I’m sure there are physical reasons why the cold river water is technically more dense than warm pool water, but I would guess it’s pretty negligible as far as human perception is concerned.
My thought is this has to do with your nervous system’s Cold Shock Response to being thrust into a bunch of cold water. So I’m not sure that I would call it a placebo, as there is a meaningful difference between jumping in the two different bodies of water, but it doesn’t have to do with the physical “hardness” of the water. It instead has to do with your neural reaction to the sudden change in temperature. To grossly over-summarize, you have a ton of cold receptors in your skin and when you suddenly flood them with activity by jumping in cold water it leads to funky (and sometimes dangerous/deadly) bodily responses.
Interestingly, once you make it through the initial Cold Shock Response there may be some anti-depressive benefits to having your neural system activated all at once in that way! Almost similar in theory to shock therapy, though obviously a whole lot different in many ways haha. Source for this: [source](https://pubmed.ncbi.nlm.nih.gov/17993252/)
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