There are no examples of Newton's first law applying to objects with zero mass! I used the only one available. Of course, it does not work with photons.D H said:Not a good example, Andrew. You are talking about a regime where Newton's laws are known to fail. Newtonian mechanics break down at relativistic velocities. In Newtonian mechanics, the only speed that all observers agree is the same is an infinite one. We live in a non-Newtonian universe, where that maximum attainable speed is finite.
Again, that is not correct. Light does not change motion when moving through a vacuum, that's Newton's first law. But it doesn't make any difference when the law applies, it's just a law, and it says what it says. Newton had no idea if it would apply to massless particles or not. Also, Newton's second law is easily applied to light, in the manner I mentioned above-- and it only gets the answer wrong by a factor of 2 because Newton's second law isn't right (in F=ma form rather than F = dp/dt form) when you are not in the rest frame of the object-- something he also didn't know and something that is not included in the laws.Andrew Mason said:There are no examples of Newton's first law applying to objects with zero mass!
Your logic is that, since the law allows for a fiction to be treated, it must be false when applied to realities?Ken G said:Therefore, if Newton's first law applies throughout that sequence, as is the claim in that law, then it would also apply to a zero-inertia object. Ergo, the first law does not refer to inertia in any way. In other words, a law that does not care what the inertia is, does not refer to inertia.
No, I said what is true: laws are just assertions, they are never responsible for when they are true. It can be part of a law to make such an assertion, in which case that is explicitly part of the law. Do you see any such thing in Newton's first law? Then it is irrelevant when the law is true, if you are simply trying to understand what the law asserts. Besides, as I said, Newton's first law works fine for particles with arbitrarily small inertia, including zero inertia, so in this particular case there is no fiction required. Of course, the law becomes questionable in quantum field applications-- again that is completely irrelevant to the issue of what the law asserts.zoobyshoe said:Your logic is that, since the law allows for a fiction to be treated, it must be false when applied to realities?
Ken G said:No, I said what is true: laws are just assertions, they are never responsible for when they are true. It can be part of a law to make such an assertion, in which case that is explicitly part of the law. Do you see any such thing in Newton's first law? Then it is irrelevant when the law is true, if you are simply trying to understand what the law asserts. Besides, as I said, Newton's first law works fine for particles with arbitrarily small inertia, including zero inertia, so in this particular case there is no fiction required. Of course, the law becomes questionable in quantum field applications-- again that is completely irrelevant to the issue of what the law asserts.
The issue in the OP is, does Newton's first law reference the concept of inertia, or indeed even require such a concept, or does that only show up in the second law? The OPer was making the case, and I agree, that the first law does not reference inertia, which means there is a "common misconception" that inertia is the reason that objects that are in motion will stay in motion if no forces act on them. Instead, when an object has no force on it, then its inertia is irrelevant, since we can simply refer to the first law (even though the second law yields the same conclusion as the first-- that just means the laws are consistent). Inertia is the concept of how much objects accelerate when forces are exerted on them. The first law is merely the assertion of what happens when no forces are exerted, and that is true independently of the inertia or even if there is any inertia. To support that argument, I cite the first law.zoobyshoe said:I have no idea what you're saying or where you're going with this.
Yes, I use it in that same sense-- note especially the part about "in the interest of..."The "law or axiom" is asserted as truth in the interest of getting traction on a problem. It provides a basis for a train of logic in analyzing something.
I see the problem, you are reading something unintended into the word "just." I do not mean that any law is somehow equal, since they are all "just" assertions, I mean that a law is just an assertion. Which is just exactly what a law is-- the point is, if the law doesn't refer to inertia, then the assertion the law is making doesn't either, and it makes not the least bit of difference if the law doesn't apply in some situation (such as in quantum mechanics, or when there is no inertia-- even though this law does apply when there is no inertia, as long as we generalize "force" to "any influence or change in the environment"). I used "just" to stress that the law is what it is, so what it asserts is independent of when it holds, and so in analyzing what a law says, there is no need to wonder about when the law is actually true, or if the law is ever actually true. Note this is consistent with the definition you just gave.The Laws or Axioms are not, therefore, "just" assertions.
