In this paper we show that other models of a Universe in dynamical equilibrium without expansion had predicted this temperature prior to Gamow. Moreover, we show that Gamow’s own predictions were worse than these previous ones.
Before begining let us list briefly some important historical information which help to understand the findings. Stefan found experimentally in 1879 that the total bolometric flux of radiation F emitted by a blackbody at a temperature T is given by F=s T4, where s is now called Stefan-Boltzmann’s constant (5.67 x 10-8 Wm-2K-4). The theoretical derivation of this expression was obtained by Boltzmann in 1884. In 1924 Hubble established that the nebulae are stellar systems outside the Milky Way. In 1929 he obtained the famous redshift-distance law.
"Captain Abney has recently determined the ratio of the light from the starry sky to that of the full Moon. It turns out to be 1/44, after reductions for the obliqueness of the rays relative to the surface, and for atmospheric absorption. Doubling this for both hemispheres, and adopting 1/600000 as the ration of the light intensity of the Moon to that of the Sun (a rough average of the measurements by Wollaston, Douguer and Zöllner), we find that the Sun showers us with 15,200,000 time more vibratory energy than all the stars combined. The increase in temperature of an isolated body in space subject only to the action of the stars will be equal to the quotient of the increase of temperature due to the Sun on the Earth’s orbit divided by the fourth root of 15,200,000, or about 60. Moreover, this number should be regarded as a minimum, as the measurements of Captain Abney taken in South Kensington may have been distorted by some foreign source of light. We conclude that the radiation of the stars alone would maintain the test particle we suppose might have been placed at different points in the sky at a temperature of 338/60 = 5.6 abs. = - 207° .4 centigrade. We must not conclude that the radiation of the stars raises the temperature of the celestial bodies to 5 or 6 degrees. If the stars in question already has a temperature that is very different from absolute zero, its loss of heat is much greater. We will find teh increase of temperature due to the radiation of the stars by calculating the loss using Stefan’s law. In this way we find that for the Earth, the temperature increase due to the radiation of the stars is less than one hundred-thousandth of a degree. Furthermore, this figure should be regarded as an upper limit on the effect we seek to evaluate."
Of course, Guillaume’s estimation of a 5-6 K blackbody temperature may not have been the earliest one, as Stefan’s law had been known since 1879. Moreover, it is restricted to the effect due to the stars belonging to our own galaxy.
We now quote from Eddington’s book, The Internal Constitution of the Stars (1988), published in 1926. The last chapter of this book is called "Diffuse Matter in Space" and begins discussing "The Temperature of Space":
Chapter XIII
DIFFUSE MATTER IN SPACE
The Temperature of Space.
256. The total light received by us form the stars is estimated to be equivalent to about 1000 stars of the first magnitude. Allowing an average correction to reduce visual to bolometric magnitude for stars of types other than F and G, the heat received from the stars may be taken to correspond to 2000 stars of apparent bolometric magnitude 1.0. We shall first calculate the energy-density of this radiation.
A star of absolute bolometric magnitude 1.0 radiates 36.3 times as much energy as the sun or 1.37 x 1035 ergs per sec. This gives 1.15 x 10-5 ergs per sq. cm. per sec. over a sphere of 10 parsecs (3.08 x 1019 cm.) radius. The corresponding energy-density by the velocity of propagation and amounts to 3.83 x 10-16 ergs per cu. cm. At 10 parsecs distance the apparent magnitude is equal to the absolute magnitude; hence the energy-density 3.83 x 10-16 corresponds to apparent bolometric magnitude 1.0.
Accordingly the total radiation of the stars has an energy-density
2000 x 3.83 x 10-16 = 7.67 x 10-13 ergs / cm3.
By the formula E=s T4 the effective temperature corresponding to this density is
3° 18 absolute
In a region of space not in the neighbourhood of any star this constitutes the whole field of radiation, and a black body, e.g., a black bulb thermometer, will there take up a temperature of 3° 18 so that its emission may balance the radiation falling on it and absorbed by it. This is sometimes called ‘temperature of interstellar space.’
One important aspect to emphasize here is that Eddington’s estimation of a temperature of 3.18 K was not the first one, as Guillaume had obtained a similar figure by 30 years earlier. Although Eddington did not quote Guillaume or any other author, it is clear that he was here following someone’s else derivation. This is indicated by the sentences ""The total light received by us from the stars is estimated [by whom?] to be ..." and "This is sometimes called [by whom?] the ‘temperature of interstellar space.’ "These sentences show that others had also arrived at this result. It is very probable that in the fifty years between Stefan’s law (1879) and Eddington’s book (1926) others arrived at the same conclusion independent of Guillaume’s work (1896).
Another point to bear in mind is that Eddington and Guillaume were discussing the temperature of interstellar space due to fixed stars belonging to our own galaxy, and not of intergalactic space. Remember that Hubble only established the existence of external galaxies beyond doubt in 1924.
