AST 248, Lecture 25 - astro.sunysb.edu · AST 248, Lecture 25 James Lattimer Department of Physics...

AST 248, Lecture 25

James Lattimer

Department of Physics & Astronomy449 ESS Bldg.

Stony Brook University

May 4, 2020

The Search for Life in the [email protected]

James Lattimer AST 248, Lecture 25

The Fermi ParadoxThe apparent contradiction between high estimates of the probability ofthe 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 notspecial 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 slingshotscoupled with solar sail propulsion.

I Robot probes are more efficient than manned probes. If the robotprobes (von Neumann probes) could make copies of themselveswhen they arrive at each stellar system, and send their offspring tofurther explore, a wave of exploration will propagate (the coralmodel). tb ≈ 100 years would be an estimate of time needed to buildnew probes from raw materials of a stellar system. Probes couldeven carry genetic information needed to populate habitable systems.

I Propagation speed is D∗vsD∗+tbvs

' 0.0075c , where D∗ ≈ 3 lt. yr.,vs ≈ 0.01c , and tb ≈ 100 years.

I To explore a sphere of 100,000 lt. yr. diameter would then take 13Myr 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 existI 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 willbe a superpredator

I They do exist but we see no evidenceI Communication is impossible due to vast distances and timingI It is too expensive to perform the von Neumann or Bracewell search

strategiesI Humans have not been searching long enough

I Communication is impossible for technical reasonsI Humans are not listening properlyI Civilizations may only broadcast for a brief time periodI 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)


The Great Filter

Another way to categorize resolutions is in terms of the Great Filterhypothesis, which says that civilizations are unlikely due to anevolutionary step being improbable.

I adequate solar systemI reproductive moleculesI simple prokaryotic single-cell lifeI complex eukaryotic single-cell lifeI sexual reproductionI mutli-cellular lifeI tool usageI development of space travelI 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 asimple inability to see evidence of existing intelligent civilizations(perhaps because it’s natural to build nanoprobes and not giantengineering structures).


Spaceflight: The Rocket Formula

v = s × lnMfuel+Mpayload

Mpayload

v is the velocity of the spacecraft, which weighs (not includingfuel) Mpayload after using the amount of fuel Mfuel . Thisimplies that v/s cannot be very much larger than 1.

The exhaust velocity s is determined by energy content of fuels =

√2Efuel/Mfuel .

Fuel Efuel/Mfuel skwh/kg km/s

H+O 3.2 3U fission 2× 107 8000 c/36H fusion 2× 108 25,000 c/12

matter-antimatter 3× 1010 300,000 c

Time Dilation:

tship = tEarth√

1− (v/c)2

If v/c = 0.99,√

1− (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 detectedby a detector. The mirror is a distance d from the light source.

I Observer Lou sees the light source, light detector and clock alllocated at exactly the same location. The time interval he notesbetween emission and detection is tLou.

I Observer Sue sees the light source, mirror and light detector alltravelling to the left with a velocity v . The time interval she notesbetween emission and detection is tSue .

I According to Lou, the light must have travelled a distance of 2d . Atspeed c , this takes a time tLou = 2d/c .

I According to Sue, who sees everything move a distance vtSue inbetween emission and detection, the light must have travelled adistancectSue = 2

√(vtSue/2)2 + d2

so that tSue = 2dγ/c ,where γ = (1− (v/c)2)−1/2.

I tSue = tLouγ


Relativistic Travel

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

I Relativity of simultaneity Two events happening indifferent locations that are simultaneous to oneobserver need not be simultaneous to another.

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

I Twin Paradox Each twin sees the otheras moving and having a slower clock.However, the traveling twin undergoesan acceleration to change directionwhich destroys the symmetry. He hasfewer clock ticks than his twin.

r


Round-Trip Voyages at 1g

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

τ t v/c d γElapsed Time Elapsed Time Maximum Maximum Distance (Maximum)on Ship (yrs) on Earth (yrs) Velocity Reached (lt.-yrs)

1 1.01 .245 .063 1.032 2.08 .462 .255 1.133 3.29 .635 .59 1.294 4.70 .762 1.08 1.545 6.41 .848 1.77 1.89

10 24.2 .987 10.26 6.1320 296.8 .9999 146.4 74.230 3613 1 1805 90340 44,100 1 22,050 11,02550 535,900 1 2.68 · 105 1.34 · 105

100 1.44 · 1011 1 7.2 · 1010 3.6 · 1010


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 andMpayload = 100 tons:

Mfuel/Mpayload ' ev/s = e10,000 = 8.6× 104340

Mfuel ' 8.6× 104348 g = 4.3× 104315 M� ' 104259MUniverse !!!

