THE ORIGIN OF COSMIC RAYS¹

R. Millikan and G. Cameron, Pasadena.

1. Introduction. In our preceding communications² a curve of high “resolving power” was given, expressing the dependence of the ionizing power of cosmic rays on depth. There we also showed that this curve testifies to the existence in the spectrum of cosmic rays of two sharp bands, separated from one another by approximately three octaves. The absorption coefficient for the band with the greater wavelength, which also plays the principal role in the ionization of the atmosphere, is approximately \(\mu = 0.35\), whereas the short-wave band consists of radiation of two wavelengths with \(\mu = 0.08\) and \(\mu = 0.04\), the second being, approximately, twice as intense as the first.

These results were obtained from an empirical analysis of the ionization curve, independently of any theory whatever. They represent the general type of solution required by the curve itself. Hence one important circumstance follows immediately: we must abandon the assumption we made at one time that cosmic rays arise in collisions of rapidly moving (with velocities

¹ Phys. Rev., October 1928.

² Millikan and Cameron, Nature, 7 July 1928; Science, 13 Apr. 1928, 401; Phys. Rev., 31, 921, 1928. The decomposition of the curve into three sharp spectral bands was presented to the Physics Circle of the California Institute on 16 Feb. 1928. The proof that these bands arise in the formation of atoms was publicly set forth on 16 March at a meeting of the Association of the California Institute and printed on 17 March in the proceedings of the Association.

up to \(216\,000\,000\) V) electrons with atomic nuclei. Indeed, in processes of this kind rays with a continuous, and not a band, spectrum would arise. Thus the existence of bands in the spectrum of cosmic rays, to which our curve bears witness, shows that these rays arise in some act of an intranuclear character, or in an act of transition from one sharply defined value of energy to another, accompanied by radiation similar to a quantum jump.

1. The general significance of the band spectrum of cosmic rays. After we had carried out the above-mentioned empirical analysis, prepared its exposition in the form in which it appeared in the June issue of Physical Review, and reported the results obtained (February 16, 1928) at a meeting of the physics seminar of the Norman Bridge Laboratory1—without in any way basing ourselves, in doing so, on any assumptions or suppositions whatever about the causes of the observed phenomena—we took up the question of finding a possible theoretical explanation for the appearance of the bands and of the energies connected with them.

It is known that if Einstein’s special theory of relativity is correct, in favor of which speaks the brilliant confirmation of the results predicted by it, not one of which has been found to be erroneous, then every radiation of energy by a system of atoms must be accompanied by the loss by this system of an equivalent quantity of mass. The expression of this fact is the universally known and constantly used equation of Einstein (1905) \(Mc^{2}=E\), where \(M\) is the mass in grams, \(c\) is the velocity of light in cm/sec, and \(E\) is the energy in ergs. Thanks to Aston’s latest very precise investigations2, and also thanks to earlier determinations of atomic weights, we know rather accurately the masses of all atoms and can therefore calculate the energies released—

—occurring in various kinds of atomic transformations. From the energy, by means of Einstein’s equation, one may pass to the frequency, and then, through Dirac’s formula1, to the penetrating power obtained in such a transformation of radiation. These calculations show that the only processes in which rays with the enormous penetrating powers we observe can arise are acts of formation of helium, oxygen, silicon, and iron from hydrogen (in the case of the last two elements—also from helium).

An additional possibility here might be the complete annihilation of hydrogen, i.e. the union of its proton with an electron. However, two arguments speak against this. First, there is no place in the observed ionization curve for such radiation, since it would be 4–5 times more penetrating than the hardest of all the above-mentioned observed radiations. Consequently, if such radiation existed, the ionization caused by it would enter into those 2.4 ions which give the “zero point” of the electroscope. But these 2.4 ions represent only 0.1 of the total ionization at the top of the curve, equal to 21 ions (this value corresponds to the ionization at a depth of 1 m below the surface of Lake Gem). Thus our hypothetical radiation cannot have any appreciable effect on the ionization curve above the value 2.4; in the lower part of the curve it can possess only a weak intensity in comparison with the softer observed rays. Secondly, such hypothetical radiation would be monochromatic and in no case could possess that banded structure which is observed in cosmic rays. Regardless of whether the process of annihilation of the hydrogen atom by the union of its nucleus with an electron actually occurs or not, it may be excluded from among the possible causes of the origin of the observed cosmic rays. As will be shown in more detail below, neither

in any of the remaining atomic transformations no amount of mass sufficient for the formation of cosmic rays disappears, apart from the indicated processes of atom formation.

3. Energy liberated in the processes of the disintegration of atoms. Radioactivity. It is easy to show that not one of the radioactive transformations can lead to the emergence of cosmic rays. Indeed, Einstein’s equation says that in such transformations only rays of substantially less penetrating power can arise. This fact is directly attested by Aston’s curve reproduced here (Fig. 1). In a radioactive process, i.e., in a process of decay, the products of decay are either an α-particle and an atom with a mass 4 units less than the mass of the original atom, or a β-particle and an atom of practically the same mass as the original one. In the latter case, as also in the case of simultaneous emission of β- and γ-rays, there is no appreciable change of mass. The only appreciable source of energy in radioactive transformations can be the change of mass connected with the emission of an α-ray. The case of the radioactivity of potassium and rubidium, which emit only β-rays, does not contradict this general rule, since all methods known up to now have led to the conclusion that in these transformations no appreciable change of mass and energy occurs.

It may be said with great certainty that the values of the mass of the proton in the atoms of all elements lie close to Aston’s smooth curve shown in Fig. 1. It follows at once from this that no atom with atomic weight less than 80 can emit α-rays. In fact, this curve has a minimum at approximately 80; consequently the act of ejecting an α-particle by an atom lighter than 80 must entail an increase in the total mass, i.e., in other words, it cannot cause the emission of energy. In other words, the process of decay of atoms with atomic weight less than 80, proceeding by the ejection of α-particles or protons, must be an endothermic process, and not an exothermic one,

i.e. it cannot occur spontaneously. This fact refutes the assertion, often made during the last 30 years, that there exists a possibility of obtaining energy by the decomposition of commonly occurring elements. If Aston’s curve is at least approximately correct, then only very heavy elements are capable of releasing energy upon decay, and elements with atomic weight greater than 80 occur very rarely. All of them taken together constitute no more than 1% of the total amount of matter1.

Fig. 1. Aston’s curve. Along the abscissa axis are plotted the atomic masses of the elements; along the ordinate axis—the packing coefficients (“packing fraction”), multiplied by 10,000, i.e. the mass defects referred to one proton \(\times 10^4\).

