THE STATUS OF THE WARP DRIVE

Transcription

1 THE STATUS OF THE WARP DRIVE Kelvin F Long, Breaking the interstellar distance barrier Symposium November 15th The British Interplanetary Society K.F.Long / BIS 15th Nov 007 / 1

2 Contents Motivation for warp drive research The Warp Drive What is it? Historical developments Where are we today? NASA Horizon Mission Methodology HMM applied to warp drive Specification of example roadmap to warp drive. Conclusions Warp drives cannot be ruled out Stephen Hawking K.F.Long / BIS 15th Nov 007 /

3 Why do we need The Warp Drive? Because of the interstellar distance barrier! Our galaxy (The Milky way) is ~50kpc (~160,000ly) in diameter, ~0.6kpc (~000ly) thick. Nearest stars 4-5ly away. We are located ~8kpc (~6,000ly from the centre). How do we travel across such vast distances in times comparable to human life? K.F.Long / BIS 15th Nov 007 / 3

4 Alternative Propulsion Methods Apollo mission: ~11km/s, ~0.004%C Pioneer spacecraft: ~11km/s, ~0.004%C Voyager spacecraft: ~17km/s, ~0.005%C Chemical rocket: (Liquid H/O), ~0.05%C The Future Solar Sail: ~0.01%C Nuclear Pulse: Orion, ~3%C Nuclear electric ion rocket:~10%c Microwave Sail: ~10%C Laser Sail: ~0%C Metallic hydrogen: ~0%C Matter-Antimatter: ~0%C C~300,000km/s K.F.Long / BIS 15th Nov 007 / 4

5 Alternative Propulsion Methods The Future Nuclear fusion: (Daedalus) ~30%C Interstellar ramjet: ~50%C Negative matter: ~70%C Fusion/matter-antimatter: ~99%C Pure photon rocket: ~99%C Self limiting technology m rel 1 v / c Tachyons particles: >>100%C (theory only) Worm Holes: instantaneous travel through non-trivial multiply connected topologies in space (but where do we find them?. Left with the only true interstellar propulsion scheme known as The Space Drive (i.e. warp drive): >100%C m C~300,000km/s K.F.Long / BIS 15th Nov 007 / 5

6 Einstein s theory of gravity: General Relativity (1915) General relativity is a theory of gravitation. It descibes how space tells matter how to move, and matter tells space how to curve.incorporates the special theory of relativity and the postulates (1) laws of physics the same in every frame of reference () speed of light the same in all inertial frames of reference, independent of the source. Also includes (3) equivalence of gravity and acceleration. But General Relativity is mathematically difficult REVOLUTION IN SCIENCE NEW THEORY OF THE UNIVERSE NEWTONIAN IDEAS OVERTHROWN London Times, November 7th K.F.Long / BIS 15th Nov 007 / 6

7 Einstein s theory of gravity: General Relativity (1915) 8 G 4 c G T The good news: GR is dynamical spacetime and allows for designer metrics via Einstein field equation. 1 The bad news: The source of the gravitational field for warp drive & worm holes is negative 8G T c G R g R 4 K.F.Long / BIS 15th Nov 007 / 7

8 General Relativity: Death of Stars All stars remain in hydrostatic equilibrium by balancing the need to gravitationally collapse with radiation pressure via fusion energy. White Dwarf (<1.4Ms): star supported by ideal gas of degenerate electrons Neutron Star (<3Ms): star supported by ideal gas of degenerate neutrons Well described by general relativity and quantum mechanics But what happens to stars >3Ms? Where Ms=1 solar mass ~10 30 kg. K.F.Long / BIS 15th Nov 007 / 8

9 General Relativity: Black Holes ds Karl Schwarzchild, 1916, found solution to Einstein field equation for spherically symmetric collapsing mass. Oppenheimer & Snyder, 1939, proved that a star >3 Ms will gravitationally collapse forming point of infinite compression (singularity) and an event horizon, from which not even light could escape. A black hole. Intervals between events well described by Schwarzchild metric: r g 1 r r escape GM c dt K.F.Long / BIS 15th Nov 007 / r g 1 r 1 dr r ( d sin d ) Note: Black holes are a mainstream astrophysical research topic today. 9

