Final answer:
Alice will exhibit a greater redshift in her spectrum than Bob since she is moving away at a faster speed, and redshift in a galaxy's spectrum is proportional to its velocity relative to the observer. This results from the expansion of space itself, aligning with Hubble's law and supporting the Big Bang theory.
Step-by-step explanation:
Considering two distant galaxies, Bob and Alice, where Bob is moving away at half the speed of Alice, it is reasonable to deduce that Alice will show a greater redshift in her spectrum than Bob. The phenomenon of redshift occurs when the galaxies move away from us, causing the light they emit to appear at longer wavelengths, towards the red part of the spectrum. According to Hubble's law, the speed at which a galaxy is receding is proportional to its distance from us, meaning that the redshift in the spectrum of a galaxy is an indicator of its velocity relative to us. Therefore, given that Alice is moving away faster, her spectral redshift will be greater.
It's worth noting that this redshift is not a result of the actual motion of the galaxies through space but rather the expansion of space itself. Edwin Hubble's pioneering work established that with double the distance, the redshift doubles, illustrating that as part of universal expansion, more distant galaxies recede at higher speeds, as evident in their profound redshifts observed from Earth. Understanding this principle helps astronomers estimate the age of the universe at about 14 billion years and affirm the Big Bang theory.