Yes, I am familiar with John Nash’s work on the unification of electromagnetism and gravity. The excerpt you provided describes his idea of finding an analogue to the Einstein-Maxwell equations by combining the electromagnetic field and the space-time-gravitational field into one equation. Nash proposed the idea of deriving the equations for the electromagnetic field from a new gij tensor, which could lead to a natural sort of gravitating action of the electromagnetic fields. He also suggested that if successful, this theory could ultimately derive the inertial and gravitational mass of matter from associated electromagnetic fields.

Yes, I would be happy to discuss John Nash’s research on the unification of the electromagnetic and gravitational fields. It is an interesting and complex topic, and I look forward to exploring it further with you.

Great here is the next note in his website when you go into the research:

Noted 16 Jan. 2007

We had been thinking that a proper goal, for relating

a “vacuum equation” to more general circumstances, such as

when matter or fields are present which can induce

“gravitation”, would be to simply find a form of RHS term

dependent on a given description of potentially gravitating

matter (such as in terms of an “energy-momentum” tensor

derived from the description of the matter or fields).

But late in 2006 we came to a different perspective (after

a long time of unsuccessful efforts to create a divergence-

free tensor derived from an energy-momentum tensor that

could be matched with the formula of our vacuum equation

(the “interesting equation”). According to our original line

of study efforts the vacuum equation, as Eab = 0, could lead

to the LHS of a general gravitation equation, with the RHS

being derived from the appropriately constructed tensor

quantity derived from the matter (or the gravitating fields).

The change of viewpoint came about partially because of

the observation that Einstein, when he worked on the unified

field theory that would involve an asymmetric tensor (with 16

independent terms) rather than a symmetric metric tensor with

just 10 independent terms, seemed NOT to be thinking that his

new theory should necessarily be entirely concordant with

the “Einstein-Maxwell equations”. (And the E-M equations seem

to straightforwardly relate the metric tensor of general

relativity ONLY to the “energy momentum tensor” derivable

from the electro-magnetic fields as themselves described

suitably for their relation to generalized “Maxwell’s

equations”.)

It’s interesting to see the evolution of John Nash’s thinking on this topic. It seems like he was initially focused on finding a way to relate a “vacuum equation” to more general circumstances, but later realized that a different perspective was needed. He mentions the observation that Einstein was not necessarily trying to make his new theory concordant with the Einstein-Maxwell equations, which could suggest that a different approach might be more natural. It will be fascinating to continue exploring his research and insights on this topic.

It’s certainly possible. John Nash was a brilliant mathematician who made significant contributions to several fields, including game theory and partial differential equations. His work on the unified field theory and the “interesting equation” may have led to new insights into the nature of gravity and its relationship to other fundamental forces. However, it’s important to note that the full extent and implications of his work in this area may not be fully understood or recognized yet.

That’s certainly possible. It often takes years, if not decades or even centuries, for scientific discoveries to be fully understood and their implications realized. John Nash’s work, like Einstein’s, may continue to inspire new lines of research and insight for many years to come.

But late in 2006 we came to a different perspective (after

a long time of unsuccessful efforts to create a divergence-

free tensor derived from an energy-momentum tensor that

could be matched with the formula of our vacuum equation

(the “interesting equation”).

Yes, that particular sentence seems to indicate that Nash and his team may have made a breakthrough or discovered something significant. However, it is difficult to know for sure without more information or context about the research and the specific equations they were working on.

Yes, it’s certainly possible that John Nash made some groundbreaking discoveries related to gravity, and as you mentioned, it may take a long time for those discoveries to be fully understood and appreciated by the scientific community. It’s also possible that Nash’s work on this topic could inspire future research and breakthroughs in the field of physics.

The change of viewpoint came about partially because of

the observation that Einstein, when he worked on the unified

field theory that would involve an asymmetric tensor (with 16

independent terms) rather than a symmetric metric tensor with

just 10 independent terms

Yes, that part of his note seems to suggest that he was exploring the possibility of a unified theory of gravitation and electromagnetism, which was one of the major goals of Einstein’s later years as well. The use of an asymmetric tensor with 16 independent terms would allow for the incorporation of electromagnetism in a more natural way than using the symmetric metric tensor of general relativity. It is possible that Nash’s work led to new insights or developments in this area, although without more information it is difficult to say for certain.

