Starship Asterisk*

At APOD 2005 May 8 page,

RJN wrote:The map indicates that the Local Group moves at about 600 kilometers per second relative to this primordial radiation... Why are we moving so fast?

If we follow "why" link, we read:

There are however some anisotropies as well, the most pronounced of which is the dipole anisotropy (180 degree scales) which is at a level of about 10 −3 of the monopole. It is mostly due to the motion of the observer against the CMB, which is some 700 km/s for the Earth.

So, "why" is still unanswered...

We're moving so fast due to large-scale cosmic expansion. As groups of galaxies collapse, the groups themselves are still moving rather quickly in reference to the rest of the universe.

Dan Cordell wrote:...the groups themselves are still moving rather quickly in reference to the rest of the universe.

so I suppose the place in Universe, where there is no dipole for long period of time (to exclude occasional motion compensation possibilities), is the center of the Universe? but how can such a "center" exist, if space is limited like hypersphere? the "center" makes sense if space is unlimited, but matter is... or not? this is puzzling me

It would be a mistake to think there is a "center" or a place where there is no dipole, as there most likely is not.

Keep in mind that there is "stuff" beyond the CMB, which is at the limit of how far we can see due to the age of the universe (~12-15gigalightyears). Thus different parts of the universe will see different things.

Does that mean that everything including the earth is moving away from one point in space or everything is moving at an equal rate away from eachother?

Dan Cordell wrote:...there is "stuff" beyond the CMB, which is at the limit of how far we can see due to the age of the universe (~12-15gigalightyears)...

meaning "stuff" which is so far away that its light hadn't yet enough time to reach us? bot how would this "stuff" get so far? either it implies "superlitic" speed, or universe was not really small by the time of Big Bang?

There is an article in the March, 2005 Scientific American that deals with your questions. Here's the link

http://www.sciam.com./article.cfm?chanI ... 414B7F0147

Matt Merlo wrote:There is an article in the March, 2005 Scientific American that deals with your questions. Here's the link

http://www.sciam.com./article.cfm?chanI ... 414B7F0147

come on, I can't read that: those "baloon" analogies and alike contempt my intelligence I heared all that crap in my classes, and - guess what - it didn't help.

but if you have some specific quote in mind, feel free to copy-paste it here.

Because of the stretching of time/space, the medium which light travels, it is possible that not all light has reached us yet.

To over simplify, the equation would be: Speed of light times the distance from the big bang plus the factor of expansion equals the total size of the universe.

S. Bilderback wrote:Because of the stretching of time/space, the medium which light travels, it is possible that not all light has reached us yet.

No-matter-what, such "stretching of time/space" cannot lead to situation where some body A would move away from another body B faster then light travels between these bodies. Otherwise 4D zero interval (which is the path of light) between A and B would not be a shortest possible interval (which is nonsense - what could be smaller than 0?). Alternatively, you could claim that GRT is false.

The acutal expansion of space can be faster than the speed of light. This is because it is not motion in a frame but the expansion of that frame. While this causes to galaxies to move apart faster than light in an outside frame, inside that frame, light still is the fastest speed.

Matt Merlo wrote:The acutal expansion of space can be faster than the speed of light.

All I see is words. Give me some math! Robertson-Walker expanding space metric in non-comoving coordinates would be a good start

Matt Merlo wrote:This is because it is not motion in a frame but the expansion of that frame.

I still insist that such frame "expansion" would also "expand" speed of light in that frame.

I'll dig up my cosmology textbook and make a more detailed post.

But, in short, yes due to expansion objects can move faster than light. However this only happened during the inflationary period of our universe.

Kevin7276 wrote:Does that mean that everything including the earth is moving away from one point in space or everything is moving at an equal rate away from eachother?

Sorta your second idea but not quite. On a macroscopic level, everything in the universe is moving away from everything else. However on a galactic/cluster scale things are moving toward their neighbors and away from everything else.

I'll see if I can find some pictures to visualize this better.

Ok this is taken directly from the excellent An Introduction to Modern Cosmology by Andrew Liddle:

"...inflation is defined as a period in the evolution of the Universe during which the scale factor was accelerating:

INFLATION <==> ä(t) > 0

Typically this corresponds to a very rapid expansion of the Universe.
Looking at the acceleration equation

ä/a = -(4πG)/3 * (ρ + 3p/c^2)

we see immediately that this implies ρc^2 + 2p < 0. Since we always assume a positive density, this requires a negative pressure,

p < - (ρc^2)/3"

Later on, we get these equations:

H^2 = (8πG/3)*ρ - k/a^2 + Λ/3

Since the first two terms rapidly become very small, it simplifies to:

H^2 = Λ/3

Since H = å/a, and Λ is a constant,

a(t) = exp[(Λ/3)^(1/2) * t]

"Thus, when the Universe is dominated by a cosmological constant, the expansion rate of the universe is much more dramatic than those we have seen so far"



Later, during the Horizon Problem section:

"Suppose for example that the characteristic expansion time, H^-1, is 10^-36 sec. Then between 10^-36 and 10^-34 sec, the Universe would have expanded by a factor:

a_final/a_initial ~= exp[H(t_final - t_initial)] = e^99 ~= 10^43

The exponential expansion is so dramatic that very large expansion factors drop out almost automatically.


