B Dimension of the photograph of a four dimensional world?

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1. Dec 21, 2016

sonutabitha

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

2. Dec 21, 2016

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.

3. Dec 21, 2016

sonutabitha

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

4. Dec 21, 2016

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?

5. Dec 22, 2016

Algr

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.

6. Dec 22, 2016

Ibix

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.

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