# Laws     [Chapter 1 Objectives]

"We try to organize facts into groups and extract common pieces of behavior (e.g., all metals carry electric currents easily; stretch of a spring varies proportional to the load). We call the extracted statement or relation a rule, a law, occasionally a principle. Thus a law is a generalized record of nature, not a command that compels nature." - Eric. M. Rogers, Physics for the Inquiring Mind.

"Scientific laws are the regularities or relations found among scientific facts. ... The essential thing to understand here is that scientific laws do not tell nature what to do or what not to do; scientific laws are the expressions of the relations observed in nature; they are man-made statements of his knowledge of the laws of nature." - Boris Podolsky, "What is science?" The Physics Teacher, 71-73 (1965)

## Scientific Laws

A scientific law (sometimes called a principle) is a powerful summary of many previously unrelated facts.

For instance, suppose that in studying the behavior of gases, you notice that whenever the pressure on the gas increases, its volume decreases. (Actually, to be really useful in science, your observations need to be more specific than this - they must be quantitative - numerical measurements.) Other competent scientists confirm your observations - they become facts. Suddenly one day, it occurs to you in a flash of insight that your data (observations) contain a pattern - the relationship between pressure and volume for an enclosed gas appears to fit the equation:

pressure x volume = a constant

Wow! This simple hypothesis says a great deal about the behavior of gases. It suggests a great many new experiments and observations that could be made. Amazingly, all of these experiments and observations indicate that your hypothesis is correct! Soon, scientists are calling your discovery a law.

A scientific law expresses our current knowledge of the laws of nature. Scientific (physical) laws are not passed - they are discovered. (The old joke "What happened before the Law of Gravity was passed?" expresses this confusion.) Scientific laws do not tell nature what to do - they tell what nature does.

## Characteristics of Scientific Laws

You probably recognized the previous example as Boyle's Law. It is typical of many physical laws in that it:

• Describes how nature behaves without explaining why nature behaves that way. Boyle's Law says that if you double the pressure on an enclosed gas, its volume will decrease by half. Boyle's Law says nothing about why a gas should behave that way.
• Are generally empirical (experimental) in nature - that is, they derive from, and generally talk about the results of experiment.
• Can be expressed most simply and concisely in mathematical form. Boyle's Law can be written as PV = k.

Here are some other physical laws you may know (or soon will know):

Name of Law

Mathematical Statement

What the Law Tells Us

Boyle's Law
PV = k

The relationship between the pressure and volume of an enclosed gas

Ideal Gas Law
PV = nRT

The relationship between the pressure, volume, and temperature of an ideal gas

Law of Reflection
i = r

The relationship between the angle of incidence and angle of reflection for a reflected light ray

Snell's Law
n1 sin q1 = n2 sin q2

The relationship between the directions of a light ray as it crosses a boundary between 2 transparent media

Newton's Second Law
Fnet = ma

The relationship between the net force on an object, its mass, and its acceleration

## How a Law Gets Replaced:

Even though a physical law has been tested many times, it sometimes happens that a new fact will be discovered which contradicts the law. In this case, the law must be discarded or modified to account for the new fact. In science, observations take precedence over everything else.

It can also happen that a law may be superseded by a more general and powerful law. In the example above, you can see that Boyle's Law is a special case of the Ideal Gas Law.

## Laws and Principles

The term "law" seems to have gone out of style in the twentieth century to be replaced by the term "principle". For example, we have Ohm's Law in the nineteenth century, and Heisenberg's Uncertainty Principle and the Pauli Exclusion Principle (actually both laws by our definition) in the twentieth century. We'll use the two terms as synonyms.     [Chapter 1 Objectives]