(January 6, 2024 at 3:26 am)neil Wrote: I posed the following question to ChatGPT: "Is it possible for spacetime curvature to produce a redshift?"
Here's what it responded with (note - errors with copy/paste formatting fixed):
Quote:Yes, spacetime curvature can produce a redshift in the context of general relativity. This effect is known as gravitational redshift, and it arises due to the warping of spacetime caused by the presence of mass and gravity.
In the presence of a massive object, such as a star or a massive galaxy, spacetime is curved. When light travels through this curved spacetime, its path is altered, and the frequency of the light changes. As a result, the observed wavelength of the light is shifted, and this shift is toward the red end of the electromagnetic spectrum.
The gravitational redshift (z) can be quantified using the formula:
z = Δλ/λ0 = GM/(c²R)
where:
The greater the mass of the object and the closer the observer is to it, the larger the gravitational redshift. Gravitational redshift has been experimentally verified and is an essential aspect of general relativity. It has practical implications, such as in the study of the redshift of light from stars near massive objects, like black holes.
- z is the redshift,
- Δλ is the change in wavelength,
- λ0 is the initial (rest) wavelength of the light,
- G is the gravitational constant,
- M is the mass of the gravitating object,
- c is the speed of light, and
- R is the distance from the center of the massive object.
Thoughts?
The problem is that you don't understand the answer.
ChatGPT got this right, but it isn't a mind-reader. It has no idea what you "really meant" with your question. It is explaining that when going through a gravity well, light changes frequency and bends in the curved spacetime. It doesn't mean it "keeps" that frequency shift when it comes back out of the gravity well.