1. Mar 13, 2013

### marcus

I got a PM with the sort of reasonable question about REDSHIFT that naturally occurs to people, and variants of which come up regularly.

So rather than answer by PM, I take the liberty of replying in open forum. Other people may want to contribute, or may be interested in the different answers, so it is really something to share rather than deal with privately.

It's quite a good question actually. The poster says "stickies" when he means, I think, to include the FAQ. I think the user looked through the FAQ, and did not find an answer. This may suggest a need to reorganize slightly so that FAQ is easier for non-scientists to use. Maybe the answer was really there, but he could not find it. It's often hard to tell why systems don't work, on the rare occasions when they don't.

Here's the question:
...I want to apologize in advance for my ignorance. I have no formal physics training...

Is it possible for the expanding universe to cause a portion of the redshift seen in distant supernova. For instance if a supernova is a certain distance away when the light starts towards us, and the space it travels across to get here is expanding, would that cause a redshift on its own? I understand there would be initial redshift because of expansion at the time the light left the supernova, but would that redshift be increased as the space the light travels across expands. Expanding the space between the troughs of the light wave itself?

My second question is, what is the theory to explain why expansion does not effect galaxies and solar systems? I keep seeing that idea mentioned in my search.

I remember reading that the Voyager probe was able to measure the Hubble constant because of the change in the actual and expected time it took the signals to reach earth from the probe and the time it took the signal to reach the probe from earth. This seems like it would be a contradiction to me.

I have looked at the stickies, including the balloon sticky, on the forum and searched for the information but I cannot seem to find the answer...

The BLUE point is good! the redshift is definitely due to the cumulative effect of what expansion has occurred all throughout the journey.

People differ as to the mental images they use to understand this cumulative effect. Some people, as you do, imagine the troughs, or the effect of expansion on the Maxwell equation of how wave propagation works. Other people imagine a chain of observers all stationary with respect to the background of ancient light, stretching along the path of the light. And since they are stationary they are all receding from each other. The gaps between them are all increasing. So they see a succession of small DOPPLER shifts as the light gets relayed down the line. And all these tiny Doppler shifts, from one observer to the next, add up.

I would not advise worrying about what the right way to imagine it is, as long as you got the basic idea. In effect, the wave is elongated by the expansion of distances and it is a cumulative process. (It does not just depend on one particular recession speed at some one particular moment.)

2. Mar 13, 2013

### marcus

Interestingly, after I wrote the above I learned by PM that the new member found the answer ON HIS OWN by looking in the LineweaverDavis SciAm article. So that's good. Finding out for yourself is always better. My first post is not needed but I will leave it because somebody else might find it useful.

Now I should try to respond to the two remaining questions (red and magenta).

Since this is a sample case of generic newcomer questions, I hope we can maintain anonymity. Not because the questions aren't good. They're good. Just as a matter of etiquette or simple courtesy.

The answer to the RED question is that galaxies (and typically also groups of galaxies) are gravitationally bound. They have enough mass to hold themselves together. Their parts are not moving with enough velocity relative to the center of mass to be able to escape (local individual speeds are less than escape velocity.)

Formally, the Hubble Law PATTERN OF EXPANSION governs distances between observers who are stationary relative to Background.
The soup of ancient light (CMB) left over from when matter was approximately evenly distributed hot gas throughout space serves as a kind of reference and gives us a CRITERION OF REST.
If you move relative to the soup, it will look slightly "bluer" or "hotter" in the direction you are going---shorter wavelengths in that part of the sky and longer "cooler" wavelengths behind you.
So we have a criterion of rest and we can imagine observers all over the universe who are at rest. They define distances between them and these expand according to Hubble Law.
Currently 1/140% increase per million years.

Two observers hovering at opposite sides of a galaxy, right at the edge, would not both be at rest. So the distance between them would not be increasing 1/140% per million years. They wouldn't be subject to Hubble Law expansion.
To see the pattern you have to be looking at much larger distances. Between widely separated clusters of galaxies.

(Distances between galaxies in our Local Group---Milky, Andromeda, Magellanic Clouds...etc---which are basically orbiting each other or colliding or whatever are not subject to expansion. the Local Group is a bound system.)

You could say that it is the soup of ancient light that is expanding and it is simply an empirical fact that galaxies are APPROXIMATELY at rest in the soup---they tend to have only minor individual random motions of a few 100 km/s. Compared with expansion rates of large distances, these individual random motions are negligible. So distances between galaxies expand approximately the way the overall large-scale geometry of the universe does.

