Chapter 1: Understanding Physical Constants

Physical constants are a fundamental aspect of our understanding of the universe, encompassing a seemingly endless list, including the Hubble constant, gravitational constant, Planck's constant, and many others. Anyone who has taken a basic science course has likely encountered constants like the speed of light or the mass of an electron. They are inescapable elements of the scientific landscape.

For physics students, the challenge often lies in memorizing these constants. Many resort to writing them down and displaying them prominently in their study areas, hoping that constant exposure will aid in retention. These constants simplify calculations and provide the correct units, allowing us to utilize them without a second thought.

However, upon reflection, the elegance of these constants and their intricate relationship with the universe can be overwhelming. They are not merely numbers to be memorized for exams; they represent profound truths about the cosmos.

From the spiral structure of DNA to the patterns of ripples in water, the design of buildings resistant to earthquakes, and the behavior of ocean waves, constants like pi reveal their presence in diverse phenomena. The question arises: how do we arrive at the values of these constants? Are they human constructs or do they inherently exist in nature? What implications do they have for physics, and can they change over time?

The Significance of Constants

The Hubble constant, for instance, provides insights into the universe's expansion and helps astronomers calculate its age. Since Edwin Hubble first calculated it in 1929, debates have continued regarding its precise value. Each advancement in technology and telescopic precision yields updated estimates, making the determination of the Hubble constant a pivotal challenge in contemporary astronomy.

The gravitational constant (G = 6.67408 × 10⁻¹¹ N m² Kg⁻²) is crucial in Newton’s Law of Gravitation. Regardless of the planet—be it Earth, Mars, or any distant celestial body—this value remains constant when calculating gravity.

Similarly, Planck’s constant (h = 6.626 x 10⁻³ J s) connects a particle's frequency to its total energy, marking a groundbreaking realization in physics that links wave and particle properties, which was pivotal for the development of quantum physics.

While we can define constants based on their roles, encapsulating them in a holistic definition is challenging. Many were identified before their physical values were established, serving as necessary representations of quantities defined in our measurement system, such as meters, newtons, and joules.

For example, the gravitational constant's units of newton meter squared per kilogram squared (N m² Kg⁻²) allow us to derive the gravitational force between two masses (F = GMm/r²). Consequently, the numerical value of a constant is contingent on the unit system employed.

Are Constants Human Constructs?

The notion that constants are simply human constructs is misleading. This perspective addresses their function rather than their essence. Moreover, some constants, like pi, are dimensionless and cannot be classified in the same way.

Pi (π) is ubiquitous in nature; it is the ratio of a circle’s circumference to its diameter, and is both irrational and infinite. Yet, pi extends beyond mathematics, appearing in various natural patterns and phenomena, such as DNA spirals, animal markings, and more. It is a constant devoid of units, and its true nature remains elusive.

The Discovery Process of Constants

Constants are not arbitrary figures but are integral to the calculations that underpin physics. While some constants are known with remarkable precision, others remain contested, always subject to measurement error based on the accuracy of our tools.

Ultimately, constants exist in the universe, interlinking various quantities. Scientists measure these constants through systematic experimentation and observation, adjusting parameters and conditions.

A profound question arises from physicist Paul Dirac's inquiry in 1937: Are the constants truly constant when considering the entire history of the universe? Given that our measurements originate from Earth, do the constants hold the same value elsewhere in the cosmos?

Evidence suggests that certain constants, such as the mass ratio of protons to electrons, remain unchanged even in extreme gravitational environments. Over many years, extensive research has sought to determine whether this ratio varies, consistently yielding the same result—indicating a fundamental constancy.

While constants like the Hubble constant may evolve due to human errors or equipment limitations, the essence of these constants—what they represent in the universe—remains a beautiful mystery that scientists continue to explore.

The first video, "How to Measure the Gravitational Constant with Lead Balls," delves into experimental techniques used to determine this vital physical constant.

The second video, "Sophia A. '21: Measuring the Universal Gravitational Constant G," highlights academic efforts to refine our understanding of gravitational principles.