The science of physics has over time changed nature from concrete/real to abstract/non-real with the pillars of modern physics of Quantum Mechanics QM and General Relativity GR reaching breathtaking levels of abstraction during the first half of the 20th century culminating today as string theory in 11 space dimensions beyond any reality.
Today with powerful computers available at no cost there is a reverse trend in the form of computation opening new capabilities of using theories of physics for practical purposes. Computation is a concrete process and computational physics starts with a concrete mathematical model and not with an abstraction.
Let us compare Newtonian mechanics in concrete and abstract formulation.
The concrete form consists of Newton's Law $F=ma$ connecting force $F$ to mass $m$ and acceleration $a=\frac{dv}{dt}$ with $v$ velocity and $t$ time. The evolution over time of any mechanical system (without viscous forces) can be computationally simulated by time-stepping Newton's Law. Concrete and general.
The abstract form states that a mechanical system evolves from $t=0$ to $t=T$ so that:
- The action $L(v)=\int_0^T(T-V)dt$ is stationary,
where $T=m\frac{v^2}{2}$ is kinetic energy and $V$ is potential energy. The condition for stationarity in differential form then reads $m\frac{dv}{dt}=F$ with $F$ gradient of $V$, which is Newton's Law.
The difference between abstract and concrete is the same as characterising a local minimum of a function $f(x)$ over variation of a real variable $x$ for $x=\bar x$ as $f^\prime (\bar x) =0$ with $f^\prime =\frac{df}{dx}$. Minimisation is abstract in the sense that no computational method is implied other than comparing the value $f(x)$ for all $x$, which can take infinite work. On the other hand, there are many methods for computing a root to the equation $f^\prime (x)=0$.
We thus see with that the concrete formulation directly opens to computational solution, while the abstract formulation does not. The pendulum thus may swing back from abstract to concrete in a 21st century filled with computation.
But we still live in the era of QM and GR, which are both abstract and uncomputable. QM is based on an abstract multi-dimensional Schrödinger equation without real physical meaning which is uncomputable because of its many dimensions. GR is based on Einstein's equation with a condensed abstract formulation which when written out for computation shows to be uncomputable.
RealQM is a new form of quantum mechanics based on a concrete computable model. RealQM + Newton offers a unified concrete continuum model covering all scales which is computable.
Ontology of physics (what is) is concrete, while epistemology of physics (what we can say) can be abstract. Computation can open ontology of physics to inspection and so feed epistemology of physics. Epistemology without ontology is empty.