I shall attempt to provide detailed answer, which is by no means a claim to be THE answer but rather a set of evaluations.
Let's establish a baseline first.
1. What Is Entanglement?
In quantum mechanics, entanglement refers to correlations between parts of a composite quantum system that cannot be described by considering each part independently. An “entangled” state of two or more subsystems (e.g., two particles) exhibits correlations stronger than any allowed by classical physics. This phenomenon has numerous theoretical and experimental consequences, such as violations of Bell’s inequalities, quantum teleportation, and quantum cryptography.
Key points about quantum entanglement:
1. Uniquely Quantum: Entanglement is specifically a quantum phenomenon.
2. Nonclassical Correlations: Entangled subsystems exhibit correlations that defy a classical local realistic explanation.
3. Resource for Quantum Information: In quantum computing and quantum communication, entanglement is a resource that enables tasks (e.g., quantum teleportation) impossible or impractical classically.
2. Entanglement vs. Time-Dependent Phenomena
A. The Meaning of “Any Time-Dependent Phenomenon”
To claim that “any time-dependent physical phenomenon can be solved via entanglement” suggests a universal applicability of quantum entanglement to describe or solve problems in both classical and quantum regimes. It implies that, if a system changes with time, one might invoke entanglement as the primary tool or conceptual framework to solve it.
1. Classical Time-Dependent Systems
Classical systems—ranging from planetary orbits to fluid dynamics to everyday thermodynamics—are typically not described in terms of quantum mechanical entanglement. While you can embed classical theories within a broader quantum framework, this is not usually practical or necessary to solve time-dependent problems in classical contexts (e.g., rocket trajectories, weather predictions, electrical circuits, etc.).
2. Quantum Time Evolution
In quantum theory, the time evolution of a closed system is governed by the Schrödinger equation (or more generally, the unitary evolution operator). Although entanglement often emerges between subsystems during time evolution, it is not always the prime variable or mechanism to solve for the entire phenomenon. Many quantum problems can be approached via standard methods (e.g., solving Hamiltonians, perturbation theory, path integrals) without requiring explicit tracking of all entanglement measures.
3. Not All Systems Are Significantly Entangled
Real physical systems in the macroscopic, classical domain often lose detectable quantum entanglement very quickly due to decoherence. For most classical time-dependent processes, quantum entanglement is negligible on human-observable scales. Therefore, it is rarely, if ever, the universal “key” to solving classical time-dependent problems.
My first Conclusion (A)
While quantum entanglement is crucial for describing nontrivial quantum phenomena, it is not the universal approach to all time-dependent systems. In classical contexts, invoking entanglement is at best superfluous and, in practical terms, usually entirely unnecessary.
I also note that we do not actually know what is the mechanism at work which results in what we observe as entanglement.
3. “Entanglement Is a Universal Law of Physics”
A. Entanglement as a Property vs. a Universal Law
It is more accurate to say that if you are working within quantum mechanics, entanglement is a fundamental property that can appear whenever you have composite systems. However, calling entanglement a “universal law” that “models the functioning of Mother Nature” in classical and quantum physics is contentious and potentially misleading.
1. Quantum Domain: Within the quantum domain, entanglement is indeed ubiquitous and can arise in a vast range of scenarios—particles, fields, condensed matter systems, etc.
2. Classical Domain: In the classical domain, phenomena are effectively described by classical models (e.g., Newton’s laws, Maxwell’s equations, classical thermodynamics) without needing entanglement.
3. Mathematical Formalism: While certain mathematical structures used in quantum theory (like Hilbert spaces) can be generalized, that does not mean every part of mathematics or physics is fundamentally “about entanglement.”
Thus, while quantum mechanics underpins our best understanding of nature, the statement that entanglement itself is the universal principle for all of mathematics or classical physics overstates its reach.
We then move to the essentialism of the phenomenon...
4. When and Why Is Entanglement Essential?
Quantum Computation and Communication: Harnessing entanglement is essential in quantum algorithms (e.g., Shor’s or Grover’s algorithm), teleportation, quantum cryptography, etc.
Many-Body Quantum Systems: Understanding complex systems—such as superconductors, quantum phase transitions, and topological phases—often relies on entanglement entropy and other measures of quantum correlations.
Tests of Fundamental Physics: Bell tests and experiments on quantum foundations rely explicitly on the presence of entanglement to demonstrate violations of classical local realism.
