Who discovered the
expansion of the Universe?
Søren Larsen
Department of Astrophysics /
IMAPP, Radboud University, Nijmegen
s.larsen@astro.ru.nl
The discovery that we live in an expanding Universe was arguably one of
the most fundamental scientific breakthroughs of the 20th century. The popular
version of the story, as it is often told, goes something like this: Upon
having developed his theory of General Relativity (GR) in 1915, Albert Einstein
found that the solutions to the field equations did not allow for a static
Universe, but instead required the Universe to be contracting or expanding. As
this seemed unsatisfactory to Einstein, he introduced an extra term involving
the cosmological constant, Λ, in the field equations. The effect of Λ is to counteract gravity, thereby allowing for a
static Universe. Over a decade later, in 1929, Edwin Hubble showed that the
radial velocities of galaxies are proportional to their distances. The Universe
indeed appeared to be expanding, and the relation between distance and velocity
(or redshift) has since been known as “Hubble's law”. The original prediction
of a non-static Universe thus appeared to be correct after all, and Einstein
renounced the introduction of the cosmological constant as his “greatest
blunder”. Recently, there has been a growing awareness of the work by Georges
Lemaître, and it has been proposed to rename the velocity-distance relation to
the “Hubble-Lemaître law”.
The real story is more complicated and involves many other individuals
who made substantial contributions throughout the 1920s, with Hubble entering
the stage relatively late. Indeed, the story starts even before Einstein had
finalised GR, at a time when nobody was concerned with the dynamics of the
Universe at large. In the following I attempt to summarise some of the main
milestones in roughly chronological order. I will focus on the period up to
about 1930, after which the existence of the velocity-distance relation and its
interpretation as evidence of an expanding Universe was no longer in much
doubt. I hope that I have not overlooked any major contributions, but would
welcome any comments on this text.
A reasonable place to start is 1913. In this year, Vesto Slipher at
Lowell Observatory published a short paper in which he presented his
spectroscopic observations of the Andromeda nebula, M31, which he had carried out in the fall of 1912 [1]. (Non-stellar
diffuse objects were then generally referred to as nebulae. I will use the term
“nebulae” and the modern term “galaxies” interchangeably.) Slipher's aim was to
measure the radial velocity of the nebula via the Doppler shift of its spectral
lines, a technique which had by then been successfully applied to individual
stars already for a few decades. It was known that stars typically have Doppler
shifts indicating positive or negative radial velocities of up to a few tens of
km/s, and there were hints that the dispersion depended on spectral class. However, obtaining good spectra for
non-stellar diffuse objects was a much more challenging enterprise.
Slipher was not the first to obtain a spectrum of M31, which was known
to exhibit absorption lines similar to those observed in the spectrum of the Sun
[2], but nobody had
so far measured the radial velocity of any galaxy. Using a spectrograph
optimised for this purpose and exposures lasting up to 3 nights, Slipher was
able to record several spectra of sufficient quality to measure a radial
velocity of about -300 km/s for M31, entirely consistent with modern
measurements. He noted that the
magnitude of the velocity was the greatest observed so far, and that this “raises the question whether the velocity-like displacement might not be
due to some other cause, but I believe we have at present no other
interpretation for it.”. He further remarked that “extension of the work to other objects promises results of fundamental
importance, but the faintness of the spectra makes the work heavy and the
accumulation of results slow”.
By 1915, Slipher had collected spectra of 15 spiral nebulae [3]. There were two
surprises: first, as was true for M31, the velocities were all much greater in
an absolute sense than those typical of stars. Second, M31 turned out to be
atypical in having a negative radial velocity; nearly all other spiral nebulae
had positive radial velocities of up to several hundred km/s. Slipher had no
real explanation for these results, but suggested that there might be a north-south
asymmetry with larger positive velocities on average for nebulae on the
southern side of the Milky Way (M31, M32, and M33 constituted half of the
northern sample), and that edge-on nebulae appeared to have higher velocities.
In hindsight, these trends were mostly spurious and a result of the small
sample size. What was clearly significant, however, was Slipher's observation
that “the average velocity of the spirals is about 25
times the average stellar velocity”. At this point, two years before Einstein's
paper on the cosmological implications of GR, Slipher had no way of
anticipating the cosmological significance of his measurements. He briefly
discussed the velocities of the nebulae in the context of contemporary work on
individual stars, noting that “This great velocity would
place these nebulae a long way along the evolutional chain if we undertook to
apply the Campbell-Kapteyn discovery of the increase in stellar velocity with
“advance” in stellar spectral type”.
