AST 248, Lecture 25

James Lattimer

Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University

May 4, 2020

The Search for Life in the Universe [email protected]

James Lattimer AST 248, Lecture 25 The Fermi Paradox The apparent contradiction between high estimates of the probability of the existence of extraterrestrial civilizations and the lack of evidence for, or contact with, such civilizations. I Drake equation arguments support the idea that the Earth is not special and that large numbers of ET civilizations exist. I Intelligent life will explore space and tend to colonize new habitats. I The timescale for exploration is not prohibitively large. Spacecraft velocities of 0.01c could be achieved through gravitational slingshots coupled with solar sail propulsion. I Robot probes are more efficient than manned probes. If the robot probes (von Neumann probes) could make copies of themselves when they arrive at each stellar system, and send their offspring to further explore, a wave of exploration will propagate (the coral model). tb ≈ 100 years would be an estimate of time needed to build new probes from raw materials of a stellar system. Probes could even carry genetic information needed to populate habitable systems. D∗vs I Propagation speed is ' 0.0075c, where D∗ ≈ 3 lt. yr., D∗+tb vs vs ≈ 0.01c, and tb ≈ 100 years. I To explore a sphere of 100,000 lt. yr. diameter would then take 13 Myr if done most efficiently. This is much less than the Galaxy’s age. I Even if tb = 5000 yr, 170 Myr needed to colonize the Galaxy. I Alternatively, a civilization could construct communication probes (Bracewell probes) and flood the Galaxy with them. James Lattimer AST 248, Lecture 25 Resolutions

I No other civilizations exist I No other civilizations have been born yet (Rare Earth hypothesis) I Intelligent life destroys itself before exploration ensues (doomsday argument) from nuclear or biological war, contamination, nanotechnological catastrophe, disastrous physics experiments, Malthusian overpopulation I Intelligent life destroys others; to be successful, an alien species will be a superpredator I They do exist but we see no evidence I Communication is impossible due to vast distances and timing I It is too expensive to perform the von Neumann or Bracewell search strategies I Humans have not been searching long enough I Communication is impossible for technical reasons I Humans are not listening properly I Civilizations may only broadcast for a brief time period I Civilizations experience a technological singularity and attain a posthuman character that is uninterested in communication. I Robot probes lose their programming or radiation effects alter or destroy them. I Aliens choose not to interact with us I Earth is purposely isolated (the zoo and/or sentinel hypotheses) I They are too alien or non-technological (or posthuman) I They are here unobserved (zoo hypothesis again)

James Lattimer AST 248, Lecture 25 The Great Filter

Another way to categorize resolutions is in terms of the Great Filter hypothesis, which says that civilizations are unlikely due to an evolutionary step being improbable. I adequate solar system I reproductive molecules I simple prokaryotic single-cell life I complex eukaryotic single-cell life I sexual reproduction I mutli-cellular life I tool usage I development of space travel I colonization explosion Any step could be improbable or always prevented by a catastrophe (natural or self-inflicted) or resource exhaustion. However, counterarguments include heterogeneous exploration, or a simple inability to see evidence of existing intelligent civilizations (perhaps because it’s natural to build nanoprobes and not giant engineering structures).

James Lattimer AST 248, Lecture 25 Spaceflight: The Rocket Formula v = s × ln Mfuel +Mpayload Mpayload v is the velocity of the spacecraft, which weighs (not including fuel) Mpayload after using the amount of fuel Mfuel . This implies that v/s cannot be very much larger than 1. The exhaust velocity s is determined by energy content of fuel p s = 2Efuel /Mfuel . Fuel Efuel /Mfuel s kwh/kg km/s H+O 3.2 3 U fission 2 × 107 8000 c/36 H fusion 2 × 108 25,000 c/12 matter-antimatter 3 × 1010 300,000 c Time Dilation: p 2 tship = tEarth 1 − (v/c) If v/c = 0.99, p1 − (v/c)2 = 1/7.1.

James Lattimer AST 248, Lecture 25 Time Dilation

I A light is emitted from a source, reflected by a mirror, and detected by a detector. The mirror is a distance d from the light source. I Observer Lou sees the light source, light detector and clock all located at exactly the same location. The time interval he notes between emission and detection is tLou. I Observer Sue sees the light source, mirror and light detector all travelling to the left with a velocity v. The time interval she notes between emission and detection is tSue . I According to Lou, the light must have travelled a distance of 2d. At speed c, this takes a time tLou = 2d/c. I According to Sue, who sees everything move a distance vtSue in between emission and detection, the light must have travelled a distance p 2 2 ctSue = 2 (vtSue /2) + d so that tSue = 2dγ/c, where γ = (1 − (v/c)2)−1/2. I tSue = tLouγ

James Lattimer AST 248, Lecture 25 Relativistic Travel

I Time dilation The time lapse between two events is relative, e.g., the twin paradox.

