Danish Institute for Advanced Study Lecture Series
Effective Field Theory of Gravity: When General Relativity and Quantum Mechanics Meet Alessandro Codello DIAS Universe
Friday, 28 March 2014 12:00, CP3 seminar room www.dias.sdu.dk
A TALE OF TWO FORCES from coulomb’s law to quantum gravity
electrostatics (gauss’s law)
V
S
flux of the electric field trough S is equal to the total electric charge in V
coulomb’s law
q Q
first published by Coulomb in 1785
coulomb’s law
q
Q 2 4πr E = �0 Q E= 4π�0 r2
Q
first published by Coulomb in 1785
coulomb’s law
q
Q 2 4πr E = �0 Q E= 4π�0 r2
Q
F = qE dV F =− dr Q V = 4π�0 r
first published by Coulomb in 1785
magnetostatics (gauss’s law)
S
flux of the magnetic field through S is zero (there are no magnetic monopoles!)
ampere’s law and lorentz’s force
2πrB = µ0 I
I
µ0 I B= 2πr
F = q(E + v × B)
faraday’s law
maxwell/ampere law
time dependent magnetic fields generate electric fields and vice versa!
vacuum maxwell’s equations
vacuum maxwell’s equations
wave equation...
...and there be light!
...and there be light!
1 8 −1 c= √ = 2.99792458 × 10 m s µ0 � 0
special relativity c time
space
understood by Einstein in 1905
special relativity c time
space
E = mc
2
fields of a moving charge 1 E∼B∼ 2 r 1 EB ∼ 4 r 1 4πr EB ∼ 2 → 0 r 2
a charge in uniform motion does not radiate...
radiation from an accelerating charge
radiation from an accelerating charge
q 1 E= 2 4π�0 R
� �� ˆ × R ˆ − v × a2 � v R ˆ R− c c c 1 � � � �3 + � �3 � R v v 2 ˆ ˆ γ 1−R· c 1−R· c � ��
� 1 ˆ � B = R × E� c ret
�
ret
radiation from an accelerating charge
radiation from an accelerating charge
radiation from an accelerating charge
classical electrodynamics
a theory of photons and electrons
quantum electrodynamics
�
�
�
Feynman diagrams (the sixties)
corrections to coulomb’s interaction
+
+ .. . photons are the mediators of electromagnetic interactions
vacuum polarization
empty space is a dielectric medium of electron-positron dipoles
running charge
an electric charge is screened by a cloud of electron-positron pairs
effective field theory
at low energy just a modified classical theory
gravity (gauss’s law)
V
S
flux of the gravitational field trough S is equal to the mass in V
newton’s law
G
foud by Isaac Newton in the 17th century
newton’s law
mM F = −G 2 r dV F =− dr
G
mM V = −G r
foud by Isaac Newton in the 17th century
gravitational radiation
only quadrupoles radiate
discovered indirectly by Hulse and Taylor in 1973 observing a system of binary pulsars
binary neutron stars
classical gravity
the source of the gravitational field is mass-energy and the field carries it: self-interaction!
.. .
.. .
+
+
+
+
+ .. .
+ .. .
+
+
+
+
+ .. .
+ .. .
=
=
curvature
energy–momentum
this incredible sum was performed by Deser 1973
general relativity
curvature
=
energy–momentum
developed by Albert Einstein in 1916
quantum gravity
.. .
.. .
quantum gravity
.. .
.. . G
c
�
corrections to newton’s interaction
corrections to newton’s interaction �
=
�
�
iκ 3 µν 2 µ ν µ ν µ ν Pαβ,γδ k k + (k − q) (k − q) + q q − η q 2 2 � � +2qλ qσ I λσ,αβ I µν,γδ + I λσ,γδ I µν,αβ − I λµ,αβ I σν,γδ − I σν,αβ I λµ,γδ � � � � � + qλ q µ ηαβ I λν,γδ + ηγδ I λν,αβ + qλ q ν ηαβ I λµ,γδ + ηγδ I λµ,αβ � � � µν, µν, 2 µν λ σ −q ηαβ I γδ + ηγδ I αβ − η q q (ηαβ Iγδ,λσ + ηγδ Iαβ,λσ ) � � λ + 2q I σν,αβ Iγδ,λσ (k − q)µ + I σµ,αβ Iγδ,λσ (k − q)ν � σν, σµ, −I γδ Iαβ,λσ k µ − I γδ Iαβ,λσ k ν � � � �� σµ, σµ, ρσ, ρσ, +q 2 I αβ Iγδ,σν + Iαβ,σν I αδ + η µν q λ qσ Iαβ,λρ I γδ + Iγδ,λρ I αβ � � � � 2 � 1 µν σµ, σν, µ 2 ν + k + (k − q) I αβ Iγδ,σ + I αβ Iγδ,σ − η Pαβ,γδ 2 � ��� − k 2 ηγδ I µν,αβ + (k − q)2 ηαβ I µν, γδ the truth behind Feynman diagrams...
corrections to newton’s interaction
V =−
� GM m r
G� G(M + m) 1+a + b + · · · c2 r c3 r 2
�
corrections to newton’s interaction
V =−
� GM m r
m3 [G] = Kg s2
G� G(M + m) 1+a + b + · · · c2 r c3 r 2 m2 Kg [�] = s
�
m [c] = s
corrections to newton’s interaction
V =−
� GM m r
41 G� G(M + m) 1+3 + + ··· 2 3 2 c r 10π c r
leading quantum corrections to newton’s law first computed in 1994 by John Donoghue
�
corrections to newton’s interaction
GM⊙ −6 ∼ 10 c 2 r⊙ G� −88 ∼ 10 2 3 c r⊙
sun
leading quantum corrections to newton’s law are incredibly small!
can we ever observe quantum gravity effects?
cosmos
can we ever observe quantum gravity effects?
cosmos maybe there are some inside here?
Thank you