It is worth pausing to reflect on the state of knowledge in 1915. Not
only did the notion of an expanding Universe still lie in the future, but the
very concept of the Universe as we understand it today had yet to emerge. While
the hypothesis of “island universes” dates back to the 18th century, the nature
of spiral nebulae and their relation with the Milky Way was still largely
unknown in 1915 - there wasn't a clear concept of Galactic versus
extra-Galactic astronomy, let alone cosmology in the modern sense.
Apparently Slipher's radial velocity measurements were not completely
uncontroversial. In 1917, he felt compelled to publish a note responding to a
suggestion by Reynolds that the velocities might not be reliable [4]. Slipher carried
on with his work and kept finding increasingly large velocities (up to 1800
km/s in 1918 for NGC 584, which would hold the record for more than a decade).
He also observed other types of objects, and found that globular clusters did
not share the same large radial velocities as the spiral nebulae, but were
instead intermediate between individual stars and the spirals in this respect.
Einstein's 1917 paper, in which the cosmological constant was
introduced, did not mention Slipher's radial velocity measurements or any other
specific astronomical observations, apart from general remarks about stellar
velocities being small compared to the speed of light [5]. In the same
year, W. de Sitter published an alternative solution to the field equations, in
which the density of matter in the Universe was assumed to be negligible. In
modern terminology, de Sitter's model has ΩΛ = 1 and Ωmatter = 0, which leads to an
exponentially expanding Universe, although the coordinates chosen by de Sitter
made this point somewhat obscure. Nevertheless, de Sitter realised that his
model predicted a relation between distance and redshift. He wrote “... the frequency of light-vibrations diminishes with increasing
distance from the origin of co-ordinates. The lines in the spectra of very
distant stars or nebulae must therefore be systematically displaced towards the
red, giving rise to a spurious radial velocity.” [6].
One of the major novel concepts in GR was, of course, the notion of
curved space-time, and it was an intriguing idea that it might be possible to
determine the radius of curvature from astronomical observations. In de
Sitter's model, with his choice of coordinates, both space and time were curved
and the radius of curvature Rc was
related to the redshift z and
distance D. Although World War I made
communication more difficult, de Sitter was evidently aware of Slipher's
measurements, and he listed radial velocities for three spirals for which
Slipher's velocities had been confirmed by other observers (Pease at Mount
Wilson, Moore at Lick). In addition to M31, these were NGC 1068 (+925 km/s) and
NGC 4594 (+1185 km/s). However, distances to spiral nebulae were still unknown
so de Sitter could only guess. His guess was 100 kpc, from which he derived a
radius of Rc=3×1011 AU
(about 1.5 Mpc). While he admitted that
“this result, derived from only three nebulae, has
practically no value”, determining the radius of curvature would be a
recurrent theme in several studies over the coming years.
A brief intermezzo about distances: it is often stated or implied that
the problem of the distances to spiral nebulae was first solved with Hubble's
discovery of Cepheid variables in M31 in 1923 (published in 1925). However, it
is worth noting that Knut Lundmark, while working on his PhD thesis in Uppsala,
estimated the distance to M31 to be about 200 kpc already in 1919, using
observations of novae [7]. While
Lundmark's distance to M31 was about a factor of four too small compared to
modern measurements, it was similar to the distance derived by Hubble from
Cepheids several years later. Lundmark's paper appears to have had relatively
little impact at the time, perhaps because it also included a wide range of
distances estimated by other methods (some of which were much further from the
correct value). We shall return to Lundmark shortly.
The now familiar (locally) linear relation between redshift and
distance was first given explicitly by H. Weyl in 1923 for de Sitter's model [8]. He expressed
the relation as Δλ/λ = tan(D/R) for wavelength λ, distance D and radius of
curvature Rc. In the limit of D << Rc, this is essentially “Hubble's law”, v = H0 D, but expressed in terms of the curvature radius
instead of what we would today call H0.
Like de Sitter, Weyl was clearly aware of Slipher's measurements, remarking: “Concerning the relation of our result to experience, namely the strong
redshifts of the spectral lines of spiral galaxies found by astronomers, I
refer to Eddington in his new book.”. Eddington's book from
1923 [9] contains a
chapter in which Einstein's and de Sitter's models are discussed in detail, and
also includes a table with 41 radial velocity measurements obtained by Slipher.
