Yeah, the thought of eternal return, or a wheel of time or similar is an ancient concept. Many religions have been based around it, and today there are plenty of people who think it or believe it a possibility.
The thought of a "big crunch" as it's known used to be prominent hypothesis after the big bang theory was established, but more recent evidence suggests that the universe is accelerating rather than slowing down as it seems it should due to gravity. If this trend continues we can reasonably assume that the Universe will simply expand indefinitely and become an endless void, thus avoiding the possible wheel of time.
However, even assuming the universe did fall back in on itself and another big bang occurred, the outcome would not automatically be the same even if the rules are the same. Remember that the laws that govern the universe set limits on what can happen, but not so stringently as to allow only one possible outcome. The best way to demonstrate this is with quantum fluctuations, which ensure that this is a universe of statistical probabilities, not certainties. You also assume that a singularity can only be compacted in one specific way, but I will point out that all the laws of the universe break down at such a state and everything becomes uniform in every way. This would in essence make any pattern beyond absolute symmetry impossible.
We can of course not say with absolute certainty that eternal return cannot happen, but current understanding seems to preclude the possibility of such a cycle.
Note: I have to nitpick one thing you said, and that is that you called the big bang an explosion. The big bang is poorly named, and the name was originally intended as a mockery of the theory yet it stuck. The correct description would be rapid expansion. I only point it out because some people use the term explosion for the big bang out of ignorance as a way to mock it, mostly creationists.
The thought of a "big crunch" as it's known used to be prominent hypothesis after the big bang theory was established, but more recent evidence suggests that the universe is accelerating rather than slowing down as it seems it should due to gravity. If this trend continues we can reasonably assume that the Universe will simply expand indefinitely and become an endless void, thus avoiding the possible wheel of time.
However, even assuming the universe did fall back in on itself and another big bang occurred, the outcome would not automatically be the same even if the rules are the same. Remember that the laws that govern the universe set limits on what can happen, but not so stringently as to allow only one possible outcome. The best way to demonstrate this is with quantum fluctuations, which ensure that this is a universe of statistical probabilities, not certainties. You also assume that a singularity can only be compacted in one specific way, but I will point out that all the laws of the universe break down at such a state and everything becomes uniform in every way. This would in essence make any pattern beyond absolute symmetry impossible.
We can of course not say with absolute certainty that eternal return cannot happen, but current understanding seems to preclude the possibility of such a cycle.
Note: I have to nitpick one thing you said, and that is that you called the big bang an explosion. The big bang is poorly named, and the name was originally intended as a mockery of the theory yet it stuck. The correct description would be rapid expansion. I only point it out because some people use the term explosion for the big bang out of ignorance as a way to mock it, mostly creationists.
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