What is observable and what is not?

In physics, there are some things that can be directly observed by experiment, and there are other things that exist only in theories and are not observable. The things of the first kind are, for example, various properties of particles, such as mass, spin, momentum, position, etc. There are lot of experimental devices which measure these properties directly: beginning from simple rulers and ending with Wilson chambers and Stern-Gerlach apparatuses. Examples of things of the second kind (non-observable) are fields and space-time.

Take for example, the electromagnetic field. There is no way one can directly measure the strength of the field (electric or magnetic) at a given point. All we can do is to place a test charge at this point and measure the force acting on this charge. One is free to think that this force appears because of the non-zero field vector created at this point by other charges. However, one can also think that there is no field and the force is simply created by action-at-a-distance from the surrounding charges. In classical electrodynamics, one also assigns certain momentum (density) and energy (density) to the fields. In the case of static fields this momentum-energy is certainly non-observable. In the case of freely propagating transversal field (= light wave) the momentum-energy can be equally well assigned to the particles of light - photons (see also discussion here ). So, the idea of electromagnetic field as a separate physical entity is somewhat suspicious.

Now consider the space-time. In modern theories the space-time is an active participant in physical processes. It can be bent, twisted, torn... It even has momentum-energy associated with it (with the "gravitational field"). However, nobody can see the space-time properties directly. What we actually see in experiments are trajectories of particles, i.e., the time dependent expectation values of the position observable r(t). These trajectories can be calculated in the Hilbert space formalism of quantum mechanics, where the notion of space-time is just not needed.

I believe that a successful physical theory should be formulated (as much as possible) in terms of directly observable quantities (= particle properties described above). I strongly believe that current crisis in theoretical physics in large part is related to our focus on abstract theoretical non-observable notions, such as fields and space-time.