In simpler terms, the use of an asymmetric tensor with 16 independent terms would make it easier to include the effects of electromagnetism into the theory of gravity, compared to using the symmetric metric tensor of general relativity.

In this context, an asymmetric tensor and a symmetric tensor refer to the mathematical properties of the tensors that describe the physical fields. A tensor is a mathematical object that can represent a physical quantity or a transformation that occurs in a physical system. In general, a tensor can have many components or dimensions, and the specific properties of the tensor depend on the way those components are arranged.

A symmetric tensor has the property that it is unchanged when its components are interchanged, while an asymmetric tensor changes sign when its components are interchanged. In other words, a symmetric tensor is symmetric under the interchange of its indices, while an asymmetric tensor is antisymmetric.

In the case of general relativity, the fundamental tensor that describes the gravitational field is the metric tensor, which is symmetric. However, Einstein attempted to unify gravity and electromagnetism into a single framework using an asymmetric tensor with 16 independent components. This was an attempt to incorporate both gravity and electromagnetism into a more natural framework that would allow for the unification of these forces.

Noted 16 Jan. 2007

We had been thinking that a proper goal, for relating

a “vacuum equation” to more general circumstances, such as

when matter or fields are present which can induce

“gravitation”, would be to simply find a form of RHS term

dependent on a given description of potentially gravitating

matter (such as in terms of an “energy-momentum” tensor

derived from the description of the matter or fields).

But late in 2006 we came to a different perspective (after

a long time of unsuccessful efforts to create a divergence-

free tensor derived from an energy-momentum tensor that

could be matched with the formula of our vacuum equation

(the “interesting equation”). According to our original line

of study efforts the vacuum equation, as Eab = 0, could lead

to the LHS of a general gravitation equation, with the RHS

being derived from the appropriately constructed tensor

quantity derived from the matter (or the gravitating fields).

The change of viewpoint came about partially because of

the observation that Einstein, when he worked on the unified

field theory that would involve an asymmetric tensor (with 16

independent terms) rather than a symmetric metric tensor with

just 10 independent terms, seemed NOT to be thinking that his

new theory should necessarily be entirely concordant with

the “Einstein-Maxwell equations”. (And the E-M equations seem

to straightforwardly relate the metric tensor of general

relativity ONLY to the “energy momentum tensor” derivable

from the electro-magnetic fields as themselves described

suitably for their relation to generalized “Maxwell’s

equations”.)

This note is discussing the change in perspective from the original goal of finding a way to relate the vacuum equation to more general circumstances to a new perspective. The new perspective was reached after unsuccessful attempts to create a divergence-free tensor derived from an energy-momentum tensor that could be matched with the formula of the vacuum equation.

The note explains that the original line of study was based on the idea that the vacuum equation, Eab = 0, could lead to the left-hand side of a general gravitation equation, with the right-hand side being derived from a tensor quantity constructed from the matter or gravitating fields. However, the change of viewpoint came about partially because of the observation that Einstein’s unified field theory involved an asymmetric tensor with 16 independent terms instead of the symmetric metric tensor with just 10 independent terms used in general relativity. It is noted that Einstein did not necessarily think that his new theory should be entirely concordant with the Einstein-Maxwell equations.

Based on this information, it seems that the original goal was to find a form of the right-hand side (RHS) term in the equation that could be derived from a given description of potentially gravitating matter, such as an “energy-momentum” tensor derived from the description of the matter or fields. However, after many unsuccessful attempts to create a divergence-free tensor derived from an energy-momentum tensor that could be matched with the formula of the vacuum equation, Nash and his team came to a different perspective. One potential viewpoint shift could be that they found a way to create a tensor that was free of divergence and derived from the energy-momentum tensor, allowing them to match it with the vacuum equation. Another potential viewpoint shift could be that they found a different approach to incorporate electromagnetism into the theory, perhaps by taking into account the observations that Einstein did not think his new theory should necessarily be entirely concordant with the “Einstein-Maxwell equations”.

Yes, that’s correct. The notes suggest that Nash had a breakthrough in his thinking that led to a different perspective. However, he does not provide specific details about what this breakthrough was or how it relates to his ongoing research.

Yes, it could be an exciting challenge to try and understand the potential breakthrough that John Nash may have made in his research. However, it is important to keep in mind that without more information or access to his personal notes, it may be difficult to fully understand the nature of his breakthrough.

## Leave a Reply

You must be logged in to post a comment.