An alternative view of Newtonian mechanics

In that earlier thread, I wrote:

to which @dga471 responded:

What I had noticed, was that Newtonian mechanics was a major reconceptualization. The older common sense view of motion must have been that moving things tended to slow down and stop. Newton’s first law said something quite contrary to that.

Once I realized that Newton was reconceptualizing motion, then it became clear Newton’s laws were not descriptions, they were definitions of his new conceptualization. And if those laws are definitions, then they become logical truths once we accept those definitions. So they cannot imply determinism. Definitions cannot have determinism as a consequence.

Here’s another way of explaining the difference, which I will over-dramatize.

According to the traditional view, Newton’s laws govern the behavior of objects, particles, etc.

We imagine particle A sensing that there is some force. So particle A pulls out his measuring instruments to measure the force, and then consults with Newton’s laws to compute the needed rate of acceleration toward particle B.

In the alternative view, particle A accelerates toward particle be because it feels like it. Maybe particle A and particle B are in love. The scientists observes that acceleration, and thereby ascribes a force of attraction, in accordance with f=ma. Thus the role of Newton’s laws is to govern the ascribing behavior of scientists.

With this alternative view, Newton’s laws are solving what philosophers might call an intentionality problem. The laws tell us how to use that terminology from physics, so that our sentences are about something (some aspect of the world). The laws tell us how to ascribe properties (such as force, mass) to reality. That ascribing of properties is usually known as “measurement”. And it is the measurements, rather than the laws, that are descriptions of reality. Newton’s laws work so well because they have vastly enhanced our ability to have accurate measurements (i.e. descriptions).

When we use Newton’s laws to make predictions, what we are really predicting are other measurements that we might make. And because the laws provide the meanings of our terminology, they enable us to understand what our predicted measurements tell us about reality.

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I only pay, recently, a little attention to physics. by way of youtube science shows and a book here by Einstein.
you put it in a way I didn’t notice before. i like it but wonder if modern physic teachers would complain.
Newtons laws to make predictions;but actually predicting other measurements.
something to think about as i seek better explanations for entry level people.

We may find out, as others comment on this thread.

This is a question for the physicists maybe, but perhaps also the philosophers of science.

This seems to be reasonable to me.

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Neil, I see nothing majorly objectionable about your “alternative view”, other than perhaps the unorthodox language used to describe it. Rather I think the issue is that there is some uncertainty and debate about what a law of nature really is. In my understanding, Newton’s laws are statements about the behavior of particles that give certain definite predictions. If particle A moves with velocity v it will keep moving with the same velocity unless it experiences a force F. We carry out measurements to verify if this is indeed the case. These measurements are usually of certain quantities (length, mass, time) that have been clearly defined. And we find that nature seems to obey Newtonian mechanics well. In the cases where it seems to not do so (e.g. a hockey puck sliding on a dry wooden table), Newtonian mechanics can give elegant explanations for that as well (it is due to friction).

In this very pragmatic, experimental picture, we do not know if Newton’s laws actually cause the particles to behave in the way they do. We have no idea if the particles “feel” or “sense” anything. We just know that the laws describe their behavior fairly well. This is the only correct sense in which we say that they “govern” the behavior of the particles. So your traditional picture where a particle makes sure that its behavior is in accordance with the laws is not one that is familiar to me. The fact that Newton’s laws turned out to be wrong for some situations seems to further vindicate this purely descriptive view.

According to you,

But I do not understand how “definitions” fit into the account of Newton’s laws that I’ve given above. I can only say that if we follow the definitions of quantities used in Newtonian mechanics, we get results which are intelligible and match the behavior of nature well.

With regards to determinism, imagine an ideal world that is perfectly described by Newtonian mechanics. The behavior of any particle A would always follow Newton’s Laws (NL): namely that if A is in a certain state S_1 at time T, then according to NL it will be in a certain state S_2 at time T+1. We can precisely describe S_1 and S_2. That’s my rough definition of what deterministic is. Even if S_1 and S_2 may be difficult in practice to describe (due to our lack of computational power, or maybe that nobody is smart enough to do the math), in principle we don’t need anything other than NL to describe them.

(How about special situations where NL cannot predict what happens next - i.e. even in principle S_1 and S_2 cannot be described? This is what @PdotdQ pointed out in the other thread. Is it still deterministic? I’m still thinking about how to further refine my definition of determinism such that it survives even in cases like these. So this is a very good question. But most of the paradigm cases in Newtonian mechanics are predictable.)

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I will echo @dga471 here. Physicists do not claim that Newton’s laws are the cause of particles behaving the way the do. Newton’s laws are a set of descriptions that matches experiments. Unless I am misunderstanding you, it seems to me that the physicists’ view is closer aligned to your alternative view than your traditional view.

I am also still puzzled how this alternative view allows one to reconcile non-determinism with Newton’s laws. I think I need more clarification on this point.

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Thanks for commenting.

Yes. I am taking the view that “laws of nature” come from scientists. That is to say, they are inventions rather than discoveries. However, such inventions are constrained by reality, because we want them to be useful.

Putting it another way: we do not start with concept, and then find laws that relate them. Rather, we invent concepts and relations as a combined package.

My only comment there, is that it takes laws + data to give predictions. We don’t get predictions from the laws alone.

