Skip to main content
Physics

Return to Question

Became Hot Network Question
edited body
Source Link
Luqman Saleem
Luqman Saleem
  • 1.4k
  • 10
  • 26

I am quite new to this topic. Please bear with me.

Suppose we are given a transformation of both space and time and space coordinate's derivatives as $$ \partial_t\to D_t=\partial_t-f(t,x)\partial_t\\ \nabla\to \mathbf{D}=\nabla+\mathbf{F}(t,x)\partial_t \tag{1} $$ $f$ is a scalar field and $\mathbf{F}$ is a vector field. Is there anyway to know what kind of coordinate transformation made the derivative transformation look like $(1)$?

Personally, the time derivative transformation given in $(1)$ looks okay to me but the space derivative transformation looks "weird" to me. I mean the space derivative is changing into time derivative... what does it mean? Is it a normal thing? Could someone please explain what is the physical meaning of this transformation.

I am quite new to this topic. Please bear with me.

Suppose we are given a transformation of both space and time coordinate's derivatives as $$ \partial_t\to D_t=\partial_t-f(t,x)\partial_t\\ \nabla\to \mathbf{D}=\nabla+\mathbf{F}(t,x)\partial_t \tag{1} $$ $f$ is a scalar field and $\mathbf{F}$ is a vector field. Is there anyway to know what kind of coordinate transformation made the derivative transformation look like $(1)$?

Personally, the time derivative transformation given in $(1)$ looks okay to me but the space derivative transformation looks "weird" to me. I mean the space derivative is changing into time derivative... what does it mean? Is it a normal thing? Could someone please explain what is the physical meaning of this transformation.

I am quite new to this topic. Please bear with me.

Suppose we are given a transformation of both time and space coordinate's derivatives as $$ \partial_t\to D_t=\partial_t-f(t,x)\partial_t\\ \nabla\to \mathbf{D}=\nabla+\mathbf{F}(t,x)\partial_t \tag{1} $$ $f$ is a scalar field and $\mathbf{F}$ is a vector field. Is there anyway to know what kind of coordinate transformation made the derivative transformation look like $(1)$?

Personally, the time derivative transformation given in $(1)$ looks okay to me but the space derivative transformation looks "weird" to me. I mean the space derivative is changing into time derivative... what does it mean? Is it a normal thing? Could someone please explain what is the physical meaning of this transformation.

Source Link
Luqman Saleem
Luqman Saleem
  • 1.4k
  • 10
  • 26

Transformation of derivatives of coordinates

I am quite new to this topic. Please bear with me.

Suppose we are given a transformation of both space and time coordinate's derivatives as $$ \partial_t\to D_t=\partial_t-f(t,x)\partial_t\\ \nabla\to \mathbf{D}=\nabla+\mathbf{F}(t,x)\partial_t \tag{1} $$ $f$ is a scalar field and $\mathbf{F}$ is a vector field. Is there anyway to know what kind of coordinate transformation made the derivative transformation look like $(1)$?

Personally, the time derivative transformation given in $(1)$ looks okay to me but the space derivative transformation looks "weird" to me. I mean the space derivative is changing into time derivative... what does it mean? Is it a normal thing? Could someone please explain what is the physical meaning of this transformation.