ** ibid., pp. 8-9. CONCLUSION: The nascent Solar System was within about 20 light-years of an exploding White Dwarf, which enriched the Proto-Solar Cloud with copious quantities of Iron-Peak compounds. And, since stellar Metallicities strongly correlate w/ Planetary Formation probabilities, this exploding White Dwarf helped beget our Planetary System, orbiting our Sun.

Standard Relativity texts describe the fabric of Space-Time as being like a proverbial rubber-sheet, which stretches under the weight of masses put upon it. Now, that analogy requires that the rubber sheet (2D "Flatland") exist in an external Gravity field, pointing perpendicular to the rubber sheet (3D "Hyperspace"). It is that Gravity field that drives the masses down into the rubber sheet. To wit, in the rubber sheet analogy: Gravity from 3D interacts w/ mass embedded in 2D "Flatland", telling it how much to warp the rubber sheet The warp of the rubber sheet tells the masses how to move This compares with the oft-said phrase, from basic textbooks, that: Mass tells Spacetime how to curve Spacetime tells Mass how to move For further emphasis, the rubber sheet analogy wouldn't work in Zero-G (!!). The rubber sheet analogy requires that the rubber sheet, representing 2D Flatland, be embedded in a 3D "Hyperspace" containing a perpendicular Gravity field — which gives Flatland masses "weight", which drives them "down" through the Hyperspace dimension, causing Flatland to curve, bend, stretch, and warp. QUESTION: Could there be something analogous for our SpaceTime ?? Perhaps our Space-Time is embedded in a higher dimensional Hyperspace, which exerts some sort of "Hyperspace Push", from Hyperspace, "perpendicular" to Space. That "Hyperspace Push" affects Mass, driving it "down", and causing curvature in Space. Then, that induced curvature in Space tells Mass, embedded in Space, how to move. In J.A.Wheeler's Journey into Gravity & Spacetime, Wheeler shows that the curvatures of Space, outside of an ideal mass (ie., in the Schwarzschild Solution), offset, leaving no "net force" acting on Space. He makes an analogy to a film of soap, stretched taught between two hoops, as they're dipped into the soapy water, pulled out, and pulled apart. Although only a 2D analogy, it shows how the 2 perpendicular radii of curvature offset, leaving the soap film in static equilibrium. But, inside a star, the curvature of Space is "contractile", and has a net curvature "upwards". To use the rubber sheet analogy, it is this net curvature that offsets the weight of the ball put on the sheet ! Thus, this net curvature, pointing "up" into Hyperspace, proves the presence of a "Hyperspace Push" force... at least for the rubber sheet Flatland analogy. Could something similar be true for real Space ??

So, from Friedmann's Equations, and the "density over-contrast" [math]\Omega_{k}[/math], you can calculate the Curvature Radius of the Cosmos to be about 300 billion light-years. Now, according to Wikipedia, the combined mass of the Observable Universe is of order 1055 kg — equivalent to a Schwarzschild Radius ("Geometric Mass") of order 1028 m, or 1000 billion light-years. And, this negelects all the "Level I Parallel Universes" which could quite conceivably exist, w/in our own normal Universe, out past & beyond our own finite visible horizon (Scientific American reports -- Majestic Universe ; History Channel The Universe -- Parallel Universes (TV)). Furthermore, Physicist Stephen Hawking has famously shown that the Big Bang is consistent w/ the catastrophic explosion of a "reverse Black Hole", albeit on a "vastly larger scale" than anything humans could conceivably see in this visible Universe (National Geographic Channel Naked Science -- Hawking's Universe (TV)). So, how could it be, that the Cosmos's Curvature Radius is actually less than the Schwarzschild Radius of the "mega-massive hyper-Black Hole" that the Cosmos could have come from ??

Thanks for the link

According to the National Geographic Channel documentary Naked Science -- Journey to Jupiter (TV), Ganymede, Callisto, Io, & Europa are Jupiter's "four largest moons". But, they are also the four innermost moons, yes ?? And, most basic textbooks observe that Jupiter's Moon System is much like a "mini-Star System". Thus, on the basis of this "Gas Giant analogy", the Sun's innermost planets ought to be the biggest planets. QUESTION: Could it be, that the four Terrestrial Planets are actually the biggest planets — in particular, bigger than the rocky cores of the Gas Giants ?? And, on the strength of the same said analogy, why wouldn't Jupiter possess "outer moons" w/ large gaseous envelopes ?? According to the same said documentary, the Galileo spaceprobe discovered Argon, Krypton, Carbon & Nitrogen in Jupiter's atmosphere at 2-3x solar concentrations. And, since these gases all condense at considerably colder temperatures than those at the present position of that planet, possibly Jupiter migrated inwards from an initially greater distance from the Sun. [Wasn't the Sun some ~30% dimmer in the deep past ?] <<I'm being booted off the computer>>

