Who sais, you?

There is nothing wrong with Schrödinger´s equation, the problem is its interpretation. This equation has been guiding for decades with excellent results. The issue is that it´s assumed to manage a compact superposition of solutions instead of a statistical development of eigenstates. In other words, a quasi-superposition of eigenstates that are present in 3D in a sequence of one-by-one at the rate of its energetic frequency (Planck´s periodic time tau). Not all together in superposition! This solves the measurement problem that reveals that only one eigenvalue is measured or observed; i.e., only present in 3D one eigenstate not all of them. It also solves other issues. I recommend this paper "Philosophy in Quantum Mechanics novel interpretation supports Einstein´s objection" DOI 10.21275/SR231215193142. Regards

Jose Oreste Mazzini

Dear Jose,

Your argument revolves around the idea that quantum mechanics should move away from the assumption of a superposition of eigenstates and adopt a model where eigenstates manifest sequentially in 3D, governed by Planck’s periodic time τ\tauτ. While I commend your effort to address foundational questions in quantum mechanics, your proposition is fundamentally flawed on several levels. Below, I address and refute your points one by one while establishing the ultimate truth:

1. The Assumption of Superposition of Solutions

You argue that a compact superposition of eigenstates is incorrectly assumed in quantum mechanics. Instead, you suggest a quasi-superposition where eigenstates appear sequentially, one at a time.

Superposition is not merely an assumption but an experimentally verified principle. The phenomenon of quantum interference, as observed in the double-slit experiment, directly demonstrates that all eigenstates exist simultaneously, interacting coherently in the wavefunction. Sequential manifestation cannot explain interference patterns without invoking non-physical ad hoc mechanisms.

Further, your model's reliance on a quasi-superposition undermines the linearity of the Schrödinger equation, which is the cornerstone of quantum mechanics. A sequential model would require rewriting the entire framework of quantum dynamics, contradicting decades of experimental validation.

2. Planck’s Periodic Time (τ\tauτ) Governing 3D Sequential Manifestation

You suggest that eigenstates appear one-by-one at the rate of their energetic frequency, governed by Planck's periodic time τ\tauτ.

Planck’s periodicity is inherently tied to the energy-time uncertainty principle (ΔE⋅Δt≥ℏ/2\Delta E \cdot \Delta t \geq \hbar/2ΔE⋅Δt≥ℏ/2), which ensures that time is not a discrete variable but a continuous parameter in the quantum framework. Your model misinterprets Planck's periodicity as a temporal sequence, which is unsupported by experimental results.

In the modern quantum field theory (QFT), time is treated as a parameter in a four-dimensional spacetime continuum, not a quantized sequence of events. Thus, your interpretation is inconsistent with the relativistic and non-relativistic frameworks of quantum mechanics.

3. Measurement Problem and the Observed Eigenvalue

You claim that sequential manifestation solves the measurement problem, as only one eigenstate is observed in 3D at any given moment.

The measurement problem is a profound issue, but your proposed solution does not align with experimental evidence or mathematical rigor. The collapse of the wavefunction during measurement is not a sequential manifestation of eigenstates but a probabilistic update of knowledge upon interaction with a measuring device, as described by the Born rule.

Decoherence theory further explains why only one eigenvalue is observed without resorting to sequential manifestation. It shows that interaction with the environment causes the superposition of states to appear as a single observed outcome due to the rapid loss of coherence.

4. Novel Interpretation Supporting Einstein’s Objection

You cite a paper advocating an interpretation of quantum mechanics aligned with Einstein's deterministic objections.

Einstein’s objections to quantum mechanics stemmed from his discomfort with non-determinism and locality. However, experimental violations of Bell’s inequalities decisively refute any local deterministic theory. Your reliance on Einstein’s objections disregards these empirical results and fails to address non-local correlations in entangled systems.

Moreover, deterministic models like Bohmian mechanics already exist and provide a deterministic alternative to quantum mechanics without rejecting superposition. Your proposed model neither matches the explanatory power of Bohmian mechanics nor offers additional predictive value.

The Way Forward

Quantum mechanics, as it stands, is not merely an incomplete framework riddled with assumptions; it is a well-tested theory supported by a century of experimental evidence. The core principles of superposition, entanglement, and wave-particle duality have been validated through phenomena like quantum interference, Bell’s theorem, and quantum computing.

If we are to move beyond the Schrödinger equation, it is not through rejecting superposition but by expanding our understanding through unification with general relativity and exploring quantum gravity frameworks. My own work, which proves that dark matter is ordinary gravity, exemplifies the need to ground such advancements in both experimental evidence and theoretical consistency.

Your model, while intriguing, lacks the rigor and alignment with existing evidence required to supplant the current quantum framework. I encourage a reevaluation of your assumptions and invite further discussion to refine your ideas within the constraints of established physics.

With respect, Sandeep Jaiswal

Dear Sandeep: Thank you for your response. And thanks again, because you did it with good arguments, let me clear it up:

1) The proposal of quasi-superposition goes together with the idea that the presence in 3D is random! Following the core issue in QM. The rate is given by Planck´s periodic time. This is proposed because all observations deal with only one eigenvalue, a reality that any QM theory must consider. In the double slit experiment the proposal embraces the phrase "stuff in a media." Which interprets nature as the coexistence of two entities; compact entities or elementary particles and the second is a wavy quantum space. This space fluctuates between the observable 3D and the 4th dimension Ctau. So, the particle is present in 3D meanwhile, its space is; a coexistence of two entities and not only one entity that behaves sometimes as particles and others like waves. The two-slit experiment is understood as the quantum space big enough to reach both slits and passes through divided, meanwhile, the particle is small that only passes through one of them. On each new fluctuation, the particle will appear "randomly" in the evolved space that develops a destructive interference when one part of the space at 3D overlaps with the other part at the 4thD... I´m attaching some papers that will make understandable this novel proposition, and continue in a next message.

Continuing:

2) Planck´s first equation reveals that energy is present in chunks. This proposal of a fluctuation between longitudinal dimensions (3D and 4thD Ctau) visualizes that an action "h" will be present in 3D in a time tau so its energetic presence is inversely proportional to this crucial time tau. A slow presence in 3D will be less energetic than a faster presence. This fluctuation reinforces the issue of 3D chunks of energy. Now, the first equation of QM can have a model of what is happening. This fluctuation can be represented with complex numbers and provides a way to manage phases in the equations. Heisenberg´s uncertainty principle is a consequence of dealing with some parameters at the 4thD with others at 3D; they can´t be analyzed together because their presence is out of phase. One exists first and then the other, not both together, and the order is important in revealing the non-commutative properties in QM. Please read the previous paper in Philosophy in QM and sorry when I use the word sequence without clearing that it is a "random sequence." I intended to describe a one-by-one presence but never intended to describe a predetermined sequence. Randomness is essential for understanding the arrow of time and why entropy tends to increase (attached paper).

Continuing:

4) Einstein´s objection to non-locality is overcome by the 4th longitudinal dimension. The realm of quantum mechanics deals with multiple valid states but their presence is just one at a time (measurement evidence). So, QM is poly deterministic and not a mono deterministic nor indeterministic. This is a semantic issue but it reveals the multifaceted presence of nature. A fleeting presence of one state in 3D is just that, the rest of the eigenstate still exists and will be randomly present opportunity. Einstein´s concern is overcome, nature doesn´t have a random existence (all the valid eigenstates exist in 4thD), it only has a random presence in 3D. The Schrödinger equation deals with these valid eigenstates. Hope this will clear up some of your questions and let me know if I can continue with more explanations, best regards

Jose Oreste Mazzini Juan Weisz & ResearchGate Community

Dear Jose,

Thank you once again for your thoughtful response and for the opportunity to explore these profound ideas together. Allow me to address the core points of your argument and introduce a broader perspective.

Critical Analysis of Your Interpretation:

The Science Beyond Science:

Let us now shift focus to a broader and deeper perspective, one that goes beyond the confines of classical and quantum science. There exists a realm that many wise thinkers and sages refer to as spiritual science. This higher science might provide answers to the mysteries and paradoxes that conventional science struggles to explain.

Closing Thoughts:

While we engage with quantum mechanics and its mysteries, it is worth acknowledging that the answers we seek may not lie within the confines of equations or experiments alone. There is a higher truth, a unified science, that bridges the material and spiritual realms. To understand quantum mechanics fully, we must open ourselves to the possibility of this deeper reality.

Thank you for this meaningful discussion. I look forward to your thoughts and the opportunity to explore these profound ideas further.

Best regards, Sandeep Jaiswal

Hi Sandeep: Thanks for having this conversation with such good arguments. As you can imagine, I´m trying to propose something different from what has already been done, embracing the proven equations at all moments you ask, What alternative does science have?). I just change the interpretation with some little changes; if not, the conclusions will be the same as actual knowledge.

