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There are various physical models to make visible how a theory works, for example:

And there are of course many more examples. But in how far do these models give a good picture of reality (the rubber sheet model certainly does not)? It depends on the theory, which can be right or wrong or of which this isn't clear yet (also, what once was thought as a true theory can later be considered as wrong, and vice-versa). Phlogiston was once thought to be a real substance and it was seen as a real stuff flowing into or out of a substance. Hans Radder in his treaty "The Material Realization of Science" treats phlogiston as a real stuff in the domain where it makes experimental predictions that can be realized. So phlogiston is real if the experiment can be described by using it and predict the correct outcome. Raising the new question which labels, as Radder calls the entities for describing reality, are the real ones. Phlogiston or heat? His attitude seems to be an agnostic one but there is a connection with the reality of the experiment (as there is in treaties by Hacking and Pickering).

Are these models merely an aid or is there a "real" connection, correspondence or whatever you call it, to the world? Or is the only real thing the math of the theories (as propagated by Max Tegmark). I guess we (almost) never can tell (or is it the opposite?), but answers can be given and it is certainly discussable.

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    I think the general view in physics is that visualisation models are useful but highly dangerous and often best avoided.
    – user20253
    Jan 13 '18 at 14:46
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    The math is a way to describe the theories. The theories may be only an approximation to reality. So one can't trust the math either. Jan 21 '18 at 1:47
  • The rubber sheet model is misleading if you think of it as explaining why things move on the paths they do (which unfortunately is often how it's presented), but if you just think of it as showing how spatial distances get distorted in a curved space (a slice of curved spacetime that assumes some simultaneity convention), then it can be totally accurate. Meanwhile if you want to have a rubber sheet model of curved spacetime, that can be done rigorously, see here.
    – Hypnosifl
    Jun 24 at 21:57
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Math is like those toy models too. Effective if and only so far as, the modelling assumptions are correct. See How The Laws Of Physics Lie. You could summarise, All models are wrong, but some are useful, because the only real thing, is the real thing. 'Model' means, shedding some of the complexity, while preserving dynamics or essential features - the 'spherical cow' nature of physics. Discussed here: Could nature have no "physical laws" at all? All scientific truths are tentative.

There is a long history of cosmological models & physics being influenced by our highest level of technology. As I argue here with the blockchain example, it is massively easier for ideas to propagate if they can be related to something people are familiar with: Is the following considered an argument or just a set of statements? If it is an argument what would be the premises and conclusion? That doesn't directly imply correctness or not, but it does mean a cultural cognitive bias towards such explanations.

Your 'Fallaco solitons' link doesn't work, I assume it went to the 'frisbee vortices' video. Helium model doesn't work either.

The fluid/gravity correspondence, is pretty widely used as a source of insight in relativistic high gravity-field physics. In particular, blackholes are thought to behave like superfluids, leading to experiments like Bose-Einstein condensates to understand Hawking radiation, which can help solve the blackhole information paradox. So in this case, the model is thought to have better insights than the mathematics.

So, it depends on the model,and how accurate the assumptions made to create it are.

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The bowling ball and rubber sheet analogy is a classic case of why popularized visualizations are not to be taken seriously.

You have a rubber sheet and you draw on it a rectangular coordinate system. At the origin you place a bowling ball. The bowling ball presses down on the sheet, distorting the sheet. The distortion is greater close to the ball, and less as you get farther away.

All well and good. A nice popularized model of Einstein's general theory of relativity.

But if you think about it too much, you get in trouble. What makes the ball press down on the rubber sheet? Ah, it must be meta-gravity, right?

Well no, wrong. The answer to this puzzle is that the bowling ball and rubber sheet model is a popularized picture for the public. It's a fable for the tourists, intended to provide nonspecialists with a vague idea of what's going on. It's not physics. It's not a physics argument. It's false as it stands. It only works as a popular model as long as you don't think about it too much.

All models are like that. First we were told that electrons spin around the nucleus of an atom like planets around the sun. That's not actually true, the electrons live in "shells" that represent energy levels. That's not actually true, the electrons are a cloud representing their quantum fields. Well that's not really true either, what's true is the math. It's the math that represents the actual physical model, and the visual models are only approximations and lies to help people get a conceptual handle on what's going on.

When you see a visual model, you should always realize that what you're seeing is not literally true; in fact it's literally false. In some cases it might be an accurate representation of what's true. In other cases, like the bowling ball and rubber sheet, it's completely false. There's no reason why the bowling ball should push down on the rubber sheet. In fact we have no idea why mass distorts spacetime, only that it does.

Not sure why one of the respondents referenced blockchain, that's a completely different category. A blockchain is a linked list where each block pointer includes a hash of its data block. All software data structures are accurately represented by pictures. Data structures aren't invisible things occurring in nature that need to be investigated by experiment. They're human-made software abstractions that can be perfectly understood by anyone who looks into the subject. Not sure why that's in here at all.

While I'm on the subject, Hilbert's hotel is another famous visualization that often causes more confusion than it's worth. Hilbert himself only mentioned it once, in a popular lecture, and never spoke or wrote about it again the rest of his life. It was forgotten for 30 years before physicist George Gamow wrote about it in a popular book, and today it's taken on a life of its own. Many people who never studied set theory or any proof-based math believe Hilbert's hotel is a mathematical argument. It's not. You can get a Ph.D. in math and never see the argument at all. But you can go online and see people arguing with it as if it's something put forth by mathematicians. And religious apologists like William Lane Craig use it to support arguments about infinite regress. It's arguable that no popularized scientific visualization has caused more general confusion than Hilbert's hotel.

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