leaving black holes
in [Relativity]
|
Prev: "Can the Second Law of Thermodynamics Be Circumvented?"
Next: Looking Under the Skirt of Nature
From: Tom Roberts on 6 Oct 2009 01:24 eric gisse wrote: > Tom Roberts wrote: >> eric gisse wrote: >>> A black hole has the unique feature of swapping the role of time and >>> space inside the event horizon. >> This is not true. Indeed, there is no way to "swap" such incommensurate >> things. > > Close enough. No, it is not, as you yourself prove: > I'm not saying something stupid like 'your clock starts ticking backwards' > but the ability to move through time and space is inverted from that of > Minkowski space. But that is not so. What is "inverted" inside the horizon is the meanings of SYMBOLS "r" and "t". Nothing more. This is strictly an issue of how one labels coordinates, and has no effect on any physical process or situation. Tom Roberts
From: Omega on 7 Oct 2009 05:30 Tom Roberts wrote: > eric gisse wrote: >> The observable universe is not like this. We are not in a black hole. > > Yes. Moreover, in the context of GR, there is a singularity in our > past (as shown by the singularity theorems; see for example, Hawking > and Ellis). The FRW manifolds have the right geometrical structure to > be models of cosmology, while none of the black hole manifolds do. If one were to apply, instead of Hubble's Law, the simple corollary "Any two points which are moving toward the origin, each along straight lines and with speed inversely proportional to the distance from the origin, will be moving away from each other with a speed proportional to their distance apart." which would put the singularity in our future rather than our past, would the resulting models of cosmology of the observable universe still be in conflict with all black hole manifolds?
From: eric gisse on 7 Oct 2009 10:55 Omega wrote: > Tom Roberts wrote: >> eric gisse wrote: >>> The observable universe is not like this. We are not in a black hole. >> >> Yes. Moreover, in the context of GR, there is a singularity in our >> past (as shown by the singularity theorems; see for example, Hawking >> and Ellis). The FRW manifolds have the right geometrical structure to >> be models of cosmology, while none of the black hole manifolds do. > > If one were to apply, instead of Hubble's Law, the simple corollary > "Any two points which are moving toward the origin, each along straight > lines and with speed inversely proportional to the distance from the > origin, will be moving away from each other with a speed proportional to > their distance apart." > which would put the singularity in our future rather than our past, No, no it wouldn't. > would the resulting models of cosmology of the observable universe still > be in conflict with all black hole manifolds? Those who do not understand should not comment. The singularity of a black hole is in the future of any observer within its' event horizon. An observer in a FRW manifold has no such destination. The white hole solution for black holes doesn't apply either.
From: Tom Roberts on 7 Oct 2009 16:19 Omega wrote: > If one were to apply, instead of Hubble's Law, the simple corollary > "Any two points which are moving toward the origin, each along straight > lines and with speed inversely proportional to the distance from the origin, I have no idea what you think that is a "corollary" of. In any case, such a physical situation is nonsensical -- I can see no plausible physical mechanism for making "points" speed up as they approach the origin. And even with such a mechanism, "points" near the origin would already have passed through the origin and must be heading away from it at infinite speed (or momentum is not conserved). Moreover, the universe we observe does not look like that at all. In particular, the expansion since the big bang has no "origin" -- speaking rather loosely, it occurred EVERYWHERE with no "center" at all. Note that the expansion phase of any of the FRW manifolds does not look at all like you describe. Nor does the contraction phase of those that have one. Tom Roberts
From: Simple Simon on 8 Oct 2009 12:35
