The Einstein-Schrodinger Theory

**Russell E. Rierson** · May19-04, 04:19 AM

The Einstein-Schrodinger Theory:

http://www.einstein-schrodinger.com/

The Einstein-Schrodinger theory is also known as "Einstein's Unified Field Theory" or "Schrodinger's Affine Field Theory" or the "Einstein-Straus Theory" or the "Hermitian Theory of Relativity" or the "Generalized Theory of Gravitation". It was developed by Albert Einstein and Erwin Schrodinger, primarily in the 40s and 50s. It is thought by some to be a unified theory of gravitation and electromagnetism. This was supposedly disproven way back in 1953, but there are a few stubborn souls such as myself who still think it is correct, and who work to prove it.

[...]

For the Einstein-Schrodinger theory to unify gravitation and electromagnetism, the field equations must closely approximate the Einstein equations and Maxwells equations. However, it is the small differences from the Einstein equations and Maxwells equations that are interesting. This is the most important reason for pursuing unified field theories, because they can lead to new physics and small corrections to the existing equations of physics.

~~WWW~~ · May19-04, 04:50 AM

Dear Russell E. Rierson,

If you ask my opinion, then no real change in any scientific field (abstract or non-abstract) will take place, if we ignore our own cognition's abilities to develop these areas.

**Russell E. Rierson** · May19-04, 05:18 AM

It seems that a lot of new math has been derived since 1953. The question is how to explain the fundamental forces in terms of a unifying symmetry?

Einstein and the unified field:

http://www.alexander-unzicker.de/ae1930.html

http://www.lrz-muenchen.de/~aunzicker/einst.html

**Blackforest** · May19-04, 08:53 AM

Dear Russel E. Rierson, to work about an unification is quite my hobby; you could have a look on my modest contribution at http://www.alititi.privat.t-online.de (in french, in englisch or in german language). Compared to all what I can read on the subject, I would say that my work is a kind of development of some other theories trying to include a polarized vacuum (described with Maxwell's Laws) in the general relativity. (e.g. Puthoff). Are you interesting in?

~~WWW~~ · May19-04, 09:04 AM

In the secont address ( http://www.lrz-muenchen.de/~aunzicker/einst.html ) I have found this question:

"The question arises: How can we join to our riemannian spaces in a naturally logical way an additional structure that provides a uniform character of the whole thing ?"

My question therefore is: What is a naturally logical way?

**Antonio Lao** · May19-04, 11:10 AM

I was wondering can gravity be unified with electromagnetism by the following:

Using only forces and no heavy math, the gravity force, $LaTeX Code: F^{-}_G$ and antigravity $LaTeX Code: F^{+}_G$ are both proportional to the difference between electric force,

and magnetic force,

.

$LaTeX Code: F^{-}_G = k(F_E - F_B)$

$LaTeX Code: F^{+}_G = ksingle-quote(F_B - F_E)$

where k and k' are the constants of proportionality.

**Russell E. Rierson** · May20-04, 04:19 AM

Originally Posted by Antonio Lao

I was wondering can gravity be unified with electromagnetism by the following:

Using only forces and no heavy math, the gravity force, $LaTeX Code: F^{+}_G$ and antigravity $LaTeX Code: F^{-}_G$ are both proportional to the difference between electric force, and magnetic force, .

$LaTeX Code: F^{+}_G = k(F_E - F_B)$

$LaTeX Code: F^{-}_G = ksingle-quote(F_B - F_E)$

where k and k' are the constants of proportionality.

Entropy and gravity become closely linked, via black hole thermodynamics. The thermodynamic arrow of time is the direction of increased entropy.

Here is mathematician John Nash's "Einstein field equation" where he talks about gravity "compression" waves:

http://www.stat.psu.edu/~babu/nash/intereq.pdf

Wave-Like Form of the Scalar Equation
It was discovered only recently by me that the scalar equation naturally derived from the tensor equation for vacuum, particularly in the case of 4 space-time dimensions, has a form extremely suggestive of waves. The scalar derived equation can be obtained by formally
contracting the general vacuum equation with the metric tensor. This results at first in an equation involving G (the scalar derived from the Einstein tensor) and the Ricci tensor and the scalar curvature R. And G, being the scalar trace of the Einstein tensor, can be expressed in term of R but this expression involves the number of dimensions, n. So we get
as the scalar equation derived from the original vacuum equation this result:

[...]