Aston’s curve makes it possible to derive easily the condition which a heavy atom must satisfy in order to be able to release energy by emitting an \(\alpha\)-particle. This release can take place only on that part of the curve which rises so rapidly with increasing atomic weight that

\[ n \cdot \Delta y > 4(0.00054 - y_n). \]

Here \(n\) is the atomic weight of the atom emitting the \(\alpha\)-particle; \(\Delta y\) is the difference of the ordinates at the points \(n - 4\) and \(n\); \(y_n\) is the ordinate corresponding to atomic weight \(n\), and 0.00054 is the value of \(y\)

for helium (see Fig. 1), i.e. the apparent mass of the proton in the $\alpha$-particle1.

This equation shows not only that only very heavy atoms can disintegrate by ejecting $\alpha$-particles and thereby lose energy, but also allows us to estimate the maximum hardness, i.e. the penetrating power, of the radiation that may arise in one or another process of radioactive decay.

Let us consider, for example, the ejection of an $\alpha$-particle by an atom of thorium. The curve shows that at $n = 232$, $y_n = 0.00031$, i.e. that the increase in the mass of the $\alpha$-particle by one gram-atom, caused by its departure from the thorium nucleus, is equal to

\[ 4(0.00054 - 0.00031) = 0.00092. \]

The loss of mass in the residue of the disintegrated thorium atom is

\[ \Delta y = 0.000034 \cdot 228 = 0.007752. \]

Consequently, the total loss of mass in the emission of the $\alpha$-ray is

\[ 0.00775 - 0.00092 = 0.00683 \ \text{g per gram-atom}. \]

According to Einstein’s equation, such a loss of mass must entail a loss of energy in the amount of $0.00683\,c^2$ erg per gram-atom. The total energy released in each act of ejection of an $\alpha$-particle is obtained by dividing this quantity by Avogadro’s number $6.062 \times 10^{23}$, i.e. it is equal to $1.004 \times 10^{-5}$ erg. But, on the other hand, we know that the energy of the fastest $\alpha$-particles ejected by radium, according to the latest tables of Kovarík and McKeehan2, is equal to 7,700,000 V, which is equivalent to $1.2 \times 10^{-5}$ erg. The energy of the $\alpha$-particles ejected by ThC is 14% greater than this value. The same tables say that the “upper limit” of the energy of the $\beta$-rays ejected by the decay products of thorium and radium is 7,540,000 V or $1.2 \times 10^{-5}$ erg3. Thus, the equa-

Einstein’s equation does in fact allow us, with great accuracy—lying within the limits of Aston’s measurement errors—to determine the maximum energy released in a given radioactive process.

Generally speaking, the loss of mass upon the emission of an α-particle supplies energy not only for α-, but also for β- and γ-rays, since these radiations in themselves are not connected with any appreciable loss of mass. Consequently, in most cases—as is also evident from the radioactive tables—the energy of α-, β-, and γ-rays is considerably less than the maximum values indicated above. Indeed, the energy of the γ-rays of radium or thorium corresponds to no more than 2,000,000 V1 (for RaC′ and ThC″), and their absorption coefficient is 4.0 per 1 m of water.2 These rays would be almost completely—i.e. to 98% of their original intensity—absorbed after passing through 1 m of water. In the fact that the energy of the hardest γ-rays is no more than 1/4 of the energy of the fastest α- and β-rays, there is nothing strange, since Meitner,3 Ellis4 and Rutherford5 have shown that the emission of a charged particle is the primary process, while the emission of γ-rays is a secondary process in radioactive decay. Thus Einstein’s equation, in connection with precise Aston measurements of atomic masses, not only shows that only very few, very heavy, and very rarely occurring elements possess the ability to emit α-rays, but also makes it possible to estimate quite satisfactorily the energy of one or another radiation. From our point of view the most essential point here is the fact that almost all possible processes of atomic decay are connected with the absorption, and not with the emission, of energy, and that not one of the possible exothermic decay processes can

could cause radiation of energy greater than that which corresponds to the fall of an electron in a field with a voltage of \(8\,000\,000\) V. The radiation corresponding to this theoretical upper limit would be 4 times more penetrating than the hardest \(\gamma\)-rays of RaC or ThC″, i.e., would be completely absorbed (to 98% of its initial intensity) in 4 m of water. Consequently, cosmic rays, which according to our measurements possess an 18-times greater penetrating power, i.e., which can pass through 70 m of water, must have an entirely different origin. They correspond to the fall of an electron in a field of \(216\,000\,000\) V, and none of the processes of atomic disintegration can supply the amount of energy necessary for their occurrence.

4. The unsuitability of all processes of gradual formation of atoms. On the other hand, Aston’s curve and Einstein’s equation show that the process of building the atoms of the most frequently occurring elements out of protons and electrons is not only capable of producing rays with such penetrating powers, but is also the only atomic process capable of doing so. This will be discussed in detail in §§ 5 and 6. However, even the preceding qualitative estimate already permits us to arrive at the conclusion that cosmic rays are ether signals informing us of the constant formation of heavy elements from light ones.

Moreover, Aston’s curve and Einstein’s equation give us entirely new information about the very nature of the processes of atom building. They show that the building of heavy atoms from light ones, since it is connected with the appearance of cosmic rays, cannot proceed by the successive addition each time of one proton. Indeed, from Aston’s curve it is evident that the maximum loss of mass in the formation of such an element as, for example, iron, by the addition of one proton to the nucleus of an element with a mass one unit less than the mass of the iron atom, would be equal to

\[ 0.00778 + 0.0008 = 0.00858 \ g \]

per gram-atom.

ORIGIN OF COSMIC RAYS

It is equivalent to an amount of energy of the same order as the energy released in the decay of thorium (i.e. 0.00683). Consequently, the ether wave arising in such an act would have only a somewhat greater penetrating power than those γ-rays which would concentrate in themselves all the energy of the radioactive transformation. As was shown above, this wave would be completely absorbed in 4 m of water.

The matter is exactly the same in the formation of any atom by adding one proton to an atom whose mass is smaller by one unit. Only in one case—when carbon is formed from boron—would the energy released be equal to (see Aston’s data):

\[ 11 \times 0.0007 + 0.0076 = 0.0153, \]

i.e. to a value approximately twice as large as the analogous value for iron. But even this radiation would be wholly absorbed in 8 m of water and would not reach even the region in which we have made our measurements of cosmic rays.

