# Physical system

A **physical system** is the part of the universe that a physicist is interested in. What is not in the system is the environment or the *surroundings*.

## Reduction

Physics is a reductionist science meaning that a physicist restricts his^{[1]} studies to that part of the universe that is as simple as possible and yet shows—as far as he can see—all the physical phenomena that are essential to his study. Reduction is a *conditio sine qua non* in the explanation of observations and is essential for the progress in the understanding of nature.

## Idealization and abstraction

Hand in hand with reduction go *idealization* and *abstraction*. Non-physicists are often
amused and puzzled by the idealizations that are common in physics. The infinitely thin, infinitely strong, yet massless, rope from which hangs a heavy mass of infinitely small diameter is proverbial. Many abstract, and consequently difficult, concepts have entered physics over the last three centuries. It takes intellectual effort to get a grasp on abstractions as "an isolated physical system strives for maximum entropy" or "the wave function of a system collapses when a measurement is performed on it". What exactly vibrates when a radio signal is emitted? Interested laymen are sometimes irritated by these abstractions that they conceive as unnecessary *Wichtigmacherei* (making oneself important) by physicists.

## State and state variables

When a natural scientist chooses part of the universe as his physical system, i.e., as his object of
study, he must define at the same time the variables that determine the *state* of the
system. Without the concept of state and state variables the concept of physical system loses much of its meaning. When
Newton considered around 1666 a physical system consisting of the point masses Sun
and Earth, he simultaneously assumed that the state of this system is uniquely
determined by two (vector) state variables, namely the position and velocity of the Earth. Further, Newton made the idealizing assumptions that the Sun is at rest and that the diameters of Sun and Earth are of no importance and may be set equal to zero, although the masses of both planetary objects are non-zero (the crux of Newton's gravitational law). When Newton later explained the origin of the tides, the actual (non-zero) diameter of the Earth entered his description.

## Time-dependence, causality, equations of motion

Most physical states are non-stationary, they change in time. The state variables—many of which are assumed to be observable (measurable)—develop in time. An important goal of physics is to discover the laws that predict the time development of the state of the physical system. It is always assumed that the time development of a state is *causal*, that is to say, time is ordered and a state at time *t*_{0} uniquely fixes the state at time *t*_{1} for *t*_{1} > *t*_{0}. The mathematical equations that describe the time-development of the state variables are the *equations of motion*. Newton wrote down the law **F** = *m***a** for the motion of a mass *m* and Schrödinger discovered *H*Ψ= *i dΨ/dt* for the causal time-development of a system's wave function Ψ.

Clearly, the goal of finding the equations of motion is a lofty one, but it must be emphasized that many systems are far too complex to even begin of thinking of formulating equations of motion. Even so, the concept of state, state variables, and their development in time is of importance also for complicated systems where the relationships between state variables and their dependence on time cannot be caught in mathematical equations.

## Isolated, closed, and open systems

We saw that a physical system does not have to be separated mechanically from the rest of the universe. Indeed, it is evident that Newton did not put the Sun and the Earth inside a vessel with non-adiabatic walls. In other words, a physical system, although conceptually separated from the universe, is not necessarily mechanically isolated from its surroundings. However, in practice it can be very convenient if a system is actually isolated, because the interpretation and explanation of measurements are eased when it is certain that no interactions with the surroundings can influence the system.

It is usually not easy for an experimentator to separate a physical system from the surroundings. For instance, a physical chemist studying a system consisting of molecules will try to observe only the molecules that he is interested in, and will try to reduce the number of other ("surrounding") molecules in the system. Thus, a thorough purification and/or high vacuum is needed. Usually, it will be necessary to shield the molecules from unwanted external fields, such as electrostatic, magnetic, and gravitational fields. (The latter field cannot be shielded, but weightless conditions are possible in space stations). For a theoretician, on the other hand, the definition of an isolated physical system is trivial, it is just the part of the universe (matter and fields) that he considers in his equations.

As stated, the system that is easiest to study is the *isolated system*, where it assumed that there
is no interaction whatever with the rest of the universe. No matter or heat can flow in or out of an isolated system. Obviously, completely isolated systems are of no interest to experimentalists, because no information leaves such a system and manipulation of the system is impossible because nothing enters an isolated system either. Thus, in the laboratory, physical systems are never completely isolated. A *closed system* is a system that does not allow exchange of ponderable matter with the surroundings, but heat may freely flow in or out. In an *open* system exchange of both heat and matter with the surroundings is allowed. For a theoretician the idealizing concept of an isolated system is of great importance and almost always applied, even in studies of closed or open systems. For instance, when a thermodynamicist considers a system with constant temperature and a constant number of molecules he assumes that his system (a closed system, heat may flow in and out) is in temperature equilibrium with a very large heat bath. The "supersystem" consisting of the original system and the heat bath is an isolated physical system.

## Note

- ↑ For linguistic reason we write "he" and "his" when referring to a physicist. This does not imply that physicists are necessarily male.