Again, to any uncertain professors or readers bearing an inexorable prejudice against populist prose: the more academic version of this General Relativistic Perspective theory is at The General Relativistic Perspective [ http://vixra.org/abs/1306.0103 ]
Light speed limits are accepted as one of the defining aspects of our reality. While exceptions have been conceived and observationally interpreted, they have never been demonstrated. The General Relativistic Time distortion equation can be shown to establish the same principle of a light-speed limit to escape velocity. What follows reasons and begins the additional equations to General Relativity|G.R.| theory; equations that will overcome the fundamental “imaginary” values contradiction inherent in the primary General Relativity time distortion equation.
The Michelson-Morley experiment established the first Relativistic equation. The [length’=length*(1-v2/c2).5] - expression was expanded by Albert Einstein into other relativistic distortion equations, as well as what is arguably the most fundamental relationship in our reality: e=mc2. The equations limited velocity in our Universe to light speed, not only because it would require infinite energy to reach that velocity, to exceed it would mean a transformation of any matter object to “imaginary” status. Though that limit has characterizations that are inherent to the theory. For instance: inside a vessel moving at a velocity of |c/(2½)| m/s there would be some observations from inside it that it was moving at the speed of light. It would be an absolute distortion; it would still take:
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727E0
1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727E0
So presuming the speed of light to be:
Using the equation introduced in The Special Relativistic Perspective:
VelocitynoSRPD = VelocitySRPD /(1+ VelocitySRPD2/c2).5
Would allow calculation of that value:
VelocitynoSRPD = 2.997~00E+08/(1+ 2.997~00E+02/c2)/2.997~00E+082/c2).5
VelocitynoSRPD = 2.997~00E+08/(2).5
VelocitynoSRPD = 2.997~00E+08/(2).5
VelocitynoSRPD = 2.1198528000038323887394410859085474720613952788636246936246969800034346551883546929356451802958658432152222E8m/s
So any velocity greater than approximately 2.119~222E8m/s would mean that observers/passengers perceived their velocity to be greater than that light. While the equation is currently conceived to have exceptions (in the beginning of things), it is accepted as a defining aspect of our Universe.
In General Relativity the principal equation is:
Time’ = Time/(1-2GM/rc2).5
Where
c – speed of light
Time – real time taken value to pass when the expression: Gravitational constant multiplied by the mass of the body divided by the product of the radius and the speed of light conditions approach zero, when the point is under no distortion.
Time’ – real time passing when the expression “GM/rc2” is greater than zero
M – Mass of object considered
r – radius of object considered
The expression |GM/rc2| is one that does have an instances |GM| would be greater than |rc2| – that would mean that the formula would describe, according to current theory, an imaginary environment. If we accept the Universe to have a mass, there is no verifiable evidence of what an imaginary (-1.5) quantity represents in directly observable phenomenon. They are used in circuit design, astronomy and other applications – but they are a logic technique, not an observable phenomenon. Electrons do not have “negative” charges; they have charges opposite to proton charges. Assignment a negative value was simply a historic occurrence of human bias, not a description of a physical phenomenon.
As in Special Relativity,the time distortion equation shows the greater number of undistorted seconds [Time] for any object/environment that would occur under the distortion [Time’]. So let us define two alternate variables, ones recognizing |Relativistic| seconds and the fact that a fewer number of |Relativistic| seconds pass for any given number of |real| seconds.
The Classic G.R. time equation is entirely from the non-relativistic viewpoint – for each second that would pass were the body under no gravitational distortion, when the body approaches any gravitational body, each second on that body will take “one_undistorted_second/(1 – 2GM/rc2)” to pass. Those residing on a Relativistic object will not perceive a slower pace of time. What their perception would be is that there would be more real time units – things happening faster outside the distorted space/time location they occupy.
The inverse equation, would be the equation using theRelativistic values. The values perceived from a Relativistic viewpoint under no distortion, would show how many of those time units would pass for the same were there distortion. Fundamentally, fewer relativistic time units will pass under distortion than each of the same when not under distortion.
The inverse equation, would be the equation using theRelativistic values. The values perceived from a Relativistic viewpoint under no distortion, would show how many of those time units would pass for the same were there distortion. Fundamentally, fewer relativistic time units will pass under distortion than each of the same when not under distortion.
