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  1. What resolution should a TV screen have so that its image were so faithful as reality as if the TV were a window?

  2. Also what would happen if Physics could reproduce a 'pixel' of the size $ l_{p}^{2} $ the square of the Planck length? Would be then this the resolution of our reality like watching through a real window?

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The angular resolution of the human eye is somewhere around 1 arc minute or about $3 \times 10^{-4}$ radians. This is based on the diffraction limit with the pupil of the eye somewhere around 5 mm. Googling will find you articles claiming various other figures for the resolution, but they're all in the region of 1 arc minute.

My TV is about 3 m away from my chair, so this resolution corresponds to a pixel size of about one millimetre. Anything smaller than this can't be resolved by the eye and is therefore indistinguishable from reality. Well, reality is 3D and has a vastly higher contrast ratio, but aside from that it's indistinguishable from reality.

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It is important to note that difference between the maximum angular resolution of an image focused at the fovea which lies within the macula of the eye (the central focus where the cones and are most dense over an area of 0.3 mm^2 and have the greatest differentiated nerve connections and the periphery of the eye. Where rod cells are far more predominant than cone cells and the density of nerve connections is progressively lower the further from the macula, in effect means that the maximum resolution and color differentiation progressively decreases the further away from the center of focus, until the very edge where rods predominate and respond only to light intensity.

Also, the way the optic chiasm performs it's primary processing of nerve impulses, nerves supplied to the outlying areas away from the central focus respond more to suddden change in intensity - ie. to movement.

If we were to take 1 eye as an example, with a maximum visual field of for the sake of argument averaging the x and y axix at 100 degrees foreward, if the maximum resolution were to be assumed across the whole field of vision horizontaly and vertically the resolution would be 100*60 pixels, and across the area of the eye would be (3000 ie. resolution across 1 radius of the field * Pi )squared gives an overall resolution of just over 88 Mega pixels, but we know this to not be valid for the whole field of vision. If we take into account the colour differentiation at normal (Room) light levels we also need to factor into the equation that we can see about ten million colours (Ref: 1). That gives a total differential resolution of 8.8*10^14 distributed over the 88 M pixels.

If you were to create a television monitor able to display this image to fill the field of view of one eye, if each and every part of that field were to be able to be seen at the maximum resolution of the eye as it scans the picture, well you can see it would need be one very detailed picture., and prohibitively expensive.

Ideally what would be needed ideally, would be a feedback system scanning eye movements, creating high resolution at that point of central focus only and a progressively low resolution towards the outer edges cutting down on cost. The eye focusing on a single point and not moving is however unnatural. There are natural small movements called saccades such as when scanning a face can occur, with or without conscious intent from between few degrees of arc to 60 degrees of arc (See Here)

Also a pixel the size of a plank length would presumably only be able to effectively produce photons of the shortest wavelength possible, ie. no shorter wavelength can exist, that in part being the definition of a plank length (See here) - not much use for watching with the naked eye.

Ref 1/ Judd, Deane B.; Wyszecki, Günter (1975). Color in Business, Science and Industry. Wiley Series in Pure and Applied Optics (third ed.). New York: Wiley-Interscience. p. 388. ISBN 0-471-45212-2.

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It is important to understand that Planck's theory of the existence of length which can be divided by zero is hotly disputed. Einstein famously said about this theory: 'madness is trying the same over and over again and expecting different results'. Theory of continuos space has never been disproven, it works in practice, I think we should stick to it. Planck's length is a fraud, lets call it as such and move on.

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    $\begingroup$ Calling the Planck length a fraud might be taking it a little to far $\endgroup$
    – psitae
    Dec 2 '16 at 21:11
  • $\begingroup$ Not until you can show me how the heck can something be divided by zero? Fraud, I tell you ;] $\endgroup$ Dec 2 '16 at 21:27

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