# ملاحظات ومراجع

#### مقدمة

(1)

Mars Odyssey, Mars Express, MRO, Mars
Orbiter Mission, and MAVEN.
(2)

NASA’s *Opportunity*and

*Curiosity*rovers. The

*Spirit*rover ceased functioning in 2011.

(3)

‘This foolish idea of shooting at the Moon
is an example of the absurd length to which vicious
specialisation will carry scientists. To escape the
Earth’s gravitation a projectile needs a velocity of 7
miles per second. The thermal energy at this speed is
15,180 calories [per gram]. Hence the proposition
appears to be basically impossible.’ Alexander
Bickerton, Chemistry Professor,
1926.
‘I am bold enough to say that a man-made Moon voyage will never occur regardless of all scientific advances.’ Lee De Forest, electronics inventor, 1957.

‘There is no hope for the fanciful idea of reaching the Moon because of insurmountable barriers to escaping the Earth’s gravity.’ Forest Moulton, astronomer, 1932.

(4)

In a 1920 editorial, the *New York Times*wrote: ‘Professor Goddard … does not know the relation of action to re-action, and the need to have something better than a vacuum against which to react.’ Newton’s third law of motion states that to every action there is an equal and opposite reaction. The reaction comes from conservation of momentum, and no medium to react

*against*is required. Such a medium would impede progress, not assist it. To be fair, the newspaper apologised in 1969 when the

*Apollo 11*astronauts were on their way to the Moon. To every publication there is an equal and opposite retraction.

(5)

Nicolas Bourbaki is the pseudonym of an
ever-changing group of mainly French mathematicians
first formed in 1935, who wrote a long series of books
reformulating mathematics on a general and abstract
basis. This was great for research mathematics, because
it unified the subject, sorted out basic concepts, and
provided rigorous proofs. But the widespread adoption of
a similar philosophy in the teaching of school
mathematics, known as ‘new maths’ met with little
success, and was, to say the least,
controversial.
#### الفصل الأول: الجذب عن بُعد

(1)

In 1726 Newton spent an evening dining with
William Stukeley in London. In a document preserved in
the archives of the Royal Society, whose archaic
spelling I’ve preserved for period flavour, Stukeley
wrote:
“After dinner, the weather being warm, we went into the garden & drank thea under the shade of some apple tree; only he & myself. Amid other discourse, he told me, he was just in the same situation, as when formerly the notion of gravitation came into his mind. Why shd that apple always descend perpendicularly to the ground, thought he to himself; occasion’d by the fall of an apple, as he sat in contemplative mood. Why shd it not go sideways, or upwards? But constantly to the Earth’s centre? Assuredly the reason is, that the Earth draws it. There must be a drawing power in matter. And the sum of the drawing power in the matter of the Earth must be in the Earth’s centre, not in any side of the Earth. Therefore does this apple fall perpendicularly or towards the centre? If matter thus draws matter; it must be in proportion of its quantity. Therefore the apple draws the Earth, as well as the Earth draws the apple.”

Other sources also confirm that Newton told this story, but none of this proves the story true. Newton might have invented it to explain his ideas. A still extant tree – Flower of Kent, a cooking apple, at Woolsthorpe Manor – is said to be the one from which the apple fell.

(2)

If an ellipse has major radius *a*and minor radius

*b*, then the focus lies at a distance from the centre. The eccentricity is .

(3)

A. Koyré. An unpublished letter of Robert
Hooke to Isaac Newton, *Isis*

**43**(1952) 312–337.

(4)

A. Chenciner and R. Montgomery. A
remarkable periodic solution of the three-body problem
in the case of equal masses, *Ann. Math.*

**152**(2000) 881–901.

An animation, and further information about similar types of orbit, is at: http://www.scholarpedia.org/article/N-body_choreographies.

(5)

C. Simó. New families of solutions in
*N*-body problems,

*Proc. European Congr. Math.*, Barcelona, 2000.

(6)

E. Oks. Stable conic-helical orbits of
planets around binary stars: analytical results,
*Astrophys. J.*

**804**(2015) 106.

(7)

Newton put it this way in a letter to
Richard Bentley, written in 1692 or 1693: “It is
inconceivable that inanimate Matter should, without the
Mediation of something else, which is not material,
operate upon, and affect other matter without mutual
Contact … That one body may act upon another at a
distance thro’ a Vacuum, without the Mediation of any
thing else … is to me so great an Absurdity that I
believe no Man who has in philosophical Matters a
competent Faculty of thinking can ever fall into
it.”
(8)

That’s slightly simplistic. Passing
*through*lightspeed is what’s forbidden. Nothing currently moving slower than light can speed up to become faster than light; if anything happens to be moving faster than light it can’t decelerate to become slower than light. Particles like this are called tachyons: they’re entirely hypothetical.

