The math of quantum physics was developed to describe the empirical results of particle experiments. The experiments came first and then came the equations which describe the experimental results. But most people aren’t going to be able to picture how particles interact by looking at equations. For most people, interpretations are needed to conceptualize how nature works.

I’d like to give a more familiar example that might help explain the usefulness of interpretations: Newton’s work on gravity. For about 1,000 years, until the 1500’s, most scientists and philosophers had accepted an interpretation of gravity developed by the Greek philosopher Aristotle: all objects are directed by an inner impulse to move towards the center of the Earth. It’s as if objects have minds with a strong drive to move towards the center of the Earth. As the mass of an object has an inherent drive towards the center of the Earth, the more mass, if dropped, the faster it would fall towards the Earth. Thus, this theory went, heavier objects would fall faster than lighter ones. The difference between how a feather and a cannon ball fall would seem to be everyday verification of this theory. Aristotle was always trying to explain his everyday observations of life.

However, sometimes everyday experiences of life are misleading. Other forces are active in the feather and cannon ball example—aerodynamics, not just gravity, is involved. Aristotle’s interpretation was not based on controlled experimental results. Aristotle, like many Greek philosophers, disdained experiments. They thought that working with one’s hands rather than with one’s mind was demeaning.

Then, in the 1500’s Galileo Galilei explored Aristotle’s interpretation of falling objects. Galileo experimented with falling objects and balls rolling down ramps and carefully noted his results. Galileo’s experiments did not support Aristotle’s interpretation. But Galileo provided no interpretation of his own.

Isaac Newton, who, as it happened, was born the same year that Galileo died, carefully studied Galileo’s experimental results. Newton developed an equation that describes the rate with which Galileo’s objects fell or rolled. Newton’s equation is the inverse square law. It takes into account a number called the “gravitational constant,” the mass of the object, the mass of the Earth, and the distance between the falling object and the Earth. Ever since Newton proposed the inverse square law of “Universal Gravitation,” physicists have been refining it and developing new physics based on it.

But, famously, Newton did not propose an interpretation as to why the inverse square law works. He did not, for example, say that one mass exerts a pulling force on other masses. The idea that objects could exert force through empty space was, in his words, “anathema.” The “pulling force” interpretation of Newton’s inverse square law came later as physicists who worked with the law imagined the mechanics underlying it.

For 300 years after Newton’s publication of the inverse square law, physicists and engineers assumed that “gravity sucks.” It has allowed them to think through the physics of how objects relate to each other in space. It is the physical explanation that engineers relied to build bridges and skyscrapers. In the 1970’s, they relied on it to send rockets to the moon. To this day, the “pulling force of gravity” is the interpretation of Newton’s equation that children learn in school.

But in the 1920’s, Albert Einstein’s work on General Relativity provided evidence that this interpretation is not accurate. It cannot account for the behavior of objects at very high speeds (a significant fraction of the speed of light) or in the proximity of planet-sized objects. So, the “attractive force of gravity” as an interpretation is not, in the end, adequate. A deeper explanation is needed. This explanation requires one to think in terms of curved space. It’s a less intuitive explanation but one that has allowed physicists to develop, for example, the field of Black Holes.

One of the most compelling reasons that people become scientists is that they are curious about how things really work. For this reason, they often start with experiments and equations and, then, come up with explanations (interpretations) as to what the equations are telling us about nature. So, the first reason for the various interpretations is the reason that scientists do science to begin with — they are led by their curiosity to increase their understanding of how the universe works—how its forces and principles interact.

Of course, sometimes, scientists, especially paradigm-breaking scientists, start with interpretations and develop experiments and/or equations based on their intuitions as to how nature might work. Long before Einstein developed the math of Special Relativity, he imagined how objects might behave when traveling at the speed of light. He called this intuitive work “thought experiments.” Grounded in these thought experiments, he later developed the equations of Special Relativity.

As a further note, there may be scientists who are able to look at equations and glean understanding from them alone. Paul Dirac, an important quantum physicist who worked in the 1950’s and 1960’s may have been one of these. He was once asked how he came up with this ideas. He answered “I play with equations.” It appears that for Paul Dirac, one equation led to another. However, even Paul Dirac often gave interpretations to his equations. For example, he predicted the existence of anti-matter based on where his equations took him.

Beyond fulfilling curiosity, there is another usefulness to interpretations: they allow expansion of the theory, which can lead to practical applications — like engineering. For example, let’s say that quantum physicists did no more than write equations in physics papers. Well, the quantum behavior of photons in photosynthesis might never have become a developing part of botany. What botanist would sit around poring through equations in a physics journal? But because physicists have tried to explain quantum physics conceptually in popular articles, usually via the Copenhagen Interpretation, botanists were alerted to a possible explanation for the mysterious workings of photosynthesis.

The theorized quantum behavior of photons in photosynthesis might turn out to very important; photosynthesis is a fundamental biochemical reaction that feeds us. And, who knows—understanding a potential quantum aspect of photosynthesis might lead to more efficient solar panels.

Interpretations of equations are needed throughout physics because we are human beings, not robots. If we were robots, we could just program ourselves with equations and shush ourselves with, “Shut up and calculate.” But we are human beings who like to turn things over in our minds, relate one scientific principle to another, and make progress by deepening our understanding of the universe.

For a bit more about quantum behavior and photosynthesis, see the end of this article about the Copenhagen Interpretation of quantum physics.