That's a rationalization based on observations and experiments. It's not an explanation.

I completely disagree. The most fundamental explanations in physics are conservation laws and their associated symmetries. Once you have reduced a concept to the associated conservation law or symmetry then you have arrived at the deepest explanation physics has

Those are not fundamental: experiments and observations are fundamental. Physics isn't mathematics.

They are the fundamental explanations. Experiments and observations do not explain on their own

What explains momentum conservation? Turtles all the way down...

@JohnDoty The question asked for an explanation, without requiring it to be either fundamental or of a specific type; one has been provided. We can debate which types could be fundamental, but it's beyond the question's requested scope.

@J.G. But the answer didn't give an explanation: it gave a rationalization. There is no reason to expect momentum conservation to be true without evidence.

@JohnDoty Maybe we disagree on what it means for one truth to explain another. Based on my construal of it, I'm giving the question & answer an upvote each.

@JohnDoty nothing explains momentum conservation with its associated symmetry (spatial homogeneity). That is why it is a fundamental explanation. The turtles end with the conservation law and its associated symmetry

@Dale So, in physics we get to choose laws and declare them true without explanation? That's mathematics, not physics.

@JohnDoty I never remotely said that. That is a strawman. In fact, I completely agree that the conservation/symmetry is discovered through experiment. But again the explanation is the rule that was generalized from experiments, not the observations themselves

@Dale OK, what do you say to the student who asks "why is momentum conserved"? Unless you give reasons, momentum conservation is a mere mathematical postulate, not an explanation.

Again, I disagree completely. You are making a false dichotomy here. Things are not categorized as “mathematical postulates” or things for which “you give reasons”. Between your strawman fallacy and your false dichotomy fallacy you may want to read a bit on fallacies

I asked for an explanation in the sense that it can be explained by some principle below that is true. Newton in his Principia Mathematica puts the action-reaction idea as a law or axiom (the chapter says "Axioms or Laws of Motion"). So, I assume that by observation he deduced the "Law" and in every experiment with bodies the "Law" is true. Hence, we can conclude that is a property of nature. But, how to explain this means that if there exists another "laws" or principles that explain it.

@Dale regarding your statement "where Newton’s 3rd law is violated in some sense", can you elaborate? It appears to contradict the following statements on the Hyperphysics web site :"Newton's third law is one of the fundamental symmetry principles of the universe...we have no examples of it being violated in nature..". Thanks

@Dale You didn't answer my question: what do you say to the student who asks "why is momentum conserved?".

@BobD Force is a bit of a fraught concept in 21st century theoretical physics. However, force is part of everyday experience, and a force gauge is one of the simplest fundamental physics instruments. This is an illustration of how unphysical theory has become.

@JohnDoty What do you mean by saying that experiments and observations are fundamental? What I would mean by the word fundamental is "a central or primary rule or principle on which something is based." (from Google's English dictionary). An experiment is not a rule or a principle. I would say an experiment or an observation gives facts that any theory must agree with. But you cannot logically derive physical statements from an experimental result alone. Theory is needed to explain and interpret experimental results; without it we just have a collection of unconnected facts.

@BobD yes, an example would be the EM force between two charges moving at different velocities. If you work out the forces on the charges they are not equal and opposite. Momentum is conserved because of the momentum in the EM field, but the forces on the charges are not equal and opposite.

@Dale Can you provide a reference for your example? I'd like to see it in full context.

I am also of the opinion the observed symmetries are not explanations.

I don't think this explanation is sufficient because you have not explained what is momentum and why it is conserved. Not the mathematical definition of momentum, but momentum as a concept.

@BobD sure, see for example physics.stackexchange.com/questions/114466/…

@Andrew The facts stand by themselves, theory or no theory. That's the nature of a foundation. The theory does not stand by itself: unless supported by the facts, it is mere mathematics.

@JohnAlexiou Momentum is a concept that connects various empirical facts together into a coherent theory.

@Dale Thanks for the link. But Pisanty makes the statement "seemingly violate Newton's 3rd law" instead of outright stating it actually violates the 3rd law. This seems to leave it open that if , per his key point, the electromagnetic field is considered as a dynamical entity of its own, on par with material particles, that perhaps not only are the conservation laws satisfied, but also the 3rd law.

@BobD sure, that is what I meant by “in some sense”. You can patch Newton’s 3rd by considering fields to be objects on which forces can act. That is not an unreasonable position. But it is also reasonable to be more strict and describe forces as interactions between classical objects. It is that strict sense in which N3 is violated.