TimeDistortedRelativisticSeconds = TimeUndistortedRelativisticSeconds * (1-2GM/rc2).5
We will not use the “real” label; what is real and what is relativistic is simply not determinable in a Universe ruled by Planck’s constant – and the simple distribution of objects. Estimations can be made of all the factors in the above equation, but they are only that, estimations. We cannot know the exact value of the variables above because the time distortion cannot really be perceived. However, we can assume, for theoretic purposes, a time not distorted by relativistic effects. To avoid the inevitable bias following a “real” label, we will assign values that presume an ideal – but it is solely a theoretic presumption, a strategy used throughout science. Then we reason the outcomes of that presumption. Defining more descriptive variables, ones that recognize we deal with General Relativity:
TimenoGRPD – seconds passing from a perspective under General Relativistic distortion when the G.R. distortion factor is unitary (no distortion)
TimeGRPD – seconds passing from a perspective under General Relativistic distortion when the distortion factor is dependent on relativistic effects
So the relationship becomes:
So the relationship becomes:
TimeGRPD = TimenoGRPD*(1-2GM/rc2).5 Equation 1
As |VelocityEscape = (2GM/r).5|, a valid expression for |1- 2GM/rc2| would be to define “2GM/r”:
VelocitynoGRPD_Escape – observed escape velocity from a General Relativistic perspective when distortion is unitary
VelocitynoGRPD_Escape = (2GM/r).5
VelocitynoGRPD_Escape2 = (2GM/r)
Thus, the equation then becomes:
TimeGRPD = TimenoGRPD*(1 - (2GM/r) * 1/c2).5
TimeGRPD = TimenoGRPD*(1 - VelocitynoGRPD_Escape2 * 1/c2).5
TimeGRPD = TimenoGRPD*(1 - VelocitynoGRPD_Escape2/c2).5 Equation 2
Formulating a new theorem armed with the above equation – rather than concluding that when objects reach the Schwarzschild limit, they become imaginary, Special Relativity logic allows the conclusion that escape velocity never exceeds light speed. The slowdown of time is accepted on a Special Relativistic Level to slow down the acceleration of the moving body. Reactions would take place at a slower pace, the accelerative force exerted by the propellant would decrease. That is one of the most fundamental declarations of Special Relativity. If you deny that acceleration slowdown, you are effectively denying the legitimacy of Special Relativity principles. While the growing mass of the accelerant would increase its propulsive force, the increased mass of the body being propelled would exactly match the increased mass of that propellant. As well, very fundamentally, the velocity of all Bosons will slow under Relativistic distortion. So surely there is a parallel in General Relativistic distortion: slowdown of time on the gravitational body would have to mean that the velocity of all Bosons would lessen. If the gravitational Boson were not slowed along with the rest, then all of the other forces that maintain the structure of the Universe would be overpowered by the gravitons and be forced into “classic” S.O.’s and collapse into a single non-radiating body. Pure matter could possible escape, but only if it passed the S.O. barrier with a vector pointed directly outward. Even the possible leakage of mass through "Hawking Radiation" [H.R.] can be contested in such a Classically envisioned body: the H.R. would be taking place at a point in Space extremely devoid of matter. Even then, for full escape from the body, the escaping particle would have to have a velocity great enough at the point it materialized - where an escape velocity was still very close to "c". Over an object so immense that even orbital velocity would fail, unless the vector of that velocity was precisely aimed so that its Apsis orbit point remained beyond the Schwarzschild border. This writer would like to emphasize that logical arguments go very much against this phenomenon. Logical arguments that establish if the absolutist view of General Relativity is relied upon, any scale of "Big Bang" could never have happened.
There is also this argument against the notion of “Cosmic Egg” present at the beginning of the Universe could not be principally Energy/Bosons because all of them would be slowed down under Relativistic distortions. Because General Relativity can be expressed in a way that shows that Relativistic forces must DIRECTLY affect gravitational forces in a way that limits escape velocity to light speed, we must either presume the Gravitational Bosons do undergo a Relativistic slowdown and that then reduces their force, or deny the legitimacy of all of General Relativity. We can be very certain that Special Relativity affects the velocity of gravitational Bosons, because if it did not, the objects we see receding at the edge of the Universe would collapse on themselves; an un-slowing Graviton would develop greater and greater proportionate energy. If you deny General Relativity, then you deny the possibility of Schwarzschild objects of any description.
This author makes no such claim and asks the reader to consider a graviton slowdown as a result of General Relativistic effects: if that gravity/graviton force did not slow down as well as the other Bosons then the force of gravity itself would appear to increase. That would mean that objects affected by the relativistic gravitational force would increase their velocity, accelerate, at a greater rate than predicted by current theory – there would be no “halt” at the Schwarzschild border, there would be an acceleration. The Time distortion would mean that whatever actions take place on the moving body (i.e. neutrons have a half-life of: 6.110E+2 ± 1.0s - or a little more than 10 minutes) would take longer, from a non-Relativistic Perspective than they would on the distorted body.
While that idea it is promoted by some thinkers, it is completely unreasonable: by that presumption no S.O. would ever grow. What effect an endlessly thickening cloak of matter/energy would bring is hard to postulate.
While that idea it is promoted by some thinkers, it is completely unreasonable: by that presumption no S.O. would ever grow. What effect an endlessly thickening cloak of matter/energy would bring is hard to postulate.
So fewer GRPD time units (e.g. seconds) will pass for any given number of non-GRPD time units. The “particulate” aspect of the graviton may be under debate, but that it moves at a relativistic speed is not - it is a Boson. If it did not, then General Relativity would be an invalid theory: Relativistic effects are just as fundamental to G.R. as they they are to S.R. Then other equations can be deduced using the time distortion effect. Square both sides:
TimeGRPD2 = TimenoGRPD2* (1-VelocitynoGRPDescape2/c2).5
Set the variable TimenoGRPD
TimenoGRPD = 1m / VelocitynoGRPDescape
VelocitynoGRPDescape = 1m / TimenoGRPD
Because the time was slowed, it would APPEAR that the escape velocity was increased by the distortion, by exactly the margin of that time distortion.
VelocityGRPDescape = 1m / TimeGRPD
So in the original equation, divide both sides with 1 metre:
TimeGRPD /1m= (TimenoGRPD/1m)*(1-VelocitynoGRPDescape2/c2).5
Invert the expression and set the TimenoGRPD variable to:
TimenoGRPD = 1m/VelocitynoGRPDescape
That would mean that mathematically |TimenoGRPD| would be:
TimeGRPD = 1m/VelocityGRPDescape
So both
VelocityGRPDescape = 1m/TimeGRPD
and
VelocitynoGRPDescape = 1m/TimenoGRPD
Then invert the equation
1m/TimeGRPD = (1m/TimenoGRPD)/(1-VelocitynoGRPDescape2/c2).5
So then it could be rewritten. Dividing both sides by one metre would not change the distortion. But by inverting the equation, the distortion could then be expressed in Velocity, not Time. General Relativistic time distortion would then make the escape velocity appear to be greater than it was:
VelocityGRPDescape = VelocitynoGRPDescape/(1-VelocitynoGRPDescape2/c2).5 Equation 3
Let us then suppose (as we do in Special Relativity) that “1-” format of the relativistic equation means that “VelocitynoGRPDescape” has an absolute limit of light speed – from a viewpoint from outside the area of distortion. In the area of distortion, escape velocity would appear greater than light speed, but only because of the time distortion. We know (or can deduce) Special Relativistic distortion effects would make a sub-light velocity appear to be greater than light from a viewpoint within the distorted area. General Relativistic distortion would be different from the one in Special Relativity: the mass of the “matter” in a body would be increased by the matching decrease in the speed of light that would have to take place if their were a time as well as a gravity distortion. The mass all of all zero-rest-mass particles/Bosons [Photon/Gluon/z meson/w meson]’s and their energy would decrease as the time distortion reduced their speed. The "discovery" of the graviton is a very debatable issue, even as to whether it exists in the same sense as the other Bosons is contested. Even if it is, it may not move exactly at the speed of light. But that marginal difference would not mean it is not a Boson – were it anything else, it would have been identified long before now. That the force/particle would reduce under relativistic distortion is not debatable. The time distortion MUST reduce the value of the Gravitational Constant. Again, it is completely unreasonable that the Gravitational Time distortion would alter the other three forces and not Gravity.
