Newton's Second Law - Empirical or Definitional?

[Marshall]

As nominal talk-show-host of this little PoS subforum, hello everybody, nice discussion! And in case anyone feels the need to lighten up there's this beautiful article in the peer-reviewed Aquatic Mammals Journal
http://www.aquaticmammalsjournal.org/in ... Itemid=112

"and further evidence, from 41 male foetal sperm whales, and 1,269 male postnatal sperm whales examined in the Southeast Pacific in 1958 to 1962, showed that male sperm whales do not possess nipples."

The males of most mammalian species are mammals in the sense that they possess vestigial nipples evolution not having taken the trouble of erasing them however male sperm whales are apparently not mammals (if we take the definition too seriously) :^D

[Marshall]

I'm not so sure you have it right (when you drift into that area) from a biology standpoint. Biologists have moved on toward a classification system that attempts to focus on a genetic trail, in the modern quantitative form taken in the discipline of cladistics. You make it sound arbitrary. Definitions are helpful, pedagogically, but that doesn't imply that they aren't targets of reconsideration. And though there is a lot of head-scratching among these researchers, where they have changed their mind here and there about the branching, depending on available data, there remains an attempt to get at the actual line of descent on the evolutionary tree.

Cladistics. You've got something there, Owl. Definitions help to structure language. Language has to adapt, and evolve. One way is by modifying the categories and adjusting the definitions to be more clever and useful.
I remember hearing a lot about cladistics when our son was in high school and audited some courses at the university. back in 1990s.
You are definitely right! Definitions have to be subject to reconsideration.

(especially in an academic discipline where language needs to be fine-tuned)

[AllShips]

I'm reminded of Nelson Goodman's maxim (used in a different context) - "A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend."

I get the impression, though I'm not entirely clear on all this myself, that certain posters aren't understanding the core issue. There have been one or two facile responses so far along the lines of "Of course it's empirical/testable - we've tested it!"

This is, of course, entirely unhelpful. We can test the hypothesis "all bachelors are unmarried" too, perhaps by conducting interviews on the street. I wouldn't worry too much about falsification though. The point is certain hypotheses do not NEED to be empirically tested.

One thing that this thread makes evident is the radically different ways those people with a science background think compared to those of a more philosophical orientation. The science folks speak as if there is such a thing as a definitive falsification in science. A philosopher of science would just smile (even Popper waffles). I don't believe theories are ever disproven. I'd suggest it's more helpful to think of them as falling from grace.

By the way, I miss Leo and his razor-sharp insight. What happened to him? I haven't been around here for long, so I'm not quite sure what's been going on, but during my brief time he struck me as THE towering intellect on this site - a truly autonomous thinker. I'd hate to think he's gone for good.

[owleye]

Well, I suppose it's easy to think of towering figures when they remain well above the frame of reference of folks who have no stake in the matter, shooting their darts from such heights.

As one of the "towering figures" on our site who, unfortunately, has given it a rest for some time now, xcthulhu, has observed, the basic issue between scientists and philosophers is that they don't really understand each other. The rift is such that the theoretical scientist puts on her own philosopher's hat, possibly drawing on some current philosophy, not for the purpose of advancing it, but rather to formulate a theory that will be subject to independent observational corroboration, one that in turn, if it becomes accepted, will unify the discipline, not leave it as a collection of various theories. It's clear that the philosopher is motivated differently, about which I've offered a considered opinion a time or two.

[TheVat]

Maybe Allships is right and I was being too glib. Note that I did say "...case by case basis." This reflect my taste for concrete examples rather than all the paradigm talk. And...

I would like to offer an empirically testable hypothesis, now that the paradigm-shattering news of nipple-less sperm whale males has sent its shock waves through the scientific world....Aging male whales can still get "cetacean tits" and may benefit from some sort of halter or "man-bra." (or "bro" perhaps) There are so very many ways that my conjecture is falsifiable.

Cheers.

[Marshall]

Far from sounding too glib, this observation seems pleasantly brief and entirely appropriate, to me at least:

Popper's falsifiability seems key here, on a case by case basis. "Mammals have tits" isn't, so it's definitional. But F=ma, is. Indeed, it's not exactly right, as Marshall noted.

Since F=ma has been known to be false for over 100 years, there is no way it could be definitional in contemporary physics. So the thread declares itself to be a light-hearted one. What's life for, if not for a little enjoyment?

Cheers yourself, and all you other towering figures :^D

[owleye]

Far from sounding too glib, this observation seems pleasantly brief and entirely appropriate, to me at least:

Popper's falsifiability seems key here, on a case by case basis. "Mammals have tits" isn't, so it's definitional. But F=ma, is. Indeed, it's not exactly right, as Marshall noted.

