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The cosmic background radiation has a wavelength about 2000 times longer than visible light. So you would need to be sitting deep in a gravitational well such that local time progresses 2000 times more slowly than distant time. Gravitational time dilation is given by the formula $\sqrt{1-r_\mathrm{S}/r}$ where $r$ is the distance from the center of the (...


12

A recent test (2018) using atomic clocks aboard two satellites found general relativity's gravitational redshift prediction to be accurate to $(+0.19 \pm 2.48)\times10^{-5}$. This was not a planned experiment and the satellites had accidentally been delivered on elliptic rather than circular orbits in 2014. They were useless for their original purpose of ...


4

If the metric of spacetime does not have an explicit dependence on certain coordinates, a corresponding quantity will be conserved along geodesics. Specifically for your question, if the metric does not depend on time, meaning that it is static and unchanging with time, energy will be conserved along the geodesic. Now, the complication comes when you talk ...


3

Therefore, for the exact same reason our "observable" universe is limited by the travel distance of photons since the CMB, our local gravitational potential shifts over time for the same reason. It's true that the gravitational field at a spacetime point is due to the matter on the past light cone of that point, but that's automatically taken into ...


2

The Hubble constant relates the proper distance and the rate of change of that proper distance with respect to cosmological epoch. Proper distance is the distance to an object at the current cosmological epoch, which you have labelled as $r$, and not its distance when the light was emitted. You correctly point out that the estimated distance based on light ...


2

You can imagine that there's another person C a short distance above B, and D above C, and so on, and this chain of people extends all the way to Earth. B doesn't have a flashlight: instead, they just let the light from A pass them by, while passively measuring its spectrum. The effect from C's point of view is just as though B is shining a flashlight that ...


2

The basic result you have found --- the photon being redshifted --- does indeed exist, and it is a crucial element of Compton scattering. The effect of the outgoing photon having lower energy than the incoming one is independent of the source of the scattering, so it should occur even for gravitationally-mediated scattering; it follows from four-momentum ...


2

Fifty years, ago, the Pound-Rebka experiment demonstrated gravitational blue shift on Earth in a tower at Harvard, to an accuracy of 10%.


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The extreme time dilation proposed can only come if you were on a planet that was orbiting a black hole. The time dilation for a circular orbit around a Schwarzschild black hole is given by $(1 - 3r_s/2)^{1/2}$, where $r_s$ is the Schwarzschild radius. Thus arbitrarily large time dilations can be achieved as an orbit approaches $1.5 r_s$, and the orbital ...


1

Redshift of photons is an observer-dependent notion. That is, if we want to know how photons get redshifted from point to point, we need to ask who is measuring their frequency. If we do not specify the observers, the question has no meaning. When one speaks of gravitational redshift, one typically implicitly refers to a class of observers that play a ...


1

Let's consider a gamma ray emitted from the surface of a $1.4$ solar mass neutron star, assuming the radius is 10 km (on the low end of what is consistent with observations from LIGO and NICER). Let's also assume the spin is small in units of the mass of the object, (a) for simplicity and (b) consistent with observations of known neutron stars. The redshift ...


1

Hi Erik Thank You for your Question. Disclaimer: I am new to Physics Stacks learning my way on the job. To answer your question. No. Hubble's law does not make sense. We observed that objects are moving away faster than they should; so Hubble's law says space is growing larger. Then again.. I also do not think Time Dilation makes sense; But I vehemently ...


1

Hubble Law works on Astronomical Scale. It works very Best at very very far off galaxies at astronomical scale. Even while talking about Andromeda galaxy which is 2.537 million light-years away we don't much talk about Hubble's law.precisely because a lot of other parameters such as gravity tend to dominate. Galaxy out there in space which is some billion or ...


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The expression $$\left( 1 - \frac{r_s}{r}\right)\frac{dt}{d\tau} = \frac{E}{mc^2} = {\rm constant}$$ would apply to an inertial observer in the Schwarzschild metric. i.e. The $\tau$ here corresponds to the proper time experienced by an inertial (free-falling) observer. Your first expression $$ \left( 1-\frac{r_s}{r}\right)^{1/2}dt = d\tau$$ would apply in a ...


1

I think there are two different questions in your question. Or maybe it is better to say that before asking your question, another question should be considered first. Your question: Can we estimate where the center of the universe is? You also ask about the rate of expansion but I think we have to address the question above first. And maybe your question ...


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