10 General Relativity: Worm Holes Einstein & Rosen (1935) published first mathematical descriptions of a wormhole. Performed coordinate transformation (letting r = u +m) on the Schwarzschild metric, removing the singularity. Solution is a mathematical representation of physical space by a space of two asymptotically flat sheets (, -) connected by a bridge (at u = 0) or Schwarzschild wormhole with a throat at A(u=0)=16pm. ds u u m dt 4( u m) du ( u m) d K.F.Long / BIS 15th Nov 007 / 10

11 ds e ( r) General Relativity: Worm Holes Further work by Wheeler (1950 s) and later by Morris & Thorne (1980 s). Constructed metric to describe spherically symmetric and static wormhole with a proper circumference r with the coordinate r decreasing from - to a minimum value at r o where the throat is located and then increasing from r o to +. Solution is horizon-less. The shape of the wormhole described by the redshift function (r) and the shape function b(r). dt dr 1 b( r) / r r d But enormous amounts of negative exotic energy required to hold open the throat. Note: Worm Holes are a mainstream astrophysical research topic today. K.F.Long / BIS 15th Nov 007 / 11

12 General Relativity: Warp Drive (Alcubierre 1994) ds dt [ dx vs( t) f ( rs ( t)) dt] dy dz r s( t) ( x xs( t)) y z For the first time, the warp drive had a consistent theoretical and mathematical basis, as a solution to Einstein s general relativity theory. K.F.Long / BIS 15th Nov 007 / 1

13 f(rs) Alcubierre Top Hat shape function rs Hyperbolic tangent function. It describes the bubble geometry so that it is equal to unity inside the warp bubble (f(rs)=1 at rs R) and goes to zero outside the warp bubble (f(rs) 0 as rsr) so that flat Minkowski spacetime is recovered as rs. The term is a wall thickness free parameter. A vehicle will be located at rs = 0. f ( r s ) tanh[ ( r s R)] tanh[ ( r tanh[ R] s R)] warp drive top hat function for the case when σ = 8 and R = vs = 1 K.F.Long / BIS 15th Nov 007 / Direction of motion 13

14 Why faster than light v(t)>c? SPECIAL RELATIVITY S S t t o 1 u / c Inertial frame of reference GENERAL RELATIVITY Accelerating frame of reference Time dilation effect, consequence of constant speed of light V(t)=0 Warp drive allows for FTL travel as measured by distant non local observer in flat spacetime. K.F.Long / BIS 15th Nov 007 / V(t)>c Superluminal speed effect, consequence of expansion/contraction of space 14

15 Warp Drive benefits Apparent faster than light speeds, as measured by distance observers. No time dilation effects, as usually expected with other space propulsion schemes due to special relativity. This is because the vehicle could be moving at subluminal speeds so that clocks on board would remain synchronised with origin and destination. No relativistic mass increase of vehicle, since ship at centre of warp bubble is at rest with respect to locally flat space. Ability to explore distance space. Technological and economic benefits to mankind. K.F.Long / BIS 15th Nov 007 / 15

16 G R g R vs ( t) df ( rs ) T n ( ) n T G rs t drs A 100m warp bubble would require a negative mass of ~10 65 grams or a negative energy of ~10 6 joules. Similarly: ~10 58 joules (1m) ~10 54 joules (1cm) Negative energy requirements for warp drive (Pfenning, 1997) 1 ~10 5 joules (1mm) 8G T c ~10 46 joules (1micron or 10-6 m) E 1 vb R 1 To put these energy requirements into perspective further, if one had a negative mass equivalent to the mass of the Earth (~10 33 grams) this would only be sufficient to form a warp bubble radius of ~10-18 m. K.F.Long / BIS 15th Nov 007 / 16

17 Warp Drive: Obstacles to technological attainment (1) Realisable metric. How do we produced such a macroscopic metric in reality (leap from mathematical to technological). Energy violation. Exotic energy violates classical GR energy conditions (weak, dominant, strong), both at superluminal and subluminal (Visser) speeds. WEC: In observer s frame of reference the energy density should be non-negative. T V V 0 Quantum inequalities. Negative energy pulse generated is constrained by a quantum uncertainty principle (1) stronger the pulse, shorter its duration () negative pulse must be followed by stronger positive pulse (3) longer the time period between pulses, the stronger the positive one. Energy Et Ford & Roman 1994, 95 time Prohibitive energy requirements. prohibitively massive negative energy required. The amount of negative energy required is also approximately proportional to the vehicle velocity squared. K.F.Long / BIS 15th Nov 007 / 17

