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Merleau-Ponty suggests that something in a state of motion takes on a different structure to something at rest. Heraclitus says you cannot step into the same river twice.

Physics today suggests that there is no such thing as a continuum. For example, in the treatment of a black-body Planck resolved the ultraviolet catastrophe by quantising energy. Classical physics is a generalisation of quantum physics.

In experience we occupy just one moment of time at any time. But we do not sense this discrete change; we feel fluid, and we feel a flow.

But nothing in modern science accounts for this "continuum". Does a continuum exist in philosophical thought? Where does it exist, and what is the idea of flux in it?

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    Space and time are continuous in quantum mechanics, and wavefunctions vary continuously across space and time. Whether any of that is metaphysically true in some way beyond its obvious predictive power, nobody knows yet, but the success of a theory with continuous spacetime certainly isn't a reason to conclude that continuous spacetime is metaphysically false.
    – g s
    Commented Dec 13, 2023 at 2:03
  • Do you equate flux with "change" and ask "How to conceptualize change?" ? Do you want to discuss whether scientific theories should be designed on a discrete or a continuous basis? - I do not understand your final sentence "Does a continuum exist in philosophical thought?"
    – Jo Wehler
    Commented Dec 13, 2023 at 4:37
  • @JoWehler I'm asking in what sense does philosophy account for a continuum. It may be that on a discrete level all we can say is that change is down to a "jump". But I want to know what happens inside that jump, and whether philosophy has another answer.
    – DanielFBest
    Commented Dec 13, 2023 at 10:49
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    Mathematics is what accounts for a continuum: The continuum of the real numbers was placed on a thoroughly rigorous basis by Cauchy, Dedekind, Cantor and others during the 19th century. And mathematics can be considered to be a portion of philosophy.
    – Daniel Asimov
    Commented Feb 15 at 0:23
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    On the other hand, nobody (to the best of my knowledge) has come up with a satisfactory theory to model the flow of time that we all experience. (Physics, for example, has nothing whatsoever to say about this common everyday phenomenon.)
    – Daniel Asimov
    Commented Feb 15 at 0:26

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Thanks to your answer to my comment I consider your question to be the following:

What is inside that jump?

  1. The answer of quantum mechanics (QM) is more radical than one would imagine on the base of Planck’s elementary quantum of action. If one observes an electron at a certain time at position A and at a later time at a different position B, then everybody asks: Which path did the electron follow in between the two timepoints, to move from A to B?

    The answer of QM: Not only that we do not know the path, because we did not make any observation in between. Even more radical: The concept of a path between A and B is not meaningful. We have to consider what is between the two observations as a wold of possibilities. The second observation at a later time at B then converts the world of possibilities into one event in reality.

  2. This lesson has to be learned from QM: Philosophy cannot prescribe to nature how electrons behave between to observations. This would be a prejudice. Instead science has to ask nature by clever experiments how nature behaves. Then science has to design the scientific theory accordingly.

    This lesson from concrete experiments on the scale of elementary particles seems to me the answer to your general question.

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