Isaac Newton (1643--1727) (see the figure below: local link / general link: newton_principia.html) certainly thought in terms of an infinite or quasi-infinite (i.e., apparently infinite) universe filled with stars (No-374--377).
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In unpublished work,
Newton
tried to construct a physically consistent STATIC MODEL of such
an infinite universe
full of stars---using
Newtonian physics,
of course
(No-374--377).
However, what if there was an STATIC infinite universe with the stars uniformly spread out on average. It seemed likely to Newton that such a system could be NOT be in stable equilibrium (i.e., at rest and always returning to being at rest given any perturbation) given Newtonian physics. Any balance of gravitational forces in such universe would give an unstable mechanical equilibrium---any perturbation would start it evolving into clumps. Newton may have been thinking that an extra hypothesis was justified to stablize the universe.
However, as aforesaid, Newton left Newton's Newtonian Cosmology unpublished, and so probably felt it was all half-baked and perhaps wrong. He liked ALL-BAKED publications that were all right. Newton may NOT have been interested enough in Newton's Newtonian Cosmology to come to a good conclusion about it. He may have assumed and some of his contemporaries did assume that God actively intervened to save the universe collapsing into clumps (No-375).
In fact, the essential problem in Newtonian cosmology was how to deal with infinite quantities: e.g., infinite space and infinite mass. Pure Newtonian physics does NOT give an answer. Extra hypotheses were needed to extend Newtonian physics
Image 1 Caption:
statues of
Isaac Newton (1643--1727)
and
Gottfried Wilhelm von Leibniz (1646--1716),
Oxford University
Museum of Natural History,
University of Oxford,
Oxford,
England.
The rivals.
Actually, when Newton was very old in 1721, he was informed of Olbers' paradox (though NOT by that name) which seems to rule out an STATIC eternal infinite universe with the stars uniformly spread out on average (see Cosmology file: olbers_paradox.html). However, the elderly Newton does NOT to have done any further significant work on Newtonian cosmology.
In the 18th century,
Thomas Wright (1711--1786),
Immanuel Kant (1724--1804)
and Johann Heinrich Lambert (1728--1777)
all speculated on
Newtonian cosmology
(see Astronomer file:
immanuel_kant.html).
Image 2 Caption:
Johann Heinrich Lambert (1728--1777):
astronomer
mathematician,
philosopher,
physicist.
One of the first to theorize
that some of the
nebulae (historical usage)
were other galaxies
and to do
Newtonian cosmology.
Wright,
Kant
and Lambert
all theorized correctly that
the Milky Way
was supported against gravitational collapse
by rotation
around the
Milky Way
center of mass.
Remarkably this theory
was NOT widely accepted by
astronomers
from 18th century
to circa 1920s.
Many astronomers believed
the Milky Way was the
whole universe, finite or otherwise,
and was STATIC on average
(IAL 26: The Discovery of Galaxies: The Discovery
of Galaxies: An Example of the Process of the Scientific Method;
Bo-75).
However, this STATIC universe
was NEVER made into a consistent
Newtonian cosmology
(Bo-75).
A logically viable compromise
theory
between the various ideas just discussed was
an infinite empty-space
universe
consisting only of Newton's absolute space,
except for a finite
Milky Way rotating about its
center of mass.
But this seems physically/philosophically unsatisfying.
Why an infinite universe
just for the Milky Way?
To return to
Wright,
Kant
and Lambert:
they all thought that at least some of the
nebulae (historical usage)
were other galaxies.
What they thought of the size and stability and motion of
their respective universes of
galaxies would take
more research into their thinking than
yours truly feels it is worthwhile to pursue.
However, Kant
went beyond Newtonian physics
and pictured a
cyclic universe
(finite or NOT)
where there was a cycle of
conflagrations and rebirths of the
universe.
It seems likely that Kant
for his cyclic universe
was reaching far back to the
stoic physics of
Greco-Roman Antiquity (c.800 BCE--c.500 CE).
Image 3 Caption:
"Conceptual animation of both
(3-dimensional physical) space distortions
and time distortions near a
spherically symmetric
mass distribution
due to general relativity (1915)
presented
by Albert Einstein (1879--1955)." (Somewhat edited.)
The rotation
in the animation is just for
viewing: the system is NOT
rotating.???
The system exhibits the
Schwarzschild solution (1916),
the first
exact (analytic) solution
in general relativity discovered by
Karl Schwarzschild (1873--1916)
while serving at the
Russian Front
in World War I (1914--1918)
(Wikipedia: Karl Schwarzschild: Life).
Sad to say, Schwarzschild
and Alexander Friedmann (1888--1925)
were on the opposite sides of the line.
Modern cosmology
on the scale of the observable universe
is treated using
general relativity (1915)
or some extension of that.
However, below the scale of the
observable universe,
is the large scale structure
and that is almost always treated using using
Newtonian physics
for gravity
and large motions of
matter.
Why?
Newtonian physics
gives almost the same answers as
general relativity
and is much less computationally demanding.
The use of Newtonian physics
is NOT the limiting
error in
structure formation
computer simulations.
Other physical input and
numerical methods
are the limiting errors.
Of course, general relativistic
structure formation
computer simulations
have been done to prove the that use of
Newtonian physics
is NOT the limiting
error.
The upshot is that there is still a vast realm for
Newtonian physics
in modern cosmology.
What of on the scale of the
observable universe
and beyond that?
There general relativity
or some extension of that must be used.
Image 4 Caption:
Alexander Friedmann (1888--1925)
serving as an aviator
in Imperial Russian Air Service,
Imperial Russian Army,
World War I (1914--1918),
1916
Aug01.