In the book, Eddington cautiously remarked that “The great
preponderance of positive (receding) velocities is very striking; but the lack
of observations of southern nebulae is unfortunate, and forbids a final
conclusion.”, but he proceeded to discuss the interpretation of the positive
radial velocities in the context of de Sitter's model. Essentially the same
formula for the velocity-distance relation was given by L. Silberstein in 1924 [10]. Silberstein's paper is interesting in that it
attempts to use the velocity-distance relation as a distance indicator, albeit
on somewhat shaky grounds: Silberstein attempted to derive the curvature radius
from observations of globular clusters, and then applied it to estimate the
distances to spiral nebulae using Slipher's radial velocity measurements. This
is a reminder that observational cosmology was still very much in its infancy,
and it was not yet clear which objects were the best cosmological probes.
Already in the early 1920s, astronomers were starting to look for
correlations between Slipher's radial velocity measurements and various
properties of the galaxies. The predominantly positive radial velocities had
caught the attention of C. Wirtz in Kiel already in 1918 [11]. Wirtz commented that it appeared as if the system
of spiral nebulae was drifting away from the solar system with a mean velocity
of 656 km/s, but also pointed out that this interpretation relied on the
assumption that the shifts of the spectral lines were caused by the Doppler
effect. In 1922, Wirtz used a compilation of 29 radial velocity measurements
available by then to show that the radial velocities tended to increase with
decreasing apparent brightness of the galaxies (increasing apparent magnitude) [12]. By 1924, 42 radial velocities were available, and
Wirtz found a strong inverse correlation between the apparent diameters of the
spirals and their radial velocities. He wrote “Er bleibt also so
kein Zweifel, daß die positive Radialbewegung der Spiralnebel mit zunehmender
Entfernung ganz erheblich anwächst” – “There is no doubt that
the positive radial velocities of the spiral nebulae increase considerably with
increasing distance” [13]. Wirtz discussed these results in the context of de
Sitter's model (with a reference to Eddington's book), but did not appear to be
aware of the prediction that the redshift-distance relation should be linear.
Instead, he gave the relation as v =
2200 - 1200 log Dm for velocity v in km/s and apparent diameter Dm in arcminutes, implying a logarithmic
dependence of the velocity on distance. In 1936, Wirtz published a brief note
reminding his peers of these results [14]. Plots of his data are given by Seitter &
Duerbeck [15].
Knut Lundmark's papers from 1924 and 1925 addressed a wide range of
issues in the nascent field of extragalactic astronomy [16][17]. In the 1924 paper, entitled “The determination of the curvature of space-time in de Sitter's world”,
Lundmark plotted the radial velocities of the spiral nebulae (“mainly due to the wonderful spectrographic work performed at the Lowell
Observatory by Dr. V. M. Slipher”) versus their distances
relative to that of M31 (based on apparent diameters and magnitudes). The plot
showed “that there may be a relation between these two
quantities, although not a very definite one.” Lundmark reiterated here
his best estimate of the distance to M31 as 200 kpc, but suggested that the
correct value might turn out to be closer to 500 kpc. He also investigated
velocity-distance relations for other types of objects, but commented that “Dr. Silberstein has not given, and will probably not be able to give,
any justification for the use of the velocities of the globular clusters for a
determination of R”. In the 1925 paper, Lundmark fitted the
velocity-distance relation with a quadratic function, obtaining v = 513 + 10.365 D - 0.047 D2 for D
in units of the distance to M31, and remarked about the coefficient m=-0.047
that “It is thought that m, although inaccurately known,
still expresses a real phenomenon.”. If this were indeed
true, the radial velocities would reach a maximum of 2250 km/s at 110 times the
distance of M31.
G. Strömberg carried out an analysis similar to Lundmark's, and
concluded that “the correlation-coefficients between distance
and radial velocities give no clear evidence of curvature in either De Sitter's
or Silberstein's sense” [18].
While de Sitter's model could account for the positive redshifts of the
spiral nebulae, it remained unsatisfactory in that galaxies (and other objects)
were treated merely as test particles in an otherwise empty Universe.
Einstein's model, on the other hand, contained matter, but was static.
Eddington commented that “It seems natural to regard
de Sitter's and Einstein's forms as two limiting cases, the circumstances of
the actual world being intermediate between them.”. Yet, it was not
immediately obvious how to find intermediate models.
