When physicists say "the math seems right but the physics is wrong" or vice versa, they are typically referring to a situation where there is a mismatch between the mathematical formalism used to describe a physical phenomenon and the underlying physical principles or observations.
"The math seems right but the physics is wrong" suggests that the mathematical equations or calculations may be mathematically consistent and internally coherent, but they fail to accurately represent or explain the observed behavior of the physical system in question. In this case, the mathematical framework may need to be revised or augmented to better align with experimental data or known physical principles.
For example, in the early 20th century, physicists encountered a discrepancy between classical physics and experimental observations at the atomic and subatomic scales. Classical physics, based on Newtonian mechanics, failed to explain phenomena such as the photoelectric effect and the behavior of atoms. The math of classical physics seemed right, but it was clear that the physics was incomplete or incorrect.
This led to the development of quantum mechanics, which introduced a new mathematical formalism that accurately described the behavior of particles at the quantum level. Quantum mechanics provided a more comprehensive and accurate understanding of the physical phenomena, resolving the inconsistencies between classical physics and experimental observations.
Conversely, when physicists say "the physics seems right but the math is wrong," they are indicating that the underlying physical principles or observations make sense, but the mathematical formalism used to describe them is either inadequate or inconsistent. In this case, the mathematical framework may need to be refined or replaced with a more suitable one.
An example of this can be found in the early attempts to describe the behavior of electromagnetic waves. The physics of electromagnetic waves, including phenomena like interference and diffraction, were well understood. However, it was the development of Maxwell's equations—a set of mathematical equations that elegantly described the behavior of electromagnetic waves—that allowed for a comprehensive and accurate mathematical formalism to explain and predict various electromagnetic phenomena.
In summary, when physicists refer to "the math seems right but the physics is wrong" or vice versa, they are highlighting a mismatch or discrepancy between the mathematical formalism and the physical principles or observations. Resolving such discrepancies often requires refining or expanding the mathematical framework, adjusting physical theories, or developing new insights to ensure a consistent and accurate description of the natural world.