Hello Dr. Adlam,
- I enjoyed your essay. What are your thoughts on (local and non-local) hidden variables? ("...there are still physicists who argue that the conclusion of Bell's theorem can be avoided, for example by the rejection of the statistical independence assumption[13], and if they're correct then perhaps we can actually have both locality and determinism..."
- Do you ever have concerns about retro-causality? One could, after all, trace information and trajectories after something has happened (i.e. an electron was sent through a double slit and measured.)
- As I'm sure you are you are aware, excavating the universe through means of experiments that are induced by artificial means (conditions that are pushed and are unlikely to be encountered in nature such as trying to probe the standard model for more elements to join the particle zoo) is in order to see the nature of unnatural phenomena (such things that are difficult to find in nature such as Higgs boson particles).
- "...Now, it's useful to know that the halting problem is undecidable, but there's nothing particularly paradoxical about this, since after all the halting problem doesn't have to be decided in finite time in reality..." I don't know if you read Sabine Hossenfelder's essay "Math Matters". She argues that matters within realms of pure maths are not very helpful in practical areas of physics. Even though mathematics is extremely relevant to physics, physics is not mathematics. The latter is intuitive. Your above quote better succinctly describes pure maths and physics.
- Conventionally related to [pure] maths, you gave an example of a problem which occurs in the physical universe that is applicable to physics and it is undecidable (using 'undecidable' in the traditional context of a mathematician).
- I would also imagine that when you write about algorithmic programs terminating in some finite time, some time t would need to be somewhat reasonable.
- "...thus it might seem natural to suppose that the universe should not be able to decide undecidable problems..." Even with infinite time it would not surprise me if one could prove that undecidable problems are still undecidable.
- I'm currently reading "Quantum Mechanics and Global Determinism" that you wrote, too.
- "...yet it seems that the universe must be able to determine the answer to this problem in finite time, in order to avoid producing examples of non-locality which violate the laws of nature..." Are there problems that could [theoretically] be solved with some infinite amount of time or would such a dilemma remain unsolvable? I suppose part of the definition of solvable implies "in some finite time"- am I correct? "...there would no longer be any paradox if it were able to solve problems which require infinite time to solve..." Indeed, I concur.
- "...Well, first and foremost, physics will need to relax its emphasis on prediction. To be clear, this does not mean that we should stop demanding empirical evidence for out theories: if our aim is to understand reality, then our theorydevelopment and theory-selection need to be anchored in facts about reality, so I'm certainly not arguing that string theory or any of its similarly afflicted fellows should get off the hook for their failure to say anything empirically novel!..." Excellent point, worded wonderfully.
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I will absolutely give you very high marks. I really enjoyed your essay, friend.
Best regards,
Dale Carl Gillman