03/12/2013 Oxford

Fundamental constants, physics and cosmology���

Jean-Philippe UZAN���

What is a constant?���

Constant : PHYS., Numerical value of some quantity that allows to characterize a body. Quantity whose value is fixed (e.g. mass and charge of the electron, speed of light) and that plays a central role in physical theories.

What is a constant?���

Constant : PHYS., Numerical value of some quantity that allows to characterize a body. Quantity whose value is fixed (e.g. mass and charge of the electron, speed of light) and that plays a central role in physical theories.

This definition asks more questions than it gives answers!������

- How many constants?��� - Are they all on the same footing?��� - What role do they play in laws of physics?��� - Can they vary? (according to the dictionary, NO!)���

Overview���

• Constants and the laws of physics��� ���

• Constants and general relativity������

• Constants and high energy physics���

• Micro-landscape������

• Fine tuning (some thoughts)���

Constants and physics���

Making a list of constants���

Studying the constant of a theory = To study the limits of this theory

Let us start to look in a book of physics (probably the best place to find constants) depends on when and by who the book was written

Any parameter not determined by the theories at hand It has to be assume constant (no equation/ nothing more fundamental ) Reproductibility of experiments.

It does not show our knowledge but our ignorance

How many fundamental constants should we consider today?

Reference theoretical framework���

The number of physical constants depends on the level of description of the laws of nature.

In our present understanding [General Relativity + SU(3)xSU(2)xU(1)]:

•  G : Newton constant (1) •  6 Yukawa coupling for quarks •  3 Yukawa coupling for leptons

•  mass and VEV of the Higgs boson: 2

•  CKM matrix: 4 parameters •  Non-gravitational coupling constants: 3 • Λuv: 1

•  c, ħ : 2 •  cosmological constant

22 constants 19 parameters

Number of constants may change���

This number is « time-dependent ».

« + » Neutrino masses

Add 3 Yukawa couplings + 4 MNS parameters = 7 more

Number of constants may change���

This number is « time-dependent ».

« + » Neutrino masses

« - » Unification

Add 3 Yukawa couplings + 4 MNS parameters = 7 more

Fundamental parameters ���&���

fundamental units���

Three classes of constants���

The classification depends on time!

•  Class A : characterizes a given physical system, e.g. : mass of the electron

•  Class B : characterizes a class of phenomena, e.g.: charge of the electron

•  Class C : universal constant, e.g.: speed of light, Planck constant, gravitation constant

Are all constants to be considered on the same footing?

The 3 fundamental constants played a role of concept synthesizers: they created bridges between concept that were incompatible before space & time spacetime particle & waves wave function

Change of classes and history of physics���

JPU, B. Leclercq, De l’importance d’être une constante (Dunod, 2005) translated as “The natural laws of the universe” (Praxis, 2008)

Λ

From units to constants���

Units systems were initially very anthropomorphic

They depend on some reference person Vary from a region to another, confusion of names etc…

French revolution 26 March 1791, pushed by Charles Maurice Talleyrand, the meter is defined as 1/40,000,000 of the length of a meridian

The metre���

International system of units���

From units to constants���

•  J.C. Maxwell (1870) « If we wish to obtain standards of length, time and mass which shall

be absolutely permanent, we must seek them not in the dimensions, or motion or the mass of our planet, but in the wavelength, the period of vibration, and absolute mass of these imperishable and unalterable and perfectly similar molecules. »

•  G. Johnstone-Stoney (1881) « Nature presents us with 3 such units »

•  Planck (1900) « It offers the possibility of establishing units for length, mass, time and

temperature which are independent of specific bodies or materials and which necessarily maintain their meaning for all time and for all civilizations, even those which are extraterrestrial and nonhuman, constants which therefore can be called fundamental physical units of measurement »

Proposal for the new SI���

http://www.bipm.org/en/si/new_si/

3 fondamental units

3

Synthetiser, limiting value,...

...

Constants

Dimensions (M, L, T)

Units (kg, m, s)

New theory ? constant ?

Fondamental parameters

Summary���

Any parameter not determined by the theories at hand - Hence, it depends on our knowledge of physics

All the constants do not have the same status - The change of status told us about the evolution of physics

We can define units from constants - Recent evolution in metrology and SI

We are left with pure numbers - Why are they constant? - Can we explain their value?

