Effort to get us all on the same page (balloon analogy)

RayYates

As an interested layman, earlier in this thread it helped me get my head around the balloon analogy when I was reminded that the 2D surface of the balloon is the entire universe. There is no inside or outside so there is no "center". Rather think of the inside of the balloon as the past, the outside of the balloon is the future.

Everything, energy, matter, space and time exist ONLY on the surface of the balloon which extends in 3 directions of space and 1 of time. That 4D space time may be closed (wrapped around on itself; exit one side you come back in the other) so there can be no CG calculation, or open (infinite) and again there can be no CG calculation.

I hope that helps a bit.

As for "What is expanding?", as I understand it, empty space has a tiny amount of energy (vacuum energy) so small that compared to gravity, it has only recently been calculated. Gravity slowed the expansion of the universe until the amount of space grew large enough that vacuum energy was able to overcome gravity between galaxies and the expansion began to accelerate.

Inside a galaxy, gravity is large enough that the galaxy is self contained and does not expand. Galaxy clusters also do not expand because they are close enough that they are gravitational bound.

Think of a rising loaf of bread. The air pockets in the bread expands, not the flour.

Is vacuum energy creating MORE space or is space stretching? Is the a meter the same between galaxies as outside galaxies. I think the consensus is that it is creating more space, otherwise the speed of light would depend on the space it was traveling through. There are some people who argue against that idea, but that is another discussion.

bapowell

Keep in mind that the expansion of space is a classical phenomenon, one that we should not need quantum mechanics (and, hence, vacuum energy) to understand.

RayYates

Sorry, I don't know what that means.

bapowell

I just mean that the expansion of space occurs as a solution to the classical equations of general relativity, i.e. the solution exists for classical matter sources (like, say, a matter-dominated FRW universe.) So, we should be able to understand the expansion of space without recourse to the vacuum energy of quantum fields -- expansion exists even in perfectly classical universes.

RayYates

Yes I see what you mean but does that also explain the observed increase in the rate of expansion. That's really what I was trying to get to.

bapowell

I see, no it doesn't. By "expansion" I took you to mean just general expansion, not the special case of accelerated expansion.

marcus

@Ray,
I thought that part of your comment was well put and quite helpful, so wanted to emphasize it. Just because we use the balloon as a 2D toy model doesn't mean that actual 3D space has to be closed and finite. Space can be open and infinite. But as you said in either case one can't expect 3D space to have a central point.
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I started a thread attempting to explain, in basic language and very briefly, the Cosmic Event Horizon (abbr. CEH). It may be useful to work it in here, as part of understanding the expansion process. Here's a second draft --- I corrected the title and added some material.
The existence of the Cosmic Event Horizon (CEH) depends on the fact that the scalefactor curve a(t) has a slope a'(t) which (although gradually decreasing for roughly the first half of the expansion age) is now slowly increasing. The scalefactor curve is very gradually getting steeper, and is expected to continue doing so.

Picture: http://ned.ipac.caltech.edu/level5/M...s/figure14.jpg
the dark solid curve labeled (.27, .73).

This has the interesting consequence that the most distant galaxy which we could, today, send a message to and expect it to arrive is only about 16 billion lightyears away. We currently see galaxies much farther away than that, and if it were not for this gentle acceleration effect we could in principle flash messages which would eventually reach them. But because of the slight acceleration they are actually "beyond our event horizon". And it works both ways: they, as of today, could not send information to us. If a star exploded today in one of those galaxies, we would never see it, no matter how long we waited.

I want to try to explain where this figure of 16 billion lightyears comes from. This is a first attempt and comments are welcome. It goes in 8 steps starting from the most basic concept. For some readers much of this will be review:

CMB rest: There is an FAQ entry for this. An observer at rest relative to the CMB sees approximately the same temperature (of the ancient light) in all directions. There is no Doppler hotspot which would indicate that he or she was moving in that direction. It's like being at rest with respect to the ancient matter when it was more uniformly spread out, or with respect to the expansion process itself.

Universe time: Time as clocked by observers at CMB rest.

Proper distance at a particular time t: What you would measure by any conventional means (radar, tape measure...) if you could stop expansion at some given moment of universe time. Stopping expansion gives you time to measure---the distance won't change while you are sending the radar pulse, for example.

