What Is Perspective Beyond Optics?

[morg]

what exactly "perspective" is?

It may be considered as a noob question, but I was thinking about the perspective itself, but not in terms of optics/eye focusing.

1. Why distant objects are smaller and close objects are larger? Does it have something to with amount of photons radiated into an observer?

2. To see a building from, let's say a different side, an observer has to do the work. Then you get an extra photons arriving to the observer. It looks like amount of 'extra' photons the observer receives is dependent of work he done. It's better to think about it in vacuum and zero gravity situation, where no extra forces are included.

3. Is there any known physical relation of photons emission and angle/distance values? When you look at rotating box (in vacuum, force needed to start this rotation), you see photons emited from atoms, then light rays are "occluded behind" other atoms, but why in this particular configuration?

4. It somehow smells about 'resolution' - the closer you get to the object, you see more details, but what exactly does it mean? More configuration of photons emitted towards you? If you have perfect resolution of sight, then, in vacuum would you see as much detail in object as you see from the close range? Light radiates from any objects in straight lines.

It all (perspective, angle of look, time, lorentz transformations, energy conservation, light) somehow has something in common, please help me to grasp it :)

 

[LostConjugate]

If an object is emitting energy in a 3 dimensional space and you are some distance away this energy is distributed over a sphere with a radius of your distance. So as you get further away you are observing a smaller and smaller part of a larger and larger sphere.

If you were in a 1 dimensional space all objects would be observed with the same amplitude no matter the distance.

By rotating around the object you are rotating around the surface of the sphere.

 

[Khashishi]

Inverse square law. The area subtended by a fixed solid angle increases with distance as d^2. Or equivalently, the solid angle that subtends a fixed area decreases with distance as d^2.

 

[LostConjugate]

Inverse square law. The area subtended by a fixed solid angle increases with distance as d^2. Or equivalently, the solid angle that subtends a fixed area decreases with distance as d^2.

Because the space is 3 dimensional, which means the surface of the sphere is 2 dimensional, which makes it inversely proportional to r^2. This is also why pi shows up in all equations measuring energy at some distance, since it is the ratio of the radius to the circumference.

 

[morg]

Space is three dimensional, so I understand the question in the terms of distance.
But there are still questions of how perspective works..

1. why it is three dimensional, not six or eight? (it's probably a fundamental question)

2. why the force and work is needed to see an object from different sides?

Let's take a cube with different colour walls. From some perspective it looks like a square, but from non perpendicular angles (after applying the force of rotating it or walking it around), the photon-emission area is larger. This additional work needed to be done to see it from all dimensions have something to do with perspective too.

It seems that the force needed to get additional "information" (light) from the object is somehow proportional to the amount of information you want to recieve.

Sorry if these questions look stupid, but I can't better get to the point: a corelation between rotation of the object in perspective and photons emission from various angles.

 

[DaveC426913]

Space is three dimensional, so I understand the question in the terms of distance.
But there are still questions of how perspective works..

1. why it is three dimensional, not six or eight? (it's probably a fundamental question)

It is a fundamental of our universe. There are exactly three spatial dimensions.

2. why the force and work is needed to see an object from different sides?

Let's take a cube with different colour walls. From some perspective it looks like a square, but from non perpendicular angles (after applying the force of rotating it or walking it around), the photon-emission area is larger. This additional work needed to be done to see it from all dimensions have something to do with perspective too.

It seems that the force needed to get additional "information" (light) from the object is somehow proportional to the amount of information you want to recieve.

Sorry if these questions look stupid, but I can't better get to the point: a corelation between rotation of the object in perspective and photons emission from various angles.

This makes no sense.

1] The photon emission does not change, whether you rotate the cube or whether you walk around it. The photon emission is a fixed sphere. Though you might intersect more of that sphere in different orientations.
2] Work has nothing to do with this. It is entirely goemetry. Look at it this way: have two observers. They each see different amounts of light emitted. No work done. This "work" thing is a total red herring.

 

[RK1992]

the reason why things look bigger as you get closer is simple and it's just down to geometry.

the angle an object subtends to your eye tells you how much of your vision it takes up (not sure why the inverse square law was being mentioned)
the angle subtended can be found with simple, rough trig.lets say I am 6'4" and i look at a man who is 6'0" tall at a distance of 100m.

as i am a few inches taller, my eyes are in line with the top of his head (although i am afraid my diagram cannot be resolved to this accuracy ;) )

...^...O<.... 100m ......>O
...1.82m...T..........T
...v.../\........../\

the angle, x, between his feet and my eye, and my eye and the top of his head, tells us how much of my vision he's occupying. the more the angle he subtends in my vision, the greater the proportion of my line of sight he takes up.

here, tanx = 1.82/100=0.0182
for sufficiently small x in radians , tanx~x so x ~ 0.0182rad ~ 1 degree

if he was 5m away, the angle would be:
arctan(1.82/5) ~ 0.349rad ~ 20 degrees

do you see why this angle is related to how distant we perceive things to be?

 

[morg]

When I started this post I was more about relation of geometry with other physical values. Like the "volume" property may be in fact an illusion (like L. Susskind suggested), leading to the holographic principle approach.

"The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a hologram which is isomorphic to the information "inscribed" on the surface of its boundary."