Constants and relativity���

Equivalence principle���

The equivalence principle in Newtonian physics

The deviation from the universality of free fall is characterized by

Second law:

Definition of weight

So that

Consider a pendumum of length L in a gravitational field g,

Then

Tests on the universality of free fall���

2014 MicroScope

Lunar laser ranging���

Current contraints���

On the basis of general relativity���

It is based on Einstein equivalence principle universality of free fall local Lorentz invariance local position invariance

The equivalence principle takes much more importance in general relativity

If this principle holds then gravity is a consequence of the geometry of spacetime

This principle has been a driving idea in theories of gravity from Galileo to Einstein

Not a basic principle of physics but mostly an empirical fact.

Underlying hypothesis

Equivalence principle •  Universality of free fall •  Local lorentz invariance •  Local position invariance

GR in a nutshell���

Physical metric

Gravitational redshift at 30 cm level���C. W. Chou,* D. B. Hume, T. Rosenband, D. J. Wineland, Science 329, 1630, (2010)

Time dilation Gravitational shift Clock B is lifted up by 33 cm

its rate is increased by 3. 4 10-17

Underlying hypothesis

Equivalence principle

Dynamics

•  Universality of free fall •  Local lorentz invariance •  Local position invariance

Relativity

GR in a nutshell���

Physical metric

gravitational metric

Solar system tests���C

ourtesy of G. E

sposito-Farèse Metric theories are usually tested in the PPN formalism

Perihelion shift of Mercury

Nordtvedt effect

Shapiro time delay

Light deflection

[Will, Liv. Rev. Relat. 2006-3]

Equivalence principle and constants���

In general relativity, any test particle follow a geodesic, which does not depend on the mass or on the chemical composition

Equivalence principle and constants���

In general relativity, any test particle follow a geodesic, which does not depend on the mass or on the chemical composition

1- Local position invariance is violated.

Imagine some constants are space-time dependent

Equivalence principle and constants���

In general relativity, any test particle follow a geodesic, which does not depend on the mass or on the chemical composition

2- Universality of free fall has also to be violated

1- Local position invariance is violated.

In Newtonian terms, a free motion implies d�p

dt= m

d�v

dt= �0

Imagine some constants are space-time dependent

Mass of test body = mass of its constituants + binding energy

d⇥p

dt= ⇥0 = m⇥a +

dm

d��̇⇥v

m�aanomalous

But, now

Needs to test GR���

•  The variation of the constants, •  the deviations from Newton law (or general relativity), •  the violation of the universality of free fall

are tied together.

Testing the constants, is testing gravity

There is a growing need to test general relativity on astrophysical scales

dynamics of galaxies and dark matter

acceleration of the universe and dark energy

but also theoretical motivations…

Constants ���and ���

high energy physics���

Field theory���

S[�, ̄, Aµ, hµ⌫ , . . . ; c1, . . . , c2]

Dynamical fields constants

The action is more than a list of symbols.���

Field theory���

If a constant is varying, this implies that it has to be replaced by a dynamical field

This has 2 consequences: 1- the equations derived with this parameter constant will be modified one cannot just make it vary in the equations

2- the theory will provide an equation of evolution for this new parameter

The field responsible for the time variation of the « constant » is also responsible for a long-range (composition-dependent) interaction

i.e. at the origin of the deviation from General Relativity.

[Ellis & JPU, gr-qc/0305099]

S[�, ̄, Aµ, hµ⌫ , . . . ; c1, . . . , c2]

Famous example: Scalar-tensor theories���

spin 2 spin 0

Motion of massive bodies determines GcavM not GM. Gcav is a priori space-time dependent

graviton scalar

Example of varying fine structure constant���

It is a priori « easy » to design a theory with varying fundamental constants

But that may have dramatic implications.

Consider

Requires to be close to the minimum

Violation of UFF is quantified by �12 = 2|⇥a1 � ⇥a2||⇥a1 + ⇥a2|

It is of the order of

Challenges���

Such terms and couplings arise naturally in many extensions of GR: - scalar-tensor theories of gravity - compactification of higher-dimensional theories - string theory: all dimensionless constants are expected to be dynamical

4D effective theory

Damour, Polyakov (1994)

Challenges: - Why are the constants so constant? (what is the stabilization mechanism at work) - Why have they stabilized to the particular values we observe?

