What is a physical model?
The scientific method involves theoretical predictions and experimental measurements. Physical Models are the domain of Theoreticians and their means of making sense of the experimentalists’ results.
A physical model is meant to be representative of some physical reality of interest, and modeled in such a way they can be systematically analyzed and predictions made that can be used to validate the model.
Must physical models be mathematical?
While many physical models are mathematical in representation, they may also be physical themselves. These models are sometimes called prototypes or proof of concept. Test pilots flying version one of an eventual new concept jet.
Here is Gaudi’s Sagrada Familia Church in Barcelona which I mentioned earlier. Notice its high towers. Gaudi didn’t just “wing” it, nor did he construct a mathematical model. He actually built a physical model, and how he built his illustrates the many ways models can be implemented.
In structural engineering, you learn stable towers follow the geometry of an upside down chain. So Gaudi created his Sagrada model by hanging chains from his ceiling and moving them around until he had the shape he wanted. He then took a picture and turned it upside down to get his final vision.