Tanelorn said:
I am not certain, but most here seem to be saying that we just don't know, one way or the other, if this Universe is truly random.
It goes further than that. So far all the theories we have are of the type that have deterministic or probabilistic interpretations. Because of that, in principle, it is unknowable.
Tanelorn said:
I think I am effectively asking whether, with a total understanding of all the Physics of the Universe, I can predict with absolute 100% certainty what I will have for breakfast ten years to the day from now, including the number of atoms of each element as well as the exact positions of all included subatomic particles at an instantaneous Planck point in time?
As it stands you have asked a meaningless question because we do not know all the physics of the universe - we have zero idea what new laws that may be discovered will tell us.
But what we do know is this. The laws we do know have initial conditions depending on real numbers and any errors in the knowledge of those initial conditions tends to grow as time goes by so that predictions made without exact knowledge gets greater and greater until it becomes totally unreliable. This is the famous butterfly effect - since a real number requires infinite precision that is impossible to obtain, even if the universe is perfectly deterministic, its useless in practice - you can't predict just about anything with any kind of certainty.
Tanelorn said:
Everything I thought I knew said that this simple question can never be answered. I didn't realize that it was even something we weren't sure of.
Yea - the universe is not only stranger than we imagine, it is stranger than most of us can imagine.
Tanelorn said:
Bill regarding Noether, doesn't this assume a Universe that is not going to change over time? Dark Energy may mean that it does change?
It assumes the fundamental laws of nature, whatever they are (caveat given a bit later) are the same. Fundamental laws mean things like Maxwell's Equations, the laws of QM, Newtons Laws, Relativity and even future laws we may not know about. It's very hard to imagine a law that is not the same regardless of time, where you are, or what direction you are oriented in - its almost by the definition of law - its not really what you would call a law unless it's like that. So basically its really the requirement, more or less, that nature is describable by laws.
That this implies conservation laws like energy, momentum etc is - well shocking. Unless you have come across it before it would be the last thing you would have thought. Its a very very deep fact about nature:
https://www.amazon.com/dp/0918024161/?tag=pfamazon01-20
'Wigner points out that the basis for answering the question posed by him, 'Why is it possible to discover laws of nature?' is explained in every elementary physics text but the point is too subtle, is therefore lost on nearly every reader. The answer, he explains convincingly, lies in invariance principles. As an example, were local Galilean invariance not true it would have been impossible for Galileo to have discovered any law of motion at all. The same holds for local translational, rotational and time-translational invariance. Inherent in Wigner's argument is the explanation why the so-called principle of general covariance is not the foundation of general relativity, which also is grounded in the local invariance principles of special relativity.'
I strongly urge you if you are interested in actually understanding why the world is as it is, to get that book and study it closely.
Now for the caveat. Noethers theorem depends on the laws of nature being in a particular form called a least action principle. All the laws of nature so far known are like that and it would be a bit shocking if any was found that isn't, but it is an assumption.
Thanks
Bill