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Let's assume our minimum meaningful resolution on black and white TV is 480P, the permutation of each frame possible to be displayed is still quite big, but still finite. A 1080P colour TV gives much bigger permutation but still finite. Say at time T0 turn on the TV and let it render all possible frames, the time it takes to render all possible frames by the TV is (T1 - T0), so after T1, any frames displayed on the TV would have been displayed during (T0 -> T1). Of course we don't live that long to see it but I am interested to see what your thoughts are.

Note: minimum meaningful resolution I meant is the resolution small enough to differentiate most events on the screen.

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    The modern standard cosmological model says the universe never passes though the same state twice due to endless expansion. That model is likely to be added to and changed with things like quantum gravity, and there are alternative models. But the current scientific answer would be no.
    – J Kusin
    Jan 4, 2022 at 20:25
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    If you have a TV with a resolution of 4x4 (x2 colors), all possible frames are 16^2, which can be displayed in ten seconds at 25fps. Such sequence has an order and can be said to loop if it repeats exactly in the same order. But life viewed on an HD TV, in addition to the large number of pixels and colors, which would take many years to make a loop, never repeats the order of frames. In addition, each frame is accompanied by a large number of environmental elements. Life is much more than TV. Assuming that life is a loop because something loops is a very naive idea.
    – RodolfoAP
    Jan 4, 2022 at 21:04
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    Are we assuming that every frame follows deterministically from the previous with no outside influence, as if each image constitutes a frame of finite existence?
    – Michael
    Jan 4, 2022 at 21:09
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    Although Nietzsche's eternal return was mainly given as a kind challenge to our attitudes about life, some scholars suggest he may have been inspired to think about it by cosmological speculations from others like Heinrich Heine (quoted in the wiki), and the "A Cosmological Thesis" section of this article quotes an argument from Nietzsche's notebooks about how matter "must pass through a calculable number of combinations".
    – Hypnosifl
    Jan 4, 2022 at 22:37
  • Yeah after having some more thought about it, I realised the idea was pretty dumb.
    – James Lin
    Jan 13, 2022 at 0:33

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Assuming a universe has only finite possible states, and infinite state changes, then some state must repeat. However that does not mean all states need to repeat, nor that each state must occur. Using your TV metaphor, it is quite possible to image the screen showing a movie once, then going black forever.

So in order for a meaningful infinite loop to occur, more conditions are required.

Often such questions are considered using the Conway Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life), such as in questions like this: Can our universe be a simulation without simulator?

Also related questions are about whether there must be copies of everything in infinite universes, like

However, for our universe, there seem to be many continuous dimensions, preventing finite states. As an example a grain of sand can be in infinitely many positions on a sheet of paper. So the universe is typically not regarded as having only finite possible theoretical states.

The universe might still be looping (and we could be living inside the first loop for all we know). But that currently does not seem necessary nor even likely.

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