How Does Wavelength Affect Photon Localization?

[scijeebus]

Well, the localization effects the probability density of a photon. The shorter the wavelength, the more localized, the higher the wavelength, the less localized. But, how do we actually know the wavelength before we measure it? If a source emits a photon, the wavelength is unknown, so how is it's localization already determined?
Furthermore, would this imply that if I move away from a gamma-ray photon at 99% the speed of light, I would measure it was a radio wave but it would still have a small localization before I measured it?

 

[eljose79]

I would like to offer some insights and clarifications on the concept of localization and wavelength of a photon.

Firstly, localization refers to the position or region in space where a photon is most likely to be found. This is determined by the probability distribution of the photon, which is influenced by its wavelength. The shorter the wavelength, the more localized the photon is, meaning it has a higher probability of being found in a specific region. On the other hand, a longer wavelength leads to a less localized photon, with a lower probability of being found in a specific region.

Now, to address the question of how we know the wavelength of a photon before measuring it - this is where the concept of wave-particle duality comes into play. According to quantum mechanics, all particles, including photons, have both wave-like and particle-like properties. This means that a photon can exhibit both wave-like behavior, such as interference patterns, and particle-like behavior, such as having a specific position and momentum. So, while the wavelength of a photon may not be known before measurement, its wave-like behavior can still give us an idea of its localization.

Moving on to the second part of the post, it is important to note that the wavelength of a photon is an intrinsic property and does not change with the observer's velocity. This means that even if you were to move away from a gamma-ray photon at 99% the speed of light, its wavelength would still be that of a gamma-ray. However, the observed frequency of the photon would change due to the Doppler effect. This is similar to how the pitch of a siren changes as it moves towards or away from you.

In conclusion, the localization of a photon is determined by its probability distribution, which is influenced by its wavelength. While the exact wavelength may not be known before measurement, the wave-like behavior of the photon can give us an idea of its localization. And the wavelength of a photon is an intrinsic property that does not change with the observer's velocity. I hope this helps to clarify the concepts of localization and wavelength of a photon.