现代五维引力的现状
The Status of Modern Five-Dimensional Gravity
摘要：
最近的批评高维扩展爱因斯坦的理论被认为是。对于弦论来说，这可能有一些道理，但如果应用于具有大量额外维度的五维理论，就被误导了。这些理论顺利地嵌入了广义相对论，确保了后者的观测支持的恢复。当时空的嵌入按照坎贝尔定理进行时，由此产生的5D理论自然解释了经典物质和真空能量的起源。此外，对5D流形中的高能表面或膜附近的运动方程的约束导致量子化和量子不确定性。这些都是对一个额外维度的适度投资的主要回报。与其徒劳地争论是否有可能“看到”第五维，不如建议将其与其他物理概念（如时间）同等对待。接受第五维度（或不接受）的主要标准应该是它的有用性。
英文摘要：
Recent criticism of higher-dimensional extensions of Einstein's theory is considered. This may have some justification as regards string theory, but is misguided as applied to five-dimensional theories with a large extra dimension. Such theories smoothly embed general relativity, ensuring recovery of the latter's observational support. When the embedding of spacetime is carried out in accordance with Campbell's theorem, the resulting 5D theory naturally explains the origin of classical matter and vacuum energy. Also, constraints on the equations of motion near a high-energy surface or membrane in the 5D manifold lead to quantization and quantum uncertainty. These are major returns on the modest investment of one extra dimension. Instead of fruitless bickering about whether it is possible to "see" the fifth dimension, it is suggested that it be treated on par with other concepts of physics, such as time. The main criterion for the acceptance of a fifth dimension (or not) should be its usefulness.
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