Ken G said:The issue in the OP is, does Newton's first law reference the concept of inertia, or indeed even require such a concept, or does that only show up in the second law? The OPer was making the case, and I agree, that the first law does not reference inertia, which means there is a "common misconception" that inertia is the reason that objects that are in motion will stay in motion if no forces act on them. Instead, when an object has no force on it, then its inertia is irrelevant, since we can simply refer to the first law (even though the second law yields the same conclusion as the first-- that just means the laws are consistent). Inertia is the concept of how much objects accelerate when forces are exerted on them. The first law is merely the assertion of what happens when no forces are exerted, and that is true independently of the inertia or even if there is any inertia. To support that argument, I cite the first law.
Doesn't seem to be the case. Newton's definition simply asserts it's dual properties of resistance and impulse without quantifying them. (If inertia is "about" something I'd say it's about mass, not acceleration.)Ken G said:Inertia is the concept of how much objects accelerate when forces are exerted on them.
Newton's Inertia is quantified by him to the extent he observes, "This force is ever proportional to the body whose force it is". What does that mean? Earlier, in the definitions, he makes it clear the word "body" will be used synonymously with "mass". In plain modern English, therefore, he's saying "inertia is directly proportional to mass", so that's no modern concept, but he says that without providing any units, hence, no way to plug it into an equation, which is what I meant when I said he didn't quantify it. (It's amazing to me how far he gets without ever offering any units of measure.)Ken G said:Newton's definition of inertia is not completely clear, because much lies in the words "power of resisting." That might be taken to refer to a quantity, as it does in the modern meaning of the term. Now inertia is taken as a quantitative attribute, proportional to mass for an object in its rest frame. That is also the same thing as (the inverse of) its acceleration when subjected to unit force. So I would say Newton's first law does not reference the modern quantifiable concept of inertia. When zero force is exerted, no object accelerates, regardless of its inertia (in the modern sense), and that is the first law.
Acceleration is the rate of change of velocity. What you are talking about is not what acceleration is, but rather a dynamical principle about acceleration.zoobyshoe said:I have to say I think acceleration is the concept of how much objects accelerate when forces are exerted on them.
I agree that the dynamical principle here is best thought of as a=F/m. But that's not the statement of what a is, it's the statement of how to calculate a. In other words, if I say "I am a physicist", that is not actually a statement of who I am, because "I" am a lot more than that, it is just attributing a property to "me." Similaly, a=F/m is attributing a property to a, that it will turn out to equal F/m, but the statement would mean nothing if we didn't already know what acceleration is. That's clear when you try to teach it to students who don't already know what acceleration is!"How much acceleration, given this mass and this force?," is asking you to solve for acceleration: a =F/m.
That all sounds like a rule about when forces are absent, not a rule about when forces are present.It does not only mention objects on which no force is acting ("Every body perseveres in its state of rest, or of uniform motion in a right line,...") but also those resisting acceleration ("...unless it is compelled to change that state by forces impressed thereon."): "Projectiles persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity."
I certainly don't think Newton was confused, I think his first two laws had very specific objectives. The first law was to say what happens in the absence of forces, to dispell the Aristotelian notion that objects would come to rest in the absence of forces. The second law was to say what happens in the presence of forces, to be able to explain what it is that forces actually do (they create acceleration, subject to inertia). So the second law is the only one that refers to inertia, in the quantifiable way we use the word now, even though the first law is called the "principle of inertia." It's two very different meanings of the word-- if the "principle of inertia" is there to dispell the idea that objects come to rest in the absence of forces, then it is not actually necessary to know anything about the quantity we call inertia today.Earlier, in the first "scholium" Newton makes the point that he must define and explain certain things to dispel "vulgar" misconceptions. As 256bits pointed out earlier in this thread, one of the things he had to quash was the then common notion that it takes a continuous force to keep an object in motion (from Aristotle, I believe). That would be the reason the law might seem to emphasize the persistence of motion and rest in the absence of force as what's important, but it's abundantly clear from the definition he understands inertia to be a reactive force, and emphatically defines it as such. Newton wasn't confused.