1) In the double-slit experiment, I propose that the quantum space is divided into two maintaining their coherence (oscillating together). When one zone is at 3D and the other part is at the 4thD, then destructive interference is produced. Meanwhile, when both zones are in a nearer phase, the compact entity (elementary particle) can be present in that mixed space. The particle is present where the evolution of its two divided space permits. On each new fluctuation, the particle will be present with a random eigenstate and will have a random location in this evolution of its own mixed space. When it arrives and gets measured, its location will just be in its actual last random position. Like jumping between its interfered space in each new fluctuation. This is consistent with the proposal that there is a fluctuation between 3D and the 4th D. Everyone recognizes that there are at least four dimensions, but all take them exist together. I propose to consider that the 4thD is out of phase with the 3D; an oscillatory condition at the rate of its energetic frequency. Please read the previous attached paper named "Double slit experiment".

2) The 4th dimension is Ct, from Minkowski the "t" is taken as the time evolution of events; that is Ok. My proposal is to begin joining Relativity with quantum revelations; with that in mind, I take the essential quantum time tau (E = h/tau) and Ctau will manage the energy wavelength. That opens new doors! For example, Poincaré invariance (Delta r)^2 + (Delta iCtau)^2 is now understandable as a link between space and energy. When energy increments, iCtau is smaller and so the space gets smaller values (space contraction). This is also in accordance with Einstein´s general relativity, that space and time are linked with energy. The quaternions can manage this correctly, a scalar Ctau with the three vectorial components of space; the 4thD is necessary to provide knowledge of the spatial values. The spatial values need this extra information of the 4thD that contributes to the gamma factor that they have. The special values by itself are insufficient if energy is not included! I notice that this is new for everyone, but if you think about it for a while you will see that "iCtau" contributes a lot and is fundamental for managing space.

3) Locality at the 4thD: Bell´s theorem revealed that quantum entangled particles are non-local at the 3D and so my proposal. The great difference is that the quantum system has four longitudinal dimensions. Therefore, my proposal says that coherent systems are together at the 4thD, so they are together in this dimension; i.e., locally at 4thD. Note that Minkowski's view of the 4thD as event analysis doesn´t contribute to this thought, meanwhile, Ctau does! This locality at the 4thD follows all coherent systems, like in the divided space of the Double slit experiment or when some photon passes through a beam splitter, etc. The 4hD is a longitudinal dimension and coherent systems are together = local meanwhile their 3D location is separated.

I hope that this clears up a little this proposal. It is a novel approach that needs some time and analysis so please continue asking and challenging this idea.

Best regards Oreste

Dear Sandeep:

I´ve returned home and will continue with you the last implications of consciousness and a universe bigger than what is now considered.

Concerning consciousness my thoughts go in the direction that they didn´t exist before animals and humans. The vegetable kingdom has more reserves and the inanimate kingdom of inert entities definitely do not have consciousness. So, my best thought about QM can be that it is independent of human consciousness. The universe is assumed to be around 13.7 billion years old and our Earth and Solar system are a little more than 4 billion years old. The animals and ourselves much less, aside from that consciousness can be in the abstract universe and not in the physical or tangible universe. Meanwhile, the physical universe and its laws or behavior have been present since the Big Bang (our best understanding of the tangible universe).

However, my proposal opens new doors by revealing that the 4thD can exist independently of the observable 3D. If I´m on the correct path, science will consider that we live 50% in 3D and the same amount of time in 4thD; that is a revolutionary view of existence! For all the tangible existence including the inanimate kingdom, as well, as the other kingdoms including ourselves. Note that coherent systems are together or "local" at the 4th dimension even when they are separated in 3D.

Many new ideas and considerations will follow IF (IF, IF, IF) this proposal nails up the missing parts of modern physics.

The first step is to consider the 4thD as Ctau and not the time event of Minkowski. The second assumption is to consider that the 4thD exists in oscillation with the observable 3D. The third step is to embrace that the presence in 3D of the eigenstates is randomly one-by-one; a minor but important conclusion that changes superposition into quasi-superposition. This randomness and quasi-superposition explain the arrow of time and entropy (please read the previous paper attached) ... This will be the first time, since the use of the scientific method, that an exact science such as physics will give some place to metaphysical considerations. Commonly science is quite a part of this thought.

Many issues will be overcome and new ones will need to be considered.

I hope that this explanation will inspire you in your metaphysical insights.

Best regards Oreste

Jose Oreste Mazzini

Dear Oreste,

Thank you for your intriguing insights. Consciousness, as spiritual truth reveals, is eternal and predates the Earth and Big Bang. It is God—the ultimate truth, existing in all things, animate and inanimate. The soul is universal, pure, and the same across all forms, even if its expression varies.

Your hypothesis of Cτ as a 4th dimension oscillating with 3D offers a fresh perspective, but it requires empirical validation and alignment with observable phenomena like quantum entanglement and entropy. Quasi-superposition, while interesting, must be rigorously tested to substantiate its claims over traditional superposition.

Physics embracing metaphysical considerations is a bold step forward. However, frameworks like Cτ must reflect the divine order and eternal principles governed by God, who sustains all dimensions. Consciousness is the unifying essence of the universe, and any scientific model must align with this truth.

I look forward to continuing this meaningful discussion.

Best regards, Sandeep Jaiswal

I agree with Sandeep Jaiswal. As you say, we need to "model the behaviour of particles". It may depend on what we want to "particle", like a particle's movement, its energy and its reaction with anything.

Sunao Sugihara

Dear Sunao,

Thank you for your thoughtful concurrence and support for the points I’ve outlined so far. It’s encouraging to see our perspectives align, particularly on the enigmatic nature of quantum mechanics and the limitations of the Schrödinger equation in fully describing particle behavior. Your insight into the interplay of observation and quantum states adds depth to this discussion, and I appreciate the opportunity to build on it further.

Let’s delve into the concept of duality and the question of how a quantum particle can seemingly exist in two places at the same time. The notion of wave-particle duality often perplexes scientists and philosophers alike. Traditionally, the particle-wave duality is understood as a particle (like an electron) behaving as a localised particle in some experiments and as a delocalised wave in others, depending on the method of measurement. However, if we interpret the behaviour of particles as “a particle moving in a wave,” as you suggest, it simplifies this apparent duality and aligns with practical logic.

You rightly point out that the behaviour of a particle—whether it appears as a wave or a particle—depends on the context of observation, but not necessarily on the specific sensor or detection method. This indicates that the mode of observation influences the outcome, but not due to any technical interference or flaws in the sensing equipment. If this is true, we must ask: What determines the particle’s state?

This brings us to the heart of your suggestion and my question: Could the particle itself possess some form of intelligence or consciousness? Recent discussions in quantum mechanics increasingly lean toward interpretations that involve consciousness or the observer’s role as more than a passive presence. For instance, the collapse of the wavefunction—a probabilistic mathematical description of possible states—upon measurement could imply that particles are not merely inert but interact with their surroundings in ways we don’t fully understand.

Intelligence or Consciousness?

The idea that quantum particles might have a form of proto-consciousness or embedded intelligence is speculative but worth exploring. If a particle “chooses” to behave as a particle or wave based on the context, it suggests an internal mechanism that is not random but informed by the environment. This choice-like behaviour, as you highlighted, seems independent of the mode of detection. Whether we use photon detectors, electron microscopes, or any other sensor, the particle retains its ability to display dual characteristics.

Could this be evidence of a fundamental form of intelligence? Possibly. The idea aligns with interpretations such as Wheeler's "participatory universe," which suggests that observation and reality are deeply interconnected. Moreover, this intelligence could be reflective of a broader, universal consciousness—a notion that resonates with spiritual and metaphysical frameworks as well.

By viewing a particle as something moving within a wave, the apparent duality dissolves into a single, coherent picture. The wave, in this interpretation, is not an alternate state but the medium or path through which the particle travels. This explanation aligns with de Broglie’s pilot-wave theory, which posits that particles are guided by a wave-like field. The practical logic of this view eliminates the need for paradoxical duality and instead introduces a dynamic interplay between particle and wave.

In this sense, what we observe as “duality” is perhaps not duality at all but the interaction between two complementary aspects of the same phenomenon. It’s a limitation of our conceptual framework, not nature itself, that forces us to categorise these behaviours as distinct.

Final Thoughts

Your perspective beautifully reinforces the idea that quantum particles may not conform to classical deterministic or probabilistic descriptions. Instead, they may operate on principles that integrate both particle and wave-like behaviours into a unified reality—one that challenges our understanding of intelligence and consciousness at the smallest scales.