Summary���

In string theory, the value of any (dimensionless) constant is effective - it depends on the geometry and volume of the extra-dimension - it depends on the dilaton

Newton Einstein String theory

Fixed spacetime Dynamical spacetime Dynamical spacetime

Fixed constants Fixed constants Dynamical constants

It opens a window on extra-dimensions Why do the constants vary so little ?

Constants allow to test the equivalence principle on astrophysical scales - time variations on cosmic scales can be easily obtained - BUT: constraints in Solar system are difficult to circonvene easily - link to dark-energy: window on the dynamics.

Structure of physical theories

Modules / energy scales / decoupling lower levels: constants / dissipation-entropy

Dirac (1937) Numerological argument G ~ 1/t

Kaluza (1919) – Klein (1926) multi-dimensional theories

Jordan (1949) variable constante= new Dynamical field.

Fierz (1956) Effects on atomic spectra Scalar-tensor theories

Savedoff (1956) Tests on astrophys. spectra

Lee-Yang (1955) Dicke (1957) Implication on the universality of free fall

Teller (1948)–Gamow (1948) Constraints on Dirac hypothesis New formulation

Scherk-Schwarz (1974) Witten (1987) String theory: all dimensionless Constants are dynamical

Oklo (1972), quasars... Experimental constraints

Micro-landscape���

Wall of fundamental constant���

[Olive, Peloso, JPU, 2010]

Idea: Spatial discontinuity in the fundamental constant due to a domain wall crossing our Hubble volume.

-Parameters - We assume only ξF is non vanishing BUT the scalar field couples radiatively to nucleons

Wall of fundamental constants (technical)���

Loop correction Finite temperature

Micro-landscape���

-1.5 -1.0 -0.5 0.5 1.0 1.5

0.5

1.0

1.5

V (�)

�

↵(�+), µ(�+), . . .

↵(��), µ(��), . . .

< RH

>> RH

Constants vary on sub-Hubble scales. - may be detected - microphysics in principle acessible

Constants vary on super-Hubble scales. - landscape ? - exact model of a theory which dynamically gives a distribution of fondamental constants - no variation on the size of the observable universe

Apparent fine tuning ���

Undistinguishable worlds���

Coarse graining���

In principle we can distinguish worlds in which the fine structure constant differs by 10-11. In practice, there is no natural physical phenomena (stars, atomic reaction,….) for which is affected by a variation of the fine structure constant by more than 10-7. All worlds in which a differs by e.g. 10-9 are « identical » until there is the emergence of observers that can construct high precision metrology experiments. When shall we say that the 2 worlds A & B are identical?

- A := B is a time dependent statement (depending on existence of observers, level of technological developments)

- I think that if we want to have worlds in which natural fundamental processes are different, a precision of order 10-5 on the constants is probably sufficient.

- This later statement is related to the anthropic domain

Anthropic domain & fine tuning���

Anthropic domain & fine tuning���

Fine tuning���

Many physical effects are sensitivive to the value of the fundamental constants.

The worst is the tuning of the cosmological constants

Coincidence ?

t0 � t� � tgal

N"

⌦m

⌦⇤

Q

D

↵,↵s,↵GPhysical parameters

Cosmological parameters They depend on extra-assumptions: -  Copernican principle -  Initial conditions

Formalizing the idea���

Both fundamental constants AND cosmological parameters appear in the discussion. We can distinguish:

- π: the values of fundamental constants [microphysics] - ω: cosmological including initial conditions [properties of cosm. solution] - localisation parameters: characterize that have been made by an observer and

which distinguish him from other observers, e.g. H0.

Micro-landscape���Anthropic domain & fine tuning���

One needs to evaluate p(π,ω|χ ∈ B0).

Conclusions���

Fundamental constants teach about��� the history of the contruction of physics��� the domain of validty of our theory [in particular general relativity]��� underlying level of description���

���23 fondamental constants -> 6 numbers���

genotype vs phenotype������How do we get some insight on the PDF of the constants?������In general constants are correlated������The anthropic domain is characterized by a local analysis���

Can we be sure that there are no other islands?���