A Quantum Model having a Mechanism for Wavepacket Reduction (Revised)

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Jan 22, 2022, 8:07:28 AM1/22/22
In the field of elementary particle physics, the particle model seems to have been widely accepted, in which it is assumed that there exist extremely small elementary particles (regardless of whether point-like or string) in reality, and that the wave function is to give the existence probability of a particle.

By double slit experiments, however, it is indicated that a single quantum can interfere with itself. With the particle model, it seems unreasonable to consider it explicable that interference fringes are to be formed in double slit experiments with flux of quanta that is so sparse that only a single quantum can be present at a time.

[See, for example,
Taylor, G.I. (1909).
"Interference fringes with feeble light"
Proceedings of the Cambridge Philosophical Society. 15. pp. 114--115.

A. Tonomura et al. (1989).
"Demonstration of single-electron buildup of an interference pattern"
American Journal of Physics. 57, 117]

So, a quantum cannot but be considered to be more of a wave than a particle. In fact, quantum waves can be so defined as to include particle features. More specifically, quantum waves are assumed to be countable and to be able to be each localized in an area that is so small that the wave can be seen as a particle. Anyway, quantum theories are formulated as theories of waves, and particles appear only in interpretations.

If quanta are waves, it means that quanta are basically considered to be only phenomena in the space-time with quantum fields, which is considered to be the only substance existing in the most extreme sense.
[Consider a long tape stretched flatly and horizontally. If you pinch the tape at a point and flip upside down, a couple of twisted parts emerge on both sides of the flipped point.
The long tape is a metaphor for one dimensional space, and the pinch and flip of the tape is that for creation of particle-antiparticle pair.]

In the following, a novel quantum model is to be proposed that has a mechanism for wavepacket reduction.

The features of the proposed model are:

Though a quantum behaves as a wave, it maintains its oneness while it exists.

A free quantum carries its energy and momentum as a whole.

For each quantum not to spread out unlimitedly, a kind of cohesive force, which may be like surface tension, is to be exerted.

[As an example, consider a photon traveling all the way from a far-away star. Without any cohesive force or some sort of cut-off mechanism, the quantum cannot but diffuse, be diluted beyond measure and end up disappearing.]
[Suppose a photon with no cohesive force is traveling in the z-direction. If x and y components of the momentum of the photon are both absolutely zero (xy-spectrum width = 0), the quantum wave of the photon is already unlimitedly spread. Otherwise (xy-spectrum width is not zero), the quantum wave will spread unlimitedly.]
[According to the traditional interpretation of quantum physics, one may assume that, as soon as the photon is detected, the existence probability of the photon completely vanishes at all points including those millions or billions of light-years away. However, any theory has its own applicability limit. From a commonsense perspective, the above assumption seems to be well beyond the limit. The problem may be which is acceptable, the above mystical assumption or introduction of unknown cohesive force.]

By virtue of the cohesive force, each quantum has only a finite size in the space even if it has specific energy and momentum.

[A free and isolated quantum is considered to be substantialized as a finite-sized wave packet (having finite length and width) and to have specific energy and momentum (if not, conservation laws can never be valid). According to the traditional theory, however, finite-sized wave packet and specific energy-momentum are not compatible. Introduction of the cohesive force makes them compatible.
So, the Kennard (not Heisenberg) inequality is supposed to fail.]

Considering experiments using half mirrors and mirrors with light that is so feeble that only a single photon can be present at a time, a free quantum wave seems to be able to change shape enormously.

However weak the cohesive force is, Feynman diagrammatic calculation method is to be fundamentally changed and renormalization may get to be needless.

Let's consider a process, A+B -> C, where each of A, B and C stands for a quantum (elementary particle).
If a part of wavepacket of quantum A and that of quantum B get to overlap one another in the space, both overlapped parts are to be compressed as their motions are impeded due to interaction between the quantum fields of A and B. Compression of overlapped part of each quantum wavepacket and the cohesive forces may result in a kind of mutual absorption between the quanta. If the domains of quanta, A and B, both reduce to the same point or extremely small area, the above process is to be able to take place.

In the case of a single-quantum double-slit experiment, A is a single quantum that is to interfere with itself, and B is on the screen.

What is acknowledged as an interaction through so-called virtual particle is actually an interaction with a kind of polarization which can transform into a set of quantum and anti-quantum.

The vacuum space fluctuates so that, in each quantum field, polarizations can occur at any time and place. Each polarization can transform into a set of quantum and anti-quantum, whose total energy and momentum are both zero.
What is acknowledged as an interaction between particle D and particle E through so-called virtual particle F is actually an interaction among quantum D, quantum E and a polarization in the quantum field of F, which is to transform into a set of quantum F and its corresponding anti-quantum whose energy and momentum are to cancel those of quantum F. If quanta D and F are to interact in the manner described in (4), quantum E and anti-quantum corresponding to quantum F are to interact in the same manner.

For example, let us consider electron-electron scattering.
If an electron is to absorb a virtual photon that is paired with a virtual anti-photon, which has negative energy, in the manner described in (4), the other electron is to absorb the virtual anti-photon in the same manner.

Then, Let's consider a process, G -> H+I.
This process is actually an interaction between quantum G and a polarization in the quantum field of H, which is to transform into a set of quantum H and its corresponding anti-quantum whose energy and momentum are to cancel those of quantum H. If quantum G interacts with anti-quantum corresponding to quantum H in the manner described in (4), quantum I is created and quantum H is substantialized.

Particle-antiparticle pair can be produced when high-energy photon collides with a nucleus or the like. In this case, G is 'high-energy photon', H is 'particle', and I is 'antiparticle' that is created by exciting the anti-quantum corresponding to 'particle' by means of part of energy of 'high-energy photon'. It should be noted that no pair can be produced without a collision with a charged particle, which is to cause a reduction of quantum wave of photon.

A strongly accelerated particle with electric charge emits a photon. In this case, photon is created by direct stirring of the photon field. It should be noted that the shape of wavepacket of a strongly accelerated quantum with electric charge is to be distorted and intermittently reduce enough to emit a photon due to the cohesive force.

You may feel that the above quantum model is quite odd and half-baked, though I suppose that my model is leastwise better than that of Copenhagen, many worlds theories and so forth.

Jeffrey Rubard

Feb 13, 2022, 1:57:22 PM2/13/22
Sounds complicated.
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Oct 21, 2022, 2:13:17 AM10/21/22
I happened to come up with a cut-off mechanism.

After being created, the size of wave packet of an isolated free quantum is to expand steadily.
The motion of the quantum wave is impeded by polarizations in quantum fields which can interact with the quantum (cf. (4)-(6)).
So, a kind of refractive index is heightened inside the wave packet of the quantum.
Then, the expansion of the wave packet is to halt at a certain point (cf. optical fiber waveguide).

Just a half-baked tentative.
I wonder whether this tentative is nonsense or not.
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