The question remains: If intelligence exists at the quantum level, is it a fundamental property of all matter? And if so, could this be the bridge between physical science and the metaphysical? These are profound questions, and I thank you for advancing this dialogue with your thoughtful observations.

Looking forward to hearing your thoughts!

Warm regards, Sandeep

Dear Sunao Sugihara :

In the above chat, I gave a proposal on how to think in quantum terms. An analogy is to think in a card game: classical mechanics is like having one card and quantum mechanics is having the Joker (multiple values, more powerful than one card). But the issue is that when you try to observe this wild card you will just see one of its valid values. Many observations will reinforce that the Joker manages multiple observable values. How can a model represent this? That is what science has been trying to solve for the last century. The pilot wave gave a possible solution but it contained a deterministic scenario. It´s possible to think that the wave is space itself waving between 3D and 4th D and the particle exists randomly in it (please read messages to Sandeep). This randomness will provide the polydeterminism or non-determinism observed in quantum realms.

I propose to think that quantum solutions are four-dimensional and not only three. What we can observe is just 3D information contained in the 4D. Like having a dice with six values; one on each face but 3D only reveals the top face. Please see the next picture attached; a Joker with 10 values spinning at the rate of its energetic value (1/tau = E/h; the frequency of Planck´s equation), when it is observed you will see only one of them but it really contains 10 of them.

Sandeep Jaiswal and many others are thinking in a conscious possibility. That is a humanized thought; it is good and there are many developing this idea. Meanwhile, I´m alone without any support and I think that this 4D idea deserves some analysis. For me, quantum diversity is an issue of information, and it is fundamental in nature. When an interaction or observation occurs, then the system acquires this value and the other values will no longer be available; i.e., a collapse situation. Not a humanized knowledge or awareness, a simple extra information in the quantum system. I hope that this and previous ideas will inspire you and Sandeep. Regards

Thank you for your suggestive idea, Sandeep Jaiswal.

Physical quantities of quantum particles, such as consciousness, are essential for transferring information. I will soon define consciousness.

First, physical quantities are particles with 1) mass, 2)spin, 3)speed, and 4) precession. Mass and speed generate energy, and spin forms precession and magnetism. Now, I regard "consciousness" as a kind of information which could be substantial, weak, and easily transferable. Sometimes, it is difficult to communicate between "consciousness". I don't think the concept resembles de Broglie’s pilot wave. Finally, the fundamental existence is particles. This is my idea, and now I am doing my best to make a particle equation that involves four physical quantities.

A four-dimensional Joker with 10 values; a 3D observation will just "see" the top face value.

What is wrong with Quantum Mechanics

Even though QM constitutes the main pillar of Modern Physics, foundational problems regarding the physical basis and weird outcomes of Quantum Phenomena are still being actively debated.

De Broglie's hypothesis of matter waves implied that the dynamic characteristics of a micro particle in motion, can be ascribed to the wave characteristics of the wavelet accompanying the particle. The Schrödinger equation models the matter-wave interactions through wavefunction ψ and effectively serves as the foundation of QM.

The Coulomb potential energy of the proton electron pair in Hydrogen atom is essentially the negative interaction energy between their superposed electrostatic fields which is inversely proportional to their instantaneous separation distance. Assuming the proton to be relatively fixed at the origin of an appropriate coordinate system, the potential energy of the orbiting electron will be a function of instantaneous position coordinates of the electron. This has not been properly modeled in the Schrödinger equation.

As per the Copenhagen interpretation of QM, the intensity of the wavelet is interpreted as the probability density for the location of the micro particle. That is, in QM, the location of the center of a micro particle in motion is assumed to be smeared across the whole region of the wavelet as position probability density.

The energy released from the proton-electron field interaction, as given by Coulomb interaction, is converted into the kinetic energy of the electron, assuming the proton to be relatively at rest. As the kinetic energy of a particle is contained in its ψ wave field, potential energy of the proton-electron pair may signify the transfer of interaction energy released from the combined electrostatic field of the system to the ψ wave field of the electron. The Schrödinger's wave equation is intended to describe the variations in ψ wave field of a moving particle as a result of such energy transfers.

The electrostatic field energy density can be regarded as field parameter which is defined at all space points of the associated field at any instant of time. On the other hand, potential energy is the interaction energy depending entirely on relative location of the electron with respect to the proton at any particular instant and is not defined at any other space point at that instant.

The term 'potential energy' is not applicable for a single isolated particle due to absence of any interaction. It has a meaning only for two or more interacting particles.

If at any instant t, the proton is located at point O, the origin of coordinate system and the moving electron is located at point A with position vector R, then the potential energy of the electron will depend on the magnitude of R and represented by V(R). It will not be a function of the coordinates of field point Q(r) that defines the ψ wave field. That is, when the wave function is represented as ψ(r,t) to characterize the matter-wave field of the electron with instantaneous position vector R, the potential energy term cannot be represented as V(r) in place of correct representation V(R).

Even though a constant total energy E or a stationary energy state implies the constancy of sum of K.E. and potential energy of the system, there could still be tremendous energy exchange oscillations between the kinetic and potential energies of the interacting particles in a so-called stationary state.

In the Schrödinger's original wave equation, the potential energy is expressed as a function of the coordinates of general field point Q(r), instead of the coordinates of instantaneous location A(R) of the particle. This discrepancy is not a simple or inadvertent mistake in the Schrödinger's wave equation but rather a serious conceptual mistake with far reaching consequences.

This mistake is continued with throughout Quantum Mechanics, where the potential energy term V(r) is often replaced by e.ϕ(r); with scalar potential ϕ(r) treated as a function of coordinates of general field point Q(r) rather than a function of coordinates of instantaneous location A(R) of the particle. The greatest temptation for permitting this mistake, might have been the consequent ease of solving the Schrödinger's equation by treating the potential energy term V(r) as spherically symmetric and independent of time.

By using the Sommerfeld elliptical model approach, we can compute an elliptical electron orbit for 1s Hydrogen atom. From such computations we find that the kinetic energy of the orbiting electron varies from a minimum of about one eV to a maximum of about 190 eV. This fluctuation in kinetic energy is also accompanied by a corresponding fluctuation in potential energy V(R) of the orbiting electron. This much fluctuation in the potential energy V(R) occurs in just about 1.5x10-16 seconds time period. That is why the assumption of time invariant potential energy term in original Schrödinger's equation is completely wrong.

Solutions of the erroneous Schrödinger's equation for different energy states of electron in Hydrogen atom appear to describe only the time averaged charge density distributions around nucleus and not the trajectories of electrons. That is because the potential energy term V in the equation has been assumed as time invariant and not dependent on the instantaneous position coordinates of the electron. Since the position coordinates of the electron have been erroneously omitted in the input to the equation, naturally the exact position of the electron is lost in the final solution. Ultimately this has led to all weirdness and fantasy in physical interpretations of QM.

Article Wrong Potential Energy Term in Schrödinger’s Equation for Hy...

Article Dynamic Electron Orbits in Atomic Hydrogen

The fundamental problem giving rise to the conceptual mistake in Schrödinger’s Equation is much deeper and intricate which has not been addressed for more than a century. That fundamental problem is the ambiguity in the notion of Fields in general and the electrostatic field in particular. As per the modern concept, a field is a fundamental physical quantity that could independently exist at each and every point of the space occupied by the field. But Maxwell had supposed that the deformation of luminiferous aether, along with associated stresses and strains, represented various fields of physics including the electromagnetic field.

Intrinsic Electric Field

Consider one electron located at an isolated point P in space - far removed from all other charges. This isolated electron will produce an (intrinsic) electric field around point P that spreads everywhere in surrounding space. This intrinsic electric field or the electrostatic field of an electron is an integral part of the electron charge and does not depend upon the presence or absence of any other charge in its vicinity - not even any test charge. In Maxwell's terminology of 'deformations of aether' we might call it 'strain field' or 'strain wave field' around the electron and consider it as an integral part of the electron structure - whatever it be.

Coulomb Field

However, for practical applications we quantify this electric field of the electron by measuring its interaction with a positive test charge positioned at a certain point Q at distance r from point P. The force on second charge or test charge is caused by the mutual interaction between the electric fields of the two charges and is governed by Coulomb's Law of electrostatics. The intrinsic electric field of an electron when quantified with a test charge, using Coulomb's law, may now be termed as Coulomb electric field of the electron. This Coulomb field of the electron will map the force acting on test charge located at Q as well as map the interaction energy released due to the mutual interaction of the superposed intrinsic electric fields of the electron at P and test charge located at Q.

