Kaysville, UT homeowners show up in large numbers to oppose warming center

[Chap]

This statement doesn’t mention “inertia” for the same reason that Lincoln’s Gettysburg Address doesn’t mention “Gettysburg Address”.

The short name for this fact is “inertia”. That’s why Newton’s First Law, which states this fact, is called “the Law of Inertia”.

You can call it that if you like. In my detailed and non-elementary studies of mechanics I have never met anybody who called it that. And as I have repeatedly shown, one can say all one needs to say about the motion of bodies in Newtonian terms without mentioning inertia at all.

Are you mixing up Newton and Galileo, perhaps?

[Chap]

Try this for size:

Because of our experience of moving things about on the surface of the earth, we tend to assume that to move something from one place to another you need to push or pull it, and If you stop pulling or pushing, it stops.

However, experience out in space teaches us that if we have a moving body far away from friction with the ground, and with no drag from moving through the atmosphere, and away from a strong gravitational field like the one we have on earth, it will just keep on going in a straight line at constant speed for ever. (OK, it may hit something or it may get pulled into the gravitational field of a star or planet. But space is very big and very empty). If you want to change that situation so that the body speeds up, slows down or changes direction, that's when you have to exert a force on it for a while.

So if there was no atmosphere at the earth's surface, and if we switched off earth's gravitational field, then if you threw a ball upwards it would simply go up in a straight line at a steady speed indefinitely. The reason it doesn't is mainly because there is a downwards gravitational force acting on the ball, so that its upwards speed steadily decreases, then passes through zero and becomes an increasing downwards speed. (Of course atmospheric drag slows it down a bit too).

Nice clear explanation. Rigorously correct physics (no?). No maths. No mention of inertia.

So what's not to like?

Physics Guy - could you kindly tell me what is wrong with my explanation? You will of course be well aware that I have written it in terms of the Newtonian physics we are discussing.

[Chap]

Just for interest, I have done a search for the word "inertia" in Newton's principia, both in its Latin version and in Motte's English translation. Result:

1. Newton states his First Law without using the word 'inertia', nor does he mention that word in his statement of the other two laws. (I have quoted the Latin and English above). If you can find a text where Newton calls his first law the 'law of inertia', please let me know.

2. In his earlier 'Definitions' we find 'inertia' mentioned in his text relating to what he calls the 'vis insita' ('the innate force'), which is the force that a body will exert on another body when that body, by contact or otherwise, interacts with the body so as to change its state of motion:

https://www.gutenberg.org/files/28233/28233-pdf.pdf

Def. III.
Materiæ vis insita est potentia resistendi, qua corpus unumquodq;, quantum in
se est, perseverat in statu suo vel quiescendi vel movendi uniformiter in
directum. Hæc semper proportionalis est suo corpori, neq; differt quicquam ab inertia
Massæ, nisi in modo concipiendi. Per inertiam materiæ fit ut corpus omne de
statu suo vel quiescendi vel movendi difficulter deturbetur. Unde etiam vis in-
sita nomine significantissimo vis inertiæ dici possit. Exercet vero corpus hanc
vim solummodo in mutatione status sui per vim aliam in se impressam facta,
estq; exercitium ejus sub diverso respectu et Resistentia et Impetus: Resistentia
quatenus corpus ad conservandum statum suum reluctatur vi impressæ; Impetus
quatenus corpus idem, vi resistentis obstaculi difficulter cedendo, conatur sta-
tum ejus mutare. Vulgus Resistentiam quiescentibus et Impetum moventibus
tribuit; sed motus et quies, uti vulgo concipiuntur, respectu solo distinguun-
tur ab invicem, neq; semper vere quiescunt quæ vulgo tanquam quiescentia
spectantur.

https://dn790007.ca.archive.org/0/items ... wtrich.pdf

Motte's English:

