12 Measurable Quantities that May Enable Questions of Cosmology to be Answered

12.1 Introduction

A discussion of a number of cosmological problems was presented including radio and optical astronomy as important observational tests of cosmological theory. The point of view adopted was that, while locally discovered laws of physics may possibly suffice to describe observations on the large scale, it is conceivable that this may not be true on the very large scale requiring extreme extrapolation. Cosmological models should therefore be constructed that are simple and can be subjected to observational tests. With respect to the distribution of matter, it is necessary to discuss not only the geometrical and kinematical aspects but also physical characteristics such as the abundance of the elements, galaxies, and galactic clusters. Models must be capable of allowing for such evolution. We cannot be sure that we know all the laws of physics required for a real understanding of the situation, and we should consider seriously any model which is simple and presents the greatest variety of experimentally verifiable conclusions.

12.2 Measurements and Observations

The observations which are most easily interpretable as of a cosmological nature with respect to galaxies are the following quantities:

1distance (brightness)

2red shift

3number of galaxies

4distribution of and (on the celestial sphere)

5color and other physical characteristics

6mean density of matter in the world

7distribution and abundance of elements

In the above list, 1 to 4 would represent a distribution in phase space. These would be expected to be predicted (as well as the other measurements) by a cosmological model.

12.3 Cosmological Models

• A.: The “Explosion” Model

The present state of the universe is the result of an explosion of a previous dense state of matter at a time of the order Hubble's constant years ago.

• B.: The “Oscillatory” Models

These are similar to the explosion model, and we are supposedly now on an expansion phase of the “oscillation” which should be followed by a “contraction” of the universe to a repetition of the cycle.

• C.: The “Steady State” Model

In this model the observational quantities on the average do not change with time. It eliminates the effects of local evolution on all statistical observations and avoids therefore a great difficulty in testing the model in contrast to other models. All observations on distant masses are past history of those distant masses. On the steady state model the average of such observations is to be the same as for nearby masses. Unless we know how to calculate the changes in distant galaxies with time as a function of a wide range of detailed information, we would not know how to interpret the data. The virtue of the steady state model is that it bypasses this problem and that it could therefore be disproved by the observations as they are all crucial.

12.4 Observational Data

• A.: Distance vs. Red Shift ( )

The best summary has been given by Sandage on the work of Sandage and Humason. According to the Cosmological Principle, at a suitable moment in time all the localities, suitably chosen, look alike.

The data is to be summarized by the relations:

where

= speed of light,

= Hubble's constant,

= distance,

= fractional shift in wave length;

defines the present observational magnitude of Hubble's constant;

where is a quantity to be discovered by the observations.

The observations to be made during the next few years should give us the required kinematical information. The predictions of the different models in regard to are not resolvable by present observations when one compares the red shift vs. bolometric magnitude. It appears that the newly-developed photoelectric image multiplier technique used at Mt. Palomar by Baum should extend the data sufficiently to make possible the resolution between models in regard to the red shift data.

In regard to the quantity , it is to have the following cosmological significance:

• B.: Red Shift and Number of Galaxies

This correlation would be an especially attractive result. However, insufficient data exist because of the laborious effort involved in examining hundreds of spectrograms of distant galaxies to obtain number counts and spectral measurements. It would be helpful to have this information obtained by mechanical means.

• C.: Color vs. Distance (Red Shift)

The absence of color effect as a function of distance (defined by red shift) as now observed by Stebbins and Whitford can be interpreted to mean there is no large space absorption and (at great distances) there are no large evolutionary effects in times of the order of one quarter of Hubble's constant. This would agree with the steady state model.

• D.: Radio Counts of Galactic Number (Number vs. Brightness (distance))

All number counts are subject to a type of error which must be avoided. In a homogeneous system the law of number ( ) versus intensity ( ) should be

If the error in is symmetric and equal at all intensities, it does not affect the gradient of the relationship which is in magnitude but will shift the curve parallel to itself. When the error is greater at small intensities, the effect is to change the gradient and is then very strongly dependent on the extent of the tail of the error distribution (the small number of large errors). The effect is to steepen the gradient, and can be calculated from the radio source data if an independent measure of the error exists.