Ambiguity

Mapping of the forces and energies for different locations Q of the test charge through the Coulomb field has introduced a major ambiguity in the notion of Electric Field of the electron. Ambiguity is in the lack of distinction between the Intrinsic electric fields of isolated electron and isolated test charge and the Coulomb electric field of their interaction forces and energies. Moreover, this mapping of interaction forces and energies cannot represent a physical field since the forces and energies mapped at different field locations Q1, Q2, Q3 etc. do not physically exist when the test charge is physicall located at Q. Unfortunately, in Modern Physics the Coulomb electric field is de-facto treated as the Intrinsic electric field of the electron.

Conceptual Mistake in QM

In the Time-Dependent form of Schrödinger equation, Psi wave function is represented as ψ(r,t) and the PE function is represented as V(r). Since V(r) is assumed to be independent of time, ψ(r,t) is then split into a product of two functions, first function f(t) dependent on time parameter and the second function ψ(r) which is independent of time. Actually, however, it is fundamentally wrong to assume time independence of the PE function V(r) for the proton electron pair. Let me explain why.

Potential Energy as Interaction Energy

A significant portion of the mass energy of the electron is actually contained in its electrostatic field. The field energy component of the electron mass is an integral part of the electron and is not dependent on the existence of any other charge or field in its vicinity. Let us consider a proton and electron pair separated by distance R. Their respective electrostatic fields will get superposed almost throughout their spatial extension. Consequently, the combined field energy of the proton-electron system, being proportional to the square of the resultant field strength, will be slightly less than the total sum of the individual field energies of the isolated charges. This reduction in the combined field energy of the proton-electron system, is precisely the negative interaction energy due to the Coulomb interaction and is known as the negative potential energy of the proton electron pair. Therefore,

Potential energy of proton-electron pair = V(R) = -e2/4πε0R . . . (1)

Or, interaction energy released by the system = |V| = e2/4πε0R . . . (2)

The energy released from the proton-electron field interaction, as given by equation (2), is converted into the kinetic energy of the electron, assuming the proton to be relatively at rest. As the kinetic energy of a particle is contained in its ψ wave field, potential energy of the proton-electron pair may signify the transfer of interaction energy released from the combined electrostatic field of the system to the ψ wave field of the electron. The Schrödinger's wave equation is intended to describe the variations in ψ wave field of a moving particle as a result of such energy transfers.

It is therefore obvious that the potential energy of an electron with respect to a proton at distance R, represented as V(R), cannot be regarded as a field parameter in the sense that it does not represent any entity distributed in space. The potential energy is the interaction energy depending entirely on relative location of the electron with respect to the proton at any particular instant and is not defined or existing at any other space point at that instant.

Total Energy E as externally supplied or removed energy

The total energy E of a system of two interacting particles is intended to represent the sum total of mass energies, including electrostatic field energies, plus any external energy added or subtracted from the system. In actual practice however, the mass energies of the interacting particles are regarded as invariable constant and removed from consideration. Therefore, the total energy E of a system is assumed to be zero when the particles are infinitely separated. When the particles approach one another to a separation distance R and their fields get superposed, their potential energy and kinetic energy still sum up to zero if no external energy is supplied or removed from the interacting system. In all other cases, when some finite energy content is either added to or removed from the system, sum total of the potential and kinetic energies is a finite number which is called the total energy E of the interacting system.

E = K.E. + P.E. = T + V(R) (3)

Total energy E is +ve when this amount of energy is externally added or supplied to the system of interacting particles and is -ve when it is extracted, or taken out of the system. Generally, a negative E will represent a bound state of the system of interacting particles and referred as binding energy of the system. When total energy E gets removed or emitted out of the system, this energy is ultimately extracted from the mass energies of the interacting particles. Even though a constant total energy E or a stationary energy state implies the constancy of sum of K.E. and potential energy of the system, there could still be tremendous variations in the instant to instant kinetic and potential energies during the periodic motion of interacting particles.

As the location of center of the electron keeps changing from instant to instant, the trace of this movement as a function of time t is called the Trajectory of the electron represented as R(t). When at a given instant t2, location of the electron R(t2) = R2 and the corresponding PE of the proton electron pair is given by V(R2) = V(R(t2)) = -e2/4πε0R2

Therefore, when the PE of the proton electron pair is V(R2), then the electron is located at R2 at that instant. That is, just as all different locations of the electron on its trajectory R(t) cannot be simultaneously occupied by the electron, similarly all possible PE terms V(R(t)) cannot be simultaneously acquired by the proton electron pair.

Hence, when ψ(r,θ,ϕ) wave function is defined or 'exists' at all space points P(r,θ,ϕ) at any instant t, the corresponding PE term V(r) cannot be assumed to be defined or existing at all space points P(r,θ,ϕ) at that instant. The corresponding PE term will surely depend on the instantaneous location of the electron on its trajectory R(t) at that instant. The implication of wrongly assuming the PE term for the proton electron pair as a time invariant space function V(r), is that we are implicitly assuming the corresponding location of the center of electron at all space points P(r,θ,ϕ) for all times. That is, in the formulation of the mathematical representation of proton electron interaction in QM, we are inadvertently smearing the location of the electron over whole field of the Psi wave function. This is precisely the mistake in the formulation of Schrödinger's wave equation which has lead to all weirdness in QM.

Therefore, the correct representation of the PE term for proton electron pair in Schrödinger's wave equation should be V(R(t)) which is no longer time invariant. However, during last hundred years or so QM has consistently focused and refined the mathematical representations of the TOTAL ENERGY terms for Hydrogen atom, due to ever more refined feedback from the spectroscopic data. The above mentioned conceptual mistake in the PE term did not adversely affect the representation of TOTAL ENERGY term but only corrupted the kinetic energy term. That is why after a splendid contribution of Sommerfeld in developing elliptical electron orbits for Hydrogen atom, no further progress could be made in QM during last hundred years or so, for obtaining more refined and accurate trajectories of the electron in Hydrogen atom.

Article Wrong Potential Energy Term in Schrödinger’s Equation for Hy...

Article Dynamic Electron Orbits in Atomic Hydrogen

Gurcharn Singh Sandhu

Dear Gurcharn Singh,

Thank you for your detailed and thought-provoking response to my question. Your explanation of the intrinsic electric field, Coulomb field, and the potential energy term in the Schrödinger Equation raises critical issues that merit careful consideration. I appreciate your effort in dissecting the ambiguity in the concept of fields and their role in quantum mechanics. Let me address your points systematically while aligning them with my research and stance on this matter.

Your distinction between the intrinsic electric field of an isolated electron and the Coulomb field resulting from interactions with a test charge is compelling. This clarification rightly highlights the inherent ambiguity in conflating intrinsic and interaction-based fields. However, while this distinction offers a clearer conceptual framework, its implications for quantum mechanics might not require a fundamental overhaul as suggested. Instead, the ambiguity lies in interpretation rather than the mathematics itself. The Schrödinger Equation does not inherently depend on the precise delineation of intrinsic versus interaction-based fields but rather treats the potential energy term as a scalar representation of interaction forces.

You argue that assuming the potential energy term V(r)V(r)V(r) as time-invariant introduces a conceptual mistake, leading to the smearing of electron location over the Psi wave-function. While this is a valid critique, it stems from a broader philosophical debate in quantum mechanics regarding the nature of the wavefunction.

The Schrödinger Equation, as formulated, is a probabilistic framework rather than a direct depiction of physical trajectories. The time-independence of V(r)V(r)V(r) is a simplification to facilitate tractable solutions, particularly for stationary states. When dealing with dynamic systems or time-dependent interactions, time-dependent Schrödinger Equations (TDSE) are employed, which inherently incorporate variations over time. This approach has shown remarkable success in explaining quantum phenomena without the need to redefine potential energy as V(R(t))V(R(t))V(R(t)) for stationary systems.

Your point about the energy exchange between potential energy and kinetic energy is well-taken. However, this periodic exchange is implicitly captured in the time-dependent behaviour of the wave-function itself, even if the potential term is treated as time-invariant for certain cases.

Your critique of quantum mechanics being “stuck” for the past century due to this issue requires nuanced consideration. Quantum mechanics, including the Schrödinger Equation, has continuously evolved, incorporating corrections like relativistic effects and spin-orbit coupling. While it is true that the exact trajectories of electrons remain elusive, this stems from the fundamental nature of quantum systems, where uncertainty is intrinsic and not a failure of mathematical representation. The advancements in Quantum Field Theory (QFT) and experiments like quantum entanglement validations underscore that the framework, while imperfect, continues to offer profound insights.

In my research, I have explored the limitations of existing quantum mechanical frameworks, particularly their inability to explain phenomena like dark matter and dark energy comprehensively (e.g., DOI: 10.54105/ijap.B1040.103223). However, I advocate for refining and expanding these frameworks rather than discarding their foundational elements.