In 1928 R.A. Millikan and Cameron (1928) found that the total energy of cosmic rays at the top of the atmosphere was one-tenth of that due to starlight and heat. In 1933 E. Regener (1933) concluded that both energy fluxes should have essentially the same value. This is a very important result with far reaching cosmological implications: It dedicates that the energy density of starlight due to our own galaxy is in equilibrium with the cosmic radiation, which for the most part is of extragalactic origin. It has always been difficult to know exactly the origin of the cosmic rays, but the fact that a major part of its components originated outside our galaxy was inferred from another measurement of Millikan and Cameron (1928). In this work they showed that the intensity of the radiation coming from the plane of the Milky Way was the same as that coming from a plane normal to it. This isotropy clearly indicated an extragalactic origin.
Regener’s work in general has been described briefly by Rossi (1964) as follows:
In the late 1920s and early 1930s the technique of self-recording electroscopes carried by balloons into the highest layers of the atmosphere or sunk to great depths under water was brought to an unprecedented degree of perfection by the German physicist Erich Regener and his group. To these scientists we owe some of the most accurate measurements ever made of cosmic-ray ionization as a function of altitude and depth.
In his work of 1933, Regener says the following (we are here replacing the term Ultrastrahlung – ultraradiation – which Regener and others utilized at that time by the expression "cosmic radiation", as this radiation is called nowadays):
However, the density of energy produced by cosmic
rays, which is nearly equal to the density of light and
heat emitted by the fixed stars, is very interesting from
an astrophysical point of view. A celestial body with the
necessary dimensions to absorb the cosmic rays – in
case of a density of 1, a body with a diameter of several
meters (5 meters of water absorb 9/10 of the cosmic rays)
– will be heated by cosmic rays. The increase in
temperature will be proportional to the energy of
absorbed cosmic rays (SU) and
the surface (O). The temperature of the body will
increase until the heat it emits – in case of black
body radiation s
. T4 . O – reaches the same
value. We then obtain a final temperature of T = 
. Substituting
numerical values we obtain 2.8 K.
This, according to Regener (1933), would be the temperature characteristic of intergalactic space, since in this region the light and heat from any galaxy would be negligible.
The following year Nernst (1938) published another paper discussing the radiation temperature in the Universe. Here he arrived at a temperature in intergalactic space as 0.75 K. Once more he discusses Regener’s work and asserts that the cosmological redshift is not due to a Doppler effect.
In the works of Eddington, Regener, Nernst and others to follow, it is important to stress the utilization of Stefan-Boltzmann’s law, which is characteristic of a black body radiation. Another point to be noted is that the energy densities of these radiations (due to star light and cosmic rays, for instance) have been measured to have the same value, indicating a situation of dynamical equilibrium. Sciama describes this situation as follows (Sciama 1971):
The cosmic ray flux almost certainly fills the Milky Way, and corresponds to an energy density in interstellar space of about 1 eVcm-3 (10-12ergcm-3). This is comparable with the energy of starlight, the turbulent kinetic energy density of the interstellar gas and, as we shall see later, the energy density of the interstellar magnetic field. This is the basis of our statement that the cosmic rays are dynamically important. They constitute a relativistic gas whose energy and pressure cannot be ignored. The near-equality of the various energy densities is probably no accident, but despite many attempts a full understanding of it has not yet been achieved.
And again on p. 185, after mentioning Penzias and Wilson’s discovery of a blackbody radiation of 3 K:
From a laboratory point of view 3 K is a very low temperature. Indeed to measure it the microwave observers had to use a reference terminal immersed in liquid helium. Nevertheless from an astrophysical point of view 3° K is a very high temperature. An universal black body radiation field at this temperature would contribute an energy density everywhere of 1 eVcm-3. As we saw in chapter 2 [p.25] this is just the energy density in our Galaxy of the various modes of interstellar excitation – starlight, cosmic rays, magnetic fields and turbulent gas clouds. So even in our Galaxy the cosmological background radiation would be for many purposes as important as the well-known energy modes of local origin.
We would like to make two remarks here. The first is that the main part of the cosmic radiation may have an extragalactic origin (see the comment on the work of Millikan and Cameron above), as may the magnetic fields which fill all space. If this is the case, then three extragalactic modes of excitation (the cosmic ray flux, magnetic fields and the CBR) would be in thermal equilibrium with one another and with energy fields generated inside our own galaxy, such as starlight and turbulent gas clouds. The easiest way to understand this fact is to conclude that the Universe as a whole is in a state of dynamical equilibrium.
The observation that in interstellar space only the very lowest rotational levels of CH, CH+, and CN are populated is readily explained by depopulation of the higher levels by emission of the far infrared rotation spectrum (see p. 43) and by the lack of excitation to these levels by collisions or radiation. The intensity of the rotation spectrum of CN is much smaller than that of CH or CH+ on account of the smaller dipole moment as well as the smaller frequency [due to the factor v4 in (I, 48)]. That is why lines from the second lowest level (K = 1) have been observed for CN. From the intensity ratio of the lines with K = 0 and K = 1, a rotational temperature of 2.3 K follows, which has of course only a very restricted meaning.
