Redshift FAQ article development

[Mordred]

I have been working on an article covering Redshift. The article is in this thread

https://www.physicsforums.com/showthread.php?p=4307715#post4307715

I would like opinions, recommendations and any other contributions that forum members feel would be good to add.

 

[Mordred]

This is a starting point in explaining Redshift for FAQ purposes.


First we need to distinquish the between RedShift and Doppler shift. In both cases the light emitted by one body and received by the other will be Red/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red end of the spectrum. As shown by the relation formula below. But there's a subtle difference,

Δf/f = Δλ/λ = v/c

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. 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)

so long as the velocity v is much less than the speed of light. A relativistic doppler formula is required when velocity is comparable to the speed of light. Doppler shift is used to describe Redshift due to inertial velocity one example is a car moving away from you the light will be Red Shifted, as it approaches you the light and sound will be blueshifted.


The Cosmological Redshift is however a redshift caused by the expansion of space. The wavelength of light increases as it traverses the expanding universe between its point of emission and its point of detection by the same amount that space has expanded during the crossing time. This is a measure of its recessive velocity over DISTANCE. The further away an object is the greater the amount of RedShift. This is given in accordance with Hubbles 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:

Hubbles Law: The greater the distance of measurement the greater the recessive velocity

velocity = H0 × distance.

Velocity represents the galaxy's recessional 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 has been calculated at different values over time, but the current accepted value is 70 kilometers/second per megaparsec, the latter being a unit of distance in intergalactic space
Any measurement of redshift above the Hubble distance defined as c=H0 = 4300 + or - 400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR for a couple of reasons.

1) Recessive velocity is distance dependant
2) Recessive velocity is not inertial velocity, the galaxies are not accelerating from us, the space between us and the galaxy is increasing.

This is given by the form.

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

1+z= λobserved/λemitted or z=λobserved-λemitted/λobserved

the symbol λ is 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


Cosmological Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity you would find the same expansion rate as your first measurement. Indeed expansion occurs the same throughout the cosmos. However Gravity and the strong Nuclear force in Galaxy clusters are 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 between two coordinates are expanding. That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogenous) and no preferred direction (isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic. 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.

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 is the more generic name given to the unknown cause of the acceleration of the universe. 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 \Lambda. the greek letter Lambda

The Gravitational Redshift is a shift in the frequency of a photon to lower energy as it climbs out of a gravitational field. The frequency of light will Blueshift as it approaches the gravity well.


Standard candles

Using standard candles to determine the Hubble constant has a long andhonorable history; it's the method used by Hubble himself. The recipe for finnding the Hubble constant is a simple one:

Identify a population of standard candles with luminosity L.
-Measure the redshift z and flux f for each standard candle.
-Compute dL = (L=4¼f)1=2 for each standard candle.
-Plot cz versus dL.
-Measure the slope of the cz versus dL relation when z << 1; this gives
H0.

For cosmological purposes, a standard candle should be bright enough to be detected at large redshifts. It should also have a luminosity which is well determined. One time-honored variety of standard candle is the class of Cepheid variable stars. Cepheids, as they are known, are highly luminous supergiant stars, As they pulsate radially, their luminosity varies
in response, partially due to the change in their surface area, and partially due to the changes in the surface temperature as the star pulsates. Type 1A supenova is a type of Cepheid.

Without the use of Cepheids measuring distances would be extremely problematic especially at extremely large distances, These distances ar too large for the parralex method which is a form of triangulation.

Any comments or idea to add will be greatly appreciated, the more suggestions that are added the more complete this article will become. As such I give permission to everyone to copy/paste or correct any portion of the above starting article to add their contributions.

 

[marcus]

Hi Mordy, you've clearly put a lot of work into this! I'll try to comment very briefly and hope that others will comment as well.
I think you have (not an FAQ exactly but) a kind of GLOSSARY of terms. That kind of thing could be quite useful.

An FAQ tries to be a list of questions that commonly occur to people so that if someone is puzzled they can look down the list and find an actual question corresponding to what they have in mind that's bothering them.

A Glossary, or Handbook of terminology, is obviously different but that's not a bad thing. There could be room for both, I suppose. A glossary could actually be more helpful to some people---a kind of "mini-encyclopedia" with very short explanations of just a few key terms and concepts.

People who work on projects like that rarely have the satisfaction of sole authorship, I believe. It is only to be expected that everything gets chewed over by several writer/editors and revised beyond recognition----or thrown out. But whatever happens your work is a kind of force vector pushing towards a final goal, the emergence of some useful glossary of terms. That's how I see it, though I could easily be wrong.

Along the way you might want to pick up the habit of using the subscript and superscript buttons that PF offers. for example:
1+z= λobserved/λemitted

could be changed using the "X₂" button right above the box, into:

1+z= λ_observed/λ_emitted

And the other thing you say " z=λobserved-λemitted/λobserved "
is not quite right, it needs "emitted" instead of "observed" in the denominator, like this:
z=(λobserved-λemitted)/λemitted

Then you mouse over something you want to make into a subscript and press the X₂ button.

My apologies if this is too elementary, in that case just pay it no mind.

 

[Mordred]

Hey Marcus I am glad for any input on this project. My original had a list of questions however I found trying to individually answer common questions ked to a lot of repeating the same things over and over again. So I tried an article that offered a source of answers. Taking what you mentioned about a quick reference of terms offered a viable quick route to the reader. That being said this
is my first FAQ/glossary I've
written. So I am definitely interested in any suggestions.

Yeah I am still working on how to post the various math forms so your advice on how to do so is also helpful. I just discovered the tab at the top on the advance post lol.

I would also like to add an explanation of the expansion rate you have often mentioned on %
The 1/140 % expansion rate. So could use your contribution in that as your best qualified to explain that aspect. Like I mentioned any contributors are more than welcome to copy paste and modify the above developing article

 

[Chronos]

Your need to use linear algebra to properly express this stuff analytically. I parted company with most of my knowledge of linear algebra years ago. It's not terribly useful to most engineers.

 

[Mordred]

EXPANSION AND REDSHIFT

1) Why is all the galaxies accelerating from us ?
2) Is Redshift the same as Dopplershift ?
3) What is causing the expansion of the Universe ?
4) Is Expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit ?
5) What is a Cepheid or standard candle ?
6) What do we mean when we say Homogeneous and Isotropic ?
7) How do we measure the distance to Galaxies ?
8) What is outside the Universe?
9) What do we mean when an object leaves our universe ?


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.

Universe: The Universe in cosmology is defined as the Observable Universe The observable universe from Earth is 46 Billion light years, or 4.3×10²⁶meters with an age as of 2013, is 13.772 ± 0.059 billion years. So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded.
One common Question posters often ask is " What is outside our Universe, this question has no meaning as without space or time you have nonexistence. Also their is no clear consensus on if the Universe is Finite or Infinite. " When an object is said to leave our universe" we mean that the object has crossed the observable universe or rather that it is redshifted to the point of non detectable.


The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometres(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 kilometres

Mpc=1 million Parsecs


In order to understand Redshift we must first need to distinquish the between RedShift and Doppler shift. In both cases the light emitted by one body and received by the other will be Red/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red/blue end of the spectrum. As shown by the relation formula below. But there's a subtle difference, between Dobblershift and redshift.

