Philosophy of Physical Magnitudes

Dimensional quantities, such as length, mass, and charge, are essential components of theories in the sciences, but they represent a world with absolute physical magnitudes or magnitude ratios in disguise. Imagine conveying the meaning of a kilogram to aliens via Morse code.

Format: Paperback / softback
Length: 58 pages
Publication date: 04 April 2024
Publisher: Cambridge University Press

Dimensional quantities, including length, mass, and charge, play a fundamental role in theories across various scientific disciplines, particularly physics, chemistry, and biology. These quantities are characterized by their combination with a conventional unit, providing a framework for quantifying and describing the physical properties of objects and phenomena. However, the nature of dimensional quantities raises intriguing questions. Do they represent absolute physical magnitudes, or are they merely magnitude ratios in disguise? This Element delves into these central inquiries by exploring the concept of conveying the meaning of a kilogram to aliens using Morse code as a communication medium.

In the realm of physics, dimensional quantities are fundamental units of measurement. Length, for instance, is measured in meters, mass in kilograms, and charge in coulombs. These quantities are interrelated through the fundamental laws of physics, such as the second law of thermodynamics and the theory of electromagnetism. The combination of a conventional unit with a dimensional quantity allows for the precise description and calculation of physical quantities.

For example, the mass of an object can be calculated by multiplying its length by its density, which is a measure of its mass per unit volume. Similarly, the charge of an object is determined by the number of protons and electrons it possesses, and the electric force between two objects is directly proportional to their respective charges.

However, the question of whether dimensional quantities represent absolute physical magnitudes or merely magnitude ratios in disguise arises. On the one hand, dimensional quantities can be interpreted as absolute values, as they are defined based on universal physical constants and principles. For instance, the speed of light in a vacuum is a constant of nature, and it is measured in meters per second (ms-1). This suggests that length, mass, and charge are absolute physical magnitudes that can be observed and measured in the natural world.

On the other hand, dimensional quantities can also be viewed as magnitude ratios. This perspective suggests that the values of dimensional quantities are relative to a specific reference frame or system of units. For example, the length of an object may vary depending on the observer's position or the units used for measurement. Similarly, the mass of an object can be expressed in different units, such as grams or kilograms, depending on the chosen reference frame.

The question of whether dimensional quantities represent absolute physical magnitudes or magnitude ratios in disguise is crucial for understanding the nature of the physical world. It has implications for our understanding of fundamental physics, such as the nature of space, time, and gravity, as well as for applications in various fields, such as engineering, chemistry, and biology.

One way to address this question is to consider the concept of dimensional analysis. Dimensional analysis is a mathematical technique that allows for the conversion between different units of measurement and the determination of the dimensions of physical quantities. By using dimensional analysis, we can examine the relationships between different dimensional quantities and determine whether they are absolute physical magnitudes or magnitude ratios.

For example, consider the mass-to-length ratio of an object. If we measure the mass of an object in grams and the length of the object in meters, we can calculate the mass-to-length ratio by dividing the mass by the length. If the mass-to-length ratio is constant for all objects, regardless of their size or shape, then we can conclude that the mass-to-length ratio is an absolute physical magnitude. On the other hand, if the mass-to-length ratio varies depending on the object's size or shape, then we can conclude that the mass-to-length ratio is a magnitude ratio.

Another way to address the question of whether dimensional quantities represent absolute physical magnitudes or magnitude ratios in disguise is to consider the effects of changing the values of dimensional quantities. For example, what would happen if all the distances or charges in the world suddenly doubled? Would we notice a difference?

If all the distances or charges in the world suddenly doubled, we would undoubtedly notice a significant difference. For example, the distance between two planets would increase by half, and the gravitational force between them would be doubled. Similarly, the electric force between two charged particles would be doubled, leading to stronger electromagnetic interactions.

However, it is important to note that the effects of changing the values of dimensional quantities are not absolute. They depend on the specific system of units and reference frame used for measurement. For example, if we change the reference frame to a system of units that is based on a different set of physical constants, the effects of changing the values of dimensional quantities may differ.

In conclusion, dimensional quantities, such as length, mass, and charge, are essential components of theories in the sciences, particularly physics, chemistry, and biology. While the nature of dimensional quantities raises intriguing questions, such as whether they represent absolute physical magnitudes or merely magnitude ratios in disguise, dimensional analysis can help us examine the relationships between different dimensional quantities and determine whether they are absolute physical magnitudes or magnitude ratios. The effects of changing the values of dimensional quantities are not absolute, and they depend on the specific system of units and reference frame used for measurement. By understanding the nature of dimensional quantities, we can deepen our understanding of the physical world and develop more accurate models and predictions for various phenomena.

ISBN-13: 9781009233682