I Is There an Absolute Maximum Density for Substances?

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There is a discussion about whether there is an absolute maximum density for substances, with black holes cited as examples of objects with maximal density relative to their size. It is noted that adding energy to a black hole causes it to grow, resulting in larger black holes having lower density. The conversation also touches on the minimum distance between particles, suggesting that this distance influences density considerations. Below the Planck length and above the Planck density, meaningful statements about density become problematic. Overall, the topic explores the limits of density in physical systems.
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This is kind of a random question. Is there a point that a substance density will max out? Or in other words that it cannot be compressed any further no matter the energy you add to the system?
 
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You could consider black holes as “objects” with the maximal density for their size. If you put in more energy they grow. Larger black holes have a lower density, although that concept is a bit tricky as they don’t have a well-defined interior volume.
 
@mfb I think we should "see" what's the minimum distance between 2 particle. I think it will also affect if we are talking about atoms or other particles (such as electrons...)
 
Below the Planck length (and above the Planck density) we can't make meaningful statements any more.
 
I am going through this course on collision detection: https://siggraphcontact.github.io/ In this link is a PDF called course notes. Scrolling down to section 1.3, called constraints. In this section it is said that we can write bilateral constraints as ##\phi(\mathbf{x}) = 0## and unilateral constraints as ##\phi(\mathbf{x}) \ge 0##. I understand that, but then it says that these constraints call also be written as: $$\mathbf{J} \mathbf{u} = 0, \mathbf{J} \mathbf{u} \ge 0,$$ where...
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