Nothing weird

Spin and mass are the invariants of the Poincaré group and every relativistic object is defined as a representation of the Poincaré group, whether in classical or quantum mechanics.

Charge doesn't have anything to do with the representation of the Poincaré group, but with the representation of another group; for electric charge the group is U(1), the group of complex numbers of unit modulus. This group commutes with the Poincaré group. This is true, also, whether in classical or quantum mechanics. So electrically charged matter is defined by the representation of the direct product of the Poincaré group and U(1).

Ι don't understand the part with the multilication of U(1)) with Poincare group giving the def of charge. Why multilication between commuting groups defined an object?

(I know def of particles is "that which transformation in irrrducible non unitsry Poincare grouptrsnsforms")

U(1) is the group of transformations relevant for describing the properties of electrically charged particles: Electrodynamics can be defined as the field theory that's invariant under global Lorentz transformations and local U(1) transformations. That's why matter fields-that carry electric charge-belong to a representation of the U(1) gauge group. They, also, belong to a representation of the Poincaré group and it does make sense to ask what is the representation of electrically charged matter under the action of both groups. The answer is that the representation is a direct product of the representation of the U(1) group and of the Poincaré group.

“Most weird Physics facts (particles are dually such and waves, things that don't turn have spin traits, charge can't be found seperately of entities)?”

- yeah, in this thread question a few really “weird” mainstreamPhysics facts are pointed, though in the mainstream the number of such facts is much larger – really all postulates of all standard physical theories, and, much more than in the standard theories, in numerous “new mainstream physics” theories, really are fundamentally weird mental constructions.

That happens since the mainstream philosophy and sciences, including physics, the fundamental phenomena/notions, first of all in this case “Matter”, “Consciousness”, “Space”, “Time”, “Energy”, “Information”, - are fundamentally completely transcendent/uncertain/irrational;

- including so really in physics everything in Matter, i.e. “particles”, “fundamental Nature forces” – and so “fields”, etc., and all their physical properties and parameters, are fundamentally completely transcendent/uncertain/irrational/“weird” also.

Really any really scientific answer to “why a postulate is as it is?” is possible only if the fundamental phenomena/notions above are scientifically defined; what is possible, and well essentially given in a few tens of cases, only in the Shevchenko-Tokarevsky’s Planck scale informational physical model, 3 main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics

https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics

https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force .

First of all in the model it is rigorously scientifically shown that Matter is based on a rather simple binary reversible logics; and so the Matter’s ultimate base is the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which [lattice] is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, fundamentally continuous, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct),

FLE “size” and “FLE binary flip time” are Planck length, lP, and Planck time, tP.

So everything in Matter exists and happens as specific disturbances in the lattice, which are created at some impacts on any the lattice’s FLE, and, after creation, the disturbances always constantly move in the utmost universal “kinematical” space with metrics (cτ,X,Y,Z) with 4D velocities that have identical absolute values be equal to the standard speed of light, c, what is determined by FLE properties, c= lP/tP; i.e. with c [bold means 4D vector]

Particles are specific disturbances – some close-loop algorithms that run on “FLE hardware”, which appear after some FLE is impacted with transmission to it a 4D momentum, P, P=mc [m is inertial mass]

- what results in motion in the lattice of sequential “FLE-by-FLE flipping point” along corresponding 4D “helix”, that has, if a particle is at absolute rest in 3D space, radius be equal to ~ the particle’s Compton length λ=ћ/P0, P0=m0c, m0 is rest mass.

Correspondingly all particles – since in this case fundamentally aren’t “points” have identical intrinsic “angular momentums” [of the flipping point] be equal to ћ. If a particle is at rest or moves with a small speed in 3D space, the observed 3D projection of the 4D “intrinsic angular momentum” is equal to ћ/2. That is just the “weird spin”. If a particle moves in the space with speed ~ c, the 4D “helix” becomes to s ~ 3D helix, and so its “angular momentums” is observed as “particle’s helicity”, which, correspondingly is equal to ћ.

The post is rather long, so now

Cheers

So let’s continue.

So [see the SS post above] every given time moment every particle always exists as 4D “FLE flipping point” that has size ~Planck length, and it interacts as just “particle-point” in QM.

If a particle is impacted by some 3D space momentum p, the flipping point moves also along essentially [though non-completely] 3D helix with radius λB=ћ/p, what is observed – and in QM called - “de Brogile wave”, i.e. really observed point-like interactions of a particle with other particles happen randomly in rather “non-point” volume, what is in QM as just “particle-wave”.

The really specific – and non-universal logical “FLEs’ marks” “fundamental Nature forces” are actualized in particles as additional to “kinematical” properties of FLE above [that are actualized at particles’ existence and motion in Matter’s “kinematical” space with metrics (cτ,X,Y,Z), more about Matter’s spacetime see the SS post above],

- as that marked FLEs in particles’ algorithms are concrete Forces “charges”. That happens in the space with metrics (g,w,e,s), in the thread question is pointed only Electric charge, e-dimension in the last metrics; the dimensions of other – Gravity, Weak, and Strong, Forces are g-,w-, and s-dimensions.

The Forces so are written in corresponding parts of particle’s algorithm “Forces charges”, and, if some FLE in “FLE flipping point” has mark of some Force, it radiates the Forces’ mediator; the mediators are “the Forces’ fields” in classical physics and QM, which are flows of mediators, and when some mediator hits in an other particle’s “FLE flipping point”, an elementary interaction happens.

More about what are Gravity and Electric Forces see the Shevchenko-Tokarevsky’s 2007 initial model Planck scale of Gravity and Electric Forces in

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces

and about what is Nuclear Force see 2023 initial mode Planck scale in

https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force http://dx.doi.org/10.13140/RG.2.2.23711.64165; all these Forces act in Matter by the same scheme.

Again, any really scientific answer to any really fundamental question is possible only in framework of the SS&VT Planck scale informational physical model, the links see in the SS post above in the thread; and are fundamentally impossible anywhere else, since authors of “answers” in this case have principally only some transcendent/uncertain/irrational imaginations about what they write. As, say, that

“…Ι don't understand the part with the multilication of U(1)) with Poincare group giving the def of charge. Why multilication between commuting groups defined an object?..”

- is a completely correct comment of really rationally and objectively thinking RG member [in this case Philippos Afxentiou, regrettably such cases are too rare in RG discussions] to really only some transcendent “explanation” of what is “charge” – and everything else in the thread question, though. Really the “explanations” are nothing more than some really basing only on that applications of existent mainstream physical theories is in many non-fundamental cases is adequate to the reality, including when in the theories “the multilication of U(1)) with Poincare group” is postulated,

- however the mainstream fundamentally isn’t able to explain – for what mystic reason that happens; including, say, for what mystic reason in Matter the Forces charges, mass of particles, etc. are as they are; and what is “Poincare group” also, which is based on for a mystic reason adequate to the reality Lorentz transformations, etc.;

- while, say, the really rigorous scientific explanation of what are Lorentz transformations and why they are as they are, can be, and is given only in the SS&VT model, in this case see https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics

Recent SS post in https://www.researchgate.net/post/NO25The_Relation_Between_Mathematics_and_Physics_1-What_Are_the_Fundamental_Quantities_in_Physicsis relevant to this thread question.

Cheers

Μr Nicolis,

Indeed wave propagation and Particle are equivalent solutions to the same mechanical problem. Wave propagation arises in phase space and the w wave front