Questions about the structure of the universe

In summary: If we existed on those universes as seen by us 'today,' then we would be however many billion years younger. But, what if we existed on those universes 'now,' without the looking back in time effect. We would still see a 14 billion year old universe, right? Just.. shifted?But in order to reach that universe in that time, we would break the speed of light, which is an impossibility. So, our particular inertial frame is finite (but infinitely expanding), right?
  • #1
tolove
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In general, what's a good way to understand the structure of the universe?

I'm especially curious about the nature of the edge of the universe. Relativistic concepts dealing with the expanding universe confuse me greatly.

Thanks for your time!
 
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  • #2
First off there is no edge of the universe, what physicists refer to as our universe is in reference to our observable universe. We simply have no means of measuring beyond that so make no definite statements. It could be infinite or finite.

here is an article covering expansion and redshift,
https://www.physicsforums.com/showpos...6&postcount=10 [Broken]

here is one on Universe geometry

https://www.physicsforums.com/showpost.php?p=4720016&postcount=86

here is what observational cosmology covers

"What we have learned from Observational Cosmology
http://arxiv.org/abs/1304.4446

my signature contains more articles to understand basic cosmology at the
http://cosmology101.wikidot.com/main

http://cosmocalc.wikidot.com/start
is a manual for the
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

lightcone calculator showing the expansion history and future expansion of the universe

those should get you started on the hot big bang model represented by [itex]\Lambda[/itex]CDM model
 
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  • #3
Mordred said:
...

I have a lot of probably misconceptions about the edge of the universe.

We have an edge of our observable universe, but no "new" things will ever be observed, correct? That means our universe is expanding at least the speed of light? So, thinking with the Lorentz transformations, the edge of our observable universe, from our perspective, is standing still in time. Which already doesn't make sense to me. But I can move on from here: this portrays an onion layer structure to our universe. From anyone perspective, anywhere in space, we observe a bubble of space-time?

What significance even comes from the universe being infinite or finite if we're already existing in an inescapable bubble?
 
  • #4
The universe does not expand at the speed of light. This is a very common misconception. Instead objects can recede from each other at light speed and beyond. This is a consequence of Hubble's Law which says that recession velocities scale linearly with separation.

The edge of the observable universe is determined by how far light has traveled since the big bang. The size of the observable universe is increasing at greater than light speed because photons receding from Earth are traveling at speeds greater than c on account of the expansion. There is no problem with special relativity here, because locally photons always travel at the speed of light -- any superluminal recession velocity observed is due to the expansion of space and is not constrained by Einstein's speed limit.
 
  • #5
Not quite, "the greater the distance the greater the recessive velocity" V=HD. This is a observer location distance dependent relation. If you change observer to the edge of the observable then the expansion is the same as here and you would see a different region for the observable universe. What constitutes your observable universe depends on your location.

edit just saw Bapowell's reply
 
  • #6
Observing the universe from a different reference frame provides no additional information. Viewed from another galaxy 'now' you would merely see a universe older and cooler than the MW [by as many years as its light travel time]. A view 'then' [when photons we now observe were emitted] provides a view of the universe as it appeared when younger and hotter than 'now' It otherwise has absolutely no effect on the extent of the observable universe.
 
  • #7
bapowell said:
The universe does not expand at the speed of light. This is a very common misconception. Instead objects can recede from each other at light speed and beyond. This is a consequence of Hubble's Law which says that recession velocities scale linearly with separation.

How does recession verse expansion make any difference? (edit) Recession allows for infinite centers kind of view, while expansion dictates a single origin, right?

Chronos said:
Observing the universe from a different reference frame provides no additional information. Viewed from another galaxy 'now' you would merely see a universe older and cooler than the MW [by as many years as its light travel time]. A view 'then' [when photons we now observe were emitted] provides a view of the universe as it appeared when younger and hotter than 'now' It otherwise has absolutely no effect on the extent of the observable universe.

If we existed on those universes as seen by us 'today,' then we would be however many billion years younger. But, what if we existed on those universes 'now,' without the looking back in time effect. We would still see a 14 billion year old universe, right? Just.. shifted?

But in order to reach that universe in that time, we would break the speed of light, which is an impossibility. So, our particular inertial frame is finite (but infinitely expanding), right?

edit edit: Wouldn't this mean that, for our frame, an infinite universe might as well be considered to be compressed into the shell of our observable universe? Which is standing still in time?
 