Scale factor a(t): This curve plots the expansion of distance as an increasing function of time. It is normalized to equal 1 at the present time. a(now) = 1. Back when distances between stationary observers were only half what they are today a(then) = 0.5. The slope a'(t) has not been constant so it's convenient to have the curve as a record of expansion history. Picture: http://ned.ipac.caltech.edu/level5/M...s/figure14.jpg
The dark solid curve labeled (.27, .73) is the one to focus on.

Fractional rate of increase of a(t): A good handle on the rate distances are increasing is the fractional or percentage increase over time. Currently the scalefactor increases by about 1/140 of one percent per million years. So any largescale distance (e.g. between galaxies free of each other's gravity and each approximately at CMB rest,) will increase at that rate. (More precisely using the latest data 1/139 of one percent per million years.) The math expression for this rate, at any time t, is a'(t)/a(t). This is the absolute increase at that time, divided by the current size at that time, IOW a fractional or percentage increase rate.

Hubble rate H(t): By definition H(t) = a'(t)/a(t), just another name for the fractional rate of expansion. The current value of the Hubble rate is denoted H_o. Or you could say H(now), or a'(now)/a(now). It would all mean the same thing. Mathematically it is a fractional rate of increase the current value of which is 1/140 of one percent per million years. (Or 1/139 using the latest data)
That's the rate that distances (between observers at CMB rest) grow, at present. Using proper distance and the universe standard timescale.
In common astronomy units it is 70.4 km/s per Mpc. 70.4 km/s is the speed a distance of one Mpc is growing.
The Hubble rate is slated to decline in future to sqrt 0.728*H_o ≈ 60 km/s per Mpc.

Hubble radius c/H(t): This is the radius within which proper distances increase at speeds less than c. If a photon is trying to get to us and can manage to get within this radius then it will begin to approach. The photon's own speed is then faster than the remaining distance is increasing, so it can make progress towards us and narrow the gap.
The google search window doubles as a calculator. Try using it to find the current Hubble radius in lightyears. I invite you to copy this into the search window:
1/70.4 km/s per Mpc
When you press return, the calculator will say 13.9 billion years.
Multiply by c and you obviously get 13.9 billion lightyears.
This is the current Hubble radius.
Photons within that radius are going to make it.

Cosmic Event Horizon ≈ c/(sqrt 0.728*H_o) ≈ 16 billion lightyears.
Photons heading for us can still make it even if they are OUTSIDE the current Hubble radius as long as the radius itself is increasing fast enough and reaches out and takes them in.
What would make c/H(t) increase? The denominator H(t) decreasing would. The Hubble expansion rate has decreased sharply in the past which is why we can see such a lot of stuff that we know is receding faster than light.
But according to the standard cosmic model H(t) though still declining is not expected to go below sqrt(0.728) of its current value.
It is expected to level out at (sqrt 0.728)*70.4 km/s per Mpc
So what will the Hubble radius be then?
Try putting this in the google window
c/(sqrt 0.728 *70.4 km/s per Mpc) in lightyears
You will get the longterm value of the Cosmic Event Horizon (abbreviated CEH)

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The number 0.728 is technical and hard to explain, so I've had to put it in *ad hoc*. It represents a constant VACUUM CURVATURE contributing to the near flatness of space, which would otherwise be negatively curved (e.g. triangles adding to less than 180 degrees). Without such an inherent constant curvature bias, (or cosmological constant) the current density of matter/energy would only be 0.272 (or about 27%) of what was needed for the observed degree of flatness. So (although in my opinion it's a bit confusing to think this way) the number 0.728 could be imagined as a fictitious energy contribution making up the rest of what would be needed without a cosmological constant.
The square root of 0.728 gets into the picture for technical reasons when we want to talk about the longterm value of the Hubble rate, the level below which it is not expected to decline (because of the acceleration in the scalefactor.)

megacal

Ray,
yes. thanks for that relatively concise explanation...I think I grok it a bit better (but don't ask me to explain it). I'm used to things having a physical center or center of gravity,
i.e. I think in 3D & have a concept of time (though maybe it's an illusion?).

When out in the desert on top of a "massive" boulder, I know it could easily crush me, but
then I realize all I see is mostly empty space, and it's very disconcerting!

