# The Scientific Method

**Introduction to physical chemistry**

**The Scientific Method:**

If we start off with no information and make a guess at something logical, then the development of that idea is mathematics, not science. Science is based upon observation first and after doing experiments, trends may be noticed and we can perhaps summarize the data into a **Natural Law.**

For example, Robert Boyle found that at constant temperature the volume of a gas is inversely proportional to the external pressure.

Guy Lussac and Avogadro also discovered natural laws for gases:

These can be written in terms of equations involving pressure, *P*, volume, *V*, temperature, *T*, and number of moles, *n*. Of course the Ideal Gas Law is a combination of all three and the constant is found by comparing to experiment: That is we find that one mole of a gas at 1 atm. Pressure and 273 K occupies 22.4 liters and this gives us the gas constant (click to enlarge):

These forms are **deduced (deduction)** from the experiments but are not necessarily understood. They are called “**empirical formulae**”: and work to describe the data but do not tell us why. For example, why is Boyle’s law,

and not

In order to understand a Natural Law we have to make some assumptions. These are called **hypotheses** and based on these, attempts are made to understand the empirical laws. In this case, the Kinetic Molecular theory makes some reasonable assumptions: the gas is dilute; particles are small relative to the total volume *V*; they collide elastically with each other and the walls, temperature is well above the boiling point. We assume we can use classical or Newtonian mechanics. From these hypotheses we obtain the ideal gas law and learn something else: The kinetic energy is proportional to the temperature. The hotter the gas, the more kinetic energy the gas has. At absolute zero of temperature, there is no kinetic energy. These ideas give us deeper insight into why the ideal gas law works. They follow from the molecular kinetic model which is called a **Theory**. A theory is an explanation of a phenomenon.

Recall we use logic (mathematics) to understand Nature. We assume that Nature follows logical steps and we, being logical beings, can understand those steps. We then derive a theory from the hypotheses that we have deduced and find the **theory** that explains the phenomenon. We then test this theory. For the ideal gas law, as the pressure increases; the temperature decreases or the density increases, the ideal gas law fails. Hence Laws are tested and usually limitations are found. We can extend the law (for example the ideal gas law can be extended to Van der Wall’s Equation), by improving it by changing the hypotheses.

Sometimes, however, laws fail when new data is found. Think classical mechanics and its breakdown to quantum mechanics. Black Body radiation could not be explained by classical mechanics. It lead to ridiculous conclusions: it predicts the night sky glows dark blue! This led to a major change after Max Planck introduced quantum ideas in 1898.

Science is a never ending effort to understand natural phenomena by observation and experiments followed by the deduction of empirical laws, then hypotheses and finally theories. The theories are used to predict and test new phenomena.

Technology is important. New effects are discovered as our technology evolves. For example J. J. Thompson could not discover the electron until it was discovered how to embed metal in glass (to make a Cathode Ray Tube).

“If we start off with no information and make a guess at something logical, then the development of that idea is mathematics, not science.” I think the opening statement is misleading. When something is logical, it comes about by the way we define what we know. If things are contrary to what we know then things seem illogical. The idea begins with the meaning we assign. This is not a mathematical process. It is as conceptual as the definition one gives something they know. Mathematics can show agreement with the idea, so to can observation and proper measurement. The idea does not develop into mathematics. Mathematics is rather like a verb to the idea. It shows agreement. Observation and experiment also must show agreement. All verbs are relative and mathematics can be just as misleading as observation. It is ultimately the end object or result that receives the action of the verb that in turn agrees with the idea. Without the objective physical result, the idea cannot become true. The whole process is the Scientific Method. The idea cannot become the mathematics any more than the subject can become the verb. The verb agrees and the object receives the action of the verb.

Quantum Theory is an idea. Its definition implies that all things come in quantum units. Experiment, mathematics, and observation should demonstrate that the objective end is also real quantum units. Modern quantum theory does not agree with the meaning of the original concept or idea. The interpretation of the mathematics, observation, and experiment is changed to agree with the desired result rather than with the original idea. In this, mathematics cannot be trusted if it follows and interpretation different than the idea. The problem is not with the mathematics, but with the interpolation. We are taught to write in three parts of speech. We should also lean to think in the same. Whenever you change the original idea to agree with you objective desire, you are making the object the subject and the idea the object in order to satisfy a psychological propensity. I say this in hopes of clarifying the purpose of the Scientific Method. It must be a complete thought, a complete science. Mathematics is only one part of the entire method.

Well I agree with you of course. I was simply trying to state that mathematics is logic without objective data and science relies on objective data to formulate hypotheses and the math follows. I disagree that mathematics cannot be trusted. Rather I would say that our use of mathematics is an approximation to what Nature does and the more we objectively know the better we should be able to reproduce the objective data.

Thanks for your comment.