Doppler Shift

By utilizing the Doppler shift, astronomers can determine the speed at which a galaxy is moving either toward or away from us. The fractional shift in wavelength, known as Delta_lambda, is calculated by dividing the radial velocity of the galaxy by the speed of light. If the wavelengths are stretched towards the red end of the spectrum, resulting in a positive Delta_lambda, it indicates that the galaxy is moving away from us. Conversely, a blueshifted spectrum signifies that the galaxy is approaching us. When this measurement is applied to the brightest galaxies in the sky, the radial velocities exhibit significant variation. Some galaxies, such as Andromeda and Triangulum, are moving towards us, while others are rapidly moving away. However, when astronomers examine fainter galaxies, an intriguing pattern emerges. The majority of these galaxies exhibit redshifted spectra, indicating that they are all moving away from the Milky Way. This discovery was initially made by Vesto Slipher in the early 20th century.

Cepheids

Determining distances in astronomy has traditionally been a challenging task. However, one method involves the use of Cepheid variable stars. Cepheids pulsate, causing them to alternate between periods of brightness and faintness with a consistent rhythm. It has been observed that the period of pulsation is closely linked to the star's luminosity. By measuring the period of a Cepheid, astronomers can calculate its luminosity, making them useful as "standard candles." By utilizing the flux-luminosity relationship and solving for the distance (d), astronomers can determine the distance to the Cepheid. However, the detection of individual Cepheids is limited to approximately 50 megaparsecs. To extend our reach even further, astronomers employ another method using standard explosions: Type Ia supernovas. These supernovas consistently explode with nearly the same amount of energy. By measuring the color and duration of the afterglow of a Type Ia supernova, astronomers can calculate its luminosity with a high degree of accuracy. These supernovas have a significant advantage in that they are bright enough to be observed across the entire universe, spanning billions of light-years away.

The Hubble Diagram

When astronomers measure the radial velocities and distances of numerous galaxies and plot them against each other, they observe a distinct pattern: a straight line relationship between velocity (V) and distance (D). This discovery, first presented by Edwin Hubble in 1929, provided compelling evidence for the Big Bang theory. The linear relationship between V and D resembles what one would expect from an explosion. However, the interpretation of this pattern is not as straightforward as galaxies simply moving away from a single point. The velocities of galaxies are not necessarily constant since gravity acts to slow them down and eventually bring them back together. Furthermore, the Hubble Diagram does not imply the existence of any privileged galaxy at the center of the universe.

No Unique ‘Center’

In an analogy using raisin bread, envision yourself inside a mass of dough, situated on a raisin among other raisins. As the dough bakes and expands, causing the bread to rise, you observe all the raisins moving away from each other at velocities proportional to their distances. The crucial point is that even if you were to switch to a different raisin, you would still perceive all the other raisins receding from you at velocities proportional to their distances. This suggests that there is no singular "center" of the expansion. Likewise, our universe contains a vast number, potentially infinite, of galaxies—comparable to the raisins in the bread—with each galaxy having a position vector denoted as r. On a particular day, we measure the positions (r-i) and velocities (v-i) of all the other galaxies. Using a coordinate system in which our galaxy, the Milky Way, is positioned at the origin, we uncover the Hubble expansion: the change in position (r-i) is equal to the product of the velocity (v-i) and time (t).

Flying to a Different Galaxy

Suppose someone travels to a different galaxy using an intergalactic spaceship and measures the distances and velocities of all the galaxies relative to their new home galaxy. In this coordinate system, where the new galaxy is at rest at the origin, the measured data is denoted as r-prime and v-prime. By employing vector algebra, the relationship between the new measurements and the original ones can be deduced. The displacement vector, r-i-prime, from galaxy one to the i-th galaxy is equal to r-i minus r1. Similarly, the velocity measured by the moving observer, v-i-prime, is v-i minus v1, as they move along with galaxy one. Replacing the r's with v-t's based on the Hubble relation observed in the Milky Way, and factoring out time, the vector in parentheses becomes v-i-prime. This implies that those who have moved will find r-i-prime equals v-i-prime times t. Consequently, everyone, regardless of their location, will arrive at the same conclusion: velocity is proportional to distance with the same constant of proportionality.

Turning Back the Clock

When considering the reversal of time in the context of the universe's expansion, it doesn't necessarily mean that all galaxies will converge to a single point. According to the theory of general relativity, the Big Bang is described as the expansion of space itself from a state of infinite density, rather than an explosion occurring at a specific location. To illustrate this, we can imagine an infinite loaf of raisin bread. As we rewind time and observe the bread "un-rise," the raisins come closer together, but the bread remains infinite in all directions. More raisins come into view, and the bread becomes denser and denser until, at time zero, it becomes infinitely dense everywhere.