Marcus,
thanks for explaining the various constants and parameters, though I don't have the math skills to put them together. It would be very helpful though, if you could do a video tutorial
showing us the equation(s) and how you derive the answer. I think even I could follow that.

Just a thought.

RayYates

marcus. I get it! I've read the entire posting twice and the concept has become clear. Thank you.

The question I'm currently grappling with is, "What is the balloon? What is space?"

I get that space time is stretchy, bendable, compressible. In regions of higher mass time moves slower, so conversely in the regions between galaxies time moves faster. So what is space? Is space inside an atom the same as the rarefied space between galaxies clusters.

I've seen it theorized that on a scale many times smaller than sub atomic particles, space is granular like some twisted up dimensions tied into a knot and arranged on a grid. Is the VACUUM nothingness of space really something?

Farahday

Marcus -
EXCELLENT explanation of expansion. It does; however, leave me with the same pertinent questions raised by RayYates:

Unless the dispersion of the elemental particles that physicists deem to comprize the observable cosmos is a local event, then the entire cosmos, itself, is expanding.

Space 'exists' - if it did not we would all be set ablaze by Sol. Just because our technology seems unable to determine its composition doesn't mean it doesn't exist - and an infinite expanse of space sans fundamental particles would require no less justification than an infinite expanse of fundamental particles sans space.

If the cosmos (everything that exists everywhere) is expanding then either existing space must be increasing in volume (which would lead us to believe it is decreasing in density) or new space is being manufactured (conjured into existence, if you will).

How would you address this issue?

CCWilson

Isn't another way the balloon analogy helps is to demonstrate how spacetime is different from three dimensional space? Most people picture the big bang as an expanding balloon, except with all kinds of stuff spread within it. If that were the case, then our universe would be unbounded - there would always be empty space beyond any position specified which could be filled later. But if someone can get his mind around the idea that three dimensional space is represented by the 2D surface of the balloon, it makes sense that moving or shining a light in any direction will still be within the limits of the spacetime of our universe.

Question: Although at this point I assume that a beam of light sent out could never theoretically make the circuit and return, because of the extreme expanision of the universe, weren't there times when a beam of photons could have circled around the smaller spacetime at that point and returned to (non-human) sender?

RayYates

You put your finger on the point exactly.

marcus

The standard view is that density is decreasing. The "steady state" idea of constant density went out of style by around 1960-1970, anyway a long time ago.

Cosmologists pretty much all accept 1915 Gen Rel as the currently best most reliable equation for how geometry/gravity evolves and is influenced by matter. Virtually all research is based on the 1915 Gen Rel equation.

According to that picture there are distances between real physical stuff, events etc. The network of distances (angles areas etc) is geometry. But distances are not made of anything, they are RELATIONS, not material substance.

In 1915 Einstein put it concisely: Dadurch verlieren Zeit und Raum den letzten Rest von physicalische Realität. (thereby lose time and space the last vestige of physical reality.)

The geometric relations among things are not a physical substance. "Space" is a word which does not refer to a material. It refers to a bunch of geometric relationships.

So it's misleading to talk about it being "manufactured".

And of course density declines as physical stuff gets farther apart.

You got it! Shining a light in any direction within our 3D world is like the 2D creatures shining a light in any direction along the curved 2D (infinitely thin) world they live in. It stays within the defined limits.

You asked a good question. Assuming the finite volume sphere-like model, could a light beam ever have gotten around, made the full circuit? The standard answer is NO. At least after the first fraction of a second I'm not sure about the first few instants. there are different scenarios. But apart from some very early business I can only speculate about, expansion has ALWAYS been too rapid for that to have happened. If something had made expansion pause long enough, sometime in the past, it could have happened. But it didn't. Or if expansion had been much slower than we think it was. But the standard reconstruction of expansion history implies that it was always outpacing the ability of a flash of light to make the full circuit.

It has been calculated what the maximum distance some photons, a flash of light, could now be from the sender, if the flash is sent at start of expansion or as close to then as you like.
So the flash has been traveling for the whole 13.7 billion year history of expansion. (Today some cosmo models go back before start of expansion into a contraction phase, but we arent including that, just the usual 13.7 billion year expansion age.)

