3. Directed intuition in astronomy

We shall be concerned here mainly with the prediction and visualization of the existence of as yet unknown bodies in cosmic space. Instead of brainstorming, which is equivalent to fumbling through the garbage of the mind, we direct our intuition along the following guide lines, beacons or sign posts.

The Boltzmann-Gibbs principle

This principle states that, if forces of attraction between dispersed particles are at work, stationary aggregates will eventually result and a variety of objects formed. Such processes of condensation of necessity release potential energy which is liberated as radiation or as kinetic energy of some of the matter that is being dispersed. All condensations can take place either slowly or rapidly. In the latter case we speak of implosions and associated explosions, that is of ejection of matter at velocities superior to any that originally existed in the system in question.

Families of objects

Objects formed as a result of the condensation of matter cover large ranges of compactness or average density. Gaps in the sequences of objects only appear to exist because the life times of some of them are short or, because they are difficult to see or to detect.

The fundamental question arises as to how compact aggregations of matter can become. This obviously must depend on the number of elementary particles involved, that is, on the mass M₀ we start with. As dispersed matter contracts, a total amount of electrical, nuclear or gravitational energy will be liberated. The system thus looses the mass M = / c² and its resulting effective mass M_eff will be

(2)

Designating the maximum mass M that can be lost as M_L, the determination of M_L is of prime interest for our understanding of the large scale distribution of matter in the universe. We shall have to mobilize both theory and observation to find out whether M_eff can ever become zero or even negative, that is, M_L = / c² > M₀. If this should be the case we would have the following complementary juxtaposition of the behavior of positive and negative charges e⁺, e^- and positive and negative masses M⁺, M^-, namely

Leaving the scheme (3) open for future discussion by the application of theories more complete than the present general theory of relativity and quantum mechanics, we submit a few cases in which it would be profitable to determine the maximum possible "packing fractions" as functions of M₀, that is

(4)

As I have shown elsewhere ⁽²⁷⁾, two cases must be considered, namely free systems and systems that are subjected to external pressure. Among the latter I have discussed aggregates of neutrons under high pressure which are located, for instance, in the centers of some types of stars. This led me to the prediction of the existence of nuclear goblins ^{(27, 28)} as very special and interesting objects of nuclear density.

We here, however, restrict ourselves to the discussion of a few gravitationally self-contained aggregates of matter that are not subjected to any integral external pressure.

Nuclear fusion and crystallization

We consider for instance a neutral swarm of protons and electrons which may condense into hydrogen atoms, hydrogen molecules, and so on, or be directly fused to iron atoms, which then condense into the solid crystalline phase of iron. Starting with say 6.02 × 10²³ H-atoms, equal to about M₀ = 1 gram, we shall end up with an iron crystal of M_eff = 0.99 grams, during which series of processes an energy of 0.01 c² = 9 × 10¹⁸ ergs will have been released.

Complete annihilation and condensation into gravitons

If the iron crystals mentioned in the previous paragraph could be completely annihilated, that is radiated away, we should end up with an object of M_eff = 0 and density = 0, that is with empty space, and the whole initial mass M₀ would have been radiated away as electromagnetic radiation.

On the other hand it is conceivable that complete annihilation of matter is not possible and that we shall end up with gravitons as the ultimate condensates of the original cloud of protons and electrons. From the fact that there are no clusters of clusters of galaxies, and the resulting possibly finite range of the gravitational forces, I have derived ⁽²⁹⁾ a preliminary value

(5)

for the rest mass of the gravitons. Speculating wildly that these might have diameters of the order of the fundamental length

(6)

the gravitons would have to be assigned a mass density of the order of

(7)

amply justifying their high penetrating power and perhaps establishing them as representatives of OBJECT HADES of the smallest effective mass.

Specific objects associated with basic lengths

There are a number of characteristic lengths that can be obtained by combinations of the fundamental physical constants. Strong reasons can be advanced that every one of these lengths is associated with some specific state of matter. Bohr's length d_B = h² / 4² m_e e² of course is well known as the determinant for the sizes of atoms, molecules and the elementary spacings in crystal lattices. How these lengths can be used for directing one's intuition in the search for new types of bodies in the microscopic, macroscopic and cosmic realms has been discussed elsewhere ^{(30, 37)}.