The very same line of reasoning shows the impossibility of constructing heavy atoms by the successive addition, one at a time, of α-particles to the nuclei of light atoms. Indeed, the greatest release of energy in processes of this kind would correspond to a disappearance of mass of

\[ 4(0.00054 + 0.0008) = 0.0054 \text{ g per gram-atom} \]

and would give radiation wholly absorbed in 3 m of water. The observed cosmic rays cannot arise from the addition to any atom of a single nucleus of hydrogen or helium and the formation of an atom heavier than the original one by one or, respectively, 4 units, since the mass defect in such a process would be too insignificant.

The results obtained by Millikan and Bowen in experiments with electroscopes on a balloon, which rose to 0.92 of the way to the “top of the atmosphere,” allow us to go still further and assert that in the earth’s atmosphere no radiation of appreciable intensity is observed,

which, in wavelength, would lie between hard $\gamma$-rays and cosmic rays. In fact, rays that would pass through 80 cm of water (this layer is equivalent to the layer of air above the highest point of the balloon’s flight) would discharge the electroscope at the summit of the flight. Yet the radiation that would arise in the construction of atoms by the successive addition of one proton or one $\alpha$-particle, by its hardness would stand precisely between $\gamma$-rays and cosmic rays. We can, therefore, draw the conclusion not only that, in such a kind of construction of atoms, cosmic rays cannot arise, but that it very probably does not occur at all, if one judges by the radiations entering our atmosphere. Processes occur in the universe that are accompanied by more powerful releases of energy.

5. Quantitative proof of the formation of helium from hydrogen in a single act. All our preceding considerations were reduced mainly to the elimination of various possible hypotheses. However, Einstein’s equation allows us to go further—from the observed penetrating power of cosmic rays, to explain quantitatively their origin.

Since atoms are built from protons and electrons—evidence of which we see in the existence of isotopes—and since the gradual construction of atoms by adding one proton or $\alpha$-particle at a time cannot serve as the source of cosmic rays, as was shown in § 4, the primary and most fundamental process of atomic construction must be the union of four protons with two electrons and the formation, in a single act, of a helium atom. Indeed, the further union of helium nuclei into the nuclei of heavier elements, if it occurs at all, must be an act considerably rarer than the formation of helium from hydrogen, since its very occurrence presupposes a multitude of such primary acts. Likewise, if heavy atoms were formed directly from hydrogen, without passing through the intermediate stage of the creation of helium, then the growing complexity of this act

with the increase of atomic weight would again lead to the fact that the most frequent event would be the formation of helium. Therefore the question of whether there is present in cosmic rays a wave corresponding to this act is the fundamental question in the problem of the building of atoms. As we shall now see, observation gives a truly remarkable answer to this question.

According to Einstein’s equation and Aston’s data, the loss of mass in the act of formation of helium is equal to

\[ 4(1.00778-1.00054)=0.029 \quad \text{g per gram-atom} \]

and the energy radiated in each such act is

\[ \frac{0.029 \times 9 \times 10^{20}}{6.032 \times 10^{23}} =4.3 \times 10^{-8}\ \text{erg}. \]

The frequency of the ether wave arising is determined from the equation \(E_1-E_2=h\nu\), whence \(4.3 \times 10^{-5}/6.547 \times 10^{-27}=\)

\[ =6.57 \times 10^{22}. \]

It corresponds to a wavelength \(\lambda=0.00046\ \text{\AA}\). To calculate the absorption coefficient of a wave of such energy (i.e. of such frequency), one may with great confidence use Dirac’s formula1, derived on the basis of relativistic quantum mechanics:

\[ \frac{\mu}{\rho} = \frac{ZN}{A}\cdot \frac{2me^4}{\nu^2c^4}\cdot \frac{1+a}{a^2} \left[ \frac{2(1+a)}{1+2a} - \frac{1}{a}\lg(1+2a) \right]. \]

Here \(Z\) is the atomic number (i.e. for water 10), \(A\) is the atomic weight (18), \(e\) is the charge of the electron \((4.774 \times 10^{-10})\), \(m\) is the mass of the electron \((9.05 \times 10^{-28})\), \(c=3 \times 10^{10}\), and

\[ a=\frac{h}{mc^2}=\frac{0.0242}{\lambda}=53. \]

Substitution of these numbers gives \(\frac{\mu}{\rho}=0.0030\), or \(0.30\) per 1 m of water, instead of the value \(0.35\) at which we arrived purely empirically. These two figures may be considered to agree within the order of those errors of measurement which we have in the upper part of the curve. Indeed, it is necessary

remember that direct observation gave \(\mu=0.22\), while the value 0.35 was obtained by subtracting from the observed curve that amount of ionization which was caused by the more penetrating components, determined from the lower part of the curve, and by selecting \(\mu\) so as best to express the magnitude of the difference thereby obtained. Errors in determining the wavelength and intensity of these more penetrating components could thus have affected, though not very strongly, the value of the coefficient \(\mu\) selected; therefore the above agreement may be regarded as quite satisfactory. We hope soon to obtain new data that will make it possible to refine these considerations somewhat.

Here it is necessary to point out yet another source of possible uncertainty in the quantitative results. Dirac’s formula gives the value of \(\mu\) for homogeneous monochromatic radiation, whereas our measurements were made on rays, some of which were transformed into secondary (with half the value \(h\nu\)), tertiary \(\left(\frac{h\nu}{4}\right)\), etc. This circumstance does not affect the preceding calculations only in one case, which possibly is the one we have. We have already indicated that after the radiation has passed through a sufficient amount of matter and has come into equilibrium with its secondary components, the composition of the beam, i.e., the ratio of the energy of any secondary ray to the primary, remains unknown. As soon as such a state has already been reached, the absorption coefficient of the mixed beam obviously becomes the same as that of the primary. Only in the case when the initial monochromatic beam arises upon passage through matter will its absorption coefficient be somewhat smaller than that of the mixed beam. Consequently, in all the foregoing we have used the assumption that, near the surface of the earth, where our measurements were made, equilibrium between the primary and secondary beams has already been reached. If this were not so, then the error introduced in this way could amount to 30–40%. But even this would not completely destroy ...

then the comparison on which our conclusion is based concerning the construction of helium from hydrogen in a single act, during which cosmic rays with \(\mu = 0.30\) arise. For a clear understanding of the fact that this conclusion is based not on a single merely quantitative agreement, we shall present under rubric (a) the experimental facts speaking in its favor, and under rubric (b) the theoretical considerations compared with them.

a. Our experimental curve, together with the flight data of Millikan and Bowen, shows that a considerable part of the ionization of the atmosphere caused by cosmic rays in the region from 1 to 10–12 m below the “top of the atmosphere” is due to one monochromatic radiation with absorption coefficient \(\mu = 0.30\) per 1 m of water. Only at great depths of 25–70 m, when almost all this radiation has already been absorbed (Fig. 2), does another radiation come into play, approximately 4 times more penetrating. Thus the radiation is completely isolated both in wavelength and in intensity.