So then deducing what the relationship of VelocityGRPDescape||VelocitynoGRPDescape would be within the area of distortion by squaring both sides:
So then deducing what the relationship of VelocityGRPDescape||VelocitynoGRPDescape would be within the area of distortion by squaring both sides:
VelocityGRPDescape2 = VelocitynoGRPDescape2/ (1-VelocitynoGRPDescape2/c2)
Multiplying both sides with (1 - VelocitynoGRPDescape2/c2), that would lead to the repositioning of the expression:
Multiplying both sides with (1 - VelocitynoGRPDescape2/c2), that would lead to the repositioning of the expression:
VelocityGRPDescape2 * (1 - VelocitynoGRPDescape2/c2) =
(1 - VelocitynoGRPDescape2/c2)*VelocitynoGRPDescape2/(1-VelocitynoGRPDescape2/c2)
and so
and so
VelocityGRPDescape2 * (1 - VelocitynoGRPDescape2/c2) = VelocitynoGRPDescape2
Expand the expression on the left side of the equation:
Expand the expression on the left side of the equation:
VelocityGRPDescape2 - VelocityGRPDescape2 * VelocitynoGRPDescape2/c2 = VelocitynoGRPDescape2
Exchange the VelocitynoGRPDescape2 and the VelocityGRPDescape2 variables
–VelocitynoGRPDescape2 - VelocityGRPDescape2 * VelocitynoGRPDescape2/c2 = – VelocityGRPDescape2
Multiply both sides of the equation with negative one [-1]
VelocitynoGRPDescape2 + VelocityGRPDescape2 * VelocitynoGRPDescape2/c2 = VelocityGRPDescape2
Compress the expression on the left side of the equation:
VelocitynoGRPDescape2 * (1+VelocityGRPDescape2/c2) = VelocityGRPDescape2
VelocitynoGRPDescape2 * (1+VelocityGRPDescape2/c2) = VelocityGRPDescape2
Divide both sides with (1+VelocityGRPDescape2/c2)
VelocitynoGRPDescape2 *(1+VelocityGRPDescape2/c2) / (1+VelocityGRPDescape2/c2) = VelocityGRPDescape2/(1 + VelocityGRPDescape2/c2)
VelocitynoGRPDescape2 *
So
VelocitynoGRPDescape2 = VelocityGRPDescape2/(1 + VelocityGRPDescape2/c2)
Take the square root of both sides and so then the real escape velocity when not distorted by General Relativistic effects:
VelocitynoGRPDescape = VelocityGRPDescape /(1+VelocityGRPDescape2/c2).5 Equation 4
Let us examine the escape velocity at the surface of an Schwarzschild Sphere with the mass of the Sun (Masssun).
RadiusSchwarzschildSun = (2*6.674286700~00E-11*1.989100~00E+30)/299,792,4582
RadiusSchwarzschildSun = 2.954269191222665029918311344788781224854878020436973142527761526153133459685~1134087483161015331701111E+03m
The escape velocity from the border of that object is (unsurprisingly):
Velocityescape = (2GM/r).5
Velocityescape = ((2*6.674286700~00E-11 * 1.98900~00E+30)/(2.954~111E+03)).5
Velocityescape = 299,792,458 m/sec
But consider: because Special Relativistic effects will make any velocity appear greater than it is, Relativistic escape velocity would appear to be GREATER than light speed. That would not mean that velocity was unattainable, it would be that distortive effects made it SEEM to be greater than light speed. Again, the escape velocity after considering Relativistic effects would not be that, those effects would slow the exertion of gravity for the Relativistic body. That is very fundamental in Special Relativity, it is confirmed by observations of the entire Universe. A body under slow down from Special Relativistic effects will not emit as much EM energy (or Strong Nuclear, Weak Nuclear or Gravitational) as it would were it not in a Relativistic Environment. So the above velocity is what escape velocity would be were there no distortion.
The dichotomy between distortions is more obvious with a phenomenon that we are certain exists: Quasars. Current theory is that Quasars are the partially collapsed centers of Galaxies. A reasonable illustration of that phenomenon would be using an established valid theoretic value for the Milky Way (9.0E+11 Solar Masses)[4]. As Quasars are singular objects, presume a Quasar to be a Galactic object, with a mass 10 times that of the Milky Way. We will also assume that half of the mass of this theoretic Quasar collapsed into an Schwarzschild object at the center.
