Gravitational Redshift: Derivation from Static Metric

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Discussion Overview

The discussion centers on deriving gravitational redshift from a static metric without relying on the equivalence principle or heuristic Newtonian approaches. Participants explore various methods and concepts related to the derivation, including geodesics and the relationship between proper time and frequency changes.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a derivation of gravitational redshift that avoids the equivalence principle and heuristic methods.
  • Another suggests solving for a null geodesic starting at two different times to determine the time between events at a specific radius.
  • A further contribution specifies the need to compare proper time along different worldlines to understand the relationship between emission and reception of signals.
  • One participant raises a question about the relationship between proper time and frequency changes, contemplating whether a quantum perspective is being applied to a classical theory.
  • A response emphasizes that time dilation can be calculated using the proper time between successive emissions and arrivals of signals, suggesting a practical approach to the problem.

Areas of Agreement / Disagreement

Participants present multiple approaches and methods for deriving gravitational redshift, indicating that there is no consensus on a single method or derivation. The discussion remains unresolved with competing views on the best approach.

Contextual Notes

Some assumptions about the nature of time and frequency, as well as the applicability of quantum concepts to gravitational redshift, are not fully explored. The discussion does not resolve the mathematical steps involved in the proposed methods.

redtree
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I am trying to find a derivation of gravitational redshift from a static metric that does not depend on the equivalence principle and is not a heuristic Newtonian derivation. Any suggestions?
 
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Solve for a null geodesic. Start one at ##(r,t_1)## and the other at ##(r,t_1+\Delta t)##. Determine the time between the events where the two geodesics cross some radius ##R##?
 
Ibix said:
Determine the time

More precisely, the proper time along a worldline of constant radius ##R## (the radius of reception), as compared with the proper time along a worldline of constant radius ##r## (the radius of emission).

Another method would be to compute the energy at infinity of a null geodesic, and then show how that relates to its energy as measured by static observers at ##r## and ##R##.
 
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Given that time and frequency are Fourier conjugates, how can changes in proper time relate directly to changes in frequency (as measured by redshift)? Or am I imposing a quantum perspective on a non-quantum theory?
 
redtree said:
Given that time and frequency are Fourier conjugates, how can changes in proper time relate directly to changes in frequency (as measured by redshift)? Or am I imposing a quantum perspective on a non-quantum theory?
You are.

To get the time dilation, all you need is the proper time between emission of successive peaks at the source and the proper time between the arrival of these peaks at the destination. The ratio between the two is the time dilation factor. You could do this calculation with two flashes of light emitted an hour apart at the source if you wanted.
 

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