I'll be happy to stipulate that the words "...is the concept of how much objects accelerate when forces are exerted on them," is a statement of a dynamical principle about acceleration, because it's still not a statement about inertia. (I wasn't trying to make any definitive statement about acceleration, of course, just pointing out your definition of inertia, which is where all those words come from, seemed, actually, to be about acceleration, if it was about anything.)Ken G said:Acceleration is the rate of change of velocity. What you are talking about is not what acceleration is, but rather a dynamical principle about acceleration.
This is an interesting read.I agree that the dynamical principle here is best thought of as a=F/m. But that's not the statement of what a is, it's the statement of how to calculate a. In other words, if I say "I am a physicist", that is not actually a statement of who I am, because "I" am a lot more than that, it is just attributing a property to "me." Similaly, a=F/m is attributing a property to a, that it will turn out to equal F/m, but the statement would mean nothing if we didn't already know what acceleration is. That's clear when you try to teach it to students who don't already know what acceleration is!
OK: Since last posting, I went back and reread his definition of force, and found something interesting I missed the first time:That all sounds like a rule about when forces are absent, not a rule about when forces are present.
He had a specific objective, to be sure, but it didn't take the next step you suppose it did. The second law Newton actually wrote was a statement about momentum, not about acceleration or inertia.I certainly don't think Newton was confused, I think his first two laws had very specific objectives. The first law was to say what happens in the absence of forces, to dispell the Aristotelian notion that objects would come to rest in the absence of forces. The second law was to say what happens in the presence of forces, to be able to explain what it is that forces actually do (they create acceleration, subject to inertia). So the second law is the only one that refers to inertia, in the quantifiable way we use the word now, even though the first law is called the "principle of inertia." It's two very different meanings of the word-- if the "principle of inertia" is there to dispell the idea that objects come to rest in the absence of forces, then it is not actually necessary to know anything about the quantity we call inertia today.
Well I'm afraid I cannot follow your reasoning there, because that certainly sounds like a statement about the modern concept of inertia to me. In particular, the inverse of inertia is the amount objects accelerate per unit net force placed upon them. This is what "inertia" means today. In science, we don't look for truth by quoting century-old manuscripts, we recognize that concepts evolve.zoobyshoe said:I'll be happy to stipulate that the words "...is the concept of how much objects accelerate when forces are exerted on them," is a statement of a dynamical principle about acceleration, because it's still not a statement about inertia.
Even that isn't true, it should be called "The principle of what causes acceleration", or "the principle of when acceleration doesn't happen." Indeed, this entire thread is about the very true fact that the term "inertia" has come to have two meanings:That last being the case, Law I can rightly be called "The Principle of Inertia."
Link me to a site that defines inertia as you do. I have about 10 physics texts, old and new, and I googled and read 3 different sites, and they all define it more or less as Newton did.Ken G said:Well I'm afraid I cannot follow your reasoning there, because that certainly sounds like a statement about the modern concept of inertia to me. In particular, the inverse of inertia is the amount objects accelerate per unit net force placed upon them. This is what "inertia" means today. In science, we don't look for truth by quoting century-old manuscripts, we recognize that concepts evolve.Even that isn't true, it should be called "The principle of what causes acceleration", or "the principle of when acceleration doesn't happen." Indeed, this entire thread is about the very true fact that the term "inertia" has come to have two meanings:
1) a vague general meaning that objects "resist" changes in motion, whatever that means, and
2) a crystal clear meaning given by what I said above. The fact of the matter is, Newton's first law in no way refers to this second precise meaning, and it really doesn't refer to the first vague meaning either, because an object receiving no force at all does not have anything to "resist". The term "resist" has no meaning in the context of Newton's first law, which is strictly a law about what happens in the absence of anything to resist. Really what the first law is, is a description of what it is that causes changes in motion, and nothing about resisting said changes. It is the second law that is all about resisting changes, once the first law has told us what causes changes in the first place.
zoobyshoe said:Link me to a site that defines inertia as you do. I have about 10 physics texts, old and new, and I googled and read 3 different sites, and they all define it more or less as Newton did.
