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

[Limnor]

Under the theories we currently accept, there is no way that rules as basic as the indistinguishability of particles could ever have changed. One basic and big thing has changed a lot over time: space has puffed like dough, by a lot. There’s a lot more room now than there used to be, everywhere. This has only happened on large scales, however.

Big collections of matter, like a galaxy or a star cluster, can keep space reined in. So the stars in each galaxy are still only about as far from each other as they always were, and they’re staying that way. The space between galaxies has expanded a lot, though, so on large scales the universe is much bigger. It’s as if the countryside stretched and grew so that towns moved apart.

That’s all still part of the unchanging basic laws as we now understand them, however, the way the continuing ascent of a baseball thrown upward is a consequence of inertia. And the growth of intergalactic space isn’t going to change particles. A crucial part of what space even means is that it’s always the same on small scales, the way the surface of the Earth always has a flat tangent plane even though on large scale the Earth’s round. Particles don’t change if space stretches. They live here and now, in the moment. That’s a big part of what particles mean.

Particles still aren’t really what they sound like. They’re not really little indestructible specks. They’re quantized excitations of fields. Don’t feel bad about having limited imagination for that, however.

No-one has an intuitive understanding of quantum field theory. We just learn the math like a deaf person learning music theory. People make little mental images and analogies here and there, for this or that aspect or scenario, but the theory itself is like a sacred text written in a language that no humans speak natively. In quantum field theory we are all adult learners struggling to manage the grammar.

I’m really enjoying the imagery of this post, PG. I’ve been thinking about the universe the Book of Mormon describes in Alma 42 as compared with your points. Alma 42 essentially describes a world in which mercy cannot triumph over justice or the universe would collapse. The universe you are describing seems different than that model, if I’m understanding your points correctly. You seem to be saying—with a humility that I appreciate—that space can expand without anything fundamental breaking.

This part was interesting to me, and perhaps more profound than you realize: “They live here and now, in the moment. That’s a big part of what particles mean.” Particles are not defined by their cosmic history or ultimate destiny, or compliance with laws lest they be destroyed. They are defined by presence.

So I’m thinking through that alignment with how Jesus is described as acting. He didn’t wait for justice to be satisfied before he healed or forgave. Mercy, to Jesus, wasn’t a delayed action, it was a local variable—presence—that was always allowed without collapsing the entire system.

All of that might be a huge stretch from what you are saying, and I’m not trying to create a physics-theology, it’s just an interesting contrast to me.

[Chap]

I’m sorry if it’s confusing, but while the fact that a thrown ball slows and eventually falls is due to force, the fact that it doesn’t just stop dead and fall right back right away, but keeps rising after release, is indeed called inertia. Inertia isn’t a quantity like mass or momentum, but it is a principle.

[...]

Please explain to me how introducing what you call the 'principle of inertia' into the discussion of the motion of a thrown ball is likely to give students a clearer picture of what is taking place than rigorously using physical concepts and Newtonian dynamics only.

For instance, supposing that we simplify the situation by considering a ball of mass M thrown upwards near the surface of the earth in a vacuum, with an initial velocity Vº, so that the distance moved upwards before falling back down is small compared to the radius of the earth, and the gravitational force F acting downwards on the ball may therefore be treated as constant, and as being the only force acting on the ball after it has been thrown.

The momentum of the ball at any instant is defined as its mass x velocity, Q = MV, and if the total force on the ball is F, then since force is rate of change of momentum. that momentum will steadily change at a rate equal to F.

The initial momentum of the ball is Qº = MVº. Since this is directed upwards, and the force is directed downwards, the upwards momentum of the ball will steadily decrease at the rate dQ/dt = -F (I wish we could use vector notation on this board!). So at a time T after the ball leaves the thrower's hand, the upward momentum will be MV = MVº - FT, assuming F and M are constant.

So V = Vº - FT/M

The implies that the upwards velocity of the ball will steadily decrease as T increases, until V becomes zero, after which point it will begin to have an increasing velocity downwards. Nice and simple, surely? How does bringing 'inertia' into the discussion help the student understand better?

I see no benefit in adopting an attitude equivalent to the old Aristotelian approach in which it is the continued motion of the ball that needs explaining (hence the concept of 'inertia'). Instead, we should take the Newtonian attitude (embodied in Newton's first law of motion) that it is any change in the motion of the ball from moving with constant speed in a straight line that needs explaining - which I submit the few lines above do very clearly.