I Relativity of simultaneity Two events happening in different locations that are simultaneous to one observer need not be simultaneous to another.

I Lorentz contraction The dimensions of an object as measured by one observer may be different than measured by another observer, e.g., the ladder paradox.

I Twin Paradox Each twin sees the other as moving and having a slower clock. However, the traveling twin undergoes an acceleration to change direction which destroys the symmetry. He has fewer clock ticks than his twin. r

James Lattimer AST 248, Lecture 25 Round-Trip Voyages at 1g

Accelerate at 1g halfway to destination; decelerate at 1g. Repeat to return to Earth.

τ t v/c d γ Elapsed Time Elapsed Time Maximum Maximum Distance (Maximum) on Ship (yrs) on Earth (yrs) Velocity Reached (lt.-yrs) 1 1.01 .245 .063 1.03 2 2.08 .462 .255 1.13 3 3.29 .635 .59 1.29 4 4.70 .762 1.08 1.54 5 6.41 .848 1.77 1.89 10 24.2 .987 10.26 6.13 20 296.8 .9999 146.4 74.2 30 3613 1 1805 903 40 44,100 1 22,050 11,025 50 535,900 1 2.68 · 105 1.34 · 105 100 1.44 · 1011 1 7.2 · 1010 3.6 · 1010

James Lattimer AST 248, Lecture 25 Problems with Interstellar Space Travel

1. Vast Distances: Nearest star (α Cen) is 4.3 lt.yr. (1.4 pc) distant. With v = 0.1c = 30, 000 km/s, need 43 years to reach it. 2. High Velocities require lots of fuel. For chemical fuel and Mpayload = 100 tons: v/s 10,000 4340 Mfuel /Mpayload ' e = e = 8.6 × 10 4348 4315 4259 Mfuel ' 8.6 × 10 g = 4.3 × 10 M ' 10 MUniverse !!! For nuclear fuel v/s 1.2 Mfuel /Mpayload ≈ e − 1 = e − 1 = 2.3 With matter-antimatter fuel, s = c, must use relativistic rocket formula: q c+v = Mfuel +Mpayload , c−v Mpayload v = 0.1c requires Mfuel /Mpayload = 0.11. Where do you get 11 tons of antimatter?

James Lattimer AST 248, Lecture 25 More Problems With Interstellar Space Travel

3. Total energy to accelerate Titanic (m = 1011 g) to v = 0.1c and slow down: mv 2 = 1011(3 · 109)2 erg = 1030 erg = 100× Earth’s annual energy usage. 4. Even moderate accelerations with high exhaust velocities require enormous power. Assume Mpayload = 100 tons, acceleration is 1g, exhaust velocity is c/12: Power = Mpayload gc/24 = 12, 250 Gigawatts. This is equivalent to 2450 Hoover Dams, or to 40% the present world-wide energy consumption rate. 5. Kinetic energy of interstellar dust becomes prohibitively large, requiring either massive shielding or high-cost magnetic deflectors.

James Lattimer AST 248, Lecture 25 Alternate Proposals

I Interstellar Ramjet (Bussard) H-fusion has s = c/12 Thrust = Mship× acceleration = Fuel collection rate ×s Fuel collection rate = collector area ×v× n Acceleration = 1g; v = 0.01c; Mship = 10 tons; n = .1 atom H/cm3 = 1.6 · 10−25 g/cm3 16 2 Collector area = gMship/(svn) = 10 cm (a circle 300 km in radius). I Solar Sails 2 Usable power of sunlight L (Rship/2d) = Rship 2 d 2 43, 000( 100 km ) ( 1 AU ) Gw = −3 Rship 2 d 2 10 ( 100 km ) ( 1 pc ) Mw. For 1g acceleration, needs power 6 gMshipc/2 = 1.5 · 10 Mw Effective L could be enhanced by using giant solar collectors and reradiating power with lasers and/or lenses.