Evidence of ancient Oceans & Plate Tectonics on Venus: See also Intelligent Life in the Universe by Peter Ulmschneider, pp. 71-72:

Regarding Gravitational Time Dilation, according to N.D. Mermin (It's About Time, pg. 176), In a uniform Gravitational Field, the lower clock runs slower than the upper one by precisely the factor 1 + g D / c2. This has, seemingly, an intriguing Semi-Classical interpretation. For, let us see what "equivalent velocity" would produce the same Time Dilation factor: [math]\gamma \equiv 1 + g \; D / c^{2}[/math] Multiplying both sides by the Rest Energy of the Test Particle, w.h.t.: [math]E_{0} + KE = \gamma \; m \; c^{2} = m \; c^{2} + m \; g \; D = E_{0} + \Delta U_{g}[/math] Thus, the lower clock ticks slower by the same amount it would, if all of its additional GPE had been converted to KE (in flat space). Yes? Mod note: moved to its own thread

Regarding the observation of Methane in Mars' atmosphere, Bennett & Shostak (Life in the Universe (2nd ed), pg. 283) say: Mars has a source of ongoing Methane production somewhere on or beneath its surface... Where could the Methane be coming from ? We know of at least three possibilities: Comet Impacts, Volcanic Activity, or Life. The first possibility is highly unlikely, since impacts are such rare events and an impact would have to have occurred quite recently for Methane to remain in the atmosphere. That leaves us w/ Volcanism or Life. A few scientists have looked at correlations between the location of Methane & Water Vapor in the Martian atmosphere, and used the results to argue that we might be actually seeing the signature of microscopic Life on Mars. However, Volcanism also seems a reasonable explanation, especially since other evidence suggests that Mars has at least some low level of ongoing Volcanic Activity. Nevertheless, even this result could have implications for the existence of Life: if there is enough Volcanic Activity to produce a detectable level of Methane, it may also mean there is enough Volcanic Heat to make pockets of underground liquid water, raising the possibility of subsurface Life. Merged post follows: Consecutive posts mergedThere seems to be some serious misunderstanding of the English language. Please ponder the differences between the following three (3) types of statements: Possibility (p > 0%) Probability (p > 50%) Certainty (p = 100%) A statement of Possibility is not a statement of Probability, much less of Certainty. Furthermore, a statement is only an Opinion, if it asserts something stronger than the evidence actually bears. Thus, to say that the universal ubiquity of Methane, across the Cosmos, suggests the Possibility of abundant Life, is factually accurate, and not an Opinion. Now, as an aside, it is this author's Opinion that abundant Life, across the Cosmos, is Probable. That is based on "hunch" & "instinct", informed by actual observations, but extrapolating beyond them. Likewise, to say that "all present, albeit primitive, Observations are completely consistent w/ abundant Life, across the Cosmos" is not an Opinion -- it's just a fact. Note, too, that it's not even a statement of Possibility, much less Probability or Certainty -- it's just an observation of an intriguing fact. ANOTHER ANALOGY: Look out across the Cosmos, w/ unaided eyes. You see the Sun, the Moon, and a bunch of planets and stars. Both the Sun & Moon appear circular in the sky; everything else is too far away to resolve as anything but pinpoints of light. Nevertheless, those primitive observations are completely consistent w/ the claim that "all heavenly bodies actually appear circular [given better observations]". Likewise, we know there's Life on Earth, and we see Methane consistent w/ Life on Mars (not to mention Methane in Molecular Clouds). It is just a factual epiphane [sp?], that these observations are completely consistent w/ Life being abundant across the Cosmos. Note that no specific probability has been assigned, meaning this is not an Opinion. It's just like saying "hey, the Sun looks round, the Moon looks round, so it could be that every light in the sky will look round, when we get around to observing them in greater detail". Yet again, that's not an Opinion, nor is it a statement of Possibility / Probability / Certainty. Merged post follows: Consecutive posts merged Let us be more precise -- "the ubiquity of Methane in the Universe is, in fact, fully explain-able by non-biological chemistry...". That is, you can, you are able, to explain observations w/ non-biological chemistry. I've never disagreed w/ that. If you can say, "The ubiquity of methane in the Universe is also consistent with the non-ubiquity of Life", then I can say "The ubiquity of Methane in the Universe is also consistent with the ubiquity of Life". It cuts both ways -- if one statement is "also consistent" w/ observations, then the other statement must be "consistent" w/ observations, also.

