Redshift FAQ article development

[Mordred]

If you feel up to it Naty1. It would be easier to see many of your proposals above if you could
quote the article. Copy it to microsoft word. That way we don't lose the math latex forms.
Then write in your changes. The cosmological constant section should only be about the constant. So that section needs changing. We can probably drop false vacuum replace in the right section your FLRW related quotes. On infinity I have the same described twice so that can be deleted in the cosmological constant section.
Hubble section needs to be prior to redshift may involve moving cosmological section up.

Those are some of the changes I see that definitely need addressing along with the reorganization of questions to a good sequence.

If your willing to try your editted version we can compare between your editted version and mine and pick the best one.

 

[Mordred]

EXPANSION AND REDSHIFT
1) What is outside the universe?
2) What is causing the expansion of the universe?
3) Is expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit?
4) What do we mean when an object leaves our universe?
5) What do we mean when we say homogeneous and isotropic?
6) Why is the CMB so vital in cosmology?
7) Why is the LambdaCDM so vital to cosmologists?
8) Why are all the galaxies accelerating from us?
9) Is Redshift the same as Doppler shift?
9) How do we measure the distance to galaxies?
10) What is a Cepheid or standard candle

These are some of the common questions I will attempt to address in the following article
First we must define some terms and symbols used.

Planck constant: h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s
Gravitational constant: G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}
Speed of light in a vacuum:c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}

The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometers (19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×10¹³ kilometers
Mpc=1 million Parsecs

Universe: A generalized definition of the universe can be described as everything that is. In Cosmology the universe can be described as everything measurable in our space-time either directly or indirectly. This definition forms the basis of the observable universe. The Hot Big Bang model does not describe prior to 10^-43 seconds. The LambdaCDM or \LambdaCDM model is a fine tuned version of the general FLRW (Freidmann Lemaitre Robertson Walker) metrics, where the six observationally based model parameters are chosen for the best fit to our universe.

The Observable universe is 46 Billion light years, or 4.3×10²⁶ meters with an age as of 2013, is 13.772 ± 0.059 billion years.
In the hot big bang model we do not think of the universe as starting from a singularity (infinitely, hot, dense point) instead measurements agree space-time as simply expanding. That expansion is homogeneous and isotropic. If you were to take a telescope and look at the night sky, no matter where you look the universe looks the same or homogeneous meaning no preferred location. As you change directions with the telescope you will find that no matter which direction you look the universe looks the same or isotropic meaning no preferred direction. These terms in cosmology are only accurate at certain scales. Below 100Mpc it is obvious that the universe is inhomogeneous and anisotropic. As such objects as stars and galaxies reside in this scale. This also tells us that there is no center of the universe, as a center is a preferred location. These terms also describe expansion. Expansion will be covered in more detail in the Cosmological Redshift section. Whether or not the universe is finite or infinite is not known. However if it is infinite now so it must be in the beginning.
Common misconceptions arise when one tries to visualize a finite universe such questions include.

"So how do we see farther than 13.772 billion light years?" The answer lies in expansion; as light is traveling towards us, space-time has expanded.
“If the universe is finite what exists outside the Universe?" If you think about this question with the above definition of the universe you will realize that the question is meaningless. One accurate answer in regards to cosmology is nonexistent.
"What makes up the barrier between our universe and outside our universe?" The short answer is there is no barrier.


The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformly, This provides strong evidence of the homogeneous and isotropic measurements and distances. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral atoms. These atoms could no longer absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Precise measurements of cosmic background radiation are critical to cosmology, since any proposed model of the universe must explain this radiation. CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. Their currently observed energy is 1/1000th of their energy as emitted.

In order to measure an objects motion and distance in cosmology it is important to properly understand redshift, Doppler shift and gravitational redshift. Incorrect usage of any of these can lead to errors in our measurements.

Doppler shift and redshift are the same phenomenon in general relativity. However you will often see Doppler factored into components with different names used, as will be explained below. In all cases of Doppler, the light emitted by one body and received by the other will be red or blueshifted i.e. its wavelength will be stretched. So the color of the light is more towards the red or blue end of the spectrum. As shown by the formula below.

\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}

The Cosmological Redshift is a redshift attributed to the expansion of space. The expansion causes a Recession Velocity for galaxies (on average) that is proportional to DISTANCE.
A key note is expansion is the same throughout the cosmos. However gravity in galaxy clusters is strong enough to prevent expansion. In other words galaxy clusters are gravitationally bound. In regards to expansion it is important to realize that galaxies are not moving from us due to inertia, rather the space between two coordinates are expanding. One way to visualize this is to use a grid where each vertical and horizontal joint is a coordinate. The space between the coordinates increase rather than the coordinates changing. This is important in that no FORCE is acting upon the galaxies to cause expansion. As expansion is homogeneous and isotropic then there is no difference in expansion at one location or another. In the \LambdaCDM model expansion is attributed to the cosmological constant described later on. The rate a galaxy is moving from us is referred to as recession velocity. This recession velocity then produces a Doppler (red) shift proportional to distance (please note that this recession velocity must be converted to a relative velocity along the light path before it can be used in the Doppler formula). The further away an object is the greater the amount of redshift. This is given in accordance with Hubble’s Law. In order to quantify the velocity of this galactic movement, Hubble proposed Hubble's Law of Cosmic Expansion, aka Hubble's law, an equation that states:

Hubble’s Law: The greater the distance of measurement the greater the recessive velocity

Velocity = H₀ × distance.

Velocity represents the galaxy's recessive velocity; H₀ is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

The Hubble Constant The Hubble “constant” is a constant only in space, not in time,the subscript ‘0’ indicates the value of the Hubble constant today and the Hubble parameter is thought to be decreasing with time. The current accepted value is 70 kilometers/second per mega parsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity. It is precisely analogous to a separation speed. If, in one frame of reference, one object is moving east at .9c, and another west at .9c, they are separating by 1.8c. This is their recession velocity. Their relative velocity remains less than c. In cosmology, two things change from this simple picture: expansion can cause separation speeds much greater even than 2c; and relative velocity is not unique, but no matter what path it is compared along, it is always less than c, as expected.

z = (Observed wavelength - Rest wavelength)/(Rest wavelength) or more accurately

1+z= λ_observed/λ_emitted or z=(λ_observed-λ_emitted)/λ_emitted

1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}

λ₀= rest wavelength
Note that positive values of z correspond to increased wavelengths (redshifts).
Strictly speaking, when z < 0, this quantity is called a blueshift, rather than
a redshift. However, the vast majority of galaxies have z > 0. One notable blueshift example is the Andromeda Galaxy, which is gravitationally bound and approaching the Milky Way.

The rate of expansion is expressed in the \LambdaCDM model in terms of
The scale factor, cosmic scale factor or sometimes the Robertson-Walker scale factor parameter of the Friedmann equations represents the relative expansion of the universe. It relates the proper distance which can change over time, or the comoving distance which is the distance at a given reference in time.

d(t)=a(t)d_o

where d(t) is the proper distance at epoch (t)
d₀ is the distance at the reference time (t_o)
a(t) is the comoving angular scale factor. Which is the. ..
r(t) is the comoving radial scale factor. Which is...

Proper distance =R(t)r

the notation R(t) indicates that the scale factor is a function of time and its value changes with time. R(t)<1 is the past, R(t)=1 is the present and R(t)>1 is the future.

z+1=1/1+z

H(t)=change in a(t)/R(t)

Expansion velocity
v=change in a(t)r

This shows that Hubble's constant is time dependant.


WMAP nine-year results give the redshift of photon decoupling as z=1091.64 ± 0.47 So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.

Cosmological Constant is a homogeneous energy density that causes the expansion of the universe to accelerate. Originally proposed early in the development of general relativity in order to allow a static universe solution it was subsequently abandoned when the universe was found to be expanding. Now the cosmological constant is invoked to explain the observed acceleration of the expansion of the universe. The cosmological constant is the simplest realization of dark energy, which the more generic name is given to the unknown cause of the acceleration of the universe. Indeed what we term as "Dark" energy is an unknown energy that comprises most of the energy density of our cosmos around 73%. However the amount of dark energy per m³ is quite small. Some estimates are around about 6 × 10^-10 joules per cubic meter. However their is a lot of space between large scale clusters, so that small amount per m³ adds up to a significant amount of energy in total. In the De_Sitter FLRW metric (matter removed model)
this is described in the form.

