Limitations of Scientific Research
In many fields of science, accepted theories and models cannot, by their very nature, be quantified or observed (i.e. lacking empirical evidence). Many of these theories are also in dispute within the field.
The best example lies with quantum mechanics. Many facets of quantum mechanics are merely mathematical models explaining the behaviour and interaction between subatomic particles. One of the major stubling blocks in quantum mechanics lies within one its' fundamental theories: Quantum superposition (all particles exist in all states at the same time). There are many interpretations of this, the standard being: Copenhagen interpretation. This states, basically, that the act of measuring (or observing) the state of a particle collapses the superposition effect, altering it's state to the value defined by the measurement. This shows that the superposition effect, while being one of the most widely accepted and fundamental principles of quantum mechanics, can never actually be observed.
Another good example for this is in the field of Paleontology. One of the fundamental pillars used for the reconstruction of fossils, especially the picturisation of what the animal looked and behaved like, is that we must use what we see today as our basis for rebuilding the past.
Take the example of the Megalodon. From only a handful of teeth and vertebre, paleontologists can tell us that the Megalodon was, basically, a 20m long Great White with similar structure and behavioural patterns. The teeth of a megalodon are similar in shape to that of a Great White so it has been assumed that it's morphology and behaviour are similar (although because the teeth are larger, it's prey would be larger). While this may be accurate, it may also be completely wrong (there is strong support for the theory that megalodon and great whites are not related, the latter being a descendant of the broad-tooth Mako shark. The only real clue that we have towards the size and behaviour is that many bones of large whales have been found with tooth marks almost identical to that of the megalodon. However, there is no evidence, other than it's similarity to the great white's, that the teeth and vertebre even came from a shark and not some other animal which happened to have similar dentition and spinal structure.
In other words, the evidence and modelling that we have in these cases, while compelling, is insufficient to enable us to reliably prove the conclusions that we have made. Or, probably more accurately, the conclusions drawn cannot be reliably disproven with current methodology and technology.
This article was previously posted on the Creation / Evolution page and rejected for Original Research. There are holes in the arguments made which need filled in and I hope that, with our combined effort, these can be filled.