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  • #8
tolove said:
How does recession verse expansion make any difference? (edit) Recession allows for infinite centers kind of view, while expansion dictates a single origin, right?

recessive velocity is a measurement of the rate of expansion and is observer and distance dependant. For the reasons already provided.

tolove said:
If we existed on those universes as seen by us 'today,' then we would be however many billion years younger. But, what if we existed on those universes 'now,' without the looking back in time effect. We would still see a 14 billion year old universe, right? Just.. shifted?

there is no way to observe the entire universe without looking back into time, the redshift is included in our measurements, see the redshift and expansion article I posted above.

tolove said:
But in order to reach that universe in that time, we would break the speed of light, which is an impossibility. So, our particular inertial frame is finite (but infinitely expanding), right?

edit edit: Wouldn't this mean that, for our frame, an infinite universe might as well be considered to be compressed into the shell of our observable universe? Which is standing still in time?

no this makes little sense, we cannot determine if our universe is infinite or finite. We can only see a finite portion (The observable universe) Those observations include the speed of light + expansion.

Think of it this way a star emits light say 13 billion years ago. The universe was smaller then, as the light approaches us the universe expands both ahead and along the path of the light beam. However the rate of expansion is LOCALLY miniscule to the beam of lights speed. So it keeps approaching us, and decreasing the distance between us and the beam. As the expansion occurs the increase in distance along the path of the beam already traveled causes the frequency of the light beam to decrease (Cosmological redshift). However expansion ahead of the beam, does not affect the beam, other than to increase its distance between us and the beam.

As the beam approaches us its already traveled part of the way, as it approaches us its recessive velocity decreases. The closer the light beam gets the less recessive velocity it will have, (assuming you had some magical means to measure the leading edge of the beam lol) also due to the less distance between us and the beam the less the rate of expansion will delay it from arriving. However the expansion history during its travel will have already reduced the frequency.

edit just a side note, the amount of expansion per megaparsec is miniscule, when people say the expansion is faster than the speed of light they are referring to a far larger unit of distance, for example the amount of expansion between us and the CMB is 3C roughly, however per megaparsec its far far slower than the speed of light [itex] H=67.3 km/s/Mpc[/itex] so [itex]H=67300 meters/sec/Mpc[/itex] as opposed to [itex]c\ =\ 2.99792458\ \times\ 10^{8}\ m\ s^{-1}[/itex] one Mpc is [itex]3.08567758 × 10^{22}[/itex] meters
 
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  • #9
tolove said:
How does recession verse expansion make any difference? (edit) Recession allows for infinite centers kind of view, while expansion dictates a single origin, right?
Hubble's Law, [itex]v = Hr[/itex], relates the recession velocity of a distant object, [itex]v[/itex], to its distance from us, [itex]r[/itex]. The expansion rate is given by [itex]H[/itex]. From this, you can see that for a given expansion rate, the recession velocity depends on separation. There is no origin necessary: imagine blowing up a balloon and consider the balloon's surface. Where is the center? There is none -- all points on the surface uniformly recede from all others with a speed proportionate to their separations.
 
  • #10
Mordred said:
...

Let our universe have two objects. Consider "us" to be at rest.

As the second object "moves" away, we take the size of the universe to be the space between the two objects.

I'd prefer this to be imagined on a 1D line, but I don't know if that breaks things.

Where is the difference between expansion and... recession? Space is created between the two objects rather than considering space to be traversed by the "moving" object? Space can be created in amounts that exceed the distance light can cover in the same interval? This feels like a wrong view...
 
  • #11
tolove said:
Let our universe have two objects. Consider "us" to be at rest.

As the second object "moves" away, we take the size of the universe to be the space between the two objects.

I'd prefer this to be imagined on a 1D line, but I don't know if that breaks things.

Where is the difference between expansion and... recession? Space is created between the two objects rather than considering space to be traversed by the "moving" object? Space can be created in amounts that exceed the distance light can cover in the same interval? This feels like a wrong view...

recessive velocity is a measurement of expansion, so in that sense there is no difference. the rate of expansion per Mpc is 67.3 km/s/Mpc. Does this sound like its anywhere close to being faster than the speed of light? I explained earlier that the points where we describe recessive velocity as being faster to the speed of light is due to a far larger unit of distance. Which quite frankly is a poor descriptive as it does depend on the unit of measure, Ie a Very large unit

The point where this occurs is called the Hubble sphere, and its a cumulative of the expansion per Mpc between us and the Hubble sphere. (67.3+67.3+67.3...keep adding up till it finally exceeds light speeds value lol.) However the rate of expansion in the individual Mpc's between us and the Hubble sphere is still 67.3 km/s/Mpc.
 
