If one were to plug "Big Bang theory" into a search engine, it would be difficult to remember that the phrase used to refer to a scientific theory and not a U.S. sitcom. But, yes, "the Big Bang theory" did originally mean the name of a cosmological model of how the universe came to be. (A scientific model is a kind of metaphor that seems to explain the evidence at hand and even suggests things that are later discovered to be true, although the model can be altered or dismissed should future evidence warrant it.)
What is the Big Bang theory?
The Big Bang theory considers the evidence that galaxies appear to be accelerating away from one another, and logically assumes that at one point they must have been closer. Much closer. So close that all the energy in the universe was condensed into a single point known as a singularity. The Big Bang theory teaches that for some unknown reason, about 13.75 billion years ago (as evidenced by the speed and location of the galaxies), something occurred that caused that energy point to expand rapidly. As it spread, the expanse cooled and formed subatomic particles, which combined into the most basic elements: hydrogen, helium, and lithium. Giant clouds of these simple atoms condensed through the pull of their own gravity and formed stars. The fusion inside the hearts of stars formed heavier elements such as carbon and nitrogen, which spread into the universe when the host stars went supernova.
The Big Bang replaced the theory that the universe had always existed in a stable state. This view had been held from Aristotle through the career of Albert Einstein, until he finally admitted that a universe with a beginning better fit the data at hand. Still, most physicists continued to believe in the steady state theory until the 1970s or 80s.
The Big Bang theory explains many quirks about the universe. Among them are background cosmic radiation, the expansion of the universe, and the distribution and appearance of cosmic bodies such as galaxies and quasars. As is often the case in physics, the Big Bang theory does not gain credence merely because it explains these phenomena, but because scientists used the theory to predict these phenomena and later discovered they were right.
Conversely, the Big Bang theory has also predicted things that have never been found. The heat of the initial expansion should have created magnets with only one pole, but no such magnets have been discovered. As energy converted into subatomic particles, corresponding antimatter particles should have also been formed, but there is not nearly enough antimatter to account for all the matter. In addition, the original stars that turned hydrogen, helium, and lithium into heavier elements have a very long lifespan, longer than what has elapsed since the Big Bang, but astronomers have yet to find any.
Ironically, the Big Bang theory does not explain the "bang." It takes current conditions and attempts to count backward in time. It assumes that all natural laws have remained the same since the beginning of the universe, but even then it cannot explain how energy could reside in a singularity or what made it explode. But atheist scientists don't treasure the Big Bang theory because it explains everything; they treasure it because it explains "enough" to be able to say, "We don't need God for this universe to have been created," as Stephen Hawking has said. Evolutionary creationists, on the other hand, accept the Big Bang, but insist that God was the cause. They take science and scientific law as far as they can, and then add God's miracles to fill in the gaps.
Other articles have discussed the methods people use to reinterpret Genesis 1 and 2 to fit evolution, whether it's through the day/age theory or the framework theory. Suffice it to say that the Bible does not support the idea that creation could be 13.75 billion years old. Genesis quite literally states that God made the Earth before the stars and light before the sun, and from a scientific standpoint, that sounds like nonsense. But Genesis 1 is the only account of creation we have that is purported to be transcribed from the testimony of the only One Who was there at the time—God. It's foolish to trust Him for redemption and restoration of our fallenness, but not trust His Word when it comes to His creative power. Atheists like the Big Bang theory because it "proves" that creation didn't need God. Old-earth creationists like the Big Bang theory because it allows them to believe in God and still accept the messages that human science inundates them with. The Big Bang theory may be a useful model for deriving new discoveries, but no scientific theory is truth.
When faced with imperfect scientific theories and the respect of men, we should always consider 1 John 2:15-17:
Do not love the world or the things in the world. If anyone loves the world, the love of the Father is not in him. For all that is in the world—the desires of the flesh and the desires of the eyes and pride of life—is not from the Father but is from the world. And the world is passing away along with its desires, but whoever does the will of God abides forever.
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How old is the Earth?
Intelligent Design Theory - What is it?
Is theistic evolution biblical? What is theistic evolution?
Truth about Creation