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As the National Academy of Sciences acknowledges, "Two amino acids do not spontaneously join in water.
Rather, the opposite reaction is thermodynamically favored." In other words, water breaks protein chains back down into amino acids (or other constituents), making it very difficult to produce proteins (or other polymers) in the primordial soup.
Either way, origin of life theorists must then explain how amino acids or other key organic molecules linked up to form long chains (polymers) like proteins (or RNA).
Chemically speaking, however, the last place you'd want to link amino acids into chains would be a vast water-based environment like the "primordial soup" or underwater near a hydrothermal vent.
However, it has also been known for decades that the Earth's early atmosphere was fundamentally different from the gasses used by Miller and Urey.
The atmosphere used in the Miller-Urey experiments was primarily composed of reducing gasses like methane, ammonia, and high levels of hydrogen.After running the experiments and letting the chemical products sit for a period of time, Miller discovered that amino acids -- the building blocks of proteins -- had been produced.For decades, these experiments have been hailed as a demonstration that the "building blocks" of life could have arisen under natural, realistic Earthlike conditions, corroborating the primordial soup hypothesis.From there, they believe Darwinian natural selection took over, favoring those molecules which were better able to make copies.Eventually, they assume, it became inevitable that these molecules would evolve complex machinery -- like that used in today's genetic code -- to survive and reproduce.Most theorists believe that there were many steps involved in the origin of life, but the very first step would have involved the production of a primordial soup -- a water-based sea of simple organic molecules -- out of which life arose.