Δf/f = Δλ/λ = v/c

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 moved towards the blue end of th 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)

so long as the velocity v is much less than the speed of light. A relativistic doppler formula is required when velocity is comparable to the speed of light. Doppler shift is used to describe Redshift due to inertial velocity one example is a car moving away from you the light will be Red Shifted, as it approaches you the light and sound will be blueshifted.


The Cosmological Redshift is however a redshift caused by the expansion of space. The wavelength of light increases as it traverses the expanding universe between its point of emission and its point of detection by the same amount that space has expanded during the crossing time indeed the amount of redshift is the total amount of expansion. This is a measure of its recessive velocity over DISTANCE. The further away an object is the greater the amount of RedShift. This is given in accordance with Hubbles 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:

Hubbles 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 has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per megaparsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as c=H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR for a couple of reasons.

1) Recessive velocity is distance dependant
2) Recessive velocity is not inertial velocity, the galaxies are not accelerating from us, the SPACE between us and the galaxy is increasing.

This is given by the form.

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

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


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 Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion occurs the same throughout the cosmos. However Gravity and the strong Nuclear force in Galaxy clusters are 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 between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic.
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.

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 is the more generic name 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

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 \Lambda. the greek letter Lambda.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing " is really a quantum vacuum with quantum fluctuations described by the Heisenburg uncertainty principle. Virtual particles pop in and out of existence all the time, As expansion occurs those virtual particles Quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models has its roots in this model. However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.

One means of relating to expansion is with the use of the a grid of squares. each horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words te coordinates do not change, the space between coordinates change. I should also note their is no clear consensus on whether the universe is finite or infinite. If its infinite now then it was infinite in the past. Same with Finite. The Big Bang model only describes the Universe from 10^-43 seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of spacetime.

WMAP data confirms that the universe is flat or close to flat.


The Gravitational Redshift is a shift in the frequency of a photon to lower energy as it climbs out of a gravitational field. The frequency of light will Blueshift as it approaches the gravity well.


Standard candles

Using standard candles to determine the Hubble constant has a long and honorable history; it's the method used by Hubble himself. The recipe for finnding the Hubble constant is a simple one:

Identify a population of standard candles with luminosity L.
-Measure the redshift z and flux f for each standard candle.
-Compute dL = (L=4¼f)1=2 for each standard candle.
-Plot cz versus dL.
-Measure the slope of the cz versus dL relation when z << 1; this gives
H₀.

The CMB, (Cosmic Microwave Background) also provides a good reference point in regards to Homogeneous and Isotropic confirmation, and of distances. However that is best described in greater detail than this article.

For cosmological purposes, a standard candle should be bright enough to be detected at large redshifts. It should also have a luminosity which is well determined. One time-honored variety of standard candle is the class of Cepheid variable stars. Cepheids, as they are known, are highly luminous supergiant stars, As they pulsate radially, their luminosity varies
in response, partially due to the change in their surface area, and partially due to the changes in the surface temperature as the star pulsates. Type 1A supenova is a type of Cepheid.

Without the use of Cepheids measuring distances would be extremely problematic, especially at extremely large distances, These distances are far too large for the parallex method which is a form of triangulation.

 

[Mordred]

I've made some changes to the above article including a bit more detail on expansion, What types of questions the article attempts to answer. I'll be adding more as I go I am considering adding spacetime Geometry to the article in regards to flat or curved spacetime but am not sure if it would make the article too lengthy

 

[marcus]

Mordy,
I don't want to seem to encourage you because I am not the gatekeeper about sticky quality and FAQ quality, the mentors are. So I'd feel bad if I encouraged you and the stuff wasn't used and you were disappointed. But. There's a but.

I actually think that is a pretty good list of very basic FAQ questions. they do reflect what many newcomers are actually wondering about. or things they ought to be asking and will realize they should be asking when they see the question.

So the "But" is that I personally think you are doing something worthwhile and are learning by it. There's some chance, I suppose, that someone will see your list and utilize all or some of it, and supply some different answers etc. use some of your wording perhaps and some from somebody else. That would be nice, it would be nice to see some use made of it.
But I CAN'T SPECULATE about that possibility. I just personally think it looks like a worthwhile activity.

I won't help, except very indirectly.

You asked me earlier why it is that there is an exact equivalence like this:

H₀ = 70 km/s per Mpc = 1/140 percent per million years.

Well, you should learn how to use the world's best online calculator, Google box.
Try calculating the RECIPROCAL of H₀, namely 1/H₀ = 1/(70 km/s per Mpc)

Paste "1/(70 km/s per Mpc)" into the Google box. Try it. (without the quotes)

Then type an equal sign, to activate the calculator. Try it.

So what you have typed in is 1/(70 km/s per Mpc)=

You should get 14 billion years. Let me know if it does not work for you and you do not get the answer 14 billion years.

If you know the reciprocal of a quantity, you know the quantity itself===it is just one over its reciprocal!

That means that H₀ = 1/(14 billion years).

Now everybody knows H₀ is the type of quantity that if you multiply a distance by it you get a speed. That type of quantity has to be a reciprocal time, because if you divide a distance by a time you get a speed. It's the only thing arithmetic you can do to a distance to turn it into a speed. Something you multiply distance by, to get speed, can only be the reciprocal of a time.

So regardless of whatever quaint units they traditionally give it to you with, H₀ really is equal to one over a time. And Google calculator tells you the time is 14 billion years. That is called the "Hubble time".

A possible way to go from there is to take that fraction H₀ = 1/(14 billion years) and divide the numerator and the denominator by 14,000.

For the numerator you get 1/14000 = 1/140 percent.
For the denominator you get 14 billion years divided by 14000, which is a million years.

That is a fractional rate of increase, an INSTANTEOUS rate it is now, which if it would continue steady for a million years would make a distance increase by 1/14000 of its length. That is the same as 1/140 of one percent.

So that is the fraction of its length that a distance grows by in a million years.

 

[Mordred]

Yeah the sticky thread aspect is something I will ask the MODS on. No matter the results writing this article has been enjoyable and provided a good learning aid for myself snd hopefully others. I'll try the methodology you just mentioned.
I do hope others like the article and use it as a simple forum based reference. I am close to completion of the article as I do not want it to get too lengthy. Neither did I want to bog it down with too much mathematics.
Thanks for your explanation and assistance thus far

 

[marcus]

Maybe that is not the best explanation. Let's try a different route.
You asked me earlier why it is that there is an exact equivalence like this:

H₀ = 70 km/s per Mpc = 1/140 percent per million years.

Well, you should learn how to use the world's best online calculator, Google box.
Try calculating the RECIPROCAL of 1/H₀ = 1/(70 km/s per Mpc)

Paste "1/(70 km/s per Mpc)" into the Google box. Try it. (without the quotes)

Then type an equal sign, to activate the calculator. Try it.

So what you have typed in is 1/(70 km/s per Mpc)=

You should get 14 billion years. Let me know if it does not work for you and you do not get the answer 14 billion years.

That means that H₀ = 1/(14 billion years)

So then multiply that by 14 billion light years. That will give the speed that a 14 billion lightyear distance is expanding. BUT THAT IS THE SPEED OF LIGHT!

Something that goes one light year in one year is going at speed of light and
1 lightyear/1 year = c.

14 billion lightyears/14 billion years = c.

So 14 billion lightyears is the distance that is expanding at the speed of light.

What is 1/140 of one percent of 14 billion lightyears?

It is a million lightyears. that is therefore the distance that is growing at 1/140 of one percent of the speed of light.

