General Relativistic Blue-Shifting for Observer on Relativistic Velocity Body

Could you repeat the question, please?

Well, yes and no...

An observer at a lower gravitational potential than a source ("downhill") will observe radiation to be blueshifted to shorter wavelengths. This is a natural consequence of conservation of energy and mass-energy equivalence, and was confirmed experimentally in 1959 with the Pound-Rebka experiment. Gravitational blueshift contributes to cosmic microwave background (CMB) anisotropy via the Sachs-Wolfe effect: when a gravitational well evolves while a photon is passing, the amount of blueshift on approach will differ from the amount of gravitational redshift as it leaves the region.

What happens if you're color blind?

Hi SolarEagle;

Thanks for the information.

What about the case where the relativistic gamma factor of the body and observer is constant thereby assuming constant relativistic mass for the observer body system and also assuming constant CMBR spectum, more specifically, a background spectrum that is precisely black body at a temperature of 2.725 K. I am assuming that for systems traveling at high but not enourmous gamma factors which are constant and bodies having a Schwarzchild radius that is less than the radius of the body, the inverse relationship would be a reasonable first order approximation.

I am aware however that the CMBR is not a perfect black body nor is it unchanging in spectrum and spherical distribution around a given observer over finite lengths of time, at least for time periods that are significantly longer than the Planck time.

Regards;

Jim

Who can say....?

It is not that simple. You still have to account for the Lorentz contraction and optical aberration effects at such velocities.

Hi Anonymous Hero;

I would think that Lorentz contraction and optical abberation would be taken care of in the additional inclusion of the associated special relativistic effects. The observer located on the surface of the the body would not experience the body nor himself or herself being Lorentz contracted, and nor would the body in its own reference frame. What I am attempting to clearly discern is whether there would be an inverse relation as I mentioned above except where the substituted mass is the relativistic mass of the body.

Now, I agree, that the already special relativistically contracted space in front of the space craft as well as the special relativistic optical abberation would be present as it would for inertial frames having a very small relativistic mass. Thus, I am assuming such special relativistic effects would be further processed by the body in a manner consistent with the inverse of the red shift as I speculated above. Afterall, the body and observer do not experience themselves as being Lorentz contracted.

Regards;

Jim

Do not forget that the Lorentz contraction also dictates what the observer on the relativistic moving mass observes, which is my original point, not the impact on the observer as you describe.

What is CMBR an acronym for?

"Can My Buttocks Rattle"?

Cosmic Microwave Background Radiation, but I like PWslack's variation better.

The CMBR is actually photons released from the early universe just after the big bang and after the universe cooled just enough to allow it to be "transparent" enough for photons to move unrestricted.

As space rapidly expanded the frequency of those hot photons dropped enormously and are now observed as photons oscillating in the microwave region of the spectrum. It is sometimes cited as a temperature of about 2.7255 Kelvins.

What is remarkable about the CMBR is that is is so homogenous in temperature. The only way that anything can cool so homogeneously implies that at one point in time the whole of those photons must have been in close enough proximity to each other to reach a common temperature, much like mixing cold and hot water in a glass will equalize.

to many assumtions

Hi Jim

If I understand your "rather simple question" correctly, then your observer will 'see' a highly blue-shifted CMBR (compared to the usual 3° K), simply due to relativistic Doppler shift. The relativistic mass does not enter the equation as far as that observer is concerned. We use only the rest-mass of the gravitating body in the Schwarzschild solution.

Unless your observer's massive body is speeding relative the 'CMB frame' at closer than 1 part in a million from the speed of light, the actual CMB photons that he sees will still be redshifted, due to the cosmic expansion.

-J

Hi Jorrie;

My question should perhaps be better stated as follows.

Suppose a space craft such as a world ship traveling at a gamma factor of 1,000 and having an invariant mass of one Earth mass is traveling in a perfectly black body sea of radiation such as for example, that having a background temperature of 2.725 Kelvins.

Would the space craft observer perceive the incomming radiation in a manner similar to that of a person on a planetary body at rest but where the at rest planetary body has an invariant mass of 1,000 Earth masses and has the same radius as the above space craft with respect to the observer's frame, and where the radiation incident on the planetary body has an effective background temperature of 2,725 Kelvins and is of the same spherical spectral and temperature distribution as would be experienced by a small space craft based observer traveling at a gamma factor of 1,000 through a perfect background temperature radiation of 2.725 Kelvin, where the radiation for the large planet based observer would be further relativistically blue shifted in a manner consistent with the planet having an invariant mass of 1,000 Earth masses.

Thus, I am assuming two effects which are compounded to blue shift the radiation for the one Earth invariant mass space craft based observer: the Special Rlativistic Dopplar shift and and a General Relativistic Doppler shift that is enhanced by the relativistic mass increase of the gamma factor 1,000 world ship.

I am assuming of course, that such high gamma factors for such massive bodies are possible to engineer as part of the thought experiment. I am also assuming that the world ship mass distribution is perfectly spherical with respect to the observer located on the world ship and that the massive stationary planet is also spherioal with respect to the person located on the massive stationary planet.

Thanks;

Jim

Hi Jim

I did write above: "The relativistic mass does not enter the equation as far as that [local, on the planet] observer is concerned. We use only the rest-mass of the gravitating body in the Schwarzschild solution." The planet does not move relative to the observer's frame of reference.

The things compounded are the CMB redshift, the Doppler shift of the planet (relative to the CMB rest frame) and the gravity blueshift caused by the planet's rest mass at the location of the observer. Hence, your two cases will only differ by the gravity blueshift of the planet, which for Earth's surface is some one part in 10⁸ (negligible).

For all practical purposes, the CMB redshift (~1000) and Doppler blueshift (~1000) will cancel for both cases, i.e. both observers will measure the CMB temperature as a 'non-redshifted' ~2725 K in the direction of travel relative to the CMB rest frame.

-J

Hi Jorrie;

Thanks for the clarification.

I now have a better understanding of the stuff I was trying to calculate.

Regards;

Jim

Simply try it and gather some empirical data.