Universe Expansion Diagram

[losfomot]

I stole this diagram from a recent post by Spyman, although I have had the same diagram in my desktop pics for years. It seems misleading to me:

 

 

A representation of the evolution of the universe over 13.7 billion years. The far left depicts the earliest moment we can now probe, when a period of "inflation" produced a burst of exponential growth in the universe. (Size is depicted by the vertical extent of the grid in this graphic.) For the next several billion years, the expansion of the universe gradually slowed down as the matter in the universe pulled on itself via gravity. More recently, the expansion has begun to speed up again as the repulsive effects of dark energy have come to dominate the expansion of the universe. The afterglow light seen by WMAP was emitted about 380,000 years after inflation and has traversed the universe largely unimpeded since then. The conditions of earlier times are imprinted on this light; it also forms a backlight for later developments of the universe.

 

This seems to be a good visual of the 'rate' of expansion, but not the expansion itself. Shouldn't the diagram be much more cone shaped to represent the expansion?

 

Here's a link to the 'nasa site'

[alpha2cen]

We know the Universe is expanding.

But we don't know detail tendency.

Until now known knowldge is like this.

 

D(t) = D₀ + kⁿ t

where

D(t); Universe diameter[arbitrary unit].

D₀; Initial Universe diameter[arbitrary unit].

k, n ; Constant.

 

k>1-----> expansion

n>1-----> accelerated expansion

 

But we do exactly define n yet.

We dont know n(t) or n-constant value.

 

case of n(t)

1) constant

2) 1st order function n(t) = a + bt

3) other function

 

This concept have to consider figure drawing.

[michel123456]

(...)It seems misleading to me:

(...)

Shouldn't the diagram be much more cone shaped to represent the expansion?

(...)

 

No, I don't think so. The horizontal 13,7 Light Years is a time, not a length. This time corresponds to a distance of 46,5 billion light-years following Wiki. The extended shape of the diagram is an indication of the expansion, because under normal circumstances (without expansion) a time of 13,7 BY should correspond to a distance of 13,7 Light years, and not 46,5 billion LY. So I think for this part the diagram is correct.

 

But IMHO the diagram is misleading for other reasons.

 

1_the diagram does not represent the entire Universe. It represents only the evolution, following the Standard Model, of our Observable Universe. The whole Universe is probably much bigger. In other words, the black surrounding of the diagram is most probably full of stars & galaxies. The diagram is misleading in the sense that any kid looking at this diagram will immediately conclude that the Universe has boundaries and is finite although it is a question still under investigation.

 

2_The diagram does not represent the Observable Universe either, but the sum of all stages of evolution of our Observable Universe following Standard Cosmology. Our Observable Universe in this diagram is the surface of a cone with the basis upon "Afterglow Light Pattern" and the summit at WMAP (which is the observator). Our current Observable Universe is only a tiny part of the diagram. It is misleading in the sense that anyone looking at the diagram may believe that we are currently looking at all this stuff, and it is not the case. (for example WMAP can not observe anything that lies in his own slice of space).

 

3_It is a space-time diagram. Space is represented as a succession of disks, growing from left to right (like a salami). The representation of WMAP should be flat, and not 3d, and all galaxies should have been represented aligned in space, flatten upon the disks, in order to clearly show that each belong to a specific slice of space. It is misleading in the sense that the whole diagram looks like a 3D shape with a volume, and it is not the case, because volumes here are represented flat.

 

4_the length from left to right of the diagram is time, not distance. But it represents also the radius of the sphere of the Observable Universe, so in this sense, it represents distance also (see the OP question). Because it is a space-time diagram, a radius is not represented as construction part of a shere, but as a height as in a triangle. It is misleading because anyone looking at information about the Observable Universe will take the answer that the O.U. is a sphere, and not a cone or a diagram like this.