Obviously there is a great meaning in this result, although it was not recognized by Herzberg. This is discussed by Sciama (1971). It should only be stressed that once more, this result was not obtained utilizing the Big Bang cosmology.
§ 6. The Cosmological Red Shift
The fundamental character of the effect under consideration raises, necessarily, the question whether it might not also be the cause of the cosmological red shift which hitherto has been interpreted as a Doppler effect. In this case, the influence of the factor l in formula (1) is given explicitly from observations. The observed red shift D l ¤ l increases for every million parsec (= 3 x 1024 cm) by 0.8 x 10-3 which corresponds to a velocity increase of 500 km/sec when interpreted as a Doppler effect. An increase by 10 km/sec – corresponding to the red shift in a B2 star with TB = 20000 K – would correspond to a path ls = 1.2 x 1023 cm.
As far as the mean temperature TS of intergalactic space is concerned, apart from the knowledge that it must be near the absolute zero, no reliable information is available. If we may interpret the cosmological red shift in the same way as the stellar red shifts, the following equation should hold:
TS4lS = T4BlB , or TS = TB (lB/lS)1/4 . (3)
"Equation (3) shows that the value TS obtained in this way does not depend strongly on the choice of lB. Taking for lB the two extremes values 107 cm and 109 cm, we get the following two reasonable values
TS = 1.9 K and TS = 6.0 K
In a recent paper Gamow (1953) [Gamow, G., 1953, Dan. Acad.-Phys. Section, 27, No. 10] derives a value for TS of 7 K from thermodynamical considerations assuming a mean density of matter in space of 10-30 g/cm3.
One may have, therefore, to envisage that the cosmological red shifts is not due to an expanding Universe, but to a loss of energy which light suffers in the immense lengths of space it has to traverse coming from the most distant star systems. That intergalactic space is not completely empty is indicated by Stebbins and Whitford’s discovery (1948) [Stebbins, J., and Whitford, A.E., 1948, Ap. J., 108, 413] that the cosmological red shift is accompanied by a parallel unaccountable excess reddening. Thus the light must be exposed to some kind of interaction with matter and radiation in intergalactic space.
The main points to emphasize here are that Finlay-Freundlich proposed an alternative to the Doppler interpretation of the cosmological redshift and arrived at 1.9 K < T < 6.0 K for the temperature of intergalactic space. This is quite remarkable.
It is important to quote here max Born (1954) when discussing Finlay-Freundlich’s proposal that this new effect might be due to a photon-photon interaction, namely
.
.
An effect like this is of course not in agreement
with current theory. It has, however, an attractive
consequence. A simple application of the conservation
laws of energy and momentum shows that a collision of
this kind is only possible if a pair of particles with
opposite momenta is created. The energy of one of these
is hn ’ = -
h d n / 2, where d n
is given by (6) [d
n = - Cn 
/ n
o]. If the secondary particles
are photons their frequency is of the order of radar
waves (for the sun v’~ 2 x 109 sec-1,
l ’ ~ 15
cm). Thus the red-shift is linked to radio-astronomy.
We need only remember here the work of Penzias and Wilson 11 years later with a horn antenna built to study radio waves which found the CBR with a characteristic wavelength of 7 cm ... This must be considered a highly successful prediction by Max Born!
In the second of these works, where the present the details of these calculations, they said the following (our emphasis in bold):
In accordance with eq. (4) [r rr m-4/3 = constant], the specification of r m’’ , r m’, and r r’, fixes the present density of radiation, r r’’. In fact, we find that the value of r r’’ consistent with eq. (4) is
r r’’ @ 10-22 g/cm3, (12d)
which corresponds to a temperature now of the order 5 K. This mean temperature for the Universe is to be interpreted as the background temperature which would result from the universal expansion alone. However, the thermal energy resulting from the nuclear energy production in stars would increase this value."
From this it is evident that their prediction in 1948 was T » 5 K and in 1949 they obtained a temperature greater than 5 K, although close to this value.
The only other prediction of this temperature by Gamow known to us prior to Penzias and Wilson discovery (beyond that of 7 K in 1953) was published by Gamow (1961) in his book The Creation of the Universe. The first edition of this book is from 1952, and here we quote from the revised edition of 1961, only four years before Penzias and Wilson. In this book there is only one place where he discusses the temperature of the Universe, namely [21, p.42, our emphasis in bold]:
The relation previously stated between the value of Hubble’s constant and the mean density of the Universe permits us to derive a simple expression giving us the temperature during the early stages of expansion as the function of the time counted from the moment of maximum compression. Expressing that time in seconds and the temperature in degrees (see Appendix, pages 142-143), we have:
Temperature = 
Thus when the Universe was 1 year old, and 1 million year old, its temperatures were 15 billion, 3 million, and 3 thousand degrees absolute, respectively. Inserting the present age of the universe (t = 1017 sec) into that formula, we find
Tpresent = 50 degrees absolute
Which is in reasonable agreement with the actual temperature of interstellar space. Yes, our Universe took some time to cool from the blistering heat of its early days to the freezing cold of today!
We discuss these predictions by Gamow and collaborators below.