Years later, an obscure mathematician from the former Soviet Union, Friedman, applied the field equations without the cosmological constant and developed a model of an expanding or pulsating universe. Friedman's universe is uniform and isotropic in three-dimensional space, but it is not static. This model changes over time and can be categorized into three scenarios: the first scenario has a negative curvature of three-dimensional space; the second has zero curvature, meaning it is flat; and the third scenario has positive curvature. In the first two cases, the universe continuously expands; in the third case, the universe expands to a maximum size before starting to contract, then expands again, and contracts once more, resulting in a pulsating universe. Friedman's model was initially published in a lesser-known journal. Later, some mathematicians and physicists in Western Europe developed similar models. When Einstein learned of these expanding or pulsating universe models, he was thrilled and believed his own model was flawed and should be abandoned, asserting that Friedman's model was the correct one.
At the same time, Einstein declared that adding the cosmological constant to the field equations of general relativity was a mistake; the equations should remain as they originally were. However, the cosmological constant, like the genie released from the bottle in "One Thousand and One Nights," could not be retracted. Subsequent scholars ignored Einstein's opinion and continued to discuss the significance of the cosmological constant. Today, there are two forms of the field equations in general relativity: one without the cosmological constant and another with it, both of which are utilized and researched by experts.
As early as around 1910, astronomers discovered that most galaxies exhibited redshift phenomena, while a few showed blueshift. These phenomena can be explained by the Doppler effect. Light emitted from a source moving away from us appears to have a lower frequency and longer wavelength, resulting in redshift. Conversely, light from a source moving towards us shifts towards shorter wavelengths, causing blueshift. This phenomenon is similar to the Doppler effect with sound. Many people have experienced this: the sound of a train approaching is sharp and piercing, while the sound of a train moving away is noticeably duller.
If we consider the redshift and blueshift of galaxies as a Doppler effect, it suggests that most galaxies are moving away from us, with only a few approaching. Further research revealed that those few blueshifted galaxies were all within our own local group of galaxies (the group containing our Milky Way). In the local group, most galaxies exhibit redshift, while a minority show blueshift, whereas galaxies in other groups are entirely redshifted.
In 1929, American astronomer Hubble summarized some observational data and proposed an empirical law stating that the amount of redshift in extragalactic galaxies (i.e., galaxies beyond our Milky Way) is directly proportional to their distance from the center of our galaxy. Since the amount of redshift due to the Doppler effect is proportional to the speed of the light source, this law can also be expressed as: the recession velocity of extragalactic galaxies is proportional to their distance from us: V = HD, where V is the recession velocity and D is the distance to the center of our galaxy. This law is known as Hubble's Law, with the proportionality constant H referred to as the Hubble constant. According to Hubble's Law, all extragalactic galaxies are moving away from us, and the farther they are, the faster they recede.
Hubble's Law aligns perfectly with the theory of cosmic expansion. The few galaxies that show blueshift can be explained by the fact that galaxies within the local group orbit around their common center of mass, so there will always be a few galaxies approaching our Milky Way at any given time. This blueshift phenomenon is unrelated to the overall expansion of the universe.
Hubble's Law greatly supported Friedman's model of the universe. However, if we examine the data plots Hubble used to derive his law, we might be surprised. The points he plotted in the graph relating distance to redshift are not clustered closely around a straight line but are rather scattered. How could Hubble confidently assert that these points should be represented as a straight line? One possible answer is that Hubble grasped the essence of the pattern while disregarding the details. Another possibility is that Hubble was already aware of the contemporary theory of cosmic expansion, leading him to boldly assume that his observations were consistent with that theory. Subsequent observational data became increasingly precise, and the points in the data plots clustered more closely around a straight line, ultimately confirming Hubble's Law through extensive experimental observations.
