Swirling Forces, Crushing Pressures Measured in the Proton
quantamagazine.org
quantamagazine.org
https://en.wikipedia.org/wiki/Hairy_ball_theorem
I'm wondering if their proton map covers that, and if the "axis" corresponds to anything familiar.
“A common problem in computer graphics is to generate a non-zero vector in R3 that is orthogonal to a given non-zero vector. There is no single continuous function that can do this for all non-zero vector inputs.”
Any solution will have a discontinuity in its output vector angles. I don't know how this problem is applied in computer graphics, but you probably want to avoid rendering objects in the vicinity of a discontinuity: you'd get some kind of flickering artifact when you cross it, with small ɛ-displacements being amplified into something much larger.
Another way to think about it is assigning cardinal directions to the Earth. Which way is north from the north pole? There's no possible way to create a map that has defined directions at every point.
The pictures in the Wikipedia article give a great intuitive understanding, particularly if you can figure out why a sphere and torus behave differently. (You can build a globally consistent map on a torus.)
No, you can not, there is no global map on the torus.
What I mean is that you can assign a direction to each point of the torus, and have it be consistent with it's neighbors (free of discontinuities) throughout the entire surface. This is in contrast to a sphere, which will always have tufts (poles) at at least one point.
Note that this only applies within the surface itself, not to it's embedding in 3d space (the donut shape we're all familiar with). If north points up on the outside edge, it'll point down to us on the inside edge, but an ant on the surface would experience no contradictions.
https://en.wikipedia.org/wiki/Torus#/media/File:Torus_cycles...
Nitpick: that should be "no single continuous deterministic function"; it's (relatively) very easy to sample uniformly randomly from the unit circle orthogonal to a given non-zero vector, but that won't give, for example, approximately the same result on two consecutive video frames, such that you could usefully orient the camera with that direction "up".
Maybe by "twisting" the author means that the field is one of torques rather than of linear forces. I guess you can make a continuous field of torques tangent to the surface of a sphere (as long as you're speaking of the "wheel" of the torque, not its pseudovector axis, being tangent to the sphere).
In addition, you can only speak of two "ways" any particular torque in such a field can go: clockwise or counterclockwise, as viewed from, say, a point inside the sphere. That would explain the one-way-or-the-other language.
The proton is fully 3-dimensional AFAICT so the vector field on the surface (if it has a surface, I'm not a physicist) can have non-tangent components, pointing inwards or outwards.
<guess> I think that the graphic assumes that the spin on the proton is pointing up (perpendicular to the sheet of paper) and the forces that are drawn are parallel to the "equator". In the "north pole"and "south pole" there are no forces.</guess>
[1] The spin is 1/2, but I guess the exact value is not important for this, only that it's not null.
> Sharper gravitational maps of both the proton’s quarks and its gluons may come in the 2030s when the Electron-Ion Collider, an experiment currently under construction at Brookhaven, will begin operations.
It would be hard to imagine the scientists are ignoring quantum effects since light + proton screams quantum, so it's unclear from the reporting alone if the lack of a quantum gravity theory is enough to make all this not particularly useful or if this is just bad reporting and the experts are confident this is the right way to do things "for reasons". My guess it's probably a mixture because the modelled answer computed from equations and the measured result seem to be aligned.
We hat this experiment set up in one of our lecture halls once a year. They had to fence off the area and it had to relax for days, but we were able to replicate the measurement during our introduction to physics lecture.
There was also a lab course on a smaller version. (Video of it, in German though: https://m.youtube.com/watch?v=8W8X71wW8F0)
> the concept of electric potential (which he called the "degree of electrification"), an early unit of capacitance (that of a sphere one inch in diameter), the formula for the capacitance of a plate capacitor, the concept of the dielectric constant of a material, the relationship between electric potential and current (now called Ohm's law) (1781), laws for the division of current in parallel circuits (now attributed to Charles Wheatstone), and the inverse square law of variation of electric force with distance, now called Coulomb's law.
(Wikipedia)
Wonder what went wrong to need so many rediscoveries by others. Reminds me of Gauss.
I might also include a certain scientific isolation. Not in the sense of isolationist tendencies, rather that there were a lot of blind men reaching across the elephant and their hands had yet to touch.
> Because of his asocial and secretive behaviour, Cavendish often avoided publishing his work, and much of his findings were not told even to his fellow scientists. In the late nineteenth century, long after his death, James Clerk Maxwell looked through Cavendish's papers and found observations and results for which others had been given credit.
and a paper from last year https://arxiv.org/abs/2310.11568
and basically the same paper from three years ago (you'll recognize one of the plots from the last article) https://arxiv.org/abs/2104.02031
"Honestly, are you never going to let this go? I had goo reason to think there was more than one proton!"
I think this seems to make the opposite assumption, which also seems questionable.
Rather than “I don’t know the ‘why’ “, I think it would be better to say “I don’t know if there is a ‘why’, nor what it is if there is one.” .
Though, really, I think the question of “why” in this context, is a little unclear as to what exactly it is asking?
