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I've heard about the fine-tuning principle and how if the fundamental constants of the Universe were changed even a slight bit, life could not exist as we know it.

However, study on this subject seems to only have really started after the discovery of relativity (or at least study based on any real empirical inferences), and focus mostly on the fundamental constants of nature, rather than the laws of nature itself. This gives rise to the question: could a universe exist that relied completely on Newtonian mechanics with no concept of relativity whatsoever?

Additionally, is there any study on this subject, and if so, where can I find it?

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I assume you mean general relativity with its curved spacetime? The principle of relativity actually comes from Newtonian mechanics, it doesn't supercede it. Einstein's contribution was to make the principle of relativity, which already existed in Newtonian mechanics, compatible with the laws of electricity and magnetism which were worked out in the generation before him. This required modifying slightly some of Newton's laws, and the further incompatibility of this modification with gravity led to the development of general relativity. –  Michael Brown Feb 18 '13 at 2:00
    
Anyway I don't see that this has anything much to do with fine-tuning, except for the coincidence that by the time people started studying cosmology in a serious way all of the relativity stuff had already been worked out. You could easily make fine-tuning arguments in a purely Newtonian universe. –  Michael Brown Feb 18 '13 at 2:02
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Ah, I see. Many people have been asking this question. There is no currently well accepted or testable framework for answering it. We don't know if there are multiple universes with different laws, or just this one with these laws. Apart from requiring mathematical/logical consistency, we don't know how or why nature chooses the ingedients and laws it does, or if more than one choice is possible. You'll find many different philosophical opinions on the topic and very little hard science. Sorry, I can't answer your question better than that. –  Michael Brown Feb 18 '13 at 2:12
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@alancalvitti Joe Zeng seems to be aware of what you are saying. He's asking whether a universe with different laws is possible. –  Michael Brown Feb 19 '13 at 1:42
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@alancalvitti Specifically, can that fantasyland rigidly adhere to the rules given to it, and still give rise to a stable universe, perhaps one that can give rise to life? –  Joe Z. Feb 19 '13 at 2:23
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3 Answers

Yes, such a Newtonian universe is at level IV in Max Tegmark's multiverse hierarchy. http://arxiv.org/pdf/0905.1283.pdf

(of course, this question (and answer) is more about philosophy than physics)

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It is somewhat about philosophy, but of a theoretical physical nature, so I put it here rather than Philosophy. –  Joe Z. Mar 8 '13 at 13:37
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You already get into trouble on the atomic scale: if you try to describe atoms as a nucleus with an electron orbiting it, you'd have to conclude they cannot exist. The reason for this is that an accelerating charged particle emits electromagnetic radiation, thereby losing all of its energy and crashing into the nucleus.

I imagine you could construct a perfectly Newtonian universe, but you'd have to introduce so many artificial constructions that it would not make any sense. Although it's probably quite arrogant to claim some fictional universe doesn't make sense if we don't even understand the actual universe (yet).

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It's this sort of theory I was looking for. I understand that we don't actually understand the universe in its entirety, but we understand it enough to know that our simplified, zero-limit approximations of the laws are inaccurate. What I wanted to know is whether a world could exist where they were accurate. –  Joe Z. Mar 8 '13 at 0:03
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@JoeZeng That's a strongly philosophically charged question and it might actually be considered off-topic because it falls outside of the realm of (our) physics. I guess you could probably get it to work self-consistently if you completely forgot about our world and created an entirely new nature. Things would look very different though and I don't think a lot of exciting stuff would happen. It'd probably be a dull place and it would definitely not be able to support life as we know it. Again, it's a philosophical question that is bound to remain unanswered with any scientifical rigour. –  Wouter Mar 8 '13 at 7:44
    
It is still a philosophical question about physics, though, which is why I put it here. –  Joe Z. Mar 8 '13 at 13:41
    
Actually, it is more of mathematics, than physics, since it isn't describing anything physical (about our universe). –  Dimensio1n0 Jun 14 '13 at 6:29
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I am not clear in what sense do you mean “Could a universe with purely Newtonian mechanics exist?” but here is my understanding of the situation.

In order to answer this question one must be based on established laws we know from our experience with our universe. It is only through these experiences that we can make inferences to situations elsewhere.

We know from our universe that there are two scales of great importance:

(i) Microscopic scale: This has taught us that for a rich universe, with ‘endless’ diversity and variation, it cannot be following rigid rules with yes or no type of choices. An inflexible universe like this would reach its final destination very quickly. It would run out of ‘ideas’ so to speak. Our universe achieves this diversity and flexibility we observe, via unpredictability and uncertainty. By this I mean that our universe operates on the basis of the laws of probability. Tiny details mater, and this is achieved by the extremely small size of Planck’s constant for example. This scale is ruled by Quantum Mechanics.

(ii) The macroscopic scale:**This is where the universe uses averages and effective collectivism in order to control **the large, and detail is not really important. This part of the universe makes no contribution to the diversity, flexibility and freedom we observe in nature. Things seem to be ordered and follow sort of rigid laws (Newtonian mechanics.)

However, it is impossible to reach scale (ii) without passing through scale (i). But scale (i) is ruled by the laws of quantum mechanics. For this reason one could conclude that an alternative universe would stagnate and reach self destruction relatively quickly.

Some people have done calculations for atomic stability by assuming smaller or larger values of Planck’s constant, or different Coulomb force law etc. They found that the atoms would not be stable under such variation of the laws of physics. One simply needs to look into the details of atomic structure, and their dependence on Planck’s constant, in order to realise the instability problems.

In conclusion: No, a purely Newtonian universe could not exist. Perhaps in my imagination, but this would be pure utopia.

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I agree, a newtonian universe would not have life to start with, and thus Newton would have not existed, since life is directly dependent on quantum mechanics. There will also not be any sun/stars since they depend on fusion, a par excellence quantum mechanical phenomenon. A science fiction world of billiard ball like atoms of Demokritos and just dark planets? –  anna v Mar 8 '13 at 13:53
    
+1 for the analysis but just because the universe is "boring" doesn't mean it can't exist. I mean, even simple universes such as Cellular Automata exist! –  Dimensio1n0 Jun 14 '13 at 6:32
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