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Two questions for you lovely and helpful forum members:

1. I have two clocks far from a massive object, relative to which I am at rest, and I let go of one of the clocks. I let it free-fall for 186,000 miles, and then I observe both clocks. Is the falling clock observed to be one second behind my local clock?

2. Slightly related: As I understand it, the sum of gravitational and potential energy of an orbiting body is invariant. In the Sun's rest frame for example, this sum could be measured as a certain number of joules; however in a different frame, free-falling alongside the orbiting body, the sum would be much smaller or zero, but similarly invariant regardless. Is this considered an example of gauge invariance?

Thank you!

1. I have two clocks far from a massive object, relative to which I am at rest, and I let go of one of the clocks. I let it free-fall for 186,000 miles, and then I observe both clocks. Is the falling clock observed to be one second behind my local clock?

2. Slightly related: As I understand it, the sum of gravitational and potential energy of an orbiting body is invariant. In the Sun's rest frame for example, this sum could be measured as a certain number of joules; however in a different frame, free-falling alongside the orbiting body, the sum would be much smaller or zero, but similarly invariant regardless. Is this considered an example of gauge invariance?

Thank you!

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