(9)

In a letter of 1907 to his friend Conrad
Habicht, Einstein wrote that he was thinking about ‘a
relativistic theory of the gravitational law with which
I hope to account for the still unexplained secular
change in the perihelion motion of Mercury’. His first
significant attempts began in
1911.
(10)

Nowadays we combine Einstein’s equations
into a single tensor equation (with ten components – a
symmetric 4-tensor). But “field equations” remains the
standard name.
#### الفصل الثاني: انهيار السديم الشمسي

(1)

The oldest minerals found in meteorites,
modern traces of the first solid material in the
pre-solar nebula, are 4.5682 billion years
old.
(2)

He wrote it in 1662–3, but postponed
publication because of the Inquisition. It appeared
shortly after his death.
(3)

A proper definition requires
vectors.
(4)

H. Levison, K. Kretke, and M. Duncan.
Growing the gas-giant planets by the gradual
accumulation of pebbles, *Nature*

**524**(2015) 322–324.

(5)

I. Stewart. The second law of gravitics and
the fourth law of thermodynamics, in *From Complexity to Life*(ed. N. H. Gregsen), Oxford University Press, 2003, pp. 114–150.

(6)

In this book the notation *p*:

*q*for a resonance means that the first body mentioned goes round

*p*times while the second goes round

*q*times. Their

*periods*are therefore in the ratio

*q*/

*p*. On the other hand their

*frequencies*are in the ratio

*p*/

*q*. Some authors use the opposite convention; others use the notation “

*p*/

*q*resonance”. Reversing the order of the bodies turns a

*p*:

*q*resonance into a

*q*:

*p*resonance.

(7)

Venus doesn’t have old craters because its
surface was reshaped by volcanism less than a hundred
million years ago. The planets from Jupiter outwards are
gas and ice giants, and all we can see is their upper
atmosphere. But many of their moons have craters – some
new, some old. *New Horizons*revealed that Pluto and its moon Charon have fewer craters than expected.

(8)

K. Batygin and G. Laughlin. On the
dynamical stability of the solar system, *Astrophys. J.*

**683**(2008) 1207–1216.

(9)

J. Laskar and M. Gastineau. Existence of
collisional trajectories of Mercury, Mars and Venus with
the Earth, *Nature*

**459**(2009) 817–819.

(10)

G. Laughlin. Planetary science: The Solar
System’s extended shelf life, *Nature*

**459**(2009) 781–782.

#### الفصل الثالث: قمر متقلب

(1)

The chemistry of uranium deposits at Oklo,
Gabon, suggests that in the Precambrian they constituted
a natural fission reactor.
(2)

R. C. Paniello, J. M. D. Day, and F.
Moynier. Zinc isotopic evidence for the origin of the
Moon, *Nature*

**490**(2012) 376–379.

(3)

A. G. W. Cameron and W. R. Ward. The origin
of the Moon, *Abstr. Lunar Planet. Sci. Conf.*

**7**(1976) 120–122.

(4)

W. Benz, W.L. Slattery, and A.G.W. Cameron.
The origin of the moon and the single impact hypothesis
I, *Icarus*

**66**(1986) 515–535.

W. Benz, W.L. Slattery, and A.G.W. Cameron. The origin of the moon and the single impact hypothesis II,

*Icarus*

**71**(1987) 30–45.

W. Benz, A.G.W. Cameron, and H.J. Melosh. The origin of the moon and the single impact hypothesis III,

*Icarus*

**81**(1989) 113–131.

(5)

R. M. Canup and E. Asphaug. Origin of the
Moon in a giant impact near the end of the Earth’s
formation, *Nature*

**412**(2001) 708–712.

(6)

A. Reufer, M. M. M. Meier, and W. Benz. A
hit-and-run giant impact scenario, *Icarus*

**221**(2012) 296–299.

(7)

J. Zhang, N. Dauphas, A.M. Davis, I. Leya,
and A. Fedkin. The proto-Earth as a significant source
of lunar material, *Nature Geosci.*

**5**(2012) 251–255.

(8)

R. M. Canup, Simulations of a late
lunar-forming impact, *Icarus*

**168**(2004) 433–456.

(9)

A. Mastrobuono-Battisti, H. B. Perets, and
S.N. Raymond. A primordial origin for the compositional
similarity between the Earth and the Moon, *Nature*

**520**(2015) 212–215.

#### الفصل الرابع: كون الساعة الآلية

(1)

See note 6 of Chapter 2 for why we don’t
call it a 3:5 resonance.
(2)

Dermott’s law, an empirical formula for the
orbital period of satellites in the solar system, was
identified by Stanley Dermott in the 1960s. It takes the
form
, where *n*= 1, 2, 3, 4, … Here is the orbital period of the

*n*th satellite, is a constant of the order of days, and

*C*is a constant of the satellite system in question. Specific values are:

*Jupiter*: = 0.444 days,

*C*= 2.0.

