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The fact that gravitational field can be simulated/canceled by inertial forces relies upon the following elementary but fundamental fact.

The gravitational coupling constant of a given body, i.e. its gravitational mass,$M$, coincides with the other universal constant associated with that body, appearing in the general law of motion, i.e. the inertial mass $m$. So if a gravitational field $\vec{g}(t,x)$ is given, the equation of motion of a body with mass $m$, immersed in that field of acceleration is, $$m\frac{d^2\vec{x}}{dt^2} = M\vec{g}(t,\vec{x})$$ and, since $m=M$ $$\frac{d^2\vec{x}}{dt^2} = \vec{g}(t,\vec{x})\:.$$ The motion, therefore, depends only on initial position and velocity of the body but not on other properties. Exactly as geodesics do in a spacetime. So, a description in terms of geodesics in spacetime is allowed this way and the geometrization of gravitational theory enters physics.

Referring to Electromagnetic field, this story stops at the first step. Indeed the corresponding of gravitational mass is the electric charge $q$ and, evidently, $q \neq m$ and so, $$m\frac{d^2\vec{x}}{dt^2} = q\vec{E}(t,\vec{x})\:,$$ whose solution depend on the ratio $q/m$, not only on the initial position and velocity.

This is the reason why there is no equivalent of equivalence principle for electric forces and any attempt to geometrically describe electromagnetic interaction must be constructed following other approaches (gauge theories) without involving things like metrics and geodesics.

The fact that gravitational field can be simulated/canceled by inertial forces relies upon the following elementary but fundamental fact.

The gravitational coupling constant of a given body, i.e. its gravitational mass,$M$, coincides with the other universal constant associated with that body, appearing in the general law of motion, i.e. the inertial mass $m$. So if a gravitational field $\vec{g}(t,x)$ is given, the equation of motion of a body with mass $m$, immersed in that field of acceleration is, $$m\frac{d^2\vec{x}}{dt^2} = M\vec{g}(t,\vec{x})$$ and, since $m=M$ $$\frac{d^2\vec{x}}{dt^2} = \vec{g}(t,\vec{x})\:.$$ The motion, therefore, depends only on initial position and velocity of the body but not on other properties. Exactly as geodesics do in a spacetime. So, a description in terms of geodesics in spacetime is allowed this way and the geometrization of gravitational theory enters physics.

Referring to Electromagnetic field, this story stops at the first step. Indeed the corresponding of gravitational mass is the electric charge $q$ and, evidently, $q \neq m$ and so, $$m\frac{d^2\vec{x}}{dt^2} = q\vec{E}(t,\vec{x})\:,$$ whose solution depends on the ratio $q/m$, not only on the initial position and velocity.

This is the reason why there is no equivalent of equivalence principle for electric forces and any attempt to geometrically describe electromagnetic interaction must be constructed following other approaches (gauge theories) without involving things like metrics and geodesics.

The fact that gravitational field can be simulated/canceled by inertial forces relies upon the following elementary but fundamental fact.

The gravitational coupling constant of a given body, i.e. its gravitational mass,$M$, coincides with the other universal constant associated with that body, appearing in the general law of motion, i.e. the inertial mass $m$. So if a gravitational field $\vec{g}(t,x)$ is given, the equation of motion of a body with mass $m$, immersed in that field of acceleration is, $$m\frac{d^2\vec{x}}{dt^2} = M\vec{g}(t,\vec{x})$$ and, since $m=M$ $$\frac{d^2\vec{x}}{dt^2} = \vec{g}(t,\vec{x})\:.$$ The motion, therefore, depends only on initial position and velocity of the body but not on other properties. Exactly as geodesics do in a spacetime. So, a description in terms of geodesics in spacetime is allowed this way and the geometrization of gravitational theory enters physics.

Referring to Electromagnetic field, this story stops at the first step. Indeed the corresponding of gravitational mass is the electric charge $q$ and, evidently $q \neq m$. This is the reason why there is no equivalent of equivalence principle for electric forces and any attempt to geometrically describe electromagnetic interaction must be constructed following other approaches (gauge theories) without involving things like metrics and geodesics.