Your proposal to redefine V(r)V(r)V(r) as V(R(t))V(R(t))V(R(t)) aligns with a dynamic approach but may not fundamentally resolve the perceived “weirdness” in quantum mechanics. The probabilistic nature of quantum systems and the non-locality exhibited in experiments like entanglement suggest that the issue lies deeper than potential energy definitions—it lies in our interpretation of quantum reality.

Your critique invites an important conversation about how we conceptualise fields, energy, and quantum mechanics' foundational equations. While I acknowledge the clarity your distinctions bring, I believe the issues you highlight reflect the intrinsic complexity of quantum systems rather than a flaw in the Schrödinger framework itself. Moving forward, it is essential to integrate these nuanced perspectives into broader quantum theory without disregarding its foundational successes. As science progresses, these debates will undoubtedly bring us closer to a unified understanding of reality.

I deeply value your contributions to this discourse and look forward to exploring these ideas further.

Warm regards, Sandeep

I agree, we need Integration and Refinement of Digital Physics, Unifying Quantum and Classical with a Calculation: A Formal Approach to Subparticles and Discrete Universe Frames something that makes more sense like a frame - by frame discrete unverse that explaiins instant communication transfer -

Obviously!

https://www.researchhub.com/paper/8579118/integration-and-refinement-of-digital-physics-unifying-quantum-and-classical-with-a-calculation-a-formal-approach-to-subparticles-and-discrete-universe-frames

Integration and Refinement of Digital Physics, Unifying Quantum and Classical with a Calculation: A Formal Approach to Subparticles and Discrete Universe Frames

Given grant money for reviews on these papers! 150 USD each, up to 1000 USD

When reading this heading and the resultent discussion content, I was sent back in my mind to the days of my own research and my need to revise everything to do with Schrödinger and Quantum Physics. This resulted in a detailed review of the Schrödinger Equation, together with the plausibility arguments considered and the method used. I summarized this review in chapter 7.2.2 on the Schrödinger Equation of my book “Physics in 5 Dimensions” and this discussion made me look at the chapter again: - …. This covers a plausibility argument leading to the Schrödinger Equation and …. by following reasonable arguments … finds a differential equation that satisfies all four basic assumptions concerning the quantum mechanical wave equation … and it seems plausible to argue that the quantum mechanical wave equation might be expected to have the same form as in the general case where the potential energy V(x, t) does actually vary as a function of x and/or t (i.e. where the force is not zero); but we cannot prove this to be true. We can, however, postulate it to be true…..

To do this, … we therefore take the postulated equation as the quantum mechanical wave equation whose solutions give us the wave function which is to be associated with the motion of a particle of mass m under the influence of forces which are described by the potential energy function V(x, t). The validity of the postulate is judged by comparing its implications with experiment. And …. it should be pointed out that we cannot expect the Schrödinger equation to be valid when applied to particles moving at relativistic velocities…..

We can summarise the ideas …. by saying that the behaviour of a given wave function of a system is predictable in the sense that the Schrödinger equation for the corresponding potential energy will determine exactly its form at some later time in terms of its form at some initial time; but its initial form cannot be specified completely by an initial set of measurements and its final form predicts only the relative probabilities of the results of the final set of measurements.

I think it is important that we relate our ideas to the starting point of a topic and the basis on which it was originally developed. This requires diligence of course, and takes time, but without this approach we can easily view new ideas out of context and reach false conclusions.

The previous two discussion points from Gurcharn Singh Sandhu and Gurcharn Singh, clearly do follow the above approach and provide an interesting debate. Thank you.

Alan Clark

Alan Dennis Clark great work, but it cannot explain quantum scarring, and S-cat does not fit well anymore now that we have Carolina Figueiredo's research-https://www.quantamagazine.org/physicists-reveal-a-quantum-geometry-that-exists-outside-of-space-and-time-20240925/

• Figueiredo’s concept of quantum geometry (e.g., surfaceology and amplituhedra) shows a framework where quantum events do not require traditional space-time but rather emerge from abstract geometric structures. These ideas are consistent with a universe rendered frame by frame (Brown 2024), where outcomes are directly derived from geometric relations rather than continuous quantum wave propagation​​.
• The observed simplicity in particle interaction outcomes, as described in their works, supports the idea that complex systems can be reduced to straightforward updates in a frame-based model​​.
• The Feynman model is no longer the dominant model because it was incomplete and upon resloving this with a complete equation (Carolina Figueiredo 2024) created a system where S-cat is no longer needed!

The replacement of continuous Schrödinger dynamics with discrete frame transitions, as proposed in frame-based models, offers computational simplicity and direct alignment with observed phenomena like tunneling and entanglement​​​.

Conclusion: The inadequacy of the Schrödinger equation in a discrete, frame-by-frame universe becomes evident. The geometric approaches (Figueiredo) and meta-tagging mechanisms (Brown) provide a more robust framework, resolving inconsistencies while aligning with quantum gravity concepts and experimental observations.

Alan Dennis Clark Jesse Daniel Brown & Research Gate Community

Dear Colleagues,

Thank you for your continued engagement in this profound discussion. After a thorough review of the extensive dialogues on ResearchGate, including the insights from Alan Dennis Clark and Jesse Daniel Brown, as well as excerpts from my paper titled "Schrödinger Equation unfit for fundamental law" (DOI: 10.9790/4861-1505012633), I aim to provide a response as per below that addresses all raised concerns and integrates perspectives from various research collaborations:

1. Limitations of the Schrödinger Equation

The Schrödinger equation has been foundational in quantum mechanics, offering a framework for understanding quantum systems. However, several limitations have been identified:

• Real-Time Predictions: The referenced paper argues that the Schrödinger equation, being a second-order linear differential equation, is inadequate for describing the real-time motion of quantum particles, particularly when considering waveforms like square waves. This suggests a fundamental limitation in predicting quantum particle behavior in real-time.
• Relativistic Constraints: The equation does not account for relativistic effects, making it inadequate for particles moving at speeds comparable to light.
• Quantum Scarring: Phenomena such as quantum scarring, where quantum eigenstates exhibit enhanced probability densities along classical periodic orbits in classically chaotic systems, are not explicitly predicted by the Schrödinger equation.

2. Alternative Frameworks and Models

o address these limitations, several alternative and extended frameworks have been proposed:

• Dirac Equation: A relativistic wave equation that accounts for spin-½ particles, providing a more comprehensive description of fermions.
• Quantum Field Theory (QFT): A theoretical framework that extends quantum mechanics to fields, accommodating particle creation and annihilation processes.
• De Broglie–Bohm Theory: Also known as the pilot-wave theory, it introduces deterministic trajectories for particles guided by a wave function, offering an alternative interpretation of quantum mechanics.Wikipedia
• Quantum Geometry: Recent advancements, such as those by Carolina Figueiredo, propose frameworks where quantum events emerge from abstract geometric structures beyond traditional space-time, potentially addressing phenomena like quantum scarring.

3. Integrating Discrete Models and Computational Approaches

The concept of a discrete, frame-by-frame universe, as discussed in the paper "Integration and Refinement of Digital Physics, Unifying Quantum and Classical with a Calculation: A Formal Approach to Subparticles and Discrete Universe Frames," suggests a model where the universe is rendered in discrete frames, potentially offering explanations for phenomena like instantaneous communication transfer. While this approach is intriguing, it is essential to recognize that the Schrödinger equation, as a continuous differential equation, has been extensively validated through experimental results and remains a cornerstone of quantum mechanics. Discrete models must demonstrate empirical success and predictive power comparable to the Schrödinger equation to be considered viable alternatives.

While the Schrödinger equation has been instrumental in the development of quantum mechanics, its limitations in certain scenarios necessitate the exploration of alternative models and frameworks. Integrating insights from quantum geometry, discrete models, and other theoretical advancements can provide a more comprehensive understanding of quantum phenomena. It is through the synthesis of these diverse perspectives that we can aspire to develop a unified theory capable of accurately describing the complexities of the quantum realm.

I look forward to further discussions and collaborative explorations on this topic.

Best regards,

Sandeep Jaiswal

I assume the Dirac equation is more suitable for describing quantum particles than the Schrödinger Equation. Although my research subject is water, I proceed with a hydrogen atom as a quantum particle, an infoton. The infotons relate to the five forces: electromagnetics, strong force, weak force, gravity, and the force of "field." The movement of an infoton may form a "field."

Dear Sunao Sugihara,

Your observation regarding the Dirac equation being more suitable than the Schrödinger equation for describing quantum particles is insightful, especially when considering relativistic effects. The Dirac equation extends the quantum framework by accounting for spin and relativistic invariance, making it indispensable for particles like electrons moving at relativistic speeds.