*Saturn*: = 0.462 days,

*C*= 1.59.

*Uranus*: = 0.488 days,

*C*= 2.24.

S. F. Dermott. On the origin of commensurabilities in the solar system II: the orbital period relation,

*Mon. Not. RAS*

**141**(1968) 363–376.

S. F. Dermott. On the origin of commensurabilities in the solar system III: the resonant structure of the solar system,

*Mon. Not. RAS*

**142**(1969) 143–149.

(3)

F. Graner and B. Dubrulle. Titius-Bode laws
in the solar system. Part I: Scale invariance explains
everything, *Astron. & Astrophys.*

**282**(1994) 262–268.

B. Dubrulle and F. Graner. Titius-Bode laws in the solar system. Part II: Build your own law from disk models,

*Astron. & Astrophys.*

**282**(1994) 269–276.

(4)

Derived from
‘QB_{1-0}’, after (15760) 1992 QB

_{1}, the first TNO discovered.

(5)

It’s tricky to measure the diameter of
Pluto from Earth, even using the Hubble telescope,
because it has a thin atmosphere that makes its edges
fuzzy. Eris has no atmosphere.
(6)

Propositions 43–45 of Book I of *Philosophiae Naturalis Principia*M

*athematica.*

(7)

A. J. Steffl, N. J. Cunningham, A. B. Shinn, and S. A.
Stern. A search for Vulcanoids with the STEREO heliospheric
imager, *Icarus*233 (2013) 48–56.

#### الفصل الخامس: الشرطة السماوية

(1)

Wigner’s remark is often misunderstood.
It’s easy to explain the *effectiveness*of mathematics. Much of it is motivated by real-world problems, so it’s no surprise when it solves those problems. The important word in Wigner’s phrase is “unreasonable”. He was referring to the way mathematics invented for one purpose often turns out to be useful in a totally different, unexpected area. Simple examples are Greek geometry of conic sections, turning up in planetary orbits two thousand years later, or Renaissance speculations about imaginary numbers, now central to mathematical physics and engineering. This widespread phenomenon can’t be explained away so easily.

(2)

Suppose, for simplicity, that all asteroids
lie in the same plane – which isn’t too far from reality
for most. The asteroid belt lies between 2.2 and 3.3 AU
from the Sun, that is, about 320 million and 480 million
kilometres. Projected into the plane of the ecliptic,
the total area occupied by the asteroid belt is
π(480^{2}− 320

^{2})

*trillion*square kilometres, that is, 4 × 10

^{17}km

^{2}. Shared among 150 million rocks this gives an area of 8.2 × 10

^{8}km

^{2}per rock. That’s the same area as a circle of diameter 58,000 km. If the asteroids are roughly uniformly distributed, which is good enough for government work, that’s the typical distance between neighbouring asteroids.

(3)

M. Moons and A. Morbidelli. Secular
resonances inside meanmotion commensurabilities: the
4/1, 3/1, 5/2 and 7/3 cases, *Icarus*

**114**(1995) 33–50.

M. Moons, A. Morbidelli, and F. Migliorini. Dynamical structure of the 2/1 commensurability with Jupiter and the origin of the resonant asteroids,

*Icarus*

**135**(1998) 458–468.

(4)

An animation showing the
relationship between the five Lagrangian
points and the gravitational potential
is at
https://en.wikipedia.org/wiki/File:Lagrangian_points_equipotential.gif.
(5)

See the animation at
https://www.exploremars.org/trojan-asteroids-around-jupiter-explained.
(6)

F. A. Franklin. Hilda asteroids as possible
probes of Jovian migration, *Astron. J.*

**128**(2004) 1391–1406.

#### الفصل السادس: الكوكب الذي ابتلع أطفاله

(1)

P. Goldreich and S. Tremaine. Towards a
theory for the Uranian rings, *Nature*

**277**(1979) 97–99.

(2)

M. Kenworthy and E. Mamajek. Modeling giant
extrasolar ring systems in
eclipse and the case of J1407b: sculpting by exomoons?
arXiv:1501.05652 (2015).
(3)

