Lemaître and

the first ideas

of a finite-age

universe

H. Kragh,

Centre for Science Studies,

Aarhus University

Based on Clausius’ version of the 2nd law of

thermodynamics, the heat death and the entropic creation

argument were widely discussed in the period ca. 1880-

1910

I. The entropy of the world increases continually

II. Our present world is not in a high-entropic state

III. Hence the world must be of finite age

……………………………………………………………

IV. If the world had a beginning, it must have been created

V. If created, there must be a creator – God

• How big is the Milky Way?

• What is the distance to

the nebulae?

• Is there anything material

outside the Milky way?

• What is the structure &

size of the spiral nebulae?

In 1923-24 Hubble discovered

cepheids in the Andromeda (he

first thought it was a nova),

which vindicated the Island

Universe theory.

Do the redshifts of the spiral nebulae

vary systematically with their distances?

?krz

M. Slipher 1912+: galactic redshifts

Hubble diagrams

1929, H ≅ 500 km/s/Mpc

1931, H ≅ 558 km/s/Mpc

Einstein’s model, which he thought was the

solution of the field equations:

static; filled with matter; spherical;

finite volume; includes cosmological

constant.

Einstein’s cosmological field equations

Alexander Friedmann, “Über die Krümmung des Raumes,”

Zeitschrift für Physik 10 (1922), 377-386.

Friedmann showed that Einstein’s equations have

dynamical solutions, corresponding to, e.g., expanding and

cyclical worlds. Although he spoke of die Zeit seit der

Erschaffung der Welt, he did not express preference for

any particular model, and he did not compare the models

with astronomical data.

Friedmann was fascinated by cyclic or periodic

models, for which (Λ = 0; M = 5 1021 msun) he

calculated a period of about 1010 years.

Georges Édouard Lemaître

physicist and priest, pioneer of big-bang cosmology

The incredible

shrinking constant

Lemaître 1927 H0 ≅ 625 km/s/Mpc

Hubble 1931 H0 ≅ 558 km/s/Mpc

WMAP 2010 H0 = 70.1 km/s/Mpc

L-E model

The Lemaître-Eddington model (1927; 1930)

The universe (which has always existed) starts in an

Einstein state and approaches a de Sitter state.

L-model

“Objects separating faster than the velocity of light are cut

off from any causal inference on one another, so that in time

the universe will become virtually a number of disconnected

universes no longer bearing any physical relation to one

another.”

Classical multiverse

A. S. Eddington, “The expansion of the

universe,” MNRAS 91 (1931), 412-416.

Lemaître’s “primeval atom” universe of 1931 Finite-space and finite-age model. Keeps cosmological constant (Λ > 0),

which secures a “stagnation phase” and solves the time-scale difficulty.

Nature, May 9, 1931 The world started in a

radioactive explosion of a

“primordial atom” of density

as an atomic nucleus.

Typed draft, with

deleted reference

to God.

Archive Lemaître,

Louvain de la

neuve.

Avoiding the ghost of determinism

A. Einstein, “Zum kosmologischen Problem der allgemeine Relativitätstheorie,”

Sitzungsber. Preuss. Akad. Wiss. 1931: 235-237.

A. Einstein & W. de Sitter, ”On the relation between the expansion and the mean density

of the universe,” Proc. Nat. Acad. Sci. 18 (1932), 213-314.

Big bang models without a big bang…

“Those solutions where the universe expands and

contracts successively while periodically reducing

itself to an atomic mass of the dimensions of the

solar system, have an indisputable charm and

make one think of the Phoenix of legend”

Lemaître, “L’univers en expansion,”Ann. Soc. Scient.

Bruxelles 53 (1933), 51-85.

”I do not see how a useful

cosmology can be built by

starting from the Phenix

nucleon gas”

Lemaître, ”The primeval atom hypothesis…,” Solvay Proceedings (1958).

