Hi Chimney Sweep:
This is a popular question here at ILP. It appears to me that the answers are fundamentally based on belief systems.
Usually this is approached from Causality. One belief system thinks that all phenomena are causal and thus deterministic. (Personally, I question whether or not the conclusion is justified from the premise). The other is typified by a quality poster named Polemarchus. He writes: “Nothing happens for a reason. Things happen. And they happen whether or not we’re able to discover a reason why they happened. Things don’t wait around for us to come up with reasons before they happen - they just happen. Events preceede the explanations we devise for them, that is, when we manage to explain them at all. Phenomena do not abide by our laws; we make our laws to account for the phenomenaâ€.
My personal opinion is that our models only work when we significantly restrict the domain of consideration.
Addressing your question more directly, some obvious things are Black Holes. They are singularities in the “fabric of spaceâ€.
Consider the single most obvious question that Physics can ask: how much does it weigh? The standard answer for our Universe is only off by 90%. Missed by just that much! (In honor of Maxwell Smart)
If you are trying to solve simple real life problems, you will find that, frequently, the solutions to the differential equations that theoretically govern particle behavior, have singularities or don’t exist at all.
Very simple resistance forces frequently can not be adequately modeled.
Some of the problems can become very complex. How would you solve the N body problem where all four forces are at play? To my knowledge there is no solution. In fact I do not believe that we can find the solution for a feather falling to the ground when we allow for air resistance.
Then there is Chaos Theory. You can check out the classic book by James Glick entitled “Chaos Making A New Scienceâ€. It will become evident that most macro phenomena are chaotic.
All of these comments regarding our current models can be overcome by simply objecting to the fact that we don’t have adequate models of how the Universe actually works.
I think that I can even overcome this objection. The following is from a previous post on ILP concerning determinism.
However, just for fun, I have been thinking about the possibility that determinism is logically inconsistent on its own ground.
I have been wondering if the belief in determinism could be analogous to the belief in axiomatic theoretical systems; and whether or not Godel’s Incompleteness Theorem might apply.
The following is a sketch of the idea.
Begin sketch
We will let the base elements of this “logic†be the spatial x, and temporal t, standard coordinate system, because determinism predicts events happening at a place and time. (This corresponds to the integers in Godel‘s Theorem).
The operators here will be the standard addition and multiplication. (These are identical to the operators in Godel’s Theorem).
We will say that r is the cause of event ej if and only if there is a predecessor event ei such that some governing dynamic which will force ei to become ej. r could be the solution to a differential equation governing a particle at (x,t). Now we let R is the set of all r‘s plus and standard logical transformation rules. (This corresponds to the transformational rules in Godel’s Theorem).
For notational purposes I will denote E as the class of all the events which will happen or that have happened. (This corresponds to the true mathematical statements).
If I can apply Godel’s theorem, then there would exist an eN in E such that eN is not the effect of any ej. (In Godel’s terminology eN is not demonstrable)
End sketch
The conclusion is that there exists some event which will happen, and this event is not the result of some other event.
While this consequence by itself is not overwhelming, the hard core fundamental belief that everything that happens must be the consequence of something else can not stand.
I think that I can extend this result to an entire class of events without much additional work
Any way welcome and I hope you enjoy your time here at ILP.