b. From the theoretical point of view, the process of formation of helium from hydrogen must be the most frequent process in the universe: first, because it is the primary and simplest of all processes of atomic construction, and, secondly, because the \(\alpha\)-particles (helium nuclei) created by it enter into the composition of many other atoms. The theoretical value of the absorption coefficient of the radiation arising in this process is precisely \(\mu = 0.3\) per 1 m of water. Further, between helium with atomic weight 4 and oxygen (or nitrogen) with an atomic weight almost 4 times greater, there are no frequently occurring elements, so that this cosmic ray must be completely isolated both on the side of high and on the side of low frequencies, and the nearest ray to it must be one 4 times more penetrating, which is what actually occurs. All theoretical facts (2) agree exactly with the experimental facts (1). Both the great intensity of this radiation, and its isolated position in the spectrum, and the nu-

the calculated value of its absorption coefficient speak in favor of the argument set forth above, although the uncertainty in the numerical values has not yet been completely removed.

6. Quantitative proof of the formation of oxygen from hydrogen. Let us now compare the penetrating powers derived from the lower part of the curve with the energies released in the formation of other frequently occurring elements from hydrogen.

Bowen’s discovery that nebulium consists of oxygen and nitrogen1, in connection with the enormous dimensions of the nebulae containing it, many of which are visible at a distance of \(20^\circ\) from the exciting star—equivalent to a vast number of light-years—showed that these gases occur in space in enormous quantities. In addition to the nebulium lines, only strong lines of hydrogen and helium and weak lines of carbon are visible in the nebulae. Therefore, judging by the composition of the nebulae, it is natural to expect to find cosmic rays corresponding to the formation of oxygen, nitrogen, and carbon from hydrogen or from helium.

The energy released in the formation of oxygen from hydrogen is

\[ 16 \times 0.00778 = 0.1245\, v \text{ per gram-atom,} \]

and the absorption coefficient of the corresponding radiation, calculated by Dirac’s formula, is \(\mu = 0.074\) per \(1\ \mathrm{m}\) of water. The radiation arising in the formation of nitrogen with the release of energy \(0.108\, v\) per gram-atom would give \(\mu = 0.086\). The mean of these two numbers is \(0.08\), i.e., it coincides with one of the coefficients that we introduced, along with \(\mu = 0.35\), in agreement with the experimental curve.

The formation of the comparatively rare carbon from hydrogen, in which an energy of \(0.9933\, v\) per gram-atom is lost, would result only in an insignificant broadening of this band toward long wavelengths, which it is impossible to detect under the conditions of our experiment. In our opinion, the quantitative agreement given above, in connection with the

by the fact that, theoretically, the band with $\mu = 0.08$ (which we shall, purely conventionally, call the “oxygen band”) must stand completely isolated between the helium and silicon bands (see below), clearly leads to the conclusion that the formation of oxygen (and nitrogen) from hydrogen in a single act really does take place.

Another path for the construction of oxygen—from a combination of 4 helium atoms—would lead to an energy loss amounting to $0.00054 \times 16 = 0.00858$ per gram-atom. This quantity coincides almost exactly with the maximum energy calculated by us above, released in a radioactive transformation; it corresponds to radiation absorbed almost entirely in $4\ m$ of water. Even if such radiation existed, it could not fall within the scope of our observations and could have been detected only in the experiment of Millikan and Bowen with a balloon. It is possible that the fact of the discrepancy between the observed absorption coefficient of the helium band (0.35) and the calculated one (0.30) is explained precisely by the presence, in the upper layers of the atmosphere, of weak radiation of this kind. Indeed, if one proceeds from the data obtained on mountain lakes, then the value $\mu = 0.30$ will correspond better to the observations than the value $\mu = 0.35$, as is seen from the curve in Fig. 2 (see below). But the coefficient $\mu = 0.30$, as we have already indicated, gives a value of the total ionization approximately 30% smaller than that which follows from the data of Millikan and Bowen1; precisely for this reason, in selecting the coefficients best agreeing with experiment, we rejected the value $\mu = 0.30$.2

Since we are dealing with gases, one can speak only of two frequencies determined by acts of construction of atoms that give the cosmic rays observed at the earth’s surface, because the only gases occurring very frequently—as compared with other elements—are hydrogen, oxygen, nitrogen, and helium. These are what give the two bands actually observed in the spectrum of cosmic rays

with $\mu=0.30$ and $\mu=0.08$. Thus the oxygen band, although established with less certainty than the helium band, is a substantial confirmation of the interpretation advanced by us.

7. Quantitative proof of the formation of silicon from hydrogen. Turning next to solids, we have three kinds of data for estimating how often a given element occurs: 1) the composition of meteorites, 2) the composition of the earth, and 3) spectral analysis of the stars. All of them reduce approximately to one and the same thing. 95% of the total mass of meteorites¹ consists of four elements: oxygen (54%), magnesium (13%), silicon (15%), and iron (13%). In exactly the same way, 76% of the earth’s crust² consists of three elements: oxygen (55%), silicon (16%), aluminum (5%), while the amount of every other element does not exceed 2%. Iron constitutes only 1.5% of the earth’s crust, but there is probably considerably more of it in the inner layers of the earth. The data of spectral analysis of the stars are less definite, but they too speak of the predominance of the above-listed elements, and among the others they give place chiefly to calcium and potassium. Calcium constitutes 1.5% of the earth’s crust and 1% of meteorites; potassium—2% of the earth’s crust and is almost entirely unnoticeable in meteorites. Thus, after oxygen, the next among the frequently occurring elements must be recognized as silicon; in addition to it, aluminum and magnesium may be of significance. But from the standpoint of cosmic rays, aluminum and silicon may be regarded as completely identical, since their atomic weights are respectively 27 and 28; magnesium, with atomic weight 24, when formed from hydrogen gives practically the same mass defect. In other words, among oxygen and iron, only the formation of silicon and its nearest neighbors can lead to the emergence of cosmic rays of noticeable intensity. The radiation arising in this way

¹ Harkins, Phil. Mag., 42, 313 (1921).

² Cecilia H. Payne. Stellar Atmospheres, Harv. Univ. Press, 1925, p. 5.

ORIGIN OF COSMIC RAYS

we shall, purely conventionally, call this band the silicon band, since silicon plays the principal role in it.