 

5_anyone looking at the diagram can ask the following question: what is happening on the left side of the Bang? In other words, what was before the Big-Bang? Many scientists struggle with this question, and no-one who have seen this diagram will easily accept the answer "there was nothing". So it is misleading in the sense that it raise uncomfortable questions.

 

6_ the same anyone may ask what happen on the far right side of the diagram. In other words, what is the future made of? Are there already stars & galaxies there, does the future already exist? Also an uncomfortable question. Following Standard Cosmology, there is nothing on the right of the diagram. Everything stops at our present time.

 

With all respects to the NASA team who produced this diagram in the good intention of instructing people. It looks like Lie To Children. I suppose that any diagram of any kind may raise questions & misinterpretations.

Besides, I may be the one who is wrong.

Edited November 17, 2010 by michel123456

[losfomot]

No, I don't think so. The horizontal 13,7 Light Years is a time, not a length. This time corresponds to a distance of 46,5 billion light-years following Wiki. The extended shape of the diagram is an indication of the expansion, because under normal circumstances (without expansion) a time of 13,7 BY should correspond to a distance of 13,7 Light years, and not 46,5 billion LY. So I think for this part the diagram is correct.

 

It is not the horizontal aspect that I am questioning... it is the vertical. Horizontal represents time... vertical represents size (expansion).

[alpha2cen]

D(t) = D₀ + kⁿ t

 

 

correction (typing miss)

 

D(t) = D₀ + kⁿ t --------> D(t) = D₀ + k t^n(t)

where

D(t); Universe diameter[arbitrary unit].

D₀; Initial Universe diameter[arbitrary unit]. Inflation point?

k, n ; Constant.

 

k>0-----> expansion

n>1-----> accelerated expansion

 

case of n(t)

1) constant, n(t) = n

2) 1st order function n(t) = a + bt

3) other function ---- n(t) has been varied with time nonlinearly

 

D₀ ; ?? Any good idea?

Edited November 18, 2010 by alpha2cen

[between3and26characterslon]

If the rate of expansion was constant for all time the diagram would be a cylinder. The steepness of the outer lines tells you the rate of expansion, the steepest lines on the diagram are during inflation where the rate of expansion was at its greatest.

 

The distance from leaft to right tells you the age of the universe.

 

The diagram tells you the rate of expansion abruptly levelled (almost) off after inflation before entering the 'dark ages', the rate was then fairly constant and the rate is increasing as you get nearer the present.

Edited November 18, 2010 by between3and26characterslon

[Spyman]

This seems to be a good visual of the 'rate' of expansion, but not the expansion itself. Shouldn't the diagram be much more cone shaped to represent the expansion?

As you and between3and26characterslon are saying the picture seems to try to show different aspects of the Big Bang and it is therefor not in proper scale, NASA appears to try to focus on the timeline with the CMBR and the rate of expansion instead of the actual increase in size.

 

According to standard cosmology the distance of the matter that emitted the CMBR was ~4o million lightyears distant from our location, when the photons took off in our direction and is thought to be some ~45 billion lightyears distant now when they arrive in our observatories.

(Cosmos Calculator Omega=0.27 Lambda=0.73 Hubble=71 Redshift=1100)

 

That would correspond to an increase in radius of ~1100 times from the left side to the right side in the picture, which would make both the CMBR and the rate of expansion to tiny to view.

Edited November 18, 2010 by Spyman

[alpha2cen]

When we were at the outside of the Galaxy, Could we see same CMB picture?

We see the cosmos in the heliosphere, and outside of the solar system, there are interstellar clouds.

Are we able to see the CMB, as if we were far away from the Galaxy?

 

 

 

[imatfaal]

A2C - yes all observers see the CMBR and all observe it having the same characteristics (red-shift etc). You could check out this thread (especially towards end) in which Michel wasn't persuaded of this fact ... http://www.scienceforums.net/topic/52438-picture-of-galaxy-from-when-expansion-only-600-million-years-old/

[Spyman]

When we were at the outside of the Galaxy, Could we see same CMB picture?