That Einstein's and de Sitter's models were special cases of a more
general set of non-static solutions of the field equations had, in fact, been
demonstrated by Alexander Friedman in 1922 [19]. Friedman derived the equations governing the
dynamics of the Universe that now bear his name, and found that the solutions
included expanding and oscillating Universes that contained matter. He also
noted that the expanding solution implied a finite age of the Universe. In 1924
he extended the analysis to cases of negative curvature. For several years,
however, Friedman's papers went largely unnoticed, and they did not explicitly
discuss the distance-velocity relation. Indeed, the 1922 paper ends by
concluding that our knowledge is insufficient to determine which of the models
is the correct one. It is well known that Einstein did not particularly like
Friedman's expanding models [20][21].
In a paper published in 1925, G. Lemaître discussed various strange
properties of de Sitter's solution, and showed that it could be recast in the
now familiar interpretation of an exponentially expanding Universe with no
curvature [22]. He (re-)derived the locally linear
distance-redshift relation and wrote: “Our treatment
evidences this non-statical character of de Sitter's world which gives a
possible interpretation of the mean receding motion of spiral nebulae”. However, he
concluded that “De Sitter's solution has to be abandoned, not
because it is non-static, but because it does not give a finite space without
introducing an impossible boundary”. The same year, Lemaître
presented the paper at a meeting of the American Philosophical Society, and
also arranged to talk to Hubble about extragalactic distances [23]. Later, in 1927, Lemaître published a paper in
which he showed that Einstein's and de Sitter's models were special cases of a
more general set of solutions (apparently unaware of Friedman's earlier work)
and that a linear distance-redshift relation was expected not only for the de
Sitter model [24]. In the same paper, Lemaître combined 43 radial
velocities (mostly from Slipher, as usual) with estimates of the distances to
provide an estimate of the slope of the velocity-distance relation, about 625
km/s/Mpc. The distances were based on Hubble's estimate of the mean absolute
magnitude of the galaxies, M = -15.2,
published the previous year [25], so it is not surprising that Lemaître’s expansion
coefficient was very similar to that determined by Hubble a couple of years later.
In his 1927 paper, Lemaître did mention the work of Lundmark and
Strömberg, noting the large scatter in their velocity-distance relations, which
had its origin in the still very uncertain distances. There is no indication that Lemaître found a
significantly smaller scatter, although the use of Hubble's estimate of the
absolute magnitudes allowed him to put the distances on an absolute scale with
more confidence (though not necessarily more accuracy) than others before him.
He did not claim that the data actually demonstrated a linear velocity-distance
relation, but simply divided the average velocity by the average distance of
the galaxies in the sample. In the 1931 English translation of the paper [26], which was published in the Monthly Notices at the
request of Eddington, Lemaître omitted the paragraph in which the numerical
value of the expansion coefficient was discussed, noting in his letter to the
editor that “I did not find advisable to reprint the
provisional discussion of radial velocities which is clearly of no actual interest.” [27].
Lemaître‘s paper provided an
important demonstration that de Sitter's model is not unique in predicting a
distance-redshift relation. Still, Lemaître‘s
preferred model differed from our modern cosmological picture. In the model
considered in the 1927 paper, the Universe was curved and started with a finite
radius in the infinite past. Lemaître estimated the initial radius to be about
20 times less than the current value, so that the largest observable redshift
would be z=20. He had thus found a solution to the problem
of infinite radius, which had bothered him in the de Sitter model, and the
solution allowed for an expanding Universe containing matter.
H. P. Robertson was addressing the difficulties with de Sitter's
solution around the same time as Lemaître. In a paper published in 1928,
Robertson showed that de Sitter's model was naturally interpreted as an
exponentially expanding Universe [28], apparently independently of Lemaître’s 1925 paper.