F. Braga-Rivas and 63 others. A ring system
detected around Centaur (10199) Chariklo, *Nature*

**508**(2014) 72–75.

#### الفصل السابع: نجوم كوزيمو

(1)

E. J. Rivera, G. Laughlin, R. P. Butler, S.
S. Vogt, N. Haghighipour, and S. Meschiari. The
Lick-Carnegie exoplanet survey: a Uranus-mass fourth
planet for GJ 876 in an extrasolar Laplace
configuration, *Astrophys. J.*

**719**(2010) 890–899.

(2)

B. E. Schmidt, D. D. Blankenship, G. W.
Patterson, and P. M. Schenk. Active formation of ‘chaos
terrain’ over shallow subsurface water on Europa,
*Nature*

**479**(2011) 502–505.

(3)

P. C. Thomas, R. Tajeddine, M. S.
Tiscareno, J. A. Burns, J. Joseph, T. J. Loredo, P.
Helfenstein, and C. Porco. Enceladus’s measured physical
libration requires a global subsurface ocean, *Icarus*(2015) in press; doi:10٫1016/j.icarus.2015.08.037.

(4)

S. Charnoz, J. Salmon, and A. Crida. The
recent formation of Saturn’s moonlets from viscous
spreading of the main rings, *Nature*

**465**(2010) 752–754.

#### الفصل الثامن: رحلة على مذنَّب

(1)

M. Massironi and 58 others. Two independent
and primitive envelopes of the bilobate nucleus of comet
67P, *Nature*

**526**(2015) 402–405.

(2)

A. Bieler and 33 others. Abundant molecular
oxygen in the coma of comet 67P/Churyumov–Gerasimenko,
*Nature*

**526**(2015) 678–681.

(3)

P. Ward and D. Brownlee. *Rare Earth*, Springer, New York, 2000.

(4)

J. Horner and B. W. Jones. Jupiter – friend
or foe? I: The asteroids, *Int. J. Astrobiol.*

**7**(2008) 251–261.

#### الفصل التاسع: الفوضى في الكون

(1)

See the video at:
http://hubblesite.org/newscenter/archive/releases/2015/24/video/a/.
(2)

J. R. Buchler, T. Serre, and Z. Kolláth. A
chaotic pulsating star: the case of R Scuti, *Phys. Rev. Lett.*

**73**(1995) 842–845.

(3)

Strictly, “dice” is the plural and “die” is
the singular, but in language as she is actually spoke,
almost everyone talks of “a dice”. I no longer see any
point in fighting this, but I’m not using the word out
of ignorance. I’m still fighting a rearguard action on
usages such as “the team are”, but deep down I know I’ve
lost that one too. I’ve also stopped trying to tell
greengrocers the difference between the plural and the
possessive, though I was sorely tempted to have a quiet
chat with the bloke up the road whose van bears the
sign: REMOVAL’S.
(4)

Nonetheless, a 6 has the same probability
as any other value, for a fair dice. In the long run,
the numbers of 6s should get arbitrarily close to 1/6 of
the number of throws. But how this happens is
instructive. If at some stage there have been, say, 100
more throws of a 6 than anything else, a 6 doesn’t
become more likely. The dice just keeps churning out
more and more numbers. After, say, a hundred million
more throws, that extra 100 affects the proportion of 6s
by only one part in a million. Deviations aren’t
cancelled out because the dice “knows” it’s thrown too
many 6s. They’re diluted by new data, generated by a
dice that has no memory.
(5)

Dynamically, a dice is a solid cube, and
its motion is chaotic because the edges and corners
“stretch” the dynamics. But there’s another source of
randomness in dice: initial conditions. How you hold the
dice in your hand, and how you release it, randomise the
result anyway.
(6)

Lorenz didn’t call it a butterfly, though
he did say something similar about a seagull. Someone
else came up with the butterfly for the title of a
public lecture Lorenz gave in 1972. And what Lorenz
originally had in mind probably wasn’t *this*butterfly effect, but a subtler one. See: T. Palmer. The real butterfly effect,

*Nonlinearity*

**27**(2014) R123–R141.

None of that affects this discussion, and what I’ve described is what we now mean by ‘butterfly effect’. It’s real, it’s characteristic of chaos, but it’s subtle.

(7)

V. Hoffmann, S. L. Grimm, B. Moore, and J.
Stadel. Chaos in terrestrial planet formation, *Mon. Not. RAS*(2015); arXiv: 1508.00917.