But maybe it is better to say "the large-scale geometry" is expanding, and since light is governed by geometry the soup of ancient photons must expand along with it. And why shouldn't geometry expand? We have no right to expect it not to. It does all sorts of things like the angles of a triangle not adding up to 180 and the sum being influenced by matter. But small scale forces (like the crystalline bonds in a piece of rock) overwhelmingly win out over large-scale geometry. So we can neglect what geometry is doing except on very large scale where everything else is negligible and you don't see bound systems of stuff.

Maybe someone else can say this more clearly.

Last edited: Mar 13, 2013
3. Mar 13, 2013

### Mordred

You mentioned the FAQ section and I wholeheartedly agree that some of the threads in the FAQ need revamping. Granted their is tons of information contained in some of them however to search for that information can take an excrutiating long time.

I would also recommend that we have a sticky thread expalining dark energy, dark matter, expansion (including what recession velocity really means), A detailed balloon analogy as part of expansion.
Also an article on Lambda CDM and hot big bang would be good as well.
Once the articles are written and confirmed on accuracy with Forum input then lock the thread to prevent overgrowth.

Also how gravity works with blackholes and how blackholes grow when they merge in relation to GR effects would also be handy

4. Mar 13, 2013

### marcus

Hi Mordy!

I appreciate your comment. the FAQ is very helpful but I suppose there is always room for improvement. The most important thing in writing an FAQ is listing the QUESTIONS, I think.
You need a list of very simple questions that really reflect what is puzzling people.
A user has to be able to look down the list and RECOGNIZE one of the questions on the list as the question that he has been wondering about. The exact forms of the answers are less critical, I think.
What we are talking about is a "self-diagnosis" process where the user has to be able to look down the list of symptoms and spot what it is that is confusing him.

I suppose ideally it would be newcomers to Forum who would contribute questions to FAQ, like what this anonymous guy is doing. The newcomers are the ones who know what the puzzling questions are. Like this guy says
A. what causes wavelengths to be stretched (i.e. redshift)?
B. why doesn't the same thing stretch rocks out, or solar systems, or galaxies?
C. what did the Voyager probe find out? Was it actually about Hubble Law expansion?

That last was the magenta question and I did not respond yet.
Can anybody else say anything about the Voyager probe. I don't think it could have had anything to do with Hubble Law, and expanding largescale geometry. We do not see those effects at solar system scale or galaxy scale either, for that matter.

5. Mar 13, 2013

### Mordred

There was a pop media article that tried to attribute the error in predicted location as opposed to its actual location, It was a while ago since I rea that article, later on I heard it had to do had something to do with equipment venting temperature as the cause of the anomoly. However I can't say for sure as both articles were pop media and it has been some time.

the FAQ at Ned Wrights tutorial is a good example of a format we could adapt on common questions. One other suggestion is the common universe from nothing question that commnly pops up. Mightbe a idea to start a thread on what ppl think are the most common questions and work from there

6. Mar 13, 2013

### marcus

Did that anomaly (that was eventually explained) involve the Voyager spacecraft or are we talking about the two PIONEER spacecraft?

I'm familiar with the Pioneer anomaly. there was never any speculated connection with expanding distances AFAIK. There was an unexplained acceleration towards the sun that was slowing down down the departure from the solar system. (Acceleration can be a slowing down as well as a speeding up)

So that suggested an unexplained force on the craft, directed towards the sun.

It was eventually explained, nothing to do with cosmology. Heat radiation from the craft itself.

If you turn on a flashlight and place it in a weightless environment it will behave analogously to a rocket. Radiating light in one direction creates a thrust on the flashlight in the opposite direction. The reaction force on something that radiates light (or infrared heat, same thing) is very very very slight. But it is real.

It turns out that the Pioneer probes were designed so that the probe radiated its waste heat (from the isotope powered electric generator) out of the side facing AWAY from the sun. this is like having a very weak rocket engine on board which thrusts the craft towards the sun. Slowing its progress away from the sun.

7. Mar 13, 2013

### Mordred

Yeah like I stated I wasnt too sure on it wasnt something I was overly interested in at the time lol.

8. Mar 13, 2013

### Mordred

Couple of points I would like to see added on a Redshift FAQ article.
How RedShift differs from doppler shift.
How gravity affects redshift as it approaches a gravity well and exits.
What happens to the energy levels of the signal as a result of the frequency change.

Just some of the important aspects I think a good coverage of redshift should include.

9. Mar 14, 2013

### 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.

Last edited: Mar 14, 2013