  • #12
Space expands. Objects in space recede on account of the expansion.
 
  • #13
tolove said:
Let our universe have two objects. Consider "us" to be at rest.

As the second object "moves" away, we take the size of the universe to be the space between the two objects.

I'd prefer this to be imagined on a 1D line, but I don't know if that breaks things.

Where is the difference between expansion and... recession? Space is created between the two objects rather than considering space to be traversed by the "moving" object? Space can be created in amounts that exceed the distance light can cover in the same interval? This feels like a wrong view...

Recession and expansion are the same. Space is not a thing and does not stretch or expand, it's just that things IN space get farther apart (see the link in my signature). This is called recession. MOVING is a whole 'nother thing. This gets a bit weird because we are using English language to describe stuff that it wasn't quite made to describe. Things cannot move greater than the speed of light but they can, and do, recede at any speed. Objects at the edge of our observable universe are receding from us at about 3c but their proper motion relative to us is negligible by comparison.

Chronos's comment about "no new information" is misleading. If you could magically move instantaneously to a galaxy 5 billion light years away, you would as he says see an observable universe that has the same characteristics as ours in that your observable universe would be the same radius as ours. You WOULD, however, see things in that observable universe that are not in our observable universe and you would see the things in our observable universe (those that you could see anyway) as being, as Chronos says, a different age that than what we see them as being.
 
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  • #14
The reason that I draw a distinction between expansion and recession is because the former is a rate, determined by [itex]H[/itex] that applies to the growth of length scales in the universe (I say space expands, but I mean that distances increase). Meanwhile, points in space recede from each other on account of this expansion with a speed given by Hubble's Law. In words, then: recession speed = expansion rate x separation.
 
  • #15
Okay, I think I have a more accurate picture now, however this new picture is equally confusing.

So, space is created? Is there any way to better understand this concept? I haven't touched quantum mechanics yet.

phinds said:
... Objects at the edge of our observable universe are receding from us at about 3c but their proper motion relative to us is negligible by comparison. ...

phinds said:
If you could magically move instantaneously to a galaxy 5 billion light years away, you would as he says see an observable universe that has the same characteristics as ours in that your observable universe would be the same radius as ours.

In other words, the balloon model is serious business. We're inside an inflating balloon and cannot leave our little subset of space. The balloon might have a center with respect to the 'actual' edge, but we'll never know, and, for us, it is a meaningless question.

I'm wanting to view the universe as a lower dimensional bubble contained in something else. Such as a soap bubble in a bucket of water. The 2D-ish soap bubble thins out in a uniform manner as it is absorbed into the 3D bucket. Is their any actual logic to this kind of perspective?

I'm wanting to use this perspective because the idea of an infinite expansion seems as arbitrary to me as claiming to be the center of the universe.

edit: The big bang implies a point, right? But this doesn't imply an actual center for the universe?
 
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  • #16
tolove said:
Okay, I think I have a more accurate picture now, however this new picture is equally confusing.

So, space is created? Is there any way to better understand this concept? I haven't touched quantum mechanics yet.In other words, the balloon model is serious business. We're inside an inflating balloon and cannot leave our little subset of space. The balloon might have a center with respect to the 'actual' edge, but we'll never know, and, for us, it is a meaningless question.

I'm wanting to view the universe as a lower dimensional bubble contained in something else. Such as a soap bubble in a bucket of water. The 2D-ish soap bubble thins out in a uniform manner as it is absorbed into the 3D bucket. Is their any actual logic to this kind of perspective?

I'm wanting to use this perspective because the idea of an infinite expansion seems as arbitrary to me as claiming to be the center of the universe.

I'm not sure whether you've got it or not, but I think your wording is confusing. The fact that no matter where we are in the universe we are at the center of our own OBSERVABLE universe has nothing whatsoever to do with the balloon analogy. We are not inside an inflating balloon because a balloon has a material, physical boundary (edge) whereas the observable universe has a horizon but there is nothing material marking it. The balloon analogy is best understood if you read my discussion of it linked to in my signature. The "balloon" actually goes away in the most realistic version of the analogy, as I explain there.

