Hacker News Reader

Comment by colordrops | Hacker News Reader

Angular momentum is an abstract concept, and an emergent property. It doesn't exist inherently in an object.

Centrifugal force is an abstraction, but angular momentum has physical reality at the subatomic level. See Feynman, chap. 17.[1] Photons have angular momentum, even though they don't have a meaningful size. This is strange, but it's reality.

[1] http://www.feynmanlectures.caltech.edu/III_17.html

Angular momentum could be encoded in the wave function.

http://arxiv.org/abs/0807.3930

That is a trivial fact, the wave function of a system completely describes the state of the system and that of course includes the angular momentum. But the wave function has nothing to do with a physical wave with physical properties, it is a pretty abstract construction and the physical properties are essentially encoded in the base vectors of the Hilbert space. I only skimmed the paper but I didn't come across something that plausibly argued that the wave function is the fundamental physical entity.

Not meaning to argue that the wave function is a physical entity but rather that particles aren't required to "exist" as a physical entity to explain experimental data.

I would say nothing is required to exists. Just take the idea that our universe may be a simulation, then nothing in the universe is real. It could then be that the real universe out there is similar to ours or we could be the Game of Life of the real universe which could be totally incomprehensible to us with concepts that aren't even imaginable in our little world. Or take Last Thursdayism, the idea that the universe somehow came into existence last Thursday with fake memories of the past in our all heads and so on. Or Solipsism. There is no way you could ever find out that something like that was true or not.

We just have to make some assumptions about the nature of the universe and accept them as axioms, otherwise you can not even start to draw conclusions. Some assumptions may look more reasonable then others but I guess that is more or less an illusion, last Thursdayism looks only unreasonable because you have already rejected the idea and accepted some other assumptions.

So what is real? Particles? Fields? Wave functions? We pretty surly don't know. Some will say the fields are the real things because they give us virtual particles and that matches experiments, others will say that fields are not real because they have gauge symmetries - gauge redundancies - and how can something that is underdefined be real? It seems certainly possible that we will be able to rule one or another view out in the future because they can not accommodate some new discovery but we are probably not yet there and there is definitely no consensus.

Not to forget that there are quite a couple of new directions in the last years and decades, like space and time emerging from entanglement, the holographic principle, gravity as an entropic force and what not. There is probably a good chance that some or all our fundamental concepts of physics as of today will not survive the next century, millennium or million years. I mean they will still exist as useful approximations but no longer been seen as fundamental.

I'm not in disagreement. I certainly could have been more careful with my original wording.

I had a gut reaction to the original commenter's statement that angular momentum was a "physical reality at the subatomic level" and should have been more direct in my response.

I mean angular momentum of macroscopic objects, which the spin of particles has little to do with.

No, they're the same thing. Feynman: "Now we would like to discuss the idea of angular momentum in quantum mechanics—or rather, the characteristics of what, in quantum mechanics, is called angular momentum. You see, when you go to new kinds of laws, you can’t just assume that each word is going to mean exactly the same thing. You may think, say, “Oh, I know what angular momentum is. It’s that thing that is changed by a torque.” But what’s a torque? In quantum mechanics we have to have new definitions of old quantities. It would, therefore, be legally best to call it by some other name such as “quantangular momentum,” or something like that, because it is the angular momentum as defined in quantum mechanics. But if we can find a quantity in quantum mechanics which is identical to our old idea of angular momentum when the system becomes large enough, there is no use in inventing an extra word. We might as well just call it angular momentum. With that understanding, this odd thing that we are about to describe is angular momentum. It is the thing which in a large system we recognize as angular momentum in classical mechanics."[1]

Yes, it's weird. Yes, it's not intuitive. But it's very real. Many experiments, such as the classic two-slit experiment, have confirmed the stranger predictions of quantum mechanics.