Since F=ma has been known to be false for over 100 years, there is no way it could be definitional in contemporary physics. So the thread declares itself to be a light-hearted one. What's life for, if not for a little enjoyment?

Cheers yourself, and all you other towering figures :^D

The question is why wasn't it shown to be false with the advent of Maxwell's equations. Indeed, the peculiarities of the orbit of Mercury would seem to have caused physicists to reject Newton under this principle, but it didn't, as far as I can tell. What the philosopher is trying to clarify is the way in which the scientific method is actually accomplished. It's an effort to clarify sociological aspects of science. I don't think the scientist is all that concerned about what the philosopher is trying to do, since, as far as I can tell, the utility of describing its method is principally pedagogical. Scientists have some sort of intuition about their method that infects the community, possibly even as B.F. Skinner once observed: peer review rewards those who conform and punishes those for misbehaving. And, in my view, the objectivity which this accomplishes is one, if not the most important, of the reasons why it's successful.

As far as I can see, scientists hold on to an accepted theory until a better one comes along. And it only makes sense that this is what happens. I should add, however, that this 'holding on' doesn't constrain the theorist, or, for that matter, the experimentalist. There's always a leading edge. And the sophistication that I'm observing in the science community has now subsumed this approach to the point that they recognize the deficiencies right from the outset, and are, with greater emphasis, on working toward some end, or as Einstein once saw his duty, toward developing a theory of everything. As Lincoln has often told us, issues remain as long as there are infinities to deal with. And, of course, Einstein's own theory has to deal with it. The quantum theorist, I think, should be thinking of what that complex number in its equations are telling her.

One question in my mind is whether the theorist is actually taking seriously the ontological aspects of their discipline, or whether its instrumental value is the more important. From where I sit, I'm thinking it's the latter.

[Marshall]

...
One question in my mind is whether the theorist is actually taking seriously the ontological aspects of their discipline, or whether its instrumental value is the more important. From where I sit, I'm thinking it's the latter.

A bunch of good reflections here, Owl. I'll just respond to the last musing. I suspect that by and large your view is right. The instrumental value (getting the simplest best-fit model given the current observations) is probably the prime consideration.
There's also the motif of elegance and the motif of unifying different theories.

But there are exceptional figures who are are driven by ONTOLOGICAL considerations to go off in directions of new theory where it is a real struggle to get instrumental value. Carlo Rovelli and the principle of "background independence" is a case in point.

QFT (quantum field theory) has been enormously successful and important. Aka as high energy particle theory, it has overshadowed all other branches of theory for a large part of the latter half of the 20th. It is the basis of the Standard Model of matter, and it has been the reason we fund all these immense collider machines. But it is built on a fixed flat spacetime geometry. It DEPENDS on a PRIOR CHOICE OF BACKGROUND GEOMETRY.

QFT was so beamingly successful for so many decades that almost nobody raised an eyebrow. The space we experience is almost flat. The flat space of 1905 Special Rel, that QFT is built on, is ALMOST right for most of what we experience. It ignores gravity, but gravity is weak compared with electromagnetism etc.

But 1915 GR teaches us a lesson about the basic fabric of existence---that it has no prior geometry. The geometry takes shape along with the matter, as a solution to the GR equation, in a kind of interplay of geometry and matter. To accord with nature (if we take the lesson of GR seriously) any theory must be BACKGROUND INDEPENDENT. No prior choice of geometry.

I can't finish this thought, have to help wife with something. But you get the idea. If you let ontological considerations guide you, you may find yourself wandering in a wilderness where instrumental value is scarce. But it may pay off in the end.

I'm back, for the moment. So there's a risk if one thinks in terms of stereotypes like "the theorist". Some theorists take ontological concerns very seriously and go in search of ways to formulate theory in a truly more realistic way (even at the temporary cost of instrumental value). Others stay in the groove that is currently paying off.

In the successful QFT everything was fields defined on a fixed geometry chosen in advance. Everything was fields, that is, except for the geometry.
But GR teaches us that geometry is itself a field. And IT defines the rates and directions of causality according to which other fields evolve.
So Rovelli bit the bullet and admitted that, to be closer to reality, the fields of QFT must be defined on another field, the geometry. there's nothing else for fields to be defined on besides another field. But how to do that, fields are traditionally defined on some kind of platform. How can you define fields on a field? It must have a new type of description to make that possible.

it's an ontological thing and a hard thing to confront. Would have been hard back in the early 1990s when everybody was having such a good time with string theory. How do you get co-authors and grad students to join you, if you are heading out into what appears to be a desert?

[Marshall]

The story of the whale:
You are sailing far offshore when you sight what appears to be an island populated by interesting animals: you see these lively shapes moving around on the island: baboons, porcupines, ostriches, armadillos,… Then as you sail closer you discover that the animals are actually not on an island but are all on the back of ANOTHER ANIMAL, a large whale.
see page 7 of
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf

[AllShips]

I just stumbled across the following passage by Carl Hempel. I sense viscerally, through the ambient cranial fog, that he is alluding precisely to my initial question and can only sigh and wish he were here so that I might pick his brains...

