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So supposing you simply freeze a relativistic fluid in place you'll get an amorphous solid with a characteristic length scale and characteristic time scale. Whi
by danbruc 11y ago
So supposing you simply freeze a relativistic fluid in place you'll get an amorphous solid with a characteristic length scale and characteristic time scale. Which are both Lorentz invariant.
Doesn't that work because the fluid has no particles in that description, because it is a continuous and smooth average about some ignored micro structure? It seems to me like you would easily loose that nice description if you replaced, for example, the smooth scalar mass density with a collection of discrete particles scattered throughout space. And that seems to be what you really want if you want to quantize space, discrete things, not smooth functions. But you seem to know physics way better than I, so I am probably missing the point, have some serious misunderstanding or something like that.
- contravariant 11y agoA relativistic fluid consists of actual discrete particles, although the quantities you can calculate will be be continuous approximations (very accurate ones). So, basically it is possible to make something discrete, with some associated length scale, but which looks the 'same' for all observers. Even I am not entirely sure how to imagine such an object though, Lorentz boosts are difficult to wrap your head around. By the way, I just realised it's a bit unclear what 'freezing it in place' means. Basically I meant that you just fix all trajectories of all particles, since there are no interactions you'll basically end up with some random straight lines. The distribution of these lines (i.e. their direction / position) will be the same for all observers.
- danbruc 11y agoI now see how that could work. I imagine creating two particle trajectories so that the distance between the particles is Lorentz invariant, i.e. it looks the same for all observers. Once you managed that you can kind of fill space with many copies making sure that the relation holds for all possible pairs. I never thought about that and it I would probably naively have dismissed the idea that you can even have two trajectories that are Lorentz invariant let alone fill space that way. And it is even more unintuitive to me that you end up with something as well behaved as a fluid and not some totally unphysical mess. Now I would really like to see a visualization of two or three such trajectories, assuming I am picturing that at least somewhat right.