Like, what properties would a statement have to have in order to be a satisfactory answer to the question?
Like, if something like color confinement is inevitable assuming SU(3) symmetry, would this answer “why” hadrons exist? Or, if the fact by itself wouldn’t, would this fact, along with a mathematical proof of it, arranged in a way reflecting the core ideas of the proof, constitute a “why hadrons exist”?
Or, is the question asking something more, like, “why is there something rather than nothing?” ? Is it asking for the first cause?
Yes, very nice! But I didn't want to go down that rabbithole as you actually need more correction factors... because a person who doesn't know, doesn't know if they know or not. ;) But functionally, they can't say they "know" - they are not conscious - so they don't know if they know or not, and they don't know what knowledge they have may contain a "why" or not, etc., i.e. there is great knowledge in history but people don't realize or have forgotten what resides in their own consciousness or history yet.
> Though, really, I think the question of “why” in this context, is a little unclear as to what exactly it is asking?
Also very good. 'how' and 'why' converge. That's why a person should make clear what they're asking. Just because 'why' and 'how' converge doesn't mean 'why' is meaningless or useless. In fact, why does something exist is different from how, since any "how" explanation is implicitly about a process of existence, yet a "why" sometimes explains mechanisms that do not "exist" yet cause what exists. That's why understanding this and enunciating it perfectly is a little beyond human eyesight for now. Philosophy exists for a reason and it's not just bullshit some thinkers made up (nor does it culminate with some semi-Wittgensteinian cop-out that words are the best we can do. What a nonsense self-contradiction).
Why means many things. People should stop conflating them and ask one by one concretely what they want to know if they truly want to know. But many people can't even realize what their real questions are without some dialogue.
Why there is something rather than nothing is that nothing can't exist. One little modern explanation: the moment you put boundary conditions on, you get virtual particles. QFT is clear about that. Without boundary conditions or a metric, there is no way to even consider the notion of a vacuum or nothingness.
Answering your question involving SU(3) symmetry requires you understand why/how SU(3) is pre-determined.
The place where "why" and "how" diverges is when involving a subject: "why am I alive" vs "how am I alive". The second one is a lot easier to answer if you consider only the biological. If you don't understand what the point of life is, it will be a lot harder to understand your distant past and a lot harder to understand your ultimate "why" i.e. your path and your purpose in this life. Consider what you know, for starters: you are like a child in this universe, growing up and learning through your life. When someone has to learn and grow, it means they're on the path to realization, mastery, and complete knowledge. I'll leave it at that for now.
Isotopes are only imperfect in the context of one labeling system. But not from a quantum viewpoint.
Once something that you thought was atomic actually shows variation you begin to suspect it is composed of smaller things.
Your comment does remind me of this though: https://en.wikipedia.org/wiki/One-electron_universe
If we are not in a one-electron universe, every electron is unique in the sense that it has an entirely unique path though spacetime, and thus can't be identical. I think what you mean is that every one of these "particles" seems to obey the same set of laws, which is not something that's unique to atoms, subatomic particles, or even larger things like molecules.
No, quite the opposite, actually. Some particles being identical is core to many quantum mechanical ideas. The distinction between Bosons and Fermions fundamentally relies on this idea.
Also, it probably isn’t true that all electrons have individual well-defined paths through spacetime.
Electrons are Fermions.
When two electrons are “in orbit” around a helium nucleus, with the atom including the electrons being in the lowest energy state, the two electrons are orbitals distinguished by their spin, but, at least if it were not for the interaction with the magnetic interaction from the spin of the nucleus, you could choose any axis along which to consider the spin direction of the electrons, and like, you would get for each of the two spin directions along that axis, one of the electrons would have its spin in that direction. But considering different axiis for the spin, you would be splitting the two up in different ways?
I’m fairly confident it isn’t possible to assign a consistent id for each electron which persists through time. (Even setting aside the “they don’t have well-defined positions” aspect)
Is mass basically a ball of balanced forces ready to explode if this balance is disrupted?
If so then it seems interesting that this tension's potential energy maps exactly to mc^2.
If nothing else, nuclear bombs made this blindingly obvious.
It is possible to show (with fairly elementary techniques) that when the excitations have a spin of 2, these excitations always reduce the energy of the system, and so produce an attractive force. If the excitations have a spin of 1, then they increase the energy of the system and so produce a repulsive force. This is why the gravitational force attracts and like charges repel each other.
But then why do unlike charges attract? The force mediator is still a spin-1 particle...
Likewise if a particle somehow had a negative mass, it would gravitationally repel particles of positive mass.
I thought it was the Higgs boson that was doing this? But obviously I misunderstood something. Could anybody explain what's the difference between those particles?
In short, gravity is correlated with energy density, which coincides with mass (via e=mc2) but the mass itself is not directly responsible for the gravity field, per se.
This is inside each of us, 100 billion billion billion times
Indeed, there are many things about the world that go in cycles. Indeed, much of how the world behaves can be seen as acting according to exact, “mechanical”, rules (like, the laws of physics), etc. .
I see what he did there.