For nuclear fuel

Mfuel/Mpayload ≈ ev/s − 1 = e1.2 − 1 = 2.3

With matter-antimatter fuel, s = c , must use relativistic rocketformula:√

c+vc−v =

Mfuel+Mpayload

Mpayload,

v = 0.1c requires Mfuel/Mpayload = 0.11.Where do you get 11 tons of antimatter?


More Problems With Interstellar Space Travel

3. Total energy to accelerate Titanic (m = 1011 g) to v = 0.1c andslow down:mv2 = 1011(3 · 109)2 erg = 1030 erg = 100× Earth’s annual energyusage.

4. Even moderate accelerations with high exhaust velocities requireenormous power. Assume Mpayload = 100 tons, acceleration is 1g ,exhaust velocity is c/12:Power = Mpayloadgc/24 = 12, 250 Gigawatts.This is equivalent to 2450 Hoover Dams, or to 40% the presentworld-wide energy consumption rate.

5. Kinetic energy of interstellar dust becomes prohibitively large,requiring either massive shielding or high-cost magnetic deflectors.


Alternate Proposals

I Interstellar Ramjet (Bussard)H-fusion has s = c/12

Thrust = Mship× acceleration = Fuelcollection rate ×sFuel 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

Collector area = gMship/(svn) = 1016 cm2

(a circle 300 km in radius).I Solar Sails

Usable power of sunlight L�(Rship/2d)2 =

43, 000(Rship

100 km )2( d1 AU )2 Gw =

10−3(Rship

100 km )2( d1 pc )2 Mw.

For 1g acceleration, needs powergMshipc/2 = 1.5 · 106 Mw

Effective L� could be enhanced by usinggiant solar collectors and reradiating powerwith lasers and/or lenses.


Alternate Proposals

I Nanotechnology SiC or C fibers, with mass of 10−−100g . A fewHoover Dams of power could accelerate this at more than 100 g ’s;velocities of 0.2c are reached within a week, and nearest stars arereached in 20 years Earth-time.

Breakthrough Starshot is an engineering project by BreakthroughInitiatives (Yuri Milner) to develop a fleet of light-sail spacecraft calledStarChip to be sent to the α-Centauri star system 4.37 lt-yrs distant.

The proposal includes a flyby mission to Proxima Centauri b, anEarth-sized exoplanet near its host star.

Maximum velociites of 0.15− 20c would allow the trip to be completedin 20-30 years, then destination starlight will provide photon pressure toallow orbital entry around it.

Of course, there will be a 4-year delay in receiving messages from thestarship.

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.


StarChip and Sprites

Propulsion is provided by a multi-km steerable phased laser array with acombined coherent power of 100 GW. A thousand centimeter-sizedprobes, weighing a few grams each, would each be accelerated from ahigh-altitude Earth orbit by the laser to the target speed, which wouldtake 10 minutes at 10, 000g acceleration. The surface area of theattached sail on each probe is planned to be about 16 m2.

On-board power is provided by a 238Pu or 241Am radioactive powersource. Each ship contains a camera, computer, navigation gear andcommunications laser, hardened to withstand extreme acceleration, cold,vacuum, solar wind and cosmic rays. They will also have to survivecollisions with space dust. On the voyage, about a thousand collisionswith particles of at least 0.1 µ m are expected, necessitating 1000 probes.

In July 2017, precursors to StarChip, named Sprites, were launched bythe Polar Satellite Launch Vehicle by ISRO from Satish Dhawan SpaceCentre. In November 2018, additional Sprites will be flown on theKickSat-2 mission.


Some Practical Proposals

Robert L. Forward, AAAS Annual Meeting, May 1986


Some Impractical Ideas

I Spacetime Hypersurfing – Alcubierre Warp DriveRequires exotic matter, which has negative energy density and repelsnormal matter. At present, exotic matter virtually exists under someconditions, and may have been the normal state of matter prior tothe inflationary epoch in the Big Bang. Exotic matter could repelnormal-matter spaceships to faster-than-light travel withoutviolating causality and without permitting time travel. Suchtravelers would experience neither accelerations nor time dilation.

I Quantum EntanglementOtherwise known as “Action at a Distance”.Some recent experiments seem to show that mass can influenceother mass, no matter how distant it might be, virtuallyinstantaneously. Perhaps this quantum mechanical effect could beutilized for “faster-than-light” travel. Very speculative.