In all these areas, time dependence and entanglement can be intertwined, but the latter does not provide a universal solution procedure for all time-dependent problems.
5. Key points bringing it all together
1. Overarching Claim: The statement “any time-dependent physical phenomenon can be solved via entanglement” is too broad and generally not true. Many classical and even quantum problems do not require entanglement as a primary tool or resource for their analysis.
2. Quantum vs. Classical: Entanglement is uniquely important in quantum mechanics. In the classical regime, the concept of entanglement does not even strictly apply, so it is not correct to say that classical time-dependent phenomena must be “solved” by invoking entanglement.
3. Universality: While quantum mechanics is considered the fundamental description of nature, calling entanglement a “universal law” is an overstatement. It is more precise to say that quantum entanglement is pervasive for quantum systems, but classical descriptions—where entanglement effects are negligible—remain valid and extremely effective in most practical time-dependent phenomena.
Final Thoughts
The postulate contains kernels of truth—quantum entanglement is indeed a central feature of quantum mechanics and, in principle, nature is quantum at all scales. However, not every time-dependent phenomenon is best approached through the lens of entanglement; classical domains and many quantum problems alike can be solved via other methods. Hence, one should be wary of overly broad claims that entanglement alone “models the functioning of mother nature” in all realms of physics and mathematics.
> “We assume the answer to this question is yes and related to a more exhaustive question
How to construct a complete universal x-t space?
A complete universal physical space is a space where x, y, z are mutually orthogonal (independent) and time t is orthogonal to x, y, z.
This is not easy and is only satisfied by Einstein’s x-t space in its special and general relativity.
Note that mathematical spaces such as Minkowski, Hilbert, Riemann, etc. are all incomplete....
Schrödinger space may or may not be complete.
However, the unit space of statistical chains of matrix B is complete and time t defined as woven in x, y, z can be shown to be normal to x–y–z.
This implies an entanglement of the system with Dirichlet walls and the source term.”
- What Does “Complete Universal x–t Space” Mean?
The statement introduces a concept of a “complete universal physical space” with four dimensions such that:
1. are mutually orthogonal (typical for spatial coordinates).
2. is orthogonal to (a notion reminiscent of spacetime treatments in relativity, where time is treated as a coordinate but with a different sign in the metric signature).
The claim this situation is “only satisfied by Einstein’s x–t space in its special and general relativity,” suggesting that standard 4D formalisms—like Minkowski space in special relativity—are incomplete.
This usage of “complete” seems nonstandard, so I'm struggling to understand the sentence.
In differential geometry and relativity, completeness often refers to geodesic completeness right ?(whether all geodesics can be extended infinitely in both directions)
or
Cauchy completeness (in the sense of metric spaces). Yet the statement seems to use “complete” in a different sense that is never fully defined (?)
2. Are Minkowski, Hilbert, or Riemann Spaces “Incomplete”?
> “Note that mathematical spaces such as Minkowski, Hilbert, Riemann… etc. are all incomplete.”
A. Minkowski Space
Minkowski space (or depending on the metric signature) is typically the mathematical setting for special relativity, a neater playing ground for the fomp x field equations as such.
In standard relativity texts, the unbounded Minkowski space is geodesically complete unless one imposes boundaries or identifies points.
Usually, there is no singularity that would break completeness.
I'm not sure how to describe it as “incomplete” or what that means.
Minkowski spacetime (infinite and boundary-free) is not “incomplete” in the typical sense.
B. Hilbert Space
A Hilbert space is a complete inner-product space in the sense of metric completeness: every Cauchy sequence converges in the space.
QM uses (complex) Hilbert spaces to describe states; the hallmark property is completeness with respect to the norm induced by the inner product.
That's why I'm also struggling to reconcile this claim about “Hilbert spaces are incomplete” - it appears to contradicts the usual definition of a Hilbert space.
C. Riemann Spaces (Riemannian Manifolds)
A Riemannian manifold can be geodesically complete or incomplete. Some Riemannian manifolds (e.g., a sphere ) are complete, while others (e.g., a punctured plane) are not.
Calling all “Riemann spaces” incomplete is far too general; one has to specify the manifold, metric, boundary conditions, etc.
The statement that these standard mathematical spaces are “incomplete” is at best idiosyncratic and at worst factually incorrect, unless I'm missing something in my understanding, which is entirely possible.