H_o\propto\sqrt\Lambda

Another term often used for the cosmological constant is vacuum energy described originally by the false vacuum inflationary Model by A.Guth. The cosmological constant uses the symbol Λ, the Greek letter Lambda.
The dark energy density parameter is given in the form:
\Omega_\Lambda which is approximately 0.685

The Doppler Redshift results from the relative motion of the light emitting object and the observer. If the source of light is moving away from you then the wavelength of the light is stretched out, i.e., the light is shifted towards the red. When the wavelength is compressed from an object moving towards you then it moves towards the blue end of the spectrum. These effects, individually called the blueshift and the redshift are together known as Doppler shifts. The shift in the wavelength is given by a simple formula

(Observed wavelength - Rest wavelength)/(Rest wavelength) = (v/c)

f=\frac{c+v_r}{c+v_s}f_o

c=velocity of waves in a medium
v_r is the velocity measured by the source using the source’s own proper-time clock(positive if moving toward the source
v_s is the velocity measured by the receiver using the source’s own proper-time clock(positive if moving away from the receiver)

The above are for velocities where the source is directly away or towards the observer and for low velocities less than relativistic velocities. A relativistic Doppler formula is required when velocity is comparable to the speed of light. There are different variations of the above formula for transverse Doppler shift or other angles. Doppler shift is used to describe redshift due to inertial velocity one example is a car moving away from you the light will be redshifted, as it approaches you the light and sound will be blueshifted. In general relativity and cosmology, there is a fundamental complication in this simple picture - relative velocity cannot be defined uniquely over large distances. However, it does become unique when compared along the path of light. With relative velocity compared along the path of the light, the special relativity Doppler formula describes redshift for all situations in general relativity and cosmology. It is important to realize that gravity and expansion of the universe affect light paths, and how emitter velocity information is carried along a light path; thus gravity and expansion contribute to Doppler redshift

Gravitational Redshift describes Doppler between static emitter and receiver in a gravitational field. Static observers in a gravitational field are accelerating, not inertial, in general relativity. As a result (even though they are static) they have a relative velocity in the sense described under Doppler. Because they are static, so is this relative velocity along a light path. In fact, the relative velocity for Doppler turns out to depend only on the difference in gravitational potential between their positions. Typically, we dispense with discussion of the relative velocity along a light path for static observers, and directly describe the resulting redshift as a function of potential difference. When the potential increases from emitter to receiver, you have redshift; when it decreases you have blue shift. The formula below is the gravitational redshift formula or Einstein shift in an uncharged, non rotating, spherical mass.
<br /> \frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}<br />

G=gravitational constant
c=speed of light
M=mass of gravitational body
r= distance from gravitational body of Mass M

Cosmic Distance ladder, also known as Extragalactic distance scale. Is easily thought of as a series of different measurement methods for specific distance scales. Previous in the article we discussed the various forms of Redshift. These principles are used in conjunction with the following methods described below. Modern equipment now allows use spectrometry. Spectrographs of an element give off a definite spectrum of light or wavelengths. By examining changes in this spectrum and other electromagnetic frequencies with the various forms of shifts caused by relative motion, gravitational effects and expansion. We can now judge an objects luminosity

Luminosity is often measured in flux where flux is

f=L/4pi r^2
inverse square law needed here...

However cosmologists typically use a scale called magnitudes. The magnitude scale has been developed so that a 5 magnitude change corresponds to a differents of 100 flux.
Rather than cover a large range of those distance scales or rungs on the ladder I will cover a few of the essential steps to cosmological distance scales. The first rung on the ladder is naturally.

Direct measurements: Direct measurements form the fundamental distance scale. Units such as the distance from Earth to the sun that are used to develop a fundamental unit called astronomical unit or AU. During the orbit around the sun we can take a variety of measurements such as Doppler shifts to use as a calibration for the AU unit. This Unit is also derived by a method called Parallax.

Parallax. Parallax is essentially trigonometric measurements of a nearby object in space. When our orbit forms a right angle triangle to us and the object to be measured
With the standardized AU unit we can take two AU to form the short leg. With the Sun at a right angle to us the distance to the object to be measured is the long leg of the triangle.

Moving Cluster Parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster.

Stellar parallax is the effect of parallax on distant stars . It is parallax on an interstellar scale, and allows us to set a standard for the parsec.

Standard candles A common misconception of standard candles is that only type 1A supernova are used. Indeed any known fundamental distance measurement or stellar object whose luminosity or brightness is known can be used as a standard candle. By comparing an objects luminosity to the observed brightness we can calculate the distance to an object using the inverse square law. Standard candles include any object of known luminosity, such as Cepheid’s, novae, Type 1A supernova and galaxy clusters.

My thanks to the following Contributors, for their feedback and support.

PAllen
Naty1
Jonathon Scott
marcus

Article by Mordred, PAllen

 

[Mordred]

Thee order in this copy makes more sense and reads smoother overall. I also added a couple of lines into the Cosmic disntance ladder. I removed the false vacuum descriptive. So overall length is a little better. Still looking at fitting some of your Ideas into the article Nay1

 

[Mordred]

Ok I've got this article modified as far as I can currently think of needed changes. I added the FLRW explanations into the end of the Hubble section.

 

[Naty1]

From your paper above:

The scale factor, cosmic scale factor or sometimes the Robertson-Walker scale factor parameter of the Friedmann equations which is a function of time which represents the relative expansion of the universe. It relates the proper distance (which can change over time, unlike the comoving distance which factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space) between a pair of objects, e.g. two galaxies, moving with the Hubble flow in an expanding or contracting FLRW universe at any arbitrary time to their distance at some reference time . The formula for this is:

d(t)=a(t)do

That appears to be the Wikipedia explanation which I have always had trouble relating to...I did not check to see if you explained proper and comoving distance...that takes some getting used to...

Instead, Consider:
Previously you described expansion terms of grid coordinates...[Is it still included??] expanding distances with the same fixed coordinate identities... I like that,,,,what I like better is the way Leonard Susskind sets up that grid...he just assigns the scale factor a[t] to each edge of the grid..

now THAT is a way anybody [I think] can understand the expansion of the scale factor over time and directly relate it to the expansion of distance in the universe...If you want to see Leonard Susskind develop that idea in a video it's Susskind Lecture 2, Cosmology, Youtube...if you watch much of the video you'll realize he uses a Newtonian model to develop the FLRW formulas...no matter, it's valid for GR too.

http://www.youtube.com/watch?v=ERjkSbdn6-4&list=PLB64419BFD176F2FD&index=41

Derivation of the FRW cosmological model from energy conservation. A Newtonian Cosmological Model…
/////////////

Also,and you may have chosen to omit this, and I already posted it above, but I did not know the Hubble parameter H =a'[t]/a[t] for a long time...I stumbled across it in Wikipedia somewhere.

It gives some insight into the relationship between the Hubble formula you do include [and also the change in H over time!] to the metric expansion within FLRW model developed from the EFE. [as a[t] is part of the metric...no need to discuss all this muck in your paper...]

this will be my last comment...or you'll be revising forever! LOL
good job.

 

[Mordred]

Your right I did inadvertently drop the grid coordinatees.

The FLRW is a wiki definition, I've been looking for one that's a bit more accurate. Also I considered the H =a'[t]/a[t] relation, never thought of using it on the grid coordinates. I'll have to think on that one but will add the grid back once I find a good spot for it.

 

[Mordred]

making a few changes or notes from my phone in the Scale factor coverage and in the Cosmic distance ladder section.

I will striaghten out tomorrow when I get to my comp.

The article has developed into a broader scope than I originally imagined.
In so far as tying it all to distance and motion measurements in cosmic distance ladder.

 

[cristo]

I've been busy for the last few weeks, and so haven't had much chance to look at this. First, I would like to applaud you for the time and effort you've put into this thread.

From the look of things, however, this does not appear to be a FAQ, but more an essay covering several topics. I see that you have included a list of questions at the beginning of the post, but it is not clear where (or if) these questions are answered in the article. You also ask some questions (liek the expansion faster than c question) that already have a FAQ dedicated to them. If you look at the other threads in the FAQ subforum, you will see each is in a thread of its own, with a well-defined question followed by a clear answer. I think if you want this to be a FAQ you need to follow a similar plan.

So, for example, which question do you think is the most important for a FAQ? Ask that question and then go about answering it. The article does not need to define everything to do with cosmology, you can assume that some things are known, and refer to other FAQ's for more information. You also need to include references.

Try to aim for a concise answer to a question, and it is likely to be much more useful to members who are new to the field wanting a quick answer or wanting to understand the topic in more detail.

 

[Mordred]

I've been busy for the last few weeks, and so haven't had much chance to look at this. First, I would like to applaud you for the time and effort you've put into this thread.

From the look of things, however, this does not appear to be a FAQ, but more an essay covering several topics. I see that you have included a list of questions at the beginning of the post, but it is not clear where (or if) these questions are answered in the article. You also ask some questions (liek the expansion faster than c question) that already have a FAQ dedicated to them. If you look at the other threads in the FAQ subforum, you will see each is in a thread of its own, with a well-defined question followed by a clear answer. I think if you want this to be a FAQ you need to follow a similar plan.

So, for example, which question do you think is the most important for a FAQ? Ask that question and then go about answering it. The article does not need to define everything to do with cosmology, you can assume that some things are known, and refer to other FAQ's for more information. You also need to include references.

Try to aim for a concise answer to a question, and it is likely to be much more useful to members who are new to the field wanting a quick answer or wanting to understand the topic in more detail.

Yeah the article went far deeper than my original goal lol. I can easily shorten down the beginning section with references to previous written FAQ articles for a start. To apply the method you described will tke some thought onto modifying the article.