So think about that distance. What percentage of its length does it increase by in a million years?

 

[Jonathan Scott]

EXPANSION AND REDSHIFT

The Gravitational Redshift is a shift in the frequency of a photon to lower energy as it climbs out of a gravitational field. The frequency of light will Blueshift as it approaches the gravity well.

This sort of explanation leads to a lot of confusion, and I find it unhelpful.

Gravitational redshift isn't something that happens to photons. A photon has constant frequency in any observer's static frame of reference. Gravitational redshift is to do with comparing results seen by different observers. An observer at a different potential will see a photon to have a different frequency compared with one generated locally by a similar process (for example a spectral line).

You can see the constant frequency aspect by considering any repetitive signal being sent along a fixed path, regardless of potential. Clearly, the number of iterations of the signal passing any point in a given amount of time must be the same. Photons work in the same way.

 

[Mordred]

Thanks Marcus for your explanation.
Yeah I agree Jonathon that statement is misleading.
I am using my phone this weekend I'll change that line on Monday. I had wanted to expand on gravitational redshift
a bit anyways.
Thanks for your input.
If anyone else can spot incorrect or misleading lines in the article I would definitely appreciate any constructive feedback. Also if anyone would like questions and answers added to the article. That would also be helpful

 

[Mordred]

EXPANSION AND REDSHIFT

1) Why is all the galaxies accelerating from us ?
2) Is Redshift the same as Dopplershift ?
3) What is causing the expansion of the Universe ?
4) Is Expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit ?
5) What is a Cepheid or standard candle ?
6) What do we mean when we say Homogeneous and Isotropic ?
7) How do we measure the distance to Galaxies ?
8) What is outside the Universe?
9) What do we mean when an object leaves our universe ?


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}

Universe: The Universe in cosmology is defined as the Observable Universe The observable universe from Earth is 46 Billion light years, or 4.3×10²⁶meters with an age as of 2013, is 13.772 ± 0.059 billion years. So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded.
One common Question posters often ask is " What is outside our Universe, this question has no meaning as without space or time you have nonexistence. Also their is no clear consensus on if the Universe is Finite or Infinite. " When an object is said to leave our universe" we mean that the object has crossed the observable universe or rather that it is redshifted to the point of non detectable.


The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometres(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 kilometres

Mpc=1 million Parsecs


In order to understand Redshift we must first need to distinquish the between RedShift and Doppler shift. In both cases the light emitted by one body and received by the other will be Red/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red/blue end of the spectrum. As shown by the relation formula below. But there's a subtle difference, between Dobblershift and redshift.

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

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 moved towards the blue end of th 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 medium
v_r is velocity of the reciever to the medium (positive if moving toward the source, negative if moving away)
v_s is the velocity of the source to the medium (positive if moving away from the reciever, negative if other direction)

The above are for velocities where the source is directly away or towards the observer and fo low velocities less than relativistic velocities. A relativistic doppler formula is required when velocity is comparable to the speed of light. Their are different variations of the above formula for Tansverse 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 Red Shifted, as it approaches you the light and sound will be blueshifted.


The Cosmological Redshift is however a redshift caused by the expansion of space. The wavelength of light increases as it traverses the expanding universe between its point of emission and its point of detection by the same amount that space has expanded during the crossing time indeed the amount of redshift is the total amount of expansion. This is a measure of its recessive velocity over DISTANCE. The further away an object is the greater the amount of RedShift. This is given in accordance with Hubbles 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:

Hubbles 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 has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per megaparsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as c=H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR for a couple of reasons.

1) Recessive velocity is distance dependant
2) Recessive velocity is not inertial velocity, the galaxies are not accelerating from us, the SPACE between us and the galaxy is increasing.

This is given by the form.

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 Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion occurs the same throughout the cosmos. However Gravity and the strong Nuclear force in Galaxy clusters are 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 between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic.
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.

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 is the more generic name 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

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 \Lambda. the greek letter Lambda.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing " is really a quantum vacuum with quantum fluctuations described by the Heisenburg uncertainty principle. Virtual particles pop in and out of existence all the time, As expansion occurs those virtual particles Quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models has its roots in this model. However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.

One means of relating to expansion is with the use of the a grid of squares. each horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words te coordinates do not change, the space between coordinates change. I should also note their is no clear consensus on whether the universe is finite or infinite. If its infinite now then it was infinite in the past. Same with Finite. The Big Bang model only describes the Universe from 10^-43 seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of spacetime.

WMAP data confirms that the universe is flat or close to flat.


The Gravitational Redshift Gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that when observed in a region of a weaker gravitational field its frequency is redshifted. When observed in a stronger gravitational field its frequency is blueshifted. The formula below is the gravitational redshift formula or Einstein shift in an unchanged, 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

when the signal is 90 degrees to the observer we need to use the Transverse Redshift formula

<br /> 1+z=\frac{1}{\sqrt{1-v^2/c^2}}<br />


Standard candles

Using standard candles to determine the Hubble constant has a long and honorable history; it's the method used by Hubble himself. The recipe for finnding the Hubble constant is a simple one:

Identify a population of standard candles with luminosity L.
-Measure the redshift z and flux f for each standard candle.
-Compute dL = (L=4¼f)1=2 for each standard candle.
-Plot cz versus dL.
-Measure the slope of the cz versus dL relation when z << 1; this gives
H₀.

The CMB, (Cosmic Microwave Background) also provides a good reference point in regards to Homogeneous and Isotropic confirmation, and of distances. However that is best described in greater detail than this article.

For cosmological purposes, a standard candle should be bright enough to be detected at large redshifts. It should also have a luminosity which is well determined. One time-honored variety of standard candle is the class of Cepheid variable stars. Cepheids, as they are known, are highly luminous supergiant stars, As they pulsate radially, their luminosity varies
in response, partially due to the change in their surface area, and partially due to the changes in the surface temperature as the star pulsates. Type 1A supenova is a type of Cepheid.

Without the use of Cepheids measuring distances would be extremely problematic, especially at extremely large distances, These distances are far too large for the parallex method which is a form of triangulation.

 

[Mordred]

This is probably the extent that I'll add for this article, leaswise I cannot think of what else to add. If anyone spots incorrect or misleading statements or has suggestions I would appreciate it.

Even if the article may or may not be used as a FAQ article I enjoyed writing it so wouldn't mind if its checked for accuracy

 

[PAllen]

I would like to argue, a la Synge 1960 and Bunn and Hogg, that Doppler and redshift, for SR, GR (including dynamic gravity like binary stars, static gravity around a dominant source, and cosmology - expansion) are a single phenomenon. The following single description covers all of these cases (first proven by Synge in 1960, and re-popularized by Bunn and Hogg):

- parallel transport emitter 4-velocity along light path to receiver. Then, in the local frame of receiver, compute Doppler using transported 4-velocity and light propagation vector.

This produces the right answer and explains all cases. Gravitational redshift and cosmpological redshift are simply special cases of Doppler that admit computational shortcuts (due to a family of static observers in the former case, and isotropy and homogeneity in the latter case). Note, in particular, that a parallel transported 4-velocy will never exceed c in any local frame. Recession velocity greater than c is really a generalization of the simple phenomenon in SR that in a given frame, two sources moving away from each other can separate at arbitrarily close to 2c (while have relative velocity - to each other - via parallel transport (trivial in SR) < c). In GR, such s separation speed can greatly exceed 2c, but it is wrong IMO to consider it a relative velocity. In GR relative velocity is non-unique due to path dependence of parallel transport, but no matter what the path, the timelike (<c) character of a vector doesn't change via transport. In the case of Doppler, there is a distinguished path - the light path from emitter to receiver which carries information about the emitter's motion to the receiver.