Like Lemaître, Robertson also showed that the resulting space-time was flat,
but he further realised that the volume accessible to observations would
nevertheless be contained within a finite horizon R which would be related to the expansion rate. Robertson wrote: “Comparing the data given by Hubble concerning the value of l [distance]
for the spiral nebulae with that of Slipher concerning the corresponding radial
velocities, we arrive at a rough verification of (17) [the linear
distance-velocity relation] and a value R=2×1027 cm.”. This
corresponds to an equivalent Hubble constant of 460 km/s/Mpc. Robertson
referenced Hubble's 1926 paper for the distances and Eddington's book for
Slipher's velocities, and although it is not clear how exactly these data were
combined to determine the value for R,
or to what extent they supported the idea of a linear distance-velocity
relation, it is thus not surprising that Robertson found an expansion
coefficient similar to that obtained by Lemaître the previous year, and by
Hubble a year later. In 1929, Robertson showed that Einstein's and de Sitter's
models were special cases and again discussed the redshifting of the light from
distant sources [29]. The paper includes references to Friedman and also
contains a note (in the context of de Sitter's solution) that “I have since discovered that these coordinates have also been employed
by G. Lemaitre, Jour. of Math. and Phys., 4, 188 (1925), and wish to take this
opportunity to correct the omission of reference to this work in my previous
paper.”. However, Robertson was at this point apparently not aware of Lemaître’s
1927 paper.
At last, this brings us to Hubble's work. Before discussing the 1929
paper on the distance-velocity relation, it is interesting to consider Hubble's
1926 paper on Extra-galactic Nebulae [25], in which he introduced his classification scheme
and discussed a variety of properties of the nebulae - morphology, absolute and
apparent magnitudes, sizes, spatial distribution, etc. - in considerable
detail. At the end of the paper, Hubble estimated the radius of curvature using
the mean density obtained from the galaxy counts and assuming Einstein's static
model. Radial velocities were only mentioned in a brief remark that mainly
served to argue that M31 and M32 are physically associated: “M32 is generally assumed to be associated with the great spiral M31,
because the radial velocities are nearly equal and are unique in that they are
the only large negative velocities that have been found among the
extra-galactic nebulae”. There is little hint that the velocity-distance
relation was on Hubble's mind at this point.
This had clearly changed by 1929, when Hubble published his first paper
on the velocity-distance relation [30]. Only a few radial velocities had been added since
the mid-1920s, with 46 measurements available to Hubble. These were combined
with individual distances to 24 galaxies, mostly using data from the 1926
paper, and based on observations of (what Hubble assumed to be) individual
supergiant stars. The scatter in the resulting velocity-distance relation
remained considerable, but Hubble's somewhat cautious remark that “For such scanty material, so poorly distributed, the results are fairly
definite.” nevertheless seems justified. The highest radial velocity remained
the 1800 km/s of NGC 584, and it was clear that the best way to establish a
more convincing velocity-distance relation was to push the measurements to
greater distances, and hence higher velocities if the relation was real. Such
efforts were already underway at Mount Wilson.
Overall, the 1929 paper has the character of a relatively brief
preliminary report (the paper is only 6 pages long, including the tables with
velocity and distance measurements and the figure showing the velocity-distance
relation). Perhaps Hubble felt some urgency to publish the results, and one can
discuss whether he gave due credit to earlier work. He did briefly mention
Lundmark's 1925 paper (with the quadratic fit to the velocity-distance
relation) but not the 1924 paper in which the velocity-distance relation was
plotted. Van den Bergh [31] has suggested that Hubble may have downplayed
Lundmark's work because of a strained personal relationship between the two
astronomers (Hubble had accused Lundmark of plagiarizing his galaxy
classification scheme [25]). However, Wirtz's papers were not mentioned
either. Although these were published in German, this would hardly have been a
hindrance for Hubble, who was quite proficient in that language [31].
One may also wonder about the lack of reference to the previous
determinations of the slope of the relation by Lemaître and Robertson. Neither
of these papers was published in the mainstream literature, and it is possible
that Hubble had not read them. However, Humason later recalled that Hubble had
come back from the IAU General Assembly in 1928 in Leiden, “rather excited about the fact that two or three scientists over there,
astronomers, had suggested that the fainter the nebulae were, the more distant
they were and the larger the redshifts would be.”. According to van den
Bergh, some of the astronomers that Hubble would likely have met included de
Sitter, Lemaître, Lundmark, Shapley, and Smart [31]. Furthermore, Robertson had obtained his PhD in
1925 from Caltech and worked there as an assistant professor from 1927-1928
before moving to Princeton. So it appears likely that
Hubble was aware of the work by both Lemaître and Robinson. On the other hand,
their contributions were primarily theoretical, and theoretical considerations
were delegated to only a brief paragraph at the end of Hubble's 1929 paper. He
remarked: “The outstanding feature, however, is the possibility
that the velocity-distance relation may represent the de Sitter effect, [...].
