During the fall semester of 1984 I visited the State University of New York at Stony Brook and taught an advanced graduate course on wave equations and quantum fields in curved space-times. This book is based on the notes for that course. I am very grateful to the Mathematics Department of SUNY, particularly Professor Michael Taylor, for arranging my temporary faculty appointment there.

The audience for the course consisted of graduate students and faculty members, mostly in mathematics but some in physics. They were assumed to have some knowledge of differential geometry and general relativity, and therefore not much time was spent on expounding those subjects. (The major exception is a chapter on connections on vector bundles and the Synge–DeWitt formalism needed for curved-space renormalization.) More time was spent on establishing a background in quantum theory and certain aspects of analysis, notably eigenfunction expansions.

Addressing such a mixed audience forces two difficult decisions – the relatively superficial one of what language to adopt, and the deeper one of what background knowledge to assume. I have an easy way out of the first problem: because of my own mixed background, the terminology which comes most naturally to me is a roughly equal mixture of the standard vocabularies of mathematicians and physicists. I have tried to say things in several different ways, to keep as many readers comfortable as possible.

When the quantum mechanics of particles appeared, circa 1925, its own inventors immediately realized that it was not really adequate for physics, for several reasons:

1. (1) It's nonrelativistic. This shortcoming can't be overcome simply by using (special) relativistic classical particle mechanics in place of nonrelativistic mechanics as the source of the equations of motion or the Hamiltonian. Attempts to do so led to relativistic wave equations, the Klein–Gordon and Dirac equations, which were afflicted with negative probabilities or negative energies, respectively. Superficially these could be eliminated by discarding half the solutions ad hoc, but the resulting theories developed inconsistencies when interactions were included.

2. (2) The states describe fixed numbers of particles. Therefore, the theory can't describe processes in which particles are produced or destroyed. Such interactions are observed experimentally, as when a proton and an antiproton annihilate into an electron, a positron, and a number of pions and photons.

3. (3) In electromagnetism (and also in gravitation) the principal object in the classical theory is a field, not a particle. It was therefore expected that the quantization process could be extended to fields.

In a sense, all these problems are the same problem. Special relativity implies the equivalence of mass and energy, hence the possibility that new particles can be produced when the particles coming into an interaction have total kinetic energy in excess of the total rest mass of the prospective products.

If a few quasars belong to some nearby galaxies, where do the majority of quasars belong? Over three thousand quasars are known now; most of them are spread over large areas of the sky where it is not immediately apparent that they are associated with any particular galaxy. One obvious answer might be, for example, that most quasars were ejected away from their galaxies of origin to mingle somewhere in intergalactic space. Perhaps only a few have been ejected so weakly that they orbit around their galaxy of origin. Perhaps only a few are seen close to the moment of their emergence, where they still show an umbilical attachment to their parent galaxy. But it is possible that sometimes a galaxy might eject many quasars and might be caught in the act of doing this. Could it have been predicted that some galaxies had many associated quasars? If so, it also might have been predicted that they would be encountered unexpectedly.

The Galaxy with the Longest Known Optical Jets, NGC 1097

In 1974, I was sitting at a viewing machine in Edinburgh, systematically scanning deep plates of the southern sky taken with the Schmidt telescope in Australia. This was part of a more than ten-year project with Barry Madore that culminated with the publication in 1987 of a two-volume Catalog of Southern Peculiar Galaxies and Associations. Someone from the Schmidt Telescope Unit brought me a deep plate of another region.

As mentioned in the first chapter, after 1966, a number of investigations built up the evidence that quasars were associated with nearby galaxies. One of the first systematic investigations of quasars over the sky was an analysis I published in 1970. I was still a faculty member at Caltech at the time, and I remember well the custom of astronomy luncheons at the Faculty Club every Friday. I would bring in new examples of quasars falling improbably close to galaxies and share these photographs with my colleagues. Finally, the consensus was communicated to me that they believed these to be specially selected cases and that as scientists they could only accept the effect if a full statistical test were performed on a complete sample. I thereupon took about six months away from normal activities, enlisted the aid of Fritz Bartlett, a radio astronomer, to program the large IBM computer which Caltech then relied upon, and proceeded to analyze the position of all the then-known 3CR quasars (Third Cambridge Catalog Revised Survey of Strong Radio Sources) with respect to all the galaxies listed in the Shapley-Ames Catalog of Bright Galaxies.