 

[Mordred]

EXPANSION AND REDSHIFT
1) What is outside the universe?
2) What is causing the expansion of the universe?
3) Is expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit?
4) What do we mean when an object leaves our universe?
5) What do we mean when we say homogeneous and isotropic?
6) Why is the CMB so vital in cosmology?
7) Why is the LambdaCDM so vital to cosmologists?
8) Why are all the galaxies accelerating from us?
9) Is Redshift the same as Doppler shift?
9) How do we measure the distance to galaxies?
10) What is a Cepheid or standard candle

These are some of the common questions I will attempt to address in the following article
First we must define some terms and symbols used.

Planck constant: h\ =\ 6.62606876(52)\ \times\ 10^{-34}\ J\ s
Gravitational constant: G\ =\ 6.673(10)\ \times\ 10^{-11}\ m^{3} kg^{-1} s^{-2}
Speed of light in a vacuum:c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}

The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometers (19.2 trillion miles). In astronomical terms, it is equal to 3.26 light-years, and in scientific terms it is equal to 3.09×10¹³ kilometers
Mpc=1 million Parsecs

Universe: A generalized definition of the universe can be described as everything that is. In Cosmology the universe can be described as everything measurable in our space-time either directly or indirectly. This definition forms the basis of the observable universe. The Hot Big Bang model does not describe prior to 10^-43 seconds. The LambdaCDM or \LambdaCDM model is a fine tuned version of the general FLRW (Freidmann Lemaitre Robertson Walker) metrics, where the six observationally based model parameters are chosen for the best fit to our universe.

The Observable universe is 46 Billion light years, or 4.3×10²⁶ meters with an age as of 2013, is 13.772 ± 0.059 billion years.
In the hot big bang model we do not think of the universe as starting from a singularity (infinitely, hot, dense point) instead measurements agree space-time as simply expanding. That expansion is homogeneous and isotropic. If you were to take a telescope and look at the night sky, no matter where you look the universe looks the same or homogeneous meaning no preferred location. As you change directions with the telescope you will find that no matter which direction you look the universe looks the same or isotropic meaning no preferred direction. These terms in cosmology are only accurate at certain scales. Below 100Mpc it is obvious that the universe is inhomogeneous and anisotropic. As such objects as stars and galaxies reside in this scale. This also tells us that there is no center of the universe, as a center is a preferred location. These terms also describe expansion. Expansion will be covered in more detail in the Cosmological Redshift section. Whether or not the universe is finite or infinite is not known. However if it is infinite now so it must be in the beginning.
Common misconceptions arise when one tries to visualize a finite universe such questions include.

"So how do we see farther than 13.772 billion light years?" The answer lies in expansion; as light is traveling towards us, space-time has expanded.
“If the universe is finite what exists outside the Universe?" If you think about this question with the above definition of the universe you will realize that the question is meaningless. One accurate answer in regards to cosmology is nonexistent.
"What makes up the barrier between our universe and outside our universe?" The short answer is there is no barrier.


The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformly, This provides strong evidence of the homogeneous and isotropic measurements and distances. As the universe expanded, both the plasma and the radiation filling it grew cooler. When the universe cooled enough, protons and electrons combined to form neutral atoms. These atoms could no longer absorb the thermal radiation, and so the universe became transparent instead of being an opaque fog. Precise measurements of cosmic background radiation are critical to cosmology, since any proposed model of the universe must explain this radiation. CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. Their currently observed energy is 1/1000th of their energy as emitted.

In order to measure an objects motion and distance in cosmology it is important to properly understand redshift, Doppler shift and gravitational redshift. Incorrect usage of any of these can lead to errors in our measurements.

Doppler shift and redshift are the same phenomenon in general relativity. However you will often see Doppler factored into components with different names used, as will be explained below. In all cases of Doppler, the light emitted by one body and received by the other will be red or blueshifted i.e. its wavelength will be stretched. So the color of the light is more towards the red or blue end of the spectrum. As shown by the formula below.

\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}

The Cosmological Redshift is a redshift attributed to the expansion of space. The expansion causes a Recession Velocity for galaxies (on average) that is proportional to DISTANCE.
A key note is expansion is the same throughout the cosmos. However gravity in galaxy clusters is strong enough to prevent expansion. In other words galaxy clusters are gravitationally bound. In regards to expansion it is important to realize that galaxies are not moving from us due to inertia, rather the space between two coordinates are expanding. One way to visualize this is to use a grid where each vertical and horizontal joint is a coordinate. The space between the coordinates increase rather than the coordinates changing. This is important in that no FORCE is acting upon the galaxies to cause expansion. As expansion is homogeneous and isotropic then there is no difference in expansion at one location or another. In the \LambdaCDM model expansion is attributed to the cosmological constant described later on. The rate a galaxy is moving from us is referred to as recession velocity. This recession velocity then produces a Doppler (red) shift proportional to distance (please note that this recession velocity must be converted to a relative velocity along the light path before it can be used in the Doppler formula). The further away an object is the greater the amount of redshift. This is given in accordance with Hubble’s Law. In order to quantify the velocity of this galactic movement, Hubble proposed Hubble's Law of Cosmic Expansion, aka Hubble's law, an equation that states:

Hubble’s Law: The greater the distance of measurement the greater the recessive velocity

Velocity = H₀ × distance.

Velocity represents the galaxy's recessive velocity; H₀ is the Hubble constant, or parameter that indicates the rate at which the universe is expanding; and distance is the galaxy's distance from the one with which it's being compared.

The Hubble Constant The Hubble “constant” is a constant only in space, not in time,the subscript ‘0’ indicates the value of the Hubble constant today and the Hubble parameter is thought to be decreasing with time. The current accepted value is 70 kilometers/second per mega parsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity. It is precisely analogous to a separation speed. If, in one frame of reference, one object is moving east at .9c, and another west at .9c, they are separating by 1.8c. This is their recession velocity. Their relative velocity remains less than c. In cosmology, two things change from this simple picture: expansion can cause separation speeds much greater even than 2c; and relative velocity is not unique, but no matter what path it is compared along, it is always less than c, as expected.

z = (Observed wavelength - Rest wavelength)/(Rest wavelength) or more accurately

1+z= λ_observed/λ_emitted or z=(λ_observed-λ_emitted)/λ_emitted

1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}

λ₀= rest wavelength
Note that positive values of z correspond to increased wavelengths (redshifts).
Strictly speaking, when z < 0, this quantity is called a blueshift, rather than
a redshift. However, the vast majority of galaxies have z > 0. One notable blueshift example is the Andromeda Galaxy, which is gravitationally bound and approaching the Milky Way.
WMAP nine-year results give the redshift of photon decoupling as z=1091.64 ± 0.47 So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.

Cosmological Constant is a homogeneous energy density that causes the expansion of the universe to accelerate. Originally proposed early in the development of general relativity in order to allow a static universe solution it was subsequently abandoned when the universe was found to be expanding. Now the cosmological constant is invoked to explain the observed acceleration of the expansion of the universe. The cosmological constant is the simplest realization of dark energy, which the more generic name is given to the unknown cause of the acceleration of the universe. Indeed what we term as "Dark" energy is an unknown energy that comprises most of the energy density of our cosmos around 73%. However the amount of dark energy per m³ is quite small. Some estimates are around about 6 × 10^-10 joules per cubic meter. However their is a lot of space between large scale clusters, so that small amount per m³ adds up to a significant amount of energy in total. In the De_Sitter FLRW metric (matter removed model)
this is described in the form.

H_o\propto\sqrt\Lambda

Another term often used for the cosmological constant is vacuum energy described originally by the false vacuum inflationary Model by A.Guth. The cosmological constant uses the symbol Λ, the Greek letter Lambda.
The dark energy density parameter is given in the form:
\Omega_\Lambda which is approximately 0.685

The Doppler Redshift results from the relative motion of the light emitting object and the observer. If the source of light is moving away from you then the wavelength of the light is stretched out, i.e., the light is shifted towards the red. When the wavelength is compressed from an object moving towards you then it moves towards the blue end of the spectrum. These effects, individually called the blueshift and the redshift are together known as Doppler shifts. The shift in the wavelength is given by a simple formula

(Observed wavelength - Rest wavelength)/(Rest wavelength) = (v/c)

f=\frac{c+v_r}{c+v_s}f_o

c=velocity of waves in a medium
v_r is the velocity measured by the source using the source’s own proper-time clock(positive if moving toward the source
v_s is the velocity measured by the receiver using the source’s own proper-time clock(positive if moving away from the receiver)

The above are for velocities where the source is directly away or towards the observer and for low velocities less than relativistic velocities. A relativistic Doppler formula is required when velocity is comparable to the speed of light. There are different variations of the above formula for transverse Doppler shift or other angles. Doppler shift is used to describe redshift due to inertial velocity one example is a car moving away from you the light will be redshifted, as it approaches you the light and sound will be blueshifted. In general relativity and cosmology, there is a fundamental complication in this simple picture - relative velocity cannot be defined uniquely over large distances. However, it does become unique when compared along the path of light. With relative velocity compared along the path of the light, the special relativity Doppler formula describes redshift for all situations in general relativity and cosmology. It is important to realize that gravity and expansion of the universe affect light paths, and how emitter velocity information is carried along a light path; thus gravity and expansion contribute to Doppler redshift