@JohnDoty the facts do stand by themselves, but they are not generalized so they cannot serve as an explanation by themselves. A list of facts, by itself, cannot tell you anything about any scenario not specifically covered in the list. They have no explanatory power without generalization

@Dale it’s just that in my experience the Hyperphysics website is very reliable. So they are probably looking at N3 in the broader view. Anyway thanks for the feedback

@BobD no worries, I also find them to be reliable. I have heard some sources take the Hyperphysics view and others take the “N3 is violated” view, so I think both are reasonable and I always try to leave the wiggle room either way. The Hyperphysics view is especially reasonable when you think that in QM everything that we call “matter” is fields. So you cannot really avoid talking about fields as something that forces act on

@Dale 👍 I think we are on the same page

@BobD The strongest "violation" of conservation of momentum is the case when two black holes of opposite spin merge. en.wikipedia.org/wiki/… says "the center of gravity can add over 1000 km/s of kick velocity. The greatest kick velocities (approaching 5000 km/s) occur for equal-mass and equal-spin-magnitude black-hole binaries, when the spins directions are optimally oriented to be counter-aligned, parallel to the orbital plane or nearly aligned with the orbital angular momentum." Of course, the momentum is carried away as gravitational waves.

@cmaster-reinstatemonica I must confess I have no idea what you are talking about. It's my limitations, not yours.

@Dale Generalization is valuable, but facts are fundamental. The results of Galileo's experiments with gravity remain solid, as foundations must, but Galileo had a generalization (acceleration), Newton had a different generalization (force and inertia), and Einstein had yet another (geometry). They all captured the data, but how can this shifting array of abstractions be fundamental? Perhaps Einstein's is the "best" (although it's very difficult to employ), but why should we have any confidence that it's the last word?

@JohnDoty I guess one issue I have with what you are saying is that modern physics feels more like an interlocked tower to me. The mass of the Higgs boson being about 125 GeV is an experimental fact. But, that experimental fact comes out of a complicated analysis of data that calculates an expected background assuming the Standard Model is correct. The fields and interactions and framework of Standard Model in turn is based on other experimental results, which were themselves rely on theoretical models to be interpreted correctly. (Eg, connecting the radius of a beam to the electron mass).

If we mean the word "fundamental" in a logical sense (what logical statements follow from other ones), I therefore think that assumptions and principles are logically fundamental to our current understanding. Of course those principles only reflect our current understanding and may change with more data. But the facts themselves cannot be understood on their own with no context for interpretation, and no statements can be derived from them, logically.

@JohnDoty but facts are not explanations. Often the facts themselves are said to be explained by some generalization

@BobD When two black holes merge, the resulting gravitational waves may carry away a tremendous amount of momentum. So much, that the resulting larger black hole is accelerated by hundreds of kilometers per second. Since there is no third object involved, the entire situation looks like two BHs spiraling in to each other until they touch, and the next moment, the resulting BH is speeding away from the scene. This is, of course, in stark violation of Newton's third law, for there is no other massive body on the scene that is accelerated in the opposite direction.

@JohnDoty regarding your question ‘what do you say to the student who asks "why is momentum conserved?"’ I tell them that we have no explanation for why that is true. We have lots of solid experimental evidence that it is true, but no explanation why our universe behaves that way. This is what makes the conservation/symmetry laws fundamental. There are no more explanation turtles, just evidence that makes us believe that last turtle

@Dale That last comment of yours is gold. Would be nice if you edited its content into your answer, somehow.

@cmaster-reinstatemonica thanks, I have added it with some modifications to fit better

@Dale So momentum conservation is unexplained dogma? Of course that's not true, as momentum conservation is an abstraction from the results of experiments and observations. Those are fundamental: without them there would be no reason to invent the momentum abstraction.

@Andrew But the theoretical interpretation can go astray. Consider the discovery of nebulium (en.wikipedia.org/wiki/Nebulium). There was nothing wrong with the observations, but the theory of the time couldn't accommodate our more modern interpretation. Theory changes, but observations remain.

@JohnDoty again, with the strawman fallacy. I recommend a bit of studying about logical fallacies

@Dale What's my straw man? If momentum conservation is based on evidence, then it is not sensible to consider it fundamental. Something based on something else isn't fundamental. Or, are you claiming that it isn't based on evidence?

@Dale Note that this issue has serious consequences. We teach physics as dogma detached from reality. You disagree? Then how, in Philip Sadler's infamous social experiment, were MIT graduates, required to pass freshman physics, incapable of solving a simple real-world physical puzzle?

