in cosmology texts well into the 1980s, though it was dismissed as an unlikely and ad hoc proposal by mainstream astrophysicists. By the 1990s and on into the twenty-first century, a number of falsifying observations have shown that "tired light" hypotheses are not viable explanations for cosmological redshifts. For example, in a static universe with tired light mechanisms, the surface brightness of stars and galaxies should be constant, that is, the farther an object is, the less light we receive, but its apparent area diminishes as well, so the light received divided by the apparent area should be constant. In an expanding universe, the surface brightness diminishes with distance. As the observed object recedes, photons are emitted at a reduced rate because each photon has to travel a distance that is a little longer than the previous one, while its energy is reduced a little because of increasing redshift at a larger distance. On the other hand, in an expanding universe, the object appears to be larger than it really is, because it was closer to us when the photons started their travel. This causes a difference in surface brilliance of objects between a static and an expanding Universe. This is known as the Tolman surface brightness test that in those studies favors the expanding universe hypothesis and rules out static tired light models. Redshift is directly observable and used by cosmologists as a direct measure of lookback time. They often refer to age and distance to objects in terms of redshift rather than years or light-years. In such a scale, the Big Bang corresponds to a redshift of infinity. Alternative theories of gravity that do not have an expanding universe in them need an alternative to explain the correspondence between redshift and distance that is sui generis to the expanding metrics of general relativity. Such theories are sometimes referred to as "tired-light cosmologies", though not all authors are necessarily aware of the historical antecedents. Specific falsified models In general, any "tired light" mechanism must solve some basic problems, in that the observed redshift must: admit the same measurement in any wavelength-band not exhibit blurring follow the detailed Hubble relation observed with supernova data (see accelerating universe) explain associated time dilation of cosmologically distant events. A number of tired light mechanisms have been suggested over the years. Fritz Zwicky, in his paper proposing these models investigated a number of redshift