Also, note, that recession velocity is a coordinate dependent quantity, while the Doppler definition I gave is coordinate independent.

 

[Mordred]

I looked up the paper written by
Bunn and Hogg.

http://arxiv.org/abs/0808.1081

I haven't read this before so I am studying what your stating. Do you recommend a better paper I would like to read it as well.

 

[Chronos]

Bunn and Hogg use incremental doppler shift to justify kinematical redshift. It works naively, but, suffers serious difficulty in nearly all cosmological models. That disqualifies it from an occams razor point of view, IMO.

 

[Mordred]

I looked into that article I posted. Then looked at several counter papers. I agree with Chronos their viewpoint has too many problems. The article above is written with the intent of a FAG reference. In that regard I prefer to stick to the mainstay teachings of the hot Big Bang, rather than the various counter models. Such as models that argue against Dark energy, dark matter and other counter models.

 

[PAllen]

Bunn and Hogg use incremental doppler shift to justify kinematical redshift. It works naively, but, suffers serious difficulty in nearly all cosmological models. That disqualifies it from an occams razor point of view, IMO.

What difficulty? In SR, Doppler results from comparison of 3 vectors: emitter 4-velocity, light propagation vector, and target 4-velocity. In GR, where comparison of vectors is path dependent, specify only that the comparison is done via parallel transport along the light path from emitter to receiver (thus light transporting emitter motion to receiver). Occams razor says, if there is one explanation for all redshift, why invent three? "Incremental Doppler" was an interpretational statement for the above mathematical fact coined by Bunn and Hogg. However, the mathematical fact was proven in all generality by Synge in 1960, in his book "Relativity: the General Theory".

 

[PAllen]

I looked into that article I posted. Then looked at several counter papers. I agree with Chronos their viewpoint has too many problems. The article above is written with the intent of a FAG reference. In that regard I prefer to stick to the mainstay teachings of the hot Big Bang, rather than the various counter models. Such as models that argue against Dark energy, dark matter and other counter models.

These other things are irrelevant. The single definition of Doppler is true as long as you have a pseudo-Riemannian manifold. There is no conflict between Big Bang and single explanation of redshift.

 

[PAllen]

Here is a more accessible reference discussing Synge's approach:

http://www.iucaa.ernet.in:8080/jspui/bitstream/11007/1135/1/211A_1994.pdf

 

[Mordred]

Thanks for that link. Going to take me a bit to go through it.
I do agree with Bunn and Hogg's description of some of the problems with the use of balloon analogy descriptives and the confusions that arise.

 

[PAllen]

As one more part of this discussion, here is Tamara Davis's article in Scientific American, where she backs off the rigid position she Lineweaver took in earlier writings:

http://astronomy.case.edu/heather/151/davis.pdf

 

[Chronos]

20 year + old papers to affirm Bunn and Hogg? Interesting, as it appears safe to assume they were unaware of WMAP results.

 

[PAllen]

20 year + old papers to affirm Bunn and Hogg? Interesting, as it appears safe to assume they were unaware of WMAP results.

There is no conflict between big bang expansion and unified explanation of redshift. Dark matter is does not modify GR, it is just matter in the stress energy tensor. Dark energy is modeled by a cosmological constant in the lambda cdm model. Thus there are no modifications to the equations of GR. Synge's proof trivially applies to these cases.

 

[PAllen]

Let me reiterate important points I think should be made:

- Gravitational redshift and cosmological redshift are convenient ways to think about special cases, but these are not distinct from Doppler in that the only reasonable generalization of Doppler from SR to GR encompasses both with one explanation and one computational procedure for all situations. Factoring out these special cases is not possible at all in general GR solutions, while the GR Doppler approach covers all situations.

- Cosmological recession velocities are not relative velocities. They correspond to separation speed in SR: growth in proper distance between two world lines using a chosen foliation of spacetime. Like an SR separation speed, they can exceed c. (Even in flat spacetime, using nonstandard foliation, you can get separation speeds greatly exceeding c; using Minkowski foliation, you can approach 2c). The most correct statement in GR is that relative velocity of distant objects is undefined; however, this really means it is non-unique due to path dependence of parallel transport. However, no matter what path is used for parallel transport, comparison of two 4-velocities of material bodies is always subluminal.

 

[Jonathan Scott]

EXPANSION AND REDSHIFT

The Gravitational Redshift Gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that when observed in a region of a weaker gravitational field its frequency is redshifted. When observed in a stronger gravitational field its frequency is blueshifted. The formula below is the gravitational redshift formula or Einstein shift in an unchanged, non rotating, spherical mass.

Sorry, but this is now actually wrong. Gravitational redshift and blueshift are not determined by to the gravitational field, but by the gravitational potential. Although the gravitational field is usually stronger in a lower potential, it is not the cause of the shift.

Also, I assume there's a typo "unchanged" for "uncharged" in the last sentence.

 

[Mordred]

Sorry, but this is now actually wrong. Gravitational redshift and blueshift are not determined by to the gravitational field, but by the gravitational potential. Although the gravitational field is usually stronger in a lower potential, it is not the cause of the shift.


Also, I assume there's a typo "unchanged" for "uncharged" in the last sentence.

Using the terms graviational potential would be more accurate. I thank you for pointing that out and yes that should have been uncharged. Good catch on both. I will correct both

 

[PAllen]

- Gravitational redshift and cosmological redshift are convenient ways to think about special cases, but these are not distinct from Doppler in that the only reasonable generalization of Doppler from SR to GR encompasses both with one explanation and one computational procedure for all situations. Factoring out these special cases is not possible at all in general GR solutions, while the GR Doppler approach covers all situations.

To say a little more on this:

Given any solution in GR, there is one universal way to compute and understand redhsift - Doppler appropriately defined for GR. Solutions with special symmetries allow picking out a special family of observers (if a timelike killing vector exists, static observers; for sufficiently symmetric non-static solutions, comoving observers). Given such a special class of observers, it is convenient (that is all) to factor Doppler between arbitrary world lines into a component characterized by the special world lines through two events, and relative velocity of emitter and or receiver to the special observer. 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.

I also want to clarify that while agreeing with Synge, Narlikar, Bunn and Hogg, that there is one universal Doppler in GR, I disagree with the interpretation that that means it is purely kinematic in origin. IMO, curvature affects light path and the behavior of parallel transport. Thus a passing gravitational wave can effect Doppler. For me, one universal phenomenon generalized from SR does not imply viewing it as purely kinematic is correct. I think this point of view distinguishes e.g. post 2009 Tamara Davis.

 

[Mordred]

EXPANSION AND REDSHIFT

1) Why is all the galaxies accelerating from us ?
2) Is Redshift the same as Dopplershift ?
3) What is causing the expansion of the Universe ?
4) Is Expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit ?
5) What is a Cepheid or standard candle ?
6) What do we mean when we say Homogeneous and Isotropic ?
7) How do we measure the distance to Galaxies ?
8) What is outside the Universe?
9) What do we mean when an object leaves our universe ?