In the de Sitter cosmology, displacements of the spectra arise from two
sources, an apparent slowing down of atomic vibrations and a general tendency
of material particles to scatter.”. This interpretation
refers to the original version of de Sitter's model, and Hubble's formulation
is reminiscent of the wording in Eddington's book: “De Sitter's theory gives a double explanation of this motion of
recession: first, there is the general tendency to scatter ... second, there is
the general displacement of spectral lines to the red in distant objects due to
the slowing down of atomic vibrations.”. One gets the impression
that Hubble had some familiarity with de Sitter's model - by far the most
established at the time - and felt compelled to mention it, but that he did not
consider it important to dwell on the differences between that and the more
recent models by Lemaître and Robertson.
The omission of reference to Lemaître is somewhat more conspicuous in
Hubble's book ``The realm of the nebulae'', published in 1936 [32]. Here Hubble reviewed the early observational work
on the velocity-distance relation by Wirtz (“the leader in the
field”), Lundmark, Strömberg, and others in some detail. He also mentioned
the theoretical work by de Sitter, Friedman, and Robertson, with a reference to
“Robertson's authoritative review” from 1933.
Robertson's review discussed Lemaître’s work to the extent that it could hardly
be overlooked, although it did not mention the comparisons with observations
done by either Lemaître or Robertson himself. By 1936, of course, the English
translation of Lemaître‘s 1927 paper had appeared, but
without the paragraph on the radial velocity measurements.
From 1930 onwards, the existence of the linear velocity-distance
relation rapidly became an established fact. New radial velocity measurements
for more distant galaxies were being obtained by Humason at Mount Wilson with
the help of a new fast spectrograph camera employing a Rayton lens at the
Cassegrain focus of the 100-inch telescope. Using these data, de Sitter
extended the velocity-distance relation to about 8000 km/s in 1930, confirming
a clear correlation [33]. De Sitter
mentioned Lemaître‘s 1927 paper and wrote that “I hope to return to the discussion of this ingenious solution in a
separate communication.” By 1931, Humason had added 46 new radial velocity
measurements, with the highest velocities extending to 19700 km/s [34]. Together with distance estimates based on the
integrated magnitudes of the brightest cluster galaxies, these measurements
firmly established the linear velocity-distance relation beyond any doubt,
although the inferred slope remained much too steep [35].
It is well known that Hubble's distances were underestimated for a
variety of reasons. Most of the objects that he assumed to be supergiant stars
were not actually individual stars, but HII regions, as demonstrated in 1956 by
Humason, Mayall, & Sandage [36]. The possibility that the brightest sources were
not individual stars was acknowledged in the Hubble & Humason 1931 paper (“The use of the brightest stars as a criterion of distance has been
criticized on the ground that clusters and groups at such remote distances
would not be distinguished from single stars.”), and again in The realm of the nebulae, although it was
dismissed perhaps a bit too easily. Another important issue was the calibration
of Cepheid period-luminosity relation. This is a story on its own, as discussed
by Baade [37]. Nevertheless, taking into
account both of these issues, the value of the Hubble constant
determined by Humason et al.\ in 1956 was still 180 km/s/Mpc, more than twice the
current best estimate. Unlike the radial velocities, which follow directly from
the spectra and were basically correct from the beginning, it took a long time
to get the distances right, and establishing the value of the Hubble constant
to ever greater precision remains a work in progress.
On the theoretical side, it became clear from the wide range of
possible models that measuring the local slope of the velocity-distance
relation alone was insufficient for determining the curvature of the Universe.
Einstein & de Sitter succinctly summarised the situation in 1932: “…we must conclude that at the present time it is possible to represent
the facts without assuming a curvature of three-dimensional space. The
curvature is, however, essentially determinable, and an increase in the
precision of the data derived from observations will enable us in the future to
fix its sign and to determine its value.” [38].
It should be evident that there is no unique answer to the question of
who discovered the expansion of the Universe. The velocity-distance relation
emerged gradually during the 1920s through the efforts of several authors, with
theoretical and observational work progressing in parallel. Evidence of the
predominantly positive radial velocities of spiral nebulae was available even
before the formulation of GR and was known to theorists. Establishing the linear
relationship with distance took longer, but this did not deter several authors
from using the available data to estimate the curvature of the Universe. In the
context of de Sitter's model, this was equivalent to determining the slope of
the distance-velocity relation (what we now call the Hubble constant), although
it was not usually formulated as such. While de Sitter's model implied an
expanding Universe, this was not immediately recognised.