I would suggest purchasing this book for a better idea of how this all works, obviously what I have here isn't complete. The book is only like $15 and it's too hard to understand, I highly recommend it.


Anyway, there you have it. During the inflationary period, the universe expanded far faster than light travels. Thus, there are things beyond our "horizon."

Dan Cordell wrote:Anyway, there you have it. During the inflationary period, the universe expanded far faster than light travels. Thus, there are things beyond our "horizon."

Wow, what an explanation When I asked about Robertson-Walker expanding space metric in non-comoving coordinates, you gave me paragraph about scale factor. How about what I am asking for? (btw, I was trying to dig it out myself, but no luck so far) The reason, is that only given that form of metric one can decide if thing you are arguing about are possible.

Sorry, I don't have anything on what you asked for nor am I too familiar with it. However I thought it best to at least explain how it's possible.

okay, let's pretend you have found that metric, and it happened to be in the form ds^2 = (cdt)^2 - g(r,...)*dr^2 - (other coordinates products). let's suppose we don't rotate, so (other coordinates products) would effectively be 0. let us now consider light-emitting object at some distance r. equation of light path would be 0 = (cdt)^2 - g(r,...)*dr^2, or (dr/dt)^2 = c^2/g(r,...). now object itself would drift according to ds^2 = (cdt)^2 - g(r,...)*dr^2 > 0, unless you would allow imaginary intervals. that yields (dr/dt)^2 < c^2/g(r,...), whatever you do to g(r,...). this is by design of relativity theory, as far as I see. feel free to point out where am I wrong here.

makc, both your math and your grammar make that post dificult to understand. What is it you're trying to say?

As for your R-W metric, it depends on the cosmology you want to use.

Recycled Electrons wrote:makc, both your math and your grammar make that post dificult to understand. What is it you're trying to say?

I am trying t say that, according to GRT, light follows shortest path (actually, 0-length path) in all possible 4D coordinate systems.

In co-moving coordinates light speed is effectively less than c, because of scale factor, but "co-moving" also means that galaxies do not run away from each other - because their coordinates "co-move" with expansion:

[url=http://www.shef.ac.uk/physics/people/edaw/]Edward Daw[/url] in [url=http://www.shef.ac.uk/physics/teaching/phy323/current_year/lectures/condensed/lec_10_comoving_coords_summary.pdf]this lecture[/url], for example, wrote:...a coordinate system in which the coordinates of objects COMOVING with the expansion remain fixed as the expansion proceeds.

Therefore, I would like to see a metric in non-comoving coords, but I can't find it anywhere.

It is more advantagous to show ideas clearly than it is to spot light one's brilliance.
Here is an analogy that may help, you can figure the exact math if you feel it necessary.

Take a 1 meter strip of elastic cord and in the relaxed position make a mark every centimeter, tack one end of the cord in a fixed position and pull the cord from the free end. From the origin, the distance between the 1 centimeter marks will not be linier, plug in the rate of expansion for the universe and you’ll have what you need.

It is only a 2 dimensional model, using basic trigonometry from the point of origin, the expansion factor can be calculated for any points on an x,y,z grid, the expansion factor is perportional the difference in space/time.

makc wrote:Therefore, I would like to see a metric in non-comoving coords, but I can't find it anywhere.

I'd be surprised if you could find it.

In classical mechanics, how many times do you find it is easier to describe a system in spherical coordinates instead of Cartesian? Fairly often, I'd suspect, unless you are truly a mathematical masochist.

Similarly, in cosmology, it is far easier to use comoving coordinates. There simply isn't much reason to use any other coordinate system, the math is needlessly complex.

For a wonderful description of how comoving coordinates relate to other coordinate systems, and also a beautiful derivation of the R-W metric, I suggest you look at "Principles of Physical Cosmology" by Phillip Peebles. It is one of the definitive texts on cosmology.

S. Bilderback wrote:Take a 1 meter strip of elastic cord and in the relaxed position make a mark every centimeter, tack one end of the cord in a fixed position and pull the cord from the free end. From the origin, the distance between the 1 centimeter marks will not be linier, plug in the rate of expansion for the universe and you’ll have what you need.

in this analogy, if there are crawling worms inside this elastic cord, they would be streatched too, and so run faster (my point). your point seems to be that worms are not affected by stretching.

I take that space inside my body is no worse than one between galaxies, and it stretches too. No? Why?

Recycled Electrons wrote:For a wonderful description of how comoving coordinates relate to other coordinate systems, and also a beautiful derivation of the R-W metric, I suggest you...

Can you suggest something online? We have real problem with printed media here.

makc wrote:Can you suggest something online? We have real problem with printed media here.

A problem with printed media? That's a new one....

The only credible sources I could give you online are all references to papers. Are you at a university? Are you familiar with NASA's ADS service?

I would guess the worms could also be stretched but probably not, I can not say what roll close proximity gravity plays in the expansion effect. But the way I see it is that it is the area between gravitational clusters that is expanding. Picture two galaxies, the gravitational force is also pulling on the space/time between them, the space/time wants to remain at a constant density so maybe it is gravity waves being converted into space/time fabric causing the expansion. Or you can use dark matter and/or dark energy instead.
Remember, the different nature of gravity waves make them the only energy that can escape a black hole's event horizon.