(8)

A. Milani and P. Farinella. The age of the
Veritas asteroid family deduced by chaotic chronology,
*Nature*

**370**(1994) 40–42.

(9)

June Barrow-Green. *Poincaré and the Three Body Problem*, American Mathematical Society, Providence, 1997.

(10)

M. R. Showalter and D. P. Hamilton.
Resonant interactions and chaotic rotation of Pluto’s
small moons, *Nature*

**522**(2015) 45–49.

(11)

J. Wisdom, S. J. Peale, and F. Mignard. The
chaotic rotation of Hyperion, *Icarus*

**58**(1984) 137–152.

(12)

K = *Kreide*, German for ‘chalk’, referring to the Cretaceous, and T = Tertiary. Why do scientists do this kind of thing? Beats me.

(13)

M. A. Richards and nine others. Triggering of
the largest Deccan eruptions by
the Chicxulub impact, *GSA Bull.*(2015), doi: 10.1130/B31167.1.

(14)

W. F. Bottke, D. Vokrouhlický, and D.
Nesvorný. An asteroid breakup 160 Myr ago as the
probable source of the K/T impactor, *Nature*

**449**(2007) 48–53.

#### الفصل العاشر: طريق ما بين الكواكب السريع

(1)

M. Minovitch. A method for determining
interplanetary free-fall reconnaissance trajectories,
*JPL Tech. Memo*. TM-312–130 (1961) 38–44.

(2)

M. Lo and S. Ross. SURFing the solar
system: invariant manifolds and the dynamics of the
solar system, *JPL IOM*312/97, 1997.

M. Lo and S. Ross. The Lunar L1 gateway: portal to the stars and beyond,

*AIAA Space 2001 Conf.*, Albuquerque, 2001.

(3)

http://sci.esa.int/where_is_rosetta/
has a dramatic animation of this roundabout
path.
(4)

One cause (among many) of World War I was the
assassination of the Austrian Archduke Franz Ferdinand
on a visit to Sarajevo. Six assassins made a failed
attempt with a grenade. Later one of them, Gavrilo
Princip, shot him dead with a pistol, along with his
wife Sophie. Initial reaction by the populace was
virtually non-existent, but the Austrian government
encouraged rioting against Serbs in Sarajevo, which
escalated.
(5)

W. S. Koon, M. W. Lo, J. E. Marsden, and S.
D. Ross. The Genesis trajectory and heteroclinic
connections, *Astrodynamics*

**103**(1999) 2327–2343.

#### الفصل الحادي عشر: كرات عظيمة من النيران

(1)

Strictly speaking, this term refers to
total energy output, but that’s closely related to
intrinsic brightness.
(2)

An animation of stellar evolution across
the Hertzsprung–Russell diagram can be found at
http://spiff.rit.edu/classes/phys230/lectures/star_age/evol_hr.swf.
(3)

F. Hoyle. Synthesis of the elements from
hydrogen, *Mon. Not. RAS*

**106**(1946) 343–383.

(4)

E. M. Burbidge, G. R. Burbidge, W. A.
Fowler, and F. Hoyle. Synthesis of the elements in
stars, *Rev. Mod. Phys.*

**29**(1957) 547–650.

(5)

A. J. Korn, F. Grundahl, O. Richard, P. S.
Barklem, L. Mashonkina, R. Collet, N. Piskunov, and B.
Gustafsson. A probable stellar solution to the
cosmological lithium discrepancy, *Nature*

**442**(2006) 657–659.

(6)

F. Hoyle. On nuclear reactions occurring in
very hot stars: the synthesis of the elements between
carbon and nickel, *Astrophys. J. Suppl.*

**1**(1954) 121–146.

(7)

F. Hoyle. The universe: past and present
reflections, *Eng. & Sci.*(November 1981) 8–12.

(8)

G. H. Miller and 12 others. Abrupt onset of
the Little Ice Age triggered by volcanism and sustained
by sea-ice/ocean feedbacks, *Geophys. Res. Lett.*

**39**(2012) L02708.

(9)

H. W. Babcock. The topology of the Sun’s
magnetic field and the 22-year cycle, *Astrophys. J.*

**133**(1961) 572–587.

(10)

E. Nesme-Ribes, S. L. Baliunas, and D.
Sokoloff. The stellar dynamo, *Scientific American*(August 1996) 30–36.

For mathematical details and more recent work with more realistic models, see: M. Proctor. Dynamo action and the Sun,

*EAS Publ. Ser.*

**21**(2006) 241–273.

#### الفصل الثاني عشر: نهر السماء العظيم

(1)

That is,
. So . Here is the mass out to radius *r*, is the rotational velocity of stars at radius

*r*, and

*G*is the gravitational constant.