The radio counts are not able to produce a cosmological answer at this time except if it were found unambiguously that the gradient was greater than or that it was found possible to observe independently the distance of sources rather than just their brightness, for in the case that they follow the law they can be assumed to be too near to have any cosmological significance.

• E.: Mean Density of Matter in the Universe

Another type of radio observation of cosmological significance is the mean density of matter. This is involved in the relation (according to some cosmological theories)

where

universal gravitational constant,

mean density ,

Hubble's constant (as a time).

The radio observations on neutral hydrogen (21 cm wavelength) in distant galactic clusters indicate appreciable addition of neutral hydrogen so that much of the matter of the universe can no longer be considered luminous. This is to the effect that will always tend to increase as methods are found to detect matter. It would be nice to know the amount of matter in intergalactic space. It is presumably largely ionized because the recombination time is about years. (Dust is exceedingly rare.) Enough dust to affect the recombination time would make intergalactic space opaque to visible radiation.

• F.: Origin of the Elements and Abundance

The recent developments (the work of Fowler, Hoyle, Burbidge, and Cameron on element generation in stars) are to be regarded as a great triumph. According to this theory, elements are being generated at present in stars that are seen at present by calculable nuclear processes. The massive stars have a shorter life and scatter themselves. They throw out their matter containing elements up to the Fe-group. This matter is caught in other stars and in turn captures neutrons (because of the larger cross-section) from light element reactions within the stars. In this way a small proportion of heavy elements will be built up. It has been possible to give explanation for some of the details in the nuclear abundance diagram - an extremely complicated picture. A particular triumph within this theoretical picture of element buildup in stars is the prediction by Hoyle of a C nuclear energy level (which was verified to exist). A cosmological requirement thus served as a prediction of a nuclear physics experiment.

According to the steady state model, there is no need to imagine a particular state of matter which was different in the past. As the formation of the elements is proceeding continuously, the overwhelming abundance of hydrogen now implies that the bulk of material is young enough not to have undergone these processes. In other models it is necessary to assume also that the material is mainly young, or that it has been in a non-reactive state until recently. To suppose that some process undid the nuclear combinations imagined as having taken place previously is very difficult and requires circumstances so far from those we know that such speculation seems unprofitable.

Discussion

BONDI remarked that is not a purely geometric quantity. The first three values given (page !!! Page Reference !!!) involve the use of the field equations of general relativity and the conservation of matter. The steady state model is flat in the large.

BELINFANTE inquired about the loss of number counts because of absorption of intergalactic matter.

BONDI replied that this could almost be ruled out because one could see so very far and the photoelectric measurements of Baum indicate there cannot be too much absorption out to the limits of observation.

DICKE observed that one could not see anything beyond that point and raised the question of the significance of number counts without going into red shift.

GOLD stated that there exist no good number counts since 15 years ago, and they do not distinguish between the models.

BONDI stated the astronomers say they cannot get such numbers easily because of the great accuracy required in brightness measurements and the steepness of the curve relating number and brightness.

GOLD remarked that the question of absorption is important but in a way the observations indicate it does not exist in fact to a significant extent.

BONDI inquired what fraction of the mass of galactic clusters is estimated to be neutral hydrogen.

GOLD replied several times the stellar masses.

DE WITT inquired about what happens to the energy-stress tensor which is not conserved in the steady-state theory.

BONDI replied that there is no clear-cut mathematical analysis. The assumption of the steady state theory is a physical hypothesis from which it is possible to make predictions, verifiable by observation, without going into the tensor calculus. McCrea suggests there is a zero point tension in the vacuum which on expansion produces outgoing energy.

DE WITT asked why protons should be chosen as the entities which are “created out of nothing.” Since they are already complicated structures, why not go all the way and use heavier nucleii - such as Fe - as well? Or is the theory to be considered purely phenomenological?

