Why are Newton’s laws of motion such a scientific landmark? One often cited reason is their reach. The same laws governing the behaviour of an apple falling in your backyard also governs the motion of celestial bodies. Another, less frequently cited reason is their parsimony. Newton needed to invoke only a very small number of concepts in the statement his laws. I examine Newton’s first of laws and argue that, in fact, it is weighed down with superfluous baggage and is completely sterile.

Newton’s first law of motion states the a body in motion will continue indefinitely with the same velocity (i.e., speed and direction) unless acted upon by an outside force. Sometimes the first law includes an addendum stating that a body at rest will remain at rest. In fact, this situation is already included in the earlier formulation since at rest is merely the special case when the velocity is null. 

What are the elements belonging to the universe described by the first law? To begin with, there is a single body and there is velocity. Since motion is mentioned, the body must be located in an extended space. And since the possibility is raised that direction may change, that space must have at least two dimensions. (In fact, change in direction is possible in even one dimension – from left to right, say. But one of the later laws relate change in motion to a – finite - force, so that velocity must be a continuous variable, making 2+ directions are necessary for directional change). 

Newton omitted some implicit features from this picture. No part of the body is assumed to have motion relative to any other part. So we are dealing with a rigid body. And the body is assumed to have a unambiguous velocity, so either the body is a particle with no extension, or the velocity spoken of refers to some computationally determined single point, such as the centre of mass, standing proxy for the body as a whole. However, the concept of mass has not as yet been introduced to NewtonWorld (=the world of the first law). We regard our body as a extensionless particle. A particle in NewtonWorld is completely describe by a single uniquely determinable property: its location. This property is permitted to change over time. But its change must be continuous. 

The first law also mentions force but, oddly, only to cite its absence. So we ignore it. What about velocity? Velocity is not a primitive, but is something that can be calculated from two more fundamental concepts: position and time. 

At the stage of the first law, the concepts belonging to NewtonWorld are a single particle, time and position inside a two or three dimensional universe. I want to raise questions about the coherence of this description. 

The first problem is Newton’s invocation of uniform motion. I maintain that concept of uniform motion is only applicable in a universe where there are multiple objects. By talking about a body in uniform motion, Newton presupposes a coordinate system fixed in space. But a fixed coordinate system independent of the position of any object is impossible to specify. The only available reference is the body itself. Motion is an inadmissible concept in NewtonWorld, and the first law might be restated as an undisturbed body at rest remains at rest. This is a tautology. 

There are other, subtler problems. Change is absent from NewtonWorld making time another inapplicable notion. 

Finally, NewtonWorld lacks the basis for a notion of space: There is no basis for choosing a direction upon which to build a coordinate system. At first, it appears as if one could at least have the foundation for one dimension, based on distance from the body. But as the body is extensionless, we lack any basis for establishing a standard unit of distance. 

We are left with an extensionless, eternally unchanged particle alone in a universe in which there is neither time nor space. The particle does precisely nothing, and is completely uninstructive for our physics. 

-2

New Comment
7 comments, sorted by Click to highlight new comments since: Today at 1:57 AM

Newton's first law is about the existence of inertial frames of reference. 

I do not believe the first law was intended to assert the existence of inertial frames of reference, else Newton would have said that explicitly. I think you may be extrapolating from Einstein.

More likely, the first law was intended to correct the then widespread Aristotelian conviction that all terrestrial motion eventually ceases. 

However, as a standalone statement it is vacuous. 

A particle in NewtonWorld is completely describe by a single uniquely determinable property: its location.

Well , no , you need mass , at least, to explain change in velocity.

The first law has nothing to say about mass. 

I suppose, you could say that mass is inherent in the notion of a particle. Yet physics has massless particles, such as the photon. On the other hand, it is true that the notion of massless particles only entered physics after Newton. 

In any case, the world of Newton's first law does not have any change in velocity. The possibility of a change of velocity is hinted at, but the first law has nothing to say about the associated circumstances. 

I wasn't talking about the first law alone, because you weren't. The first law does not fully describe NewtonWorld.

If you are saying that the First Law is unable to stand on its own, then I agree with you. 

If you are saying that NewtonWorld is not just about the first world, then I have to provide a clarification. I, as the founder of NewtonWorld (just for this article) declare by fiat that it encompasses only the first law (plus Kant's synthetic, a priori knowledge). I agree that the name NewtonWorld is misleading and I wish I had chosen a different name. So, sorry for the confusion.

New to LessWrong?