Compact stars

Instead of starting out with 6 × 10²³ hydrogen atoms to make a crystal of iron we now choose a cloud of about 10⁵⁷ of them and let them condense into a star of the type of the sun. In this case the loss of mass due to the liberation of gravitational potential energy will be of the order of

Sun:

(8)

The next step in condensation might lead us to a white dwarf star with a mass density of the order of ~ 10⁶ grams/cm³ and a loss of mass accompanying its condensation from a dispersed cloud of H-atoms of,

White Dwarf:

(9)

Progressing to further pseudostable and even more compact configurations, and bypassing the possibility of pygmy stars, we come to the neutron stars^{(31, 1)} with a mass density greater than 10¹² grams / cm³ and a mass loss due to the gravitational energy liberated in the transition from the dispersed state equal to

Neutron Star:

(10)

I first presented the possibility of neutron stars in my lectures on astrophysics at the California Institute of Technology in the spring of 1933, suggesting that they are formed by implosions from ordinary stars, with resulting liberation of tremendous energy. That could explain the extraordinary luminosity of supernovae and the ejection of cosmic rays ^{(32, 33, 34)} of sufficient intensity to account for the observations and consisting of all nucleons with individual energies up to 5 × 10¹⁹ esu or 1.5 × 10²² electron volts. In recent years all of these predictions have been confirmed. But during the intervening thirty years from 1933 until 1965 astronomers chose to ignore my theories and predictions. In 1959 A. G. W. Cameron wrote ⁽³⁵⁾, "With the discovery of hydrogen-to-helium conversion processes and other mechanisms of nuclear-energy generation, together with the studies of stellar evolution and white dwarf star models, it became generally believed that white dwarf stars were the inevitable end points of stellar evolution.... Apparently only Zwicky has continued to believe that neutron stars were formed in supernova explosions." As late as 1964, H. Y. Chiu summed ⁽³⁶⁾ "The other alternative that neutron stars may be the remnants of supernovae has so far been accepted only with skepticism. Moreover there is no astronomical evidence yet that such stars even exist."

In November 1933 I presented the theory of the origin of supernovae and of cosmic rays as being caused by the implosion of stars into neutron stars in a big physics seminar at the California Institute of Technology. A staff correspondent, whom I had briefed on the subject after the seminar, reported as follows in the Los Angeles Times of Dec. 8, 1933, partly with remarkable accuracy,

Mount Wilson Observatory astronomers and California Institute of Technology scientists whispered excitedly to each other as Zwicky unfolded what his associates characterize as probably the most daring theory of cosmic ray origin.

Dr. Zwicky's theory provides the first theoretical picture of the strangest heavenly bodies known to astronomers, the super-temporary star (supernova).

Only two such phenomena have been observed in historical times, Tycho's star of 1572 in our own Milky Way and the star of 1885 in the great Andromeda nebula.

The old astronomer's data regarding the 1572 star, according to Zwicky, were accurate enough for him to calibrate many of the star's peculiar qualities. At the start Zwicky estimates this star measured about 500,000 miles in diameter, ... , then in less than a week this diameter shrank to only nineteen miles, being compressed into this small ball of neutrons.

The speaker, a former collaborator of Dr. Albert Einstein in Switzerland filled six blackboards with equations, the last of which demonstrated that the present intensity of cosmic rays as recorded near the Earth is almost exactly that to be expected if the rays emanate from these neutron stars of which one is born every 1000 years in galaxies like our Milky Way.

In contradistinction to the professional astronomers, who ignored my views for thirty years, the reporters kept going strong on supernovae, neutron stars and cosmic rays, at least for a few years. In the Los Angeles Times of January 19, 1934, there appeared an insert in one of the comic strips, entitled "Be Scientific with Ol'Doc Dabble" quoting me as having stated

"Cosmic rays are caused by exploding stars
which burn with a fire equal to 100 million
suns and then shrivel from 1/2 million miles
diameters to little spheres 14 miles thick."
          Says Prof. Fritz Zwicky,
           Swiss Physicist

This, in all modesty, I claim to be one of the most concise triple predictions ever made in science. More than thirty years had to pass before the statement was proved to be true in every respect. I think even David Hilbert would have been pleased since, in his will (as relayed to me by Professor H. Kienle, former director of the Observatory at Göttingen) he had left us with the admonition to be brief in all writings and to try to present our life's work in ten minutes.

Ultimate compact bodies. Objects HADES H.

We shall not dwell here on the question as to how many pseudostable types of compact cosmic bodies there might exist ⁽³⁰⁾ between the neutron stars and the configurations of ultimate limiting mass M_eff = M₀ - M_L. Some of these have recently been given the name "Black Holes." This, however, in my opinion is an unfortunate misnomer, since they are not holes at all, but objects of the greatest compactness. I have therefore proposed to call ⁽³⁰⁾ them OBJECTS HADES H. Some suggestions were also made in another place ⁽³⁰⁾ as to what objects HADES might consist of. But these will not be further elaborated here except for a few remarks later on as to how and where objects HADES of large initial masses might be found.