a physics brief | .... on Newton's first law of motion |

Is Newton's first law redundant? . . . . . . its justification and significance. An explanation for students of philosophy and the history of science.
Part 1: What the problem seems to be Isaac Newton gave us three laws of motion. They form the foundations of classical mechanics; they are the basis of scientific achievements ranging from explaining the motions of the planets, through engineering the dynamics of automobiles and planes, to mastering moon-landings. But do we need all of his three laws? Expressed succinctly Newton's laws are: - A body will remain at rest or move with a constant velocity
^{1}unless acted upon by a force. - Force is equal to mass multiplied by acceleration.
- To every action there is an equal and opposite reaction.
These laws have been handed down generation to generation. But for some non-professional physicists they raise doubts The "redundancy hypothesis" argument is easy to understand. Two premises lead to a deductive conclusion. The first premise comes directly from Newton's second law which asserts that "force is equal to mass multiplied by acceleration". The second premise is the definition of acceleration. It is that an acceleration means a change in velocity. (The acceleration, of course, can be negative meaning that the velocity is decreasing.) No acceleration means no change in velocity So the two premises are: Premise 1: If there is no force then there is no acceleration From these a conclusion may be deduced: Conclusion: If there is no force then there is no change in velocity The conclusion is that a change in velocity can only occur if a force is present. But this is just what Newton's first law states. In other words, it appears that the first law can be derived from the second, and if it is nothing more than a consequence of the second, then the first law is redundant. The argumentation presented above uses the logic of categorical statements but some might be more familiar with the mathematical exposition. So let us come to the same conclusion using the familiar mathematical formula for Newton's second law which was published, some thirty years after the death of Newton, by the Swiss-born mathematician, Leonhard Euler (1707-1783): F = m . d (where F represents the applied force, m is the inertial mass and d If we make the force, F, equal to zero, then d which on integration gives: v = constant. In otherwords if there is no force then there is no change in velocity. And this again is just what the first law states. Thus both a logical argument and a mathematical formula seem to arrive at the same conclusion: Newton's first law can be derived from his second. If this is true then the first law is redundant. BUT IS IT TRUE? Part 2: Where the fallacy lies The arguments above are like a good conjuring trick; they are impressive but built around a deception. The truth is that Newton's first law limits the scope of the second law: it is an independent rule. The key to unmasking the deception lies in understanding what Newton meant by "force". Newton published his laws of motion on July 5, 1687 in a work which is commonly referred to as "The
Principia" For Newton, force is intimately connected with the frame of reference (or co-ordinate system) in which
acceleration is measured. This leads to an important asymmetry: a force will cause an acceleration but
an acceleration might not necessarily be caused by a force. An object can appear to accelerate when,
in reality, it is the reference frame which is accelerating If the reference frame is accelerating then a body otherwise at rest will appear to be accelerating
away. Only in a framework which is stationary or moving with a constant velocity will But the above phrase The deception in the "redundancy hypothesis" can now be seen. When we said that the acceleration is zero because the force is zero we were saying that accelerations can only occur because of Newtonian forces. In other word we are limiting our choice of reference frame to only inertial systems. But such inertial frames of reference have properties that are defined by Newton's first law. Thus we did not derive Newton's first law from his second, we built it into our argument when we eliminated any possible acceleration other than those driven by a force. Let us first see how this deception was smuggled into our mathematical argument based around Euler's equation. By assuming that there can be no
acceleration when there is no force, we have defined the "x" in "d Similarly the sleight of hand occurs in the first premise of the logical argument. "If there is no force then there is no acceleration" is logically equivalent to saying "If there is an acceleration then there is a force". But this is only true in an inertial frame. Thus the first premise defines the reference frame as being inertial, which, in turn, is defined by Newton's first law. The argument's conclusion was, therefore, just a rephrasing of this premise. So the conjuring trick is explained: the magician was able to pull the rabbit out of the hat because he had just, a split-second beforehand, put it there himself ! Part 3: Why the mistake arises Newton took great care in formulating his laws. We are told in Richard S. Westfall's comprehensive biography of Isaac Newton Leibniz fully understood the implication of Newton's first law. It assumed that space existed in its own right even if matter was not present. (It is in this 'absolute space'
that the inertial frameworks exist.) But this was a concept which the philosopher utterly rejected. Leibniz's preference was for space and the motion of bodies to be defined relative to other objects. For him
there was no 'absolute space' which was common to his 'possible worlds'. The space in any world was defined through the arangement of matter in it. All such 'possible worlds' would be different and so
no universal, absolute space could permeate them all In the history of science there has rarely, if at all, been such a bitter dispute than that between Newton and Leibniz. There was little love lost between the two.
But as a supreme logician Leibniz realised that Newton's first law was not derived logically from his second but was a separate metaphysical claim. So Leibniz attacked Newton's
first law from this direction Why is it that the independance of the first law now seems to trouble some modern readers? The reason, as has already been inferred, is that it is quoted out of context. Simply stating the first law as 'a body will remain at rest or move with a constant velocity unless acted upon by a force' assumes a knowledge of the foundations which Newton had errected at the beginning of the 'Principia' to support this statement. In particular it assumes to know what Newton meant by 'force'. The 'Principia' is rarely read today but without it Newton's statement of the first law can lead, as we have seen, to a
misconception: to the error of the 'redundancy theory'. Furthermore without this back-ground knowledge the first law seems to have a different purpose:
that of opposing the theories of Aristotle. In the Aristotelian world the absence
of a force on a moving body would eventually cause it to come to rest in its 'natural' place. For Aristotle, unlike Newton or Descartes, motion could only be maintained through
the constant presence of a 'moving' force. If the
'Principia' is not read then it seems that Newton by insisting that natural motion will continue without the presence of a force, is just opposing the Aristotelian tradition.
But while this rejection of Aristotle might be read into Descartes' formulation
of his first law, Newton was saying more If we are not inclined to read the 'Principia' how might the first law be better formulated? Using modern terminology such a re-phrasing might be: It compels us to understand that not every acceleration results from a universal force
Part 4: Footnotes [1]. Velocity is just the speed along a defined straight line. A change in velocity can therefore
be a change in speed in the same direction or the same speed in another direction (or a different speed and a different
direction). For the scientifically inclined velocity is a vector quantity and speed a scalar; the less
scientifically inclined should read the first law as saying that 'A body will remain at rest or move with a constant speed in a straight line unless acted upon by a force'. |

© 2010-2013 Stephen Harris |