the best of worlds, the worst of worlds
TRANSCRIPT
THE BEST OF WORLDS, THE WORST OF WORLDS...
Alejandro Jenkins
High Energy Physics, FSU
LNS Nuclear & Particle Physics Colloquium,
MIT
8 Nov. 2010
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HISTORY OF THIS UNIVERSE
Source: NASA, WMAP science team
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COSMIC MICROWAVE BACKGROUND (CMB)
Electromagnetic radiation, made 377,000 years after initial singularity, when protons combined with electrons to make neutral hydrogen
Predicted by Gamow in ‘46, actively searched for by Dicke et al. in the 60’s
Accidentally discovered by Penzias & Wilson in ’64 [Nobel Prize ’78]
First precision measurements in ’89 by COBE (NASA) [Nobel Prize ’06 to Smoot & Mather]
2001 WMAP (NASA); 2007 Planck (ESA)
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Source: NASA
COSMOLOGICAL QUANDARIES
Flatness problem: Why is the geometry of the universe so close to being Euclidean?
Horizon problem: Why is the universe so homogeneous?
Monopole problem: Why aren’t magnetic monopoles abundant?
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5
Illustration from D. Castelvecchi, “The Growth of Inflation,” Symmetry, Dec. 2004 / Jan. 2005. Notebook on display at Chicago planetarium
Brief period of exponential expansion, sometime between 10-36 and 10-32 s after initial singularity
From a billionth of the size of a proton, to maybe the size of an orange
Increase in volume by at least 1078
Proposed by Alan Guth to address the flatness, horizon, and monopole problems
Predicted the correct (scale-invariant) spectrum for primordial density pertubations, as reflected in the CMB
P�(k) � k�3
INFLATION
INFLATIONARY MULTIVERSE
Illustration from Andrei Linde, Sci. Am., Nov. 1994
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EXTRA DIMENSIONS
From Bousso & Polchinski, Sci. Am. Sep. 2004
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STRING LANDSCAPE
Bousso & Polchinski, op. cit.
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FUNDAMENTAL VS. ENVIRONMENTAL
Inflation & string theory seem to describe something more than observable Universe
Quantities we think of as fundamental could instead be environmental
Analogies: sizes of planetary orbits, speed of sound, etc.
Kepler, Mysterium Cosmographicum (1596)
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COPERNICAN PRINCIPLE
Human life doesn’t have privileged position in the universe, or in the scheme of physics
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Andreas Cellarius, Harmonia Macrocosmica (1661)
ANTHROPIC PRINCIPLE
Observed conditions have to be compatible with the existence of conscious, intelligent life, and this is a non-trivial restriction
from ESA website
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WORD OF CAUTION
The anthropic principle was named by Brandon Carter (’74) but use in modern science dates back at least to Boltzmann in 1877
It’s always been controversial
Steven Weinberg: “A physicist talking about the anthropic principle runs the same risk as a cleric talking about pornography: no matter how much you say you are against it, some people will think you are a little too interested.”
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BEST OF WORLDS?
Various arguments about physics being fine-tuned for life, such as:
3-α synthesis of carbon in stars (Hoyle, ’64)
proton-neutron mass difference
cosmological constant
John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle,(Oxford U. Press, New York, 1986), 706 P.
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WORST OF WORLDS?A teleologist [...] praises the wise arrangement which provides that planets do not collide, that land and sea are kept apart, that all is not petrified by cold nor roasted by heat, that the Earth’s axis is inclined so that there is no eternal spring and fruit might ripen, etc., etc.
Arthur Schopenhauer (1788-1860)
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But these and all similar things are simply necessary conditions. If there is to be a world at all, if its planets are to exist at least long enough for a ray of light from a remote fixed star to reach them [...] then, of course, it cannot be framed so unskillfully that the very scaffolding threatened to collapse [...]
Against the palpably sophistical proofs of Leibniz that this is the best of all possible worlds, we may even oppose seriously and honestly the argument that it is the worst of all possible worlds.
– Schopenhauer, The World as Will and Idea, vol. III, ch. 46, (1818)
WORST OF WORLDS? (BIS)
Leonard Susskind, The Cosmic Landscape: String Theory and the Illusion of Intelligent Design,(Little, Brown and Co., New York, 2005), 416 P.
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MAYBE NEITHER?
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AJ & Gilad Perez, Sci. Am., Jan. 2010
UNITS
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c = 1
� = 1
[length] = [time] = [energy]�1 = [mass]�1
me = 0.5 MeV
MPl = (8�G)�1/2 = 2� 1018 GeV
COSMOLOGICAL CONSTANT
Λ is like a constant energy density of otherwise empty space-time
Λ>0 causes space-time to stretch exponentially (inflation)
Λ<0 causes space-time to re-collapse (“Big Crunch”)
Current rate of expansion of the universe consistent with Λ>0
Unnaturally small, by 123 orders of magnitude!
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� � 10�123M4Pl
Gµ� = M�2Pl Tµ� � �gµ�
Space-time curvature
Cosmological constant
Matter & energy
COSMOLOGICAL CONSTANT
Weinberg (’87) predicted Λ>0, before it was measured (’98)
This was anthropic, worst-of-worlds reasoning:
Λ as big as can be, while still allowing Universe to develop some structure
No convincing dynamical explanation of smallness of Λ (“dark energy”)
Only minor increase of Λ could be offset by other parameters
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BAYESIAN STATISTICS
AJ & Gilad Perez, op. cit.
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Multiverse theory in trouble if
Anthropic constraint
Multiverse distribution
pmeasured({�i}) � p({�i}|observer)
� p(observer|{�i}) · p({�i})
r � pmeasured{�⇥i }pmeasured{��i }
⇥ 1
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Bayesian statistics with a single data point!