On Oct 7, 1:19 pm, Tom Roberts <tjrob...(a)sbcglobal.net> wrote: > Omega wrote: > > If one were to apply, instead of Hubble's Law, the simple corollary > > "Any two points which are moving toward the origin, each along straight > > lines and with speed inversely proportional to the distance from the origin, > > I have no idea what you think that is a "corollary" of. You've snipped mid-statement. I'm sorry for not being clear enough. I'd meant that the statement is a "corollary" to Hubble's Law: Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart. Algebraically, this is equivalent to saying that if: The origin x0 = 0 and point x1 is closer to the origin than point x2 (for simplicity, assuming the same constant of proportionality) and velocity v1 = (N)(x1 - x0) = (N)(x1) and velocity v2 = (N)(x2 - x0) = (N)(x2) then v2 - v1 = (N)(x2 - x1) The next step is: Any two points which are moving toward the origin, each along straight lines and with speed inversely proportional to distance from the origin, will be moving away from each other with a speed proportional to the difference of the reciprocals of their distances from the origin." Algebraically, this is equivalent to saying that if: The origin x0 = 0 and point x1 is closer to the origin than point x2 and velocity v1 = -(N)/(x1) and velocity v2 = -(N)/(x2) then v1 - v2 = -(N)[(1/x1) - (1/x2)] At this point it is sufficient to note that, first: (1/x1) - (1/x2) = (x2 - x1)/[(x1)(x2)] second: when the distances from the origin are large compared to the distance between the points, v1 - v2 becomes immeasurably close to N0(x2 - x1) where N0 ~= N/[(x1)(x2)] ~= N/[(x1)^2]. This is the situation under consideration. Which brings us back to (more accurately stated, still trying to be pithy): Any two points which are moving toward an arbitrarily distant origin, each along straight lines and with speed inversely proportional to the distance from the origin, will be moving away from each other with a speed proportional to their distance apart. This, however is not the rule under which I operate. The rule is considering objects in Newtonian free fall, and goes as follows: Any two points which are moving toward the origin, each along straight lines and with speed proportional to the square root of the reciprocal of their distances from the origin, will be moving away from each other with a speed proportional to the square root of the difference of the reciprocal of their distances from the origin. Again, for simplicity, assuming the constant of proportionality, e.g. as would occur for objects dropped from the same height, this is equivalent to: v1 v2 = [(2GM)^1/2] [(1/x1 1/x2)^1/2] > > In any case, such a physical situation is nonsensical -- I can see no plausible > physical mechanism for making "points" speed up as they approach the origin. And Instead of "points", substitute "objects". i.e. Those same "points" that Hubble observed. Those same points for which the conservation of momentum applies. The mechanism is gravitation. > even with such a mechanism, "points" near the origin would already have passed > through the origin and must be heading away from it at infinite speed (or > momentum is not conserved). For "ordinary" sources of gravitation, their surfaces would prevent the objects from passing through the origin, and for a black hole, the central singularity would prevent same: "This occurs because spacetime has been curved so much that the direction of cause and effect (the particle's future light cone) points into the singularity." > > Moreover, the universe we observe does not look like that at all. In particular, > the expansion since the big bang has no "origin" -- speaking rather loosely, it > occurred EVERYWHERE with no "center" at all. > > Note that the expansion phase of any of the FRW manifolds does not look at all > like you describe. Nor does the contraction phase of those that have one. > This is the point that I'm trying to make: The result of the above is that the observation of the accelerating separation of the galaxies is easily explained as being due to the tidal force one would experience within a black hole, and is not due to expansion. In fact, it is a simple matter (since I've done something similar, using the Newtonian approximation of a highly idealized version where all of the effective mass is located about the singularity) to calculate the size of the black hole that would result in the observed Hubble constant and negative deceleration parameter, and our position within it. Since this demonstrates that the observed accelerating separation of celestial objects can be attributed to gravitation alone (objects in freefall within a black hole) it thus obviates the need for an anomalous big bang event and an aethereal dark energy and, by Occam's Razor, is worth considering. This would eliminate the first and most compelling of the 3 pillars upon which the big bang rests (not that I have anything against the big bang). While all of this seems obvious to me, your incredulity indicates that I am probably missing something fundamental. Thank you very much for your time and consideration. > Tom Roberts |