3. “Time Defined as Woven in ” and Orthogonality
The claim that “time can be shown to be normal (orthogonal) to ” is reminiscent of the idea that in special relativity’s standard inertial frame, the time axis is orthogonal (in a Minkowski sense) to the spatial axes. But the usual Lorentzian metric has signature or , so this “orthogonality” differs from the Euclidean sense.
1. In special relativity, we typically do not say is orthogonal to in a purely Euclidean sense. We say they are orthogonal in the Minkowski metric sense, meaning (or with a sign change convention).
2. In general relativity, the situation is even more complex: the local Minkowski structure is tangent-space-based, and globally the metric can be curved.
The notion of “time is orthogonal to space” is standard in a Minkowski sense, yet the statement lumps Minkowski space as “incomplete” and then claims a new structure “fixes” that. This is contradictory no ?
4. “Implication of Entanglement with Dirichlet Walls and the Source Term”
The statement finishes with:
> “This implies an entanglement of the system with Dirichlet walls and the source term.”
Here, it seems the author is conflating or mixing few things;
Quantum entanglement - A specific quantum-mechanical correlation phenomenon.
Boundary conditions (“Dirichlet walls”) - A typical PDE or wave-equation notion in classical or quantum problems (e.g., a particle in a box with Dirichlet boundary conditions on walls).
Source term - Typically refers to a forcing function or inhomogeneous term in PDEs.
Points to note:
1. Entanglement usually refers to the quantum state of multiple subsystems. Having boundary conditions in, say, a 1D or 3D PDE problem does not automatically give “entanglement” with the boundary. Quantum mechanical wavefunctions can vanish at a Dirichlet boundary,
but
that alone is not the same as entanglement.
2. Mixing Classical PDE Notions and Quantum Entanglement - let's say you have a quantum field in a cavity (Dirichlet boundary), which exhibit entangled modes. However, the statement that “time is woven in x, y, z” and “this implies entanglement” is not a standard derivation in physics.
There is no obvious necessity that the orthogonality of time to space yields entanglement with boundary conditions.
it is unclear how the premises about “completeness” and “orthogonal time” lead to the conclusion about “entanglement with Dirichlet walls and a source term.”
My main pointa to summarize
1. Non-Standard Use of “Completeness.”
The most glaring issue is the author’s characterization of spaces like Minkowski or Hilbert as “incomplete,” which runs contrary to standard definitions.
Do you mean “not physically complete” in the sense that Minkowski space alone does not address all phenomena? (such as gravitational singularities in general relativity), that needs to be clarified.
2. Orthogonality of Time and Space
Yes, in special relativity, time is “orthogonal” to space in a Minkowski sense, but that is already well-established. It is not something that Minkowski space “fails” to capture.
3. “Universal x–t Space”
Phrases like “construct a complete universal x–t space” are not standard in physics. We typically talk about spacetimes that can be geodesically complete or incomplete, but “universal” is vague without rigorous definitions.
4. Entanglement and Dirichlet Walls
The leap to quantum entanglement from statements about 4D geometry is non-sequitur. Boundary conditions in PDEs do not by themselves imply quantum entanglement.
In standard mathematical physics, Minkowski space is a perfectly valid (and indeed standard) model for special relativity, Hilbert space is by definition complete (in the sense of Cauchy completeness), and boundary conditions do not automatically yield “entanglement.”
A quantum or classical system is composed of n objects where there is mutual energy density entanglement.
The microscopic entanglement of the energy density is expressed by the entries of the transition matrix Bnxn as bij and the macroscopic entanglement of the energy U is expressed by the spatiotemporal evolution of the system,
U(x,y,z,t+dt)=B nxn U(x,y,z,t) . . . . (1)
Equation 1 leads to,
U(x,y,z,t) = D(N). (b+S) + IC. B^N. . . (2)
IC is the vector of initial conditions.
D(N)=B+B^2+B^3+....B^N
Equation 2 shows how the system of n objects is entangled with the boundary conditions of wall b and the source/sink term vector S.
It is obvious that equation 2 simultaneously solves the system for any BC and IC.
Needless to say, equation 1 and equation 2 are complete in the sense that:
They offer a continuous solution without singularities for U and can resolve any physical situation (classical or quantum) as well as mathematical (integration, differentiation, summation of integer series, etc.).
In fact, it is complete in the sense that it is a unified field theory.
A. Einstein overcomplicated both the theory of special relativity and the theory of general relativity by assuming too many unnecessary assumptions [1].
