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sg1 poke

Science Fascinates Me although I am really bad at it


Note I think it is really cool that there are scientists working on the theories of wormholes. Equations and theorems of general relativity, quantum mechanics, and special relativity are included in this section because I believe that the real stuff is vastly more interesting than anything that I could come up with. John Crichton is a scientist and his specialty was astrophysics, so this is the arcane mathematics he works with. A small taste of quantum physics makes my head spin, imagine what it was doing to the crew of Moya. I have included links to the actual pages where these theories are presented. If you are interested, please feel free to read further. On with the story...

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"What 'cha doin', Crichton?" Chiana asked as she leaned closely over John Crichton's shoulder where he sat in the Center Chamber. She looked down at the incomprehensible symbols John was scribbling madly in his notebook. His brow furrowed in thought as he paused admiring the elegance of the equations that floated from his pen on to the paper. "You have to stop soon or later, old man, or you'll wither away from not eating or sleeping."

"I know, I know, Pip, just let me get this one idea down here. Ok? I'll stop soon." John replied absent-mindedly without looking up from his work.

"You've been at this for a weeken. Where is this dren getting you? We barely see you and when we do, you're scribbling that stuff. This isn't like you. Even the Princess notices that you aren't here even when you are."

"Hmmm?"

"Old man, you aren't even listening. This is tinked," Chiana slapped John on his face lightly, then turned sharply and marched out of the Center Chamber.

John Crichton was consumed by the wormholes swimming behind his eyelids as well as the equations that described their positions, compositions, and uses. He truly couldn't sleep or eat. He knew that there was something wrong with this single-mindedness of his. He had a feeling that he shouldn't have this knowledge and that he had to get it down on paper before it was stripped from his mind. His fears rode on his shoulders goading him on in his discovery of the depth of this knowledge he had been given so suddenly. His head ached terribly and he found that he couldn't keep any food down for long. He knew he looked haggard and drawn. That his hands trembled and he hadn't really recovered from his trips into the light fantastic. He tried not to pay attention to the strange dizzy spells where it seemed that he saw his twin in the blue swirls of the wormhole equations. He could almost reach out to him and touch but then he lost it amidst the formulas and minutia of quantum physics. He knew if he could just comprehend the entirety of the knowledge he had been handed he could figure out what was happening. So he continued to write feverishly.

Natural wormholes can be found by searching for GNACHOs (Gravitationally Negative Anomalous Compact Halo Objects).

wormhole model

Constructed wormholes come in two types: Morris-Thorne Wormholes used as spatial shortcuts by manipulating planet-masses of energy, might be able to snatch from the quantum foam, inflate to a useful size, and stabilize by placing a Casimir-effect spherical capacitor in the wormhole mouth. Visser cube wormholes use negative-mass cosmic strings as its edges with six faces, each connected to different locations.

If a mass M were compressed inside a critical radius rs, nowadays called the Schwarzschild radius, then its gravity would become so strong that not even light could escape. The Schwarzschild radius rs of a mass M is given by

rs = 2 G M / c2

where G is Newton's gravitational constant, and c is the speed of light. For a 30 solar mass object, like the black hole in the fictional star system here, the Schwarzschild radius is about 100 kilometers.

Schwarzschild's geometry is described by the metric (in units where the speed of light is one, c = 1)

ds2 = - ( 1 - rs / r ) dt2 + ( 1 - rs / r )-1 dr2 + r2 do2  .


John looked up from his writing to see Jool standing at the doorway with her hands on her weirdly clad hips. Her hair was flaming red as she stared at him. "What?" he asked.

"We've been comming you for at least half an arn," Jool said testily. "I was nominated to come up here and drag you down to the maintenance bay. D'Argo needs you and you have to take your nose out of those equations before they consume you alive. Crichton, I'm worried about you. Come down and help D'Argo with that ship of his.

John shook his head and raising his hand and distantly waving it at Jool, he said, "Tell D I'll be down shortly. I just have to get these ideas down and I'll stop. I promise."

"You said that two arns ago, Crichton." Jool said petulantly. "What is so important about these wormholes that it is eating you up alive?"

John looked up from his work and Jool noted his bloodshot eyes, unshaved pale face and whitened lips. He looked crazed. She had to get him to stop. She was seriously afraid for his sanity. She still had no explanation for his earlier losses of consciousness, but he wouldn't let her examine him. John simply returned to his computations.

The quantity ds denotes the invariant spacetime interval, an absolute measure of the distance between two events in space and time, t is a `universal' time coordinate, r is the circumferential radius, defined so that the circumference of a sphere at radius r is 2 pi r, and do is an interval of spherical solid angle.

In general relativity, clocks at rest run slower inside a gravitational potential than outside.

In the case of the Schwarzschild metric, the proper time, the actual time measured by an observer at rest at radius r, during an interval dt of universal time is (1 - rs/r)1/2 dt, which is less than the universal time interval dt. Thus a distant observer at rest will observe the clock of an observer at rest at radius r to run more slowly than the distant observer's own clock, by a factor

( 1 - rs / r )1/2 .

This time dilation factor tends to zero as r approaches the Schwarzschild radius rs, which means that someone at the Schwarzschild radius will appear to freeze to a stop, as seen by anyone outside the Schwarzschild radius.

In the case of the Schwarzschild metric, a distant observer at rest will observe photons emitted by a source at rest at radius r to be redshifted so that the observed wavelength is larger by a factor

( 1 - rs / r )-1/2

than the emitted wavelength. The redshift factor tends to infinity as r approaches the Schwarzschild radius rs, which means that someone at the Schwarzschild radius will appear infinitely redshifted, as seen by anyone outside the Schwarzschild radius.