18 Warp Drive: Obstacles to technological attainment () Energy source. Source of negative energy unknown. Classical physics does not allow it, but it is not prohibited by laws of quantum physics (i.e Casimir effect). Energy conservation. Source to power the warp drive must produce a lot more energy than has gone into to create it. Momentum conservation. No expelled rocket mass for warp drive. So the warp drive will be essentially pushing on space itself, which supposes the properties of space provide for a reaction mass. Secondary law of thermodynamics. The presence of negative energy may conflict with this law of physics. Where the generation of negative energy will also produce an equal amount of positive energy which could be used to power a perpetual motion machine, without any external energy input. K.F.Long / BIS 15th Nov 007 / 18

19 Warp Drive: Obstacles to technological attainment (3) Causal disconnection. Causal disconnection of warp bubble from external negative energy region in wall, so that it could not be controlled or contained. It would have to be continuously generated externally. This is a result of the formation of past and future event horizons when v>c. All signals would also be quickly overtaken. Hence may need Krasnikov tube for external control. Causality violations. Possible presence of causality violations or closed time-like curves, where effects precedes cause. Alternatively, FTL communication may be possible. Although the laws of physics may prevent this, such as by the Hawking chronology protection conjecture. Comoving scale factor. Where the warp bubble size increases, commoving to the scale factor of the expanding universe. K.F.Long / BIS 15th Nov 007 / 19

20 Warp Drive: Obstacles to technological attainment (4) Wall thickness. Wall thickness extremely dense and thin with respect to the bubble radius (i.e ~10-3 m, of order ~100Planck lengths) as constrained by the quantum inequality restrictions of negative energy in curved space-times. Collision risk. Collision with approaching matter-radiation. Rocks and dust that approached forward end experience enormous compression forces and lead to an explosion of particles when released. Energy distribution. For warp bubble to move forward, must distribute negative energy source ahead of itself. But how can it do this when the bubble is already superluminal. This is the need one to make one paradox, unless can distribute it tachyonically. K.F.Long / BIS 15th Nov 007 / 0

21 Warp Drive: Obstacles to technological attainment (5) Unruh effect. Warp bubble surrounded by heat bath of radiation in the direction of motion, which increases in temperatures as the velocity increases, so require significant radiation shielding. The Unruh effect is a consequence of an accelerating observer in a vacuum.potential infinite blue shift (Natario). a kc Tidal forces. At the boundary between the internal flat space part of the metric and the external flat normal space, enormous tidal forces will be present due to the extreme warpage. Must isolate vehicle within the warp bubble from these forces. T Stability & Control. By what mechanism is the negative energy to be induced or controlled (i.e. manipulation of extra dimensions of space or by tapping the zero point energy field). K.F.Long / BIS 15th Nov 007 / 1

22 The way forward: options Option (1): give up, warp drive will always remain fantasy (i.e. science fiction). FANTASY Option (): accept answers, impossible to a civilisation insufficiently advanced, but maybe possible in thousands of years. FAR FUTURE Option (3): Re-work the theory Metrical dynamics Re-formulate QFT Minimise energy requirements Better description of physics (i.e. gravity) K.F.Long / BIS 15th Nov 007 /

23 VDG metric (Chris Van Den Broeck, 1999) VDB modified Alcubierre geometry, keeping the surface area of the warp bubble microscopically small while simultaneously expanding the spatial volume inside the bubble by a factor 1+a. VDB warp bubble described ~ as a small Alcubierre bubble (with thickness located at radius R ~ from the centre) surrounds a neck leading to a pocket (with thickness from the centre) with a large internal volume, and flat region in the middle. VDB regions are labelled IV, III, II and I respectively where regions I and III are flat. Function f(r s ) has r s R f ( r s ) 1 properties: ~ ~ R rs R 0 f ( rs ) 1 R R R r s f ( r s ) 0 ds dt B ( r s )[( dx v s f ( r s ) dt) dy dz ] requires ~10 33 g negative mass K.F.Long / BIS 15th Nov 007 / 3