We assume that it is possible to reformulate Einstein's relativity in matrix form, statistical chains of matrix B or any other appropriate matrix formulation.
In other words, we can statistically derive Einstein's special relativity in 4D x-t unit space only via the new concepts of 4D x-t unit space.
It is obvious that there is no need to literally follow Einstein's thought experiment using the sphere of light observed in two inertial frames.
We introduce the concept of control volume V as a closed volume contained in closed surface area A insulated from the surrounding space by Dirichlet boundary conditions [2]
We draw Einstein's conclusion about special relativity in the simplest and most direct way.
It is clear that this new approach should be different from Einstein's approach in his Sphere of Light thought experiment, a thought experiment in which two observers from two inertial frames independently measured the speed of light relative to their own repository.
We explain the new approach in 3 successive steps:
Step 1
Construct a closed control x y z cubic volume V enclosed in a closed surface A where the boundary conditions in A are subject to Dirichlet BC which implies an isolated system where the total macroscopic propability inside the cube is equal to that of the integer space = 1.
The well-known divergence theorem for the first of the 4 Maxwell EMW equations is expressed as follows:
Div. E = ρ / ε. . . (1)
By applying the well-known divergence theorem in 3D+t space, we obtain,
∫∫E. dA = ∫∫∫ S(Rho) . dV/ε. . . (2)
By analogy between the divergence theorem (equation 2) and the Laplacian theorem, taking into account the fact that the divergence theorem applies to a vector field while the Laplacian operator applies to a scalar energy field U, we arrive at,
∫∫ U(E) . C dA Sav )=
∫∫∫ Nabla ^2 U dS dV+ ∫∫∫ S(U) dV. . . . . (3)
Sav is the average absorbance at the Dirichlet walls.
Equation 3 is what we call the Laplacian theorem.
Step 2
The second step is to apply eq 3 to the simple case of the free cooling curve (S=0 and BC=0) we arrive at,
d/dt)partial ∫∫∫U(x,y,z,t) dx dy dz= ∫∫ U(E) . C .dA Sav ) . . . . (3*)
C is the speed of the wave entanglement =330 m/s for sound and 3 E8 for EMW.
Equation 3 * is compeltely new and expresses the energy continuity in 4D x-t space.
With slight manipulation of equation 3 and taking into account that the average time elapsed for the entanglement signal to go from free nodes forward to the walls and come back is C/Ls where Ls=4V(L^3)/A(6L^2) then Eq 3* reduces to,
Now to solve equation 4 that is to find theC=T1/2 *log 2 * L^2/ α. . . . (4)Equation 4 is a generalised form of Einstein special theory of relativity.Or,T1/2 is the half-time or the time in seconds elapsed for the median temperature to fall to half its value at t=0.log 2= 0.693and α is the thermal diffusivity.L^2 for standard aluminum and steel cubes with a side length of 10 cm is 1.E-2.
It is clear that the time dependent solution for the midpoint MP(corresponding to the center of mass CM) in any 3D geometric object as that shown in Fig,1 is given by,
U(t)= U(0) . Exp - λ* t. . .... (4)
📷 Fig.1 A 3D cube discretized into 27 equally spaced free nodes and equipped with thermometer holes to measure the temperature T as a function of time t.
The exponent λ* can be found either theoretically or experimentally.
Step 3
i-Theoretically in universal time t* .
ii- Experimentally in real time t.
We have shown theoretically that for the freecooling curve BC=0 and S=0 (Dirichlet boundary conditions zero and source term zero),
B^N. IC = (0.5+0.5 RO)^N .IC. .... . .
IC is the vector of initial conditions at t=0.
The theoretical cooling curve is shown in Figure 2 [1,2].
B is the 27x27 transition matrix.
Using the midpoint theorem, we can find an expression for the decay exponent λ* as follows:
λ* = Log (0.5+0.5 RO). . . . . . . . . .(5)
The experimental cooling curves T as a function of t sec in real time are to be found experimentally.
In 2022 the Author performed experimental cooling curves on different metals of different shapes [1,2] and found out that equation t holds unconditionally for all values of RO∈ [0,1]as shown in Fig. 2.
C=T1/2 *log 2 * L^2/ α. . . . (6)
Or,
t is the real time and T1/2 is the half-time or the time in seconds elapsed for the median temperature to fall to half its value at t=0.
log 2= 0.693
and α is the thermal diffusivity.