HIGGS MECHANISM
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As explained to William Waldegrave (UK minister of science) by Prof. David J. Miller, 1993
Illustrations by CERN, from Prof. Miller’s website
“Vacuum”:
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Massive particle:
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Higgs boson:
HIGGS MECHANISM, CONT.
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�ud
⇥
L
; uR, dR
� =�
⇥+
⇥0
⇥; �c � i�2��
Lflavor = �yuq̄L�cuR � ydq̄L�dR + h.c.
For each !lavor, we have
Coupled to Higgs doublet
by
Higgs potential
V (�) = �µ2�†� + ���†�
⇥2
��⇥ =�
0v/⇤
2
⇥gives vacuum expectation value (VEV)
HIGGS MECHANISM, CONT.
Gives f a Dirac mass:
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v =�
µ2/�
Sheldon Glashow: “toilet of the Standard Model”
μ2, λ, and y’s are free parameters
μ2 subject to large, additive quantum corrections
�µ2 = � |yf |2
8�2⇥2
UV + . . .
Expect μ2 ~ (100 GeV)2, while ΛUV2 ~ (1018 GeV)2
mf =1�2yfv
WEAK SCALE
v also sets range of weak nuclear force
Responsible for radioactive β-decay (interconverts protons and neutrons)
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1range
�Mweak =12gv
Mystery: the weak force isn’t weak enough!
Old Gargamelle bubble chamber, CERN
GAUGE HIERARCHY PROBLEM
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M2weak
M2Pl
� 10�32
Hierarchy seems to require implausible fine-tuning of parameters (as first pointed out by Ken Wilson in the 70’s)
This has motivated 30+ years of theoretical work: supersymmetry, technicolor, little Higgs, large extra dimensions, etc.
All propose new physics, yet unseen, just above Mweak
WEAK SCALE: WORST OF WORLDS?
By analogy to cosmological constant, can this be resolved anthropically?
Agrawal, Barr, Donoghue & Seckel ’98, argued that, if all other parameters of the SM are fixed, stable atoms require:
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Argument based on quark masses, relative to ΛQCD (scale of strong nuclear force)
0 < Mweak � 5M�weak
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Un
In other universes!
From the pages of
THE WEAKNESS WAY OF LIFE
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Harnik, Kribs & Perez, ’06Image: AJ & Perez, op. cit.
WEAKLESS UNIVERSE, CONT.
Harnik, Kribs & Perez, ’06Image: AJ & Perez, op. cit.
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BARYOGENESIS
Why was Universe formed with more matter than antimatter?
Requires breaking charge-parity (CP) symmetry
Weak sector of SM breaks CP (Kobayashi & Maskawa ’73, Nobel Prize ’08) but by far too little to explain observed matter abundance
Whatever explains baryogenesis here could also work in weakless universe
Weakless universes may have heavy relic baryons and leptons
Might cause trouble, or not
Plausible to find some weakless universes without heavy relics
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�⇥b ⇥ 10�2�⇤b�⇤b � 10�10
WHY DO WE SEE A WEAK FORCE?
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In Standard Model, particle masses given by
Gauge hierarchy problem:
Observed masses suggest scale-invariant distribution for yf’s
vacuum expectation value of the Higgs field
Our v2 is ~ 1032 times too small
Yukawa coupling
p(v) � v2
M2pl
for 0 < v < Mpl
p(y) � 1y
Common feature of complex dynamics
(“Benford’s Law”)
QCDΛ
1 GeV 10 GeV100 MeV10 MeV1 MeV0.1 MeV0.01 MeV 100 GeV
u d bs c te μ τ
Mweak
cf. Donoghue, Dutta, Ross & Tegmark, ’09
mf =1�2yfv
HIERARCHY PROBLEM IN MULTIVERSE
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Oram Gedalia, AJ & Gilad Perez, arXiv:1010.2626
M
y
weak
f
10-15
10-12
10-9
10-6
10-3
10-18
MPl
eud
10-21
10-24
FLAVOR PUZZLE
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CSM = det�YuY †
u YdY†d
⇥� 10�22
Summing over ;lavors:
“Jarlskog determinant:”
For generic, order-‐one complex matrices, we’d have:
CSM � 0.1
Large hierarchies of masses and mixings
Not subject to large quantum corrections, but certainly not anthropic!
Lflavor = �(yu)ij q̄iL�cuj
R � (yd)ij q̄iL�dj
R + h.c.
FLAVOR DYNAMICS
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Flavor puzzle should be resolved dynamically
30 years of work on possible models generically gives
y � �Q
ε universal, Q flavor-dependent (cf. Froggat & Nielsen ’79; Dimopoulos & Susskind ’79; Eichten & Lane ’80; Kaplan ’91; Arkani-‐Hamed & Schmaltz ’99)
For p(Q) � Qn
Far more likely to live in weakless universe, unless n < -‐ 21
If n < -‐ 21, getting observed Yukawas drives ε << 1
Could be hierarchy problem of its ownOram Gedalia, AJ & Gilad Perez, arXiv:1010.2626
OUTLOOK
Possible that fundamental theory won’t predict observed world uniquely
Statistics in multiverse & anthropic principle may be relevant to theoretical physics
Our current ideas of the string theory landscape / inflationary multiverse seem too unrestrictive
Our nuclear interactions do not seem typical of congenial universes
Still need better understanding of dynamics of multiverse (or whatever’s out there)
Expect new physics at LHC
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THANK YOU!39
Cornelis Saftleven,(Dutch, circa 1612 - 1681),The College of Animals,oil on canvasDallas Museum of Art