24 The Krasnikov tube (Sergei Krasnikov, 1998) Warp ship could not create its own warp path. It would need to be laid out in advance by subluminal ships. Like an interstellar superluminal subway. Alternatively, it would make a trip to a destination at subluminal speeds (with relativistic effects) dragging space behind you, then on the return trip you ride back on the tube of warped space. Calculations show that the total negative energy density is also unphysically large (~10 61 g for a 1m long by 1m wide tube) and the maintenance of the tube will require wall thicknesses of order a few Planck lengths. Gravel & co. introduced inner tube within original Krasnikov tube. For a similar tube of length 1m the negative energy requirement is reduced requiring ~10 30 g of negative mass ds ( dt dx)( dt kdx) d d K.F.Long / BIS 15th Nov 007 / 4

25 NASA Breakthrough Propulsion Physics Project ( ) Three visionary breakthroughs were identified (1) Mass: propulsion that requires no propellant () Speed: propulsion that circumvents existing speed limits (3) Energy: breakthrough methods of energy production to power such devices. K.F.Long / BIS 15th Nov 007 / 5

26 NASA Horizon Mission Methodology [HMM] Based on specific hypothetical future called a Horizon Mission, impossible but (space) mission having capabilities and performance levels that cannot be met, even by extrapolating current technologies. Horizon missions may also be capabilities or axioms. Can provide new and relevant insights and spark exciting visions Mission is outside current paradigms so difficult to extrapolate future from linear extension of our knowledge HMM is a way of thinking outside these paradigms and gaining insights into modern requirements to define roadmap. Hypothetical future horizon The present Part of horizon illuminated Part of horizon un-illuminated K.F.Long / BIS 15th Nov 007 / 6

27 HMM six stages 1. Create future horizon mission. leap outside flash beam to create extraordinary future beyond our reach (the horizon acts as an artifice that blocks linear, extrapolative thinking).. Construct new frame of reference. For thinking based on that future (boundaries, rules and context) 3. Identify implicit engineering assumptions. Underlying the horizon. 4. Generate alternatives to accomplish mission. Stimulate the imagination to generate breakthrough based alternatives to accomplish that future 5. Identify current requirements. Linking alternatives to the present by identifying requirements, applications and implications 6. Identify technology steps. Return to the present by identifying high technology directions and determining the next steps and issues ( stepping stones ). Then define road map to accomplish the mission. K.F.Long / BIS 15th Nov 007 / 7

28 The Mission Statement A hypothetical future where a space vehicle has typical transit times to nearby stars limited to a few years times scale, so that solar systems within ~10-0 light years radius can be practically reached, travelling at or exceeding motion at the speed of light as measured by distant observers. The vehicle should have a controllable and sustainable mechanism that isolates the vehicle from any absolute reference frame, and interacts with the properties of space, matter or energy to induce a unidirectional acceleration of the vehicle within the bounds of conservation principles and consistent with empirical observations. K.F.Long / BIS 15th Nov 007 / 8

29 HMM The Warp Drive: Roadmap Part of horizon illuminated Hypothetical horizon Subluminal propulsion New materials for deep space missions Physics coupling, space, matter, energy Exotic matter Faster, powerful computers Science cultural shift Legal & moral framework Technological, cultural of social stepping stones K.F.Long / BIS 15th Nov 007 / 9

30 Conclusions Lots of obstacles defined for the warp drive proposal But potential for future revolutions in the concept State of physics knowledge not yet mature. The warp drive cannot be ruled out yet! Questions? Anything that is theoretically possible will be achieved in practice, no matter what the technical difficulties, if it is desired greatly enough. It is no argument against any project to say: The ideas fantastic! Most of the things that have happened in the last fifty years have been fantastic, and it is only by assuming that they will continue to be so that we have any hope of anticipating the future. To do this to avoid that failure of nerve for which history exacts so merciless a penalty we must have the courage to follow all technical extrapolations to their logical conclusion. A.C.Clarke - Profiles of The Future K.F.Long / BIS 15th Nov 007 / 30