And now two things are notable about the form of this resulting scalar equation: (1): If n = 2 there is a singularity and this simply corresponds to the fact that the Einstein G-tensor is identically vanishing if n = 2, so there isnt any derived scalar equation of this type for two dimensions. (2): For n = 4 we find the nice surprise that the scalar equation entirely simplifies and then asserts simply that the scalar curvature satisfies the wave operator (which is a d'Alembertian if we think in terms of 3 + 1 dimensions).
So the scalar equation is

[]R = 0 PROVIDED that n = 4

[...]

But I don't myself understand either renormalization or the general theory of quantiza-tion. (To me it seems like \quantum theory" is in a sense like a traditional herbal medicine used by \witch doctors". We don't REALLY understand what is happening, what the ulti-mate truth really is, but we have a \cook book" of procedures and rituals that can be used
to obtain useful and practical calculations (independent of fundamental truth).)

**Antonio Lao** · May20-04, 09:45 AM

Tensors are higher dimensional generalized vectors beyond the three we normally encountered. Their transformations created the calculus of tensors. To keep things simple, I am only using tensor of rank 0 and rank 1 in my research. A rank 0 tensor is really just a scalar and a rank 1 is really a vector in the usual sense. A rank 2 is, I think, a matrix. What is a rank 3 tensor? Is it a cube? What is a rank 4 tensor? Is it a hypercube?

**Antonio Lao** · May20-04, 11:48 AM

Expanding the gravity form

$LaTeX Code: G^{-} = k(qE - qv \\times B)$

$LaTeX Code: G^{-} = kq(E - v \\times B)$

$LaTeX Code: G^{-} = kqL$

where $LaTeX Code: L = E - v \\times B$ and if the positions of v and B are interchanged then L is the Lorentz force.

But the question is, in reality, who decides the changing of position for v and B? In vector analysis, this distinction is taken care of by the introduction of axial and polar vectors. But is this necessary? Aren't we introducing a directionality into the equation by putting v before B? Aren't all physical equations supposed to be in directionally symmetric forms? It seems that a principle is needed to assert this type of invariance of nature, the Principle of Directional Invariance.

Further, let $LaTeX Code: Lsingle-quote = v \\times B - E$ . So depending on the positions of v and B in the equations:

$LaTeX Code: G^{-} = kq(E - v \\times B)$ or $LaTeX Code: G^{-} = kq(E + v \\times B)$ and for the antigravity forms: $LaTeX Code: G^{+} = ksingle-quoteq(v \\times B - E)$ or $LaTeX Code: G^{+} = -ksingle-quoteq(v \\times B + E)$ .

And $LaTeX Code: (E - v \\times B) \\equiv (v \\times B - E)$ at only the vacuum where $LaTeX Code: \\nabla \\cdot E = 0$ and $LaTeX Code: \\nabla \\cdot B = 0$ and v is equal to the speed of light in vacuum.

**quartodeciman** · May20-04, 12:13 PM

Einstein's unified field theory (relativistic theory of the non-symmetric field) was not the first such unification theory (Weyl theory, Kaluza-Klein theory) and certainly isn't the last such unification theory, but as far as I know it is the only one whose main result has been written in frosting on a cake.

**Russell E. Rierson** · May21-04, 04:03 AM

Originally Posted by Antonio Lao

Expanding the gravity form

$LaTeX Code: G^{-} = k(qE - qv \\times B)$

$LaTeX Code: G^{-} = kq(E - v \\times B)$

$LaTeX Code: G^{-} = kqL$

where $LaTeX Code: L = E - v \\times B$ and if the positions of v and B are interchanged then L is the Lorentz force.

But the question is, in reality, who decides the changing of position for v and B? In vector analysis, this distinction is taken care of by the introduction of axial and polar vectors. But is this necessary? Aren't we introducing a directionality into the equation by putting v before B? Aren't all physical equations supposed to be in directionally symmetric forms? It seems that a principle is needed to assert this type of invariance of nature, the Principle of Directional Invariance.

