One of the constant things that one encounters in the world of science is idealization. Nevis Laboratories define physics as the study of matter and energy. It's supposed to be a guide to the world around us. Physicists create experiments to see the outcomes of certain activities. However, the world is a messy and complicated place. When physicists explain a particular phenomenon, they simplify the complex forces that interact with physical bodies into something understandable. To do this, they often employ idealizations, which remove the negligible parts of the interaction. But does removing these minor parts of the calculation lead to erroneous results?
Galileo and The Scientific Method
To understand physics and why idealizations are necessary, we must first look back at how experimentation in science came to be. Many ideas in classical physics came from philosophers who thought about things and developed theories based on their observations. Philosophers like Aristotle spent their time using observations and assumptions to create the foundation of classical physics. Unfortunately, as Physics World notes, Aristotle's statements on physics have proved a barrier to experimental physics for most of its history. The Aristotelian model of physics didn't hold with experimentation but rather an observation of the physical phenomenon. Galileo changed this view when he burst onto the scene in the 1580s.
Galileo's approach to science was to craft experiments that would explore the phenomenon he was interested in. In some cases, this was possible. One of Galileo's most famous experiments was to throw two weights off the top of the Leaning Tower of Pisa and note that both weights hit the earth simultaneously. Aristotle assumed that the heavier weight would fall faster, but Galileo's experiment shows that the fall rate of both was the same. Many of Galileo's experiments were done with idealizations built into them. In the case of the falling weights, idealizations would be regarding wind resistance, which would be negligible, and every other external force acting on the weights.
Today's Idealizations and Physics
Galileo couldn't create experiments that ignored things like wind resistance because the technology of the time was limiting. He could derive experiments that limit the external factors acting on the physical bodies he studied. In modern physics, we do this all the time because many things don't add to or detract from a calculation. The aim of performing an experiment is to see how close experimental data matches the theoretical data. In some cases, this match is evident and apparent, as in the case of Galileo's falling weights. However, more and more, it takes a concerted effort and multiple sets of data to draw a solid conclusion about a particular physical phenomenon.
One of the best examples of idealizations in modern physics is any calculation regarding a tennis ball. For the analysis, physicists assume that the ball has no weight or dimensions. Obviously, when you hold a tennis ball in your hand, it has both things, but they don't impact the overall calculation. Physicists can then use this "stripped-down" tennis ball to see if the ball’s motion matches what physics tells us should happen. In all cases, it supports the theory that we're investigating (most likely, Newton's Laws of Motion, for example). We also use idealizations when investigating other phenomena. For example, when looking at interference patterns using a red laser, we assume that the laser is monochromatic and collimated. While most of the light coming from a red laser is red, not all of it is, but enough of it is to ignore the rest of the colors. Similarly, while most of the light rays coming out of the laser are traveling in the same direction, we can make the assumption that all the rays are doing so, even though this isn't true. These assumptions make no difference to the final result of the calculation but make the lives of physicists that much easier.
Does It Always Work?
Some things can be simplified and broken down into a more straightforward method of understanding, while others cannot. For example, if one looks at a soccer ball that's kicked to curve past a goalkeeper, one might be tempted to treat it the same way as the tennis ball mentioned above. Unfortunately, if one does that, everything breaks down. The forces acting on the ball to air resistance and even the curve of the ball, each of these impacts how the ball moves in the air. Removing any one of them could lead to an erroneous result. So how do we determine what to keep and what to leave out? The answer, again, is experimentation.
Physics allows us to observe the world around us and draw conclusions, but those conclusions can be challenged when new data comes along. However, if we have theories that match the physical phenomena we observe in idealized experiments, we can safely assume that those theories are true. All it takes to rethink physics is an observation that goes against the established laws of physics. While it doesn't often happen in classical physics, world-changing observations do occur in other branches of the field, such as theoretical and subatomic physics. Knowing where to make the assumptions comes from seeing what interacts with what and to what extent. Mathematics can't model the world perfectly, but we don't need it to. We just need it to approximate the world to a certain level of tolerance.