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}

Universe: The Universe in cosmology is defined as the Observable Universe The observable universe from Earth is 46 Billion light years, or 4.3×10²⁶meters with an age as of 2013, is 13.772 ± 0.059 billion years. So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded.
One common Question posters often ask is " What is outside our Universe, this question has no meaning as without space or time you have nonexistence. Also their is no clear consensus on if the Universe is Finite or Infinite. " When an object is said to leave our universe" we mean that the object has crossed the observable universe or rather that it is redshifted to the point of non detectable.


The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometres(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 kilometres

Mpc=1 million Parsecs


In order to understand Redshift we must first need to distinquish the between RedShift and Doppler shift. In both cases the light emitted by one body and received by the other will be Red/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red/blue end of the spectrum. As shown by the relation formula below. But there's a subtle difference, between Dobblershift and redshift.

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

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 moved towards the blue end of th 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 medium
v_r is velocity of the reciever to the medium (positive if moving toward the source, negative if moving away)
v_s is the velocity of the source to the medium (positive if moving away from the reciever, negative if other direction)

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. Their are different variations of the above formula for Tansverse 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 Red Shifted, as it approaches you the light and sound will be blueshifted.


The Cosmological Redshift is however a redshift caused by the expansion of space. The wavelength of light increases as it traverses the expanding universe between its point of emission and its point of detection by the same amount that space has expanded during the crossing time indeed the amount of redshift is the total amount of expansion. This is a measure of its recessive velocity over DISTANCE. The further away an object is the greater the amount of RedShift. This is given in accordance with Hubbles 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:

Hubbles 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 has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per megaparsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as c=H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR for a couple of reasons.

1) Recessive velocity is distance dependant
2) Recessive velocity is not inertial velocity, the galaxies are not accelerating from us, the SPACE between us and the galaxy is increasing.

This is given by the form.

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 Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion occurs the same throughout the cosmos. However Gravity and the strong Nuclear force in Galaxy clusters are 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 between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic.
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.

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 is the more generic name 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

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 \Lambda. the greek letter Lambda.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing " is really a quantum vacuum with quantum fluctuations described by the Heisenburg uncertainty principle. Virtual particles pop in and out of existence all the time, As expansion occurs those virtual particles Quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models has its roots in this model. However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.

One means of relating to expansion is with the use of the a grid of squares. each horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words te coordinates do not change, the space between coordinates change. I should also note their is no clear consensus on whether the universe is finite or infinite. If its infinite now then it was infinite in the past. Same with Finite. The Big Bang model only describes the Universe from 10^-43 seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of spacetime.

WMAP data confirms that the universe is flat or close to flat.


The Gravitational Redshift Gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that when observed in a lower gravitational potential from a higher gravitational potential relative to the observer its frequency is redshifted. When observed in a higher gravitational potential from a lower gravitational potential relative to the observer, its frequency is blueshifted. 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

when the signal is 90 degrees to the observer we need to use the Transverse Redshift formula

<br /> 1+z=\frac{1}{\sqrt{1-v^2/c^2}}<br />


Standard candles

Using standard candles to determine the Hubble constant has a long and honorable history; it's the method used by Hubble himself. The recipe for finnding the Hubble constant is a simple one:

Identify a population of standard candles with luminosity L.
-Measure the redshift z and flux f for each standard candle.
-Compute dL = (L=4¼f)1=2 for each standard candle.
-Plot cz versus dL.
-Measure the slope of the cz versus dL relation when z << 1; this gives
H₀.

The CMB, (Cosmic Microwave Background) also provides a good reference point in regards to Homogeneous and Isotropic confirmation, and of distances. However that is best described in greater detail than this article.

For cosmological purposes, a standard candle should be bright enough to be detected at large redshifts. It should also have a luminosity which is well determined. One time-honored variety of standard candle is the class of Cepheid variable stars. Cepheids, as they are known, are highly luminous supergiant stars, As they pulsate radially, their luminosity varies
in response, partially due to the change in their surface area, and partially due to the changes in the surface temperature as the star pulsates. Type 1A supenova is a type of Cepheid.

Without the use of Cepheids measuring distances would be extremely problematic, especially at extremely large distances, These distances are far too large for the parallex method which is a form of triangulation.

 

[Mordred]

I applied the corrections Jonathon mentioned.

 

[Mordred]

To say a little more on this:

Given any solution in GR, there is one universal way to compute and understand redhsift - Doppler appropriately defined for GR. Solutions with special symmetries allow picking out a special family of observers (if a timelike killing vector exists, static observers; for sufficiently symmetric non-static solutions, comoving observers). Given such a special class of observers, it is convenient (that is all) to factor Doppler between arbitrary world lines into a component characterized by the special world lines through two events, and relative velocity of emitter and or receiver to the special observer. 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.

I also want to clarify that while agreeing with Synge, Narlikar, Bunn and Hogg, that there is one universal Doppler in GR, I disagree with the interpretation that that means it is purely kinematic in origin. IMO, curvature affects light path and the behavior of parallel transport. Thus a passing gravitational wave can effect Doppler. For me, one universal phenomenon generalized from SR does not imply viewing it as purely kinematic is correct. I think this point of view distinguishes e.g. post 2009 Tamara Davis.

I have to agree with the above on its validity, I'm thinking the statement you made here may be suitable as part of the closing statement on the article, I've seen numerous papers that use the different observers as you described. I could probably use your help in adding this to the article, without causing confusion. If you can see an easy straightforward means of adding this to the article without causing confusion I could use some help on that.

 

[PAllen]

I have to agree with the above on its validity, I'm thinking the statement you made here may be suitable as part of the closing statement on the article, I've seen numerous papers that use the different observers as you described. I could probably use your help in adding this to the article, without causing confusion. If you can see an easy straightforward means of adding this to the article without causing confusion I could use some help on that.

Sure, I can help with that. I may not get to it till tonite or tomorrow. If anyone else has ideas in the mean time, don't necessarily wait for me.

 

[Jonathan Scott]

EXPANSION AND REDSHIFT

The Gravitational Redshift Gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that when observed in a region of a weaker gravitational potential its frequency is redshifted. When observed in a stronger gravitational potential its frequency is blueshifted.

This isn't going very well.

Gravitational potential isn't weaker or stronger (and I wouldn't know which you would assume to mean which without additional information). You can say it's higher or lower, as those terms fit very naturally both with Newtonian gravity and with the everyday sense of objects being higher or lower.

Also, saying "observed in a region..." is misleading. It's the observer's relative gravitational potential (or equivalently the relative time rate at the observer location) which determines the result, even if the observer is observing something happening elsewhere.

I don't have time to rewrite this right now, but I think you need to take more care to find a way of expressing it which is both helpful and technically accurate.

 

[Mordred]

This isn't going very well.

Gravitational potential isn't weaker or stronger (and I wouldn't know which you would assume to mean which without additional information). You can say it's higher or lower, as those terms fit very naturally both with Newtonian gravity and with the everyday sense of objects being higher or lower.

Also, saying "observed in a region..." is misleading. It's the observer's relative gravitational potential (or equivalently the relative time rate at the observer location) which determines the result, even if the observer is observing something happening elsewhere.

I don't have time to rewrite this right now, but I think you need to take more care to find a way of expressing it which is both helpful and technically accurate.

Fair enough, you would probably find it surprising how many references for he definition of gravitational redshift use terms such as "observed in a region" or weaker and stronger.
However I can relate to a more detailed and accurate definition than many of the online definitions one comes across. I removed the "observed in a region" and added the expression from a higher to lower gravitational potential and vice versa.