We see the cosmos in the heliosphere, and outside of the solar system, there are interstellar clouds.

Are we able to see the CMB, as if we were far away from the Galaxy?

Anyone anywhere can observe the CMBR, unless they are somehow locally shrouded from the surrounding universe, but depending on relative position different observers will see different parts of it.

 

The CMBR is explained as a relic radiation permeating the Universe that remains from the Big Bang and is not something locally to our Solar system or the inside of Milky Way galaxy.

 

In cosmology, cosmic microwave background (CMB) radiation (also CMBR, CBR, MBR, and relic radiation) is a form of electromagnetic radiation filling the universe. With a traditional optical telescope, the space between stars and galaxies (the background) is pitch black. But with a radio telescope, there is a faint background glow, almost exactly the same in all directions, that is not associated with any star, galaxy, or other object.

http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation

[alpha2cen]

 

The CMBR is explained as a relic radiation permeating the Universe that remains from the Big Bang and is not something locally to our Solar system or the inside of Milky Way galaxy.

 

 

Has CMBR not been affected by Universe expansion?

Are middle ages CMBR and present CMBR same waves?

For example

middle ages Universe CMBR----------------------> Present CMBR

very short wave..............................................> long micro wave?

 

When we throw a stone in the circular pond, at first the water wave length is short, but time pass by the water wave length will be longer and longer .

[Spyman]

Has CMBR not been affected by Universe expansion?

Are middle ages CMBR and present CMBR same waves?

For example

middle ages Universe CMBR----------------------> Present CMBR

very short wave..............................................> long micro wave?

 

When we throw a stone in the circular pond, at first the water wave length is short, but time pass by the water wave length will be longer and longer .

The CMBR has been stretched/redshifted to a wavelenght of ~1100 times longer by the expansion of the Universe.

 

The energy of photons was subsequently redshifted by the expansion of the Universe, which preserved the blackbody spectrum but caused its temperature to fall, meaning that the photons now fall into the microwave region of the electromagnetic spectrum. The radiation is thought to be observable at every point in the Universe, and comes from all directions with (almost) the same intensity.

http://en.wikipedia.org/wiki/Big_Bang_cosmology#Cosmic_microwave_background_radiation

 

This recombination event happened at around 3000 K or when the universe was approximately 379,000 years old. This is equivalent to a redshift of z = 1,088.

http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation

[alpha2cen]

When we were at the outside of the Galaxy, Could we see same CMB picture?

We see the cosmos in the heliosphere, and outside of the solar system, there are interstellar clouds.

Are we able to see the CMB, as if we were far away from the Galaxy?

 

 

I'm afraid, but how about this paper.

Something strange.

 

http://ia64.phys.iit.edu/OCS/index.php/PSAPS-CSAAPT/2010/paper/view/7

 

[Spyman]

What are you afraid of?

 

There exists a lot of different ideas on the internet, some are made by reputable scientists while others are from crackpots which either lack knowledge or merge to much faith into their models.

 

The idea of "a very slow moving Earth located next to the epicenter of the Big Bang" are not in accordance with current scientific cosmological consensus.

Edited December 2, 2010 by Spyman

[Widdekind]

To my understanding, the "Visible Universe (VU)" is the backwards lightcone, of Earth, on the present time-slice of spacetime (shown above in a (1+1)D in 3D visualization). Whereas, the Hubble Volume (HV) is that spatial section, along the current time-slice of spacetime, corresponding to, and coming forward in time from, the VU (an arc-length, along the spatial circle, of the present time-slice, of that "vase" of (1+1)D in 3D spacetime).

[Widdekind]

Fig. 1 --

Visible Universe (VU)

and corresponding forward-projected

Hubble Volume (HV)

indicated. Note that documentaries, like NGC's

Journey to the Edge of the Universe

(DVD), explore the former, not the latter. Mankind has

no news

about the

current conditions

in the

HV

, being only aware of the archaic pasts of that present.

