Do all measurements need to be normalised?

[mysearch]

By way of a general inquiry, I was wondering whether all measurements in astrophysics need to be normalised for the effects of velocity and gravitation. By way of a broad generalisation of the relativistic effects being considered:

Time Effects:
o Time runs slower with reduced radius [r] from mass [M].
o Time runs slower due to any relative velocity [v].

Spatial Effects:
o Space expands with reduced radius [r] from mass [M].
o Space contracts due to velocity [v] along the path of motion.

In the context of large-scale cosmology, there is the perception of the CMB frame of reference. Therefore:

Might astrophysics use this preferred frame for determining the effects of the Earth’s relative velocity?

Presumably our normal perception of time and space, here on Earth, are affected by our relative velocity with respect to CMB and our position within the gravity well of the Earth itself, then our local solar system and finally the Milky Way. While I have yet done any calculations

Are these relativistic effects too small to be of any significance in astrophysics measurements?
Is there any need to normalise astrophysics measurements to flat spacetime?

Finally, by way of another thread of general inquiry:

Does astrophysics have any standard reference of time, e.g. atomic clocks?
How is distance to some remote object determined, e.g. cepheid variables and redshift?
Are relativistic effects ever taken into consideration?

Appreciate that these questions might be too broad in scope, but would appreciate any thoughts or links to further information. Thanks

 

[marcus]

...
Are these relativistic effects too small to be of any significance in astrophysics measurements?...

...Finally, by way of another thread of general inquiry:

Does astrophysics have any standard reference of time, e.g. atomic clocks?
How is distance to some remote object determined, e.g. cepheid variables and redshift?
Are relativistic effects ever taken into consideration?

The general question of how distances are determined is an interesting one. Terrence Tao has a lecture on "the cosmic distance ladder". various other people have written clear introductory essays on that. Maybe one of the others here will recommend links. There is a series of ways, starting with parallax (trigonometry) ranging of nearby stars. Each method is used to calibrate/check the next method up the ladder. So they work their way farther and farther out.

About relativistic corrections, the first thing to do is estimate the size of the effect. The CMB dipole tells us that the Earth is moving around 370 km/s relative to CMB and that is about 1/1000 of the speed of light.

You know the common relativistic correction factor of sqrt(1 - beta²)

Well if beta = 1/1000 then beta² is a millionth.

So 1 - beta² = 1 - 0.000001 = 0.999999

And sqrt(1 - beta²) = 0.9999995 = even closer to 1.

So there is essentially no relativistic correction. It practically amounts to multiplying or dividing numbers by a number that is essentially one.

 

[marcus]

You mentioned the gravitational correction too. Depth in gravitational field slows time down.

Someone else may want to answer more precisely but I would say that there is not much reason to correct for our depth, either in the solar system's field or in the galaxy's.

You can get a handle on how deep we are down in our gravity hole by estimating how big a kick it would take to send a spacecraft out of the solar system and out of the galaxy. Escape velocity. It is not much compared with the speed of light.

A good rule to remember is that escape from circular orbit is sqrt 2 times the circular orbit speed. Our solar system is going about 250 km/s in its orbit around the center of the galaxy. so multiply that by 1.4. You get about 350 km/s.

Escape from solar system might bring it up to a total of 400 km/s. That's a measure of how deep we are.

This is about the same order of magnitude as the other speed. Intuitively, I'd guess that any general relativistic time correction is not going to amount to much. Not something to worry about.

When we say the age of expansion is 13.7 billion years there is already so much imprecision that we are not going to worry about our depth in gravitational field. Someone out at "infinity" in the wide open spaces between the clusters of galaxies---who is not down deep in gravitational potential----he would probably also measure the age as 13.7 billion years.

Yes his clocks are going a wee bit faster than ours, so maybe for him it is would be
13.70001 billion years. Just kidding I haven't estimated the size of the correction. Could just as easily be 13.7001.

but nobody is looking at the 6th decimal place. the original estimate of 13.7 was only accurate to 3 significant figures.

You see the general point I'm making.

 

[mysearch]

Hi Marcus,
Many thanks for both inputs. I just wanted to check whether I was over-looking any obvious factors regarding the composite effects of special and general relativity. The development of GPS is often cited as tangible case where the relativistic effects of velocity and gravity have to be accounted. However, in the GPS case, I assume it is orbital velocity of the satellite rather than the relative velocity with respect to CMB that is the major issue. Doing some quick calculations regarding the gravitational effects, which I haven’t checked, the value of 2GM/rc^2 at the surface of the following object would be:

Black Hole = 1
Neutron Star = 3.01E-01
Sun = 4.25E-06
Earth = 1.40E-09

Again, the gravitational effects seem minimal, especially at greater radii, unless the application requires an accuracy of 6-9 decimal places, which I assume GPS must. In the context of gravity, the relativistic factor (1-Rs/r) introduces the parameter [r] as the coordinate radius, which appears to be defined as the circumference [C] divided by [2Pi]. In curved spacetime, the value of [r] does not align to flat space geometry and it is often conceptually implied that value of [r] is calculated by first measuring [C]. However, it was not obvious how this might be practically done within the context of astrophysics here on Earth, if flat space geometry could not be assumed. Again, many thanks.