| 1. | Anti - de sitter space , although it is infinite , has a “ boundary , ” located out at infinity
反德西特空间虽然无穷大，却有个位于无穷远的“边界” 。 |
| 2. | A crucial aspect of anti - de sitter space is that it has a boundary where time is well defined
反德西特时空的一个特殊性质是它有个边界，边界上还有明确的时间轴。 |
| 3. | To have a spacetime as large as the visible universe , the theory must have about 1060 colors
如果我们希望有个和可见宇宙一样大的反德西特时空，则色荷的数目必须大约是1060 。 |
| 4. | For four - dimensional anti - de sitter space , the boundary has two space dimensions and one time dimension
对于四维的反德西特空间来说，边界则是三维的，其中两维是空间，一维是时间。 |
| 5. | In particular , does anything similar hold for a universe like ours in place of the anti - de sitter space
尤其是类似的概念是否在和我们这个世界相似的宇宙中也成立，而不是仅出现在反德西特空间中？ |
| 6. | The extra coordinate is precisely the coordinate needed to describe motion within the four - dimensional anti - de sitter spacetime
这额外的坐标正好符合需求，它能描述物体在四维反德西特时空中的运动！ |
| 7. | The number of colors on the boundary determines the size of the interior ( the radius of the escher - like sphere )
四维反德西特时空内部的大小（即前面提过像艾雪图中球的半径） ，取决于边界上粒子理论中色荷的数目。 |
| 8. | Just as the boundary of the escher print is a circle , the boundary of four - dimensional anti - de sitter space at any moment in time is a sphere
就如同艾雪版画的边界是个圆，四维反德西特空间的边界在任何时刻都是个二维的球。 |
| 9. | Thus , if two particles have a 40 percent chance of colliding in the interior , the two corresponding collections of particles on the boundary should also have a 40 percent chance of colliding
譬如说，如果两个粒子在反德西特时空内有40 %的机率会相互碰撞，则在边界上两组相对应的粒子也应该有40 %的机率会撞在一起。 |
| 10. | Stated simply , the idea is as follows : a quantum gravity theory in the interior of an anti - de sitter spacetime is completely equivalent to an ordinary quantum particle theory living on the boundary
简单来讲，全像理论的想法是：位于反德西特时空内部的量子重力论，会完全等价于一个位在边界上的一般量子粒子理论。 |
