A a quantum particle has a wavefunction that is the solution of the Schrödinger equation, with Hamiltonian the Hamiltonian of the single particle, defined as an operator in Hilbert space. This does NOT imply that a quantum particle occupies a finite volume in space and time.

The accepted definition of a quantum particle is one subject to Schrödinger dynamics as opposed to Newtonian dynamics.

This implies some limitation on physical size or volume V.

In other words there exists a critical volume Vc where if V> Vc the particle is subject to Newtonian classical mechanics.

The quantum particle itself has a wave function which is the Schrödinger solution which extends through entire space and time.

On the other hand, the world of quantum particles is the one that is estimated to be equal or smaller than an atom (atomic and subatomic world), which means that Vc is approximately the size of an atom. Objects at this scale do not behave the same as objects at the visible scale via visible light (λ in the range 4000 A to 7000 A)

a particle whose de-broglie wavelength (e.h. h/mv) is much smaller than physical size of the particle is classical particle. otherwise it is quantum. Note, even massive objects vibrate with certain velocity, and putting rms velocity at de-broglie eqaution may provide de-broglie wavelength

We can give the exact definition of quantum particles : A particle that could be exist in multiple positions in a particular time in its path.

To grasp the classical-quantum transition regime, one needs to introduce the notion of decoherence of quantum states by the environment, that is, other particles interacting with the considered particles and not explicitly included in the Schrödinger equation. There is an Wikipedia article "Quantum decoherence" that explains it in more details. Actually the Schrödinger (or Dirac) equation tells you exactly what happens when no perturbation by the environment is included: the wave function spreads with time starting from a compact distribution. Classical physics can be seen as an emergence from decoherence of quantum states. Perturbations from the outer world "observe" the considered particles and localize them. So the scale Vc depends both on the considered particle and the environment.

“What is the correct definition of a quantum particle?”

- for a really scientific answer to the question above it is evidently necessary before to answer scientifically to questions – “what is “particle”?”, and “what is “quantum”?” – i.e. why and how they are as they are?.

The answers to the last questions are fundamentally impossible in mainstream physics, since in this case is necessary before to understand what are all really fundamental phenomena/notions, first of all in this case “Matter” – and so everything in Matter, i.e. “particles”, “fields”, etc. , “Consciousness”, “Space”, “Time”, “Energy”, “Information”; which are fundamentally completely transcendent/uncertain/irrational in mainstream philosophy and sciences, including mainstream physics, and so in every case when the mainstream addresses to any really fundamental problem, then result completely inevitably is a transcendent/mystic something.

The phenomena/notions above can be, and are, really scientifically defied only in framework of the Shevchenko-Tokarevsky’s 2007 “The Information as Absolute” conception, recent version of the basic paper see

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

https://arxiv.org/abs/1004.3712 ,

- where it is completely rigorously proven that there exist nothing else than some informational patterns/systems of the patterns that are elements of the absolutely fundamental and absolutely infinite “Information” Set, which exists absolutely objectively, because of It fundamentally – logically - cannot be non-existent; and so exists absolutely eternally, having no Beginning and no End. At that the utmost general definition of the absolutely so fundamental phenomenon/notion Information” is

“Information is something that is constructed in accordance with the set/system of absolutely fundamental Rules, Possibilities, Quantities, etc. – the set/system “Logos” in the conception”.

Including so Matter absolutely for sure is some informational system/the Set/s element; and what is Matter more concretely see the Shevchenko-Tokarevsky’s Planck scale informational physical model, in this case it is enough to read one of 3 main the model’s papers

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

More see at least 2-nd link, though to understand that all what is in the links is really scientifically grounded it is necessary to read 1-st link also, here only a few main points:

(i) – as that is shown in the conception, because of that the “Logos” element “Change” is logically self-inconsistent, so there fundamentally cannot be continuous changes;

- and to overcome this logical prohibition of changes it is necessary to pay by two points: to make some change it is necessary to spend some portion of “Logos” element “Energy”, however on some scale of changes of something its state is uncertain – “illogical”. In the system Matter that is QM scale, where the changes are randomly “quantized”;

(ii) – in accordance with really foundational and really outstanding in physics von Weizsäcker “Ur-hypothesis” and Fredkin-Toffoli finding, Matter is based on binary reversible logics, and so the Matter’s ultimate base is, as that is postulated in the SS&VT model above, 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, c= lP/tP. So really everything I n Matter exists and happens ultimately on the Planck scale

Including particles are specific disturbances in the lattice.