I WormholesEinstein himself suggested the idea that black holes could beconnected and thus form wormholes connecting different parts ofspace time. However, the difficulty with avoiding causality paradoxesrenders this idea very speculative. They would also seem to beimpractical, since there is no way of knowing where the other end ofa wormhole would be, in space or in time.


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 wouldtravel by contracting space in front of it and expanding space behind it,which would result in effectively faster-than-light travel. The Alcubierredrive would shift space around the spacecraft so that the object wouldarrive at its destination faster than light in normal space. Effectively, thiswould involve backwards time travel for the spaceship.

It has not been proven that this particular solution of Einstein’s equationsis physically meaningful.

Even if meaningful, such a drive may be impossible to construct, as itrequires the creation of negative energy density (also called exotic)matter. (Note that exotic matter is not antimatter.) Experiments tocreate microscopic amounts of such matter, which have to utilize somebizarre aspects of quantum mechanics (like the Casimir Effect), arepresently inconclusive and ultimately might prove to be impractical.


Alcubierre Warp Drive

And even if both the previous obstacles are overcome, it may be that thereconciliation of general relativity with quantum mechanics eliminates theAlcubierre solution.

Occupants of the spaceship would experience no acceleration or timedilation.

It is argued that construction of such a drive id possible only if spacetimecould be distorted in advance along the entire trajectory of thespacecraft. This means a voyage to a star X light years away wouldrequire that someone begins working on warping space between us andthe star at least X years before the trip begins.

Recently, someone might have proven that to construct an AlcubierreWarp Drive requires an Alcubierre Warp Drive.

Occupants of the spacecraft could not alter their trajectory or changespeeds, for example, to prevent collision with an asteroid.

It is possible that decelerating at the destination releases particlesgathered in transit in an enormous explosion, destroying the vicinity ofthe destination.


Quantum Mechanics and General Relativity

Although there is yet no unified theory of physics encompassing bothquantum mechanics and general relativity, a number of recentconnections have been found.

I Quantum entanglement was theorized in 1935 by Einstein, Podolskyand Rosen: a connection between widely separated quantumsystems. A measurement of one will determine the state of theother. Instantaneous implies infinite signal speed.


AdS-CFT Correspondence

In a model universe known as an anti-de Sitter space, the effects ofgravity at a point in theinside are equivalent toa quantum field on theboundary. The patternof triangles becomesdistorted near theboundary and seemto resemble patterns ofquantum entanglement.


Using Black Holes

Schwarzschild (non-rotating) black hole

Kerr (rapidly rotating) black hole


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 absorbmicrowaves and convert them to electricity.

I Pharmacology, molecular nanotechnology (diamonoidmechanosynthesis)

I Orbital towers or space elevators possible, would permit low-costorbital 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 energyI Access to zero gravityI Long-term expansion of land area available to human race.I Control of environmentI Location at top of Earth’s gravity wellI First step to interstellar colonization


Solar Power Satellite Design Parameters

I Geostationary orbit: 22,300 milesI Circular satellite antennae at least 1 km diameter to avoid losses due

to diffraction and sidelobesI Elliptical ground antennae (rectennae) about 10× 14 km, composed

of many short dipole antennae connected via diodes. Crops andanimals could be raised underneath them, since antennae are thinenough to permit sunlight to penetrate.

I Desired microwave intensity is 23 mW/cm2, so each antennatransfers 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 junctiongallium arsenide solar cells are used.

I Major cost is that of space launches. Will be reduced by economiesof scale. Mass-to-power ratio would be about 1 kg/kW, or 104 tonsfor each antenna. At present, the launch cost is as high as theenergy returns over a 10-year timespan.

I Using materials from the moon or asteroids could ultimately reducecosts.

I Another strategy for reducing launch costs involves using spaceelevators.


Solar Power Satellite


Constraints for Space Habitats

I Most material should originate from Moon, or possiblyasteroids or comets. Use electromagnetic mass drivers toinject material from lunar surface into Earth orbit.

I Earth-normal gravity required in living and most workingquarters. Axial area is zero-gee. Diameter must be greaterthan 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 exteriorsurface, which corresponds to about 2–3 feet thickness, isneeded. Less could be more harmful than none at all.

I System of mirrors and louvers needed to permit solarlighting and heating.

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


Stanford Torus


O’Neill Cylinder


Bernal Sphere


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