[Chap]

MODS: I have a feeling that a thread split to shift the sciency stuff elsewhere would be entirely out of place ....

[Whiskey]

MODS: I have a feeling that a thread split to shift the sciency stuff elsewhere would be entirely out of place ....

Agree. That is the core of the topic and discussion. Keep the sciency stuff here. PG is the king of stuff.

[canpakes]

MODS: I have a feeling that a thread split to shift the sciency stuff elsewhere would be entirely out of place ....

Threads meander. I see no issue here. : )

[Physics Guy]

Inertia may have been a concept in Aristotelian physics, but it was and is also part of Newtonian dynamics. Newton's First Law is often called "the Law of Inertia". As I said, the meaning of the First Law in modern terms is that the laws of motion are differential equations of second order rather than first.

One thing this means is that there are rules about how momentum changes, but that any momentum is in principle possible at any given instant. To pin down a full history of motion, the laws need input: an initial position and an initial velocity. In this sense force alone is never a full explanation of motion in Newtonian mechanics. The initial conditions are also part of the story.

If an object had such-and-such a velocity initially, you can ask how it got that velocity, and the answer will be that some force acted, previously to that initial time—after the object began, at some even earlier time, with some other velocity. You can't get away from having to take some initial velocity, at some point in time, as an input. So, to the question, "Why is this ball flying upward?" the naïve answer, "Because it was launched up at high speed a few moments ago" is also an accurate Newtonian answer. Unless you want to get all into the biomechanics of pitching, you're just going to declare that the moment of release was the initial time, and the initial velocity was so much, and that's why the ball's rising. The stuff about gravity and deceleration is then not the answer to why the ball is rising, but to why its ascent is slowing. Why it's rising is that it started out rising, and hasn't yet had time to fall back.

With a thrown ball you can indeed get into biomechanics if you want, and understand how the ball accelerates in the pitcher's hand. Then you can push back your initial time to before the ball gets released, and you'll spend more time talking about force. It will still be true, though, that once the ball leaves the pitcher's hand, and is subject only to gravity and air resistance, the forces on the ball are suddenly weaker, and so it takes the ball a while to slow down and fall back. The fact that weak forces take a while to reverse high velocity is still the fact of inertia. The coefficient M in Newton's F = M a is called the "inertial mass".

All of that is true about baseballs, though it might be confusing for students who aren't used to calculus and tend to think in Road-Runner-and-Coyote physics. I'm not used to teaching such students. At high school level you might well be right that even saying the I-word is just going to mess up the students. As an analogy for Big Bang cosmology, though, it's quite important to emphasise this point about initial velocity explaining continuing velocity.

This is because in the case of the Big Bang we don't have any analog of pitching biomechanics. We can't say anything about why the universe started expanding. It's just an initial condition. If anyone wants to know why the universe is expanding, the answer is that it started out expanding fast, and still hasn't had time yet to slow down and stop. That's all we can say. I mean, we can say it in an equation, and all, quantitatively, but that's what the equation is saying. It's a second-order equation with a fast-expansion initial condition. It's inertia.

Whether the expansion will eventually slow down and contract in a Big Crunch, as the gravity of everything hauls space back in, or whether the initial expansion rate was above a kind of escape velocity so that space will continue expanding forever, is an open question. Both options are theoretically possible, and observational evidence keeps flipping back and forth every few decades, so it's hard to be sure.

[Chap]

Newton's First Law is often called "the Law of Inertia".

Forgive me for insisting, but I think we may have a cultural difference here. In an education that I can honestly say had a lot of physics in it (please excuse my reticence about in real life stuff, but trust me on this), I have never heard the Newton's First Law being called anything but ... the "First Law", and I have certainly never thought of calling it anything else myself.

One thing this means is that there are rules about how momentum changes, but that any momentum is in principle possible at any given instant.

Yes, of course.

All of that is true about baseballs, though it might be confusing for students who aren't used to calculus and tend to think in Road-Runner-and-Coyote physics. I'm not used to teaching such students. At high school level you might well be right that even saying the I-word is just going to mess up the students

I am interested in how, when teaching intelligent students with a good grasp of mathematics, one should discuss Newtonian dynamics in a way likely to cause the least possible confusion. I don't care what level the students are at, frankly. Physics is so often taught in a confusing way that people who are some good way into the subject are often subject to quite unnecessary confusions because of the way they have been taught previously.