Gravitational Redshift describes Doppler between static emitter and receiver in a gravitational field. Static observers in a gravitational field are accelerating, not inertial, in general relativity. As a result (even though they are static) they have a relative velocity in the sense described under Doppler. Because they are static, so is this relative velocity along a light path. In fact, the relative velocity for Doppler turns out to depend only on the difference in gravitational potential between their positions. Typically, we dispense with discussion of the relative velocity along a light path for static observers, and directly describe the resulting redshift as a function of potential difference. When the potential increases from emitter to receiver, you have redshift; when it decreases you have blue shift. The formula below is the gravitational redshift formula or Einstein shift off the vacuum surrounding an uncharged, non rotating, spherical mass.
<br /> \frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}<br />

G=gravitational constant
c=speed of light
M=mass of gravitational body
r= the radial coordinate (measured as the circumference, divided by 2pi, of a sphere centered around the massive body)

The rate of expansion is expressed in the \LambdaCDM model in terms of
The scale factor, cosmic scale factor or sometimes the Robertson-Walker scale factor parameter of the Friedmann equations represents the relative expansion of the universe. It relates the proper distance which can change over time, or the comoving distance which is the distance at a given reference in time.

d(t)=a(t)d_o

where d(t) is the proper distance at epoch (t)
d₀ is the distance at the reference time (t_o)
a(t) is the comoving angular scale factor. Which is the distance coordinate for calculating proper distance between objects at the same epoch (time)
r(t) is the comoving radial scale factor. Which is distance coordinates for calculating proper distances between objects at two different epochs (time)

Proper distance =\frac{\stackrel{.}{a}(t)}{a}

The dot above a indicates change in.

the notation R(t) indicates that the scale factor is a function of time and its value changes with time. R(t)<1 is the past, R(t)=1 is the present and R(t)>1 is the future.

H(t)=\frac{\stackrel{.}{a}(t)}{a(t)}

Expansion velocity
v=\frac{\stackrel{.}{a}(t)}{a}

This shows that Hubble's constant is time dependant.



Cosmic Distance ladder, also known as Extragalactic distance scale. Is easily thought of as a series of different measurement methods for specific distance scales. Previous in the article we discussed the various forms of Redshift. These principles are used in conjunction with the following methods described below. Modern equipment now allows use spectrometry. Spectrographs of an element give off a definite spectrum of light or wavelengths. By examining changes in this spectrum and other electromagnetic frequencies with the various forms of shifts caused by relative motion, gravitational effects and expansion. We can now judge an objects luminosity where absolute luminosity is the amount of energy emitted per second.

Luminosity is often measured in flux where flux is

f=\frac{L}{4\pi r^2}

However cosmologists typically use a scale called magnitudes. The magnitude scale has been developed so that a 5 magnitude change corresponds to a differents of 100 flux.
Rather than cover a large range of those distance scales or rungs on the ladder I will cover a few of the essential steps to cosmological distance scales. The first rung on the ladder is naturally.

Direct measurements: Direct measurements form the fundamental distance scale. Units such as the distance from Earth to the sun that are used to develop a fundamental unit called astronomical unit or AU. During the orbit around the sun we can take a variety of measurements such as Doppler shifts to use as a calibration for the AU unit. This Unit is also derived by a method called Parallax.

Parallax. Parallax is essentially trigonometric measurements of a nearby object in space. When our orbit forms a right angle triangle to us and the object to be measured
With the standardized AU unit we can take two AU to form the short leg. With the Sun at a right angle to us the distance to the object to be measured is the long leg of the triangle.

Moving Cluster Parallax is a technique where the motions of individual stars in a nearby star cluster can be used to find the distance to the cluster.

Stellar parallax is the effect of parallax on distant stars . It is parallax on an interstellar scale, and allows us to set a standard for the parsec.

Standard candles A common misconception of standard candles is that only type 1A supernova are used. Indeed any known fundamental distance measurement or stellar object whose luminosity or brightness is known can be used as a standard candle. By comparing an objects luminosity to the observed brightness we can calculate the distance to an object using the inverse square law. Standard candles include any object of known luminosity, such as Cepheid’s, novae, Type 1A supernova and galaxy clusters.

My thanks to the following Contributors, for their feedback and support.

PAllen
Naty1
Jonathon Scott
marcus

Article by Mordred, PAllen

 

[Passionflower]

I would suggest:

The formula below is the gravitational redshift formula or Einstein shift between two static observers in the vacuum surrounding an uncharged, non rotating, spherical mass.
<br /> \frac{\lambda}{\lambda_o}=\frac{1}{\sqrt{(1 - \frac{2GM}{r c^2})}}<br />

G=gravitational constant
c=speed of light
M=mass of gravitational body
r= [STRIKE]distance from gravitational body of Mass M[/STRIKE] the radial coordinate (measured as the circumference, divided by 2π, of a sphere centered around the massive body)

 

[Mordred]

good suggestion I'll change that

 

[Jonathan Scott]

good suggestion I'll change that

I don't think this is going the right way for an FAQ. I think an FAQ should contain simple and direct answers, and if these answers aren't the "whole truth", then the answers can accompanied by appropriate qualifiers.

I think that simple concepts are more important than being absolutely precise. If something requires more complexity, I prefer to see a simple statement that covers most cases followed by more details or disclaimers relating to more obscure cases where necessary, rather than an initial statement which is technically accurate but unhelpful.

I also disagree with the suggested way of describing gravitational redshift. There are obviously alternative ways of describing the same situation, but describing locations in a static field as effectively having a velocity relative to one another is unhelpful and misleading. I think that it is simplest to consider gravitational redshift in a static situation as just another manifestation of gravitational time dilation. Exactly the same rule covers watching a standard clock at a different potential, or any other regular process.

I also find it helpful to understand that in most situations which do not involve extreme gravitational potentials (that is, anywhere except near neutron stars or black holes) one can use Newtonian approximations, where the fractional difference in the time rate is simply the Newtonian potential difference in dimensionless (energy per energy) units, typically a sum of terms of the form $-Gm/rc^2$.

For the space station example I mentioned earlier, if the radius is $r$ and the angular velocity is $\omega$ then the speed is $v = r \omega$. The radial acceleration (equivalent to the gravitational field) is $-v^2/r = -r\omega^2$. The effective potential is the integral of the field radially from the center to radius $r$, which is $-\tfrac{1}{2} r^2 \omega^2$. For dimensionless units (energy per energy) we divide by $c^2$, so the effective potential is $-\tfrac{1}{2} r^2 \omega^2 / c^2$ which is equal to $-\tfrac{1}{2} v^2/c^2$, and this then gives fractional change in the time rate due to the effective gravitational potential, which is fortunately exactly the same as the time dilation seen as a Special Relativity velocity effect (for non-relativistic speeds).

 

[Naty1]

I just can't help myself...a few more comments [sorry!]:

'gravitational redshift' has nothing to do with your ten questions. Why is it here??

Seems like a needless complication to me...BUT if you are going to leave it, you should explain in a one liner in the three categoeries of redshift the difference between redshift in GR, in cosmology [expansion of distance] and due to gravity.

You currently write: "Doppler shift and redshift are the same phenomenon in general relativity."...
if you want to include that I'd suggest something like:

"Doppler shift and redshift are the same phenomenon between observers in general relativity with static distances...but not in cosmology where vast distances vary and standard distant frames have relative velocity ...hence they are different than GR...


Some redshift of faraway objects is due to cosmological expansion and some to Doppler shift. How much of that redshift is due to the Doppler shift and how much is due to the expansion is arbitrary.

Doppler shift is based on frame based differences, not expansion; Doppler shift is a particular explanation/interpretation of redshift.

ok, I am going to noodle out and watch tv! and try a new Spanish wine!

 

[PAllen]

I don't think this is going the right way for an FAQ. I think an FAQ should contain simple and direct answers, and if these answers aren't the "whole truth", then the answers can accompanied by appropriate qualifiers.

I think that simple concepts are more important than being absolutely precise. If something requires more complexity, I prefer to see a simple statement that covers most cases followed by more details or disclaimers relating to more obscure cases where necessary, rather than an initial statement which is technically accurate but unhelpful.

I also disagree with the suggested way of describing gravitational redshift. There are obviously alternative ways of describing the same situation, but describing locations in a static field as effectively having a velocity relative to one another is unhelpful and misleading. I think that it is simplest to consider gravitational redshift in a static situation as just another manifestation of gravitational time dilation. Exactly the same rule covers watching a standard clock at a different potential, or any other regular process.

