5.1 ``Physical'' versus ``Astronomical'' Methods
There is a common (mis)perception that some methods for determining H0 based on simple physical principles are free from the types of systematics that often affect distance indicators (``physical'' versus ``astronomical'' methods). However, the fact remains that aside from nearby geometric parallax measurements (d < 100 pc), astrophysics enters all distance and H0 determinations! These methods include the gravitational lens time delay method, the Sunyaev Zel'dovich methods for clusters of galaxies, and theoretical modeling of type Ia and II supernovae.
For example, it is certainly true that the gravitational lensing method is premised on very solid physical principles (e.g. Refsdael 1964, 1966; Blandford & Narayan 1992). Unfortunately, the astronomical lenses are not idealized systems with well-defined properties that can be measured in a laboratory; they are galaxies whose underlying (luminous or dark) mass distributions are not independently known, and furthermore they may be sitting in more complicated group or cluster potentials. A degeneracy exists between the mass distribution of the lens and the value of H0 (e.g., Kundic et al. 1997; Keeton and Kochanek 1997; Schechter et al. 1997). This is not a method based solely on well-known physics; it is a method that also requires knowledge of astrophysics. Ideally velocity dispersion measurements as a function of position are needed (to constrain the mass distribution of the lens). Such measurements are very difficult (and generally have not been available). Perhaps worse yet, the distribution of the dark matter in these systems is unknown. In a similar way, the Sunyaev-Zel'dovich method is sensitive to the clumping of X-ray gas, discrete radio sources, the projection of the clusters, and other astrophysical complications.
Hence the methods for measuring H0 cannot be cleanly separated into purely ``physical'' and ``astronomical'' techniques. Rather, each method has its own set of advantages and disadvantages. In my view, it is vital to measure H0 using a variety of different methods in order to identify potential systematic errors in any one technique. All methods require large, statistically significant samples. This is one of the current weakest aspects of the Sunyaev-Zeldovich and gravitational-lens methods, for example, where samples of a few or only 2 objects, respectively, are currently available. In contrast, it is a clear disadvantage that many of the classical distance indicators (e.g., the Tully-Fisher relation and at present, even the type Ia supernovae) do not have a well-understood physical basis. However, there are many cross-checks and tests for potential systematic effects that are now feasible and are being carried out for large samples of measured extragalactic distances (see Section 5.4 below). Assuming that systematic effects can eventually be understood and minimized, ultimately, the measurement of H0 by a geometrical (or optical) technique at large distances will be crucial for establishing the reliability of the classical distance scale. For gravitational lenses, however, a considerable amount of work will be required to increase the numbers of systems with measured time delays, obtain velocity dispersion profiles for the faint lensing galaxies, constrain the lens models and test for other systematic effects, if this goal is to be reached.
Below, progress on H0 measurements based on gravitational lenses, the Sunyaev Zel'dovich effect, and the extragalactic distance scale is briefly summarized.