EUR 33.-Is there any evidence/example for a non-deterministic phenomenon?

pure act, everything which exists is sustained in existence with actuality or animation. We see a graduating scale of entities that experience act at different intensities, for example vegetative life in its simpler variety does not demonstrate a capacity for sensation or movement; Animals do. Therefore animals experience or are more conscience of the actuality of existence because they have the proper accoutrements . And humans having a rational capacity experience the actuality of non changing substances such mathematically abstracted laws in the physical universe and immaterial substances like thought.therefore it's logical to conclude that there is a pure state of act which exists in the highest experience of actuality of which we are participating.

without being too technical, can we assume that worldly phenomena, no matter how complex, is still deterministic? like lightning strikes or number of hits that starmind will get on say 28th of February.

For a theoretical physicist or mathematician, it makes perfect sense, but it means nothing to the rest.

That is why I never write my answers like this.

This is the solution of Leo: What do you think about it? I very much like it...
In quantum theory, any system that one wishes to describe is fully specified by its "wavefunction" or "state vector" (same thing, slightly different formalism). The state vector of the system evolves according to the Schrodinger equation, which is fully deterministic. The schrodinger equation is not relativistic, but for relativistic problems the framework of quantum field theory does the same job, and again the evolution is fully determinisic. In quantum theory, this determinism is often phrased as the time evolution being unitary. Unitarity implies determinism, because a unitary matrix is always invertible, therefor it provides a one-to-one map between the present and any point in the future.

The only part of quantum theory that is not deterministic, is the process of a measurement on the system. In the Copenhagen interpretation, such a measurement is accompanied by a sudden, not deterministic, not inverible change of the wavefunction, called "collapse of the wave function". This description of measurements is a way to compare the mathematical world of quantum theory with experiments in a laboratory. In those cases it works very well, however, one has to keep in mind that such a measurement includes interaction of the system with a (macroscopic) outside measurement device. In effect, the quantum system under study of a few to maybe a few hundred atoms suddenly has to interact with on the order of 10^23 additional atoms (the device). The paradigm of wavefunction collapse descibes the effect of this very well, but this does not show that the evolution of the new "full system" of the quantum system + measuring device at any point evolved non-unitary.

Conclusion:

The measurement process in quantum mechanics is the only candidate for a non-deterministic process in physics. There is currently to my knowledge no conclusive evidence if it is actually non-deterministic or if it is actually deterministic but just very complex.

CAVEAT:

The process of black hole evaporation through the Hawking process can be argued to be non-unitary. However, this is a fully theoretical construction. Hawking radiation has never been observed. The question if Hawking radiation violates unitarity is called the "information paradox", and is still unresolved.