That part was my over-dramatization. I agree that we have no idea what it could even mean to say that particles feel or sense.

But that’s an unrealistic picture of reality.

It pretends that we are sitting outside of reality, and observing what happens. But we are ourselves part of reality. When we talk about being in state S_1, it is not at all clear what we are saying. Because we define states in terms of other states. We define distance with a measuring rod. But we cannot say what is the length of the measuring rod, except that it is its own length. Everything we say about reality, we have had to anchor to other parts of reality. We are not sitting outside of reality and applying external standards. So I am looking at Newton’s laws as part of how we anchor our statements to reality.

I should add that I agree with @swamidass, that this is more an issue for philosophers than for scientists.

This seems closer to the philosophy known as instrumentalism, which is in contrast to scientific realism, which believes the claims of science in a more literalistic manner (i.e. electrons really exist, instead of just being a way for scientists to understand the results of certain experiments). The major argument against instrumentalism is the “Miracle” argument: if laws of nature are mere inventions - mere patterns in the human brain that make us able to think about phenomena better - then why have they been so successful in not only explaining past empirical observations but predicting new ones?

An example that I like to bring up is the magnetic moment of the electron. We can predict and measure this quantity accurately up to 12 decimal places based on straightforward assumptions of quantum field theory, without having to fudge any factors or plug in arbitrary constants. (Note also that QFT was developed far before we had the technical capability to make these precise measurements. So this is not a case of a theory developed specifically to conform to our current measurements.) If quantum field theory is only an invention by scientists, how can it be such a phenomenally successful invention?

It is true that physics assumes certain definitions for fundamental quantities such as mass, time and length. These definitions are prior to physics itself, including Newton’s Laws. When Newton stated his laws he made references to bodies, motion, and other quantities which people already agreed upon before. So if you are saying that Newton invented new concepts to redefine reality, you are probably right with regards to higher-level concepts such as force. But I would push back on the notion that he redefined all reality in that way. If that were the case then Newton’s theory would be unfalsifiable. We would not be able to test it, because that assumes that the supporters and skeptics of the theory already agree upon certain basic concepts such that they could agree on a test. Clearly that is not the case - we can perform tests that verify that, say, the inverse squared law of gravity is correct. (In fact, there are precision measurement labs in the world which test this with the utmost precision at this very moment.)

Likewise, if the airplane were a mere invention, then how come it is so successful in transporting us around the world?

Yet we know the airplane is an invention. That word “mere” is the mistake. Airplanes were invented for transportation. Laws of physics were invented for prediction. It should not be considered a miracle, that an invention actually serves the purpose for which it was invented.

That “no miracles” argument has other problems. If Newton’s laws are true about reality, as the “no miracles” argument asserts, then how was Einstein able to come up with relativity? From my perspective, that isn’t a problem – relativity was simply a better invention.

I did not suggest that Newton redefined all of reality. My comment was about redefining concepts, which is not the same as redefining reality. As far as I know, he went with existing concepts for length/distance.

I’m not a historian. But I somehow have the impression that the distinction between mass and weight was due to Newton or perhaps Galileo. In earlier times there was only weight. So mass was also a new concept. And Newton’s definition of time in terms of the mean solar day seems to have been new. Newton’s laws are not consistent with natural solar time, but they work pretty well with mean solar time.

I’ve never been a fan of falsificationism. Falsficationism is itself unfalsifiable.

We do not test whether theories are true. We test whether they make good predictions.

I agree. Falsification is unhelpful framework. Explanatory power is a much better framework, and I mean this in a specific way.

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This is not the right comparison, and I had tried to preempt this objection in my reply to you. If quantum electrodynamics (QED) were a theory that was specifically crafted to match all the experimental results that we already had, then you would be right - it would be no more special than a well-constructed airplane. But QED was proposed way before we had the capability to test it to 12 decimal places. In fact, quantum mechanics started out in the 1920s to describe the results of relatively crude experiments like the Stern-Gerlach experiment. But it turns out that the basic postulates of quantum theory, taken to their logical conclusions, are able to hold strong for almost a century. The fair comparison would be if a Cessna designed to fly 15,000 feet above the ground turned out to be able to take us beyond the Solar System. (In fact, I don’t think airplanes have any functionality with the precision of 12 decimal points.) To me, that would point to the fact that there’s something fundamentally special about that Cessna - more than just a human construction for a limited purpose.

But Einstein didn’t completely overthrow Newton’s laws. He still had to respect its basic principles applied in the right circumstances. And indeed, special relativity reduces perfectly to Newtonian mechanics in the right limits. Many theories throughout the history of physics followed this beautiful correspondence principle. This seems to point to a unifying set of principles underlying all of the laws which our theories are gradually approximating better and better.

I don’t quite understand how this has to do with opposing falsificationism. Whether theories merely make good predictions or actually reflect an aspect of nature-as-it-really-is is separate from the issue of how we are supposed to separate good from bad theories, which is what falsificationism is all about. (In fact, traditional Popperian falsificationism would say that we cannot verify that theories are true, only that they are false.) Anyway, I think we’ve digressed from the original topic.

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Why are not the ‘laws’ just descriptions? And where there are discrepancies, the descriptions are just not accurate or precise enough?