At first look, it might seem like Newton's first law is talking about that, but as I said, it's not. The first law, instead, tells us when we have nothing to resist-- when there is no force. So the first law is a description of what things do when they have no reason to do anything else-- and that is, they keep doing what they were doing. Note there is nothing to "resist" if all that is being stated is what happens when there is no reason for anything else to happen, the "default mode" has nothing to do with "resistance". The second law, on the other hand, has everything to do with resistance. So any time "resistance" is mentioned in the same breath as inertia, the second law is being referenced, not the first.
Not at all! A better way to look at it is that the second law is consistent with the first law in the case of a null net force.Studiot said:I find this a perverse refutation of the proposal that 'inertia is to do with the first law' since the first law is a special case of the second law!
What I requested was a link to a site that defines it as you did :"Inertia is the concept of how much objects accelerate when forces are exerted on them". Instead you have linked to two sites which are saying, in effect, "Inertia is the concept of how much objects DON'T accelerate when forces are exerted on them, how much they RESIST acceleration." The concept of inertia as a resistance is the one your definition does not have.Ken G said:Easy. Google "inertia." In the first hit: (http://en.wikipedia.org/wiki/Inertia)
"Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass."
Second hit (http://www.physicsclassroom.com/class/newtlaws/u2l1b.cfm):
"All objects resist changes in their state of motion. All objects have this tendency - they have inertia. But do some objects have more of a tendency to resist changes than others? Absolutely yes! The tendency of an object to resist changes in its state of motion varies with mass. Mass is that quantity that is solely dependent upon the inertia of an object. The more inertia that an object has, the more mass that it has. A more massive object has a greater tendency to resist changes in its state of motion."
So, both of these hits have it perfectly correct-- inertia is the tendency to resist changes in motion, quantified as the inverse of the acceleration you get per unit force applied, and it depends only on mass (and is generally taken to equal mass). At first look, it might seem like Newton's first law is talking about that, but as I said, it's not.
The first law, instead, tells us when we have nothing to resist-- when there is no force. So the first law is a description of what things do when they have no reason to do anything else-- and that is, they keep doing what they were doing. Note there is nothing to "resist" if all that is being stated is what happens when there is no reason for anything else to happen, the "default mode" has nothing to do with "resistance". The second law, on the other hand, has everything to do with resistance. So any time "resistance" is mentioned in the same breath as inertia, the second law is being referenced, not the first.
Exactly. And the first law takes on even larger significance when modified by GR to say that in the absence of forces, objects follow the paths determined by gravity, generalizing the concept of what it means to "keep moving like it was." As D H said, to know how a force changes the motion (2nd law), you first have to know what the motion would have been without the force (1st law). So the first law ended up being quite a bit more profound than the second law! The irony is, the "inertial frames" do not depend on the "inertia" of the objects, and indeed even light is ruled by the limiting inertial frames set by gravity.D H said:The modern view (Ken G: "In science, we don't look for truth by quoting century-old manuscripts, we recognize that concepts evolve.") is that the first law establishes the framework in which the other two laws are valid. This framework is that of an inertial frame of reference.
There's no important distinction in those phrasings, my comments were not intended to carry the way inertia depends on the acceleration achieved, what was relevant to the discussion about the first law was simply that inertia is the concept that relates to how much acceleration you get. I assume everyone here knows F=ma, so the sense of the dependence was not the issue.zoobyshoe said:What I requested was a link to a site that defines it as you did :"Inertia is the concept of how much objects accelerate when forces are exerted on them". Instead you have linked to two sites which are saying, in effect, "Inertia is the concept of how much objects DON'T accelerate when forces are exerted on them, how much they RESIST acceleration."
I am fine with the concept being about resistance to change, that's what I've said all along. My point, and the point of the whole thread, is that the first law does not reference the inertia of the body, because the first law has nothing to do with "resistance." So if you feel resistance is crucial, you are making my point for me, thank you.The concept of inertia as a resistance is the one your definition does not have.