Space is not created, things IN space just get farther apart.
 
  • #17
tolove said:
We're inside an inflating balloon and cannot leave our little subset of space. The balloon might have a center with respect to the 'actual' edge, but we'll never know, and, for us, it is a meaningless question.
No, nothing is inside the balloon. We are on the 2D surface -- it is analogous to the real 3D space of the universe. The balloon nicely illustrates that no one single point on the balloon is central, however, from its vantage point, it sure appears to be. As long as the balloon is homogeneously inflated, all points recede from all others according to Hubble's Law.

The big bang implies a point, right? But this doesn't imply an actual center for the universe?
No, the big bang implies a beginning (a point in time only).
 
  • #18
bapowell said:
The reason that I draw a distinction between expansion and recession is because the former is a rate, determined by [itex]H[/itex] that applies to the growth of length scales in the universe (I say space expands, but I mean that distances increase). Meanwhile, points in space recede from each other on account of this expansion with a speed given by Hubble's Law. In words, then: recession speed = expansion rate x separation.

Fair enough. Thanks for pointing that out.
 
  • #19
http://www.astro.ucla.edu/~wright/balloons.gif just a visual aid

edit:not a very good one though lol tends to have the directions of expansion wrong I'll see f I can locate a better one.

this one isn't bad they give three different animations

https://www.e-education.psu.edu/astro801/content/l10_p4.html

ignore the descriptive explosion though lol, some of their wording on the site isn't precise, other descriptive's are just plain wrong. So just use the animations lol

ignore this as well

"The idea is that we live in a universe with three spatial dimensions that we can perceive, but that there exist "extra" dimensions (maybe one, maybe more than one) that contain the center of the expansion. Just like the two-dimensional beings that inhabit the surface of the balloon universe, we cannot observe the center of our universe. We can tell that it is expanding, but we cannot identify a location in our 3D space that is the center of the expansion."

its too bad the article itself is so poorly worded, the animations I wanted to post merely as a visual aid showing 1d rubber band analogy, raisin bread/balloon analogy and the redshift. Its the only site I found that had all 3. Unfortunately I couldn't just copy the animations. So ignore all the descriptives on the site, far too many errors
 
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  • #20
My wording is very poor, thank you all for helping me fix it. I'm trying to focus on one thought at a time. Sorry for not replying to everything that's being said!

This particularly is trouble for me:

phinds said:
... Space is not created, things IN space just get farther apart.

I asked two cosmology professors "does space grow" today. I got both a yes and a no.

I guess the next step is to ask for more detail? Here's my thinking:

Things become further apart if space in between them increases. The increase in space of the universe isn't explained by relative velocities alone. So we have extra space that was never traversed. Therefor... empty space grows..?

But this also confuses me because the idea of space growing is rather crazy as well. What happens to space that is grown inside a galaxy? Galaxies are held together with a ridiculous amount of energy. Does grown space leak out like some kind of gas? Problems! Haha, maybe that would make sense. Galaxies leaking space and all.

edit: I like that a lot actually. Is matter turning into space a thing that's been studied?
 
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  • #21
Think about this. You have two cars on a highway. One is parked and the other is 5 miles away and going 60 miles and hour. After 5 minutes, the moving car is now 10 miles away from the parked car. Did the highway grow? Now just take away the highway but keep the relative motion the same with the cars out in space and you have exactly the same situation. Nothing expanded except the distance between the cars.

I understand your problem with this. In is natural to think, well SOMETHING grew in between them, but the problem is that space isn't "something", it's just a framework. The road IS "something", which is why that's a flawed analogy and I said you have to take away the road.

And by the way, getting two different answers the way you did is not unusual from non-cosmologists. Even well known cosmologists will use that phrasing (and even worse terms like "stretching") when discussing this stuff for the layman. This is one of those things that popular science TV shows ALWAYS get wrong because it's just too damned complicated and confusing to try to explain it the way we are in this thread.
 
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  • #22
phinds said:
Think about this. You have two cars on a highway. One is parked and the other is 5 miles away and going 60 miles and hour. After 5 minutes, the moving car is now 10 miles away from the parked car. Did the highway grow? Now just take away the highway but keep the relative motion the same with the cars out in space and you have exactly the same situation. Nothing expanded except the distance between the cars.

I understand your problem with this. In is natural to think, well SOMETHING grew in between them, but the problem is that space isn't "something", it's just a framework. The road IS "something", which is why that's a flawed analogy and I said you have to take away the road.