Further, let $LaTeX Code: Lsingle-quote = v \\times B - E$ . So depending on the positions of v and B in the equations:

$LaTeX Code: G^{-} = kq(E - v \\times B)$ or $LaTeX Code: G^{-} = kq(E + v \\times B)$ and for the antigravity forms: $LaTeX Code: G^{+} = ksingle-quoteq(v \\times B - E)$ or $LaTeX Code: G^{+} = -ksingle-quoteq(v \\times B + E)$ .

And $LaTeX Code: (E - v \\times B) \\equiv (v \\times B - E)$ at only the vacuum where $LaTeX Code: \\nabla \\cdot E = 0$ and $LaTeX Code: \\nabla \\cdot B = 0$ and v is equal to the speed of light in vacuum.

The gravity tensor should be able to rotate into the electromagnetic tensor and the electromagnetic tensor should be able to rotate into the gravity tensor.

Time
^
|
|
|
|-------------->space

G
^
|
|
|
|-------------->EM

Here is an interesting quote:

http://www.einstein-schrodinger.com/

In the well established "General Theory of Relativity", the Einstein equations are the field equations which describe the allowed values of the gravitational field. In the Einstein equations, the gravitational field is not a single number but is instead represented by the metric g_ik, which is a 4x4 matrix containing 4x4=16 components. However it is required to be symmetric, meaning that

g_ik= g_ki (for every combination of i=0,1,2,3 and k=0,1,2,3)

Therefore, g_ik really only has 16-6=10 independent components.

Maxwell's equations are the field equations which describe the allowed values of the electromagnetic field. In Maxwell's equations, the electromagnetic field F_ik is also a 4x4 matrix containing 4x4=16 components. However, it is required to be antisymmetric, meaning that

F_ik= -F_ki (for every combination of i=0,1,2,3 and k=0,1,2,3)

In this case, for elements along the diagonal of the matrix we have
F_ii = -F_ii, which can only be true if they are zero. Therefore, F_ik has just 16-6-4=6 independent components.

In the Einstein-Schrodinger theory, the field equations are written in terms of a matrix N_ik with no symmetry properties, so that it has a full 4x4=16 independent components. Therefore, it could potentially contain both the metric and the electromagnetic field. For example we could have,

N_ik=g_ik+F_ik

By this definition and the symmetry properties of g_ik and F_ik, it is easy to see that the symmetric part of N_ik would be the metric

g_ik=(N_ik+N_ki)/2

and the antisymmetric part of N_ik would be the electromagnetic field

F_ik=(N_ik-N_ki)/2

This method for combining the metric and the electromagnetic field is meant as a simple example and does not actually work...

It does not work but it is still interesting...

**Blackforest** · May21-04, 05:19 AM

Originally Posted by Antonio Lao

Expanding the gravity form

$LaTeX Code: G^{-} = k(qE - qv \\times B)$

$LaTeX Code: G^{-} = kq(E - v \\times B)$

$LaTeX Code: G^{-} = kqL$

where $LaTeX Code: L = E - v \\times B$ and if the positions of v and B are interchanged then L is the Lorentz force.

But the question is, in reality, who decides the changing of position for v and B? In vector analysis, this distinction is taken care of by the introduction of axial and polar vectors. But is this necessary? Aren't we introducing a directionality into the equation by putting v before B? Aren't all physical equations supposed to be in directionally symmetric forms? It seems that a principle is needed to assert this type of invariance of nature, the Principle of Directional Invariance.

Further, let $LaTeX Code: Lsingle-quote = v \\times B - E$ . So depending on the positions of v and B in the equations:

$LaTeX Code: G^{-} = kq(E - v \\times B)$ or $LaTeX Code: G^{-} = kq(E + v \\times B)$ and for the antigravity forms: $LaTeX Code: G^{+} = ksingle-quoteq(v \\times B - E)$ or $LaTeX Code: G^{+} = -ksingle-quoteq(v \\times B + E)$ .