I also find it helpful to understand that in most situations which do not involve extreme gravitational potentials (that is, anywhere except near neutron stars or black holes) one can use Newtonian approximations, where the fractional difference in the time rate is simply the Newtonian potential difference in dimensionless (energy per energy) units, typically a sum of terms of the form $-Gm/rc^2$.

For the space station example I mentioned earlier, if the radius is $r$ and the angular velocity is $\omega$ then the speed is $v = r \omega$. The radial acceleration (equivalent to the gravitational field) is $-v^2/r = -r\omega^2$. The effective potential is the integral of the field radially from the center to radius $r$, which is $-\tfrac{1}{2} r^2 \omega^2$. For dimensionless units (energy per energy) we divide by $c^2$, so the effective potential is $-\tfrac{1}{2} r^2 \omega^2 / c^2$ which is equal to $-\tfrac{1}{2} v^2/c^2$, and this then gives fractional change in the time rate due to the effective gravitational potential, which is fortunately exactly the same as the time dilation seen as a Special Relativity velocity effect (for non-relativistic speeds).

I only have a moment now, but it looks like we won't reach consensus on this. In my view, if you ask "what is Doppler in GR?", there is only one reasonable answer. From this, which is not hard to explain (if you gloss over parallel transport, as I did in my wording), all red shifts are special cases. So to answer is Doppler different from gravitational redshift? with 'yes' is simply a lie, since the latter is direct consequence of it. Same for cosmological redshift - if you compute Doppler in the only possible way in GR for co-moving observers in RW solution, you get the so called cosmological redshift. So how can you call it different? Further, I think popular treatments that describe gravitational redshift as a general phenomenon in GR are wrong, in that it can only be defined at all in special cases (sufficiently static geometry). My aim was to make our answers better than popular misleading answers.

 

[PAllen]

I also disagree with the suggested way of describing gravitational redshift. There are obviously alternative ways of describing the same situation, but describing locations in a static field as effectively having a velocity relative to one another is unhelpful and misleading. I think that it is simplest to consider gravitational redshift in a static situation as just another manifestation of gravitational time dilation. Exactly the same rule covers watching a standard clock at a different potential, or any other regular process.

In my view, time dilation, as an observable, is a corollary of Doppler. Observed rate of a process viewed from a distance must match Doppler, because light emission itself functions as a clock. So to me, it is Doppler->gravitational redshift=gravitational time dilation.

 

[Passionflower]

So to answer is Doppler different from gravitational redshift? with 'yes' is simply a lie, since the latter is direct consequence of it.

I think in GR a Doppler shift is a combination of spacetime and path curvature.

 

[PAllen]

I think in GR a Doppler shift is a combination of spacetime and path curvature.

Agreed, as I described in the wording I supplied for the FAQ. In general, it is an inseparable combination of two world lines and the spacetime geometry between them (which affects light path and how information about 4-velocity of emission event is carried to reception event).

 

[Mordred]

For myself I've seen numerous articles with gravitational redshift as different from Doppler, as well as various proofs that it is a special case of Doppler. In order to approach both views would be an article in and of itself.

From the sounds of the responses from the Moderators the article itself will need to be broken down into a smaller 1 question=1 answer format rather than an extensive overall process to reach cosmic distance measurements as this one was approaching. That in and of itself will require extensive rewriting.
However the Doppler vs gravitational redshift is an interesting point of discussion.

 

[Jonathan Scott]

The relative gravitational time dilation in a static situation is already there in the metric, and is completely independent of the path by which signals travel (provided that the path is also static), so this seems a much simpler way to describe it.

Also, any description which equates a gravitational potential difference to a "relative velocity" is potentially seriously misleading, as it suggests that there is a fixed velocity difference along a general path which travels from one to another, which is not true. There is a fixed potential difference, which means that the change in kinetic energy is a fixed proportion of the initial energy, but the velocity difference is dependent on the initial velocity. When this is applied to the special case of light propagation, then there is a unique meaning, but there's no change of local speed involved, so calling this a relative velocity seems unhelpful.

It is obviously true that if you look at the same phenomenon in a different way you should get the same physical result, as I've recently mentioned for the spinning space station. However, the most general way is not necessarily the most useful. I think it is more helpful to understand simple special cases in detail and then to be aware that there are ways of uniting them into a general but more complex scheme.

 

[Naty1]

Pallen: I just read your posts around #19 - #30 for the first time.

Those really clarify nicely some cornerstone concepts

"...Doppler appropriately defined for GR is the one universal way to compute and understand redshift...In the cases of static observers, we call the Doppler for these special observers gravitational red shift; in the case of comoving observers we call it cosmological red shift... a parallel transported 4-velocity will never exceed c in any local frame..."

Nicely done...!

Well don't get too carried away! [LOL] because now I am back to fretting about comoving observers: that in widely separated cosmological expansion observations, redshift due to the Doppler shift and that due to expansion is arbitrary...coordinate based... We end up with superluminal expansion...etc.. why if we can avoid it?? ...

ah well, I'll save that for another day.

 

[Mordred]

Pallen: I just read your posts around #19 - #30 for the first time.

Those really clarify nicely some cornerstone concepts



Nicely done...!

Well don't get too carried away! [LOL] because now I am back to fretting about comoving observers: that in widely separated cosmological expansion observations, redshift due to the Doppler shift and that due to expansion is arbitrary...coordinate based... We end up with superluminal expansion...etc.. why if we can avoid it?? ...

ah well, I'll save that for another day.

lol what really bugs me is in replies to the question " Is expansion really faster than the speed of light and how does this not violate GR"

the common answer on the forum is " yes at the edge of the observable universe its 3c " then they briefly explain how it doesn't violate GR with its "due to expansion and expansion does not need to follow GR"

the problem with that answer is its misleading and doesn't correctly answer the question.

 

[PAllen]

The relative gravitational time dilation in a static situation is already there in the metric, and is completely independent of the path by which signals travel (provided that the path is also static), so this seems a much simpler way to describe it.

A metric component g00 has no coordinate independent meaning, in general. To say it has the meaning commonly attributed to it in e.g. SC geometry, you need to:

- Note that static observer's have tangent vectors such that all other components of the metric do not contribute to their proper time. Then this still gives only the relation between coordinate time and proper time for a particular family of observers.
- To convert the above to something observable (coordinate independent) you must examine how one static observer observes clocks or light from another static observer. This is a computation of Doppler. Only Doppler and differential aging are observables, not time dilation.
- Then you note that Doppler is static between a pair of static observers.
- Then you can say that observed redshift and dime dilation between two static observers can be determined from a potential difference.

The view that gravitational time dilation is direct observable in GR, with a definition in terms of the metric (in the general case) has led to numerous fundamental misunderstandings displayed on these forums. Thus I think it is crucial to counter the very attitude you present - that gravitational redshift= gravitational time dilation is a general feature of GR; that a component of the metric in some coordinate basis describes something physically significant; that there is any general way to separating gravitational redshift from Doppler.

Basically, you are ok with common treatments that I view as half way between misleading and just plain wrong.

Also, any description which equates a gravitational potential difference to a "relative velocity" is potentially seriously misleading, as it suggests that there is a fixed velocity difference along a general path which travels from one to another, which is not true.

My descriptions have emphasized that relative velocity is not unique in GR, but that for Doppler, what counts is relative velocity determined by parallel transport along the light path. Please read the wording I contributed to the FAQ - it very carefully makes these points in as succinctly as possible. Because there is one specific path that matters for Doppler (the path actually taken by light), there is a static relative velocity between static observers, for the purpose of Doppler].

There is a fixed potential difference, which means that the change in kinetic energy is a fixed proportion of the initial energy, but the velocity difference is dependent on the initial velocity. When this is applied to the special case of light propagation, then there is a unique meaning, but there's no change of local speed involved, so calling this a relative velocity seems unhelpful.

This is all backwards. GR does not natively have any concept of potential difference. Nor does it have any native concept of KE of light changing, apart from Doppler in curved spacetime. The existence of a potential as a useful, non-fundamental, computational trick that derives from the special case of a timelike killing vector picking out a family of observers for which Doppler takes a remarkably simple form. Then you can use this to facilitate determination of Doppler in static spacetime by first considering Doppler between static observers (based on potential difference), then computing strictly local SR Doppler between each world line and a corresponding static world line.

Note also, that the idea there is a unique (for Doppler purposes only) relative velocity between static world lines in a static GR solution makes nice contact with the idea that in SR, Doppler between front and back of a rocket can be attributed to velocity of emitter at emission event relative to velocity of absorber at target event. Thus, just as SR has no need to introduce pseudo-gravity to explain any redshifts in flat spacetime, GR does contains only one fundamental notion for observed spectral shifts.

It is obviously true that if you look at the same phenomenon in a different way you should get the same physical result, as I've recently mentioned for the spinning space station. However, the most general way is not necessarily the most useful. I think it is more helpful to understand simple special cases in detail and then to be aware that there are ways of uniting them into a general but more complex scheme.

I remain convinced that pretending that, for GR, Doppler, gravitational redshift, and cosmological redshift are three separate phenomena is simply wrong. And to the extent that so much literature gives this impression, we should, on PF work against this bad practice.