[1] http://www.feynmanlectures.caltech.edu/II_34.html

I think something is being lost in translation here. An object made of multiple particles could potentially have one at dead center that is spinning perfectly, and this would be of the same sort of angular momentum as that at the quantum level. But a particle sitting out on the edge of an object is subject to the forces of those surrounding it, keeping it moving in a circle instead of a straight line. Instead of microscopic particles, imagine a bunch of marbles connected by loose springs in a 3D mesh. If you spin this around, are you suggesting that something is happening besides the simple fact that springs are tugging and pushing at marbles to constantly affect their linear motion to appear circular? It's like suggesting somehow that a line on a screen is not made of pixels.

Spin angular momentum seems to be a pretty intrinsic property of (fundamental) particles. What do you understand as inherent properties of objects? Position? Charge? Mass? Velocity? Energy? Linear momentum? Spin? And why? What if the object is composite? What about quantum physics, e.g. superposition states?

The angular momentum of a spinning bucket of water has approximately nothing to do with the intrinsic angular momentum of the particles, though. Statistically, we'd expect all of the intrinsic spins of the electrons and quarks to cancel out entirely.

Rather, the angular momentum is due to the fact that the straight-line motion of all the atoms on the left side of the bucket is opposite in direction to the straight-line motions of all the atoms on the right side of the bucket. (With respect to the reference frame of the center of gravity of the bucket, etc, etc.)

They are nonetheless related, if you would align the spins in the water and the (metal) bucket you would make the bucket and/or water spin to conserve the angular momentum. [1] They are surly different but it is not some accident of history that both are called angular momentum, they are really both angular momentum.

[1] https://en.wikipedia.org/wiki/Einstein–de_Haas_effect

What is the point you're arguing against? I know perfectly well that conservation of angular momentum is a thing. I know perfectly well that the intrinsic property that we call 'spin' of an electron is really angular momentum. I know that a spinning bucket also has real angular momentum.

So, I'm not sure what you're trying to tell me.

The central point made by colordrops is that angular momentum in a macroscopic object is 100% (accurate to at least ten decimal places) due to synchronicity of linear momenta.

What colordrops wrote at least suggest that he thinks that circular motion and angular momentum are not fundamental but can be expressed or understood in terms of linear motion and linear momentum. As far as I can tell today this is not true, they are independent concepts and one can not be fully understood in terms of the other, neither by looking at circular motion as piecewise linear motion nor by looking at linear motion as circular motion about a point infinitely far away. I only brought up spin because it makes the point pretty clear - or maybe not - that angular momentum is a fundamental concept that can not be recast in other terms, especially it is not just the sum of many linear momenta.

Look at the 2-body gravitational system -- let's say Earth-Moon. Let's put our non-rotating reference frame at the barycenter. At any given moment, Earth has a definite position and velocity, and the Moon has a definite position and linear velocity. If we know these positions and velocities (and masses), we can derive anything else we'd like to know about the system. Including its angular momentum.

This would also be true of any system such that the size is large enough to render the quantum spins statistically close to zero.

Sure but you make an arbitrary choice here, you choose to use Cartesian coordinates. Lagrangian and Hamiltonian mechanics make it more clear that this is more or less an arbitrary choice and that there are other sets of generalized coordinates to describe the problem, something that is in some sense less obvious in Newtonian mechanics because things usually become pretty hard to deal with.

Yes, every choice of coordinates is capable of describing the physics of a system. Yes, you could certainly argue that Cartesian coordinates are a natural choice or in some sense special, derivatives are especially simple and whatnot. But I still think that something is lost when one disregards rotations and angular momentum, they seem to capture an important aspect of the structure of space, its isotropy.

Then again every equivalent description should capture the same things, just maybe not in an obvious way. And then again the existence of spin angular momentum hints at the fact that there is really more to it. As I said, I am really not sure. I used to think of rotations as emergent from translations and I kind of changed my mind but I am probably still on the edge.

Reply on news.ycombinator.com