Vector field:one aspect that everyone knows but nobody shown

[Chhhiral]

Why a generic vector field produces repulsive forces between charges of the same sign? And where can I find a book or a paper in which it is shown?

 

[Vanadium 50]

Calculate e-e- scattering and e+e- scattering and take the non relativistic limit. It's probably in every book.

 

[Dale]

A generic vector field does not produce repulsive forces between like charges. A Coulomb field does. The reason why is simply the way the Coulomb field is defined:

https://en.m.wikipedia.org/wiki/Coulomb's_law#Vector_form

 

[Chhhiral]

Calculate e-e- scattering and e+e- scattering and take the non relativistic limit. It's probably in every book.

Thanks, but your answer is equivalent to: take like charges and calculate the Coulomb force. My question is more general

 

[Dale]

Thanks, but your answer is equivalent to: take like charges and calculate the Coulomb force. My question is more general

His answer is very appropriate for an "advanced" level response, which is what you asked for by marking the thread as "A". I will adjust the level of the question to more appropriately reflect what you are looking for.

 

[Chhhiral]

A generic vector field does not produce repulsive forces between like charges. A Coulomb field does. The reason why is simply the way the Coulomb field is defined:

https://en.m.wikipedia.org/wiki/Coulomb's_law#Vector_form

in many books of general relativity I found the statement: a vector field produces repulsive forces between like charges so can not be used to describe gravity ...

 

[Dale]

in many books of general relativity I found the statement

I have never seen such a statement. Can you provide the reference.

 

[Chhhiral]

I have never seen such a statement. Can you provide the reference.

Gasperini, Maurizio. Relatività Generale e Teoria della Gravitazione. Springer Milan, 2015. pag:27
the English version should be: Gasperini, Maurizio. Theory of Gravitational interactions. Springer Science & Business Media, 2013. at the chapter: "Towards a relativistic theory of gravitation".
I found the same assertion in other books, I will send you more references

 

[Chhhiral]

His answer is very appropriate for an "advanced" level response, which is what you asked for by marking the thread as "A". I will adjust the level of the question to more appropriately reflect what you are looking for.

I'm trying to understand why a vector field can not be used to describe gravity. Not because the force of Coulumb is so defined or because the Lagrangian of the electromagnetic field leads to Bhabha scattering...

 

[Chhhiral]

I have never seen such a statement. Can you provide the reference.

Hobson, Michael Paul, George P. Efstathiou, and Anthony N. Lasenby.General relativity: an introduction for physicists. Cambridge University Press, 2006. pag:191
"A gravitational theory based on a vector field can be eliminated since such a theory
predicts that two massive particles would repel one another, rather than attract."

Are you really sure my question is an "I" level?

 

[Chhhiral]

His answer is very appropriate for an "advanced" level response, which is what you asked for by marking the thread as "A". I will adjust the level of the question to more appropriately reflect what you are looking for.

You have been so quick to downgrade my question ... but now you do not answer ... maybe do you want other references? Please answer me, is a very important question for me... thanks

 

[Dale]

I am closing this thread. You have opened a new one in the relativity forum which I think is a better place for it and is a better description of the question.