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Immediately, by definition. By causality sphere he means light cone [0]. If you want to simulate an entity, you only need to simulate the entity and the content

Immediately, by definition. By causality sphere he means light cone [0]. If you want to simulate an entity, you only need to simulate the entity and the contents of its light cone. Anything outside the cone could not have a causal impact on the entity without FTL travel. Of course, an entity's light cone is still likely to be quite large, especially if your simulated universe is old. [0]: https://en.wikipedia.org/wiki/Light_cone https://en.wikipedia.org/wiki/Light_cone

pdonis 13y ago
an entity's light cone is still likely to be quite large, especially if your simulated universe is old. And the light cone (more precisely, the past light cone) keeps getting larger, so in fact the "amount of universe" that needs to be simulated increases without bound as time goes on.
- delluminatus 13y ago
  Some back-of-the-envelope calculation leads me to believe that for a given location in space and time, its past light cone contains 1/8th of the spacetime between the beginning of the universe and the location.
  - pdonis 13y ago
    I'm not sure how you're doing the calculation, but your answer is not correct. Our current best-fit model of the universe has it being spatially infinite, which means the "volume of spacetime" between the Big Bang and "now" (more precisely, between the Big Bang and the "comoving" surface of simultaneity that passes through the Earth right now--now" is relative so you have to specify what simultaneity convention you're using) is infinite. Since the volume of any past light cone is finite, it will be effectively zero compared to the total volume of spacetime up to any surface of simultaneity. (But as you go to later and later surfaces of simultaneity, the volume of the past light cone of any event on the surface of simultaneity still increases without bound.) Even in spatially finite models (which are not conclusively ruled out by the data we have, though they are unlikely to be correct), the fraction of spacetime between the Big Bang and a given "comoving" surface of simultaneity that is occupied by the past light cone of an event on that surface of simultaneity is not constant; it gets larger as you go to later surfaces of simultaneity.
haldean 13y ago
Except you have to have been simulating outside the light cone so that, once the light cone expands to include that space you know its state. So in reality, if you're interested in location V at time t, you have to simulate everything that will end up within the sphere centered at V at time t, not just whatever is in the sphere instantaneously.
- delluminatus 13y ago
  Yes, which is why the light cone is actually described as a 4D object that exists in spacetime, not a 3D sphere. Some back of the envelope calculation indicates that the spacetime "volume" of the light cone of an object is 1/8th of the spacetime volume of the universe up to that point. So using the light cone would net you an 8x speedup over a brute-force Universe render. Nothing to write home about if you have infinite computing power.

pdonis 13y ago

an entity's light cone is still likely to be quite large, especially if your simulated universe is old. And the light cone (more precisely, the past light cone) keeps getting larger, so in fact the "amount of universe" that needs to be simulated increases without bound as time goes on.

delluminatus 13y ago
Some back-of-the-envelope calculation leads me to believe that for a given location in space and time, its past light cone contains 1/8th of the spacetime between the beginning of the universe and the location.
- pdonis 13y ago
  I'm not sure how you're doing the calculation, but your answer is not correct. Our current best-fit model of the universe has it being spatially infinite, which means the "volume of spacetime" between the Big Bang and "now" (more precisely, between the Big Bang and the "comoving" surface of simultaneity that passes through the Earth right now--now" is relative so you have to specify what simultaneity convention you're using) is infinite. Since the volume of any past light cone is finite, it will be effectively zero compared to the total volume of spacetime up to any surface of simultaneity. (But as you go to later and later surfaces of simultaneity, the volume of the past light cone of any event on the surface of simultaneity still increases without bound.) Even in spatially finite models (which are not conclusively ruled out by the data we have, though they are unlikely to be correct), the fraction of spacetime between the Big Bang and a given "comoving" surface of simultaneity that is occupied by the past light cone of an event on that surface of simultaneity is not constant; it gets larger as you go to later surfaces of simultaneity.

haldean 13y ago

Except you have to have been simulating outside the light cone so that, once the light cone expands to include that space you know its state. So in reality, if you're interested in location V at time t, you have to simulate everything that will end up within the sphere centered at V at time t, not just whatever is in the sphere instantaneously.

delluminatus 13y ago
Yes, which is why the light cone is actually described as a 4D object that exists in spacetime, not a 3D sphere. Some back of the envelope calculation indicates that the spacetime "volume" of the light cone of an object is 1/8th of the spacetime volume of the universe up to that point. So using the light cone would net you an 8x speedup over a brute-force Universe render. Nothing to write home about if you have infinite computing power.