James Lattimer AST 248, Lecture 25 Alternate Proposals

I Nanotechnology SiC or C fibers, with mass of 10 − −100g. A few Hoover Dams of power could accelerate this at more than 100 g’s; velocities of 0.2c are reached within a week, and nearest stars are reached in 20 years Earth-time. Breakthrough Starshot is an engineering project by Breakthrough Initiatives (Yuri Milner) to develop a fleet of light-sail spacecraft called StarChip to be sent to the α-Centauri star system 4.37 lt-yrs distant. The proposal includes a flyby mission to Proxima Centauri b, an Earth-sized exoplanet near its host star. Maximum velociites of 0.15 − 20c would allow the trip to be completed in 20-30 years, then destination starlight will provide photon pressure to allow orbital entry around it. Of course, there will be a 4-year delay in receiving messages from the starship. A secondary goal is to detect Earth-crossing asteroids. The design concept is being explored with initial funding of $100 million, with a launch by 2036.

James Lattimer AST 248, Lecture 25 StarChip and Sprites

Propulsion is provided by a multi-km steerable phased laser array with a combined coherent power of 100 GW. A thousand centimeter-sized probes, weighing a few grams each, would each be accelerated from a high-altitude Earth orbit by the laser to the target speed, which would take 10 minutes at 10, 000g acceleration. The surface area of the attached sail on each probe is planned to be about 16 m2. On-board power is provided by a 238Pu or 241Am radioactive power source. Each ship contains a camera, computer, navigation gear and communications laser, hardened to withstand extreme acceleration, cold, vacuum, solar wind and cosmic rays. They will also have to survive collisions with space dust. On the voyage, about a thousand collisions with particles of at least 0.1 µ m are expected, necessitating 1000 probes. In July 2017, precursors to StarChip, named Sprites, were launched by the Polar Satellite Launch Vehicle by ISRO from Satish Dhawan Space Centre. In November 2018, additional Sprites will be flown on the KickSat-2 mission.

James Lattimer AST 248, Lecture 25 Some Practical Proposals

James Lattimer AST 248, Lecture 25 Robert L. Forward, AAAS Annual Meeting, May 1986 Some Impractical Ideas

I Spacetime Hypersurfing – Alcubierre Warp Drive Requires exotic matter, which has negative energy density and repels normal matter. At present, exotic matter virtually exists under some conditions, and may have been the normal state of matter prior to the inflationary epoch in the Big Bang. Exotic matter could repel normal-matter spaceships to faster-than-light travel without violating causality and without permitting time travel. Such travelers would experience neither accelerations nor time dilation. I Quantum Entanglement Otherwise known as “Action at a Distance”. Some recent experiments seem to show that mass can influence other mass, no matter how distant it might be, virtually instantaneously. Perhaps this quantum mechanical effect could be utilized for “faster-than-light” travel. Very speculative. I Wormholes Einstein himself suggested the idea that black holes could be connected and thus form wormholes connecting different parts of space time. However, the difficulty with avoiding causality paradoxes renders this idea very speculative. They would also seem to be impractical, since there is no way of knowing where the other end of a wormhole would be, in space or in time.

James Lattimer AST 248, Lecture 25 Alcubierre Warp Drive

A speculative idea based on Miguel Alcubierre’s (Mexican physicist) solution to Einstein’s equations incorporating negative mass. Instead of exceeding lightspeed with a local space, a spacecraft would travel by contracting space in front of it and expanding space behind it, which would result in effectively faster-than-light travel. The Alcubierre drive would shift space around the spacecraft so that the object would arrive at its destination faster than light in normal space. Effectively, this would involve backwards time travel for the spaceship. It has not been proven that this particular solution of Einstein’s equations is physically meaningful. Even if meaningful, such a drive may be impossible to construct, as it requires the creation of negative energy density (also called exotic) matter. (Note that exotic matter is not antimatter.) Experiments to create microscopic amounts of such matter, which have to utilize some bizarre aspects of quantum mechanics (like the Casimir Effect), are presently inconclusive and ultimately might prove to be impractical.

James Lattimer AST 248, Lecture 25 Alcubierre Warp Drive

And even if both the previous obstacles are overcome, it may be that the reconciliation of general relativity with quantum mechanics eliminates the Alcubierre solution. Occupants of the spaceship would experience no acceleration or time dilation. It is argued that construction of such a drive id possible only if spacetime could be distorted in advance along the entire trajectory of the spacecraft. This means a voyage to a star X light years away would require that someone begins working on warping space between us and the star at least X years before the trip begins. Recently, someone might have proven that to construct an Alcubierre Warp Drive requires an Alcubierre Warp Drive. Occupants of the spacecraft could not alter their trajectory or change speeds, for example, to prevent collision with an asteroid. It is possible that decelerating at the destination releases particles gathered in transit in an enormous explosion, destroying the vicinity of the destination. James Lattimer AST 248, Lecture 25 James Lattimer AST 248, Lecture 25 Quantum Mechanics and General Relativity

Although there is yet no unified theory of physics encompassing both quantum mechanics and general relativity, a number of recent connections have been found.

