From the viewpoint of Islamic philosophers...
From the viewpoint of Islamic philosophers, (1) causality is not limited to the natural phenomena which figure in experimentation, but is a general law of existence, applicable to the material and the immaterial; (2) the cause whose existence is confirmed by this principle need not be subject to experimentation, nor it need be of a material nature; (3) the fact that experimentation does not disclose a specific cause of a certain phenomenon does not imply a failure on the part of this principle, for it does not rest on experimentation.
These salient points differentiate the mechanistic, materialistic interpretation of the law of causality from its theological interpretation. Causality and Microphysics: Inevitable uncertainty entered the realm of modern physics as a result of experimentation with subatomic particles. If the position of an electron were to be accurately measured, radiations of very small wavelength would have to be used for the determination.
But such radiations possess quanta of high energy, and would alter the momentum and energy of the electron by impact. Similarly, to measure the momentum of an electron, quanta of low energy would have to be used. The wavelengths of such quanta being large, the position of the electron would be correspondingly indeterminate.
Heisenberg's Principle of Uncertainty followed from the wave-particle duality of matter and radiation, and from the fact that the characteristics of objects were usually unavoidably altered during the course of experimentation. The indeterminacy at the subatomic level meant that there could be only probabilistic knowledge of subatomic events. This fact made the physicists and erroneously according to al-Sadr abandon belief in the universality of the principle of causality.
Not only that, they came to interpret the causal fixity and regularity of macroscopic events as a statistical phenomenon, analogous to the stability of, say, suicide rates. Al-Sadr points out that the doubts raised by scientists in microphysics are based on a specific notion of the principle of causality different from the notion of it held by Muslim philosophers. According to the latter notion, the principle is not based on experimental evidence and stands above experimentation.
Moreover, the limits of experiment prove only our inability to apply it in some fields, not the invalidity of this principle in those fields.