I have literally never met a single serious scientist who claimed that the Schrödinger equation constituted a unified field theory.

1]December 26, 2019

Schrödinger’s Unified Field Theory

Posted by John Baez

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Erwin Schrödinger fled Austria during World War II. In 1940 he found a position in the newly founded Dublin Institute for Advanced Studies. This allowed him to think again. He started publishing papers on unified field theories in 1943, based on earlier work of Eddington and Einstein. He was trying to unify gravity, electromagnetism and a scalar ‘meson field’… all in the context of classical field theory, nothing quantum.

2]A Unified Field Theory Based on a Rotating de Broglie Wave Packet

Louis M. Houston The Physics Department, The University of Louisiana at Lafayette, Lafayette, LA, USA. DOI: 10.4236/jamp.2019.72026 PDF HTML XML 980 Downloads  2,185 Views

3]

The Fundamental Problems of the Unified Field Theory.

IOSR Journal

https://www.iosrjournals.org › papers › Version-1

etc...etc...@Jürgen Weippert

Reference 1 is not a publication at all.

Reference 2:

1) It's an SCIRP publication. SCIRP's academic integrity is under severe doubts so I would not rate that very serious. https://en.wikipedia.org/wiki/Scientific_Research_Publishing#Academic_integrity

2) If you look into it, you see that the author modifies the Scrödinger equation, so it does not support your claim.

3) It also writes about general relativity which is not part of the Schrödinger equation.

In reference 3 you also refer to a predatory publisher (https://www.researchgate.net/post/Are-international-organization-of-scienctific-research-IOSR-and-Journal-of-ChemistryEducation-research-and-practice-predators-journals-or-real), so this is also not a serious support for any claim.

I checked out the blog post of "reference 1". It does not contain the claim that Schrödinger or Baez consider the Schrödinger equation a unified field theory, either.

Answer II continued

The quantifiable theory of room acoustics was established based on Wallace Sabine's theory of reverberation in 1898.

Sabine's theory of reverberation, founded over a century ago, is experimental and has never been proven since.

Assuming that the speed of sound in air C, at NPT is 330 m/s, the Sabines formula for TR (60 db) simply noted TR, reduces to [1],

TR = 0.161 V/AS,. . second. . . . . (1)

Where S is the average absorption.

However, the B-matrix strings provide the first rigorous proof of Sabine's reverberation theory as follows:

dU /dt =-U.Const.2π.Area/Volume. . . (2)

Equation 2 applies to sound energy in audio rooms and the thermal diffusion equation with Dirichlet boundary conditions.

A simple algebraic manipulation of equation 2 gives,

TR =(1/2 π) V / A S,. . second. . . . . (3)

Or,

TR =(0.160) V / A S,. . second. . . . . (3*)

Equation 3* shows that the Sabines formula (equation 1) is quite precise and that the chains of the matrix B, product of the Cairo statistical theory, are a unified field theory.

Additionally, equation 3* attaches statistical significance to the constant π.

1-Theory and design of audio rooms-Reformulation of the Sabine formula, ResearchGate, IJISRT review,

October 2021

To be continued.

Answer III continued

In fact, the Sabine theory of reverberation time sets up a satanic trap or explosive minefield.The giant scientist W. Sabine presented his imperial formula for reverberation time TR as follows:TR = 0.161 V/AS,. . second. . . . . (1)Where S is the average absorption.

He also proposed a sort of derivation of his formula that makes it a sort of theory.

Sabines defined a statistical length Ls as the average statistical distance between two reverberations or successive sound reflections on the walls, floor and ceiling of the audio room as,

Ls = 4 V/S. . . . . (2)

Equation 2 forms a satanic trap or explosive minefield, not because it is inaccurate but because no single scientist has been able to understand its interpretation for over a century.

Since the time of W. Sabine, many physicists and mathematicians have proposed an improvement or reformulation of Sabine's reverberation formula, but they have fallen into the satanic trap of using equation 2 without rigorous proof [1] .

This means that they added nothing to the theory of absorption of sound energy by reverberation.

On the other hand, matrix chain B which is a product of the statistical theory of Cairo techniques offers the solution without the need for equation 2 or any other statistical assumptions. It predicts and proves an exponential decay of the energy density of sound in audio rooms like [2],

U(t)=U(0) Exp(- λ t)

Furthermore, the statistical theory of Cairo techniques proposes an expression to evaluate λ in terms of average absorption S being minimum for a maximum S = 1.This minimum proposed by the chains of matrix B should be Log(2)=0.693

This means that λ cannot be zero and that energetic decay by diffusion has a maximum rate. It is surprising that W. Sabine noticed this fact and measured it experimentally as a value very close to the one mentioned above.