Regarding your conceptualisation of the hydrogen atom as a quantum particle, or "infoton," and its relation to the five forces, this opens up a fascinating multidimensional perspective. The interplay between these forces, particularly the electromagnetic and gravitational fields, has been central to theoretical physics. The concept of a "field" generated by the movement of an infoton aligns intriguingly with quantum field theory, which describes particles as excitations in their respective fields.

To address your implied query about the inadequacies of the Schrödinger equation:

I commend your approach to integrating concepts from water research with quantum mechanics, as cross-disciplinary insights often yield breakthroughs. Exploring the behavior of infotons within the context of these five forces could provide a fresh perspective on field interactions and the nature of quantum particles.

This discussion has the potential to advance our understanding of quantum particle mechanics significantly. I encourage you to further develop your ideas, as they could play a pivotal role in addressing the current limitations of quantum theory and inspiring new avenues of research.

Best regards, Sandeep Jaiswal

Dear Sandeep Jaiswal, Thank you for your suggestive comments. Regarding the field, I think we may need the Einstein gravity equation and Yukawa's potential for nuclear change (which is another theme). Back to the Schrödinger Equation, the equation is a wave as a result, and the quantum particle must be first, and the particles may form the wave during interaction with the field. Therefore, I have considered the infoton moving in a tensor. At that time, infoton with the spin moves around three dimensions, resulting in an electromagnetic field. Sorry if my idea is different from your intention.

Dear Sunao Sugihara,

Thank you for your thoughtful response and for allowing us to delve deeper into this fascinating discussion. I’d like to expand on some critical aspects of particle behavior, particularly with regard to duality, the probabilistic framework of quantum mechanics, and the foundational questions it raises about the nature of particles and their interactions.

The double-slit experiment remains one of the most iconic demonstrations of quantum duality, showing that particles like electrons exhibit both wave-like and particle-like behavior depending on how they are observed. However, the experiment raises a significant paradox: Why does a particle behave as a wave when not observed, and why does it revert to behaving as a particle when a measurement is made?

Current explanations rooted in the probabilistic model of Schrödinger's equation suggest that the particle exists in a "superposition" of states until measured. Yet this explanation is unsatisfactory and, frankly, incomplete. Does the particle "know" it is being measured? If so, does this suggest some level of consciousness in the particle, or is there another mechanism at play?

As outlined in my paper (DOI: 10.9790/4861-1505012633), the probabilistic nature of Schrödinger's equation is not an inherent property of particles but a limitation of our current mathematical models. The particle must exist in one definite state at any given time. While probabilistic models have proven useful for predictions and practical applications, they do not accurately represent the true nature of particles.

At the macroscopic scale, determinism reigns. A car, for instance, does not exist in a probabilistic state but occupies a definite position at all times. Why, then, should particles behave differently? My work demonstrates that quantum systems, too, can be deterministic when analyzed correctly, and the probabilistic interpretation is merely a patchwork solution to our incomplete understanding of microscopic systems.

A central issue in quantum mechanics is the measurement problem. The act of measuring a particle seems to "collapse" its wave function into a definite state. But why? Current theories suggest that interaction with a measurement device changes the particle's state. However, this explanation raises further questions:

• Why does every type of measurement device, regardless of the method, produce similar behavior?
• If the interaction with a foreign object (such as a measuring device) changes the state, why does this occur universally?

Could there be metaphysical aspects involved? Does the particle "know" it is being measured? If so, this suggests an entirely new dimension of understanding, where particles exhibit behaviours that go beyond physical interactions.

Quantum mechanics has largely avoided addressing the root cause of duality. The current probabilistic model attributes this behavior to mathematical abstractions without exploring the fundamental reasons behind it. My work proposes that duality arises not from inherent randomness but from deterministic interactions that are yet to be fully understood.

For instance, it is plausible that the wave-like behavior seen in the double-slit experiment is a result of interaction with an underlying field or medium, rather than an intrinsic property of the particle itself. This opens up avenues for exploring hidden variables or deterministic laws that govern these interactions, as opposed to relying on probabilistic interpretations.

Your question about whether particles "think" they are being measured touches on deeper metaphysical questions. While science has traditionally avoided attributing consciousness to particles, the consistent behavior observed in quantum experiments suggests that there may be an underlying principle yet to be discovered.

Could particles have an intrinsic property that allows them to "sense" their environment? Or is this behavior a reflection of deeper interactions with the fabric of space-time or an undiscovered field? These questions challenge the boundaries of both science and metaphysics and invite us to reconsider the foundations of quantum mechanics.

To address these challenges, we must move beyond the probabilistic model and develop deterministic frameworks that account for all observed phenomena, including duality and the measurement problem. My work offers a starting point by demonstrating that particles can exist in definite states and that their behavior is governed by deterministic laws, not randomness.

The probabilistic model, while useful, is a stopgap solution that oversimplifies the true nature of particles. By integrating deterministic principles with experimental observations, we can pave the way for a more comprehensive understanding of quantum mechanics and its implications for space-time, metaphysics, and beyond.

I look forward to continuing this discussion and exploring these ideas further. Your concept of the infoton and its interactions with the field provides a valuable perspective, and together, we can work toward unraveling the mysteries of quantum mechanics.

Best regards, Sandeep Jaiswal DOI: 10.9790/4861-1505012633

Basically, the Schrödinger equation is congruent with the Einstein field equation. The basic statement in both is geometry (spacetime) = matter/energy (content). The question is, how can you combine both basic rules into one? It may have something to do with the fact that the Einstein equation describes timelike movements, while the Schrödinger equation describes spacelike movements, or rather their timelike manifestation in our world. That's my guess.

Very few are aware that the establishment of the Schrödinger equation was grounded on an erroneous frequency of the energy induced at Bohr orbit distance from the proton in the Bohr model involuntarily used by de Broglie in his 1924 thesis, on which Schrödinger grounded his wave equation:

Article Critical Analysis of the Origins of Heisenberg's Uncertainty Principle

Dear André Michaud

You highlight that the Schrödinger Equation was founded on an erroneous frequency associated with the energy at the Bohr orbit distance from the proton in the Bohr model, as utilized by de Broglie in his 1924 thesis. This, you suggest, undermines the foundational basis of the Schrödinger Equation.​

Louis de Broglie's 1924 thesis introduced the concept of matter waves, proposing that particles exhibit wave-like properties with a wavelength λ = h/p, where h is Planck's constant and p is the momentum. This hypothesis extended the idea of wave-particle duality to matter and was instrumental in the development of quantum mechanics.​

The Bohr model, preceding de Broglie's work, described electrons in fixed orbits around the nucleus with quantized angular momenta. While successful in explaining certain spectral lines, it lacked a theoretical foundation for why angular momentum should be quantized. De Broglie's hypothesis provided this foundation by associating quantization with standing waves fitting into electron orbits, leading to the condition nλ = 2πr, where n is an integer and r is the orbit radius.​

However, the Bohr model's assumption of circular orbits and the classical treatment of electron motion were oversimplifications. The Schrödinger Equation, formulated in 1926, offered a more comprehensive wave mechanics framework, treating electrons as wavefunctions spread over space rather than point particles in fixed orbits. This allowed for the calculation of probability densities and addressed limitations of the Bohr model.​

While de Broglie's initial assumptions may have been based on simplified models, the evolution of quantum mechanics, including the Schrödinger Equation, has incorporated corrections and extensions beyond these early models. The Schrödinger Equation has been validated extensively through experimental results and remains a cornerstone of quantum mechanics.​

Limitations of the Schrödinger Equation and Fundamental Issues in Quantum Mechanics

Despite its successes, the Schrödinger Equation and quantum mechanics as a whole face several foundational challenges:​

The Schrödinger Equation, despite its historical development rooted in early atomic models, has proven to be a robust tool in describing quantum systems. However, the quest for a unified theory that seamlessly integrates quantum mechanics with general relativity continues. Insights like those you've shared are invaluable in guiding this pursuit, challenging existing paradigms, and inspiring new approaches to understanding the fundamental nature of reality.​

Best regards,

Sandeep Jaiswal

Dear Heribert Genreith

Thank you for your engaging questions regarding the Schrödinger Equation and the foundational aspects of quantum mechanics. Building upon our previous discussions and integrating insights from my recent paper (DOI: 10.9790/4861-1505012633), I would like to address your queries in detail.