MassGalaxy = 9.00~00E+11*MassSun= 1.7901900~00E42
MassGalactic_Scale_Quasar = (Mass_galaxy*10)/2 = 89509500~00E42kg
The radius of such a quasar:
Schwarzschild_RadiusGalactic_Scale_Quasar = 2*G MassGalactic_Scale_Quasar /c2
Schwarzschild_RadiusGalactic_Scale_Quasar = 2*6.6742867E-11*89509500~00E42kg/c2
Schwarzschild_Radius_ Galactic_Scale_Quasar =1.329421136050199263463240105154951551184695109196637914137492686768910056858~
Schwarzschild_RadiusGalactic_Scale_Quasar = 2*6.6742867E-11*89509500~00E42kg/c2
Schwarzschild_Radius_ Galactic_Scale_Quasar =1.329421136050199263463240105154951551184695109196637914137492686768910056858~
3010339367422456899265500E16m
The gravity of that that galactic S.O. would have a relatively low gravity for such a massive object:
Gravity_at_SchwarzGalactic_Scale_Quasar = G* MassGalactic_Scale_Quasar /Schwarzschild_RadiusGalactic_Scale_Quasar2
Gravity_at_SchwarzGalactic_Scale_Quasar = 6.674286700~00E-11m3 kg-1 s-2*3.9778400~00E40kg/(1.329~500E16m)2
Gravity_at_SchwarzGalactic_Scale_Quasar = 3.380250074130310905450427280400458344741277930982899552067532453282419896945~
0404479301663193408947219E0m/s2
0404479301663193408947219E0m/s2
The classic distortion figure a little farther out at the Schwarzschild + Planck (assuming a Planck length of 1.61625200~00E-35m[5]) position would be slightly higher
Distortion_at_Schwarz_plus_PlanckGalactic_Scale_Quasar=1/(1-G*MassGalactic_Scale_Quasar/~
(Schwarz_RadiusGalactic_Scale_Quasar*+PlanckLength)*c2)).5
Distortion_at_Schwarz_plus_PlanckGalactic_Scale_Quasar=1/(1-2*6.674286700~00E-11*~
(Schwarz_RadiusGalactic_Scale_Quasar*+PlanckLength)*c2)).5
Distortion_at_Schwarz_plus_PlanckGalactic_Scale_Quasar=1/(1-2*6.674286700~00E-11*~
(3.9778400~00E40m+1.61625200~00E-35m)*c2)).5
Distortion_at_Schwarz_plus_PlanckGalactic_Scale_Quasar=2.8679841836291672832927940418666606353385128841173538731232128264255719731918~
6011963551682033731013657E25
6011963551682033731013657E25
Then one full meter out:
Distortion_at_Schwarz_plus_OneGalactic_Scale_Quasar = 1/(1-G*MassGalactic_Scale_Quasar/~
(Schwarzschild_RadiusGalactic_Scale_Quasar*+1.00~00E0)*c2)½
Distortion_at_Schwarz_plus_OneGalactic_Scale_Quasar = 1/(1-2*6.674286700~00E-11*~
(3.9778400~00E40m+1.00~00m)*c2).5
Distortion_at_Schwarz_plus_OneGalactic_Scale_Quasar = 1.153005262802472798610383754105265318724509987632026208133745347997919177536~
2401858051426201056821477E8
2401858051426201056821477E8
The proportion of those distortions:
ProportionDistortions = Distortion_at_Schwarzschild_plus_PlanckGalactic_Scale_Quasar / Distortion_at_Schwarzschild_plus_OneGalactic_Scale_Quasar
ProportionDistortions = 2.867~657E25/1.153~477E8
ProportionDistortions = 2.487399039843321386792545690131076813125363900623257046785457996710252908516~
7725215849005758669400567E+17
7725215849005758669400567E+17
The distortion reduced by a factor of 2.487~567E+17 over one metre less one Planck Length.
Compare those values to a confirmed Astronomic phenomenon: a neutron star. Presuming a simple radius of 9.1E+3m for that neutron star (in the 4U 1820–30 binary) with a mass 1.58*MassSun[6]:
MassNeutron_star = 1.58* MassSun
MassNeutron_star = 3.14277800~00E30
MassNeutron_star = 3.14277800~00E30
GravityNeutron_star = G* MassNeutron_star /RadiusNeutron_star2
GravityNeutron_star = 6.674286700~00E-11*3.14277800~00E30/(9.100~00+3)2
GravityNeutron_star = 2.533003430316700881536046371211206376041540876705711870547035382200217365052~
5298876947228595580243932E+12
5298876947228595580243932E+12
As opposed to the distortion:
DistortionNeutron_Star = 1/(1-G*MassNeutron_Star / (RadiusNeutron_Star*c2)½
Distortion Neutron_Star = 1/(6.674286700~00E-11*3.14277800~00E30/(9.100~00+3)*c2)½
Distortion Neutron_Star = 1.137577275654691133853099930891286065705437408574509224719599293543012992677~
0864907636131976660586994E0
0864907636131976660586994E0
Those Galactic vs. the Neutron star predictions surely does not jibe.
An alternative: is it reasonable that an object under General Relativistic slowdown exerts the same gravitational pull as it would were it not under Relativistic distortion? If gravitational force were not lessened, is it reasonable that anything would be distorted by General Relativistic factors? Consider then, escape velocity when General relativistic concerns are taken into account:
VelocitynoGRPDescape = VelocityGRPDescape/(1 + VelocityGRPDescape2/c2).5
VelocitynoGRPDescape = 299,792,458/(1 + 299,792,4582/299,792,4582).5
VelocitynoGRPDescape = 2.119852800003832388739441085908547472061395278863624696980003434655188354692~
9356451802958658432152222E+0
The above is what that “General Relativistic” escape velocity would be. It should be noted that in the non-Relativistic world, there is no limit to what the escape velocity could be. G.R. would take any escape velocity, though, no matter how high, and limit it to c – lightspeed.