 

[PAllen]

Well don't get too carried away! [LOL] because now I am back to fretting about comoving observers: that in widely separated cosmological expansion observations, redshift due to the Doppler shift and that due to expansion is arbitrary...coordinate based... We end up with superluminal expansion...etc.. why if we can avoid it?? ...

lol what really bugs me is in replies to the question " Is expansion really faster than the speed of light and how does this not violate GR"

the common answer on the forum is " yes at the edge of the observable universe its 3c " then they briefly explain how it doesn't violate GR with its "due to expansion and expansion does not need to follow GR"

the problem with that answer is its misleading and doesn't correctly answer the question.

I agree that common answers in terms of expanding space make a very simple idea easily explainable in SR into something mysterious (I have not emphasized in this thread that using Milne foliation you can get arbitrary recession speeds even in flat spacetime). There is nothing going on here beyond the difference between growth of proper distance between world lines using a chosen foliation (for which neither SR nor GR poses any upper bound), versus relative velocity, which uniquely < c for SR, and not unique in GR (but always < c).

However, to answer Naty1, there is a very good reason such coordinates are used in cosmology and why it is useful to talk about recession velocity as normally defined. That is that in these coordinates, the isotropy and homogeneity observed by all comoving observers is made manifest.

 

[Ich]

I remain convinced that pretending that, for GR, Doppler, gravitational redshift, and cosmological redshift are three separate phenomena is simply wrong. And to the extent that so much literature gives this impression, we should, on PF work against this bad practice.

I'm absolutely with you. Especially the common statement that cosmological redshift is not a doppler shift is really evil.
However, I'd also like if you'd use coordinate-dependent statements as well, as Jonathan Scott promotes it.
For example,

that a component of the metric in some coordinate basis describes something physically significant

this one's true: g_tt in static coordinates describes a significant symmetry. Of course, this symmetry may not be exact, as in an expanding spacetime where you use "static" coordinates on a small patch, but still, is has some merit.

I'm under the impression that much of the discussion is about words rather than physics.
For example, I understand why you want to call the "Synge-type" redshift a Doppler shift. But couldn't we call it "GR redshift" or something like that instead and use the name "Doppler shift" as close as possible to its pre-relativistic meaning? This would imply that you use "gravitational redshift/time dilation" as its counterpart, too.

My reasoning: those words have some relatively well defined meaning to the layman or semi-expert reader, and as such could help to intuitively explain the rather "fuzzy" and complicated world of GR, where for example GR redshift is well defined, but way beyond the mathematical abilities of 99% of the readership. Just start talking about path dependency of the procedure, and you'll lose all those that don't have the necessary geometrical background.
But if you define an observer, doppler and gravitational redshift are complementary description of reality: doppler is two-way redshift, while gravitational redshift is one way only. The former is accompanied by a changing distance, the latter is what's left for obervers at rest wrt each other.
Of course, the very meaning of "chaqnging distance" or "at rest" becomes fuzzy at large timescales, large distances in a changing spacetime, but they're useful in most circumstances except large scale cosmology. And their meaning is relatively clear to most readers.

So why not say "GR redshift" is the canonical description in GR, the other descriptions are "human made" distinctions.
Where, in the coordinates the readers are most familiar with, redshift can be split into doppler and gravitational. But such coordinates are not suitable for too large an area in a dynamic spacetime.
Where, in the case of a cosmological symmetry, one can alternatively use cosmological redshift, which doesn't describe a different physical phenomenon - every cosmological redshift can also be explained as a combination of doppler and gravitational redshift in their domain of applicability, after all. But, given said symmetry, cosmological redshift's domain of applicability is truly universal, that's why we're using this additional concept, too.

I agree that common answers in terms of expanding space make a very simple idea easily explainable in SR into something mysterious

Which is kind of my point: You wouldn't describe e.g. solar system mechanics in FRW coordinates. Also, the canonical "Synge-type" redshift isn't of much use - at least not as misleading an mystic as the FRW description, but just plainly useless.
You'll use a quasistatic background, even if the universe isn't static, and you'll use the potential and the notion of (relative or absolute, doesn't matter) velocity that comes with this assumed, not really exact background. You'll do highscool physics and e.g. calculate the effect of universal expansion on solar system dynamics without any difficulties: It's simply the gravity of the additional matter/energy within the system.
That's an example how practical and useful a quasistatic background with its quasiNewtonian physics is. Doppler shift and gravitational redshift/time dilation also belong to this extremely useful heuristic, why don't you encourage their usage?

 

[PAllen]

Which is kind of my point: You wouldn't describe e.g. solar system mechanics in FRW coordinates. Also, the canonical "Synge-type" redshift isn't of much use - at least not as misleading an mystic as the FRW description, but just plainly useless.
You'll use a quasistatic background, even if the universe isn't static, and you'll use the potential and the notion of (relative or absolute, doesn't matter) velocity that comes with this assumed, not really exact background. You'll do highscool physics and e.g. calculate the effect of universal expansion on solar system dynamics without any difficulties: It's simply the gravity of the additional matter/energy within the system.
That's an example how practical and useful a quasistatic background with its quasiNewtonian physics is. Doppler shift and gravitational redshift/time dilation also belong to this extremely useful heuristic, why don't you encourage their usage?

I only have a moment now, but a few comments:

- Doppler in GR (what you call Synge redshift) in the solar system is impractical computationally, agreed, but precisely accurate all the same (as to physical concepts and math).
- I do not oppose use of any what you describe here; it is what I do (as I'm sure what anyone does) to make a computation. However, I do feel it is important to understand that there is a single core phenomenon, with special cases that simplify and are given special names. The wording I proposed for this does suggest the utility of the special case treatment. Perhaps emphasis can be shifted. Here is what I contributed to this section:

"Gravitational Redshift describes Doppler between static emitter and receiver in a gravitational field. Static observers in a gravitational field are accelerating, not inertial, in general relativity. As a result (even though they are static) they have a relative velocity in the sense described under Doppler. Because they are static, so is this relative velocity along a light path. In fact, the relative velocity for Doppler turns out to depend only on the difference in gravitational potential between their positions. Typically, we dispense with discussion of the relative velocity along a light path for static observers, and directly describe the resulting redshift as a function of potential difference. When the potential increases from emitter to receiver, you have redshift; when it decreases you have blue shift. "

I don't mind a shift in emphasis, but I do feel it is important to get across that starting from SR Doppler and asking "what is Doppler in GR", an accurate answer leads, as a derived consequence, the asymmetric redshift between sufficiently static observers, as well as to the cosmological redshift.

Also, what I see as really in common between these and possible additional special cases is:

- symmetries pick out some family of observers between which GR Doppler takes a simple form.

Whenever this is true, you can then treat Doppler for general observers by applying the simple formula for special observers, combined with local pure SR Doppler for emitter motion relative to coinciding special observer; similarly for target motion relative to its coincident special observer.

 

[PAllen]

I could agree with calling the single GR phenomenon "GR redhsift" rather than "GR Doppler" as long as we get across that it is the GR generalization of SR Doppler, and includes SR Doppler as well as well as gravitational redshift as special cases.

However, as for how to classify cosmological redshift, the following paper:

http://arxiv.org/abs/1111.6704

proposes a specific definition of kinematic (which you need not agree with, but at least they pose a precise one), such that much of cosmological redshift is considered due to spacetime curvature rather then kinematic (despite being symmetric).

Personally, I prefer the concept of a preferred (by symmetries) family of observers picking out a simple form GR redshift, that can be used to analyze general observers. We give the name 'gravitational redshift' to static observer's (asymmetric)shift, and 'cosmological redshift' to comoving observer's shift (which is symmetric).

 

[Mordred]

I've seen this debate numerois times in the past in regards to redshift being ill defined. That was one of the reasons I was pleased to having PAllens assistance. The viewpoint above is one that I agree with.
I've been thinking of how to go about modifying the article.
The article I feel can be narrowed down to two questions. The others being covered by other FAQs in the subforum.

1) Is redshift the same as Doppler shift?
2) How do we determine a stellar objects location (and inherently motion.)

 

[PAllen]

I want to clarify why I think it is most accurate to view the single phenomenon in GR as "Doppler in curved space time". Ich earlier proposed a dichotomy between gravitational redshift for situations where distance does not grow and shift is asymmetric; versus Doppler where distance grows (or shrinks) with symmetric red (blue) shift.

I think this distinction is misleading because it implies that gravitational redshift must be distinguished from Doppler even for SR. At the fundamental level, this is absurd. The case of an accelerating rocket is strictly explained by Doppler, and shows that the attachment of symmetry to Doppler is restricted to inertial motion. Once you have non-inertial motion in SR, you find asymmetric Doppler between world lines, with distance not changing (depending on who measures it how). Furthermore, to first order (but not higher order) asymmetric shift between static observers in GR has exactly the same explanation as a pure Doppler effect when viewed in inertial frame (as the SR rocket case).