I don't want to seem aggressive, and I apologise if I seem to be, But your long response does nothing to answer my question, when after giving a clear and I believe accurate description of the physics of a simple case of a ball thrown upwards in terms of mass, velocity, momentum, force and time without mentioning 'inertia', I asked:

How does bringing 'inertia' into the discussion help the student understand better?

[Rivendale]

Newton's First Law is often called "the Law of Inertia".

Forgive me for insisting, but I think we may have a cultural difference here. In an education that I can honestly say had a lot of physics in it (please excuse my reticence about in real life stuff, but trust me on this), I have never heard the Newton's First Law being called anything but ... the "First Law", and I have certainly never thought of calling it anything else myself.

One thing this means is that there are rules about how momentum changes, but that any momentum is in principle possible at any given instant.

Yes, of course.

All of that is true about baseballs, though it might be confusing for students who aren't used to calculus and tend to think in Road-Runner-and-Coyote physics. I'm not used to teaching such students. At high school level you might well be right that even saying the I-word is just going to mess up the students

I am interested in how, when teaching intelligent students with a good grasp of mathematics, one should discuss Newtonian dynamics in a way likely to cause the least possible confusion. I don't care what level the students are at, frankly. Physics is so often taught in a confusing way that people who are some good way into the subject are often subject to quite unnecessary confusions because of the way they have been taught previously.

I don't want to seem aggressive, and I apologise if I seem to be, But your long response does nothing to answer my question, when after giving a clear and I believe accurate description of the physics of a simple case of a ball thrown upwards in terms of mass, velocity, momentum, force and time without mentioning 'inertia', I asked:

How does bringing 'inertia' into the discussion help the student understand better?

I have to agree that inertia was more of a impediment rather than a essential element to link fundamental concepts during my 30 year career teaching physics. It reminds me of professors from the 60s and 70s insisting that the Krebbs cycle be thoroughly understood for basic biology. Physics is full of diminutive concepts that can be land mines for students but it also doesn't excuse teaching down to a student. I would prefer "making it accessible ". But I could be wrong....

[Gadianton]

This means that it is in fact possible to have the same drink again, or step in the same river twice. It’s just very unlikely.

I'm trying to follow the logic here. I feel like some slight-of-hand is going on: an attempt to draw a wrong conclusion about the macroscopic world based on the quantum world. Perhaps a test? My outline:

1) Quantum indistinguishability. (good so far)
2) "cold clouds" verify quantum indistinguishability. (good so far)
3) two same drinks are possible? (because two cold clouds can be identical??)

From what I'm gathering from my buddy deepseek (that's right, MG and Whiskey, I'm using AI), a cold cloud is an example of something macroscopic that behaves like quantum particles in a way we can test because it conforms to a simple, single wave function. The first question is, can the case for beer be extrapolated from the case of a cold cloud? I think yes: it's wave function is vastly more complicated but Boltzmann beers seem like theoretical possibility. And so two beers can be the same if two cold clouds can be the same.

But can two cold clouds really be the same? swapping particles within cold cloud A is different than saying cold cloud A and cold cloud B are indistinguishable -- or is it? Cold cloud A is the one we created in the lab yesterday, and cloud B is the one we created this afternoon. Framing in this way, however, may beg the question, as we force a classical description. However, I'm not sure we can avoid begging the question one way or another, either we fall into quantum language that assumes "yes" or classical language that assumes "no". We get stuck in interpretation. Suppose in our lab, we have Paul traps to confine two clouds on separate sides of the lab. If both clouds happen to fall into the exact same state, can we really say they are identical given that they are literally separated from each other by our traps?

[Chap]

It may be worthwhile in this context to look at Newton's own statement of the first law.

Newton's Philosophiæ Naturalis Principia Mathematica (English: The Mathematical Principles of Natural Philosophy) was first published in Latin in 1687.

Here is the first law as there stated, followed by a brief paragraph giving its practical significance.

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

Lex. I.
Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in
directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

Projectilia perseverant in motibus suis nisi quatenus a resistentia aeris retar-
dantur & vi gravitatis impelluntur deorsum. Trochus, cujus partes cohærendo
perpetuo retrahunt sese a motibus rectilineis, non cessat rotari nisi quatenus
ab aere retardatur. Majora autem Planetarum & Cometarum corpora motus
suos & progressivos & circulares in spatiis minus resistentibus factos conservant diutius.

In 1729 Andrew Motte produced an English translation:

https://en.wikisource.org/wiki/The_Math ... otion#Law1

Law I.
Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impress'd 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. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve the motions both progressive and circular for a much longer time.