Hubble's 1929 paper was one of several important milestones, but more
important than the paper itself was the resulting extensive follow-up programme
that was initiated at Lick, Mount Wilson, and Palomar to extend the radial
velocity measurements to greater distances, thereby corroborating the earlier
results. By 1931, no doubt could remain
about the existence of a linear distance-redshift relation, and the programme
culminated with the publication of 800 radial velocities by Humason et al. in
1956, extending to 60 000 km/s. In the introduction, the authors paid tribute
to Hubble (who had passed away three years earlier), writing: “These spectrographic and photometric data are now available in
considerable numbers ... chiefly as the result of Hubble's inspiring influence
on his colleagues.”
The importance of the work by Lemaître and Robertson (as well as
Friedman) lay primarily in their theoretical contributions, which marked a
departure from de Sitter's model - the only model which, up until then, could
account for the radial velocity measurements. Both authors gave the modern
interpretation of the velocity-distance relation as a signature of an expanding
Universe, and provided quantitative estimates of the slope of the relation
prior to Hubble's 1929 paper. However, it is difficult to argue that they
demonstrated the existence of the linear distance-redshift relation much more
convincingly than Wirtz or Lundmark before them (neither Lemaître nor Robertson
actually published plots of the distance-velocity relation).
With the realisation that the possible solutions to the field equations
were not restricted to those of Einstein and de Sitter, it became clear that
determining the curvature of space required measuring the departures of the velocity-distance relation from linearity. Many
of the main observational tests to accomplish this were laid out in detail by
Sandage in 1961 [39], but definitive results were only obtained in the
last decade of the 20th century. It is somewhat ironic that, after a century of
attempts to determine the curvature, it remains “possible to
represent the facts without assuming a curvature of three-dimensional space.”
[1] V. M. Slipher, “The radial velocity of the
Andromeda Nebula,” Lowell Obs. Bull., vol. 1, 1913.
[2] J. Scheiner, “On the spectrum of the great
nebula in Andromeda.,” Astrophys. J., vol. 9, p. 149, Mar. 1899.
[3] V. M. Slipher, “Spectrographic
Observations of Nebulae,” Pop. Astron., vol. 23, pp. 21–24, 1915.
[4] V. M. Slipher, “Radial velocity
observations of spiral nebulae,” Obs., vol. 40, pp. 304–306, 1917.
[5] A. Einstein, “Kosmologische Betrachtungen
zur allgemeinen Relativitätstheorie,” Sitzungsberichte der Königlich
Preußischen Akad. der Wissenschaften, p. 142, 1917.
[6] W. de Sitter, “On Einstein’s Theory of
Gravitation and its Astronomical Consequences. Third Paper.,” Mon. Not. R.
Astron. Soc., vol. 78, no. 1, pp. 3–28, Nov. 1917.
[7] K. Lundmark, “Die Stellung der
kugelförmigen Sternhaufen und Spiralnebel zu unserem Sternsystem,” Astron.
Nachrichten, vol. 209, no. 24, pp. 369–380, 1919.
[8] H. Weyl, “Zur allgemeinen
Relativitätstheorie,” Phys. Zeits., vol. 24, pp. 230–232, 1923.
[9] A. S. Eddington, The mathematical
theory of relativity. Cambridge University Press, 1923.
[10] L. Silberstein, “The Curvature of de
Sitter’s Space-Time derived from Globular Clusters,” Mon. Not. R. Astron.
Soc., vol. 84, no. 5, pp. 363–366, Mar. 1924.
[11] C. Wirtz, “Über die Bewegungen der
Nebelflecke,” Astron. Nachrichten, vol. 206, no. 13, pp. 109–116, 1918.
[12] C. Wirtz, “Notiz zur Radialbewegung der
Spiralnebel,” Astron. Nachrichten, vol. 216, no. 24, pp. 451–452, 1922.
[13] C. Wirtz, “De Sitters Kosmologie und die
Radialbewegungen der Spiralnebel,” Astron. Nachrichten, vol. 222, no. 2,
pp. 21–26, 1924.
[14] C. Wirtz, “Ein literarischer Hinweis zur
Radialbewegung der Spiralnebel,” Zeitschrift für Astrophys., vol. 11, p.
261, 1936.
[15] W. C. Seitter and H. W. Duerbeck, “Carl
Wilhelm Wirtz - Pioneer in Cosmic Dimensions,” ASP Conf. Ser., vol. 167,
p. 341, 1999.
