Gravity Warps Space & Time: A cm Difference?

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SUMMARY

The discussion centers on the concept of gravity's effect on the measurement of space and time, specifically questioning whether a centimeter in a high gravity area differs from a centimeter in a low gravity area. It is established that while a ruler in high gravity would still measure a centimeter, the proper length is influenced by the warping of space-time. The use of Riemann Normal Coordinates is highlighted as a mathematical framework that allows for local flatness in measurements, despite the differing metrics observed by an outside observer.

PREREQUISITES
  • Understanding of general relativity and its implications on space-time.
  • Familiarity with Riemann Normal Coordinates and their application in physics.
  • Basic knowledge of proper length and metric tensors in differential geometry.
  • Concept of local flatness in curved spaces.
NEXT STEPS
  • Research the principles of general relativity and its effects on measurements in gravitational fields.
  • Study Riemann Normal Coordinates in detail and their role in general relativity.
  • Explore the concept of proper length and how it is calculated in curved space-time.
  • Investigate the implications of local flatness in various physical scenarios.
USEFUL FOR

Physicists, students of general relativity, and anyone interested in the implications of gravity on measurements in space-time.

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If gravity warps space as well as time, does that mean that a cm in a high gravity area would be smaller than a cm in a low gravity area?
 
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To you, a cm would still be a cm. For example, if you'd put your ruler next to an object in a high gravity area, the ruler would also be warped and you'd still get the same measurement. What you're actually measuring is the proper length (I think that mathematically, it just occurred to me, you're using Riemann Normal Coordinates, in which the space is locally flat). To an outside observer, however, the object would look differently, because the metric at that point is different.
 

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