The answer is a clear "yes". Read below why:
At a longer wavelength (λ2>λ1) and lower frequency (f2<f1), the photon carries less energy (E2<E1) than the light emitted at the source, where: λ2, f2, E2, represent the wavelength, frequency and energy of the observed photon, respectively, and λ1, f1, E1 respectively represent the wavelength, frequency and energy of the same photon when emitted at the source.
The statement highlights how the properties of a photon, particularly its energy, wavelength, and frequency, change as it travels from its source to an observer. This change is a fundamental aspect of wave-particle duality and the behavior of electromagnetic radiation. When the photon has a longer wavelength and lower frequency at the observer's location, it carries less energy than it did when it was initially emitted, and vice versa.
Relevant equations:
f = (ℓP/tP)/λ; E = hf; Hence, E ∝ 1/λ or E ∝ f, '
Accordingly, photons with a shorter wavelength (λ2<λ1) and increased frequency (f2>f1) carry increased energy (E2>E1) compared to light emitted at the source.
Cosmic and relativistic motion play a key role in the energy-frequency state of the traveling photon wave between its source and observer.
When measuring the compression of wavelengths associated with gravitational wells, the compression itself corresponds to an increased frequency due to cosmic and relativistic effects, and therefore represents the extra energy added to the detected photon signal compared to its proper frequency or wavelength, while still maintaining its momentum.
Note the Planck ratio of ℓP/tP = fλ and the Planck equation E = hf.
Furthermore, since the redshift represents the correspondingly lower frequency of increased wavelength, the blueshift represents the opposite due to increased energy, decreased wavelength, and corresponding increased frequency.
Photon Energy, Wavelength, and Frequency: photon energy (E) is related to both its wavelength (λ) and frequency (f) through the Planck equation, E = hf. This equation shows that as the wavelength increases (λ2 > λ1), the frequency decreases (f2 < f1), and vice versa. Consequently, a longer wavelength corresponds to a lower frequency and, as a result, lower energy, while a shorter wavelength corresponds to a higher frequency and higher energy.
Relevance of Planck's Equation: Planck's equation, E = hf, is fundamental in describing the energy of photons. This equation demonstrates that changes in frequency directly affect the energy of the photon, which is a well-established principle in quantum mechanics.
Cosmic and Relativistic Effects: The role of cosmic and relativistic effects in altering the observed properties of photons. These effects can lead to changes in the wavelength and frequency of photons as they travel through the universe. For example, gravitational fields can cause gravitational redshift, which results in the observed photon having a longer wavelength and lower frequency.
Wavelength Compression in Gravitational Wells: when photons pass through gravitational wells, such as those caused by massive celestial objects, their wavelengths can be compressed. This compression corresponds to an increased frequency due to the effects of gravity and relativity. Importantly, you note that this change in frequency represents additional energy added to the detected photon signal compared to its proper frequency or wavelength.
Redshift and Blueshift: The concepts of redshift and blueshift. Redshift occurs when an observed photon has a longer wavelength and lower frequency than expected, leading to decreased energy. Conversely, blueshift occurs when the observed photon has a shorter wavelength, higher frequency, and increased energy compared to its source.
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