Reiteration, ''Consistency of Total Photon Energy: We reiterate the core principle that in strong gravitationalfields, the total energy of a photon remains constant, as expressed by the equation Eg = E. The equation underscores that the total energy of a photon Eg remains unchanged despite the influence of a strong gravitational field. This constancy of energy is a fundamental property of photons in such environments, emphasizing their resilience to external forces (4) (PDF) Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects. Available from:
www.researchgate.net/publication/374264333 [accessed Oct 12 2023]. (Photon Interactions in Gravity and Antigravity: Conservation, Dark Energy, and Redshift Effects)
This short paragraph is misleading and wrong. What happens to a photon in a gravitational field is the following:
- h∆f=hf/c²g∆H.
h is Planck’s action constant. f is the photon frequency, ∆f is the change of the photonfrequency, c is the speed of light, g is the gravitational field strength, H is the height in the gravitational field, h∆f is the energy gain or loss of the photon according of changing its height in the gravitational field by ∆H.
We get ∆f/f=g∆H/c². g is the mean value between H and H+∆H.''
The Author Answers:
I see your pointing out, 'this short paragraph is misleading and wrong';
So let me explain the basic difference between the equation I provided, Eg = E and your equation h∆f (= ∆E).
It's evident that "Eg = E" and "hΔf = hf/c²gΔH" address different aspects of a photon's interaction with gravitational fields. Wherewas, my explanations highlights that "Eg = E" focuses on the conservation of the total energy of a photon within an external gravitational field, while "hΔf = hf/c²gΔH" pertains to local energy changes within a single gravitational well. Additionally, the mention of "Δλ/λ" as a representation of intrinsic energy changes helps differentiate these concepts further.
1. Your explanation, 'what happens to a photon in a gravitational field is the following:
h∆f=hf/c²g∆H.
where "h∆f" represents the energy gain or loss of a photon as it changes its height in a gravitational field by ∆H. It quantifies the energy change of the photon due to its change in height within the gravitational field. This aligns with the concept that a photon loses energy as it moves away from a massive object (the source of gravity) or "escapes a gravitational well."
The equation "∆f/f = g∆H/c²" in the quoted text is a simplified form that shows the relative change in photon frequency (and hence energy) as a function of the gravitational field strength (g) and the change in height (∆H) within the gravitational field. It is consistent with the idea that a photon loses energy (or experiences a change in frequency) while moving within a gravitational well.
However, the inconsistency arises when one equation focuses on local energy changes within a single gravitational well, while the other equation takes into account the cumulative effect of multiple gravitational fields:
(A1) what is incosnsistent in your presentation is that, the change in height (∆H) mentioned in the previous comment is specific to the source gravitational well that the photon is escaping. It represents the change in altitude or position within that particular gravitational field. It does not directly take into account other gravitational fields that the photon may encounter in its transit path.
The equation "hΔf = hf/c²gΔH" and the equation "0 = Δρ - Δρ" describe different aspects of a photon's interaction with gravity.
(a) "Eg" represents the energy state of a photon within an external gravitational field, and "Eg = E" signifies the conservation of energy, meaning that a photon's total energy within a gravitational field remains the same as its initial intrinsic energy "E." Despite any local changes in energy or frequency that might occur as a photon moves through gravitational fields (as represented by ΔE), the total energy of the photon remains constant, with respect to (Eg). The idea that within a gravitational field, even though there may be local variations or changes, the overall energy of the photon does not change, and the equation ΔEg = 0 is a reflection of this conservation of energy. This is consistent with the broader principles of physics, where the conservation of energy is a fundamental concept.
(b) Your equation: "hΔf = hf/c²gΔH" focuses on how the energy (and frequency) of a photon changes due to the specific gravitational well it is within. In this context, ΔH represents the change in height or position within a particular gravitational field, which indeed influences the photon's energy. This equation primarily pertains to the effects of a single gravitational field.
Whereas, my equation presented, "0 = Δρ - Δρ" refers to the concept of effective deviation, emphasizing how photons respond to multiple gravitational fields along their path. It suggests that even though photons may experience local changes in momentum as they move through different gravitational fields, the net change in momentum over the entire journey equals zero. This principle aligns with the concept of geodesics in general relativity, where particles, including photons, follow curved paths determined by the combined gravitational influences of all massive objects in their vicinity.
The inconsistency arises when your equation focuses on local energy changes within a single gravitational well, while the other equation takes into account the cumulative effect of multiple gravitational fields.
To provide a more comprehensive and consistent description of a photon's journey, it's important to consider both the local changes in energy within specific gravitational wells (as in "hΔf = hf/c²gΔH") and the overall path and effective deviation that accounts for all gravitational fields encountered (as in "0 = Δρ - Δρ").
(A2) It is well established fact that the photon expends energy while escaping a gravitational well (its source)," is a fundamental concept in general relativity. In this context, a photon is considered to lose energy as it climbs out of a gravitational well. The relevant equation that describes this phenomenon is known as the gravitational redshift equation, which is derived from Einstein's theory of general relativity.
The gravitational redshift equation is as follows:
Δλ/λ = GM/(rc²)
Where:
Δλ/λ is the relative change in the wavelength of light emitted by the photon.
G is the gravitational constant.
M is the mass of the object creating the gravitational well (the source of gravity).
r is the radial distance from the center of the gravitational well to the location of the photon.
c is the speed of light in a vacuum.
This equation shows that as a photon moves away from a massive object (the source of gravity), its wavelength increases. In other words, the photon loses energy as it escapes the gravitational well. This effect is commonly referred to as gravitational redshift or gravitational blueshift, depending on the direction of the photon's motion.
So, when the photon escapes a gravitational well (such as the gravitational field of a massive celestial body), it does so with less energy than when it was closer to the source of gravity. This concept is a key prediction of general relativity and has been experimentally confirmed.
The equation "Δλ/λ = GM/(rc²)" focuses on the local change in energy within a single gravitational well and how this affects the photon's wavelength and energy. This equation takes into account the gravitational field produced by a single massive object.
On the other hand, "0 = Δρ - Δρ" considers the overall path and effective deviation of the photon as it encounters multiple gravitational fields along its journey. It accounts for the cumulative effects of these fields on the photon's trajectory.
The inconsistency arises when your equation focuses on local energy changes within a single gravitational well, while the other equation takes into account the cumulative effect of multiple gravitational fields. To provide a more comprehensive and consistent description of a photon's journey, it's important to consider both the local changes in energy within specific gravitational wells (as in "Δλ/λ = GM/(rc²)") and the overall path and effective deviation that accounts for all gravitational fields encountered (as in "0 = Δρ - Δρ").
"Eg" represent the total energy of a photon within an external gravitational field and I am not focusing on changes in the photon's intrinsic energy represented by "Δλ/λ," then the context and interpretation of your equations would be specific to the total energy state of the photon as it encounters external gravitational fields. (Eg) does not represent (Δλ/λ) which is inherent to photons intirnsic energy (E - ΔE).