[16] K. Lundmark, “The determination of the
curvature of space-time in de Sitter’s world,” Mon. Not. R. Astron. Soc.,
vol. 84, p. 747, 1924.
[17] K. Lundmark, “The Motions and the Distances
of Spiral Nebulae,” Mon. Not. R. Astron. Soc., vol. 85, no. 8, pp.
865–894, Jun. 1925.
[18] G. Stromberg, “Analysis of radial velocities
of globular clusters and non-galactic nebulae.,” Astrophys. J., vol. 61,
p. 353, Jun. 1925.
[19] A. Friedman, “Über die Krümmung des Raumes,”
Zeitschrift für Phys., vol. 10, no. 1, pp. 377–386, Dec. 1922.
[20] M. Heller, “Friedman’s Cosmological Views,” Acta
Cosmol., vol. 13, p. 65, 1985.
[21] H. Nussbaumer, “Einstein’s conversion from
his static to an expanding universe,” Eur. Phys. J. - Hist., vol. 39,
pp. 37–62, 2014.
[22] G. Lemaitre, “Note on de Sitter’s Universe,”
J. Math. Phys., vol. 4, pp. 188–192, 1925.
[23] S. Mitton, “Georges Lemaitre: Life, Science
and Legacy.” 2016.
[24] G. Lemaître, “Un Univers homogène de masse
constante et de rayon croissant rendant compte de la vitesse radiale des
nébuleuses extra-galactiques,” Ann. la Société Sci. Bruxelles, pp.
49–59, 1927.
[25] E. P. Hubble, “Extragalactic nebulae.,” Astrophys.
J., vol. 64, p. 321, Dec. 1926.
[26] G. Lemaitre, “A Homogeneous Universe of
Constant Mass and Increasing Radius accounting for the Radial Velocity of
Extra-galactic Nebulae,” Mon. Not. R. Astron. Soc., vol. 91, no. 5, pp.
483–490, Mar. 1931.
[27] M. Livio, “Mystery of the missing text
solved,” Nature, vol. 479, no. 7372, pp. 171–173, Nov. 2011.
[28] H. P. Robertson, “On relativistic
cosmology,” London, Edinburgh, Dublin Philos. Mag. J. Sci., vol. 5, pp.
835–848, 1928.
[29] H. P. Robertson, “On the foundations of
relativistic cosmology,” Proc. Natl. Acad. Sci., vol. 15, pp. 822–829,
1929.
[30] E. Hubble, “A relation between distance and
radial velocity among extra-galactic nebulae,” Proc. Natl. Acad. Sci.,
vol. 15, no. 3, pp. 168–173, Mar. 1929.
[31] S. van den Bergh, “Discovery of the
Expansion of the Universe,” J. R. Astron. Soc. Canada, vol. 105, p. 197,
Aug. 2011.
[32] E. P. Hubble, The realm of the nebulae.
New Haven and London: Yale University Press, 1936.
[33] W. de Sitter, “On the magnitudes, diameters
and distances of the extragalactic nebulae and their apparent radial
velocities,” Bull. Astron. Institutes Netherlands, vol. 5, p. 157, 1930.
[34] M. L. Humason, “Apparent Velocity-Shifts in
the Spectra of Faint Nebulae,” Astrophys. J., vol. 74, p. 35, Jul. 1931.
[35] E. Hubble and M. L. Humason, “The
Velocity-Distance Relation among Extra-Galactic Nebulae,” Astrophys. J.,
vol. 74, p. 43, Jul. 1931.
[36] M. L. Humason, N. U. Mayall, and A. R.
Sandage, “Redshifts and magnitudes of extragalactic nebulae.,” Astron. J.,
vol. 61, p. 97, Apr. 1956.
[37] W. Baade, “The Period-Luminosity Relation of
the Cepheids,” Publ. Astron. Soc. Pacific, vol. 68, p. 5, Feb. 1956.
[38] A. Einstein and W. de Sitter, “On the
Relation between the Expansion and the Mean Density of the Universe,” Proc.
Natl. Acad. Sci., vol. 18, no. 3, pp. 213–214, Mar. 1932.
[39] A. Sandage, “The Ability of the 200-INCH
Telescope to Discriminate Between Selected World Models.,” Astrophys. J.,
vol. 133, p. 355, Mar. 1961.