 

Fig. 2 --

'Augmented' time-slices of

(2+0)D

overlain. Time-slices of Cosmic spacetime do not simply "expand like a balloon", but rather "expand like a balloon

whilst

'sliding down through the time hyper-dimension'

". Higher-D time-slices also show, that most Cosmic real-estate exists, relative to Earth's position at an (arbitrary) Cosmic 'hyper-pole', near the Cosmic 'hyper-equator', at relative 'hyper-latitudes'

near 90 degrees

, a "

quarter turn around the rim of the cup

" of Cosmic spacetime.

(This is true even more, in full

(3+0)D

.)

Thus, most E.T.I.s who do exist, would exist, "

half way to the other side of space

", from Earth, which would probably be far out beyond our own

HV

.

 

Fig. 3 --

Repeat of previous figure, highlighting

HV

, on current time-slice of Cosmic spacetime, on 'augmented'

(2+0)D

time-slice surface.

Edited December 4, 2010 by Widdekind

[between3and26characterslon]

Is CMBR something we see at a distance or is it the sum of what we see between here and the edge of the observable universe (less matter of course). That diagram would appear to show it as a wall.

[michel123456]

 

Fig. 2 -- 'Augmented' time-slices of (2+0)D overlain. Time-slices of Cosmic spacetime do not simply "expand like a balloon", but rather "expand like a balloon whilst 'sliding down through the time hyper-dimension'".

 

I follow till there. And agree.

After this point, please clarify. Thank you.

 

Note: the Visible Universe is correctly represented in fig.1 as 2 (curved) lines. Those 2 lines represent Earth's past light cone. And the VU is the SURFACE of the cone. The inside part of the volume of this cone is not part of the Visible Universe.

Edited December 4, 2010 by michel123456

[Widdekind]

I follow till there. And agree.

After this point, please clarify. Thank you.

 

Note: the Visible Universe is correctly represented in fig.1 as 2 (curved) lines. Those 2 lines represent Earth's past light cone. And the VU is the SURFACE of the cone. The inside part of the volume of this cone is not part of the Visible Universe.

 

Yes, our VU is the (3D hyper-)surface of Earth's backwards light-cone, cutting backwards (in time) across Cosmic spacetime. The latter is 4D, and Earth's backwards light-cone is a 3D 'slice' of that spacetime fabric. Please note, that the correct term is "our VU", not "the VU", since our VU is the backwards lightcone 'slice', of global Cosmic spacetime, from Earth's particular present position. To wit, VU's vary with both space & time of 'starting inquiry'. I myself have struggled for years, to keep track, of all these details, but they can & do add up, to make or break clear comprehension of the (core) concepts.

 

The VU is indicated as a thick, solid, light blue line, on the unaugmented (1+1)D in 3D spacetime diagram. On the 'augmented' spacetime diagram, which 'overuses' the 3Ds we have available for visualization, 'augmenting' the circular loop of space (1D curved around in 2D), at each time slice, into a sphere (2D curved around in 3D) as a translucent overlay. In the 'augmented' spacetime diagram, Earth's backwards light-cone is the 'stack' of 'rings' on the surfaces of those (2+0)D in 3D spherical surfaces. The interior of those 'rings' is shaded, simply to show, the region of the universe in Causal Contact with Earth, on any given time-slice.

 

On any given time-slice, (A) in the 'unaugmented' ST diagram, the part of our VU lying on that time-slice, consists of two 0D points, on the 1D circle of space; (B) in the 'augmented' ST diagram, the part of our VU lying on that 'augmented' time-slice, consists of a 1D 'ring', on the 2D sphere of space. Similarly, in full (3+1)D in 5D (?) spacetime, the part of our VU, intersecting any given 3D hyper-sphere of space, is a 2D sphere (spherical shell).

