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> You can't just simulate 'observable areas'. Everything needs to be simulated. I can't make sense of this. Whatever is outside the causality sphere is by defi

by wreegab 13y ago

> You can't just simulate 'observable areas'. Everything needs to be simulated. I can't make sense of this. Whatever is outside the causality sphere is by definition irrelevant.

chiph 13y ago
At what point do objects & events outside the causality sphere stop influencing things inside it?
- deleted 13y ago
  [deleted]
- delluminatus 13y ago
  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.
entendre 13y ago
unless we start factoring in quantum entanglement
jcutrell 13y ago
Here's a basic way of understanding this. Take a piece of paper. Focus a camera on that piece of paper. Turn on an overhead light. Did the paper change? Now, imagine this not only to be a visual representation as limited as this, but instead causality. Then the causality sphere is, theoretically, as big as the universe itself.
- delluminatus 13y ago
  I don't understand your analogy at all, but it seems to me that an object's light cone at a given time is necessarily smaller than the universe (in volume of spacetime). Also, you could control the size of the cone by controlling the duration of the simulation.
  - jcutrell 13y ago
    Clarification is necessary I suppose. The concept being discussed is the limited scope of simulation. However, it can be assumed that everything affects (or can affect) everything else. The only way to know whether or not one thing may affect anything else is to simulate it. How could you know the sphere of causality without simulating everything? An object's light cone is not a property of the object; it is the result of the properties of the object as they related to the light shining on that object. If the source of that light isn't represented in a simulation, then unless that object produces the light itself, the object must be dark or the simulation isn't accurate. The discussion is about simulating a universe. Unless there are truly discrete systems within that universe, you can't do that simulation within a limited frame. I think what the author was alluding to, though, was to say that the actual rendering of the view, rather than the calculation of the view, would be limited to the current frame of reference.
    - delluminatus 13y ago
      I think I see what you mean, but isn't it true that if there is light shining on the object, then the lamp must be in the light cone? It is literally impossible for something outside the light cone to have any physical impact on the object at all. We do know the sphere of causality already, no computation needed: it is the sphere defined by the distance light has had time to travel. You don't need to simulate anything outside that zone to know that it is impossible for matter outside it to physically impact the center. Think of it this way: if you want to simulate Earth through the year 2000, you know you don't need to simulate Alpha Centauri after 1996, since it is more than 4 light years away. You can know this without doing any computation at all.

by wreegab 13y ago

> You can't just simulate 'observable areas'. Everything needs to be simulated. I can't make sense of this. Whatever is outside the causality sphere is by definition irrelevant.

chiph 13y ago

At what point do objects & events outside the causality sphere stop influencing things inside it?

deleted 13y ago
[deleted]
delluminatus 13y ago
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.

entendre 13y ago

unless we start factoring in quantum entanglement

jcutrell 13y ago

Here's a basic way of understanding this. Take a piece of paper. Focus a camera on that piece of paper. Turn on an overhead light. Did the paper change? Now, imagine this not only to be a visual representation as limited as this, but instead causality. Then the causality sphere is, theoretically, as big as the universe itself.

delluminatus 13y ago
I don't understand your analogy at all, but it seems to me that an object's light cone at a given time is necessarily smaller than the universe (in volume of spacetime). Also, you could control the size of the cone by controlling the duration of the simulation.
- jcutrell 13y ago
  Clarification is necessary I suppose. The concept being discussed is the limited scope of simulation. However, it can be assumed that everything affects (or can affect) everything else. The only way to know whether or not one thing may affect anything else is to simulate it. How could you know the sphere of causality without simulating everything? An object's light cone is not a property of the object; it is the result of the properties of the object as they related to the light shining on that object. If the source of that light isn't represented in a simulation, then unless that object produces the light itself, the object must be dark or the simulation isn't accurate. The discussion is about simulating a universe. Unless there are truly discrete systems within that universe, you can't do that simulation within a limited frame. I think what the author was alluding to, though, was to say that the actual rendering of the view, rather than the calculation of the view, would be limited to the current frame of reference.
  - delluminatus 13y ago
    I think I see what you mean, but isn't it true that if there is light shining on the object, then the lamp must be in the light cone? It is literally impossible for something outside the light cone to have any physical impact on the object at all. We do know the sphere of causality already, no computation needed: it is the sphere defined by the distance light has had time to travel. You don't need to simulate anything outside that zone to know that it is impossible for matter outside it to physically impact the center. Think of it this way: if you want to simulate Earth through the year 2000, you know you don't need to simulate Alpha Centauri after 1996, since it is more than 4 light years away. You can know this without doing any computation at all.