I Quantum entanglement was theorized in 1935 by Einstein, Podolsky and Rosen: a connection between widely separated quantum systems. A measurement of one will determine the state of the other. Instantaneous implies infinite signal speed.

James Lattimer AST 248, Lecture 25 AdS-CFT Correspondence In a model universe known as an anti-de Sitter space, the effects of gravity at a point in the inside are equivalent to a quantum field on the boundary. The pattern of triangles becomes distorted near the boundary and seem to resemble patterns of quantum entanglement.

James Lattimer AST 248, Lecture 25 James Lattimer AST 248, Lecture 25 James Lattimer AST 248, Lecture 25 Using Black Holes

Schwarzschild (non-rotating) black hole

Kerr (rapidly rotating) black hole

James Lattimer AST 248, Lecture 25 Space Settlements

Motivations: I Solar power: An array 100 km on a side can collect Earth’s entire power consumption, worth $3 billion per hour. Energy beamed as microwaves to rectennae which absorb microwaves and convert them to electricity. I Pharmacology, molecular nanotechnology (diamonoid mechanosynthesis) I Orbital towers or space elevators possible, would permit low-cost orbital transportation. I Could serve as base for space mining. I Not practical for reduction of population: world-wide population growth is N(b − d) ' 270, 000 persons per day. Advantages over planetary colonization: I Access to perpetual solar energy I Access to zero gravity I Long-term expansion of land area available to human race. I Control of environment I Location at top of Earth’s gravity well I First step to interstellar colonization

James Lattimer AST 248, Lecture 25 Solar Power Satellite Design Parameters

I Geostationary orbit: 22,300 miles I Circular satellite antennae at least 1 km diameter to avoid losses due to diffraction and sidelobes I Elliptical ground antennae (rectennae) about 10 × 14 km, composed of many short dipole antennae connected via diodes. Crops and animals could be raised underneath them, since antennae are thin enough to permit sunlight to penetrate. 2 I Desired microwave intensity is 23 mW/cm , so each antenna transfers between 5 and 10 Gigawatts of power. I Optimum microwave frequency is about 2.45 GHz. I With monocrystalline silicon solar cells (14% efficiency), the satellite would need 50 - 100 km2 collector area; 2/3 less if triple junction gallium arsenide solar cells are used. I Major cost is that of space launches. Will be reduced by economies of scale. Mass-to-power ratio would be about 1 kg/kW, or 104 tons for each antenna. At present, the launch cost is as high as the energy returns over a 10-year timespan. I Using materials from the moon or asteroids could ultimately reduce costs. I Another strategy for reducing launch costs involves using space elevators.

James Lattimer AST 248, Lecture 25 Solar Power Satellite

James Lattimer AST 248, Lecture 25 Constraints for Space Habitats

I Most material should originate from Moon, or possibly asteroids or comets. Use electromagnetic mass drivers to inject material from lunar surface into Earth orbit.

I Earth-normal gravity required in living and most working quarters. Axial area is zero-gee. Diameter must be greater than about 1.8 km to keep rotation rate low. D = 2gP2/(2π)2 = 1.8(P/1 min)2 km.

I To protect against cosmic rays and solar radiation, shielding of several tons per square foot of exterior surface, which corresponds to about 2–3 feet thickness, is needed. Less could be more harmful than none at all.

I System of mirrors and louvers needed to permit solar lighting and heating.

I Torus (Stanford), sphere (Bernal), or cylinder (O’Neill) geometry favored because of longer sightlines, lessens claustrophobia, permits weather.

James Lattimer AST 248, Lecture 25 Stanford Torus

James Lattimer AST 248, Lecture 25 James Lattimer AST 248, Lecture 25 James Lattimer AST 248, Lecture 25 O’Neill Cylinder

James Lattimer AST 248, Lecture 25 James Lattimer AST 248, Lecture 25 Bernal Sphere

James Lattimer AST 248, Lecture 25 James Lattimer AST 248, Lecture 25