 

[PAllen]

I'm not sure you're going to like all of this, but here is my take, trying to change as little as possible:

EXPANSION AND REDSHIFT

1) Why is all the galaxies accelerating from us ?

is -> are

2) Is Redshift the same as Dopplershift ?
3) What is causing the expansion of the Universe ?
4) Is Expansion, faster than light in parts of the Universe, and How does this not violate the faster than light speed limit ?
5) What is a Cepheid or standard candle ?
6) What do we mean when we say Homogeneous and Isotropic ?
7) How do we measure the distance to Galaxies ?
8) What is outside the Universe?
9) What do we mean when an object leaves our universe ?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}

Universe: The Universe in cosmology is defined as the Observable Universe The observable universe from Earth is 46 Billion light years, or 4.3×10²⁶meters with an age as of 2013, is 13.772 ± 0.059 billion years. So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded.
One common Question posters often ask is " What is outside our Universe, this question has no meaning as without space or time you have nonexistence. Also their is no clear consensus on if the Universe is Finite or Infinite. " When an object is said to leave our universe" we mean that the object has crossed the observable universe or rather that it is redshifted to the point of non detectable.The parsec (symbol: pc) is a unit of length used in astronomy, equal to about 30.9 trillion kilometres(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 kilometres

Mpc=1 million Parsecs


In order to understand Redshift we must first need to distinquish the between RedShift and Doppler shift. In both cases the light emitted by one body and received by the other will be Red/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red/blue end of the spectrum. As shown by the relation formula below. But there's a subtle difference, between Dobblershift and redshift.

Replace the above paragraph with:

Doppler shift and redshift are the same phenomenon in general relativity. Often, however, you will 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/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red/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 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 moved towards the blue end of th 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 medium
v_r is velocity of the reciever to the medium (positive if moving toward the source, negative if moving away)
v_s is the velocity of the source to the medium (positive if moving away from the reciever, negative if other direction)

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. Their are different variations of the above formula for Tansverse 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 Red Shifted, as it approaches you the light and sound will be blueshifted.

Add here:

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 redhsift 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.

The Cosmological Redshift is however a redshift caused by the expansion of space. The wavelength of light increases as it traverses the expanding universe between its point of emission and its point of detection by the same amount that space has expanded during the crossing time indeed the amount of redshift is the total amount of expansion. This is a measure of its recessive velocity over DISTANCE. The further away an object is the greater the amount of RedShift. This is given in accordance with Hubbles 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:

Replace above paragraph with:

The Cosmological Redshift is a redhsift attributed to the expansion of space. The expansion causes a recession velocity for galaxies (on average) that is proportional to DISTANCE. 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 Hubbles 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:

Hubbles 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 has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per megaparsec, or Mpc. The latter being a unit of distance in intergalactic space described above.
Any measurement of redshift above the Hubble distance defined as c=H₀ = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR for a couple of reasons.

1) Recessive velocity is distance dependant
2) Recessive velocity is not inertial velocity, the galaxies are not accelerating from us, the SPACE between us and the galaxy is increasing.

Delete the two bullets above and replace the last sentence of the prior paragraph with:

This does not violate GR because a recession velocity is not a relative 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.

This is given by the form.

formula

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 Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion occurs the same throughout the cosmos. However Gravity and the strong Nuclear force in Galaxy clusters are 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 between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic.
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.

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 is the more generic name 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

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 \Lambda. the greek letter Lambda.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing " is really a quantum vacuum with quantum fluctuations described by the Heisenburg uncertainty principle. Virtual particles pop in and out of existence all the time, As expansion occurs those virtual particles Quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models has its roots in this model.

have their roots

However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.

One means of relating to expansion is with the use of the a grid of squares. each

capitalize: Each

horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words te

.
te -> the

coordinates do not change, the space between coordinates change. I should also note their is no clear consensus on whether the universe is finite or infinite. If its infinite now then it was infinite in the past. Same with Finite. The Big Bang model only describes the Universe from 10^-43 seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of spacetime.

WMAP data confirms that the universe is flat or close to flat. The Gravitational Redshift Gravitational redshift or Einstein shift is the process by which electromagnetic radiation originating from a source that when observed in a lower gravitational potential from a higher gravitational potential relative to the observer its frequency is redshifted. When observed in a higher gravitational potential from a lower gravitational potential relative to the observer, its frequency is blueshifted. The formula below is the gravitational redshift formula or Einstein shift in an uncharged, non rotating, spherical mass.

Replace above paragraph with:
The Gravitational 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 red shift as a function of potential difference. When the potential increases from emitter to receiver, you have red shift; 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

when the signal is 90 degrees to the observer we need to use the Transverse Redshift formula

<br /> 1+z=\frac{1}{\sqrt{1-v^2/c^2}}<br />

What does this have to do with gravitational redshift? It seems to belong under the introductory Doppler section.

Standard candles

Using standard candles to determine the Hubble constant has a long and honorable history; it's the method used by Hubble himself. The recipe for finnding the Hubble constant is a simple one:

finnding -> finding

Identify a population of standard candles with luminosity L.
-Measure the redshift z and flux f for each standard candle.
-Compute dL = (L=4¼f)1=2 for each standard candle.
-Plot cz versus dL.
-Measure the slope of the cz versus dL relation when z << 1; this gives
H₀.

The CMB, (Cosmic Microwave Background) also provides a good reference point in regards to Homogeneous and Isotropic confirmation, and of distances. However that is best described in greater detail than this article.

For cosmological purposes, a standard candle should be bright enough to be detected at large redshifts. It should also have a luminosity which is well determined. One time-honored variety of standard candle is the class of Cepheid variable stars. Cepheids, as they are known, are highly luminous supergiant stars, As they pulsate radially, their luminosity varies
in response, partially due to the change in their surface area, and partially due to the changes in the surface temperature as the star pulsates. Type 1A supenova is a type of Cepheid.

Without the use of Cepheids measuring distances would be extremely problematic, especially at extremely large distances, These distances are far too large for the parallex method which is a form of triangulation.

 

[Mordred]

I looked over your proposed changes. currently on my phone atm, however I didn't see anything I would object to. In many sections it will give the article a better descriptive. I'll rewrite the article hopefully tomorrow.

 

[Naty1]

A few comments:

However Gravity and the strong Nuclear force in Galaxy clusters are strong enough to prevent expansion.

Strong force is irrelevant...drop that...

but the real point is that the assumptions in GR that lead to an expanding distance [not expanding 'space'] of homogeneity and isotropism do not apply at galactic scales because
of lumps of mass [planets,stars, black holes,etc]


Here are my favorite descriptions on Redshift and Doppler shift collected from various discussions in these forums. If a particular description phrasing catches your fancy and clarifies something, use it; if not, that's ok too. [I may have slightly edited some comments attributed to particular people.]

https://www.physicsforums.com/showthread.php?p=3910924#post3910924
Are Photons Redshifted

Lineweaver and Davis: the universe cools as it expands, much as compressed air in a scuba tank cools when it is released and allowed to expand. The microwave background radiation currently has a temperature of about 2.73 Kelvin, whereas the process that released the radiation occurred at a temperature of about 3,000 Kelvin. Expansion z over the 13.7 Billion years has been about z = 1090: [3,000/1090 = 2.73] appx energy conservation does not hold in expanding geometry


CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. They have lost more than 999/1000 of their original energy.