And by the way, getting two different answers the way you did is not unusual from non-cosmologists. Even well known cosmologists will use that phrasing (and even worse terms like "stretching") when discussing this stuff for the layman. This is one of those things that popular science TV shows ALWAYS get wrong because it's just too damned complicated and confusing to try to explain it the way we are in this thread.

This car model doesn't portray what's happening, though.

In order for it to be a fair comparison, their distance after 5 minutes would have to be further than 10 miles apart. In which case, I would want to say that the highway grew.
 
  • #23
The easiest and safest visualization of space increasing is to simply think of it in terms of geometry.
The distance or volume of space increases, Space itself is not a substance, energy or material, it has no properties other than distance or volume. The increase in volume/distance is simply filled with the energy-mass content of the universe already present.
A good treatment and one that is applicable, is to think of a fluid, or ideal gas. The metrics involved in Cosmology are essentially ideal gas treatments. As the volume of space increases the density of that ideal gas decreases as well as the temperature. Just like classic gases. Though you also have to consider quantum effects such as virtual particles and quantum tunneling, but that's a different subject

On my initial post I included a Universe Geometry article, look at the term critical density, Critical density is the calculated value that would have a flat and static (Non expanding/contracting) universe. The energy-density to pressure relation of each particle species is defined by the equations of state (Cosmology). The universe geometry is an energy-density, (corresponding pressure) relation between positive pressure (gravity/matter) and negative pressure (Cosmological constant). Expansion and the geometry (flat, curved) pressure distributions affects the path of light rays

So remember an increase in space is simply a geometric change in volume/distance that is simply filled with the contents of the universe. Space is neither created, destroyed, or stretched/compressed. Multimedia tends to use the simplest and often confusing terms due to time constraints and sales of their programming. You have to admit some of the terms used do get a lot of attention :rolleyes:

here is the critical density portion from that article,

The topography of the universe is determined by a comparison of the actual density (total density) as compared to the critical density. The critical density is represented by the following formula

[itex]\rho_{crit} = \frac{3c^2H^2}{8\pi G}[/itex]

[itex]\rho[/itex]=energy/mass density
c=speed of light
G= gravitational constant.

density is represented by the Greek letter Omega [itex]\Omega[/itex] so critical density is [itex]\Omega crit[/itex]
 
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  • #24
tolove said:
This car model doesn't portray what's happening, though.

In order for it to be a fair comparison, their distance after 5 minutes would have to be further than 10 miles apart. In which case, I would want to say that the highway grew.

OK, I see what you're saying. I was just trying to move you away from the false notion that space is "something" that can grow/stretch/etc. If the expansion of the universe were not accelerating, then you would have the same problem with your misunderstanding and the car/road analogy WOULD be valid. Why do you think that the acceleration is what causes space to "grow" if simple expansion does not make it do the same thing? Perhaps the illogic of that will help you see the flaw in your logic.

As Mordred said, it's all just geometry.
 
  • #25
phinds said:
OK, I see what you're saying. I was just trying to move you away from the false notion that space is "something" that can grow/stretch/etc. If the expansion of the universe were not accelerating, then you would have the same problem with your misunderstanding and the car/road analogy WOULD be valid. Why do you think that the acceleration is what causes space to "grow" if simple expansion does not make it do the same thing? Perhaps the illogic of that will help you see the flaw in your logic.

As Mordred said, it's all just geometry.
In place of "space grows," we should use "things inexplicable separate." This is related to the Ether fallacies.

But this separation isn't normal... why is it special? What is it?

I don't think I have an understanding of what it means for a distant object to be swept past the speed of light.
 
  • #26
Dynamic geometry is your answer. If I have a triangle with 3 angles that add up to 180 degrees (like the triangles you deal with in school) and the geometry of the plane changes then the triangle changes shape. Those angles are no longer the same and they will not add up to 180 degrees anymore. Because the shape of the triangle has changed there will be points on it that have moved closer together or further away. The distance between the points has changed, but no space has been "created" or "taken away". It's all about distances.

Extending this from 2d into our 4d spacetime, we get the same effect. The geometry of the universe changes and the distance between objects which aren't bound together grows. If you think of it as distances increasing instead of space being created then the dilemma goes away. Nothing is being "swept" along with space.

