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https://www.physicsforums.com/showthr...=548148&page=3 [Broken],

post #36,

Peter Donis posted this:

"....But we *can* describe a generic spacetime in GR using a curved geometry (*which* curved geometry depends on the specific spacetime), and we *can* describe any given curved geometry using various coordinate charts, and transform between them.

We can also show that any physical observable in GR (such as the spacetime curvature observed around a given object by an observer traveling on a given worldline) is described by an invariant, something that is the same in all coordinate charts."

Can someone explain the last sentence a little further. I realize gravitational spacetime curvature is an invarient, but I'm not sure about the "....any physical observable..." part. What does that mean?? I'm taking "worldine" as any timelike curve...with a comoving observer....

So, how do I compare the the boldface statement, for example, with the fact that different speed observers would measure a different size,or say, different kinetic energy, for the object, dependent on their relative velocities.

thanks....

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# What is an invarient observable in GR

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