These are two different ways of looking at the same phenomena:

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

[In the great 2007 thread Wallace, Chronos and Oldman take a different view than expressed here [and there] by Marcus...you can read the posts from the 40’s thru 50’s and see the pros and cons. ]

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.

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.

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...

These ‘conflicting’ viewpoints stem 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.”


# Doppler shift is based on [relative velocity] frame based differences, not expansion, Hence photon frequency and wavelength can be viewed as fixed just like in a static Spacetime.. Doppler shift is a particular explanation of redshift, with a particular formula.

You takes your pick

Marcus: A photon emitted from a star at a moderate distance from center of a galaxy will suffer a grav. redshift from the galaxy gravity which is roughly the same size as from the star itself. And that effect (of the star’s gravity) is so tiny that it took sophisticated technique to measure. In the CMB, the grav redshift (so called Sachs-Wolfe effect) is about 10-5 or one thousandth of one percent. It is interesting, but it doesn’t compete in size with the cosmological redshift which for a typical galaxy is several hundred percent. In other words, recession effect overwhelms gravity effect.

Redshift Definition
Doppler Shift
The Doppler effect (or Doppler shift)….is the change in frequency of a wave for an observer moving relative to the source of the wave. .. The frequency of the sounds that the source emits does not actually change….but the received frequency does change… ….. The use of the Doppler effect for light in astronomy depends on ……absorption lines …..where the Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines of an approaching astronomical light source exhibit a blue shift and those of a receding astronomical light source exhibit a redshift…..
Mentz: If A and B use Doppler shift to measure each others clocks then when separating they each see the other’s clock run slowly ( red spectral shift);if they are approaching they each see the other clock running faster ( blue spectral shift)
Jonathan Scott: “In a static situation, gravitational red shift or blue shift is not something that “happens to” photons. It is purely due to relative differences in observer potential, which affects the time rate of the observer’s clocks.
The photon itself has constant frequency relative to a static coordinate system, but an observer at a higher or lower potential will see it to have a different frequency compared with a photon created locally by means of a similar process, for example a particular transition between energy levels.”
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.
PAllen: but gravity or no, at any point along the light path, there are observers who will measure every possible frequency (different states of relative motion between observers). So trying to factor out change due to gravity versus relative motion means identifying which of these frames at different places and times are ‘statically related’, thus differences in frequency are then considered due to gravity.
However, in general, there is no unique or preferred way to make such a global assignment; thus no unambiguous way to separate out gravity from relative motion. In effect, such an assignment amounts to a choice of coordinates. For any such choice, you can say “yes, there is mass/energy producing curvature”, but different choices lead to different divisions of gravitational versus Doppler shift.
Doppler Effect: Frame invariant
PALLEN: The Doppler effect is completely determined by the relative velocity of source and target. Both of these velocities are frame dependent, but the relative velocity between emitter at event of emission and receiver at event of detection is frame invariant. Thus all observers agree on the Doppler measured by a given detector from a given source.

Mathematically, relative speed is defined by parallel transport of 4-velocity from one event to another (Only in SR is this path independent, thus unique), then dot product of transported source 4-velocity with unit 4-vector 4-orthogonal to target 4-velocity. Dot products are invariant - period. (In a standard inertial frame in SR, parallel transport leaves a vector unchanged).
DrGreg:
To show that the Doppler effect is frame invariant you don’t have to do any math at all—just look at the definition ν r /ν s .

ν s is measured by the source using the source’s own proper-time clock.

ν r is measured by the receiver using the receiver’s own proper-time clock.

All observers, whatever coordinates they are using, agree on what the source and receiver’s proper times are (associated with a 2π phase change), therefore agree on the two frequencies, therefore agree on the Doppler factor.
The Doppler effect is mutual between two inertial world lines (each acting as source and target relative to the other). Between an inertial world line and a non-inertial world line it is not mutual….. A light source in forced circular motion around an inertial target is always red shifted. A target in forced circular motion about an inertial light source will see its light always blue shifted.


Cosmological redshift is typically considered distinct from Doppler redshift because it is a relation between distance and redshift rather than speed and redshift, under the assumption that both source and target are motionless relative to center of mass of the local matter (here, local is quite large - galaxy or galaxy cluster).
Marcus:
Don’t think of the redshift as a Doppler [relative velocity] effect. It is not the result of some particular speed. The formula involves the entire [varying] factor by which distances have been expanded during the whole time the light has been traveling.
PeterDonis: The law governing the relationship of emitted to observed photon energies (or frequencies) is general and applies in any spacetime. The 4-momentum of the photon gets determined at the emitter; then it gets parallel transported along the photon’s worldline from emitter to observer; then you contract that 4-momentum with the observer’s 4-velocity to get the observed energy (or frequency if you throw in a factor of Planck’s constant). That “parallel transport” process is actually where the “redshift” occurs in an expanding universe; the expansion alters the 4-momentum of the photon as it travels (or at least that’s one way of looking at it), whereas in a static universe the photon’s 4-momentum would “stay the same” as it traveled.

 

[Mordred]

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

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 kilometres(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 kilometres
Mpc=1 million Parsecs

Universe: The Universe in cosmology is defined as the Observable Universe The Observable universe from Earth is 46 Billion light years, or 4.3×10²⁶ meters with an age as of 2013, is 13.772 ± 0.059 billion years. So how do we see farther than 13.772 billion years, the answer lies in expansion. As light is traveling towards us, spacetime has expanded.
One common Question posters often ask is " What is outside our Universe, this question has no meaning as without space or time you have nonexistence. Also their is no clear consensus on, if the Universe is Finite or Infinite. " When an object is said to leave our universe" we mean that the object has crossed the observable universe or rather that it is redshifted to the point of non detectable.


The CMB, (Cosmic Microwave Background) The CMB is thermal radiation filling the Observable universe almost uniformaly, This provides strong evidence of the Homogeneous and Isotropic measurements and of 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. The CMBR has a thermal black body spectrum at a temperature of 2.72548±0.00057 Kelvin. CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. They have lost more than 999/1000 of their original energy

Doppler shift and redshift are the same phenomenon in general relativity. Often, however, you will 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/Blue shifted ie its wavelength will be stretched. So the color of the light is more towards the red/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 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 moved 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 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 reciever using the source’s own proper-time clock(positive if moving away from the reciever)

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 Tansverse 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 Red Shifted, 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.


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. 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 Hubbles 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:

Hubbles 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 has been calculated at different values over time, this is essential as the rate of expansion varies over time but the current accepted value is 70 kilometers/second per megaparsec, 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 Redshift is distance dependant as mentioned above, if you were to teleport to the other side of the galaxy where you measured that greater than light recessive velocity, you would find the same expansion rate as your original location relative to an equal distance. Indeed expansion occurs the same throughout the cosmos. However Gravity in Galaxy clusters are 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 between two coordinates are expanding. This is important in that no FORCE is acting upon the galaxies to cause expansion. That expansion is homogeneous and isotropic. In other words, there is no preferred location (Homogeneous) and no preferred direction (Isotropic). Keep in mind these terms describe the universe on large scales. Indeed below 100 Mpc we know that galaxy clusters, large scale clusters are not homogeneous or isotropic.
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.

