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Is any 'continuous' thing (fluids, light, time, etc...) truly continuous? Or is it really batch but at just such a high frequency that it appears to us as continuous?

I.e. it appears to me that the water coming out of my faucet is continuous, but if I hit it with a high frequency strobe light I can see that it is, in fact, not continuous and is composed instead of batches moving very quickly.

What about large bodies of fluids? Are oceans/lakes continuous (ignoring interactions with/presence non-fluid components)? How about pockets of air?

What about time? This is the only one I would, preliminarily, consider truly continuous. I know of Planck time, but this appears to me to be a human inability to detect smaller values, not a true minimum batch size.

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  • $\begingroup$ The water is continuous. It is still moving in the darkness between flashes when you don't see it. Strobes create a freeze frame visual effect $\endgroup$ Aug 24, 2021 at 16:12
  • $\begingroup$ Related: physics.stackexchange.com/q/568833/195139 $\endgroup$
    – Sandejo
    Aug 24, 2021 at 17:19
  • $\begingroup$ @AdrianHoward Water molecules are not continuous. $\endgroup$
    – Sandejo
    Aug 24, 2021 at 17:20
  • $\begingroup$ @Sandejo yes, but the flow is continuous, $\endgroup$ Aug 24, 2021 at 21:13

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It depends on the observation resolution. In case of low light intensity (photon by photon) nothing is continuous. It is some sort of inclusive picture that gives a continuous image (very dependent on the exposition time or on the number of photons taken into account for one photo frame).

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  • $\begingroup$ I am referring to true existence, not observational resolution. Your answer suggests that it is truly continuous, just sometimes can not appear so? $\endgroup$
    – Runeaway3
    Aug 24, 2021 at 16:25
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    $\begingroup$ Re: your comment here. We do not know and will not know about true existence, as there is no way to prove that a theory will never be proven wrong in the future with additional / more precise evidence. The best we can do is our current model of true existence, which is just about the best we have given the current experimental evidence. $\endgroup$ Aug 24, 2021 at 16:53
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To summarize my answer quickly:


In our current model of physics, there are plenty of fundamental* things which are actually continuous. Whether the fundamental things remain continuous as science makes progress, nobody can say.


Now it's time to substantiate that statement. All it takes, though, is to find any variable which we model as continuous, and doesn't have an accepted**, more fundamental, discrete origin. There is not only one, there are many:

  • Time, as a parameter
  • Distance (x,y,z), as a parameter
  • The real and complex parts of the wave function at any given point; any spinor component thereof
  • The eigenfunctions of field eigenstates
  • Possible outcomes of measurements of position, momentum, energy, and other variables, depending on the particular system (e.g. not including bound states).

This list could be extended but since one was enough I'll stop here.

*What is and isn't fundamental isn't always a question which is answerable by the scientific method. I have used my own (not absurdly uncommon) notions of the meaning of that word.

**I will not consider explanations which are not accepted by the scientific community at this time. Not accepted $ \neq $ false, but there are too many alternatives and most are at best unverified.

How does this mesh with the seemingly opposite answer of Vladimir Kalitvianski? His current answer (paraphrased) is that single photons are discrete, as are any finite number of photon measurements. This is correct but it does not imply that all variables are fundamentally continuous; it only talks about photons in particular. From an experimental perspective, we have variables which at least seem to be continuous, in the sense that at all measured resolutions we have achieved, they were not discontinuous (take the double slit for positions, for example). This allows for the possibility for a number of continuous variables, up to our current knowledge / precision.

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