L^2 for standard aluminum and steel cubes with a side length of 10 cm is 1.E-2.
It is worth mentioning that,
i-expression 3 is valid for small control volumes L^3 where the L/C entanglement time is practically zero.
ii-When the distance L is of the order of interstellar distances like that of general relativity, the entanglement time is considerable and equation 3 must be modified.
iii- λ* has a minimum of log 1/2=- 0.693 and a maximum of zero.
The cooling curve fitted to the theoretical results and experimental results is shown in Fig.2
📷
Figure 2. Experimental cooling curve compared to the theoretical cooling curve fitted to a standard 10 cm cube of Russian low-carbon steel.
Step 3
*The curve fitting in Fig.2 shows that:
experimental and theoretical results for a standard steel cube with a side of 10 cm coincide at RO = 0.22 for Russian low-carbon steel.
The curve also shows that t1/2=100 s.
ii-Another fitted curve like that of Fig.2 shows that:
for a standard aluminum cube with a side of 10 cm made from high quality Egyptian aluminum
t1/2=45 sec.
Where t1/2 is the half-time of freecooling or the time t elapsed for T to drop to half of its initial value (T=1/2 T(0))
The free cooling curve (BC = 0 and S = 0) in 4D unit space via B-matrix chain technique predicts that the speed of the entanglement signal C as,
C=t1/2 *log 2 * L^2/ α. . . . (6*)
Or,
Again t is the real time and t1/2 is the half-time or the time in seconds elapsed for the median temperature to fall to half its value at t=0.
log 2= 0.693
and α is the thermal diffusivity.
Also note that you need to substitute in equation 8 a cube of side 10 cm L^2 = E-2 m^2.
In order to solve Equation 6 for the speed of light C, we must first measure T1/2 experimentally and substitute its value into Equation 6.
This is the reason why the author measured the half-time of the cooling curve T1/2 in the middle for an aluminum cube of side 10 cm and found it equal to 45 seconds and that of a cube in steel similar to 100 seconds the thermal diffusivity α can be found from thermal tables.
Again, for the aluminum cube T1/2 found experimentally at 45 seconds and α found from the thematic tables is equal to 1.18 E-5 m^2 / sec.
By substituting the numerical values of T1/2 and that of thermal diffusivity α found in the thermal tables of equation 6 we obtain,
C = 2.9 E 8 m/s, which almost corresponds to the speed of the EMW equals 3 E8 m/s in a vacuum.
**Similarly, replacing the numerical values of t1/2 = 100 s and that of thermal diffusivity of steel α found in the thermal tables of equation 8 by α (steel) = 2.7 E-5 m ^2 /s, we obtain:
C = 2.9 E 8 m/s, which almost matches the speed of the EMW in a vacuum.
The two independent experiments on aluminum and steel give the same value for C = 2.9 E8 m/s.
This shows that entanglement exists in classical physics in the same way as in quantum physics and has a finite maximum flow velocity of C=3E8.
Now if this is the case, the question now is how the solution of the thermal diffusion equation in 4D unit space relates to the speed of light C?
The answer is simple: Mother Nature operates and signals entanglement in classical physics as well as in quantum mechanics at speed C.
Note again that the above analysis proves that:
energy entanglement exists in classical physics in the same way as quantum mechanics.
This also somehow proves Einstein's theory of special relativity, C=constant = 3E8 m/s without the need of the hypothesis of constancy of the speed of light C or Lorentz transformations x-t.
In addition it proves that energy density entanglement exists in classical physics (time dependent heat diffusion) in the same way as in quantum mechanics.
1-Researchgate, IJISRT journal, unitary space, Laplacian theorem and velocity of light c, August 2024
2-Researchgate, IJISRT journal, unitary space, Laplacian theorem and velocity of light c, August 2024
Now if the proposed universal 4D x-t unit space is not entirely new and has been successfully applied over the last four years to solve almost all types of classical and quantum physics in addition to pure mathematics such as finite digital in 1D, 2D, 3D and the summation of entire geometric series, etc. [1,2,3,4].
And if all this is not complicated and as clear as sunlight, why is there fierce resistance from 2020 to 2024?
The answer is simple and linked to the old guard of brainwashed physicists and mathematicians who blindly believe in incomplete 3D+t (R^4) space. They continue to apply it to energy density entanglement and defend it until their last breath.
Note that most of these iron guards occupy influential positions.