Figure 2-1 shows the striking result of those computations. It shows how the separations on the sky between a set of radio quasars and cataloged galaxies steadily decreases as brighter and brighter galaxies are considered—that is, the association with these quasars is stronger as galaxies closer to us in space are considered.

The discovery of the association with normal galaxies of peculiar, high-redshift companions made it clear that most of the excess redshifts of these smaller galaxies must be of nonvelocity origin. In contemplating the staggering problem this raises, it occurred to me that the magnitude of these excess redshifts might extend down to rather small amounts. On a macroscopic scale nature should not be discontinuous. Where would we look for examples of these smaller excess redshifts? The obvious answer is: in the wellknown companions of large, nearby galaxies. Therefore, in 1970, I looked at the redshifts of the long-accepted physical companions of the nearest large galaxies like M31 and M81. The companion redshifts were systematically greater! I remember feeling a sense of wonder that this obvious effect had gone unnoticed, and a little awe that the high excess redshift phenomenon had been supported in such an unexpected and unequivocal way by these systematic small excess redshifts.

The reason that this systematic redshift could not arise from a velocity (Doppler effect) is that these companions had long been accepted by all astronomers as belonging to the dominant galaxies. In that case they should be in orbit around these central galaxies and we should see on the average as many coming towards us (relative blueshifts) as going away from us (relative redshifts). If their mean velocities were away from us then these companions would be drifting away from the central galaxy and always just in the direction we happened to be looking.

The observational evidence presented in the first nine chapters requires that objects and events in the universe are much different than has been commonly supposed. Exactly how the universe does work in detail, of course, cannot be specified with certainty at this moment. It is possible such a time can never come. Nevertheless, it will be fascinating to discuss some of the advances in understanding that might result from this new observational evidence.

The Empirical Results

We have emphasized previously that only one well-documented example of an extragalactic, nonvelocity redshift is required to overthrow the current assumption that all extragalactic redshifts are caused only by velocity of recession. Table 11-1 recapitulates a dozen independent proofs of the phenomenon of nonvelocity redshift explored in this book. The table has been arranged in its present form in order to summarize these many different cases and also in order to fore stall an old game with which I unfortunately have had much experience. The game goes something like the following: “In such an important matter we want to consider only the most conclusive proof which exists. Which proof is the most conclusive? Ah yes, that one is very interesting. We will adopt that one as our experimentum crucis. But now, of course, there is always the remote chance that it could be an accident, and we cannot overthrow an important principle on only one example.”

The opposite page shows a photograph of three quasars closely grouped around a large galaxy. The chance of these three quasars accidentally falling so close to a galaxy is between 10−5 and 10−7, that is about one chance in a million. This is an enormously interesting observation because the quasars, with high redshifts, are conventionally supposed to be far behind, and unrelated to the galaxy which has a much lower redshift. Nevertheless, there was an attempt to suppress the discovery and observation of these quasars. When finally submitted to the Astrophysical Journal, publication was held up nearly 1½ years. An anonymous referee stated, “The probability arguments are completely spurious.”

What is the truth about this matter? Are the quasars related to the galaxy or not? And why the emotion, intrigues, and deadly professional combat which the subject has inspired for the last 20 years? To answer these questions, I believe, gives insight into the state of knowledge in astronomy today and also illuminates the passions, prejudices, and power relations in a modern science. We can explore the consequences of this for human knowledge toward the end of this book, but first, let us just follow for a while the thread of one particular story, the history of the claimed association of quasars with galaxies.

In 1966 while checking galaxies in my newly completed Atlas of Peculiar Galaxies, I noticed that radio sources, including some quasars, fell close to, and aligned across, some of the particularly disturbed galaxies.

From the first time that people started to look closely at galaxies it was clear that galaxies could eject material. By the early 1900's moderate-sized telescopes and the advent of photography had enabled individual galaxies to be examined. Among the brightest of these galaxies was M87 (Messier 87. also called NGC 4486 and, with the coming of radio astronomy, Virgo A). A photograph published by Heber Curtis in 1918 showed a luminous spike originating from its nucleus. It was like a fountain of material emerging from the center of the galaxy. It was always clear that it was ejected and it was always called the “jet” in M87.