@JohnDoty Of course. All knowledge in science is provisional. Theories can change and our understanding of what is a fundamental principle and what is an approximate or derived consequence can (and has!) changed. But if you take your train of thought to its logical endpoint, you can't trust that you really know what a reading of "10 volts" means on a voltmeter, because the definition of voltage depends on Maxwell's equations, and maybe some future theory will replace Maxwell's equations and the concept of voltage with something better. You have to assume something to make progress.

@Andrew But the reading of 10V remains a fact. You may reinterpret the reading in the context of shifting theory of what voltage means, but the reading remains. Any new theoretical framework must be able to accommodate old observations. "According to our new theory 10V read with electrostatic technology means an acclivity of 7.76 Greylocks."

@JohnDoty the straw man is saying that it is a dogma, which you have done repeatedly. I am not interested in your fallacious diatribes. Instead of misrepresenting others you should think about how a collection of facts, with no generalization, can be an explanation

@Dale Dogma: "a principle or set of principles laid down by an authority as incontrovertibly true."

@JohnDoty exactly. ”Dogma” is not at all an accurate description of my position. Hence your statements identifying it as such is a strawman fallacy

@Dale You said that we have "no explanation why our universe behaves that way". So, what is the justification for using the idea? Well, we do know, from experiment, that the universe does behave that way. But then, how can the abstract idea be considered "fundamental"? It's utterly and completely dependent on the experimental evidence: that's what's fundamental.

@JohnDoty yes the justification for the conservation law (and its associated symmetry) is experimental evidence. That is why we believe it to be a true explanation, as I already stated previously and which you chose to ignore in favor of your strawman. The evidence is not itself an explanation but it does justify the explanation.

Physics is an experimental science. Theories are only of value insofar as they accurately predict experimental outcomes. A theory is more than math, it also must have a mapping between the math and experimental results. That is my opinion. Anytime you state or imply that I denigrate or ignore experimental evidence then you are misrepresenting my opinion and the resulting argument is fallacious

@Dale So, what you're calling an explanation isn't fundamental, since it rests on the justification provided by the evidence.

@JohnDoty I have been as careful as I can to call it a “fundamental explanation”, and not just “fundamental”. I have even bolded explanation repeatedly. Yes. The fundamental explanation rests on the justification provided by the evidence. The evidence is a justification for the explanation, not an explanation in itself. As I already clearly and repeatedly stated.

@Dale But is it really an explanation? After all, Newton worked out his third law from the evidence without using it. By itself, it's inadequate as an explanation, since without the fundamental evidence it is mere dogma.

There are generally many paths from the evidence to conclusions about the physical world. Physics gets to be fun when they reach different conclusions, and the discrepancy may be resolved by collecting more evidence. But since there are many paths, it is not correct to call any one of them fundamental.

@JohnDoty Stop with your inane strawman statements. “Dogma” in no way describes my position. That you consistently revert to obviously fallacious rhetoric shows the exceptional weakness of your position.

@Dale I understand that you do not believe your position is dogmatic. I understand that your internal model of physics is not fundamentally dogmatic. But presenting "laws" as explanations is dogmatic, since the "laws" are questionable abstractions of the evidence.

In short, your repeated attempts to misrepresent my arguments say more about you than they say about me.

If you want to have a substantive discussion then please refrain from your habit of misrepresenting my opinion and arguments. In the absence of that restraint then our discussions will just be more of this, me making some argument, you attacking a strawman, and me objecting to your fallacious statements. It is boring, is it not?

Well, yes, it's boring to have you present abstractions as dogma and insist that it isn't. "The laws of physics are subject to empirical falsification." Indeed, but if you present a law as a fundamental explanation for a phenomenon, you are implying that the law drives the phenomena. But, in fact, laws "are subject to empirical falsification", so the phenomena drive the law.

I never presented an abstraction as a dogma, that is entirely your strawman, not mine. It is not a question of what "drives" what. The OP asked for an explanation. The data is not an explanation as I have already mentioned several times. So the fact that the "phenomena drive the law" in no way changes the fact that the fundamental explanation is the most basic law we can abstract from the data.

Perhaps your problem is that you don't understand English words like "fundamental". Fundamental comes from the same root as foundation. It is the lowest portion of a building and it supports the remainder of the building. Simply because something is a foundation, does not imply that there is nothing beneath it. Foundations are laid on the ground, not floating in space

Furthermore, a foundation is something that is human-created, which is built on top of something natural. So in that sense it is even more appropriate to describe the human-created law as the fundamental explanation, rather than the natural phenomena that justify the law

If you want to act like a grown-up and have a productive discussion that is fine. But at this point I am only going to engage with you on a substantive discussion. If you want to spout more fallacious strawman arguments then I am not even going to respond. You are free to have the last word if you want that to be yet another fallacy