&gt;I don&#x27;t see how the exact structure could be important. No matter what it exactly looks like you would probably introduce a preferred reference frame, the frame in which the space quanta are at rest. Or looking at it the other way round, you would observe different lengths when you measure those space quanta from different reference frames no matter what the exact structure is but that contradicts the assumption that they are fundamental and have observer independent properties.<p>Well, you can make a Lorentz invariant theory of an ideal gas, this gives you what&#x27;s called a relativistic fluid. This can be formulated in a completely Lorentz invariant way, meaning that things like the temperature and the average speed of the particles will be the same for every observer. This also implies that the average distance between particles will be the same for all observers. Which combined with the average speed, will give you a characteristic time.<p>So supposing you simply freeze a relativistic fluid in place you&#x27;ll get an amorphous solid with a characteristic length scale and characteristic time scale. Which are both Lorentz invariant.<p>&gt;Quantum physics and special relativity fit nicely together, the standard model and its parts are relativistic quantum field theories. The problems arise when one tries to combine general relativity and quantum physics. When someone says quantum physics and relativity are incompatible he pretty surly means general relativity not special relativity.<p>I was talking about general relativity; quantum field theories almost always use special relativity, it&#x27;s trivial to combine those two. But it is even possible to extend (classical) Yang-Mills field theory from special to general relativity in a very natural way. But for some reason it&#x27;s very difficult to &#x27;quantize&#x27; the resulting field theory.