Violating Newton's Laws.

Every so often someone proposes an experiment that seems to violate Newton's Third law. It's an attractive idea, for then you could make a device that moves itself without external input of either force, momentum, or energy. Some call such a device a "reactionless thruster". Imagine, a rocket that requires no fuel!

A correspondent raises this possibility.

Consider the possibility that there might exist two unusual particles, with the remarkable property that particle A is attracted to particle B and particle B is repelled by particle A. Together they would form a system that continuously accelerates in one direction, particle A always chasing particle B.

The force of B on A and the force of A on B are shown below. These are the only forces that act on each particle.

       o---> F              0---> F
       A                    B

Clearly this situation assumes that these two particles disobey Newton's third law. The perpetrator of this idea apparently assumes that Newton's second law (or something very much like it) applies to each particle, for he says that the system (both particles) accelerates because of these forces. Is this process, and these particles, even possible?

The only known repulsive force in classical physics is that of two like charges repelling each other. Unlike charges attract each other. These forces obey Newton's third law scrupulously. So this hypothetical problem isn't a system of ordinary charges. These must be very extraordinary particles. Something is screwy here.

When two bodies with mass collide, there is, during the collision, an action-reaction pair of contact forces that is repulsive. But these forces are symmetric, equal size and oppositely directed, obeying Newton's third law. No surprise here, for the source of these forces is the electrical forces that arise due to atoms and molecules during the deformation of the bodies, and they all obey Newton's third law.

That doesn't apply to this imaginary particle interaction. There are no known particles in nature that behave this way. This would be a vastly different place if there were.

But let's remember our Freshman physics. Newton's laws apply to systems and also to each and every part of systems. Let's imagine a boundary defining our imagined system, enclosing both particles. What is the external force acting on this system? Zero. We stated in the condition of the problem that no other forces act on any part of the system. Therefore Newton's second law applied to the entire system tells us the system's center of mass can't be accelerating. Whoops!

Here's where we realize we are in serious trouble. In the real world Newton's laws apply to systems as well as all individual parts of systems in all possible situations. This is a point students often "know" but they may fail to appreciate its far-reaching implications. The inventor of this hypothetical system says both particles are accelerating, because of the action of their assumed mutual forces. So he is also assuming that Newton's second law applies to each of them. But if applied to the system Newton's second law tells us the system's center of mass is not accelerating. Try as you might, there's no way you can satisfy Newton's laws for the particles and the system by any imagined motion of the two bodies. Geometry prevents it.

We begin to realize that you can't violate Newton's third law without also violating Newton's second law. They are logically linked, and you can't have one without the other. This is an insight you don't get by simply examining the two equations F = ma and F₁₂ = -F₂₁ separately. It's almost as if these two equations (along with Euclidean geometry) taken together "knew" you might try someting impossible and thwarted your attempt.

So, the heck with it. Let's cheerfully asssume we have violated both of Newton's laws. What serious consequences could that have? A few come to mind. We would be violating

• the conservation of energy,
• the conservation of linear momentum,
• the conservation of angular momentum,
• and the laws of thermodynamics.

Likewise this system gains momentum continually without any external force acting on it. This system therefore violates conservation of momentum.

We could constrain the particles to move only on a circular track, and therefore violate conservation of angular momentum.

Since the laws of thermodynamics for systems of particles are logically derivable from Newton's laws, and these hypothetical particles violate Newton's laws, then we have just demolished thermodynamics as well.

Given the initial assumptions, these two bodies will accelerate continually until they exceed the speed of light. Oh, oh! Relativity theory goes down the drain.

We have shown equal size forces, but the previous arguments only depend on the direction of the forces, not their size.

These results should be no surprise to anyone who really understands the logical connections between physics laws. The conservation laws are mathematically derivable from Newton's laws. So are the laws of thermodynamics. The conservation laws are also logical consequences of the geometry of the universe and the symmetry of physical processes under various geometric transformations. It all ties together, and modifying or destroying one part of it brings the whole logical structure crashing down. More seriously it would destroy parts of physics that have been thoroughly tested and found valid.

That sly fox, Isaac Newton, likely knew that his second law F = ma was simply inadequate and useless without the third law. [Newton's first law can be considered the special case of the second law when the body m is at rest (its acceleration is zero).] Newton didn't speculate why the third law should be true in nature. His famous comment "I feign no hypothesis" might have been his way of saying "Don't waste my time with unanswerable questions."

