I have had a question for a while now, and I mull it over from time to time. Not really knowing what to do with it, I want to put it here and let other people play with it too. I suspect that this question may make a strong point about epistemology and knowledge in general, and I'm looking forward to feedback.
The motivation for my thinking is the current debate between quantum loop gravity and string theory, the details of which are not needed for this discussion (which is good, because I don't know them!). All that's needed is that we have two theories here that posit fundamentally different mechanisms of behavior for reality--two different and incompatible claims as to what is really going on--and yet our ability to measure is not sufficiently refined to choose which is the better theory. The way I originally had this explained to me (by a physicist working to advance string theory) is that the theory is a couple of decimal places ahead of what we can currently measure.
Now, I expect measurements will catch up with those theories eventually, but it makes me wonder about something. Suppose that we're far in the future, and we have much more refined instrumentation and technique for making measurements. In fact, we're very near being able to measure at the Planck scale, or if needed, something beyond that--a place where it becomes physically impossible, for whatever set of reasons, to make better measurements.
Suppose, then, that we have two different and incompatible explanations of reality that make identical predictions down to this limit, perhaps even that could be resolved with a few more decimal places of accuracy in measurements (that we cannot have due to physical limitations). This is what I'm wondering about.
Is it conceivable that we could hit a place where our theories are able to make more accurate predictions than we can experimentally verify? More importantly, if so, could such theories actually be different and incompatible (or must there be some uniqueness requirement that prevents it)? Of key importance, does this, if such a limitation exists, present a strong argument that we have no basis upon which to claim that our theories actually describe reality?
Even if there is no real physical limitation for obtaining more accurate data, this problem may still exist in a softer sense. It is conceivable that our theoretical models will always be able to be at least a few decimal places of accuracy ahead of what we can measure, rendering a soft version of the same question.
Anyone that wants to play with it, in comments or otherwise, is strongly encouraged to do so.