Newton isn't mentioned, but it seems that F=ma is what Hempel would consider to be a correspondence rule. Is this correct?



"Next, some brief remarks on the concept of correspondence rules as constituents of a scientific theory. The customary designation of the sentences in question as "rules", or as coordinative or operational "definitions" strongly conveys the suggestion that they constitute truths guaranteed by terminological legislation or convention. But this idea is untenable for several reasons, among them the following.

A theory will often provide us with several general principles that link, say, a theoretical quantity to different kinds of experimental finding; each of these might thus be said to represent a rule of correspondence for the theoretical term in question. But the theory providing these principles implies, briefly, that if one of the alternative experimental methods yields a certain value for the theoretical quantity, then the other methods will yield the same value. But it cannot be a matter of terminological convention whether matters in fact turn out that way.

And even if a sentence is initially introduced as true by stipulation, this is only an ephemeral trait, carrying no guarantee of immunity to revision in response to new empirical findings and further theoretical developments: "conventionality is a passing trait, significant at the moving front of science, but useless in classifying the sentences behind the lines." "

[TheVat]

"...is what Hempel would consider to be a correspondence rule. Is this correct?"

I think he nailed it, in terms of the relationship between theory and experiment. Today, as the news informs us, there is a correspondence between the theoretical gravitational waves of GR and experimental results from a polar observatory. These waves certainly weren't guaranteed by "terminological legislation." That's a great quote. Thanks.

[AllShips]

Hi all. Long time no see!

I just wanted to mention that anyone interested in the initial question I posed in this thread will find THE definitive treatment of the subject in Ernest Nagel's 1979 "The Structure of Science"in the section concerning mechanical explanations.

Fascinating stuff and marvelously enlightening. The entire book is a veritable treasure trove; a masterpiece.

Are Newton's three axioms of motion simply definitions devoid of any empirical content? Are they a priori truths? Are they inductive generalizations derived from observation? Are they falsifiable or not?

Spend a few pennies and find out. Enjoy!

[Faradave]

Interesting thread AllShips! Glad to see you're still around. Sorry to be so late to the party but that's just as well since I'm no philosopher.

I notice in the OP that you, intuitively migrate from "Laws of Motion" to "Newton has not derived new insight into the nature of force, but is instead simply redefining force for us." I was sad to see this distinction go undeveloped in subsequent posts.

It seems clear from the later inclusion of electromagnetism that Newton's "Laws of Motion" are more correctly deemed "Laws of Force". Changes in particle motion are merely a consequence of force. Newton may be forgiven, as Physics was essentially Mechanics in his day and he had his hands full in shifting the paradigm from the Aristotelian model (it is natural for an object to decelerate, i.e. come to rest) to his own (in isolation from forces, an object in motion is unaccelerated).

I am further inclined to forgive Newton the unnecessary restriction (to motion) in view of his greater accomplishment. Greater even than the specifics of the laws was his unification of celestial and terrestrial mechanics, advancing the notion that the laws of physics apply everywhere (and everywhen). The pursuit of unification may be seen as the pursuit of fundamentals and has been a cornerstone of science ever since. It might be reasoned for example, that if a law is true throughout spacetime, that it relates directly to the underlying architecture of that continuum. Einstein is justly famous for capitalizing on this for gravitation but I think it goes far beyond that, yielding every "universal" law and "constant".

Speaking of gravitation, upon which Newton was focused, did we forget to mention his other expression of force, F = Gm₁m₂/r²? It wasn't just F = ma!

I believe that with F = ma, Newton gave us not just a force law but the grand unified force law. Under this, the expression of force may differ somewhat, e.g. for electromagnetism F = k_eq₁q₂/r². From the obvious similarities we should assume that electromagnetism and gravitation are very closely related. Presuming a different equation describing the strong nuclear force, we must yet explain its exceedingly short range. And we must call into question whether the weak force should be properly considered a force at all. The power that F = ma gives us is to say that if it doesn't accelerate a particle, it's not a force.

I'm suggesting that Newton inadvertently handed us the solution which Einstein died in vain trying to find. I believe Einstein was mistaken in attempting to formulate a unified field when he would have been better off seeking a unified force. F = ma makes no distinction between forces because, a force is a force of course of course. It's telling us, there is only one kind!

[AllShips]

Thanks Faradave. All very enlightening.

Well, I'm no scientist, and you seem very knowledgeable, so would you mind answering a quick, and I suspect not-as-simple-as-it-appears question?

We're commonly told there are four fundamental forces of nature. We're also commonly told (unless I'm misunderstanding) that under Einsteinian physics, gravity is not a force at all, but rather, simply the curvature of spacetime.