According to Aston’s curve and Einstein’s equation, the energy released in the formation of silicon and hydrogen is equal to

\[ 28(0.00778+0.00050)=0.232\,v \text{ per gram-atom.} \]

Dirac’s formula gives for such radiation an absorption coefficient \(\mu=0.041\) per \(1\) m of water. This value is very close to the empirical coefficient \(0.04\), by which our curve from \(30\) to \(70\) m depth is in fact determined. The energy of this radiation corresponds to the fall of an electron in a field of \(216\,000\,000\) V. There is no doubt that cosmic rays with such penetrating power really exist. Here again it may be said that what is especially significant is not the quantitative agreement, but the very fact that, after the oxygen band, only the silicon band can have appreciable intensity; in other words, between oxygen and iron only silicon (and its nearest neighbors) can give a band of cosmic rays, which is indeed observed.

There exists, however, still another path for the formation of silicon, causing the appearance of rays comparable in hardness with cosmic rays. This is the combination in a single act of seven \(\alpha\)-particles, i.e. helium nuclei, into a silicon atom. In this process energy is released in the amount

\[ 28(0.00054+0.00050)=0.029\,v \text{ per gram-atom,} \]

exactly equal to the amount of energy released when 4 hydrogen atoms combine to form helium. Such radiation could not be separated from the helium band, but it would have to be no less than seven times less intense, since before its appearance the act of forming helium from hydrogen must occur at least 7 times. The possibility of its appearance does not, of course, affect the preceding considerations in any substantial way.

8. Formation of iron. Thus, on the basis of data on the relative abundance of the elements in the universe, use-

using Aston’s curve and Einstein’s and Dirac’s formulas, theoretically substantiated the existence of all three observed cosmic-ray bands.

Since neither between silicon and iron nor beyond iron are there frequently occurring elements, only one more cosmic-ray band can have appreciable intensity, with a frequency greater than that of the silicon band—namely, the band corresponding to the formation of iron from hydrogen. Calcium and potassium, which appear fairly often in astrophysical data, can give only a very weak satellite to the silicon band on the side of higher frequencies; while nickel and titanium, from the point of view of cosmic rays, coincide with iron. The hypothetical band corresponding to the formation of iron from hydrogen would be associated with a loss of energy of magnitude

\[ 56(0{,}00778 + 0{,}00080)=0{,}48\, v \text{ per gram-atom} \]

and would have an absorption coefficient \(\mu = 0{,}019\). The existence of such radiation could be detected only by careful measurements in the lower part of the curve. The resolving power we have so far attained does not permit any conclusions to be drawn on this point. We assert, however, that the existence of such radiation is not in contradiction with our curve and even, as will be seen below, makes it possible to bring the theoretical data into somewhat better agreement with the experimental data.

Just as for silicon, there is for iron another possible mode of origin in which cosmic rays may be formed, namely—the combination of 14 helium atoms into one iron atom. In such a process there is liberated an energy of magnitude

\[ 56(0{,}00054 + 0{,}00086)=0{,}075\, v \text{ per gram-atom}. \]

The resulting radiation practically coincides with the radiation arising in the formation of carbon from hydrogen. In other words, it ought to enter into the composition of the oxygen band. We have no data that would make it possible to decide whether it exists or not. Further,

one could also imagine the formation of iron from 2 atoms of silicon, but in such an act there would be liberated an energy

\[ 56(0.00080 - 0.00050) = 0.0168\,\tau \]

per gram-atom, and radiation would arise that is absorbed in 8 m of water (see above). The experiments of Millikan and Bowen show that, if such radiation exists, its intensity must be weak. In exactly the same way, the formation of iron from 4 atoms of nitrogen would give an energy

\[ 56(0.0008 + 0.0002) = 0.056\,\tau \]

per gram-atom, and would produce radiation approximately twice as penetrating as in the formation of helium from hydrogen. Our curve does not testify to the existence of such radiation of any appreciable intensity.

9. Construction of the cosmic-ray curve.
From the preceding considerations it is clear that, if in a first approximation one takes the rate of the process of formation of a given element to be proportional to its total quantity in the universe, then the problem of the origin of cosmic rays is greatly simplified by the fact that, besides hydrogen, we have only four frequently occurring elements: helium, oxygen, silicon, and iron.

The first two of these—helium and oxygen—can be formed in only one way: by the union, in a single act, of the required number of hydrogen atoms, in which cosmic rays arise. The fact that this is precisely how matters stand is proved by the quantitative agreement between the observed and the calculated penetrating powers.

In the case of silicon there are two possible paths of formation: the union, in a single act, of 28 atoms of hydrogen or of 7 atoms of helium. We have direct positive evidence that the first of these processes actually occurs, since the ray corresponding to it is indeed detected by our curve. We have no positive evidence that the second process does not occur, since the rays corresponding to it would fall in the helium band—the most intense of all the bands. But there exist

some indirect indications, allowing one to conclude that it is less probable than the first process. In fact, the experiments of Millikan and Bowen show (see below) that the formation of oxygen from four particles is in any case an exceedingly rare event; meanwhile it is hardly possible to think that the formation of silicon from seven particles occurs more often.

As for the last of the frequently occurring elements—iron—there exist many different possible ways of its formation. We shall, however, by analogy with oxygen and silicon, assume that the most probable is its formation directly from hydrogen in a single act.

Wishing to construct the theoretical path of the resulting curve of cosmic rays, we took as our starting point those mean proportions in which oxygen, silicon (i.e. silicon + aluminum + magnesium), and iron are found in meteorites and in the earth’s crust, namely \(55\%\), \(26\%\), and \(7\%\). Assuming further that these atoms are formed from hydrogen precisely in such proportions, we determined, with the aid of Gold’s tables, the relative intensity of the radiations corresponding to them, after these radiations with \(\mu=0.08\), \(\mu=0.04\), and \(\mu=0.02\) had passed through \(30\ \mathrm{m}\) of water. In this way the numbers O \(1.4\); Si \(2.9\); Fe \(1.8\) were obtained, which show that at such a depth the influence of oxygen and iron is approximately the same, while the influence of silicon is about twice as great as either of them. For the further construction we divided, in these proportions, the total amount of ionization at a depth of \(30\ \mathrm{m}\), choosing it because precisely at this depth the helium band disappears (\(\mu=0.30\)). Experiment shows that this ionization is equal to \(1.79\) ions per \(1\ \mathrm{cm}^3\), of which \(0.45\) each we assigned to iron and oxygen, and the remaining part, about twice as large, to silicon.

