Energy vs wavelength for a photon in GR

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Discussion Overview

The discussion revolves around the behavior of a photon following a geodesic near a large mass in the context of general relativity, specifically focusing on the relationship between energy, wavelength, and frequency as the photon approaches the mass. The conversation includes theoretical considerations and implications for observers at different potentials.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that as a photon approaches a large mass, its wavelength shortens, raising questions about energy conservation and frequency stability.
  • One participant argues that if the wavelength changes, the frequency must also change if the velocity remains constant, referencing the relationship v=fλ.
  • Another participant states that energy is not globally conserved in general relativity and notes that observers along the geodesic would measure different frequencies and wavelengths while the speed of light remains constant at c.
  • There is a discussion about the perspective of observers at different potentials, with one participant suggesting that each observer experiences time dilation and thus sees different energy values for the photon.
  • Questions arise about the feasibility of measuring wavelength changes from a nearby spaceship, with considerations of the spaceship's motion relative to the mass affecting observations.
  • A participant expresses uncertainty about how to interpret the increase in momentum (E/c) and whether this could be compensated by an increase in amplitude due to the observed shortened wavelength.

Areas of Agreement / Disagreement

Participants generally agree on the phenomenon of wavelength shortening as a photon approaches a mass, but there are multiple competing views regarding energy conservation, frequency changes, and the implications for different observers. The discussion remains unresolved with respect to the interpretation of these effects.

Contextual Notes

Limitations include assumptions about observer positions, the effects of motion on measurements, and the implications of time dilation on energy observations. The discussion does not resolve how these factors interact in a general relativistic framework.

Pierre007080
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If a theoretical single photon followed a geodesic toward a large mass in space, I understand that the wavelength would shorten as it approached the mass. How would the energy be conserved within the photon, because the frequency must surely remain the same?
 
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Pierre007080 said:
If a theoretical single photon followed a geodesic toward a large mass in space, I understand that the wavelength would shorten as it approached the mass. How would the energy be conserved within the photon, because the frequency must surely remain the same?

If the wavelength changes, then the frequency will change if the velocity is constant, because [itex]v=f\lambda[/itex].

Energy is not globally conserved in the general theory of relativity. If a chain of observers along the geodedic studied these photons, they would find the speed is the same c, but the frequency and wavelength are different.
 
Pierre007080 said:
If a theoretical single photon followed a geodesic toward a large mass in space, I understand that the wavelength would shorten as it approached the mass. How would the energy be conserved within the photon, because the frequency must surely remain the same?

From the point of view of any single observer, the energy would remain constant but the coordinate speed of light would decrease, so the magnitude of the momentum, E/c, would increase as the photon moved towards a lower potential.

From the point of view of separate observers at different potentials, each of them is time-dilated according to their potentials, so they see different energy values.
 
Hi Mentz 114,
Thanks for your response. I think I understand your answer about the chain of observers along the geodedic ... but is it allowed for the observer to be in a nearby spaceship observing (from a distance) the shortening wavelength and even a slowing of the speed of light?
 
Pierre007080 said:
Hi Mentz 114,
Thanks for your response. I think I understand your answer about the chain of observers along the geodedic ... but is it allowed for the observer to be in a nearby spaceship observing (from a distance) the shortening wavelength and even a slowing of the speed of light?

As Jonathan has said, the coordinate speed of light will change. But I don't see how it is possible to measure the wavelength from a distance.

What is observed will depend on what the spaceship is doing. For instance it might be moving (wrt the mass) or hovering.
 
Thanks Guys,
To conceal my ignorance, I think that I must stick to Jonathan's "single observer" status! How will this momentum (E/c) increase be interpreted? Would there be an increased "amplitude" to compensate for the observed shortened wavelength?
 

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