But then it was ignored. A generation later, during the 1950's, radio astronomy began to explore the skies and immediately discovered unavoidable evidence of ejection outward from the nuclei of many different galaxies. In particular, a jet of radio emitting material was discovered emerging from the nucleus of M87. It was coincident with the original optical jet. But radio astronomers were only easy with the concept of charged particles (electrons, for example) bending in magnetic fields and therefore emitting the energy (synchrotron radiation) which they detected with their receivers. Therefore they classified the jet in M87 as “optical synchrotron” radiation, implying that it was a hot gas, would expand and dissipate and thus, if you waited a little while, the problem would go away.

Redshifts and the Hubble Law

In 1924, Edwin Hubble demonstrated that the small, hazy patches of light we see in the sky on a dark night—the galaxies—are really enormous islands of billions of stars, like our own Milky Way galaxy seen at a great distance. Study with large telescopes revealed that the fainter and smaller a galaxy appeared, the higher, in general, was its redshift. Redshift describes the fact that the characteristic lines in its spectrum due to hydrogen, calcium, and other elements appear at longer (redder) wavelengths than in a terrestrial laboratory. This effect was most simply attributed to a recession velocity of the emitting source—like the falling pitch of a receding train whistle. It was therefore concluded that the fainter and smaller the galaxy, the more distant it was, and the faster it was flying away from us. This is the velocity interpretation of the redshift-apparent brightness relation, the standard interpretation of the so-called Hubble law.

About this time, Einstein was writing equations that attempted to describe the behavior of the entire universe, the totality of what exists. His equations pointed to its probable instability. Gravitation was either strong enough to be in the process of contracting the universe or too weak to prevent its expansion. In view of the extant conclusions about galaxy recession velocities, it was natural to interpret them as due to expansion of the universe.

The conventional view of quasars is that they are normal galaxies which have, for some reason, superluminous nuclei which enable them to be seen at great distances in the universe. But if quasars really were these kinds of galaxies, we should expect to see them clumping into the clusters or superclusters that characterize the distribution of galaxies on the largest scales. Attempts have been made to relate some quasars with faint, adjacent galaxies of the same redshift. But no conspicuous clusters are evident. Moreover, it is completely clear that we do not see clusters or groups of quasars all having closely the same redshift. The conclusion forced on the conventional believers is that quasars are so rare that we seldom see a cluster of galaxies with one; that is, far less than one quasar exists per average supercluster.

But if we look around the quasars we do see, to a faint enough level, we should see the galaxies that accompany them in their clusters and superclusters. Wide-field Schmidt telescopes, since the invention of high-detectivity emulsions, can routinely register galaxies to a limiting apparent magnitude fainter than 23. That corresponds to a redshift for a normal galaxy of at least z ≈ 0.5.

We should be able to easily see faint, rich clusters of galaxies around quasars out to this redshift and beyond. We do not. (You can believe that if we did we would have heard an enormous amount about it!) Clearly, this is an outstanding violation of the cosmological assumptions.

What every astronomer measures in the spectrum of a galaxy is the percentage by which a line is shifted from its laboratory wavelength. Astronomers habitually say they measure a velocity. That is incorrect. What they measure is a redshift, what they infer is a velocity. The only astronomer I ever knew who was meticulously accurate about this was Fritz Zwicky, who always used the term “indicative” recession velocity. For consistency with general astronomical usage we have expressed large redshifts as fractional shifts (Δλ/λ), but for smaller redshifts multiplied them by the velocity of light in km s−1 as if they were Doppler velocity shifts. (The speed of light is approximately 300,000 km s−1).

Corrected Values of the Solar Motion

Even though we have consistently used the correct term—redshift or blueshift—for the measured quantity (whatever may cause the shift) we still have to remove from this measure the effect of any bona fide motions that we do know about, such as the orbital velocities of the earth around the sun and the sun around the galactic center. Redshifts of galaxies are initially measured with respect to the telescope that observes them. Then they are normaly given a small correction for the earth's motion around the sun (less than 30 km s−1) and called heliocentric redshifts. The motion of the sun must then be removed.

The motion of the sun with respect to the coordinate frame of the nearby galaxies consists mainly of a rotation of the solar neighborhood around the center of our own Galaxy.