Thus, I think the correct approach is to start from observations like the above to explain there is one phenomenon in GR responsible for all spectral shifts, and that it is Doppler generalized to curved spacetime. The special cases arise from approximate or exact symmetries picking out a family of observers (static; comoving) for which Doppler takes a simple form.

I don't think I will budge from these core postions:

- Is gravitational redshift different from Doppler? NO.
- Is cosmological redshift different from Doppler? NO.
- Must photons be viewed as losing energy for cosmological redshift any more than they
must be viewed as losing energy for Doppler or gravitational redhsift? NO ( I do agree that
there are valid ways of looking at both the gravity and cosmological situations that involve
photons losing energy - but such a view is not required).
- Despite the fact that there is no reason to view 'individual' photons as losing energy, there is a fundamental conservation issue in FLRW cosmology. But I view the core issue as the inability to even define total energy for such spacetime; and that there is not necessarily any reason to expect energy conservation because of time asymmetry.

 

[Ich]

Doppler in GR (what you call Synge redshift) in the solar system is impractical computationally, agreed, but precisely accurate all the same (as to physical concepts and math).

Right, as in "you're in a balloon", if you know that old joke.

However, I do feel it is important to understand that there is a single core phenomenon, with special cases that simplify and are given special names.

That's ok. However, I'd say the core phenomenon concerning redshift is the parallel transport of the wave vector along the null curve. That you get the same result by transporting the four velocity of the emitter is fine, and it may add some insights that would otherwise be lost. For example, it's interesting that gravitational redshift can be seen as an application of redshift due to relative velocity. I played with the idea, too, but my experience is that you confuse your audience rather than enlight them. I also think that the definition of gravitational redshift as being due to relative velocity between static observers is a bit on the progressive side of mainstream - I won't challenge its validity, but I doubt it's the most helpful interpretation. We should not set this as a standard interpretation, IMHO.

I don't mind a shift in emphasis, but I do feel it is important to get across that starting from SR Doppler and asking "what is Doppler in GR", an accurate answer leads, as a derived consequence, the asymmetric redshift between sufficiently static observers, as well as to the cosmological redshift.

As said, my feeling is that this is a bit too general. Starting from SR, you have doppler shift due to relative velocity = position change. Going to GR, you may either generalize Doppler to include shift between static observers as well, or you may keep that distinction and differentiate between doppler and gravitational shift. Both are valid, but I think the latter approach is much more suitable to pick the readers up from where they already are.
I'm just talking about the wording. Call it GR redshift, feel free to explain how it can be seen as a generalisation of a Doppler shift, but use the word "Doppler" for the following:

Personally, I prefer the concept of a preferred (by symmetries) family of observers picking out a simple form GR redshift, that can be used to analyze general observers. We give the name 'gravitational redshift' to static observer's (asymmetric)shift, and 'cosmological redshift' to comoving observer's shift (which is symmetric).

I agree and add: looking at emitters with some relative velocity wrt said static observers, you get the most appropriate definition of Doppler shift, which you simply multiply with the gravitational shift to get the total result. As you can see, I'm rather with Peacock in that interpretation than with Ostvang. You can split the effects in every type of cosmology, at least as far as "static" has - at least as an approximation - some well-defined meaning that can be interpreted as "not moving".
I just want to save this Doppler definition for the GR case, too. It's way too useful to be discarded.

 

[PAllen]

I agree and add: looking at emitters with some relative velocity wrt said static observers, you get the most appropriate definition of Doppler shift, which you simply multiply with the gravitational shift to get the total result. As you can see, I'm rather with Peacock in that interpretation than with Ostvang. You can split the effects in every type of cosmology, at least as far as "static" has - at least as an approximation - some well-defined meaning that can be interpreted as "not moving".
I just want to save this Doppler definition for the GR case, too. It's way too useful to be discarded.

Which galaxies are not moving in an FLRW cosmology?

 

[PAllen]

FYI: I see no problem with an FAQ suggesting that there are more than one valid way of viewing things. Twin FAQs are famous for that. Thus, while I strongly resist a claim Doppler is definitely not the same gravitational redshift I could easily go along with:

- looked at one way, the distinction is.
- looked at another way, they are the same.

 

[Ich]

Which galaxies are not moving in an FLRW cosmology?

There are none. But in order to construct a "SR-like" coordinate system, you'd provide some observers that are at rest wrt each other (as measured by vanishing two-way redshift between adjacent observers) instead of some that we know to have relative velocity. And you'd use those to take the place of Einstein's clocks in his inertial frames, not the moving galaxies, of course.
In other words: You can always use Normal Coordinates, and by doing so you'll always gain some intuitive insight.
Because Normal Coordinates translate this fuzzy GR world into the concepts that most of us are familiar with.

Thus, while I strongly resist a claim Doppler is definitely not the same gravitational redshift I could easily go along with:

- looked at one way, the distinction is.
- looked at another way, they are the same.

Great. I don't make such claims, and my goal is to prevent unsubstantiated claims like: cosmological redshift is not a doppler shift. So we agree, there's a useful notion of "doppler" against "gravitational" redshift also in GR, and there's the coordinate-independent fact that redshift is generally explained by parallel transport (of the source or the signal, whatever).

 

[PAllen]

There are none. But in order to construct a "SR-like" coordinate system, you'd provide some observers that are at rest wrt each other (as measured by vanishing two-way redshift between adjacent observers) instead of some that we know to have relative velocity. And you'd use those to take the place of Einstein's clocks in his inertial frames, not the moving galaxies, of course.
In other words: You can always use Normal Coordinates, and by doing so you'll always gain some intuitive insight.
Because Normal Coordinates translate this fuzzy GR world into the concepts that most of us are familiar with.

Of course if a free faller does this near a planet, they conclude there is pure relative motion Doppler between 'static' bodies. Meanwhile the static bodies do not fit the 'relatively motionless' criteria you give (no vanishing redshift). So, setting up 'as close to Minkowski' coordinates over a region of interest in GR leads to:

- Cosmological redshift is clearly Doppler
- gravitational redshift is also clearly Doppler.

Great. I don't make such claims, and my goal is to prevent unsubstantiated claims like: cosmological redshift is not a doppler shift. So we agree, there's a useful notion of "doppler" against "gravitational" redshift also in GR, and there's the coordinate-independent fact that redshift is generally explained by parallel transport (of the source or the signal, whatever).

Almost. I agree that there is derived, practical, approach of 'gravitational redshift'. But attaching more significance to it implies that one must distinguish Doppler between non-inertial world lines in SR from that between inertial world lines. Conceptually, this last is silly. However, for SR as much as GR, there are common situations where the 'gravitational redshift heuristic' simplifies problem solving enormously.

Also, the parallel transport is the 'second order' phenomenon sensitive to curvature. The 'first order' difference between inertial Doppler and non-inertial Doppler (to coin a phrase) has nothing to do with parallel transport, because that is a no-op in SR. In any case, we don't necessarily have to agree (completely or at all); we only have to agree that there are a couple of valid ways of looking at these issues.

 

[nonspace]

Dear PAllen!

Do you agree that space is expanding (or stretching of space )?

 

[PAllen]

Dear PAllen!

Do you agree that space is expanding (or stretching of space )?

It is, mathematically, a coordinate dependent effect (in that you can construct an apparent expanding space for flat, Minkowski spacetime - see the Milne universe). However, in the real world, the division between space and time leading to expanding space is preferred by physical symmetries of the universe and experience of observers: we observe isotropy and homogeneity at large scales; so do other galaxies. Any separation of spacetime into space and time that manifests these symmetries will show expanding space.

So, to sound like Clinton, it depends on what the meaning of is is; but mostly the answer is yes.

 

[Mordred]

FYI: I see no problem with an FAQ suggesting that there are more than one valid way of viewing things. Twin FAQs are famous for that. Thus, while I strongly resist a claim Doppler is definitely not the same gravitational redshift I could easily go along with:

- looked at one way, the distinction is.
- looked at another way, they are the same.

This is an accurate statement. I tried showing that in the article with your assistance on the GR viewpoints. After the long weekend I plan to pull the excess expansion details out. Develop the Article to the two view points.
The section on cosmic distance ladder I will use for a second article covering how distances and motion ae measured.
The trick will be writing the two articles without repeating as both articles involve redshift in a fsshion.

 

[Naty1]

PALLEN:...

I see no problem with an FAQ suggesting that there are more than one valid way of viewing things. Twin FAQs are famous for that. Thus, while I strongly resist a claim Doppler is definitely not the same gravitational redshift I could easily go along with:

- looked at one way, the distinction is.
- looked at another way, they are the same.

It's even more important than that! It's absolutely necessary for perspective...One reason is that many if not most readers will have not exhaustively studied all the detailed math of cosmology and likely not of GR either...If Tamara Davis can provide alternative perspectives, and such alternatives are real,and valuable, and they ARE, so should we...

