The constancy of the speed of light in a vacuum, as described by Albert Einstein's theory of special relativity, is a fundamental principle in modern physics. It states that the speed of light in a vacuum is always the same for all observers, regardless of their relative motion. This principle has been extensively tested and confirmed through experimental observations.
On the other hand, redshift is a phenomenon that occurs when light from distant objects, such as galaxies or stars, is stretched as the universe expands. As space expands, the wavelength of the light traveling through that space is also stretched, leading to a redshift.
The reconciliation of these concepts lies in the understanding that the constancy of the speed of light holds locally in a small region of spacetime. It is a local property that applies within a reference frame and to observers in relative motion within that frame. However, the expansion of the universe affects the overall cosmological scale, and as a result, the wavelength of light traveling through space is stretched due to this expansion.
In the context of cosmology, the expansion of the universe causes the scale factor of the universe to increase over time. As a result, the wavelength of light emitted from distant sources gets stretched as it travels through expanding space, resulting in a redshift. This redshift is a consequence of the changing metric of spacetime on cosmological scales and does not violate the constancy of the speed of light locally.
In summary, the constancy of the speed of light and the phenomenon of redshift are reconciled by understanding that the constancy of the speed of light holds locally within reference frames, while the redshift arises from the expansion of the universe on cosmological scales. These concepts are part of our current understanding of physics and have been supported by extensive observational evidence.