That the redshift factor is the same as the time dilation factor (well, so one's the reciprocal of the other, but that's just because the redshift factor is, conventionally, a ratio of wavelengths rather than a ratio of frequencies) is no coincidence. Photons are a good clocks. When a photon is redshifted, its frequency, the rate at which it ticks, slows down.


John couldn't explain to his crewmates his terrible feeling that something was coming to a head. That he had a very short time to master this deluge of information that was poured into his brain by the Ancient. That something terrible was going to happen and he needed to finish his efforts. He could feel the power of the wormholes growing, yet he felt curiously weak and nauseated as if he had been stricken with radiation sickness. He continued to ignore Jool as she stood over him waiting.

Eddington-Finkelstein coordinates differ from Schwarzschild coordinates only in the relabelling of the time. The relabelling is arranged so that radially infalling light rays (yellow lines) move at 45o in the spacetime diagram. Finkelstein time tF is related to Schwarzschild time t by

tF = t + ln|r - 1|

in units where the speed of light and the Schwarzschild radius are one, c = 1 and rs = 1.

Free-fall coordinates reveal that the Schwarzschild geometry looks like ordinary flat space, with the distinctive feature that space itself is flowing radially inwards at the Newtonian escape velocity

v = (2 G M / r)1/2  .

The infall velocity v passes the speed of light c at the horizon.


The next time John looked up, Jool was gone having given up on her crewmate and his farbot need to kill himself. John wiped the sweat from his forehead with his fist, He put his hand on the newest page of his notebook and caught the drop of blood before it landed. "What the…?" he thought to himself. He pressed his fingers to the bridge of his nose seeking to stem the flood of blood that gushed from his nose. He used to blood to write the last equations.

Picture space as flowing like a river into the black hole. Imagine light rays, photons, as canoes paddling fiercely in the current. Outside the horizon, photon-canoes paddling upstream can make way against the flow. But inside the horizon, the space river is flowing inward so fast that it beats all canoes, carrying them inevitably towards their ultimate fate, the central singularity.

Does the notion that space inside the horizon of a black hole falls faster than the speed of light violate Einstein's law that nothing can move faster than light? No. Einstein's law applies to the velocity of objects moving in spacetime as measured with respect to locally inertial frames. Here it is space itself that is moving.


John was lost in the swirling of the wormhole as it collapsed into the star that destroyed the dreadnaught. He felt his twin struggle with the extreme weakness that accompanies the sores and internal bleeding of intense radiation exposure. He touched his twin's mind where it too struggled with the knowledge that he was at the end of his rope and Aeryn would be left alone. He felt that despair and shared it's intensity.

MoyaJohn felt an indescribable sadness that he wouldn't ever see his radiant Sun again or touch her hair running his fingers through its fine curls or over her cheeks where she lay on one of Talyn's bunks that lined his corridors. John shook his head at these random thoughts that didn't belong in his world. His world was bereft of Aeryn. There was no warmth left, no love, no soul. These things he gave over to his twin unwillingly, just as unwillingly he was sharing TalynJohn's last moments. Together, the twins mouthed their mantra to Aeryn as she sat beside their prone body struggling for breath, "Don't worry about me, I've never felt better."

John shook his head and shivered as if someone just walked over his grave. He struggled with his pen in suddenly numb fingers.

The shell of exotic matter has negative mass and positive surface pressure. The negative mass ensures that the throat of the wormhole lies outside the horizon, so that travellers can pass through it, while the positive surface pressure prevents the wormhole from collapsing.

In general relativity, one is free to specify whatever geometry one cares to imagine for spacetime; but then Einstein's equations specify what the energy-momentum content of matter in that spacetime must be in order to produce that geometry. Generically, wormholes require negative mass exotic matter at their throats, in order to be traversible.

While the notion of negative mass is certainly bizarre, the vacuum fluctuations near a black hole are exotic, so perhaps exotic matter is not utterly impossible.

wormhole equation

Where b(r) determines the spatial shape of the wormhole, and Phi(r) determines the gravitational redshift. This solution has the property of having no horizons or excessive tidal forces to deal with which makes it safe for humans to travel through. But it does have one unfortunate drawback. In order to hold the throat open there has to be a negative energy density inside. There is no no known material that has this property. Though electro-magnetic vacuum fluctuations are sometimes measured to have negative energy densities and are correspondingly called ``exotic''. In order to keep the wormhole open it needs to be threaded with exotic matter that will create a tension to push the walls apart. This exotic matter would have the curious effect of defocusing light as it passed through.

wormhole model

This network of wormholes and black holes is known as the quantum foam. There are certain probabilities that wormholes will pop in and out of existence at this level. If we assume that we, or some other society, are sufficiently advanced that we can observe this quantum foam and manufacture exotic matter, then it might be possible to reach into this microscopic universe and capture a wormhole. By pouring exotic matter into it we might be able to blow it up to a macroscopic size. We would then be poised to embark on the greatest journey imaginable.


His work was done, the Ancient's gifts were complete. He knew how to call, manipulate, and travel the wormhole paths.

D'Argo, Chiana, and Jool found John lying comatose on the floor of the Center Chamber in a pool of blood that streamed from his ears, eyes, and nose.


(bibliography: Traversable Wormholes; Whiteholes and Wormholes; and NASA Goes FTL)</i>

Comments

GAWD! You know I love when you go technobabble on me girl! But I feel like I overdosed on it too. LOL You definiately put the 'rush' feel to this, but seriously you may want to cut back on the equations stuff. You don't want people to feel like your re-creating Through the Rabbit Hole.

This was great. Poor MJohn feeling TJohn's sickness and slow death. Yikes!

Love ya hon, and let me know how the testing went. *hug*