In the great 2007 thread Wallace, Chronos ,Oldman, Marcus, others take different views ...you can read the posts from the 40’s thru 50’s and see the pros and cons.

https://www.physicsforums.com/showthr...nt+flow&page=4

One view:

I do think it is better to think of (photons) as being redshifted by being observed in a different frame ...Now as t ticks along, the scale factor a(t) increases. Therefore two observers who are both at rest wrt to the CMB, but who have different times t will therefore be in different frames (have different metrics). This is what leads to photons being redshifted when observed and emitted at different times.

[Contrast that observational persective with one from above:

ICH:

... in order to construct a "SR-like" coordinate system, you'd provide some observers that are at rest wrt each other (as measured by vanishing two-way redshift between adjacent observers) instead of some that we know to have relative velocity.

As 'obvious' as that seems now, it took me [because I am not too bright] a long time to realize that on my own terms...]

a concurrence...from the old thread:

I tend to agree, photons are not redshifted by traveling through the universe, they are redshifted only because they are observed in a different frame from which they were emitted.

a dissent!...
Marcus: # 48...

I am not comfortable with that because among other things I see cosmologists doing inventories of the energy density which are implicitly estimated IN A CMB FRAME...

[If photons are not physically redshifted as they travel though an expanding space, how did the universe cool from about 3,000 to about 3 degrees K today??]

These ‘conflicting’ viewpoints stem in part from this as explained by Chalnoth elsewhere:

… You get some total redshift for faraway objects due to cosmological expansion. How much of that redshift is due to the Doppler shift# and how much is due to the expansion between us and the far away object is completely arbitrary.”

Another 'physical view: In the CMB a grav redshift is the so called Sachs-Wolfe effect...
and another: Chronos:

Redshift is a frame dependent measurement. If you were approaching a distant galaxy at the same speed as it is receeding, you would see no redshift.

But reconciling these different perspectives, showing how they relate,explaining the physical results, is not so easy!

 

[Naty1]

PAllen:

- Must photons be viewed as losing energy for cosmological redshift any more than they must be viewed as losing energy for Doppler or gravitational redhsift? NO ( I do agree that there are valid ways of looking at both the gravity and cosmological situations that involve photons losing energy - but such a view is not required).

Still seems REQUIRED to me...How does one avoid explaining that the universe has cooled...via a redshift or Doppler... of about 1,000 corresponding to an early temperature of 3,000 degrees to about 3 degrees currently?

In other words, wow things get from an opaque, charged plasma of about 3,000 K, a surface of last scattering which blocked photons, to the current 'clear and uncharged' environment?? Something physical seems to have changed!

I have not quite figured that out to my own satisfaction! Thanks

 

[PAllen]

PAllen:


Still seems REQUIRED to me...How does one avoid explaining that the universe has cooled...via a redshift or Doppler... of about 1,000 corresponding to an early temperature of 3,000 degrees to about 3 degrees currently?

In other words, wow things get from an opaque, charged plasma of about 3,000 K, a surface of last scattering which blocked photons, to the current 'clear and uncharged' environment?? Something physical seems to have changed!

I have not quite figured that out to my own satisfaction! Thanks

Well, let me answer in part with a question: Suppose a collapsed star stopped short of forming a BH with horizon, and had a 3000K black body radiating surface (as experienced on the surface). To all observers well away, there is 2.7K black body radiation. For this it is routine (and Jonathan Scott agrees with this perspective) to say the no photons lost energy. Simply that 3000K on the collapsed surface corresponds to 2.7K far away; thus the photon was emitted at local temp of 3000K=2.7K far away perspective, and didn't change at all along the way to being received. Yet this is not considered a violation of conservation of energy or a mystery at all - just a difference in time and energy scale between different locations. For cosmology, instead of different time and energy scale varying by location in a static geometry, you have different time and energy scales at different cosmological times. Thus, there really is no reason you need consider CMB photons to have lost energy over time - instead you can equally well (a la gravity well case) consider the energy scale changed over time, and that the two scenarios are equivalent.

Does this mean there is no conservation of energy problem in FLRW cosmologies? Unfortunately, it doesn't address this issue. There is a fundamental difference between 'sufficiently static geometry' in 'sufficiently flat very large region', where we can define quasi-local energy in a consistent way (and for which 3000k photon near the collapsed surface adds the same total energy as a 2.7 K photon far away), coming up with a conserved quantity. For FLRW cosmologies, all known ways, within GR, of totalling energy for the universe fail (they require either asymptotic flatness or something close to it). Thus, my point of view (shared by Tamara Davis post 2009), is the total energy of the universe is undefined, so the failure of conservation cannot even be posed. But none of this is related to whether photons must be considered to change energy from emission to absorption in cosmology.

 

[Naty1]

PAllen:

...3000K on the collapsed surface corresponds to 2.7K far away; thus the photon was emitted at local temp of 3000K=2.7K far away perspective, and didn't change at all along the way to being received.

That's another nice example...so ok, I guess the dichotomy I am struggling with is my 'flat space' mind with the vagaries of 'curved space-time'...

Towards the end of the article linked above, Tamara Davis expands this perspective a bit..., so I guess these ideas are as 'good as it gets'...thank you once again!

...because in small enough regions
the universe makes a pretty good approximation
of flat spacetime. But in flat spacetime
there is no gravity and no stretching of waves,
and any redshift must just be a Doppler effect

So we can think of the light as making many
tiny little Doppler shifts along its trajectory.
And just as in the case of the police car—where
it would not even occur to us to think that photons
are gaining or losing energy—here, too, the
relative motion of the emitter and observer
means that they see photons from different perspectives
and not that the photons have lost energy
along the way.
In the end, therefore, there is no mystery to
the energy loss of photons: the energies are being
measured by galaxies that are receding from
each other, and the drop in energy is just a matter
of perspective and relative motion.

 

[Naty1]

PAllen...
I did not mention it in my prior post but I do understand [I think] about FLRW cosmologies not addressing energy conservation...On the other hand, I don't really understand this part of your prior post and I am remiss in skipping over it:

...There is a fundamental difference between 'sufficiently static geometry' in 'sufficiently flat very large region', where we can define quasi-local energy in a consistent way (and for which 3000k photon near the collapsed surface adds the same total energy as a 2.7 K photon far away), coming up with a conserved quantity.

I'm confused by this description because I don't see how you are disentangling motion and curvature...I assume near the 'collapsed surface' there is curvature [a change in gravitational potential??] and hence gravitational redshift as a photon is emitted ...If there is no curvature and a 'static' geometry, [do you mean 'no expansion'??] then should I not expect to see the photon at distance as emitted, unchanged, at 3,000 K??

 

[Ich]

Hi PAllen,

Meanwhile the static bodies do not fit the 'relatively motionless' criteria you give (no vanishing redshift).

I think you misread what I wrote. I was talking about vanishing two-way redshift, which clearly vanishes for static observers. Sending light down the potential, you get gravitational blueshift, which is exactly canceled by the redshift on the way back if there is no radial motion between the observers.

I agree that there is derived, practical, approach of 'gravitational redshift'. But attaching more significance to it implies that one must distinguish Doppler between non-inertial world lines in SR from that between inertial world lines.

Why is that? This is a coordinate based concept, we're not talking about right or wrong here, we're talking about "useful" or "useless". If it's useful, use it. If not, let it be.

Conceptually, this last is silly.

Well, using fictitious concepts like a "gravitational field" may in fact be "silly" at times. That's no reason to generally forbid its use, as they may be very helpful in other situations.
Remember what you're arguing against: There are those who insist that one must not see cosmological redshift as a doppler shift. Why would you insist that one must not see redshift (under the appropriate circumstances) as a "gravitational" redshift. Why would you forbid it, when it's clearly of use somtimes? (If that's your intention at all, I may have misunderstood you.)

Also, the parallel transport is the 'second order' phenomenon sensitive to curvature. The 'first order' difference between inertial Doppler and non-inertial Doppler (to coin a phrase) has nothing to do with parallel transport, because that is a no-op in SR.

Comparison via parallel transport is trivial in SR and yields standard relative velocity, at least for the frame where the compared events are simultaneous. If the events are null-separated, you might also want to interpret the result as a gravitational redshift, if it suits your purposes. No special significance to it, it may just be useful and even reflect something important in nature.
I think there may be a misunderstanding concerning my use of "first" and "second order" effects: in a homogeneous universe, if you make a series expansion of redshift as a function of normal distance (in the quasistatic frame), the Hubble flow will show up as a first order effect, while the gravitational potential is parabolic with distance. I did not intend to say that, generally, gravitational redshift is a second order effect. Sorry for the confusion.

BTW, this thread's going too fast for my limited (and phase-shifted) time online.
To sum up, my point is: there are times to call a redshift cosmological, doppler, or gravitational. Don't call it "doppler" under all circumstances, you're going to sow confusion. It's good to say that GR itself doesn't care about these concepts, it's ok to say that the redshift concept you propose is kind of "canonical" in GR, and it's ok to explain that it might be seen as related to a doppler shift. But there's no use henceforth calling every redshift "doppler".
Make of it what you will, I'll have a look at this thread from time to time and be happy to answer to your (and anybody's) comments, if it doesn't disturb the many strands in this discussion.