The post is rather long already, so more in a next post, now

Cheers

Dear All,

I have succeeded to formulate a concept that is realistic and that captures reality in metaphysical terms, which can be used to prove the existence of the graviton particle:

Article Fizikailag-metafizikailag bizonyítható a graviton létezése

(Hungarian)

Has English translation:

- abstract:

Research Proposal Physico-metaphysical proof of the existence of graviton (Fiz...

- conclushion:

Chapter Physico-metaphysical proof of the existence of graviton

and graviton:

Chapter 230902-En-H-Gr-t

Onto this article, where was created the term of a priori entity an universal form of electric-magnetic matter can be said that the quantum is an elementary a priori entity which is the building particle of ordinary matter every particle sub this dimenshion is a quantum... somewhat here cen be used definition of Prof. Ismail Abbas : a bit transformed

'This implies some limitation on physical size or volume V.

In other words there exists a critical volume Vc where if V> Vc the particle is subject to Newtonian classical mechanics.'

(In my opinion, these is an erroneous conclusions:

Newton's concept can only be applied to the solid state of ordinary matter; Newton could not plausibly explain the cause of the phenomenon of garvitation! )

Dear Ismail Abbas .

It seems to me that a particle whose wavelength λ=h/p (according to de Broglie or like a photon) is comparable to characteristic size of the problem or experiment interested us, can be called quantum. When the interference picture due to wave properties of particle does matters.

With regards, Mikhail Dulin.

For an ensemble of N particles, the coherence length is also important. Also it is λ=h/p, where quantum of action h belongs to all N particles (and connects them into one), and (small) momentum p corresponds to that of one particle in the ensemble: p=P/N.

The coherence length λ may turn out to be quite macroscopic. Especially at low temperatures.

In the framework of real physics, a quantum particle is a “portion” that cannot decrease further.

An example of this is a photon; it is a quantum particle at any wavelength, since any decrease in wavelength automatically leads to the formation of another photon, whose energy does not decrease (which is logical for reducing portions), but increases.

All other signs (Hamiltons, Schrödinger equations, consciousness, information, logos, etc.) are secondary in comparison with this real physical definition, since mathematics, abstract philosophy and metaphysics only describe real physical effects and phenomena (to one degree or another approaching reality), rather than replacing them.

Let’s continue the SS post, page 1, 3 days ago now, above:

…. particles are specific cyclical disturbances in the lattice, which appear if some the lattice’s FLE is impacted with transmission to it of some 4D momentum P, [“bold” means 4D vector in the 4D space with metrics (cτ,X,Y,Z)], and propagates after the impact in the lattice only as some sequential flipping of FLEs. In the momentum is infinitesimal, that causes propagation of “FLE flipping point” along some straight line in the lattice [and, correspondingly, in 4D space above] with 4D speed c, c= lP/tP.

However if the momentum isn’t infinitesimal, since the flipping point cannot propagate in the lattice with speed more than c, the flipping FLEs start to precess, and so the flipping point propagate, in first approximation, along some 4D “helix” with the speed that is determined by FLE parameters, and so is identical for all/every particles, and is equal to c√2; but the “helix front” propagates with 4D c.

Just this “FLE flipping point” is a particle, while the created closed cyclic FLE sequences are specific for particles cyclic binary algorithms, that move in the 4D space with 4D velocities c, having the momentum P=mc, and energy E=Pc=ћω, ω is the frequencies the algorithms tick with which.

Besides, what seems as rather rational, since follows from, or at least is consistent with, all experimental data, the “front projection of a particle’s helix” is the circle with radius be equal to the Compton length of the particle, λ=ћ/m, the “space” length of a particle’s algorithms is equal to λ, the logical length [number N of FLEs in an algorithm ] is N=λ/lP.

Really in Matter exist two main types of particles: “T-particles” that are created by directed along the specific spatial cτ-axis, which, if are at rest in the 3DXYZ space, move only in cτ-dimension with speed c, and so have inertial “rest masses” at attempts to accelerate a particle in “ordinary” well observable by human 3D space; say, that are electrons, protons, etc.; a T-particle at rest in 3D space has momentum P0 and inertial mass m0.