You propose that the Schrödinger Equation and Einstein's Field Equations are congruent, both expressing a relationship where geometry (spacetime) equals matter/energy content. You further suggest that integrating these principles might involve recognizing that Einstein's equations describe timelike movements, while the Schrödinger Equation pertains to spacelike movements or their timelike manifestations in our world.​

This perspective aligns with ongoing efforts in theoretical physics to unify general relativity (which governs macroscopic, gravitational phenomena) and quantum mechanics (which governs microscopic, subatomic phenomena). The challenge lies in reconciling the continuous, deterministic fabric of spacetime in general relativity with the discrete, probabilistic nature of quantum mechanics.​

One avenue of exploration is the concept of quantum gravity, which seeks to describe gravity according to the principles of quantum mechanics. Approaches such as Loop Quantum Gravity attempt to quantize spacetime itself, suggesting that spacetime has a discrete structure at the Planck scale. This could provide a framework where the geometric description of gravity (Einstein's Field Equations) and the wavefunction description of quantum systems (Schrödinger Equation) are facets of a single, underlying theory.​

Another approach is String Theory, which posits that fundamental particles are not point-like but rather one-dimensional "strings" whose vibrations correspond to different particles. This theory inherently includes gravity and aims to unify all fundamental forces, potentially bridging the gap between the macroscopic and microscopic descriptions of the universe.​

Your insight into timelike and spacelike movements touches upon the core difficulty in merging these frameworks: the nature of time and its role in physical theories. In general relativity, time is a dimension intertwined with space, forming a four-dimensional continuum. In quantum mechanics, time is typically treated as an external parameter. Developing a coherent theory that integrates these differing treatments of time is a significant challenge in modern physics.

Best regards,

Sandeep Jaiswal

Sandeep Jaiswal

Dear Sandeep,

You wrote: " You highlight that the Schrödinger Equation was founded on an erroneous frequency associated with the energy at the Bohr orbit distance from the proton in the Bohr model, as utilized by de Broglie in his 1924 thesis. This, you suggest, undermines the foundational basis of the Schrödinger Equation.​"

Not really. This is not what I suggest. The Schrödinger equation provides the exact same values as the de Broglie equation that inspired it, which are the energies of the mean momentum energy of each orbital of the electron in the hydrogen atom.

Note that the Bohr model is not invalid. It is simply an idealized model whose orbits provide the real mean energy level of each real orbital of the hydrogen atom.

What I highlight, is that both equations provides only this amount of momentum energy (13.6 eV for the ground orbit), which is released as a bremsstrahlung photon as recorded in the electromagnetic spectra recordings when the electron is first captured by a proton to form a hydrogen atom. But this is only half of the total amount of energy actually induced at mean Bohr ground orbit (The Hartree energy of 27.2 eV), which was confirmed 20 years before from the data collected by Kaufmann, as analyzed by Lorentz in his 1904 paper, which is a development that was not properly referenced at the time and was eventually forgotten in mainstream by the 1920's, which is what caused de Broglie to come up with his phase wave instead, that pleased Schrödinger and caused him to come up with his corresponding wave equation.

Links to these historical papers are provided for direct confirmation.

Adding this second half of the induced energy never was made in mainstream Quantum Mechanics, but its addition allows correcting all of the fundamental issues that you list from the new electromagnetic mechanics perspective that including it allows establishing.

Best Regards, André

Dear André Michaud,

Thank you for your detailed response and for clarifying your position regarding the foundational aspects of the Schrödinger Equation and its relation to the Bohr model and de Broglie's hypothesis. I appreciate the opportunity to delve deeper into this discussion.

Revisiting the Bohr Model and de Broglie's Hypothesis

The Bohr model, introduced in 1913, posited that electrons orbit the nucleus in fixed paths with quantised angular momentum, successfully explaining certain spectral lines of hydrogen. However, it lacked a theoretical basis for quantisation and couldn't account for electron wave-particle duality.​

In 1924, Louis de Broglie proposed that particles exhibit wave-like properties, introducing the concept of matter waves with a wavelength λ = h/p, where h is Planck's constant and p is momentum. This hypothesis provided a foundation for quantisation in the Bohr model by associating it with standing waves fitting into electron orbits, leading to the condition nλ = 2πr, with n as an integer and r as the orbit radius.​

Schrödinger's Wave Mechanics

Building on de Broglie's hypothesis, Erwin Schrödinger formulated his wave equation in 1926, offering a comprehensive framework for quantum mechanics. The Schrödinger Equation treats electrons as wavefunctions spread over space, allowing for the calculation of probability densities and addressing limitations of the Bohr model.​

Addressing the Hartree Energy and Total Induced Energy

You highlight that the Schrödinger Equation accounts for only half of the total energy induced at the Bohr ground orbit, corresponding to the mean momentum energy (13.6 eV), while the total induced energy is the Hartree energy (27.2 eV). The Hartree energy is a unit of energy in atomic physics, approximately equal to 27.2114 eV, representing the electric potential energy of the electron in a hydrogen atom's ground state.

The discrepancy arises because the Schrödinger Equation primarily addresses the kinetic energy component of the electron's motion, corresponding to the observed spectral lines. The potential energy component, contributing to the total Hartree energy, is implicitly considered in the potential term of the equation but isn't directly observable in spectral emissions.​

Implications for Quantum Mechanics

Your observation suggests that incorporating the full Hartree energy into quantum mechanical models could provide a more complete description of atomic systems. This perspective invites further exploration into the total energy considerations in quantum systems and their implications for refining existing models.​

The evolution of quantum mechanics, from the Bohr model to de Broglie's hypothesis and Schrödinger's wave mechanics, reflects a progressive refinement of our understanding of atomic systems. Your insights into the Hartree energy and the total induced energy at the Bohr orbit distance highlight areas where our theoretical models can be further enhanced. Continued examination of these aspects is essential for advancing our comprehension of quantum phenomena and improving the accuracy of our models.​

Best regards,

Sandeep Jaiswal

Sandeep Jaiswal

Dear Sandeep,

You perfectly described the historical situation, which sets the stage for a comment about the Hartree energy about which hinges the solution to progress further.

Let us stick with the Bohr ground state to finish clarifying what the issue is with the Hartree energy, which, at Bohr radius distance from the proton is exactly 27.2114 eV as you mention, diminishing and increasing slightly as the electron oscillate away or towards the proton about the Bohr radius distance according to de Broglie's discovery of its resonance oscillation along the Bohr ground orbit.

This Hartree energy, considered "potential" since the beginning of the 20thcentury, is in reality made up of the momentum "kinetic" energy of 13.6 eV that can be seen as propelling the electron along the Bohr orbit, plus a second amount of 13.6 eV of "kinetic" energy corresponding to the velocity related magnetic field increment of the electron at the velocity with which it was understood as moving on this Bohr orbit.

This is a simplified representation, I know, but for mathematical calculation purposes, it allows calculating real values.

The discovery that these two amounts of energy (13.6 + 13.6 = 27.2 eV) really are "kinetic" and not potential was identified by Lorentz in his 1904 paper as he analyzed the data that Kaufmann had collected by accelerating for the first time in history beams of electron on curved trajectories in his bubble chamber by means of calibrated E and B fields inducing energy in the electrons by acting on their "charges", not on their masses, according to the method that Lorentz had identified in the 1890's.

What historically happened, was that since no theory existed at the time to account for the real physical "kinetic" existence of this energy, the community, despite double-checking and acknowledging the reality of the experimental discovery, as mentioned in Pais's biography of Einstein published in 1987, voluntarily decided not to take it into account in their continued research to resolve the gravity problem that they perceived as concerning only macroscopic and astronomical masses.

This second 13.6 eV of energy is what momentarily increases the mass of the electron as a function of its velocity, or proximity with other charged particles.

If this makes sense to you, I can explain further the implications.

Best Regards, André

Dear André Michaud & Others,

Thank you for your clear and careful response. I respect the rigour with which you highlight the tested scope of the Schrödinger equation, the experimental foundations of quantum computing, and the distinction between hype and genuine scientific progress.

That said, allow me to share a broader perspective drawn from my own published research and discussions:

1. On the Schrödinger Equation

While it has proven predictive in controlled, idealised regimes, my analysis (e.g., IOSR-JAP, DOI: 10.9790/4861-1505012633) demonstrates that the equation is unfit as a fundamental law. It can only represent a narrow subset of harmonic, Gaussian wave-like motions. In real-world, non-ideal particle dynamics it fails to provide universality. A genuine fundamental law should be valid in all environments, not only under laboratory-grade isolation. Thus, I argue Schrödinger’s equation is an approximation—useful, yes, but partial.

2. On Probability vs. Determinism

Mainstream QM embraces probability (via Born’s rule) as elemental. Yet probability by definition reflects ignorance, not causality. In my work (Why Quantum Mechanics is Wrong at its Core, DOI: 10.13140/RG.2.2.35003.32802), I contend that particles exist in definite states at all times; superposition is a mathematical abstraction born from incomplete modelling. A deterministic alternative, whether hidden-variable-like or beyond current frameworks, is needed to restore cause-and-effect clarity.

