> Theoretical physics is highly mathematical, but it aims to explain and predict the real world. Theories that fail at this “explain/predict” task would ultimately be discarded. Analogously, I’d argue that the role of TCS is to explain/predict real-life computing.
Incidentally, real-life computing depends quite a lot on the laws of the physics of the universe we live in. This has been known quite clearly since the theoretical discovery of quantum computing, with the resultant split of classical complexity theory and quantum complexity theory.
Morever, physics also determines what sort of devices you can make and with what performance. The real-life speed of solving NP-complete problems depends on the absolute and relative performance of transistors, CPUs, memories etc.
Hence, I submit that TCS has the same relationship to Physics as does Mechanical Engineering to Physics.