3 ms·

It seems all of these "problems" arise because you're taking particles to have no volume (point masses). This feels like a garbage in garbage out kind of deal.

It seems all of these "problems" arise because you're taking particles to have no volume (point masses). This feels like a garbage in garbage out kind of deal. If your starting assumptions are physically impossible, it's not surprising to get strange results.

heavenlyblue 8y ago
>> It seems all of these "problems" arise because you're taking particles to have no volume (point masses). No, these problems arise, as the parent had said - because those zero-point particles have a non zero probability of occupying the same coordinates if you're simulating their positions using e.g. floating-point variables.
- dahfizz 8y ago
  This is a very straightforward consequence of using zero volume point masses.
- Ay_Ay_Ron 8y ago
  In your example, floating point numbers are an abstraction for the underlying math which assumes space is continuous. If we're talking about events over a continuous sample space, the probability of two particles being in exactly the same space is identically zero since we can only assign finite probabilities to _intervals_.
xelxebar 8y ago
The blowup shown by Xia doesn't rely on point particles. It works just the same even for "small spheres". I didn't really make that clear. Your thought is in good company though. Lots of physicists over the years have worked to remove point particles from the classical theories. This issue is that these fixes tend to end up fixing nothing (like with Newtonian gravity), or producing nonsense and contradictions elsewhere. A famous result in electragnetism, if we replace point charges with tiny charged spheres, we get solutions where particles accelerate exponentially without any external forces. Not at all obvious, but what the hell, right? Anyway, to take a card from your deck and muse haphazardly, my guess is that these problems are extremely hard to avoid when dealing with a continuum. There is some interesting work on discrete theories, but I'm not all that informed about them.

heavenlyblue 8y ago

>> It seems all of these "problems" arise because you're taking particles to have no volume (point masses). No, these problems arise, as the parent had said - because those zero-point particles have a non zero probability of occupying the same coordinates if you're simulating their positions using e.g. floating-point variables.

dahfizz 8y ago
This is a very straightforward consequence of using zero volume point masses.
Ay_Ay_Ron 8y ago
In your example, floating point numbers are an abstraction for the underlying math which assumes space is continuous. If we're talking about events over a continuous sample space, the probability of two particles being in exactly the same space is identically zero since we can only assign finite probabilities to _intervals_.

xelxebar 8y ago

The blowup shown by Xia doesn't rely on point particles. It works just the same even for "small spheres". I didn't really make that clear. Your thought is in good company though. Lots of physicists over the years have worked to remove point particles from the classical theories. This issue is that these fixes tend to end up fixing nothing (like with Newtonian gravity), or producing nonsense and contradictions elsewhere. A famous result in electragnetism, if we replace point charges with tiny charged spheres, we get solutions where particles accelerate exponentially without any external forces. Not at all obvious, but what the hell, right? Anyway, to take a card from your deck and muse haphazardly, my guess is that these problems are extremely hard to avoid when dealing with a continuum. There is some interesting work on discrete theories, but I'm not all that informed about them.