#### الفصل الثالث عشر: عوالم فضائية

(1)

X. Dumusque and 10 others. An Earth-mass
planet orbiting α
Centauri B, *Nature*

**491**(2012) 207–211.

(2)

V. Rajpaul, S. Aigrain, and S. J. Roberts.
Ghost in the time series: no planet for Alpha Cen B,
arXiv:1510.05598; *Mon. Not. RAS*, in press.

(3)

Z. K. Berta-Thompson and 20 others. A rocky
planet transiting a nearby low-mass star, *Nature*

**527**(2015) 204–207.

(4)

“Earthlike” here means a rocky world, with
much the same size and mass as the Earth, in an orbit
that would allow water to exist as a liquid without any
special extra conditions. Later we require oxygen as
well.
(5)

E. Thommes, S. Matsumura, and F. Rasio. Gas
disks to gas giants: Simulating the birth of planetary
systems, *Nature*

**321**(2008) 814–817.

(6)

M. Hippke and D. Angerhausen. A statistical
search for a population of exo-Trojans in the Kepler
dataset, ArXiv:1508.00427 (2015).
(7)

In *Evolving the Alien*Cohen and I propose that what really counts is

*extelligence*: the ability of intelligent beings to pool their knowledge in a way that all can access. The Internet is an example. It takes extelligence to build starships.

(8)

M. Lachmann, M. E. J. Newman, and C. Moore.
The physical limits of communication, Working paper
**99–07–054**, Santa Fe Institute 2000.

(9)

I. N. Stewart. Uninhabitable zone,
*Nature*

**524**(2015) 26.

(10)

P. S. Behroozi and M. Peeples. On the
history and future of cosmic planet formation, *Mon. Not. RAS*(2015); arXiv: 1508.01202.

(11)

D. Sasselov and D. Valencia. Planets we
could call home, *Scientific American*

**303**(August 2010) 38–45.

(12)

S. A. Benner, A. Ricardo, and M. A.
Carrigan. Is there a common chemical model for life in
the universe? *Current Opinion in Chemical Biology*

**8**(2004) 676–680.

(13)

J. Stevenson, J. Lunine, and P. Clancy.
Membrane alternatives in worlds without oxygen: Creation
of an azotosome, *Science Advances*

**1**(2015) e1400067.

(14)

J. Cohen and I. Stewart. *Evolving the Alien*, Ebury Press, London, 2002.

(15)

W. Bains. Many chemistries could be used to
build living systems, *Astrobiology*

**4**(2004) 137–167.

(16)

J. von Neumann. *Theory of Self-Reproducing Automata*, University of Illinois Press, Urbana, 1966.

#### الفصل الرابع عشر: نجوم مظلمة

(1)

In units that make the speed of light equal
to 1, say years for time and light years for
space.
(2)

R. Penrose. Conformal treatment of
infinity, in *Relativity, Groups and Topology*(ed. C. de Witt and B. de Witt), Gordon and Breach, New York, 1964, pp. 563–584;

*Gen. Rel. Grav.*

**43**(2011) 901–922.

(3)

Animations of what it would look like when
passing through these wormholes can be found at
http://jila.colorado.edu/~ajsh/insidebh/penrose.html.
(4)

B. L. Webster and P. Murdin. Cygnus X-1 – a
spectroscopic binary with a heavy companion?, *Nature*

**235**(1972) 37–38.

H. L. Shipman, Z. Yu, and Y. W. Du. The implausible history of triple star models for Cygnus X-1: Evidence for a black hole,

*Astrophys. Lett.*

**16**(1975) 9–12.

(5)

P. Mazur and E. Mottola. Gravitational
condensate stars: An alternative to black holes,
arXiv:gr-qc/0109035 (2001).
#### الفصل الخامس عشر: خصلات وفراغات

(1)

Colin Stuart. When worlds collide,
*New Scientist*(24 October 2015) 30–33.

(2)

You may object that “currently” has no
meaning because relativity implies that events need not
occur simultaneously for all observers. That’s true, but
when I say “currently” I’m referring to *my*frame of reference, with me as observer. I can conceptually set distant clocks by making changes of one year per light year; viewed from here, they will all be synchronised. More generally, observers in “comoving” frames experience simultaneity the way we would expect in classical physics.