A Russian-Soviet
aviator,
ballonist,
mathematician,
meteorologist,
physicist,
pioneering cosmologist,
and discoverer of the
eponymous
Friedmann equation
in 1922.
See also Astronomer file:
alexander_friedmann.html,
Wikipedia: Alexander Friedmann,
The MacTutor
History of Mathematics archive: Aleksandr Aleksandrovich Friedmann.
But for most research in modern
cosmology,
all that is needed from
general relativity
is the
Friedmann equation
(see Astronomer file:
alexander_friedmann.html).
The fundamentally correct derivation
of the Friedmann equation
is from general relativity
plus the assumptions of
the cosmological principle
and the perfect fluid
(see
IAL 30: Cosmology: Einstein, General Relativity, and the Einstein Universe:
Einstein's Simplifying Assumptions for the Einstein Universe).
The solution of Friedmann equation
is the
cosmic scale factor a(t)
which gives the scaling up of the
observable universe
as a function of
cosmic time t.
Of course, there are many solutions of
the Friedmann equation.
Analytic solutions
give the behavior for relatively simple evolutions of a(t)
and numerical solutions are needed otherwise.
In fact, the Lambda-CDM model
well after the radiation-matter equality time (t=51.7(8) kyr)
(i.e., well after the
(radiation era (inflation end 10**(-32) s ? -- 51.7(8) kyr))
is governed by
an analytic solution
(e.g.,
Jeffery
2026, p. 25???).
The Friedmann equation models
all naturally predict the
expansion of the universe
or the contraction of the universe.
A static universe
only occurs for a fine-tuned
of the cosmological constant (AKA Lambda, Λ)
(see
IAL 30:
Cosmology: Einstein, General Relativity, and the Einstein Universe).
Actually, the theoretical
Hubble's law
is a direct consequence of the
Friedmann equation.
Alexander Friedmann (1888--1925)
must have known this, but did NOT explicitly show it in his published works.
Georges Lemaitre (1894--1966)
is justly credited with the explicit
discovery
of the theoretical
Hubble's law
in 1927
(see Astronomer file:
georges_lemaitre_cartoon.html).
So both the theoretical
expansion of the universe
and Hubble's law were
predictions of Friedmann equation
before their observational
discovery
by Edwin Hubble (1889--1953).
In fact, with reasonable extra hypotheses,
the Friedmann equation
(and the 2nd Friedmann equation too)
can be derived from
Newtonian physics
plus the assumptions of
the cosmological principle
and the perfect fluid
also used in the
derivation
from general relativity.
We will NOT give NOR
explicate this
derivation.
However, the derivation is extremely
useful in understanding
the Friedmann equation
and in teaching it in
cosmology courses,
where, in fact, general relativity
is mostly skirted since one CANNOT do everything.
Remarkably, the
Newtonian physics
derivation
of the
Friedmann equation
was first done
in 1934
by William McCrea (1904--1999)
and E.A. Milne (1896--1950)
which was 12
years
after Alexander Friedmann (1888--1925)
first derived it in 1922
from general relativity
(Wikipedia: Friedmann equations;
Wikipedia:
Friedmann-Lemaitre-Robertson-Walker metric: Newtonian interpretation).
Could the
Friedmann equation
have been derived before
the discovery of
general relativity?
Yes. The Friedmann equation
could have been derived as early as the
18th century.
Johann Heinrich Lambert (1728--1777)
could have it if he had just followed the NOT very hard right mental path.
However, he could NOT have understood that
the integration constant
that turns up determines the
curvature of space since understanding this
integration constant
needs general relativity.
He would have thought of
Euclidean space (i.e., flat space)
universe.
Also, it was probably beyond his physical intuition
to hypothesize that
the Friedmann equation
does allow for the non-conservation of mass.
The hypothesis can just be introduced as wild speculation, but more physically motivated
path to it uses
thermodynamics,
E=mc**2,
and
general relativity
(or at least an extra
hypothesis instead of),
none of which we available to
Lambert.
Actually, the chief problem
18th century
and 19th century
astronomers had in a
derivation
of Friedmann equation
in Newtonian cosmology
was that they had to replace the assumption of
Newtonian absolute space
(the singular fundamental
inertial frame)
by the assumption
that all free-fall frames
unrotating with respect to the
observable universe
constituted an infinite set of
fundamental inertial frames
(see
Mechanics file:
frame_basics.html).
In practice, when doing
celestial mechanics
those 18th century
and 19th century
astronomers
effectively made this replacement all the time.
But they did NOT make the mental leap that it should be done in principle.
The mental leap was done by
Albert Einstein (1879--1955)
in deriving general relativity (1915).
The transverse distances getter shorter compared to the
radial distances as you go deeper into the
gravitational well due to
(3-dimensional physical) space distortions.
The clocks run slower compared to those of
outside observers the deeper you go into the
gravitational well
due gravitational time dilation.
Yours truly thinks this
animation is qualitatively accurate, but
will NOT swear to it.
Image 5 Caption:
Examples of interesting
cosmic scale factor solutions a(t):
the de Sitter universe (1917),
the Λ-CDM model
(the
standard model of cosmology (SMC)
since circa
1995:
e.g., Scott 2018, p. 10),
Einstein-de Sitter universe (1932)
(which is NEITHER the
Einstein universe (1917) NOR
the
de Sitter universe (1917)),
a linear growth solution
(e.g., the empty universe or Rh=ct universe (2011)),
and the
positive curvature universe (AKA closed universe).