1-Revision of Sabine's reverberation theory following a different approach

to Eyring's theory

Toshiki Hanyu 1*

1 Nihon University, Junior College, Dept. of Architecture and Living Design, 7-24-1 Narashinodai, Funabashi, Chiba, 274-8501 Japan, 2021.

2-Theory and design of audio rooms-Reformulation of the Sabine formula, ResearchGate, IJISRT review,

October 2021.

Answer IV continued

In the previous answers we have shown that Sabines' theory of reverberation is based on two profound equations or corner pillars, namely:

Ls = 4 V/S. . . . (1)

For all 3D geometric shapes.

And,

U(t)=U(0) Exp(- λ t) . . . (2)

which is the time dependence of the sound-energy density decay in audio rooms.

Note that both equations 1,2 are physico-statistical in nature and have no rigorous mathematical proof.

On the other hand, equations 1,2 are contained in the string mechanics of matrix B as expected.

*Equation 1 which has never been explicitly proven mathematically is conditional but a deep theorem in itself.

Equation 1 leads to the following rule which we call the AB rule:

The AB Rule: 3D bodies of different shapes cannot have the same volume-to-surface ratio unless they have exactly the same volume and surface area.

Note again that the AB-rule is only true under certain conditions.

**Equation 2, which has also never been explicitly proven theoretically, is another deep theorem in itself.

The statistical mechanics of matrix B predicts:

U(t)=U(0) . [B]^N. . (3)

Where N is..

Equation 3 is the matrix-mechanical statistical equivalence of Eq. 2.

In fact, the equation. 3 results in,

U(t)=U(0) Exp(- λ* t) . . . (4)

If we recall that in 4D unit space, time t is equal to N dt and dimensionless time is simply N.

N is the number of repetitions or iterations.

We can find a calculation expression for the exponential decay coefficient λ*.

To be continued.

Answer V continued

The time-dependent solution of the sound energy density in audio rooms is given by:

U(t)= B^N*U(0) . . . (1)

where U(0) is the sound intensity vector in the audio room before the source is suddenly cut off.

Figure 1 shows a cubic sound room discretized into eight equally spaced free nodes.

The statistical transition matrix B for this room is given by,

RO 1/6-RO/6 0 1/6-RO/6 1/6-RO/6 0 0 0

1/6-RO/6 RO 1/6-RO/6 0 0 1/6-RO/6 0 0

0 1/6-RO/6 RO 1/6-RO/6 0 0 1/6-RO/6 0

1/6-RO/6 0 1/6-RO/6 RO 0 0 0 1/6-RO/6

1/6-RO/6 0 0 0 RO 1/6-RO/6 0 1/6-RO/6

0 1/6-RO/6 0 0 1/6-RO/6 RO 1/6-RO/6 0

0 0 1/6-RO/6 0 0 1/6-RO/6 RO 1/6-RO/6

0 0 0 1/6-RO/6 1/6-RO/6 0 1/6-RO/6 RO

In fact, the time-dependent solution given by equation 1

forms a geometric sequence r^N.

In other words, equation 1 reduces to U(t)=r^N U(0) where N is the dimensionless time (t=N dt) or the number of iterations and dt is the time step .

Note that geometric sequences are the discrete version of exponential functions, which are continuous.

If we assume that RO represents the average sound absorption, then the matrix mechanical solution (Eq 1) has the following properties:

1- minimum value of RO=0 and maximum RO=1/2.

For RO .GE. 1/2 the solution is unstable and diverges to infinity as expected.

2-The solution can be expressed as an exponential function,

U(t)=U(0) Exp(- λ* t) . . . (4*)

Note that the reverberation time TR is inversely proportional to Sav or RO.

The following Table 1 shows the values ​​of r and λ* for different values ​​of RO:

RO 0 0.1, 0.2 0.3, 0.4 0.5

r 0.5 0.55 0.6 0.65 0.7 0.75

λ* 0.693 0.598 0.511 0.431 0.357 0.287

Table 1 shows that the exponential decay of energy density by diffusion has a maximum rate or maximum exponential decay coefficient value of 0.693.

What is quite striking is that this astonishing fact was discovered and measured experimentally by W. Sabine more than a century ago.

Answer VI (continued)

Fig.1 A cubic sound room with eight free nodes.

Figure 1 is presented to show how the 8 free nodes in the audio room are ordered and numbered in the 8x8 statistical transition matrix B.

There are few permutations for canonical arrangement and numbering that can be used in Matrix B where Figure 1 is one.

In conclusion, we affirm that,

i- The Sabine formula for reverberation time in TR audio rooms is the most accurate. The only drawback is that it is an experimental formula that contains no rigorous mathematical proof.

ii- The only derivation of the Sabine formula for reverberation time in audio rooms is accessible via the statistical chains of matrix B.

iii- Other mathematical derivations done to mathematically derive Sabine's formula for reverberation time are physically wrong.