The only thing "special" about it is that it is completely unlike anything you've ever dealt with in your day to day life. The geometry of the Earth doesn't change. Your kitchen table doesn't go from flat to curved. But, as we've also learned in the quantum world, the universe does NOT obey our expectations.
 
  • #27
Drakkith said:
... If you think of it as distances increasing instead of space being created then the dilemma goes away. Nothing is being "swept" along with space. ...

velocity = distance / time.. a velocity means we apply the Lorentz transformations from our perspective? The Lorentz transformations break for v>=c... at least from my understanding of them. Is this something that is accounted for through dynamic geometries (I'm completely unfamiliar)?
 
  • #28
tolove said:
In place of "space grows," we should use "things inexplicable separate." This is related to the Ether fallacies.

Absolutely not. Things get farther apart because of the expansion of the universe. What is not understood is why the expansion is ACCELERATING and we call the reason for that "dark energy", with the "dark" being a placeholder word for "we don't know WHAT is causing this".

I don't think I have an understanding of what it means for a distant object to be swept past the speed of light.

But is IS NOT moving faster than c. You continue to refuse to accept geometry and insist on thinking of recession as being the same as proper motion which is just isn't. As long as you continue to conflate the two, you are not going to get anywhere with this.
 
  • #29
tolove said:
velocity = distance / time.. a velocity means we apply the Lorentz transformations from our perspective? The Lorentz transformations break for v>=c... at least from my understanding of them. Is this something that is accounted for through dynamic geometries (I'm completely unfamiliar)?

Again, you are insisting on velocities greater than c and there aren't any. The proper motion of the distant galaxies is trivial compared to c.
 
  • #30
tolove said:
velocity = distance / time.. a velocity means we apply the Lorentz transformations from our perspective? The Lorentz transformations break for v>=c... at least from my understanding of them. Is this something that is accounted for through dynamic geometries (I'm completely unfamiliar)?

Yes, this is accounted for under General Relativity. Special Relativity only holds for non-expanding space. I'm sorry, I wish I had a good link for you that would help explain this, but I don't.
 
  • #31
Drakkith said:
Yes, this is accounted for under General Relativity. Special Relativity only holds for non-expanding space. I'm sorry, I wish I had a good link for you that would help explain this, but I don't.
finding simple good links is the trick lol,

for the OP, the GR factor is in front of you, its in the critical density formula. Let me show you

[itex]\rho_{crit} = \frac{3c^2H^2}{8\pi G}[/itex]

[tex] c= 8\pi G = 1[/tex]

which is in the metrics is normalized to equal 1. (makes differential geometry calculations easier, think of it as simply a representative assignment)

This site may help, however your geometry metrics will be needed, there simply isn't a good way to explain without referring to differential geometry. The metrics I posted in the Universe geometry is about the simplest form I've run across. The Einstein field equations are tricky to explain by comparison. Not sure this will help or not as you've shown difficulty seeing the math relations involved in recessive velocity.

http://math.ucr.edu/home/baez/einstein/einstein.html

this site is good for covering the Einstein field equations, please note they also refer to space-time in geometry terms

just a side note, the energy-density of the the cosmological constant that contributes to expansion is

[tex]\rho_{vac} = \frac{\Lambda c^2}{8\pi G}[/tex]
 
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  • #32
I noticed that the Redshift and expansion link is no longer working, too old a thread so here is the article.



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

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

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

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

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

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

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


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

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

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

[tex]\frac{\Delta_f}{f} = \frac{\lambda}{\lambda_o} = \frac{v}{c}=\frac{E_o}{E}=\frac{hc}{\lambda_o} \frac{\lambda}{hc}[/tex]

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

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

Velocity = H0 × distance.

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

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

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

1+z= λobservedemitted or z=(λobservedemitted)/λemitted

[tex]1+Z=\frac{\lambda}{\lambda_o}[/tex] or [tex]1+Z=\frac{\lambda-\lambda_o}{\lambda_o}[/tex]

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

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

Ho[itex]\propto\sqrt\Lambda[/itex]

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

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

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

[tex] f=\frac{c+v_r}{c+v_s}f_o[/tex]

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

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

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

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

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

d(t)=a(t)do

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

[tex]Proper distance =\frac{\stackrel{.}{a}(t)}{a}[/tex]

The dot above a indicates change in.