The diameter of the "throat" of a (single) Singularity-induced Wormhole is surely essentially said Singularity's Schwarzschild Radius (rs). But, to get an rs of even ~1 meter would require a mass comparable to the planet Jupiter. (Carl Sagan once said, separately, but aptly, "we're talking about ships the size of worlds".) Perhaps you could reduce this by some measurable factor, by creating a cluster of smaller Singularities bunched up -- like dimpling a rubber sheet w/ your five fingers, instead of one big fist. Even so, the tremendous stretching of Space-Time, across light-years' of (Hyper-)space, would obviously stretch everything to shreds. Note that, to my understanding, Hyperspace is the 5th (& higher??) dimension(s), through which 4-dimensional Spacetime curves. You can visualize this, w/ 1 space + 1 time dimension (2D) curving in 3D space. So, by this comparison, while a trip through Hyperspace could cut down the distance -- much like a line straight through the Earth is shorter than around its surface -- you would still be traveling light-years across Hyperspace -- much like the diameter of the Earth is still comparable to its circumference. Maybe you could create a spherical shell-shaped Singularity, inside of which the Spacetime Curvature remained small, even as the Singularity-shell stretched across HS, and contacted another region of Spacetime. Then, once the Wormhole was opened, the inner contents could be "rotated" around into the far-side of the WH -- to wit, the Destination -- and then the Singularity "evaporated" or otherwise closed, leaving the "cargo" in the Destination system. Speaking of which, for small-mass Singularities, the Evaporation Radiation could be quite intense too.

DH, I know you don't misquote people like this to their faces. I didn't discount it. I acknowledged it. I just also acknowledged that "present observations are also completely consistent"... w/ the abundance of Life. You have agreed to everything I said, yet are flaming me. All flame, no substance. The ubiquity of Methane is consistent w/ the ubiquity of Life, as DH himself has (tacitly) acknowledged, w/ his own words, "[the data] is also consistent w/ the non-ubiquity of Life". The current data could go either way, as I've said repeatedly, over & over, again & again, w/ a thousand different analogies, including: "the jury's still out, but it looks promising" "it's half-way thru the 1st inning, and Life is up 1-0" This is preposterous. How come DH can flame, & misquote, & misconstrue me, and nobody holds him to anything ? Merged post follows: Consecutive posts mergedA surprisingly pertinent observation (Andrew Franknoi. [Disney Learning] Wonderful World of Space, pg. 78.): The more things change, the more they didn't -- Wisdom There's nothing new under the Sun -- Wisdom

I understand, that Hyperspace is the higher-dimensional (5+ dimensions) space inside of which our 3+1 dimensional Spacetime is embedded. In the above attached figures, Spacetime is the curved line (1-D), containing the two stars (M1 & M2) and the "Space Warper" (m); and, Hyperspace is the plane of your computer monitor (2-D), inside of which that (exceedingly schematic) 1-dimensional curved Spacetime is embedded.

Possible Solution to above-posed Problem -- "Space Warped" Wormholes, created inside other Wormholes, might "make it back" to the desired destination Gravity Well, across Hyperspace Attached is another exceedingly schematic diagram, depicting a "compound double Wormhole", which might "make it back" to Real Space, from "deep in Hyperspace".

Possible Problem -- "Space Warped" Wormholes, created in an in-sufficiently curved regions of Spacetime, might "miss" the desired destination Gravity Well, across Hyperspace Attached is another exceedingly schematic diagram, depicting a hypothetical "Hyperspace miss", from a man-made Wormhole, created in an in-sufficiently curved region of Spacetime.

Attached is an exceedingly schematic diagram, indicating how a Wormhole might possibly be created, between the curved Spacetimes, of the Gravity Wells, of two massive objects (stars, say). From within the Gravity Well of one star, a "Space Warper" would compact matter, to create a Singularity of exceedingly curved Space Time. This new -- and completely man-made -- Gravity Well would "branch off" through Hyperspace, until it encountered the Gravity Well of the second star. Presumably, once the patch of Spacetime surrounding the "Space Warper" came into contact with a patch of Spacetime in the second star's Gravity Well, they could "merge", allowing the "Space Warper" to appear near the second star.