Rarely does anyone propose anything that they think violates Newton's second law. Clearly they don't see the connections.

But are these laws universal?

Newton's laws of mechanics implicity "assumed" that such force influences propagate instantaneously, and no one in his day even realized that light speed was finite. Electric and magnetic fields hadn't been invented then, either. Now we know about these things, but we have relativity theory to deal with such high speed phenomena. I'm not expert in this, but I accept the verdict of those who are: that these facts present no challenge to Newton's laws, once they are interpreted properly.

What about Newton's law of gravitation? It is often asserted that gravitation is the fundamental force of nature that we know the least about, even though it dominates our everyday life. Is the gravitational force subject to the universal speed limit? Why is it an inverse square law rather than inverse cube or something else?

Let's look at that last question. All the forces, electric, magnetic and gravitational obey an inverse square law. The electric force has been studied in the laboratory, and that "2" in the denominator is known to some 10 decimal places. Is this mysterious? Is this surprising? Or should we have expected that?

Consider this classical analysis. Take light as an example. The intensity of light from an isotripic point source propages with an inverse square law. This is fully expected, for it follows from the law of conservation of energy. The energy spreads out over an ever enlarging volume of space. We measure it at a given distance, and find that, integrated over a sphere of radius r, the total energy reaching that sphere's surface is the same as it was for any smaller radius sphere, and will be the same for any larger radius, assuming no light absorbtion or production in space. After all, the area of a sphere is proportional to the square of its radius in Euclidean spaces. [And our local neighborhood in the universe has been shown to be Euclidean as well as we can measure.] So the inverse square propagation of light energy is only what one would expect from Euclidean geometry and the law of conservation of energy.)

The same geometric argument applies to electric fields, and, so far as we can measure, gravitational fields. Again, nature is telling us that conservation of energy is just an inevitable conseqence of the geometry of the universe. Again we are confronted with the observed fact that in nature, many things are "tied to each other." Speculative tinkering with any part of it affects many other parts of it. [1]

The perceptive student may notice another "problem" with Newton's laws. The inverse square law of gravitation predicts that two particles very close to one another would exert a tremendous force on each other, for 1/R² goes to infinity as R goes to zero. What is the small scale limit where the law "breaks down"? This interesting problem is more technical than I care to consider here, but has no effect that I can think of on any experiment you might do in a university undergraduate physics laboratory. Nor can it serve as the basis of an over-unity perpetual motion machine.

Historical precedents.

The Baron Munchausen bootstrap principle at work.

The reader probably has already realized that this two-particle system might have been inspired by the fantastic tale of Baron Munchausen, who once saved himself from a perilous situation when mired in a bog by reaching up and lifting himself and his horse by his own hair (a pigtail). See: Baron Munchausen. Later variants of this tall tale had him lifting himself by his own bootstraps. This may be the first literary example of a violation of Newton's Laws. It is humorous because readers immediately recognize that nature doesn't work that way.

Endnotes.

Physics includes a wide variety of laws, theories and principles, and they can be expressed by equations accompanied by explanatory words. Many of these equations are logically (mathematicaly linked) with others. These are the "backbone" of the subject, and I have called them the "fundamental" or "core" equations. [I'm not aware of any accepted name for this concept.] Other equations represent laws, usually of narrower scope, that describe some particular process, but have only tenuous (and sometimes not fully well-known) links with other laws. These laws are the ones most likely subject to change by scientific advances.

The fundamental equations are those that have survived the most extensive testing, over the widest range of phenomena. For example, Newton's laws have met the test of experiment in gravitational interactions of the planets, industrial machinery, electrical machinery, and natural processes in geology, meteorology and just about every other branch of physical science.

The bottom line is that the fundamental core of laws are so logically and physically intertwined and so thoroughly tested that altering any one of them would affect nearly everything else. Therefore it is highly unlikely that new discoveries will invalidate one of these laws. And if one of them were to be invalidated, the entire structure of basic laws would need to be modified. That's a daunting task for any would-be candidate for a Nobel prize. In fact, whenever an experiment seems to invalidate one of the fundamental laws, the most likely reason is that the experiment was faulty, or some un-noticed influence affected the outcome. Quite often the reason is a simple mathematical blunder.

—Donald E. Simanek, Feb, 2010, revised June 2011.

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