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Ormehuller og Tidsrejser15. April 2009
Lars V. T. OcchioneroInstitut for Fysik og Astronomi, Aarhus Universitet
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”Kan en momentan kubus eksistere?”
- H. G. Wells, Tidsmaskinen (1895)
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”Kan en momentan kubus eksistere?”
- H. G. Wells, Tidsmaskinen (1895)
1D
2D
3D 4D
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Relativitetsteori
Lorentz transformationer
Tidsforlængelsen
Invariant størrelse
t '=t /
ds2=−cdt 2dx2dy2dz2
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Relativitetsteori
Metrik
Minkowski metrik
ds2= ∑ ,=0
3
g dx dx=g dx
dx
g==[−1 0 0 00 1 0 00 0 1 00 0 0 1
] pol =[−1 0 0 00 1 0 00 0 r2 00 0 0 r2 sin2
]
G = c = 1
ds2=−dt2dx2dy2dz2
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Schwarzschild metrik G = c = 1
g=[−1−r S /r 0 0 0
0 1−rS / r −1 0 0
0 0 r2 00 0 0 r2 sin2
] rS= 2GM
c2 =2M
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Schwarzschild sort hul
t
r
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Kruskal – Szekeres
U= r2M−1
1/2
e r /4M cosh t4M , r2M
V= r2M−1
1/2
e r /4M sinh t4M , r2M
U=1− r2M
1/2
e r /4M cosh t4M , r2M
V=1− r2M
1/2
e r /4M sinh t4M , r2M
G = c = 1
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Kruskal – Szekeres
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Ormehul Creator:inkscape 0.46
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Ormehul
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Einstein – Rosen Bro
Albert Einstein Nathan Rosen
- 1935
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Ikke brugbar
Eksistens Horisont Ustabilitet Tidevandskræfter
Creator:inkscape 0.46
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”Brugervenlige” ormehuller
Opfylder generel relativitetsteori Ingen Horisont Svage Tidevandskræfter Begrænset tidsforbrug Lavet af ”ikke-umuligt” materiale Stabil Mulig at opbygge
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”Brugervenlige” ormehuller
Ja... med negativ energi, ”eksotisk stof”
Kip Thorne
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Eksotisk stof
Casimir effekt
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Eksotisk stof
Kan begrænses til arbitrært små mængder
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Tidsrejser
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Billiardbordet
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Causalitetsproblemer
Gammel mand givermig tegninger til tidsmaskine mm.
Jeg bygger tidsmaskinen
Jeg går tilbage forat give mig tegninger
over tidsmaskinen mm.
Hvem opfandt tidsmaskinen?
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Skyd din egen forfader
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Forsvinder McFly?
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Vær din egen bedstefar
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Causalitetsbevarelse
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”Bananskæl” princippet
Allen Evrett, ”Time travel paradoxes, path integrals, and the many world interpretation of quantum mechanics”
(2004)
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Multivers
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Multivers
Bedste bliverfødt
Jeg bliver født
Jeg bliver sur på bedste
Jeg går tilbage
i tiden
Bedste dræbtJeg bliver ikke født
...
...
U-1
U-2
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Hvor er de?
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”Let's do the time warp again...”
Ormehuller er ikke (teoretisk set) umulige Tidsrejse = Paradoks
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Fiktion
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Litteratur
[1] Michael S. Morris og Kip Thorne, ”Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity” (1987)
[2] Richard H. Price, ”General relativity primer” (1981)
[3] Robert W. Fuller og John A. Wheeler, ”Causality and Multiply Connected Space-Time” (1962)
[4] A. Einstein og N. Rosen, ”The Particle Problem in the General Theory og Relativity” (1935)
[5] Ulrik I. Uggerhøj ”Tid, den Relative Virkelighed” (2005)
[6] Stephen Hawking ”The Universe in a Nutshell” (2001)
[7] Christoffer J. Fewster og Thomas A. Roman, ”On Wormholes with arbitrary small quantities of exotic matter” (2005)
[8] James B. Hartle, ”Gravity, An introduction to Einstein's general relativity” (2003)
[9] I. D. Novikov, ”Time machine and self-consistent evolution in problems with self-interaction” (1992)
[10]Allen Evrett, ”Time travel paradoxes, path integrals, and the many world interpretation of quantum mechanics” (2004)