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 is the more generic name 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

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.
This False vacuum inflationary model is one that describes a total energy balance of zero, where gravity is the negative energy. In this model what we term as "Nothing " is really a quantum vacuum with quantum fluctuations described by the Heisenburg uncertainty principle. Virtual particles pop in and out of existence all the time, As expansion occurs those virtual particles Quantum tunnel between the false vacuum and the true vacuum, becoming real particles. The full explanation is a little more involved than this quick explanation however this model is often referred to as a "Universe from Nothing" or the "Ultimate free lunch" . Many of our current inflationary models has their roots in this model. However one fundamental problem with all inflationary models is "Runaway expansion" Once the process starts no one has found a mechanism to stop expansion.
One means of relating to expansion is with the use of the a grid of squares. Each horizontal and vertical crossing on that grid is a coordinate. In expansion the space between all coordinates not gravitationally bound expand equally. In other words the coordinates do not change, the space between coordinates change. I should also note their is no clear consensus on whether the universe is finite or infinite. If its infinite now then it was infinite in the past. Same with Finite. The Big Bang model only describes the Universe from 10-⁴³ seconds and is not considered as starting from a black hole singularity, rather its properly described as a rapid expansion of spacetime.

WMAP data confirms that the universe is flat or close to flat.


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 red shift as a function of potential difference. When the potential increases from emitter to receiver, you have red shift; 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 /> 1+z=\frac{1}{\sqrt{1-v^2/c^2}}<br />


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

Standard candles
Using standard candles to determine the Hubble constant has a long and honorable history; it's the method used by Hubble himself. The recipe for finding the Hubble constant is a simple one:

Identify a population of standard candles with luminosity L.
-Measure the redshift z and flux f for each standard candle.
-Compute dL = (L=4¼f)1=2 for each standard candle.
-Plot cz versus dL.
-Measure the slope of the cz versus dL relation when z << 1; this gives
H₀.

For cosmological purposes, a standard candle should be bright enough to be detected at large redshifts. It should also have a luminosity which is well determined. One time-honored variety of standard candle is the class of Cepheid variable stars. Cepheids, as they are known, are highly luminous supergiant stars, As they pulsate radially, their luminosity varies
in response, partially due to the change in their surface area, and partially due to the changes in the surface temperature as the star pulsates. Type 1A supenova is a type of Cepheid.

Without the use of Cepheids measuring distances would be extremely problematic, especially at extremely large distances, These distances are far too large for the parallex method which is a form of triangulation.

 

[Mordred]

I've applied the changes that PAllen supplied, I've also removed the strong Nuclear force statement. Also i used your definition of Vs and Vr. Looking at some of the other statements you supplied Naty1. I wanted to apply one set of changes first then look at modifying to some of the ideas you presented. Also as this is now a cooperative effort, I'd like to hear PAllen's input on some of your ideas.

The improvements are coming along nicely in my humble opinion, with the feedback were now getting this should develop nicely Thanks everyone

 

[PAllen]

I've applied the changes that PAllen supplied, I've also removed the strong Nuclear force statement. Also i used your definition of Vs and Vr. Looking at some of the other statements you supplied Naty1. I wanted to apply one set of changes first then look at modifying to some of the ideas you presented. Also as this is now a cooperative effort, I'd like to hear PAllen's input on some of your ideas.

The improvements are coming along nicely in my humble opinion, with the feedback were now getting this should develop nicely Thanks everyone

I can review this tonite, and also think about the information Naty1 collected. Probably won't be till late EST.

 

[Mordred]

Lineweaver and Davis: the universe cools as it expands, much as compressed air in a scuba tank cools when it is released and allowed to expand. The microwave background radiation currently has a temperature of about 2.73 Kelvin, whereas the process that released the radiation occurred at a temperature of about 3,000 Kelvin. Expansion z over the 13.7 Billion years has been about z = 1090: [3,000/1090 = 2.73] appx energy conservation does not hold in expanding geometry


CMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. They have lost more than 999/1000 of their original energy.

I like this statement, would be good under the CMB section.

 

[Mordred]

One other thing I can see needing improvement is answering question 7. The Standard candle section is inadequate. I could use some suggestions on that section. For full revamp on that portion.

 

[PAllen]

One other thing I can see needing improvement is answering question 7. The Standard candle section is inadequate. I could use some suggestions on that section. For full revamp on that portion.

This is outside my knowledge base. Hopefully someone else can provide more information.

 

[Mordred]

Here is the format I am thinking of replacing the standard candle section.

Cosmic Distance Ladder starting with fundamental distances, then Parallax and some of different types of parallax, including moving cluster parallax stellar parallax.
follow up with standard candles. Then cephieds.
I am currently jotting down ideas for the above items to cover.

Cosmic Distance ladder, also known as extragalactic distance scale. Is easily thought of as a series of different
measurement method's at different distance scales.
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 ditance scales. The fust 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 astronaumical 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.

Parralax. Parralax 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. The Sun at right angle
to us the distance to the object to be measured.

Still working on this jotting down ideas

 

[PAllen]

Lineweaver and Davis: the universe cools as it expands, much as compressed air in a scuba tank cools when it is released and allowed to expand. The microwave background radiation currently has a temperature of about 2.73 Kelvin, whereas the process that released the radiation occurred at a temperature of about 3,000 Kelvin. Expansion z over the 13.7 Billion years has been about z = 1090: [3,000/1090 = 2.73] appx energy conservation does not hold in expanding geometryCMB photons were emitted at about 3000 Kelvin and are now 2.73 Kelvin blackbody radiation. They have lost more than 999/1000 of their original energy.

I like this statement, would be good under the CMB section.

In terms of wording this, I would avoid describing photons as losing energy. Just as with light emitted from a neutron star, many (most?) relativists do not consider that photons lost energy escaping; instead they always had less energy from the point of view of distant observers (while having expected energy locally to the emission). It is equally possible to view CMB photons this way, only you say they have less energy as observed 'now' than as observed 'back then' - a difference in spacetime frame not a loss of energy along the way. Just as with gravitational redshift, there are strong proponents on both sides of this. We can sidestep such controversy with wording like:

"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."

As to the Lineweaver I would strengthen "approximate energy conservation does not hold in expanding geometry" to "total energy of the universe cannot be defined for an expanding geometry, so the question of conservation cannot even be posed on the scale of the universe". For the purposes of this FAQ I don't think we need to get into the technicalities that ADM energy is the only reasonable candidate for total energy in GR, and it is undefinable for an RW cosmology. Another argument is that Noether's theorem would not be expected to apply to an expanding geometry, so there is no basis to expect energy conservation.

Otherwise, this is great information to add.

 

[PAllen]

Here is the format I am thinking of replacing the standard candle section.

Cosmic Distance Ladder starting with fundamental distances, then Parallax and some of different types of parallax, including moving cluster parallax stellar parallax.
follow up with standard candles. Then cephieds.
I am currently jotting down ideas for the above items to cover.

That sounds great.

 

[Mordred]

Already modified the CMB section in the article. Also moved it up in the article. Location is better suited there.

 

[PAllen]

The article is looking really good now. I have only a few comments at this point:

1) You have the phrase: " Many of our current inflationary models has their roots in this model." Change "has" to "have".

2) The formula you give for gravitational redshift is is instead the formula for transverse doppler, which seems out of place here (probably out of place in the whole article). You need to restore the correct formula from earlier versions of this article.

3) As suggested in a post above, change the wording about CMB energy to:

""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."

 

[PAllen]

On Naty1's collection of observations, I think the key points of view mentioned are reasonably addressed in the current article. You (Mordred) have already incorporated the temperature decline.