We must consider Special Relativity distortion as well in determining what the escape velocity will be with both distortions included. The S.R. time equation is a parallel to Equation 1 above:
TimeSRPD = TimenoSRPD*(1 - VelocitynoSRPD2/c2)½ Equation 5
Using exactly the same logic [introduced in A Special Relativistic Perspective] used in Equations 2 and 3, that would lead to:
VelocitySRPD = VelocitynoSRPD/(1 – VelocitynoSRPDc2/c2).5 Equation 6
And:
VelocitynoSRPD = VelocitySRPD/(1 + VelocitySRPD2/c2).5 Equation 7
The mathematical validity of equations 1 through 7 was confirmed using 39 different velocitynoSRPD|| velocitynoGRPDescape values ranging from 1.00~00E-500 to c-1.00~00E-500. The calculations were done to 2000 decimal places, and the largest inequality was 1.00~00E-1992. An irrational inequality that is inevitable with all irrational number calculations. The Special Relativistic effects would slow down the interactions whatever body concerned was having with the external environment – as was stated before, those interactions would include gravity. Although those bodies would be distorted in terms of mass, it has been established since Galileo that mass does not effect the gravitation acceleration (be it positive or negative acceleration) so the lessening of the mass of the body escaping would not affect the gravitational slowdown. Using Relativistic Perspective equation 7 above to determine to what degree that S.R. slowdown distortion would have on the escape velocity:
VelocitynoSRPD = (2.119~222E+08)/(1 + (2.119~222E+08)2/299,792,4582).5
VelocitynoSRPD =1.7308525632731957604232687639438429944002051081837595813347804518115016399681490831568265359509419994E+08
As a double check, we can determine the special relativistic time distortion of that speed:
TimeSRPD = TimenoSRPD/(1 – Velocityescape2/c2).5
Assuming a one second passage for TimenoSRPD, the equation becomes
TimeSRPD = 1/(1 – (1.730~994E+8)2/299,792,4582)½
TimeSRPD = 1.224744871391589049098642037352945695982973740328335064216346283625480188728~
6575132699297165523201174E0
6575132699297165523201174E0
Multiply the real speed by that time distortion:
VelocitySRPD = (1.224~174E0)*(1.730~994E+8)
VelocitySRPD = 2.119~222E+8
This mathematic reasoning is supported by an uncontestable fact. In an Einsteinian Universe, a one kilogram object moving at a real (non-relativistically distorted) speed of light would have infinite units of momentum because of relativistic mass distortion. Conservation of energy/matter/mass should also be considered. Objects falling towards one another under gravitational forces acquire both speed and mass because of relativistic effects. On current theory then, both objects would gain a possibly infinite amount of mass because of relativistic effects. Even if the object continually slows and does not actually pass the Schwarzschild barrier, from a relativistic perspective, the velocity is continually increasing because of the time distortion – and so it gains mass. The minor object (or layer of matter surrounding the S.O.) would eventually gain enough mass to become an Schwarzschild object itself. The question then becomes: are they both moving towards one another at the speed of light? A simple conservation of energy issue then arises – where did that infinite (or “approaching infinity”) matter/energy come from? That simple infinity issue is another argument against the existence of a “Classic” S.O. Even if you accept that there is some sort of stoppage (or “slowage”) at the S.O. border, there is no limit to how much kinetic energy the body will gain under S.R. – a reasoning revealing an inconsistency in Classic G.R.
If you accept that the time distortion limits escape velocity, would it not be doing so by lessening gravitational force? For relativistic slowdown to take place, the velocity of all Bosons – EM/photons, Strong Nuclear/gluons, and Weak Nuclear/W||Z bosons (as it would have to for simple execution of molecular, ionic and even nucleic reactions) – the escape velocity would continually slow in its increases. Then the gravitation phenomenon would be affected by the absolute limit to escape velocity. Because the gravity is determined by the inverse square of the radius and not the square root of that radius, it would have no limit in its level – it would simply slowdown the rise of that level. Contrary to modern scientific thought, Schwarzschild objects are escapable – or at the very least: orbit-able.
The EM force (that is basic to both the attraction that opposite charges and the repulsion “like” charges impose on our reality) would lessen, but the KINETIC energy that increasing temperature would bring upon the particles/atoms would mean that those particles/atoms would face both increasingly energy collisions with one another, and decreasing binding force. It adds an argument to the simple existence of Population II star at the core – despite the fact that those stars are recognized as the older population, they have a structure that would be appropriate to stars that were newly formed more recently after the BB and somehow managed to maintain their youth 14 billion years into our time. But consider: if a star is older, that would mean that it would create a greater number of higher Periodic table elements – both through the “pulsing” of variables stars (that would provide times of abnormal compression) and novae. Both of those represent catastrophic action in a star’s lifetime, even if they do not match Supernovae activity. Unless you accept the argument of slowed down Gluons, leading to more fragile nucleii – broken apart by the energy they absorbed emanating from the much denser star population at the galactic centre.
Such reasoning is supported by another consideration: think of the slowdown of Gluons where G.R. distortions were great – say at a Galactic core. Meaning that higher atomic number elements would break down – and so at the Galactic core would be the greatest number of Population II stars with the highest ratio of low atomic number elements – as there are. There currently is an unfortunate “reverse logic” employed to explain the aspects of Population II stars: because they are “older” and formed from a higher hydrogen/helium proportion clouds they have not formed higher Atomic number elements. That would be completely illegitimate reasoning. Because they are older, they would have formed more of the higher elements. There is also the concern that the enormously higher rate of background radiation would speed the maturation of any object in the core, and increase the occurrence of stellar scale catastrophic events. It is completely unreasonable to then suppose that only the “heavy” elements (with a higher Atomic number than Iron) would be ejected from the core. If it were formed in the core it would need a greater amount of energy to escape that core. It would receive no more kinetic energy, proportionately, from the simple explosive actions. The other repulsive force, EM pressure, would be pushing at a denser object – the mass of atomic scale objects would increase by the cube of the radius, whereas the pressure area would only increase by the square of that radius. Moreover, the EM pressure would not be pressing against a “flat” sail, but against a spherical one. Only the radiation that pressed against the relative center of the half sphere would push it directly out – any EM force that pressed against the portions that were at a greater and greater angle to the repulsive force from the center of the galaxy would not receive as much outward pressure. So there would be a lower and lower pressure/mass proportion. Additionally the centre radiation would not be pressing exclusively outward. A very large proportion of EM force would be generated by objects not at the exact centre of the core, and would be generating inward radiation pressure. Finally, the greater and greater Relativistic effects the closer one came to the Galactic S.O. would slow the velocity of outward pushing photons – lessening the kinetic energy they transmitted in terms of both mass and velocity.