- and “S-particles” that are created by directed along some 3D space line, now known only photons, that move in 3D space with 3D c – i.e. with standard “speed of light”.

If a having rest mass particle is impacted by some 3D space momentum, p, – what mostly happens in physical practice, its 4D momentum P=P0+p, so the observed 3D projection of its 4D “helix” is a “de Brogile wave” with length λB=ћ/p.

Besides all [at least fundamental] particles FLE flipping points, which move along 4D “helixes”, have, correspondingly, 4D “angular momentums” relatively to “helixes axes” be equal to ћ, the observed 3D projections of these “angular momentums” is observed in in 3D space as that the “particle’s spin” is ћ/2.

The post is rather long already, so more in a next post, now

Cheers

Let’s continue the SS posts series on pages 1, 2 ,above:

- in the post wordings “4D “helix”” and “4D“angular momentum”” are in quotations, since in 4D space the 4D angular momentum M as vector production Pxr doesn’t exist - as that doesn’t exist in mathematics, similarly 4D rotation axis doesn’t exist as well. So 4D angular momentum – which really essentially determines particles states at interactions, is some either tensor or “bi-vector”, that M 3D projection is 3D vector “spin” really only partially reduces some uncertainty of current state of a particle – additionally concretizing the fundamental “logical” uncertainty [ see in the first SS post on page 1].

So, though a particle constantly exists as a currently flipping the lattice’s FLE, i.e. as “~Planck length size point particle”, since the observed QM scale is extremely larger than Planck scale, particles are observed as “ways” – what in mainstream QM is called “ the wav-particle duality”, the flipping FLE state isn’t described by the point’s 4 independent coordinates, but by some combinations of all, at least utmost universal 4 coordinates in the 4D space above.

That essentially is described by mainstream QM, but QM really is based on completely transcendent postulates

[say, in QM “spin” is postulated as a “quantum number” of “particle-infinitesimal point”, what is, of course, strange; in QM elementary T-particles have spins=ћ/2 for/by some mystic reason/way – while why? – see above, including so from that neutrinos are fermions completely for sure it follows that neutrinos have non-zero rest masses; in QM all given type particles for some mystic reason are identical – while that is quite natural in the SS&VT model – that are simply copies of the same informational systems “algorithms”, what is typical in information, etc.],

- so, say, in QM a having rest mass [T-] particle, if is at rest in 3DXYZ space, has uniform probability to be in any point in whole infinite space, what looks as again strange – and really that doesn’t happen, of course; really in this case T-particle moves only in the cτ-dimension with speed of light, occupying at that in the 3D space only a 3D volume that has size ~ particle’s Compton length.

Every change of everything in Matter on Planck scale happens eventually as a sequence of elementary changes on 1 bit, but further that really also essentially happens on QM scale, say, at some particle’s 3D angular momentum observable spin-flip events,

- and that is always also happens as changes of the physical action on the elementary step be equal to Planck constant ћ [ including that happens at creation of some particle, which is some “gyroscope” with the “angular momentum” be equal to ћ].

Correspondingly in Matter really the physical action, S, isn’t some abstract mathematical function, which, for unknown , reason, is very useful at analysis of motion and interactions of bodies, that is fundamental physical phenomenon, that has not lesser importance for material objects/events/processes, than energy and momentum, when - “the least action principle” really is as that “in Matter everything happens provided minimum number of binary elementary logical operation/ changing of information in an material object/system minimum number of bits”.

Note also, that so really QM uncertainty with a well non-zero probability isn’t completely arbitrary – as that is in Heisenberg inequality ΔpΔx≥ћ/2, it is determined by just the action: every change happens provided the condition ΔS=ћ:, as, say, ΔpΔx=ћ;

- and ΔtΔE=ћas well, and such uncertainty is experimentally observed; however – see 2-nd main paper of the SS&VT Planck model, https://www.researchgate.net/publication/367397025_The_Informational_Physical_Model_and_Fundamental_Problems_in_Physics , really it this equation should be as Δ(ct)ΔP=ћ.

Cheers