Webpage title: Does Real Quantum Randomness Play a Role in Evolution?

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Real quantum randomness may play a significant role in evolution by influencing the complexity and information content necessary for life to emerge. In a deterministic universe, the information would remain constant, raising questions about the potential for life to evolve without randomness. The discussion highlights the importance of patterns and complexity in life, suggesting that both deterministic and random processes are essential for creating and maintaining living organisms. While deterministic systems can encode vast amounts of information, randomness can enhance complexity and facilitate the emergence of new patterns. Ultimately, a balance between determinism and randomness appears crucial for understanding the evolution of complex lifeforms.
DrZoidberg
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I'm womdering if real quantum randomness is important for evolution to work. In a universe without randomness i.e. where the future is predetermined, the amount of information contained inside the universe would be constant. No matter how old it is, the information content of the universe would be the same as that of the equations describing the laws of physics there. So is it possible for life to evolve anyway and what is the minimum amount of information necessary for complex lifeforms to emerge?
What about simulating evolution in a computer? If the simulation uses only pseudo random numbers will that put limits on the complexity of the virtual lifeforms?
 
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DrZoidberg said:
I'm womdering if real quantum randomness is important for evolution to work. In a universe without randomness i.e. where the future is predetermined, the amount of information contained inside the universe would be constant. No matter how old it is, the information content of the universe would be the same as that of the equations describing the laws of physics there. So is it possible for life to evolve anyway and what is the minimum amount of information necessary for complex lifeforms to emerge?
What about simulating evolution in a computer? If the simulation uses only pseudo random numbers will that put limits on the complexity of the virtual lifeforms?
I don't think the amount of information is related to determinism vs. randomness, it's related to the issue of discreteness vs. continuousness. Determinism won't create information, that's true, but it also doesn't limit the information that is already present in the initial state. Old-style Newtonian mechanics was completely deterministic, but also involved an unlimited amount of information, because positions and velocities were treated as exact and continuous. So even a single particled encoded an infinite amount of information in every instant-- regardless of whether its motion was determined or random or anything else.

But I think what you are really asking is, how much information is required to have a living creature? If the initial data is patterned, then introducing randomness will increase the complexity and the information content. Yet patterns seem important for life-- we tend to associate life with a local drop in entropy, so a reduction in the information and an increase in patterning. Yet the patterns must themselves be highly complex. It seems to me that this must involve processes that can create and reproduce simple patterns out of what is originally random, and also processes that can increase complexity, perhaps via a dose of randomness, but deterministic processes could do it too (witness artificial intelligence and cellular automata and so on).

So I don't know, but I'd guess that you need some determinism to have life, because there has to be something predictable to maintain the delicately balanced processes that life requires. But there also needs to be some processes involved that are either effectively random, or really random-- but I don't see where that difference is ever crucial. The key seems to be a kind of balancing act between having patterns and having complexity, and certainly the mathematical treatment of chaotic phenomena can exhibit both patterned and unpatterned behavior while still being deterministic. That doesn't seem to be the key issue, but probably AI needs to be vastly more advanced than it is now to answer your question.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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