Physical constant

Key takeaways

Physical constant belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Physical constant to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Physical constant from memory before moving on to harder problems.

Reference excerpt

A physical constant is a non-varying quantity that appears in a theory or model of some physical phenomena. Some physical constants appear in models of fundamental phenomena and impact many parts of physics. These constants include the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε0, and the elementary charge e for examples. Tables of the numerical value of these fundamental physical constants or universal constants are carefully maintained and widely consulted. Some physical constants are coefficients or parameters assumed to be constant in specialized models without being universal constants. Examples include the characteristic time, characteristic length, or characteristic number (dimensionless) of a given system, or material constants (e.g., Madelung constant, electrical resistivity, and heat capacity) of a particular material or substance. Physical constants cannot be explained by the theory that incorporates them but their values may be determined by other, more fundamental theories. Dimensioned constants include the values set by the International System of Units convention in the defining constants and the derived units built upon those constants, as well as many nonstandard constants still in widespread use as units. Dimensionless constants are characteristics of natural phenomena and their values must be measured experimentally. Dimensionless constants may be fundamental, like the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, or they may arise from empirical dimensional analysis.

Characterizations

Dimensioned vs dimensionless Physical constants can have dimensions or be dimensionless. The numerical value of a dimensioned constants, those with units, depend upon the system of units adopted for a model description. The numerical values of dimensionless constants are independent of the system of units and must be measured experimentally.

Fundamental vs specific Physical constants can be fundamental, have a very broad arena of application, or be specific to a field or a single model. The question as to which constants are "fundamental" is neither straightforward nor meaningless, but a question of interpretation of the physical theory regarded as fundamental. Jean-Marc Lévy-Leblond proposed a classification schemes of three types of constants:

A: physical properties of particular objects B: characteristic of a class of physical phenomena C: universal constants The same physical constant may move from one category to another as the understanding of its role For example, c, the speed of light, was originally considered a property of light, a specific system (class A above). The discovery and verification of Maxwell's equations connected the same quantity with an entire system, electromagnetism (class B above) When the theory of special relativity emerged, the quantity became a fundamental constant (class C). The set of physical constants considered to be fundamental change as physical models change. Constants fundamental in one theory may be explained in terms of constants in a more fundamental theory.

Relationship to units

Numerical values Whereas the physical quantity indicated by a physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on choice of unit system. The term "physical constant" refers to the physical quantity, and not to the numerical value within any given system of units. For example, the speed of light is defined as having the numerical value of 299792458 when expressed in the SI unit metres per second, and as having the numerical value of 1 when expressed in the natural units Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself is a single physical constant.

International System of Units

All of the units in the International System of Units are defined in terms of seven fixed numerical values of defining constants including three fundamental constants: the speed of light in vacuum, c; the Planck constant, h; and the elementary charge, e. The other defining constants are less familiar, like the hyperfine transition frequency of cesium, written symbolically as ΔνCs Seven more familiar and historically connected base units are built from these defining constants. For example, the SI unit for mass, the kilogram, can be written in terms of defining constants as:

1 kg = ⁠(299792458)2/(6.62607015×10−34)(9192631770)⁠⁠c2/hΔνCs⁠.

Natural units

It is possible to combine dimensional universal physical constants to define fixed quantities of any desired dimension, and this property has been used to construct various systems of natural units of measurement. Depending on the choice and arrangement of constants used, the resulting natural units may be convenient to an area of study. For example, Planck units, constructed from c, G, ħ, and kB give conveniently sized measurement units for use in studies of quantum gravity, and atomic units, constructed from ħ, me, e and 4πε0 give convenient units in atomic physics. The choice of constants used leads to widely varying quantities.

Number of fundamental constants The number of fundamental physical constants depends on the physical theory accepted as "fundamental". Currently, this is the theory of general relativity for gravitation and the Standard Model for electromagnetic, weak and strong nuclear interactions and the matter fields. Between them, these theories account for a total of 19 independent fundamental constants. There is, however, no single "correct" way of enumerating them, as it is a matter of arbitrary choice which quantities are considered "fundamental" and which as "derived". Uzan lists 22 "fundamental constants of our standard model" as follows:

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Physical constant

Start with the simplest possible case. Write down what Physical constant claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Physical constant before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Physical constant ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Physical constant

In research: Physical constant appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Physical constant in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Physical constant is common in secondary-school and first-year university syllabi. It links to neighbouring topics Physical constants, so understanding it makes those chapters shorter.
In everyday life: Look for Physical constant outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Physical constant in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Physical constant means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Physical constant out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Physical constant in simple terms?

A physical constant is a non-varying quantity that appears in a theory or model of some physical phenomena. Some physical constants appear in models of fundamental phenomena and impact many parts of physics.

Why does Physical constant matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Physical constant?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Physical constant.