DEFINITION III.
The vis insita, or innate force of matter, is a power of resisting, hy
which every body, as much as in it lies, endeavours to persevere in its
present state, whether it be of rest, or of moving uniformly forward
in a right line. This force is ever proportional to the body whose force it is ; and differs
nothing from the inactivity of the mass, but in our manner of conceiving
it. A body, from the inactivity of matter, is not without difficulty put out
of its state of rest or motion. Upon which account, this vis insita, may,
by a most significant name, be called vis inertia, or force of inactivity.
But a body exerts this force only, when another force, impressed upon it,
endeavours to change its condition ; and the exercise of this force may bo
considered both as resistance and impulse ; it is resistance, in so far as the
body, for maintaining its present state, withstands the force impressed; it
is impulse, in so far as the body, by not easily giving way to the impressed
force of another, endeavours to change the state of that other. Resistance
is usually ascribed to bodies at rest, and impulse to those in motion;
but motion and rest, as commonly conceived, are only relatively distin
guished ; nor are those bodies always truly at rest, which commonly are
taken to be so.

It is notable that Newton is using the language of force (vis), a physical quantity.

You can call the First Law what you like, of course.

[bill4long]

That Chap thinks "staight lines" though spacetime are a thing is adorable.

We are talking Newtonian physics here. Or hadn't you noticed?

You said...

...experience out in space teaches us that if we have a moving body far away from friction with the ground, and with no drag from moving through the atmosphere, and away from a strong gravitational field like the one we have on earth, it will just keep on going in a straight line at constant speed for ever.

You left Newtonian physics with that statement. And given your usage of the infinitive verb and inclusive pronoun, you're including our experience of today in that statement. Or did you mean to say something else?

Nothing goes in a absolute straight line anywhere. Strong or weak gravity, spacetime is mangled in such as way by the aggregate gravitational effects, stretching all the way back to the Big Bang, that there is absolutely nothing like absolutely "straight line" travel. It it is fairly imperceptable and irrelevant at relatively short distances. Okay, sorry, I'm being an azzhole. Happy New Year.

[Physics Guy]

Whoever last edited the Wikipedia page for inertia also uses the term as I do. It really is the standard usage. I’ll agree that it doesn’t actually come up all that often explicitly, because it frequently goes without saying, but if one ever does want to draw attention to the second-order nature of dynamics, the term is there.

There is nothing wrong with your description of how objects move. It’s just long, especially if this object moving in space is only an analogy for something quite different, like the scale factor of the universe, or for that matter like a swinging lever or a spinning top. Having to say all that, just to remind people that things tend to keep going, is kind of a rabbit hole. It’s nice to be able to allude to the general principle that your description illustrates, without having to recite it all.

If inertia is relatively seldom mentioned explicitly in modern physics, Newton’s original formulations of his mechanics are as good as never mentioned at all. His language was archaic, even after translation to English. For example his use of “vis insita” for “inertia” is impossible today, precisely because it calls this innate property a force—and in modern terms it isn’t a force. “Vis” may be the Latin for “force”, but not in the specific sense of physics; it’s a vague term. In Newton’s time momentum, inertial mass, and kinetic energy were all called “vis” by different people; the specific modern concept of force was not yet established. Even though Newton’s concepts won out, his language was, naturally, pre-Newtonian. Nobody bothers about it today.

[Physics Guy]

There actually is a valid concept of a straight line in curved spacetime—or at least of straightness. The trajectory of a compact object in curved spacetime is a geodesic: a path of shortest length between two points. On the surface of a sphere, for example, geodesics are great circles. So it actually is precisely meaningful to speak of a straight path on the surface of a sphere, and in other curved spaces.

In flat spacetime, geodesics are indeed lines. In the vicinity of, say, a sun, geodesics are corkscrews through time (for bound orbits). In the case of the Earth, though, for instance, the corkscrew is so extremely stretched out that it is awfully close to being a straight line. In a year of time, which is a light-year of length, the corkscrew only twists once, and its radius (one Earth orbit radius) is a tiny fraction of a light year. If you had a wire in this shape, you’d call it pretty damn straight. In the curved spacetime of the Sun’s Schwarzschild metric it really is exactly straight, but curvature in the solar system is weak enough that it’s also almost a line.