GOLD said that if any more basic heavy particles were to be made they would end up as protons and hence hydrogen gas. To assume the creation of Fe would seem very artificial and is in fact unnecessary.

BONDI pointed out that the evolutionary history of any galaxy required the pre-existence of matter and in the steady state model this means cold hydrogen gas is the simplest hypothesis and reasonable.

GOLD remarked that one is forced to the supposition of the coming into being of the matter anyway, as it could not have been around for an indefinite period without going into heavier elements.

DE WITT said that the creation of matter required the existence of some unknown dynamical process as a precursor to the creation which forces the production of protons rather than something else.

SCIAMA remarked that any future detailed formulation of the theory would have to account for the production of protons.

BERGMANN emphasized that the principle of equivalence of the general theory carried with it certain detailed consequences which includes the conservation of the stress tensor which follows from the covariance and action principles.

BONDI stated that what one has is something which is interpreted as having components measurable in the form of stress.

BERGMANN replied that whatever it is which is conserved is stress by definition. If expansion and creation occur simultaneously, stress can be conserved only by having influx of matter along with efflux so that the concept of creation is superfluous. The steady state hypothesis requires true creation which is a violation of stress conservation. It is conceivable that the principle of equivalence and the action principle may require modification from the other point of view.

PIRANI proposed that one envisage a Dirac type distribution of states which contributed to the energy tensor and condensed into the protons at the required rate.

BERGMANN said this could not lead to steady state.

PIRANI said it could.

GOLD pointed out that if creation is denied currently, it cannot be maintained for the past; and this issue cannot be avoided on any theory.

BERGMANN stated that he did not favor the explosion hypothesis either.

SCIAMA felt that the conservation equations as now known are interpreted too seriously. One could devise a more complicated theory with conservation equations arising from identities. The extra variable in such a theory could allow for creation.

WHEELER took the point of view that one should not give up accepted ideas of wide applicability such as general relativity but should investigate them completely. The two things left in question are the expansion and the creation of elements. The first does not appear to cause any difficulty in general relativity theory. Hydrogen can be created out of heavy elements by the reaction of matter in stars. This process continued sufficiently far will get one down to the absolute zero of temperature. There is a well defined state of absolute zero and, in the beginning, for not too great a mass, one has iron. If the mass is too great, the composition of the interior is pushed into neutrons. A neutron core star undergoing explosions will throw large quantities of neutron-rich matter into space which yields hydrogen.

GOLD questioned whether such a process could yield 99 hydrogen and helium.

WHEELER replied that no detailed calculation had been made but would not say that it could not be explained within the present framework of accepted ideas.

BERGMANN inquired about the thermodynamic analysis of the neutron core model leading to the hydrogen clouds from the point of view of entropy.

WHEELER said that initially it is a neutron situation at absolute zero under high pressure.

BONDI commented on the fact that Einstein's proposal of the Cosmological Principle 40 years ago occurred at a time without knowledge of the galaxies. The extension of the range of observation by radio and optical means has shown that a homogeneous system obeying the Cosmological Principle demands the distance vs. recession-velocity relation according to McCrea and Milne. The body of evidence in support of the Cosmological Principle makes it an astounding prediction, more striking, in a sense, than those of general relativity

WHEELER remarked that Einstein said also that symmetric motions say nothing about laws of motion. What is simple in physics are the laws of motion and not the motions themselves as, for example the situation in hydrodynamics with turbulence. The Cosmological Principle is not in the same category as other physical laws because it is not a fundamental law.

BONDI said its fundamental character may be debatable but not its success.

ERNST questioned if a steady-state theorist would drop the generalized Cosmological Principle if observations did not fit the steady-state theory.

BONDI replied, “Like a hot brick.”

ERNST continued with the statement that this would perforce leave only the stress-tensor and asked where could one go from there.

BONDI said he would drop the subject.

GOLD remarked that the steady-state theory is certainly successful in the sifting of observational data.