Basic Physics Facts Often Overlooked by Physics PhD Students

PhD students in physics, despite their deep understanding of specialized research areas, often find themselves ignorant of fundamental and basic physics facts. This phenomenon is not uncommon in the field, and it can hinder their overall understanding and problem-solving skills. In this article, we explore some of these basic physics facts that are sometimes overlooked, and discuss how the gap in foundational knowledge can affect their academic and professional careers.

The Speed of Light in a Vacuum

In the realm of theoretical physics, the speed of light in a vacuum is a fundamental constant, but its relationship with the metric tensor is not as well-known. Specifically, the speed of light is proportional to the square root of the G00 element of the metric tensor. This connection is discussed by Hilo et al. in their paper Deriving of the Generalized Special Relativity GSR by Using Mirror Clock and Lorentz Transformations, where they explore the relationship between special relativity, general relativity, and the metric tensor. ([8])

Basics of Classical Thermodynamics

Classical thermodynamics, which is a cornerstone of physics, often receives limited coverage in undergraduate curriculums. Concepts such as energy, heat, and work are frequently misunderstood or treated vaguely. Graduates often gain a better understanding of energy conservation through analytical mechanics, specifically in systems invariant under time translation. ([9])

Conic Section Orbits

A classic example of orbits, two-body orbits in Newtonian mechanics, are indeed conic sections. However, it is surprising to learn that radially symmetric potentials, such as r^{2epsilon}, do not generally yield closed orbits. This difference is attributed to an additional symmetry leading to the conservation of the Laplace-Runge-Lenz (LRL) vector. This knowledge is particularly relevant in both classical and quantum mechanics and is explained in John Baez's essay. ([10])

Physical Constants and the Buckingham Pi Theorem

The values of physical constants, such as Newton's gravitational constant, are not typically memorized, as they can be easily looked up. The Buckingham Pi Theorem, a simple theorem for dimensional analysis, is a handy tool for understanding the relationships between dimensions in physical equations. This theorem is crucial for scaling and simplifying physical problems, yet it is not always emphasized in curriculums. ([11])

The Problem of Inertia and Dimensional Analysis

The concept of inertia, while foundational, is not always covered in depth. Understanding the principle of inertia is critical for grasping classical mechanics. Additionally, dimensional analysis, a powerful tool for problem-solving and theoretical physics, is a skill that many graduate students may develop later in their careers. ([12])

Brachistochrone and Fermi Estimates

The brachistochrone problem, which involves finding the path of quickest descent, is well-known, but the fact that this path is a cycloid is less familiar. Moreover, the period of oscillations on a brachistochrone is constant, which is a special property in a uniform gravitational field. Another useful technique is Fermi estimation, which allows for quick and efficient problem-solving. While many students can derive a series solution or numerically solve such problems, applying Fermi techniques in real-world scenarios is often overlooked. ([13])

The Periodic Table

The periodic table, while essential for understanding atomic and molecular interactions, is often not as well-known as it should be. Some physics graduates may not have memorized fundamental aspects of the periodic table, making it a basic yet critical area of knowledge. ([14])

Noether's Theorem and Action Principles

Noether's theorem, which connects symmetries and conservation laws, is a fundamental principle in physics. However, many students, including some PhD candidates, may not be fully aware that the action principle is the linchpin of this connection. A clear understanding of this theorem and its applications is crucial for advanced research in mechanics and quantum field theory. ([15])

Geometric and Fourier Optics

While geometric optics, such as the lens equation, is a fundamental topic, it is often forgotten or misunderstood. Similarly, Fourier optics, particularly diffraction patterns, are essential for understanding interference and wave-particle duality. However, many PhD students, including the author, may lack the ability to explain why optical microscopes cannot resolve objects smaller than the wavelength of light. This is due to the Fourier transform of the grating and the wave nature of light. ([16])

In conclusion, while physics PhD students may excel in their specialized fields, they can still benefit from reinforcing fundamental concepts. Filling these gaps can enhance their problem-solving skills and overall understanding of the discipline. Further, a solid grasp of these basic physics facts can contribute to a more robust and well-rounded physicist, capable of both advanced research and practical application.