Photography in 4D World: Time & Space

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Discussion Overview

The discussion revolves around the dimensionality of a photograph when considering time as a dimension in a four-dimensional space. Participants explore the implications of this concept from both Newtonian and relativistic perspectives, examining how a photograph can be represented in such a framework.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that a photograph can be viewed as a (2+1)d object, where the two spatial dimensions correspond to the plane of the photograph and the additional dimension represents time, albeit in a static manner.
  • Others argue that in Newtonian terms, a camera maps points in three-dimensional space onto a two-dimensional plane at a specific time, while in relativistic terms, it involves a more complex mapping that includes time as a dimension.
  • A participant questions whether the photograph remains fundamentally two-dimensional if time is considered a dimension, suggesting that without a temporal element, it is merely a snapshot of the present.
  • Another viewpoint emphasizes that while a photograph captures light at a specific moment, it does not inherently include a temporal dimension unless one considers a dynamic representation, such as a video screen.
  • One participant notes the importance of understanding "now" in the context of relativity, suggesting that the description of a photograph relates to a null surface, specifically the past light cone of the camera.

Areas of Agreement / Disagreement

Participants express differing views on the dimensionality of a photograph in relation to time, with no consensus reached on whether a photograph can be considered to have a temporal dimension or if it remains fundamentally two-dimensional.

Contextual Notes

There are unresolved assumptions regarding the definitions of dimensions and the implications of time in the context of relativity, as well as the nature of what constitutes a photograph versus a dynamic image.

sonutabitha
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If time is a dimension, what would be the dimension of a photograph in such a space?
 
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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.
 
Ibix said:
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.
 
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?
 
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sonutabitha said:
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.
 
Algr said:
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.
 

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