Having thus fixed the starting point, i.e. the value of the ionization at a certain definite point for each of these three radiations with \(\mu=0.08\), \(\mu=0.04\), and \(\mu=0.02\), we can, with the aid of Gold’s tables, construct for each of them the complete ionization curve for all depths. These results are given in Table 1 and graphically show—

Origin of Cosmic Rays

TABLE I.

zation in Fig. 2. In Fig. 2 the area between the horizontal straight line and the first curve represents the total ionization caused by the formation of iron; the area between

Fig. 2. Comparison of the experimental data with the theoretical curve constructed from the true absorption coefficients. The abscissae are depths; the ordinates are ionization in ions per cm³ per sec. Dots denote observations on Lake Arrowhead; circles denote observations on Lake Gem.

the iron curve and the next curve—the ionization caused by the formation of silicon, and, finally, the area between the silicon curve and the next curve—the ionization caused by the formation of oxygen. As the initial point for helium we took the difference between the observed ordinate at 10 m and the ordinate of this latter curve at the same point, and then, using Gold’s tables, calculated the value of the ionization at all depths caused by the formation of helium. The total magnitude of this ionization is expressed by the area enclosed between the two upper curves. From the drawing it is evident that the theoretical curve constructed in this way is superposed on the observed points quite satisfactorily. Of course, one need not attach special significance to this synthetic curve, since the average content of the elements in meteorites and in the earth’s crust is not yet sufficiently well known to serve as a measure of the rate of their formation. Nevertheless, both the curve and the table are to a certain extent significant, since they show that, for constructing the observed curve of cosmic rays, 4 elements are sufficient: helium, oxygen, silicon, and iron; they clearly depict the course of the dependence of the ionization caused by each of these 4 elements on depth (for example, it is seen from them that the total ionization caused by the formation of iron is so small that it may be entirely neglected without appreciable error, whereas 80% of the ionization in the upper layers is due to the helium band); they give a certain indirect indication of the possibility of the formation of iron from hydrogen, since the most accurately determined, remarkable experimental points near 12 m fit the curve better when the coefficient 0.02 is added than when only purely empirical coefficients are used1.

10. Thermodynamic and kinetic points of view on the origin of cosmic rays.

All our arguments up to now have been purely thermodynami-

cosmical character. We did not concern ourselves with the mechanism of the construction of atoms, but limited ourselves only to selecting those atomic transformations which suit our purpose under the condition that the fundamental energy relations be valid. Although physics has always regarded such a method of investigation as the most reliable, we cannot ignore the kinetic side of the question either.

At first sight it presents great difficulties. Indeed, we have, first of all, assumed that positive electrons can gather in one place, despite the forces of mutual repulsion, and, after the addition of a certain number of negative electrons (which for the light elements is not more than half the number of positive ones), be transformed into a new nucleus with a positive charge from 2 to 92. Meanwhile we have clear evidence of the validity of the inverse-square law down to distances of the order of \(10^{-12}\) cm. The introduction of the electron’s own rotation, which makes it a magnetic dipole attracting a dipole of the opposite sign with a force inversely proportional to the cube of the distance, may help us in describing the mechanism by which two positive electrons are bound by one negative one—as happens, for example, in the helium atom—and in explaining the fact that in the formation of helium from hydrogen energy is not absorbed, but is lost; yet even in this case there remains the necessity of expending work in order to bring positive charges together to distances of intranuclear order, at which magnetic forces may begin to act. The magnitude of this work is so enormous that at none of the temperatures known to us can there arise such kinetic energy with which a proton could approach another proton to a distance of intranuclear order. In fact, at the very highest of the temperatures reigning inside stars—that is, at \(40\,000\,000^\circ\) C—the maximum energy in the spectrum of black radiation belongs to a wavelength of \(1\,\text{\AA}\), which not only cannot bring protons together to a distance of \(10^{-13}\) cm, but cannot even tear \(K\)-electrons from heavy atoms, since for this a wave of \(0.2\)–\(0.7\,\text{\AA}\) is required. Thus

Thus high temperatures cannot help us solve the problem of the formation of atomic nuclei. Most likely, they even counteract this formation.

The second difficulty in the kinetics of the construction of atoms consists in explaining, from the point of view of probability, the possibility of the meeting of 4 protons and 2 electrons in one place and under conditions capable of entailing the formation of a helium atom. Of course, this difficulty becomes still greater in passing to oxygen, silicon, and iron.

To escape from the first difficulty, we propose—as will be discussed in more detail below—to regard the formation of the nucleus as a phenomenon for which, for reasons unknown to us, the still uninvestigated conditions of low temperatures and densities existing in interstellar space are especially favorable.

A possible way out of the second difficulty is as follows. Without as yet touching upon the question of how electrons and protons arise—whether by the condensation of radiation or otherwise—we may in any case assert that they exist in space in large quantities. Under the influence of mutual attraction, one of the electrons begins to approach a proton by means of quantum jumps, in which the spectrum of atomic hydrogen arises, frequently encountered in the spectra of stars and nebulae. In this process, even when the electron reaches the quantum orbit nearest to the nucleus, the total mass defect caused by its presence will be insignificant. Further, we may imagine that this normal atomic hydrogen is capable of attaching to itself one more proton, yielding an ionized molecule of hydrogen, which—according to data from positive-ray spectrography—is a stable system. Up to this point the protons and electrons have not been sufficiently close to one another to cause an appreciable mass defect. Let us now suppose that two such ionized hydrogen systems collide with one another. It will be natural to assume that under ordinary conditions this collision will proceed according to the generally accepted laws of the kinetic theory of gases. But let us now imagine that, by the expi-

conditions of collision for a long, long time, governed by as yet unknown laws of probability, will turn out to be precisely such that 4 protons and 2 electrons will combine, forming a helium nucleus. In this case, almost the entire loss of mass will occur at the very moment of collision, so that the magnitude of the emitted energy will still be equal to \(4(0.00778—0.00054)\); but we shall thereby avoid the difficulties connected with the probability of 6 electrons (4 positive and 2 negative) meeting in one place. The process of their gathering proceeded step by step, but the actual formation of the nucleus occurred in a single instant. These considerations may be extended to oxygen, silicon, and iron. It is possible that this accumulation of electrons, preceding the formation of nuclei, is facilitated by the low temperature possessed by interstellar space. In other words, the energy of impacts may hinder that accumulation of electrons which, according to what has just been said, must precede the formation of nuclei. It would be interesting to investigate whether hydrogen, under laboratory conditions at the temperature of liquid helium, does not show a tendency to transform into helium.

In general, the kinetics of the building of atoms should differ only slightly from the kinetics of the formation of complex molecules and crystalline structures. In this latter case the difference is great only if the atoms in the crystal take their places gradually; if, however, the greater part of them does this at once, then the two problems are essentially in many respects similar to one another. Let us note that the building of crystals is facilitated not by a high, but by a low temperature, and this circumstance, as we shall see below, is in all probability characteristic of the process of the building of atoms.

