[“What’s changed in the last ~50 years” series]
Fundamental particles have properties; but not due to any constituents (cf. Feynman’s dilemma for an electron’s charge ).
So, mathematical patterns of … localized “knots” (tangles or twists as in Möbius strips) – particular symmetries – of space-time energy?
A landscape of colliding (interacting) ripples …
How to describe “charge” – electric, color, (mass) …
And, of course, how does gravity emerge? … space-time is bendy …
Different facets … blind men touching (parts of) an elephant?
This post was inspired by an excellent article by Natalie Wolchover for Quanta Magazine.
• Quanta Magazine > “What Is a Particle?” by Natalie Wolchover, Senior Writer/Editor (November 12, 2020)
(quote) It has been thought of as many things: a pointlike object , an excitation of a field, a speck of pure math that has cut into reality. But never has physicists’ conception of a particle changed more than it is changing now.
Perspectives (as discussed in the article)
- Collapsed wave function.
- Excitation of a field.
- An “irreducible representation of a group” (re mathematical sets of transformations that can be done to objects).
(quote) In 1939, the mathematical physicist Eugene Wigner identified particles as the simplest possible objects that can be shifted, rotated and boosted.
For an object to transform nicely under these 10 Poincaré transformations, he realized, it must have a certain minimal set of properties, and particles have these properties. One is energy. Deep down, energy is simply the property that stays the same when the object shifts in time. Momentum is the property that stays the same as the object moves through space.
A third property is needed to specify how particles change under combinations of spatial rotations and boosts (which, together, are rotations in space-time). This key property is “spin.” … Wigner showed that, deep down, “spin is just a label that particles have because the world has rotations,” said Nima Arkani-Hamed, a particle physicist at the Institute for Advanced Study in Princeton, New Jersey.
If you rotate an electron by 360 degrees, its state will be inverted, just as an arrow, when moved around a 2D Möbius strip, comes back around pointing the opposite way.
[Yet] … discoveries showed that elementary particles don’t just have the minimum set of labels needed to navigate space-time; they have extra, somewhat superfluous labels as well.
Just as particles are representations of the Poincaré group, theorists came to understand that their extra properties reflect additional ways they can be transformed. But instead of shifting objects in space-time, these new transformations are more abstract; they change particles’ “internal” states, for lack of a better word.
Ah, yes, there’s charge.
- Vibrating strings.
- “Deformation of the Qubit Ocean.”
(quote) In 2010, Van Raamsdonk, a member of the it-from-qubit camp, wrote an influential essay boldly declaring what various calculations suggested. He argued that entangled qubits might stitch together the space-time fabric.
… the lower-dimensional system that encodes information about that bendy space-time is a purely quantum system that lacks any sense of curvature, gravity or even geometry. It can be thought of as a system of entangled qubits.
… whenever a system of qubits holographically encodes a region of space-time, there are always qubit entanglement patterns that correspond to localized bits of energy floating in the higher-dimensional world.
- What we measure in detectors.
(quote) “The coolest thing,” according to Dixon [SLAC National Accelerator Laboratory], is that scattering amplitudes involving gravitons, the putative carriers of gravity, turn out to be the square of amplitudes involving gluons, the particles that glue together quarks. We associate gravity with the fabric of space-time itself, while gluons move around in space-time. Yet gravitons and gluons seemingly spring from the same symmetries. “That’s very weird and of course not really understood in quantitative detail because the pictures are so different,” Dixon said.
… the amplituhedron — a geometric object that encodes particle scattering amplitudes in its volume.
So, a particle by any other name?  What’s the takeaway for mere mortals? Practical implications?
Both particle and theoretical physicists continue to use the term particle. That word is so embedded in our everyday experience. Clearly, some grasp beyond classical mechanics is important. Something beyond a billiard ball view of objects. Much as understanding modern space exploration using a heliocentric elliptical model of the solar system rather than a geocentric model with epicycles.
What insights will the next 50 years bring?
Group theory, Poincaré group
Spin, spin labels, degrees of freedom
Is mathematical representation of an elementary particle the same as the particle? Is representation always a simplification? A descriptive model?
Do we only model the surface of space-time?
 See Note #5 in my post “Swaying quantum vacuum energy vs compelling charge.”
In that post, I commented: Anyway, an alternative is that the electron has none of the structure (or “complex structure”) of the theories Feynman discussed. That it is not a “sphere of charge.” That we use a relational model in which “charge” is not an internal property per se.
 And reading about topology, there are ways that, for example, a spherical shape is topologically the same as a point. Much like a trajectory for an object may be calculated using its center of mass – a point, but that’s a simplification. So, while an extended space-time tangle might be point-like mathematically, that’s a reduced description of reality.
The center of mass is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton’s laws of motion. … In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass.
• Quanta Magazine > “In Topology, When Are Two Shapes the Same?” by Kevin Hartnett, Senior Writer/Editor (September 28, 2021)
[Diagram] A three-dimensional ball is homotopy equivalent to a single point. You can continuously deform the ball to the point without ever ripping it.