(3)

N. J. Cornish, D. N. Spergel, and G. D.
Starkman. Circles in the sky: finding topology with the
microwave background radiation, *Classical and Quantum Gravity*

**15**(1998) 2657–2670.

J. R. Weeks. Reconstructing the global topology of the universe from the cosmic microwave background,

*Classical and Quantum Gravity*

**15**(1998) 2599–2604.

#### الفصل السادس عشر: البيضة الكونية

(1)

Less than that! According to NASA it was
12% of a pixel.
(2)

Based on Type Ia supernovae, temperature
fluctuations in the CMB, and the correlation function of
galaxies, the universe has an estimated age of 13.798 ±
0.037 billion years. See Planck collaboration (numerous
authors). Planck 2013 results XVI: Cosmological
parameters, *Astron. & Astrophys.*

**571**(2014); arXiv:1303.5076.

(3)

M. Alcubierre. The warp drive: hyper-fast
travel within general relativity, *Classical and Quantum Gravity*

**11**(1994). L73–L77.

S. Krasnikov. The quantum inequalities do not forbid spacetime shortcuts,

*Phys. Rev. D*

**67**(2003) 104013.

(4)

See Note 2 of Chapter 15 on simultaneity in
a relativistic universe.
#### الفصل السابع عشر: الانتفاخ الكبير

(1)

The current figure for the temperature is
2.72548 ± 0.00057 K, see D. J. Fixsen. The temperature
of the cosmic microwave background, *Astrophys. J.*

**707**(2009) 916–920.

Other figures mentioned in the text are historical estimates, now obsolete.

(2)

This phrase is reused from Terry Pratchett,
Ian Stewart, and Jack Cohen. *The Science of Discworld IV: Judgement Day*, Ebury, London, 2013.

(3)

Penrose’s work is reported in: Paul Davies.
*The Mind of God*, Simon & Schuster, New York, 1992.

(4)

G. F. R. Ellis. Patchy solutions, *Nature*

**452**(2008) 158–161.

G. F. R. Ellis. The universe seen at different scales,

*Phys. Lett.*A

**347**(2005) 38–46.

(5)

T. Buchert. Dark energy from structure: a
status report, *T. Gen. Rel. Grav.*

**40**(2008) 467–527.

(6)

J. Smoller and B. Temple. A one parameter
family of expanding wave solutions of the Einstein
equations that induces an anomalous acceleration into
the standard model of cosmology,
arXiv:0901.1639.
(7)

R. R. Caldwell. A gravitational puzzle,
*Phil. Trans. R. Soc. London*A

**369**(2011) 4998–5002.

(8)

R. Durrer. What do we really know about
dark energy? *Phil. Trans. R. Soc. London*A

**369**(2011) 5102–5114.

(9)

Marcus Chown. End of the beginning,
*New Scientist*(2 July 2005) 30–35.

(10)

D. J. Fixsen. The temperature of the cosmic
microwave background, *Astrophys. J.*

**707**(2009) 916–920.

(11)

The stars in galaxies are bound together by
gravity, which is thought to counteract the
expansion.
(12)

S. Das, Quantum Raychaudhuri equation,
*Phys. Rev.*D

**89**(2014) 084068.

A. F. Ali and S. Das. Cosmology from quantum potential,

*Phys. Lett.*B

**741**(2015) 276–279.

(13)

Jan Conrad. Don’t cry wolf, *Nature*

**523**(2015) 27–28.

#### الفصل الثامن عشر: الجانب المظلم

(1)

Quasi-autonomous non-governmental
organisation.
(2)

K. N. Abazajian and E. Keeley. A bright
gamma-ray galactic center excess and dark dwarfs: strong
tension for dark matter annihilation despite Milky Way
halo profile and diffuse emission uncertainties, arXiv:
1510.06424 (2015).
(3)

G. R. Ruchti and 28 others. The Gaia-ESO
Survey: a quiescent Milky Way with no significant
dark/stellar accreted disc, *Mon. Not. RAS*

**450**(2015) 2874–2887.

(4)

S. Clark. Mystery of the missing matter,
*New Scientist*(23 April 2011) 32–35.

G. Bertone, D. Hooper, and J. Silk. Particle dark matter: evidence, candidates and constraints,

*Phys. Rep.*

**405**(2005) 279–390.

(5)

Newton’s second law of motion is
, where *F*= force,

*m*= mass,

*a*= acceleration. MOND replaces this by , where is a new fundamental constant that determines the acceleration below which Newton’s law ceases to apply. The term is an unspecified function that tends to 1 as

*x*becomes large, in agreement with Newton’s law, but to

*x*when

*x*is small, which models observed galactic rotation curves.