[Chap]

For example his use of “vis insita” for “inertia” is impossible today, precisely because it calls this innate property a force—and in modern terms it isn’t a force. “Vis” may be the Latin for “force”, but not in the specific sense of physics;

Pardon me, but I think you are not paying close enough attention to Newton's words, in Latin or in English. He does NOT say that 'vis insita' (innate force) is inertia. He says that vis insita can also be called vis inertiae (inertial force, lit 'force of inertia). I agree that in Newton's time 'force' included a wider range of reference that does the modern term. But when Newton says: "But a body exerts this force only, when another force, impressed upon it, endeavours to change its condition" it is surely obvious that here 'force' is being used in its modern sense.

I think our dialogue is ceasing to be interesting. You are welcome to call Newton's first law whatever you like, so long as you do not insist that the only clear way to discuss N's laws and their application with students necessitates introducing the term 'inertia', which is patently untrue.

[Physics Guy]

I guess it doesn't strictly necessitate using the term "inertia". I do have to teach the concept and fact of inertia. I have to teach F = m a, that a mass responds to a force with an acceleration rather than an instantaneous change of velocity. "Inertia" is the standard name for that fact, so I have to teach them the fact of inertia. I could perhaps refrain from teaching its standard name.

It would leave my students handicapped in future discussions with other physicists, not knowing a commonly used technical term, at least until they googled it or looked it up in a dictionary or encyclopedia. Never having heard the term "inertia" in the simple context of linear motion would also leave students confused when they came to study rotations of rigid bodies and discovered the inertia tensor, when they came to special relativity and heard about inertial frames, or when they came to learn about non-inertial frames and heard the Coriolis and centrifugal forces called "inertial forces".

Not mentioning that the principle of integrative response to force has a standard technical name would also deprive my students of the meta-knowledge that this second-order-dynamics thing is important enough to have a short name—that it's a concept that deserves a line in their mental table of contents, not just in the index.

If I were to avoid mentioning standard names for concepts, why should I stop at inertia? Should I not also refuse to say "conservation law", because nobody needs the term "conservation law" to be shown that something stays constant in time? Should I not also omit mention of relativity, because nobody needs the term "relativity" to learn the Lorentz transformations? What about terms like "symmetry", "gauge invariance", "unitarity"? They're all just general labels that nobody needs to get specific results, and they're not measurable quantities. Should I try to teach all of these other basic concepts without ever speaking their names?

[malkie]

I guess it doesn't strictly necessitate using the term "inertia". I do have to teach the concept and fact of inertia. I have to teach F = m a, that a mass responds to a force with an acceleration rather than an instantaneous change of velocity. "Inertia" is the standard name for that fact, so I have to teach them the fact of inertia. I could perhaps refrain from teaching its standard name.

It would leave my students handicapped in future discussions with other physicists, not knowing a commonly used technical term, at least until they googled it or looked it up in a dictionary or encyclopedia. Never having heard the term "inertia" in the simple context of linear motion would also leave students confused when they came to study rotations of rigid bodies and discovered the inertia tensor, when they came to special relativity and heard about inertial frames, or when they came to learn about non-inertial frames and heard the Coriolis and centrifugal forces called "inertial forces".

Not mentioning that the principle of integrative response to force has a standard technical name would also deprive my students of the meta-knowledge that this second-order-dynamics thing is important enough to have a short name—that it's a concept that deserves a line in their mental table of contents, not just in the index.

If I were to avoid mentioning standard names for concepts, why should I stop at inertia? Should I not also refuse to say "conservation law", because nobody needs the term "conservation law" to be shown that something stays constant in time? Should I not also omit mention of relativity, because nobody needs the term "relativity" to learn the Lorentz transformations? What about terms like "symmetry", "gauge invariance", "unitarity"? They're all just general labels that nobody needs to get specific results, and they're not measurable quantities. Should I try to teach all of these other basic concepts without ever speaking their names?

The physical concept that dare not speak its name!