So from a General Relativistic Perspective, the “1-” equations are just as valid as “1+” – unless the calculations are done for an area with a high gravitic distortion. Unless that gravitic distortion is very local – producing strong tidal effects or variance of gravitational force over distance from the source of that force. The variance between the two will be great enough for the observer to use whichever form he or she thinks appropriate. On simple planetary gravitational field, with minimum observable tidal effects or motions, the “1-” flavour would be the most useful. Though were your holiday cabin were on a body appearing to have high gravitational distortion (i.e. almost all the radiation around you seems extremely blue-shifted) the best strategy would be to use the blue shift to make an estimate of your point within that gravitational distortion and use the “1+” flavour for your calculations. Relativity is, as we know now, the most accurate view of the macro world – but it has complexities that are not always appreciated.
An alternate current view to stoppage at the border is that a body falling towards a S.O. would continually accelerate, and exceed the speed of light at the border of the S.O. They see that as the only alternative, if the body surrenders to normal relativistic powers to somehow stop at the border, for time not to proceed within the S.O. – or to become imaginary.
The same thinkers see Schwarzschild objects will distort space sufficiently to allow – either on escape or descent – to exceed the speed of light. There are no mathematical necessities for that. The procession of time is altered by General Relativistic powers. By any standard you would care to apply, for observers within the S.O., because of the distortion of time, their velocity increases at a rate than can be accounted for by the “Relativistic” gravity and their apparent velocity could exceed light speed.
The hypothesis that time will “stop” at the border is a fundamentally unreasonable supposition. In Special Relativity, there is no suggestion that because time slows, the object itself slows. The notion is also completely inconsistent with the notion of Hawking “leakage” (accepting the reasoning in this paper means that the physical conditions never arise or are needed for Hawking particle escape). Still, if that idea is accepted, you cannot have both the development of spontaneous matter creation and a “halted” environment. There is also the simple consideration that if matter/antimatter pairs form as is postulated, they would not disappear when they combined, they would produce Electromagnetic Radiation energy: that would be captured by the S.O. entirely because the gravity would affect the velocity of the Bosons directly and immediately, something that does not happen with matter objects. As well, relativistic effects would also be slowing down the EM/Bosons velocity absolutely - that's what relativistic distortion does.
Schwarzschild borders are simply a point where escape velocity reaches light speed even if you do not accept R.P. reasoning – not a barrier/obstruction. Even accepting entirely (under protest) the current notions of a real light speed being reached by objects falling from infinity to its Schwarzschild border, turn that viewpoint over. The Schwarzschild definition does not include the distance the object would travel beyond the border before returning to the S.O. The escape velocity of the Earth at its surface is approximately 1.1813E+04 m/s. That does not mean that any object with a lesser velocity will not move upward until achieving it. The object moves up in a parabolic course, the dimensions of that parabola determined by its velocity and the degree of the tangency of the flight path. An object then gaining tangentially a given orbital speed would achieve that orbit. Even if current limits of Schwarzschild objects are accepted as they are (excepting the “imaginary” conjectures), the fundamental of gravity/projectile/escape velocity/relativistic theory means projectile objects can pass the Schwarzschild border, simply not fully escape. Escape into orbit, then assuming a permanent orbit around that S.O. is possible without any concessions to this theory.
Let us examine mathematically the predictive values of General Relativity and General Relativistic Perspective. What we can perceive and define of our Universe (or this local one) is finite. As there are no absolute values for the mass of our Universe, we will simply assume for theoretical purposes, that mass of matter to be exactly, to 100 decimal places:
Again, the above mass is solely a theoretical presumption. We will also presume the mass of all various forms of energy present to have a value 10 times greater than the matter. The ratio of matter to energy is a gigantically debated issue – this paper will not cite any value as a “Reference”. A value ten times greater is as valid as any other estimate and this is solely an illustration, not a declaration:
MassUniverse = (3.00~00E+52) + 10*(3.00~00E+52)
MassUniverse = 3.300~00E+53kg
We will presume that the matter||energy in the Universe is still existent as a “Cosmic Egg” and has a radius of 1 Planck length. The Schwarzschild radius of our Universe would then be:
SchwarzschildRadiusUniverse = 2GMassUniverse/c2
SchwarzschildRadiusUniverse = 2*6.674286700~00E-11 *3.300~00E+53/299,792,4582
SchwarzschildRadiusUniverse = 4.901256010776127192564691286412436801579155129175009486874271296719793080770~
6370966112528958119055686E+26
Under current theory, that radius would represent the point where gravity/distortion became infinite, then “imaginary”. What that state is, precisely, is un-debatable, and currently unknowable. A point a single Planck length beyond the above Schwarzschild marker the gravity would be:
GravitySchwarzschildUniverse = 6.674286700~00E-11*(3.300~00E+53)/(9.802~73E+26 + 1.1.61625200~00E-35)2
GravitySchwarzschildUniverse = 9.168621030617183757315606686515297763897558089797389316842084126429656168223~
2936442964513890451657332E-11
It is a rational presumption that the principal G.R. equation is not applicable when a body has the mass and dispersion as has our Universe. That would yield an unreasonable distortion value for such a widely dispersed matter/energy environment. Although strict application of current theory would argue relativistic effects somehow distorts space and time sufficiently so that Schwarzschild borders represent a time stoppage. That is surely a powerful argument that a disperse body would not exert the same relativistic distortion as one with the matter|energy collapsed to the Planck length radius. So let us examine what current relativistic equations predict a single Planck Length beyond the Schwarzschild radius of such a collapsed body (and presuming a simple 1 second of time) the distortion will be:
RelativityClassicPlusPlanck – Distortion 1 Planck length beyond Schwarzschild radius
RelativityClassicPlusPlanck = Time/(1- 2GMassUniverse/rc2).5
RelativityClassicPlusPlanck = 1/(1- 2*6.674286700~00E11*3.300~00E+53/
(4.584335E+26 + 1.61625200~00E-35m)*299,792,4582).5
RelativityClassicPlusPlanck = 7.787788601496931472715238228069253458235269509154633166712427009092658673359~
9009924018192730848455929E+30
So current theory espouses a point where gravity is of the order of 4.584~350E-11m/sc2, the distortion will be 7.787~929E+30. Notions of Universe “expansion” should be incorporated. If we accept General Relativity as a valid COMPLETE theory, the above must have been true at some point in the history of the universe.