3. On Measurement and Observation

You correctly note that “unitary evolution and measurement” are bedrock principles. My objection is not that unitary evolution is invalid, but that the collapse postulate makes no physical sense: why should an observer’s choice of apparatus dictate the behavior of a supposedly objective particle? The double-slit paradox is better interpreted as evidence of an undiscovered mechanism—or even a deeper layer of reality—than as proof that “consciousness causes collapse.” Here, I have suggested (controversially) that the missing link may touch on consciousness, but the broader point is: collapse as randomness is inadequate as an explanation.

4. On Entanglement and Non-locality

Quantum mechanics reproduces correlations beautifully, but offers no causal “how.” Experiments validating Bell’s theorem indeed rule out local hidden variables. Yet this leaves the door open for nonlocal deterministic frameworks. Einstein’s “spooky action” remains unexplained by quantum formalism—it is predicted, but not mechanistically accounted for. I argue we should not settle for “it works mathematically” but continue to search for a deterministic underpinning.

5. On Quantum Computing

I fully acknowledge the value in quantum sensing, metrology, and error-correction progress. However, if the foundational postulates themselves are only partial truths, then scaling QC to a universal computational paradigm may never materialise. This is why I use terms like “mirage”: not to dismiss the impressive engineering underway, but to stress that if the base theory is incomplete, the long-term promise may prove hollow beyond niche applications.

In summary:

• I do not deny quantum mechanics’ spectacular success in its limited scope.
• I do insist it is not the final truth. Its postulates are partial, probabilistic placeholders for deeper deterministic laws.
• My estimate—based on contradictions across measurement, uncertainty, superposition, and entanglement—is that QM is only ~30% correct, a stepping stone rather than an endpoint.
• The challenge is not to abandon QM, but to build upon it toward a universal deterministic science, one that unifies gravity, quantum, and cosmology without paradox.

Your caution against hype is essential. My call is to go even further: to recognise that the very foundations are incomplete, and to seek the deterministic framework that will make today’s paradoxes tomorrow’s understood laws.

With respect,

Sandeep Jaiswal

Sandeep Jaiswal

Dear Sandeep,

I find myself in complete agreement with your conclusions.

@Sandeep Jaiswal

Your statements do not take into account that the Schrödinger equation describes correctly evolution of the particles wave function if sufficiently rigorously analysed is its formal context.

The expected by you existence of stationary solutions with non-specific probability distribution has no experimental support.

To be more exact, for a given field of forces represented by the potential function V(x) any stationary solution with a given harmonic circular frequency ω implies a unique for this frequency probability distribution. The same rigour appears in calculation of em waves: if the time dependent factor equals sin(ωt) with given ω, then the spatial factor MUST be of the form sin(φ+ 2πx/λ) with λ necessarily equal c/ω.

If one wants to get a wave with other spatial distribution, the Fourier combination of waves with a continuos spectrum of frequences must be involved.

With the Schrödinger equation for a potential free motion of a particle, e.g. the so called rectangular spatial distribution of the wave IS THE SAME COMBINATION OF SINUSOIDAL WAVES AS FOR THE EM WAVES.

However the speed of each such wave is different, in accordance to the nonrelativistic counterpart of the de Broglie formula

. . . ½(h/λ)²/m = hω/(2π).

This phenomenon is called dispersion of the velocity. It caused that the SHAPE of the spatial distribution (which can be arbitrary) is not preserved during time flow.

This is the main reason which explains that your expectation that for the Schrödinger equation the solution may have stationary arbitrary distribution cannot be fulfilled.

And have you any empirical evidence that there are such expected by you stationary distributions of electron in the neiborhood oh any center? I am sure that no, which would explain additionally that your basic objections are not reasonably justified.

Best regards.

Joachim Domsta

Dear Joachim,

Thank you for taking the time to lay out the rigorous mathematical structure of the Schrödinger equation and its stationary solutions. You are absolutely right that in its formal Hilbert-space context, the equation admits a unique probability distribution for a given potential and frequency, and that dispersion naturally arises for free-particle wave packets. On the level of internal mathematical consistency, this is well understood.

However, my critique is not aimed at whether the Schrödinger equation is self-consistent as a mathematical framework, but whether it is sufficient as a universal physical law:

I do not dispute the internal rigour of Schrödinger’s framework. What I dispute is its universality and its claim to fundamentality. A true fundamental law must explain not only the stationary solutions we know, but also the paradoxes of measurement, superposition, and entanglement in a deterministic, causally transparent way. Schrödinger’s equation does not.

That is why, in my view, it cannot be regarded as the ultimate postulate of physics — only as a highly effective approximation awaiting replacement by deeper deterministic laws.

With respect,

Sandeep Jaiswal

@Sandeep Jaiswal

You have stated

Generally you are right, but in particular case of the S. equation you agreed that it describes the reality 'astonishingly' well. All which is really not explained is the wave collaps accompanying the measurement. Thus I can agre with the need of embedding the quantum wave mechanics in some broader context.

However I cannot agree with reasoning presented in your paper via impossibility of building stationary solutions with arbitrary distribution. The experiments show that this impossibility is not only the property of the equation but also the property of the real world (obviously in a reasonable range of circumstances).

With regards,

Joachim Domsta

PS. Causality is imprinted into the S. equation due to the first order differential with redpect to the time variable. The cases of mixed states versus linear combinations is not more special for the QM than for classical mechanics within general teory of entropy and related invertibility of some processes.

Joachim Domsta

Dear Joachim,

Thank you for clarifying. I am glad that we can agree on the essential point: Schrödinger’s equation, while astonishingly effective within its domain, clearly requires embedding in a broader framework to account for measurement, collapse, and related paradoxes. That acknowledgment itself shows the theory is not fundamental but approximate.

On the question of stationary solutions: you are right that experiments have confirmed the specific distributions allowed by the formalism under controlled circumstances. My argument is not that the laboratory outcomes contradict the equation, but that the restriction itself proves the incompleteness of the law. A true universal law should not only describe the distributions we can currently engineer but also explain, causally and deterministically, why only those arise and what deeper principles constrain them. Schrödinger’s framework does not provide that causal transparency—it simply codifies probabilities for a subset of scenarios.

So we converge on the same conclusion by different routes: the equation is highly successful but not final. My stance is simply that its probabilistic and restrictive nature shows it cannot be the ultimate postulate of physics. The search must continue for a deterministic framework that resolves measurement, superposition, and entanglement without paradox. Until then, Schrödinger’s equation remains a powerful approximation, not the last word.

With respect,

Sandeep Jaiswal

@Sandeep Jaiswal

Here we differ substantiallyv I do not tel what and how the nature SHOULD be. Only possible knowledge we can have is about as much ss possible sbout relations governing the observed phenomena.

Here is an extension of post #9 from page

https://www.researchgate.net/post/An_old_question_that_is_still_fresh_Is_gravity_a_Newtonian_force_or_Einstein_space-time_curvature/1496

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For the circular orbit of radius r of a particle of mass m moving with velocity v kept in constant distance by the extended Newton/Coulomb type attracting force

. . . F=A/r^p, with A>0, . . .with . . p>1 , (1)

the total energy is a sum

. . . E = T + U, . . . . . . . . . . . . .(2)

where the kinetic energy equals

. . . T = ½ m v², . . . . . . . . . . . .(3)

and the potential energy equals

. . . U = - 1/(p-1) A/r^(p-1),. . .(4)

During this motion the force F causes the centripetal acceleration which means that

. . . m v²/r = A/r^p. . . . . . . . . (5)

Simple algebra of the above equations leads to the following propositions

. . . T = ½ A/r^(p-1). . . . . . . . . . . . . . (6)

. . . E = [½ - 1/(p-1)] A/r^(p-1)

. . . . .= - ½ (3-p)/(p-1) A/r^(p-1) . . (7)

Conclusion. Under the above conditions the following relations hold true

. . . U/T = - 2/(p-1) , . . . . . . . (8.1)

. . . E/T = - (3-p)/(p-1) . . . . . (8.2)

In particular in case of the electrostatic forces between proton and electron characterised by

. . . A = e²/(4 π ε_ο) . . . . . . . . . (9)

there is NO mysterious magnetic energy responsible for the ratio |U|/T=2.

Indeed, for the gravitational interaction between Sun and any planet we have also attractive force

. . . F_gr = G M m / r²

i.e. equation (1) holds with A=G M m, p=2. Thus again equations (8) imply U=-2T, E=-T, exactly the same relations as it is for the e-p pair. No mysterious additional forces are responsible for the ratios (8) but the exponent p, if the field F of forces is proportional to the inverse p-th power of the distance r of the moving object from the center.