Lemaître and the phoenix-universe

”According to Lemaître’s theory, all the matter in the universe was once packed

within a single, gigantic atom, which … burst, its fragments forming the stars of

which our universe is built. …”

Lemaître’s big bang as described in Popular Science Monthly 1932.

”I do not think that many cosmogonists have yet been

persuaded by the theory of Lemaître. It is usually

regarded as a brilliantly clever jeu d’esprit rather

than a sober reconstruction of the beginning of the

world.”

E. W. Barnes, Scientific Theory and Religion (Cambridge, 1933).

”Lemaître’s hypothesis is the wildest speculation of all

… an example of speculation run mad without a shred

of evidence to support it.”

J. H. Plaskett, ”The expansion of the universe,” J. Roy. Soc. Canada 27

(1933), 235-252.

”We must be careful to keep

our judgements uninfected by

the demands of theology and

unswerved by human hopes and

fears.”

”The discovery of models,

which start expansion from a

singular state of zero volume,

must not be confused with a

proof that the actual universe

was created at a finite time in

the past.”

Tolman warns against

”the evils of autistic and

wishfulfilling thinking” in

cosmology

http://www.time.com/time/magazine/0,9263,7601270425,00.html

G. Lemaître & M.S. Vallarta, ”On Compton’s

latitude effect of cosmic radiation,” Phys. Rev.

43 (1933), 87-91.

The study of cosmic rays

”gives some experimental

support to the theory of

super-radioactive origin of

the cosmic radiation.”

”The last two thousand

million years are slow

evolution … ashes and

smoke of bright but very

rapid fireworks.”

Computational cosmology?

In their calculations of energies and

trajectories of charged particles in

the Earth’s magnetic field, seen as a

test of the primeval-atom hypothesis,

Lemaître and Vallarta made use of

MIT’s differential-analyzer computer

developed by Vannevar Bush.

”Compton’s result … gives some experimental

support to the theory of super-radioactive origin

of the cosmic radiation.”

Lemaître & Vallarta 1933

Lemaître and the cosmological constant (I)

G. Lemaître, ”Evolution of the expanding universe,” Proc. Nat. Acad. Sci. 20 (1934), 12-17.

Lemaître and the cosmological constant (II)

”Since I have introduced this term I

had always a bad conscience. … I

found it very ugly indeed … and am

unable to believe that such an ugly

thing should be realized in nature.”

Einstein to Lemaître, 26 Sep 1947

”The theory remains open to new

developments which may connect the

theoretically unknown value of the

cosmical constant with other constants

of physics. It is a logical convenience

found by a happy accident.”

Lemaître to Einstein, 3 Oct 1947

A theory not only of stellar energy production, but

also of the origin of the universe in a state

characterized by extreme heat [~ 2 × 1011 K] and

density [~ 1015 g/cm3].

Weizsäcker attempted to ”draw from the

frequency of distribution of the elements

conclusions about an earlier state of the universe

in which this distribution might have originated.”

– But he did not combine his theory with the

Friedmann equations of general relativity.

“Über Elementumwandlungen im Innern der

Sterne, II,” Phys. Zs. 39 (1938), 633-646.

Nuclear archaeology

To reconstruct the history of the

universe by means of

hypothetical cosmic or stellar

nuclear processes, and to test

these by examining the resulting

pattern of element abundances.

Elements are ”hieroglyphs” of

the cosmic past.

Pioneered by C.F. von Weizsäcker,

G. Gamow and R. Alpher, relying

on empirical data of V.

Goldschmidt.

Scientific legitimation of divine creation?

In 1951 pope Pius XII argued

that modern cosmology

(Lemaître; Gamow) confirmed

the Christian dogma of

creation.

Physics and astronomy had

proved the ”existence of an

unchangeable Ens a se,” which

has created the world out of

nothing.

Lemaître was unhappy with

the pope’s address. Pius XII G. Lemaître