 

Edited December 5, 2010 by Widdekind

[michel123456]

Widdekind I don't understand your "augmented" mode. In this diagram, a sphere is represented as a disk, because 3D space has been reduced to 2D. I doubt you can reintroduce 3D space without getting errors.

 

Actually I am at a point I agree with all I understand from your post. especially with this:

Earth's backwards light-cone is the 'stack' of 'rings' on the surfaces of those (2+0)D in 3D spherical surfaces.

 

My position on the subject has been throwned in the trash can some time ago. If you are not afraid you can still find it here. post #6 discuss the same diagram. I hope you will enjoy it, since I believe it is not far from your point of vue. Rules of this forum do not authorize to repost garbage.

Edited December 5, 2010 by michel123456

[Widdekind]

Widdekind I don't understand your "augmented" mode. In this diagram, a sphere is represented as a disk, because 3D space has been reduced to 2D. I doubt you can reintroduce 3D space without getting errors.

 

A 'disk' is a solid circular 2D planar shape. There are no 'disks' in the above figure. In the original, 'unaugmented' figure from NASA, space is represented by 1D, and time by 1D, and the curvature of the resulting 2D spacetime is indicated by the 3D perspective -- hence the term (1+1)D in 3D.

 

Again, 1D space, being curved, 'closes' in on itself, in a closed loop -- in 1D, space is a circle, or ring. It is hollow. By extension, 2D space, being curved, 'closes' around, into a spherical shell -- in 2D, space is a hollow spherical shell. In 3D, closed curved space is the 3D hyper-spherical surface, of a 4D hyper-sphere (or, hyper-ball). Again, it is hollow.

 

That higher dimensional, interior region, is part of Hyperspace, the higher dimensional space through which spacetime can be considered to curve. Being 'closed off', within & inside the fabric of spacetime, one could call it "Interior Hyperspace", or simply "Sub-space" -- which is what, to my knowledge, it happens to be called, in the StarTrek sci-fi show (when Federation HQ sends a subspace signal to the Enterprise, on the other side of space).

 

This is an important point to keep clear for comprehending ST diagrams:

 

• the Visible Universe (VU) is the backwards light-cone, it is a 2D spherical shell (centered on Earth) at every time-slice, so that the "time-stack" of the 2D spherical shells is a (2+1)D "onion" of such shells, "blurred over" across the time dimension (a little like a deck of cards "smeared over" to the side)
  
• The Causally Connected Universe (CCU) is all the spacetime interior to the VU / lightcone, it is the "time stack" of the 3D (hyper-spatially warped) "spheres" (or "balls") out to the VU (hyper-)surface, so that the CCU "time-stack" is a (3+1)D section of space-time
  

I suppose one could call these the "Seen Universe" and the "Known Universe", or some such. Note that the book Geometry, Relativity, & the 4th Dimension says that, since mass curves space, and since the combination of matter & anti-matter must yield flat empty space (after mutual annihilation), then matter & anti-matter must cause spacetime to curve in opposite hyper-spatial directions. To wit, if matter in a closed Cosmos causes spacetime to "pinch" outward, into Exterior Hyperspace ("convex hyperspatially outward"), then anti-matter would "pinch" inward, into Interior Hyperspace (Subspace). The impression is given, that, since a closed Cosmos has a "baseline preference" (my words) for being "convex outward / concave inward", that that preference translates into the observed preference for matter over anti-matter, seemingly suggesting a kind of confirmation of the closure of the Cosmos.

 

 

Edited December 7, 2010 by Widdekind

[michel123456]

A 'disk' is a solid circular 2D planar shape. There are no 'disks' in the above figure. In the original, 'unaugmented' figure from NASA, space is represented by 1D, and time by 1D, and the curvature of the resulting 2D spacetime is indicated by the 3D perspective -- hence the term (1+1)D in 3D.