And $LaTeX Code: (E - v \\times B) \\equiv (v \\times B - E)$ at only the vacuum where $LaTeX Code: \\nabla \\cdot E = 0$ and $LaTeX Code: \\nabla \\cdot B = 0$ and v is equal to the speed of light in vacuum.

Sorry that I introduce me in this discussion and sorry if my question seems to be a little bit simple (I am just an amateur and I like physics) but to get an answer to your question who "...decides the changing of position for v and B? In vector analysis, this distinction is taken care of by the introduction of axial and polar vectors. But is this necessary? Aren't we introducing a directionality into the equation by putting v before B? Aren't all physical equations supposed to be in directionally symmetric forms?" ... would it not be relevant to make a systematic analysis of the following equation u x w = [matrix].w + rest (E) -whwere "x" between u and w is here the wedge product- ? (which is indeed one of my preoccupations in the work that you can visit on this forum). This equation (E) is exactly the equation allowing me to calculate the temporal variations of the Poynting's vector making use of the Maxwell's equations in vacuum to get a dynamic equation valid for the vacuum... Blackforest

**Antonio Lao** · May21-04, 08:40 AM

Originally Posted by Blackforest

would it not be relevant to make a systematic analysis of the following equation u x w = [matrix].w + rest (E) -whwere "x" between u and w is here the wedge product- ?

I'm still not clear about your equation? Please elaborate more. Thanks.

**Blackforest** · May22-04, 11:26 AM

Originally Posted by Antonio Lao

I'm still not clear about your equation? Please elaborate more. Thanks.

See the attachment (Discussion.doc) for the answer. Thank you for the question. Blackforest

**Russell E. Rierson** · May23-04, 11:16 PM

Abhay Ashtekar has some excellent ideas IMHO:

http://cgpg.gravity.psu.edu/people/A.../articles.html

QUOTE

Imagine there is no space and time in the background; no canvas to
paint the dynamics of the physical universe on. Imagine a play in
which the stage joins the troupe of actors. Imagine a novel in which
the book itself is a character...

Yes, one can still do physics without sacrificing any mathematical
precision. In classical physics, Einstein taught us how to do this by
weaving the gravitational field into the very fabric of space-time. In
the resulting theory, general relativity, there is no background
space-time, no inert arena, no spectators in the cosmic dance. Matter,
through its gravity, tells space-time how to bend and curved
space-time, in turn, tells matter how to move. However, classical
physics is incomplete; it ignores the quantum world. Can we fuse the
pristine, geometric world of Einstein's with quantum physics, without
robbing it of its soul? Can we realize Einstein's vision at the
quantum level?

END QUOTE

"Space" could be a Bose Einstein condensate at the Planck scales?

http://www.mcs.vuw.ac.nz/~visser/cqg-bec.pdf

QUOTE:

Such equations can be used, for example, in discussing
Bose–Einstein condensates in heterogeneous and highly nonlinear systems.
We demonstrate that at low momenta linearized excitations of the phase of the
condensate wavefunction obey a (3 + 1)-dimensional d'Alembertian equation
coupling to a (3 + 1)-dimensional Lorentzian-signature ‘effective metric' that
is generic, and depends algebraically on the background field. Thus at low
momenta this system serves as an analogue for the curved spacetime of
general relativity. In contrast, at high momenta we demonstrate how one
can use the eikonal approximation to extract a well controlled Bogoliubovlike
dispersion relation, and (perhaps unexpectedly) recover non-relativistic
Newtonian physics at high momenta. Bose–Einstein condensates appear to
be an extremely promising analogue system for probing kinematic aspects of
general relativity.

end quote.

If it can be formulated in terms of "background independence"...?

**Antonio Lao** · May24-04, 10:49 AM

Isn't the search for a background the same as the search for an absolute rest frame of reference like the aether frame?

I think what both special and general relativity theory are telling us is that spacetime is the absolute background of all of reality which include the quantum reality. Spacetime is used in quantum field theory, in superstring theory, and in M-theory as well.

But in the quantum domain, the reality of quantized spacetime is the same as the quantization of one-dimensional space. A plausible theory can be built and this theory can describe the true meaning of mass and charge.