martinbn said:
Then my question remains. Which problems? Give me a specific example.
To be a bit more descriptive: unification, i.e. dissolving dichotomies, as occurring in the history of theoretical physics is a completely philosophical method: unification is to make into a logically consistent unity which are separate concepts based on a philosophical analysis of what is necessary and what is contingent; when a unification occurs successfully, the new concept often automatically fulfills certain uniqueness and existence criteria, i.e. is automatically an application of some theory in pure mathematics, whether that field of pure mathematics has already been discovered or not.
Concrete examples are littered in the history of physics, e.g. the idea that uniform motion and rest are unified in one concept is a product of philosophy. Also, the idea that the apple falls and the moon orbits i.e. falls with a sufficient acceleration are essentially due to the same cause, is a result of philosophy. Likewise, the unification of energy and mass, as well as the unification of gravitation and spacetime curvature, are products of philosophy. Having the conceptual unification is practically a prerequisite for finding the correct mathematics describing the unification!
It is very important to realize and recognize that once the philosophical unification is achieved, the correct mathematical model of this unification - often by searching through applications in pure mathematics or creatively applying pure mathematics - follows quickly; this process is non-commutative i.e. the order in which it is done matters w.r.t. getting the wanted result! The philosophical conceptualization has to occur before the mathematization; this is because if one starts with mathematics and then tries to conceptualize, there are literally an infinite amount of roads that can be taken, while given some concept it is much easier to then mathematicize (cf. Bayes' theorem).
Even stronger, the forced unification of two independent mutually inconsistent mathematical frameworks which each are valid and work seperately, such as the theories of electricity and magnetism, Newtonian mechanics and Maxwellian electrodynamics, or inertial motion and accelerated motion, into a single new mathematical framework automatically tends to lead to more unifications.
Characteristic of unification is that more comes out than is put into the unification, e.g. unifying the mathematics and of electricity and magnetism automatically leads to a mathematical model of light; these are unexpected consequences of the unification which are typically completely unintended but instead follow necessarily and objectively as a side effect of the unification. Feynman, the last theoretician who had mastered unification, described this process as the new idea 'being simpler than what it is was before' i.e. that more comes out of a unification than was originally put into it.
It goes without saying that the two most important open problems in theoretical physics today, namely quantum gravity - i.e. the successful unification of (the mathematical frameworks of) quantum theory and general relativity - and the measurement problem in QT - i.e. the unification of the mathematical frameworks of unitary evolution and measurement - can only be solved by the philosophical method of unification.
Lastly, unlike practically all of the other methods learned in theoretical physics - i.e. mathematical methods - unification is clearly not reducible to a routine, algorithmic, purely deductive exercise before the unification has actually been successfully achieved, because successful unification is a genuinely creative process. This means that unification cannot be 'divided and conquered' like most simpler problems can be in physics, and it has instead to be done 'in one go' by a single mind, i.e. it has to be capable of being carried out as a derivation from first principles.
The relative unfamiliarity in learning how to properly do unification as a method - which is a fault of the physics education system - and the prevalence of remaining 'low hanging fruit' i.e. physics problems which can be divided and conquered, or even directly experimentally approached without changing or inventing any theories or inventing new mathematical reformulations of existing theories, goes a long way of explaining why even with so many physicists today alive and practicing, these problems remain; even worse, if a young person wants a good career, they best avoid such problems and just integrate themselves without resistance into existing hot research programs. This is why these problems are so difficult and why progress w.r.t these problems is so slow.