The distortion at slightly less than 1 metre (1m - Planck-Length) further:
RelativityClassicPlusOne – Distortion 1 metre beyond Schwarzschild radius
RelativityClassicPlusOne = 1/(1-(6.67424800~00E-011)*(3.300~00E+53)/((4.90690E+26m) + 1.0E00~00m)*299,792,4582).5
RelativityClassicPlusOne =3.13089636071720751315687050814678053094541022988564~
13467063929598984441119541219002201433391441965992E+13
The proportion of the two distortions
ProportionDistortions = 7.787~929E+30/3.130~992E+13
ProportionDistortions = 2.4873990398433214803445049736963688028511124433316516~
255318139313987561023732430163206772861086519461E+17
So distortion reduces by a factor of more than 248 quadrillion over the course of travel a little less than one metre in a 9.168~330E-11m/s2 gravity environment. Again, acceptance of G.R. means the above must have been true at some point in the history of the universe.
Distortion at the same radii for Relativistic Perspective is (the inverse to make them comparable, because the RP value is inverse to Classic Relativity):
Relativistic_PerspectivePlusPlanck – distortion under RP 1 Planck Length beyond the Schwarzschild limit
Relativistic_PerspectivePlusOne – distortion under RP 1 metre beyond the Schwarzschild limit
Relativistic_PerspectivePlusPlanck = 1*(1+2*6.674286700~00E-11*3.300~00E+53/(4.901~690E+26m + 1.616252~00E-35m)*299,792,4582)½
Relativistic_PerspectivePlusPlanck = 1.414213562373095048801688724209698078569671875376948073176679732161294336516~
6080980880283130333904338E0
Relativistic_PerspectivePlusPlanck = 1.414213562373095048801688724209698078569671875376948073176679732161294336516~
6080980880283130333904338E0
The distortion 1 metre beyond the Schwarzschild radius –
Relativistic_PerspectivePlusOne = 1*(1+2*6.674286700~00E-11*3.300~00E+53/(4.901~690E+26 + 1.00~00E0m)*299,792,4582)½
Relativistic_PerspectivePlusOne = 1.414213562373095048801688723849021764359666322977795019315603032923383397382
7223768697435237104111410E0
7223768697435237104111410E0
The numbers are so close the difference rather than the ratio between them is more revealing:
DifferenceDistortions = 1.414~338E0 - 1.414~410E0
DifferenceDistortions = 3.60676314210005552399153053861076699237910939133885721218284789322979292796095690470000E-28
That a gravity of 4.584~350E-11m/s2 can incite distortions ranging to 1.414E0 is extraordinary – though both sets of distortion do require a concentration to quantum linear dimensions of the matter||energy concerned. Though surely a difference of 3.606~00E-28 is more reasonable. Classic theory also espouses a distortion progression from 5.506~838E+30 to an infinite||imaginary value, travelling 1.61625200~00E-35m in 9.168~514E-11m/s2 gravitational field (the actual difference between the two gravities being less than Planck’s Constant).
Although a distortion of “1.414213562~338E0” does seem extraordinary for such a low gravity, consider that we speak of time, a dimension that functions in a fundamentally different way than the linear dimensions. Also consider the “slope” of the distortion – it would reduce at a very slow pace. The distortion at twice the Schwarzschild radius would be:
(2*4.901~690E+26m)*299,792,4582).5
Relativistic_PerspectiveTwice_Schwarsz = 1.224744871391589049098642037352945695982~
9737403283350642163462836254801887286575132699297165523201174E0
9737403283350642163462836254801887286575132699297165523201174E0
The proportion of those two distortions:
ProportionDistortions = 1.414~338E0 / 1.224~174E0
ProportionDistortions = 8.660254037844386467637231707529361834714026269051903140279034897259665084544~
0001854057309337862428784E-1
Surely the above is a more reasonable proportion for gravity of the order 8.660~784E-11m/s2. There is also this final point: Space/Time distortion (whether it be Classic/Newtonian or Relativistic/Einsteinian) depends on an objects mass concentration at the center of the gravitational field (or all along a simple one dimensional line). If it is not, then all of the tangential forces/distortions exerted by any mass, not along that simple line would be weakened by the greater distance from whatever measuring point is used. That would not invalidate either the Classic or Relativistic distortion values - it would simply mean that distortion would have to be calculated using integral calculus rather than simple operators. As all the basic Relativistic equations do.
The Probability of a Cosmic Egg
The earliest that current theory will venture in time is the moment of the Big Bang. The usual line for that moment/instant is that there can be no way we can know what preceded that. While there is some logic to that, we can never (ever, ever, ever!) say that we have all the knowledge that exists for any particular topic – that declaration has been made incalculable times in history on an unknowable number of topics. The only absolute that can be declared from that line of data is that we can never know when we have determined all the data and theory for any particular topic – and that while the number of statements for any issue is indeterminate, they cannot be infinite. An infinite statements declaration would be that the ordered aspects of our reality are greater than the disordered aspects.
So let us make what is a reasonable postulation: the Big Bang was preceded, at some time, by a maximal state of disorder. That is surely more reasonable than a declaration of maximum order in the beginning of reality. Entropy is one of the most certain conjectures in all of Science.