11. The place of origin of cosmic rays. At the present time all observers have come to the conclusion that, if a directional effect in cosmic rays exists at all, then in any case it is small. We have not at all found the presence of such an effect, contrary to the results of Kolhör-

ster1 and Büttner2. In any case, it may be said that cosmic rays fall upon the earth almost uniformly from all directions. This means that they originate either 1) in interstellar and interplanetary spaces, in particular in nebulae, or 2) in stars more or less regularly distributed over the celestial sphere. Only these two alternatives exist. In both of these regions matter exists under conditions as yet unexplored. The entire history of physics over the last 30 years allows us to reckon with the possibility that in this new field of observation matter behaves in a way unknown to us and unexpected.

Of the two alternatives indicated above, we consider it possible, “with a certain degree of confidence,” to reject the second and to substantiate the first on the basis of the following considerations.

I. If the presence of matter in large quantity and at high temperature promotes those atomic processes in which cosmic rays arise, then it should be expected that the sun, because of its proximity, sends the earth a far greater quantity of these rays than any other star. Meanwhile all observers agree that the intensity of cosmic rays at noon and at midnight is the same3. This can only mean that the conditions existing near the sun and in the sun itself—and possibly also the conditions in the other stars—do not favor those atomic processes in which cosmic rays arise.

Hence, since the rays come to us constantly, by day and by night, and almost uniformly from all directions—according to some observers with an accuracy of the order of the accuracy of our measurements—we almost inevitably come to the conclusion that these atomic processes are favored by the conditions existing in interstellar space. If, however, in passing from some point of interstellar space to the center of a star, the favorable conditions for the construction

atoms disappear; as soon as we pass from outer space to the surface of the star, it is utterly impossible to imagine that they will reappear on the way from the surface to the center, since the physical conditions here will all the time be changing in one direction. Thus, from the preceding we may conclude that stars not only are not sources of cosmic rays, but that, probably, the basic processes of atom formation do not take place in stars at all.

II. The same conclusion can also be reached from an entirely different point of view—proceeding from the data we have obtained on the absorption coefficients and the total energy of cosmic rays.

The hardest of the rays we have observed are absorbed completely—i.e. to 98% of their initial intensity—in 70 m of water. This means that even if atoms are being built up in stars, the cosmic rays arising in the process cannot escape outward and are converted into heat¹, except for those rays which arise in the very outer layers of the star, equivalent in their absorptive capacity to, approximately, 100 m of water.

Meanwhile, we have found that the energy brought into the earth’s atmosphere by cosmic rays is nearly equal to 0.1 of the total energy reaching the earth from all the stars except the sun². This fact means that if cosmic rays originated in stars, their intensity at the place of origin would not exceed, by more than a factor of 10, the intensity observed in the earth’s atmosphere, since these rays, being absorbed in the stars, would there be converted into heat and would produce from the stars a greater flux of energy than that which is actually observed. In other words, if one seeks the source of cosmic rays in the stars, then from our measurements of their absorption coefficients and total energy

¹ Let us recall that, as we have already shown in Phys. Rev. 28, 866, 1926, rays of this kind, upon passing through matter, are converted into heat without any change of frequency or of the absorption coefficient in the remaining beam.

² Millikan and Cameron. Phys. Rev., 31, 928, 1928.

It follows that the total flux of heat from the stars is due only to the process of atom formation occurring in their very outermost layers, with an absorptive capacity equivalent to 100 m of water; within the stars themselves there occurs neither the construction of atoms nor any other processes capable of supplying heat.

But to suppose that atoms can be created only at the surface of a star and at a depth of 100 m, and that after that this suddenly, all at once, becomes impossible, is plainly absurd. Thus we again arrive at the conclusion to which we have already been led by the absence of cosmic radiation in the sun: that the observed cosmic rays arise not at all in the stars, but under the influence of precisely the opposite conditions existing in interstellar space.

These considerations, from two entirely different points of view, lead to the conclusion that the flux of heat coming from the stars has as its source something quite different from those processes of atom construction in which cosmic rays arise. Jeans1 and Eddington2, proceeding from other considerations, based on the duration of the life of the stars, have already repeatedly pointed to the necessity of finding for this flux of heat a source more intensive than the process of atom construction. We can now go further and say that atom construction does not occur in the stars at all, or at least does not occur to such an extent that the stars could emit a large quantity of cosmic rays, since if that were so, the total output of energy by the stars would be greater than it actually is.

It is known that Eddington and Jeans found such a source of stellar heat not in the process of construction of atoms, but in the process of their destruction, which, as they suppose, constantly occurs within the stars. In this process the protons are constantly converting all their mass

in energy, in accordance with the requirement of Einstein’s equation. As was already indicated above, we have sought in vain among the cosmic rays for a ray corresponding to this act. Let us recall that the mass defect in the formation of one gram-atom of silicon from hydrogen—and with it there arises the hardest of the observed cosmic rays, since iron rays are still to a certain extent hypothetical—is equal to 0.23%. According to Einstein’s equation, the complete annihilation of the mass of hydrogen would cause the appearance of a ray approximately 4 times (more precisely, \(1.00778:0.23\) times) more penetrating than this ray. The absence of radiation of such frequency is, of course, not an argument against the fact that such a process actually takes place inside stars, where both temperature and density have enormous values. The impossibility of detecting this radiation shows rather that, if this process really takes place—as Eddington and Jeans think—then it takes place precisely inside stars, where the radiation produced is hidden from us by an impenetrable screen of matter—a screen which converts all the energy of the ray, before it emerges, into heat. If cosmic rays arose in stars, they would be hidden from us in exactly the same way.

On the other hand, the fact that alongside the process just considered of the annihilation of atoms there also occurs a process of the formation of atoms which, as our experiments show, proceeds outside the stars and possesses energy of the same order of magnitude as the energy radiated by the stars, is truly remarkable. Indeed, comparing it with Eddington’s reasoning, we immediately obtain the following incomplete cycle of processes, experimental evidence for each of which is given in parentheses:

1) in interstellar space there exist, in large numbers, electrons and protons (spectroscope data);

2) these electrons, under the influence of the conditions prevailing in interstellar space, i.e. low temperature and rarefaction of matter, condense into atoms (cosmic-ray data);

3) these atoms then, under the influence of gravitational forces, accumulate into stars (telescope data);

4) in the interior of stars, under the influence of enormous temperatures, densities, and pressures, some stray proton, possibly once belonging to the nucleus of a heavy atom, transforms all its mass into an ether impulse of energy, which turns into heat, maintains the temperature of the star and the flux of energy emitted by it (data on the duration of stellar lifetimes—Eddington—Jeans).

