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Space Phenomenon
Quantum Singularity.
Generally considered to be singularities whose mass and initial sizes at collapse are small. Where small, is less than three solar masses. The laws of physics would prevent these masses from collapsing by the Pauli Exclusion Principle and Neutronic Degeneracy Pressure. However, data from COBE has shown that the wrinkles in space-time at 300,000 years from the Big Bang, are the seeds of galaxies. This is where matter conglomerated, as predicted by Guth’s and the later modifications of Inflationary Theory.
In the early Universe, it was possible for matter to be condensed much more intensely than today. This can be seen experimentally, whereby hot explosions can lead to catastrophic matter collapse. Experiments show that intense hydrogen bombs on Earth condense matter in a similar way. If the early universe was hot and small then it would be possible for denser areas to suffer gravitational collapse creating small black holes. These could theoretically be created artificially. Hawking 1988, describes Wheeler’s theory that if one took all the heavy water in the world and built a hydrogen bomb, the pressures at the center would create a quantum singularity. Wheeler was also the first person to use the term black hole, though the term black star or dark star had existed for some time previous.
It seems unlikely that the Romulans would choose such a method for creating their singularities to power their ships. It would be very energy intensive not to mention environmentally unsound. However, with the advent of matter antimatter energies it could be feasible to create quantum singularities with greater ease.
Singularity Image From The NASA Homepage http://www.nasa.gov/newsinfo/research.html
In the episode Hunters, Taylor 1997, a relay station in the Delta Quadrant is located that uses a quantum singularity as a power source. The implication here is that the station has been constructed around a natural object as opposed to the singularity having been created for the purpose.
However while approaching the object the Voyager is shaken by gravitational radiation. At this point they are still at two light years from the object. We are told the singularity measures 1 cm in diameter, therefore it must have a Schwarzschild Radius of 0.005 metres.
It is comparatively easy to deduce the mass of the singularity by re-arranging the equation:
Rsch = 2GM/c2
Where G is the gravitational constant of the universe
c is the speed of light in a vacuum
M is the mass of the object.
\ .005 = 2 * 6.668*10-11 * M /299, 792, 500
449377715281250 = 1.3336-10*M
M equals 3,369,658,932,822,810,437,912,417.52 kilograms to two decimal places. M = 3.4*1024 Kg.
Now all we need use are Newton’s equations of gravity to calculate the acceleration due to gravity the Voyager would feel at a distance of two light years.
Using
g = -GM/r2
Where r is the separation from the centre of mass. As the Voyager was at 2 light years its separation would be 2*1016 m. it must be noted that normally one would need to add the diameter of the object to the separation but at 2 light years this would be negligible what ever the size of the object and since the singularity is only 1 cm in diameter we can safely ignore this as it falls well outside our margin of error. The negative sign just indicates the acceleration acts towards the object and can be ignored:
g = 6.668*10-11 * 3.4*1024 / (2*1016)2
g = 0.000,000,000,000,000,000,561,722,144,101,562,5 ms-2
g = 5.617221441015625*10-19 ms-2
the acceleration due to gravity is 5.6*10-19 ms-2
to 1 d.p. compared to 9.81 ms-2 on Earth.
At 1 kilometre the acceleration would be 2,246,88,857.64 ms-2
which is enough to cause extreme damage as is seen by the level of damage
inflicted on the Hirogen ships.
Sternbach and Okuda 1991, tell us that the Enterprise can withstand 19.5 ms-2 without unrecoverable damage. However, the S.I.F. comes into play and boosts this by at least 125,000%. Let us assume therefore for arguments sake the Voyager can withstand 24,375 ms-2 before being irreparable damaged.
For g to equal 24375 ms-2 the Voyager would need to be at a distance of:
r = Ö 6.668*10-11 *3.4*1024 / 24375
r = Ö 226712000000000000 / 24375
r = Ö 9301005128205.13 metres
r = 3,049,754.93 metres to two decimal places.
The USS Voyager would need to be situated at a distance of over three thousand kilometres to be safe from the implosion.
Constants and equations from Kaufmann 1991 and Hey & Walters 1987.
Hawking showed that black holes actually radiate energy, which at the time was completely contradictory to the train of thought. According to the principles of quantum mechanics particle pair production will occur within any region as long as they annihilate within the time described by the uncertainty principle: Δt ~ħ/2mc2 Given that these fluctuations can take place within a gravitational field of a black hole it becomes possible for the particles to become separated across the Schwarzchild Radius or between regions where the particle speed is not greater than the acceleration due to gravity in that region. In this case only one particle will emerge and without its pair will not annihilate and therefore will manifest as a real particle. In this process gravitational energy from the black hole has been converted into both rest and kinetic energy for the particle. Hawking showed that the radiation has a thermal spectrum with a temperature inversely proportional to the mass of the black hole. The black hole would continue radiating energy at an exponential rate as it aged until finally the energy would be released in a explosion. For standard black holes the evaporation rate is negligible and they could not be used for energy devices for alien cultures but primordial and artificial quantum singularities would radiate enough energy to be viable devices. However quantum singularities will demonstrate an explosive end to its life.
The mass of the singularity at the instance before the final explosion.
Mass at t = 1
t*h*c^4
= 10,240*pi^2 *
(G2*M3)
5.35141877
= 101064.749 *
4.45E-21 *
M3
divide either side by
101,064.7
5.295E-05
= 4.45E-21 *M3
divide either side by
the Gravitational Constant squared
1.1909E+16
= M^3
cube root either side
to give mass at t = 1
228363.146 kilograms
two hundred and
twenty eight thousand three hundred and sixty three kilogrammes emitted in the
final second.
Knowing this we can
calculate the heat it emits in the final second
heat emitted at t = 1
h*c^3
/ 16*pi^2*k*G*M
1.785E-08
/ 3.3183*10-26
5.38*10+17 kelvins
Given the temperature
we can calculate the energy flux using Stefan's law
F = sigma*T^4
F = 4.747*10+63
energy per square
meter per second
which is vast,
however the size of the singularity is small.
Size of Singularity is given by
2*G*M/c^2
3.0455E-05
/ 8.9876E+16
size =
3.39E-22
radius of 3.39E-22 metres so
has a surface area of
surface area of 4 pi
r^2
1.4429E-42 metres squared
we can divide the
energy flux by the surface area to give absolute emitted energy in one second
6.8493*10+21 joules in the last second of life
Now 1 megatonne =
2,977,789,639,020,840 joules.
Therefore in the
final second the singularity gives up:
2,300,136
megatonnes
In the Weapons Section of this site we calculate the explosive yield of the photon torpedo . We rate the explosive yield as around 95.73 megatonnes, that means that the end life explosion of a quantum singularity would emit 2,4027.33 (to 2 d.p.) times the energy contained in a photon torpedo detonation.
In Star Trek other aliens use the energy given off by singularity evaporation; the most famous being the Romulan Star Empire. The D'deridex-Class Romulan War Bird uses an artificial quantum singularity at its core. The first physicist to theorise the creation of artificial singularities was John Wheeler who theorised that the world's heavy water could be used in the creation of a hydrogen bomb capable of compressing matter down to the limit whereby it would collapse to form a black hole. The pressures generated could reach a critical density of 1017 kilograms per cubic metre which would be sufficient to compact matter. The bomb would need to weigh several billion tonnes making it an economically unfeasible effort. More recently research into atomic accelerators has been under criticism from some quarters for the possible risk of singularity creation. Fortunately the energy cost to compact matter using modern accelerators to create the smallest possible singularity is of the order of 1019 giga-electron volts some 1015 times greater than the most powerful accelerator.