B Photography in 4D World: Time & Space

[sonutabitha]

If time is a dimension, what would be the dimension of a photograph in such a space?

 

[Ibix]

Idealising the image as being one face of a physical piece of paper, it's a (2+1)d object, although there's nothing interesting about the time-like direction since (apart from any overall motion/deformation/damage/etc of the photograph) nothing changes.

Loosely, in Newtonian terms you regard a camera as mapping points (x,y,z) onto a plane (x,y) at a given time T-z/c (to allow for the finite speed of light) - it chooses a value of the time parameter and drops the z coordinate, in other words. In relativistic terms you'd regard it as taking points in the plane (x,y,z,T-z/c) and mapping them onto a plane (x,y) - so dropping the z and t coordinates. The only real difference is whether you regard time as a parameter or a dimension.

 

[sonutabitha]

Idealising the image as being one face of a physical piece of paper, it's a (2+1)d object, although there's nothing interesting about the time-like direction since (apart from any overall motion/deformation/damage/etc of the photograph) nothing changes.

Loosely, in Newtonian terms you regard a camera as mapping points (x,y,z) onto a plane (x,y) at a given time T-z/c (to allow for the finite speed of light) - it chooses a value of the time parameter and drops the z coordinate, in other words. In relativistic terms you'd regard it as taking points in the plane (x,y,z,T-z/c) and mapping them onto a plane (x,y) - so dropping the z and t coordinates. The only real difference is whether you regard time as a parameter or a dimension.

So are you saying that the photograph will be still 2 dimensional? I am considering time as a dimension not a parameter.

 

[Ibix]

Objects are, in general, (3+1) dimensional. Idealising a photo as one surface of a piece of paper then it's (2+1) dimensional. There are two spacelike directions in the plane of the photo and it has extent in time. But the extent in time is boring because a photo is still only a recording of the light that struck it when it was exposed.

Why are you asking?

 

[Algr]

If time is a dimension, what would be the dimension of a photograph in such a space?

You are simply describing the world as it is now. Unless you add a temporal dimension into the photo, in which case you are describing a TV screen.

 

[Ibix]

You are simply describing the world as it is now. Unless you add a temporal dimension into the photo, in which case you are describing a TV screen.

You need to be a bit careful about what you mean by "now" in relativity, which is why I answered as I did (at least at time of writing this thred is labeled A). In fact you are describing part of a null surface, the past light cone of the camera.

Otherwise, yes. Still curious in what context the OP wanted to know.