The Night Watchman

A Small Beacon in the Night of Unreason
raised and maintained by Per-Olof Samuelsson


Einstein and Newton

This is a question I sent to The Objective Standard, with an answer from David Harriman and a follow-up question from me. – By the way, I highly recommend this magazine. Among many other interesting essays, it contains long extracts from Harriman’s forthcoming books, The Anti-Copernican Revolution and The Inductive Method in Physics.

(Whether my question is of general interest or just interesting to me, I don’t know.)

First, a short quote from Harriman to set the context for my question:

Newton’s laws have not been contradicted by any discoveries made since the publication of the Principia. Rather, all subsequent discoveries in physics have presupposed his theory and built on it. His laws have been the rock-solid foundation for the work of every physicist of the past three centuries, and they continue to be applied today in countless ways. […] There are cases where his laws have been torn from the context in which they were discovered and applied to a realm far removed from anything he ever considered. The cases to pertain to bodies moving at near light-speed, which is about ten thousand times the speed of Earth in its orbit around the sun; or they pertain to subtle effects of very strong gravitational fields, none of which could be measured until more than a century after Newton; or they pertain to the behavior of subatomic particles, a realm that physicists did not begin to study until two centuries after Newton. ("Isaac Newton: Discoverer of Universal Laws", The Objective Standard, Vol. 3, No 1.)

I have a question about Newton, relating to the commonly held superstition that Newton has been "refuted" by Einstein. I am no expert on physics, so I am curious what an expert thinks about it. ("Expert" here obviously refers to David Harriman.)

In 1987 I read an article on Newton by Petr Beckmann (occasioned by the 300-year anniversary of the Principia) where he writes among other things:

…every motion in today’s world, from load-lifting cranes to earth-circling satellites, can be derived from the three laws unveiled in the Principia three hundred years ago this month.

Yes, I said every motion, without excluding the motion of elementary particles at speeds close to that of light. And I will not eat my words, for the myth that Einstein denied Newton’s Three Laws is spread by the cribbing rehashers and rehashing cribbers who have never studied either Newton or Einstein first hand. It is one of the numerous myths that are already appearing in the popular press celebrating the Principia’s anniversary…

I defy anyone to show me the place [in Principia] where Newton uses force as mass times acceleration. Although the definition is perfectly correct for masses moving "slowly" (compared to the speed of light), Newton’s uncanny genius was far too careful to overlook the possibility that mass might be variable: he never took it out of the momentum entity (mass times velocity), leaving Einstein a law to use with variable mass without need for the slightest modification.

By searching the web, I also found the following quote from Beckmann (from his book The history of pi), where he makes the same point:

Contrary to widespread belief, Newton's laws of motion are not contradicted by Einstein's Theory of Special Relativity. Newton never made the statement that force equals mass times acceleration. His Second Law says
F = d(mv)/dt
and Newton was far too cautious a man to take the m out of the bracket. When mass, in Einstein's interpretation, became a function of velocity, not an iota in Newton's laws needed to be changed. It is therefore incorrect to regard relativistic mechanics as refining or even contradicting Newton's laws: Einstein's building is still anchored in the three Newtonian foundation stones, but the building is twisted to accommodate electromagnetic phenomena as well. True, Newton's law of gravitation turned out to be (very slightly) inaccurate; but this law, even though it led Newton to the discovery of the foundation stones, is not a foundation stone itself.

And the person who quoted Beckmann wrote:

In translation, the second law reads "The change of momentum is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed." Newton defines momentum as follows: "The quantity of momentum is the measure of the same, arising from the velocity and quantity of matter conjointly."

Or, in the symbolic terms of Newton's calculus, F = d(mv)/dt.

Newton did not know whether or not mass was constant, and he was too careful a scientist to assume so by placing it outside the differential. During the next 200 years, physicists assumed, for convenience, that mass was constant and began to write F = ma or F = m dv/dt. It is this later day shortcut which proved to be incorrect, not Isaac Newton's original law.

What do you think of this?

David Harriman’s answer:

Beckmann is right that Newton's laws have not been disproven by any later discoveries in physics. But my own view differs from Beckmann's in two ways.

The first and most important difference concerns the contextual nature of knowledge. To claim that a generalization is true is to claim that it applies within a specific context of knowledge. Within the realm of phenomena studied by Newton, his laws are valid and have not been contradicted by any discoveries made in the past three centuries. However, it has been discovered that the laws need to be modified in certain ways for strong gravitational fields, atomic physics, and bodies travelling at near light-speed. These phenomena do not contradict Newton's theory, because they are outside the scope of the theory.

The second difference pertains to physics. I don't accept the idea that the mass of a body changes depending on how other bodies move with respect to it (or depending on what frame of reference we choose). I see no need for the concept of "relativistic mass." Rather, the expression for momentum should just be changed. For bodies travelling at near light-speed, the momentum is not simply the product of mass and velocity, but this product divided by the square root of 1 - V2/C2.

I hope this answers your question.

My follow-up question:

Thanks for your answer!

If I understand Beckmann correctly, he not only says that Einstein’s physics does not contradict Newton’s second law, but that it is actually encompassed by the second law – and that Einstein is actually building on it, rather than contradicting or refuting it. (And Newton himself couldn’t know this, simply because he had no experience with bodies moving close to the speed of light.)

I see that you disagree with this, but for me this opens another question:

If the second law has to be modified for velocities close to that of light, at exactly what velocity does this modification have to set in?

I would think that if the law has to be modified, it would have to be modified for every velocity. The difference would be that for normal velocities, such as we experience everyday, the deviation would be too slight to have any practical significance – even so slight as to be virtually imperceptible.

A couple of years ago, I argued relativity with some people on the net. It was mainly about aspects of the theory that I regard as nonsensical (such as space contraction and time dilation), but someone told me that if one uses atomic clocks, one can note the difference (the "time dilation") even if one of them is stationary and the other one is moving at the pace of a fast stroll. I do not know if this is true, but if I’m right in the paragraph above, it would make sense.

By the way, I read through Beckmann’s A History of pi the other day, and although what he wrote about Newton made sense to me, he said some other things that I thought were just crazy. For example, he accepts the "probabilistic" interpretation of quantum mechanics (he didn’t argue for it, he merely took it for granted). He also accepts the notion that axioms are "mere assumptions", to be replaced by other assumptions at will. He is also extremely hostile to Aristotle. (But if you know anything about Beckmann, you probably already knew this.)

(I received no answer to this. Hopefully, there will be something on this question in Harriman’s forthcoming book, The Anti-Copernican Revolution.)


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