Well, how are these two apparently inconsistent claims reconciled? Is gravity a force or not? Are there three or four fundamental forces?

My suspicion is that the confusion here (well, MY confusion anyway) may arise from scientists' reluctance to concede that a respected forebear's theory is simply WRONG, perhaps because it was such a stunning intellectual achievement, and because it still yields accurate predictions at the practical level. (The theory "all birds fly" is clearly false, but gets a lot of stuff RIGHT nevertheless.)

A little clarification would be much appreciated. Thanks!

Edit : I should add that all I've said above refers to current science as standardly construed (if there is such a thing). How would "The Average Scientist" answer? Faradave's own views on the matter are expressed above, i.e. there's only ONE fundamental force (unless I've misunderstood)

[Faradave]

You seem pretty well grounded in science and philosophy to me. But it's not my intention to lead the innocent astray, if that is the case. I tend to unconventional interpretations and personal theories, so what I say should be taken as food for thought.

We're commonly told there are four fundamental forces of nature. We're also commonly told ... that gravity is not a force... rather, simply the curvature of spacetime...Is gravity a force or not?

I think you are best off considering gravity as a force. I certainly do. What distinguishes force expressed as gravitation from expression as electromagnetism(EM) is the directness of interaction.

You are doubtless aware of Newton's third law (N3), which I interpret (watch out) as, Forces are always observed in pairs. Well, two particles interacting electrically are thought to do so by each acting upon the other, a fairly direct mechanism. By contrast, two particles interacting gravitationally are considered to do so by the effect each has on the continuum separating them, a less direct mechanism.

So you will find electric interaction modeled by particles emitting so called "force carriers" (virtual photons) at each other. And while the standard model also predicts a force carrier for gravity (the graviton), it has so far, not been forthcoming.

Now to me, there is no reason the same force can't do both. Generally speaking, what a force, as an object, does to space is one thing (gravitation) and what it does to a particle is another (EM). The other two "forces" can be similarly imagined but that would be asking a bit much in this discussion. It can be said that this model needs no force carriers, since a force may be seen as an object in itself.

I think it would be fair to say that if pressed, Einstein would admit that how a mass causes space to curve may be construed as a force. He would have preferred the term "field" as would all those espousing quantum field theory today. Nevertheless, if you press them as to: A field of what?, the answer will boil down to a field of potential force. That is, a set of locations where a test object would experience a force (and in doing so become half of a Newtonian pair).

In my view, a reasonable corollary to N3 would be, Unpaired forces are unobserved. This has the decency to allow for Newton's own impression that there is conservation of force (conventionally supplanted by conservation of energy). I find this much more appealing than expecting forces to simply disappear every time they are not paired. We can't observe what forces do when they are off duty but we can easily surmise that it is generating fields.

[AllShips]

Thanks for taking the time to explain that, Faradave.

[Threepwood]

Perhaps we can regard F=ma as a triumph of intuition. I think of it as a deep 'guess' about the way in which the universe functions, i.e. there are things in the universe which influence one another according to mathematical rules, and that we will observe patterns/distributions in space of the quantity which we measure as mass x acceleration, and that these patterns will be a function of the types of objects and their spatial relations. The empirical evidence confirms that this is the correct way to think about physics, in general.

[Threepwood]

Another deep idea implicit in F=ma is that the more 'isolated' an object is, the more it tends towards a state of constant velocity (not speed), and the less massive the object, the more easily it tends towards this isolated state of constant velocity. Again, empirical observation validates this idea, in general.

[Faradave]

the less massive the object, the more easily it tends towards this isolated state of constant velocity.

Welcome, Threepwood

You've obviously given this some thought but have you considered Galileo's view? All objects (m₁) exhibit equal gravitational acceleration (by m₂).

F = Gm₁m₂/d² and since F/m₁ = Gm₂/d² = a is the same, regardless of how small m₁.



As a welcome-aboard gift, I offer: ΣF = γm₀√(a²),
which combines Newton's laws, updated relativistically.
Zero acceleration corresponds to zero net force, N1.
m₀ is invariant mass, γm₀ is relativistic (or total) mass, γ = (1-v²/c²)^-½ (the Lorentz factor)
The relation of ΣF to acceleration is N2.
√ has +/- roots which corresponds to the observed force pair, N3.

[Threepwood]

Oh yeah, thanks Faradave! I did understand that at one point but got muddled.. :-) I think I meant that by taking an isolated system and then just reducing the masses of all the objects in the system, we make the objects tend towards constant velocity relative to one another. Maybe.

[Threepwood]

Anyway, I don't think I'm adding anything to what has already been said here (after looking properly at the multitude of great posts on this thread!). I think I'll read the Nagel book recommended by AllShips. Cheers!