The fact that gravitational field can be simulated/canceled by inertial forces relies upon the following elementary but fundamental fact.

The gravitational coupling constant of a given body, i.e. its gravitational mass,$M$, coincides with the other universal constant associated with that body, appearing in the general law of motion, i.e. the inertial mass $m$. So if a gravitational field $\vec{g}(t,x)$ is given, the equation of motion of a body with mass $m$, immersed in that field of acceleration is, $$m\frac{d^2\vec{x}}{dt^2} = M\vec{g}(t,\vec{x})$$ and, since $m=M$ $$\frac{d^2\vec{x}}{dt^2} = \vec{g}(t,\vec{x})\:.$$ The motion, therefore, depends only on initial position and velocity of the body but not on other properties. Exactly as geodesics do in a spacetime. So, a description in terms of geodesics in spacetime is allowed this way and the geometrization of gravitational theory enters physics.

Referring to Electromagnetic field, this story stops at the first step. Indeed the corresponding of gravitational mass is the electric charge $q$ and, evidently, $q \neq m$ and so, $$m\frac{d^2\vec{x}}{dt^2} = q\vec{E}(t,\vec{x})\:,$$ whose solution depend on the ratio $q/m$, not only on the initial position and velocity. 

This is the reason why there is no equivalent of equivalence principle for electric forces and any attempt to geometrically describe electromagnetic interaction must be constructed following other approaches (gauge theories) without involving things like metrics and geodesics.

The fact that gravitational field can be simulated/canceled by inertial forces relies upon the following elementary but fundamental fact.

The gravitational coupling constant of a given body, i.e. its gravitational mass,$M$, coincides with the other universal constant associated with that body, appearing in the general law of motion, i.e. the inertial mass $m$. So if a gravitational field $\vec{g}(t,x)$ is given, the equation of motion of a body with mass $m$, immersed in that field of acceleration is, $$m\frac{d^2\vec{x}}{dt^2} = M\vec{g}(t,\vec{x})$$ and, since $m=M$ $$\frac{d^2\vec{x}}{dt^2} = \vec{g}(t,\vec{x})\:.$$ The motion, therefore, depends only on initial position and velocity of the body but not on other properties. Exactly as geodesics do in a spacetime. So, a description in terms of geodesics in spacetime is allowed this way and the geometrization of gravitational theory enters physics.

Referring to Electromagnetic field, this story stops at the first step. Indeed the corresponding of gravitational mass is the electric charge $q$ and, evidently $q \neq m$. This is the reason why there is no equivalent of equivalence principle for electric forces and any attempt to geometrically describe electromagnetic interaction must be constructed following other approaches (gauge theories).

The fact that gravitational field can be simulated/canceled by inertial forces relies upon the following elementary but fundamental fact.

The gravitational coupling constant of a given body, i.e. its gravitational mass,$M$, coincides with the other universal constant associated with that body, appearing in the general law of motion, i.e. the inertial mass $m$. So if a gravitational field $\vec{g}(t,x)$ is given, the equation of motion of a body with mass $m$, immersed in that field of acceleration is, $$m\frac{d^2\vec{x}}{dt^2} = M\vec{g}(t,\vec{x})$$ and, since $m=M$ $$\frac{d^2\vec{x}}{dt^2} = \vec{g}(t,\vec{x})\:.$$ The motion, therefore, depends only on initial position and velocity of the body but not on other properties. Exactly as geodesics do in a spacetime. So, a description in terms of geodesics in spacetime is allowed this way and the geometrization of gravitational theory enters physics.

Referring to Electromagnetic field, this story stops at the first step. Indeed the corresponding of gravitational mass is the electric charge $q$ and, evidently $q \neq m$. This is the reason why there is no equivalent of equivalence principle for electric forces and any attempt to geometrically describe electromagnetic interaction must be constructed following other approaches (gauge theories) without involving things like metrics and geodesics.