 

Again, 1D space, being curved, 'closes' in on itself, in a closed loop -- in 1D, space is a circle, or ring. It is hollow. By extension, 2D space, being curved, 'closes' around, into a spherical shell -- in 2D, space is a hollow spherical shell. In 3D, closed curved space is the 3D hyper-spherical surface, of a 4D hyper-sphere (or, hyper-ball). Again, it is hollow.

 

That higher dimensional, interior region, is part of Hyperspace, the higher dimensional space through which spacetime can be considered to curve. Being 'closed off', within & inside the fabric of spacetime, one could call it "Interior Hyperspace", or simply "Sub-space" -- which is what, to my knowledge, it happens to be called, in the StarTrek sci-fi show (when Federation HQ sends a subspace signal to the Enterprise, on the other side of space).

 

 

This is not the way I understand the diagram.

 

What I understand goes like this:

 

In real life (not in any diagram) we observe the Universe all around us. Let's call that the Visible Universe in order to have a common ground. This VU is a sphere all around us, in which we can pin all visible astral objects. If we choose ONLY the astral objects that correspond to a certain distance D, we can pin all these objects upon the surface of a sphere of radius D. This spherical surface will correspond also to a certain period of time T in the past. See right part of figure1 below, distance D is represented by the blue arrows inside of a sphere, and all arrows have the same length equal to the radius of the sphere.

fig.1

 

The projection of all points of this sphere in 2D is a disk containing the flatten image of all astral objects that were upon the surface of the sphere. This Disk corresponds also to time T. The superposition of all times between the Big Bang till now are represented by the superposition of all such disks in the original diagram.

Edited December 7, 2010 by michel123456

[Widdekind]

I respectfully disagree. The surface of sphere is 2D, so its "down-projection", to 1D, must be a 1D object -- to wit, a line. The "down-projection" of a 2D spherical shell, is a 1D linear ring.

 

Your diagram looks to me, like it projects the 2D surface of a spherical shell, onto a 2D disk-planar shape. That is not really a down-projection, which would lose 1 full dimension (-1D).

[Widdekind]

Can I ask, is it possible, that 'global' Cosmic spacetime is 'spinning', rotating around the central 'time-like' axis ??? What if the 'original singularity' had had a rotational spin ???

 

Edited December 8, 2010 by Widdekind

[michel123456]

I respectfully disagree. The surface of sphere is 2D, so its "down-projection", to 1D, must be a 1D object -- to wit, a line. The "down-projection" of a 2D spherical shell, is a 1D linear ring.

 

Your diagram looks to me, like it projects the 2D surface of a spherical shell, onto a 2D disk-planar shape. That is not really a down-projection, which would lose 1 full dimension (-1D).

 

From Wolfram Mathworld: Spherical shell:"A spherical shell is a generalization of an annulus to three dimensions. A spherical shell is therefore the region between two concentric spheres of differing radii." The same exactly in Wikipedia

It looks to me a spherical shell is a 3D object.

 

Can I ask, is it possible, that 'global' Cosmic spacetime is 'spinning', rotating around the central 'time-like' axis ???

 

 

Don't forget that another observator anywhere else in the Universe is supposed to observe the same thing as we do. The rotating motion is not easily compatible.

And first of all we have to agree on what this diagram represents.

 

The weird thing is that basically I agree with your points.

Let's try to find a common ground:

Your point comes from this (from Wiki):

"In higher mathematics, a careful distinction is made between the sphere (a two-dimensional spherical surface embedded in three-dimensional Euclidean space) and the ball (the three-dimensional shape consisting of a sphere and its interior)."

It is spherical shell of zero thickness.

Let's go with it.

In order to reduce this "two-dimensional spherical surface" in a circle, you can go like this:

fig.2

In this fig.2, it is not a projection anymore, but a section of the sphere. The good thing is that radius is conserved and can be measured accurately on the reducted image. The bad thing is that we have lost most astral abjects.

There is a way to conserve all objects, but I need time to make the diagram.

Edited December 8, 2010 by michel123456