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

[tex]H(t)=\frac{\stackrel{.}{a}(t)}{a(t)}[/tex]

Expansion velocity
[tex] v=\frac{\stackrel{.}{a}(t)}{a}[/tex]

This shows that Hubble's constant is time dependant.



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

Luminosity is often measured in flux where flux is

[tex]f=\frac{L}{4\pi r^2}[/tex]

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

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

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

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

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

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

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

PAllen
Naty1
Jonathon Scott
marcus

Article by Mordred, PAllen
 
  • #33
phinds said:
Again, you are insisting on velocities greater than c and there aren't any. The proper motion of the distant galaxies is trivial compared to c.

Thanks for bearing with me and continuously pointing me back to this idea.

Mordred said:
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.

This kind of separation distance is meaningless unless there is a third frame that we can claim to be at rest. We have a separation distance with just two objects when thinking about the expansion of the universe.

This is because separation due to inflation is a concept in differential geometry, which is completely new to me. I think I need to spend some time with geometry, then come back to this thought.
 
  • #34
tolove said:
This kind of separation distance is meaningless unless there is a third frame that we can claim to be at rest. We have a separation distance with just two objects when thinking about the expansion of the universe.

This is because separation due to inflation is a concept in differential geometry, which is completely new to me. I think I need to spend some time with geometry, then come back to this thought.
You seem to think that there is such a thing as absolute rest. There is not. I don't know what Mordred means by their relative velocities remaining less than c, while their recession velocities are greater: what's the difference?

Imagine an expanding grid, the tick marks increase as the grid expands. Draw two dots on the expanding grid. They move apart as the grid expands. Eventually they get far enough apart that they begin receding at faster than light speed, [itex]v_{\rm rec} > c[/itex]. Now imagine one sends a beam of light towards the other (say from A to B). Locally, the velocity of light is always c (this is called its peculiar velocity). From B's perspective, though, this light is traveling at [itex]v_{\rm rec} - c > 0[/itex] -- i.e. the light is initially moving away from B. In other words, light is not special when we talk about recession velocities in the expanding universe -- we add and subtract it just like it's a classical object.
 
  • #35
Yeah that section isn't correct I'll have to fix that. That section was PAllen's contribution, though I probably mistranslated what he had when I did the final draft. Thanks for pointing it out

edit most likely I'll just delete that particular line, its not needed to show that recessive velocity isn't a greater than c violation
 
Last edited:
<h2>1) What is the current theory about the structure of the universe?</h2><p>The current theory about the structure of the universe is the Big Bang theory, which suggests that the universe began as a single point and has been expanding ever since.</p><h2>2) How is the universe organized?</h2><p>The universe is organized into different structures, including galaxies, galaxy clusters, and superclusters. These structures are made up of stars, gas, and dark matter.</p><h2>3) What is dark matter and how does it affect the structure of the universe?</h2><p>Dark matter is a type of matter that does not interact with light and therefore cannot be seen. It makes up about 27% of the universe and plays a crucial role in the formation and structure of galaxies and galaxy clusters.</p><h2>4) Are there any theories about the shape of the universe?</h2><p>Yes, there are several theories about the shape of the universe. Some suggest that it is flat, while others propose a spherical or saddle-shaped universe. However, the exact shape is still unknown and is a topic of ongoing research.</p><h2>5) How do scientists study the structure of the universe?</h2><p>Scientists use various methods to study the structure of the universe, including telescopes, satellites, and computer simulations. They also analyze data from cosmic microwave background radiation, which provides information about the early universe.</p>

1) What is the current theory about the structure of the universe?

The current theory about the structure of the universe is the Big Bang theory, which suggests that the universe began as a single point and has been expanding ever since.

2) How is the universe organized?

The universe is organized into different structures, including galaxies, galaxy clusters, and superclusters. These structures are made up of stars, gas, and dark matter.

3) What is dark matter and how does it affect the structure of the universe?

Dark matter is a type of matter that does not interact with light and therefore cannot be seen. It makes up about 27% of the universe and plays a crucial role in the formation and structure of galaxies and galaxy clusters.

4) Are there any theories about the shape of the universe?

Yes, there are several theories about the shape of the universe. Some suggest that it is flat, while others propose a spherical or saddle-shaped universe. However, the exact shape is still unknown and is a topic of ongoing research.

5) How do scientists study the structure of the universe?

Scientists use various methods to study the structure of the universe, including telescopes, satellites, and computer simulations. They also analyze data from cosmic microwave background radiation, which provides information about the early universe.

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