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### 1st Law and Newtonian space and time.

One of the most important consequences of the First Law is that it defines what we mean by an inertial frame of reference.

 An inertial reference frame is a reference frame where isolated bodies are seen to move in straight lines at constant velocity.

An observer at rest with respect to an inertial frame of reference is called an inertial observer. The laws of physics devised by Newton take a particularly simple form when expressed in terms of quantities measured by an inertial observer (such as positions, velocities, etc.). For example, an inertial observer will find that a body on which no forces act moves in a straight line at constant speed or is at rest.

All motion occurs in space and is measured by time. In Newton's model both space and time are unaffected by the presence or absence of objects. That is space and time are absolute, an arena where the play of Nature unfolds. In Newton's words,

Absolute space in its own nature, without relation to anything external, remains always similar and immovable.

...absolute and mathematical time, of itself, and from its own nature, flows equally without relation to anything external, and by another name is called duration.

Space and time were taken to be featureless objects which served as a universal and preferred reference frame (see Fig. 4.9 for an illustration). A consequence of this is that a given distance will be agreed upon by any two observers at rest with respect to each other or in uniform relative motion, for, after all, they are just measuring the separation between two immovable points in eternal space. In the same way a time interval will be agreed upon by any two observers for they are just marking two notches on eternal time.

Newton's assumptions about space and time are the foundation of his theory of Nature and were accepted due to the enormous successes of the predictions. Eventually, however, experimental results appeared which disagreed with the predictions derived from Newton's theory. These problems were traced to the fact that these basic assumptions are not accurate descriptions of space and time (though they do represent a very good approximation): space and time are not absolute (Chaps. 6, 7. The realization that Newton's theory required revisions came to a head at the beginning of the XXth century. In the two decades from 1905 to 1925 a completely new framework was constructed and has now replaced Newton's ideas. These theories comprise the special and general theories of relativity and quantum mechanics.

Do we know that the current theories of space and time are the truth? The answer is no: we do know that the current theories explain all the data (including the one explained by Newton and more), but we cannot determine whether they represent the ultimate theories of Nature. In fact, we expect them not to be the last word as there are many unexplained questions; for example, why should the proton be precisely 1836.153 times heavier than the electron? Why should space have 3 and not 25 dimensions? etc.

But in the 17th century there was no inkling of these problems and very few scientist questioned Newton's hypothesis. In particular Newton constructed his mechanics to comply with Galilean relativity: an observer in uniform motion with respect to another cannot, without looking outside his laboratory, determine whether he is at rest or not. And even if he looks outside, he cannot decide whether he is in motion or the other observer is. In fact for two inertial observers moving relative to each other the question, which of us is moving?'' is un-answerable and meaningless. The only thing to be said is that they have a certain relative velocity.

Next: 2nd Law Up: Mechanics. Previous: Mechanics.

Jose Wudka
9/24/1998