So a simple theoretical quantification of that maximum disorder would be to take the arbitrary (but valid) conjecture of the mass and dimension of that beginning state of reality made earlier in this paper. All of the suppositions in what follows are NOT declarations, simply valid hypotheses. Given a Universe mass then of 3.300~00E+53kg in its smallest definable size: a sphere with a radius of a Planck length of 1.61625200~00E-35m. Whether the radius of such an object is the valid assignment or its diameter is completely indeterminate, but as Dr. Heisenberg would be sure to insist, that indeterminacy is unimportant in dealing with such values. The volume of such an object would be, presuming an exact value for Pi[Π] of:
Π = 3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679[8]
The volume of such a sphere would be:
VolumePlanck_Length_Radius_Sphere = 4/3 * 3.14159~70679 * (1.61625200~00E-35m)3
VolumePlanck_Length_Radius_Sphere = 1.768369885434202079507147238893627740359859351537154975532281952266201492621~
0138833151332495218536642E-104m3
So its density would be:
DensityPlanck_Length_Radius_Universe = 1.10000~00000E+53kg/1.76836~36642E-104m3
DensityPlanck_Length_Radius_Universe = 6.220418075768736321868186142489014910725936543453693816842706596534912145621~
2038275796549968562449735E+156kg/m3
2038275796549968562449735E+156kg/m3
Such an object is proposed to explode at an ultra-light velocity. The radius of the Universe currently is another gigantically debated issue; simply as a theoretic conjecture, we will presume it to be the Schwarzschild radius:
SchwarzschildRadius_Universe = 4.90125~55686E+26m
The volume of such a sphere would be:
VolumeSchwarzschild_Radius_Universe = 4/3 * 3.14159~70679 * (4.90125~55686E+26m)3
VolumeSchwarzschild_Radius_Universe = 1.879761702653645110612123155040117515394246609027155535730199641778064279312~
4794953512339102169496117E+79m3
4794953512339102169496117E+79m3
So its density would be:
DensitySchwarzschild_Radius_Universe = 1.10000~00000E+53kg/1.87976~96117E+79m3
DensitySchwarzschild_Radius_Universe = 5.85180556900982968402019906538330179656551~
34352906313314365492472454000792183783133228187249600913613E-27kg/m3
The ratio of those two values:34352906313314365492472454000792183783133228187249600913613E-27kg/m3
RatioDensities = DensityPlanck_Length_Radius_Universe/DensitySchwarzschild_Radius_Universe
RatioDensities = 6.22041~49735E+156/5.85180~13613E-27
RatioDensities = 8.503929944236036805799030784534274012447726619835565609562627823067622218097~
5429436359240452987861280E+183
5429436359240452987861280E+183
So what current science conjectures is that matter/energy bodies expand at light/ultra-light velocities at densities varying by a multiple factor of 8.50392~61280E+183. How could the “Cosmic Egg” ever come to be if that were true?
A Summary
Current thought regarding space expansion in the Big Bang theory - both the space expansion required by current theory in the beginning and observed space expansion can be explained by the more Universal view of relativity of this paper. This paper supports the Einsteinian limit of light speed, and does not deny it, as current theory does, though it does redefine certain aspects of that limit. It proposes a number of unassailable additional equations to relativity, as well as one:
Current thought regarding space expansion in the Big Bang theory - both the space expansion required by current theory in the beginning and observed space expansion can be explained by the more Universal view of relativity of this paper. This paper supports the Einsteinian limit of light speed, and does not deny it, as current theory does, though it does redefine certain aspects of that limit. It proposes a number of unassailable additional equations to relativity, as well as one:
VelocitynoGRPDescape = VelocityGRPDscape/(1+ VelocityGRPDescape2/c2)2
Its veracity is perhaps a little more debatable, but only if fundamental tenets of relativity are challenged. The original General Relativity equation:
Time’ = Time/(1-2Gm/rc2)½
Declares the entire Universe to now be or have been imaginary. Under Classic Relativity, it is the estimation of Universal mass you use that determines what radius is given the Universe Schwartzchild. Your only choice then is whether you accept Relativistic Perspective or deny it and insist on both that the fundamental, original General Relativity was entirely complete and that the Reality you occupy is beyond the imagination.
That would, perhaps, be something Science Fiction fans would be more adaptable to. Though we would be leaving the gigantic majority of the population out in the cold.
References
[1] The NIST Reference on Constants, Units and Uncertain – Fundamental Physical Constants: Speed of light in Vacuum
http://physics.nist.gov/cgi-bin/cuu/Value?c|search_for=universal_in
[2] The NIST Reference on Constants, Units and Uncertainty – Fundamental Physical Constants: Newtonian Constant of Gravitation
[2] The NIST Reference on Constants, Units and Uncertainty – Fundamental Physical Constants: Newtonian Constant of Gravitation
[3] Sun Fact Sheet - National Space Science Data Centre http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
[4] The Masses of the Milky Way and Andromeda Galaxies – Cornell University Library http://arxiv.org/abs/1002.4565
[5] The NIST Reference on Constants, Units and Uncertainty – Fundamental Physical Constants – Planck Length (lp) http://physics.nist.gov/cgi-bin/cuu/Value?plkl
[6] THE MASS AND RADIUS OF THE NEUTRON STAR IN 4U 1820–30 http://iopscience.iop.org/0004-637X/719/2/1807
[7] The Glenn Research Centre “ON the EXPANSION of the UNIVERSE” http://www.grc.nasa.gov/WWW/k-12/Numbers/Math/documents/ON_the_EXPANSION_of_the_UNIVERSE.pdf
[8] Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. English translation by Catriona and David Lischka.
There is also a more Academic flavoured version at:
[8] Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. English translation by Catriona and David Lischka.
A Printable version of this Page is at:
There is also a more Academic flavoured version at:
This site was authored by David G. Taylor
I can be contacted on my Cell: 780-9996134
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My e-mail is: dgtaylor@telusplanet.net
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