(6)

J. D. Bekenstein, Relativistic gravitation
theory for the modified Newtonian dynamics paradigm,
*Physical Review*D

**70**(2004) 083509.

(7)

D. Clowe, M. Bradač, A. H. Gonzalez, M.
Markevitch, S. W. Randall, C. Jones, and D. Zaritsky. A
direct empirical proof of the existence of dark matter,
*Astrophys. J. Lett.*

**648**(2006) L109.

(9)

S. Clark. Mystery of the missing matter,
*New Scientist*(23 April 2011) 32–35.

(10)

J. M. Ripalda. Time reversal and negative
energies in general relativity, arXiv: gr-qc/9906012
(1999).
(11)

See the papers listed at
http://msp.warwick.ac.uk/~cpr/paradigm/.
(12)

D. G. Saari. Mathematics and the ‘dark
matter’ puzzle, *Am. Math. Mon.*

**122**(2015) 407–423.

(13)

The phrase “the exception proves the rule”
is widely trotted out to dismiss awkward exceptions.
I’ve never understood why people do this, other than as
a debating ploy. It makes no sense. The word “prove” in
that context originally had the meaning “test” – just as
we still *prove*bread dough; that is, test to see if it’s the right consistency. (See en.wikipedia.org/wiki/Exception_that_proves_the_rule.) The phrase goes back to ancient Rome, in the legal principle

*exceptio probat regulam in casibus non exceptis*(the exception confirms the rule in cases not excepted). Which means that if your rule has exceptions, you need a different rule. That does make sense. Modern usage omits the second half, producing nonsense.

#### الفصل التاسع عشر: خارج الكون

(1)

The *truly*fundamental constants are specific combinations of these quantities that don’t depend on the units of measurement: ‘dimensionless constants’ that are pure numbers. The fine structure constant is like that. The numerical value of the speed of light does depend on the units, but we know how to convert the number if we use different units. Nothing I say depends on this distinction.

(2)

B. Greene. *The Hidden Reality*, Knopf, New York, 2011.

(3)

What matters is that there’s some fixed
number that’s bigger than the number of states of any
patch. Exact equality isn’t
required.
(4)

Numbers with huge exponents like these
behave rather strangely. If you look on the web you’ll
find that the nearest exact copy of you is about *metres*away. I replaced that with light years, which are much bigger than metres. But actually, changing the units makes very little difference to the

*exponent*, because metres is light years, and the exponent is a 129-digit number, just like 10

^{128}. Their ratio is 1.000…00011 with 125 zeros.

(5)

B. Greene. *The Hidden Reality*, Knopf, New York, 2011, p. 154.

(6)

L. Carroll. *The Hunting of the Snark*, online free at https://www. gutenberg.org/files/13/13-h/13-h.htm.

(7)

G. F. R. Ellis. Does the multiverse really
exist? *Sci. Am.*

**305**(August 2011) 38–43.

(8)

O. Romero-Isart, M. L. Juan, R. Quidant,
and J. I. Cirac. Toward quantum superposition of living
organisms, *New J. Phys.*

**12**(2010) 033015.

(9)

J. Foukzon, A. A. Potapov, and S. A.
Podosenov. Schrödinger’s cat paradox resolution using
GRW collapse model, *Int. J. Recent Adv. Phys.*

**3**(2014) 17–30.

(10)

Known as a “ket” vector in Dirac’s
formalism for quantum mechanics. The right-hand end of a
brac*ket*, OK? Mathematically, it’s a vector rather than a dual vector.

(11)

A. Bassi, K. Lochan, S. Satin, T. P. Singh,
and H. Ulbricht. Models of wave-function collapse,
underlying theories, and experimental tests, *Rev. Mod. Phys.*

**85**(2013) 471.

(12)

J. Horgan. Physicist slams cosmic theory he
helped conceive, *Sci. Am.*(1 December 2014); http://blogs.scientificamerican.com/cross-check/physicist-slams-cosmic-theory-he-helped-conceive/.

(13)

F. C. Adams. Stars in other universes:
stellar structure with different fundamental constants,
*J. Cosmol. Astroparticle Phys.*

**08**(2008) 010.

(14)

V. Stenger. *The Fallacy of Fine-Tuning*, Prometheus, Amherst, 2011.

(15)

That is, on a log/log scale and in a
specific but wide range of values, the region of
parameter space for which stars can form has about one
quarter the area of the whole space. This is a
rough-and-ready measure, but it’s comparable to what
fine-tuning proponents do. The point isn’t the 25%: it’s
that any sensible calculation of the likelihood makes it
far bigger than
10^{47−}.

#### خاتمة

(1)

Adam G. Reiss and 14 others. A 2.4%
determination of the local value of the Hubble constant,
http://hubblesite.org/pubinfo/pdf/2016/17/pdf/pdf.