2 ms·

I don'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

by danbruc 11y ago

I don'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. Relativity does not allow for fundamental lengths because you can mix space and time by going to a different reference frame. You could maybe say that you have quanta of spacetime with some proper length, quanta that look like separation in space to some observers and like separation in time to others, but no idea if that makes any sense and it probably has not less problems than quanta of space. 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.

contravariant 11y ago
>I don'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. Well, you can make a Lorentz invariant theory of an ideal gas, this gives you what'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. 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. >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. I was talking about general relativity; quantum field theories almost always use special relativity, it'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's very difficult to 'quantize' the resulting field theory.
- 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 ago
    A 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 ago
      I 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.

by danbruc 11y ago

contravariant 11y ago

>I don'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. Well, you can make a Lorentz invariant theory of an ideal gas, this gives you what'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. 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. >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. I was talking about general relativity; quantum field theories almost always use special relativity, it'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's very difficult to 'quantize' the resulting field theory.

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 ago
  A 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 ago
    I 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.