All the preceding is based on direct experiment. However, the discovery of the second element of this incomplete cycle, namely that the supply of protons and electrons is constantly expended in the formation of atoms, the birth signal of which is cosmic rays, immediately raises the question of how this process can last for whole epochs—in other words, why have all the basic bricks of matter not long since been exhausted? And the only answer that can be given to this question is to complete the cycle and accept that the supply of these bricks is constantly renewed at the expense of the condensation of radiation into protons and electrons, proceeding by a mechanism as yet entirely unknown.

Such an approach is a new point of view on a conclusion, part of which, at least, has long been known. Indeed, Einstein’s equation itself, allowing the transformation of mass into radiant energy, requires the existence of the reverse process as well, unless one rejects the generally accepted form of the second law of thermodynamics. In other words, from a purely thermodynamic point of view, equilibrium in a closed system containing radiation and matter can occur only if the transformation of mass into radiant energy is a reversible process. An attempt to develop thermodynamics on the basis of a cycle containing this process was recently made by Stern1, Tolman2, and Zwicky3.

But in our preceding arguments we have gone further than they did. Indeed, the mere assumption of the reversibility of the above-mentioned process is in itself insufficient to avoid “heat death,” i.e. the gradual annihilation of all energy capable of being utilized. The essence of the second principle consists in the assertion that an isolated system tends toward a state with constant temperature, characterized by the law of black-body radiation for the distribution of radiant energy and of the velocities of gas molecules. The simple supposition that radiant energy can be transformed into atoms in no way changes the consequences of the second principle, since the atoms turn out to be endowed with kinetic energies corresponding to the temperature of the radiation from which they arose, and the matter must on average be precisely so—if one proceeds from the second principle—since otherwise, in an isolated system of a given temperature, a difference of temperatures would arise. Indeed, from the Einsteinian point of view, radiation is corpuscular by its very nature.

On the other hand, if one regards the universe as a closed system, then the only way to avoid “heat death” is the assumption that after potential energy has been transformed into heat, it can somewhere, in some way, again wholly assume its potential form; in particular, that the kinetic energy of light quanta can be wholly transformed into the potential energy of statically attracting systems. Herein lies the essence of the hypothesis we have made above: that only under the conditions of temperature and pressure prevailing in interstellar space is radiant energy transformed into protons and electrons, which then draw together under the influence of mutual attraction, cluster into heavier atoms, and, by means of constant mutual collisions of these atoms, again transform their potential energy into heat, forming new “hot masses” (stars) in space. This hypothesis contradicts the second principle of thermodynamics as applied to the entire universe, and moreover to

to this contradiction by the observed properties of cosmic rays. From the point of view of terrestrial phenomena of the usual scale, to which it has been successfully applied up to now, the second principle remains valid. The essentially new element which we have introduced into the experimental data consists in the fact that the process of formation of atoms takes place not in the stars, i.e. not in those parts of the universe where matter possesses great densities and temperatures, but exclusively in interstellar spaces, where both density and temperature are equal to zero. Our direct experience does not, it is true, relate to the formation of the lightest of the elements—hydrogen—from radiant energy; but the inclusion of this process among the other “violent” processes, occurring only in interstellar space, is a natural extension of our observations, since one must expect that hydrogen is created in the same place as those elements for which it serves as the building material. In making this generalization, we deny the reversibility of the process of transformation of matter into radiation at ordinary temperatures and pressures. This is why our conclusions differ from those of Stern and Tolman, and why we can regard the universe as being in a state of equilibrium, although one which does not satisfy the condition of microscopic reversibility.

In a certain formal sense, our assumption may not be considered a violation of the second principle, since in Carnot’s formulation it says: the efficiency coefficient is \((T_1 - T_2)/T_1\), i.e. heat is in fact completely converted into work when \(T_2\) is absolute zero. Nevertheless, by our assumption we deny the applicability of ordinary thermodynamic concepts to cosmic processes. It should be noted, however, that doubts as to the applicability of these concepts to the cosmos as a whole have been expressed repeatedly. Our hypothesis is hardly more radical than Einstein’s hypothesis in 1905, and its value cannot be rejected until we have obtained information about the behavior of matter in interstellar space. It seems to us the least radical of the three possible hypotheses based on the validity

equation of Einstein, $Mc^2 = E$. These three hypotheses are as follows:

1. The first hypothesis—Jeans and others—is that electrons, and consequently atoms and molecules as well, are transformed into radiant energy, and moreover this process is in no way reversible. Jeans’s recent statement reads1: “Thus both observation and theory lead to the conclusion that the universe is dissolving into radiation. Our situation is similar to that of polar bears on an iceberg which has broken away from the general mass of ice surrounding the pole and is gradually melting as it passes into equatorial latitudes, tending toward complete disappearance.”

This is the old hypothesis of “heat death.” It does not contradict the observed facts and, before Einstein’s work, was regarded as an inevitable consequence of the second principle, provided only that the universe be regarded as a closed system. Science, however, has always objected to such an illegitimate extrapolation of our limited terrestrial experience. After Einstein’s discovery, this hypothesis encountered the further difficulty that it introduces into thermodynamics a single process that fails to satisfy the condition of microscopic reversibility required by the modern interpretation of the second principle.

1. The second possible hypothesis—Stern, Tolman, and Zwicky—says that the above-mentioned processes are everywhere reversible. This hypothesis leaves the second principle in force, including the microscopic reversibility destroyed by Jeans’s hypothesis; but, as was shown above, it does not avoid “heat death,” and it is not confirmed by the fact that the process of building up atoms, in which cosmic rays arise, does not occur everywhere—for example, not in the stars—but exclusively only in the depths of interstellar spaces.

2. The third hypothesis, presented here, just as radical as the first, contradicts microscopic reversi-

… but, on the other hand, it makes it possible—in contrast to (1) and (2)—to avoid “heat death.” Likewise, it asserts just as decisively as the second hypothesis that radiant energy can be transformed into atoms, but it agrees better with the data on cosmic rays, which indicate that the processes of atom creation occur only in interstellar space.

1. J. H. Jeans. Nature 121, 467, 1928. ↩↩↩↩↩↩↩↩↩↩↩↩↩

2. Tolman, Proc. Nat. Acad., 14, 268, 348, 353 (1928). ↩↩↩↩↩↩↩

3. Zwicky, Proc. Nat. Acad., July 1929. ↩↩↩↩

4. Ellis and Wooster, Proc. Camb. Phil. Soc., 22, 844, 1925. ↩

5. Rutherford and Wooster, Proc. Camb. Soc., 22, 834, 1925. ↩