That maximum distance is called the PARTICLE HORIZON and it is calculated to be about 46 billion lightyears. The farthest a flash of light can have gotten (with the help of expansion) in the whole 13.7 billion year history is only 46 billion lightyears. We're fairly sure now that the circumference of the entire U, if it isn't actually infinite, is considerably bigger than that, by over a factor of 10.

There was something in a NASA report from the WMAP mission about this, by a bunch of authors: Komatsu et al. I can get the link if you want. Maybe somebody else has something more recent, I'm not entirely sure and would be happy to be corrected if there's some better information.

CCWilson

I'm sure this is a silly question, Marcus, but if indeed shortly after the big bang photons and particles could return to sender, because initial expansion hadn't been fast enough to disallow it, is it possible that this would have caused some sort of chain reaction, and could that have been the cause of the hyperinflationary period that is supposed to have occurred?

marcus

To recap the main content of this thread, the balloon analogy is to help understand and imagine the GEOMETRY of expansion. Not the physics. It helps to watch the animation carefully
http://www.astro.ucla.edu/~wright/Balloon2.html
notice the galaxies stay in the same place while getting farther apart.
The photons always move at the same speed, say a centimeter per second depending on the size of the image on your computer screen.
In the analogy, all existence is concentrated on the infinitely thin 2D sphere.
The distance between two galaxies can be increasing faster than light (faster than one cm per second) and yet a photon may be able to get from one to the other. You can see this kind of thing happen even before you understand conceptually how it happens. And the analogous thing happens in the real 3D universe. (The distances to most of the galaxies which we observe today are increasing >c and were increasing >c when they emitted the light which we are now getting from them. Watch the animation to get an intuitive feel for these things, which may at first seem paradoxical.
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Since the balloon thread is about the geometry of Hubble law expansion I will say a bit about Hubble law. If you are a beginner you should experiment with one of the online cosmology calculators, like this one:
http://www.einsteins-theory-of-relat...ocalc_2010.htm
Put various redshifts in and study the results. Redshift z=1 for nearby galaxies, z=9 for the most distant galaxies confirmed so far, 1090 or thereabouts for the ancient light (the CMB or background).
Put sample redshifts in and find the corresponding distances and the rates those distances are increasing. It will also tell what the Hubble rate was in the past, back when the light we are now seeing was emitted.

The most recent official figure for the current Hubble rate itself is 70.4 km/s per Mpc. You are encouraged to learn to calculate with it. For example, as exercise paste this into the google search window (which doubles as a calculator) and press return:

70.4 km/s per Mpc in percent per million years

Google calculator knows how to express a rate of change as a percent per million years.

You will get 1/139 of one percent per million years.
It will actually say "0.00719973364 percent per million years"
but 0.0072 is very nearly the same as 1/139

That is the percentage rate that distances (beyond the immediate neighborhood of our group of galaxies) are currently growing. According to standard cosmo picture the rate is destined to continue declining approaching about 1/160 in the limit.

1/139 percent per million years is the same as
a millionth of a percent in 139 years.
So if you want to picture how rapidly distances in our universe are expanding think of a distance, and think of waiting 139 years, and then finding that it has increased by a millionth of a percent.
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The socalled HUBBLE RADIUS is the distance which, today, is increasing at exactly the speed of light. It is 13.9 billion lightyears. It's just the same number as 1/139 but flipped, with the decimal point moved.
Saying that according to standard model 1/139 will go down to around 1/160 in the longrun is the same as saying that the Hubble radius which is now 13.9 will increase to 16 billion lightyears in the long term. But these are glacially slow changes really unimaginably slow. So we think of the Hubble rate as constant, for the time being. (It has been much larger in the past, though.)
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There are a lot of questions to ask about the Hubble rate. Notice that it is a fractional rate of distance increase, not an absolute rate. How can the fact that it has been and will be declining be compatible with the talk one hears about "acceleration"?

Well, fractional or percent rate is not the same as absolute rate. If you take a given distance and plot the CURVE OF WHAT IT WILL BE IN THE FUTURE you will find the curve has increasing slope. That's true even though at every future time the PERCENTAGE INCREASE will be getting less and less. Percentage increase is not the same as slope. One can be steadily decreasing while the other increases. Your bank savings account can grow by an increasing absolute dollar amount each year even though the bank is gradually reducing the percentage interest they give you, because the PRINCIPLE is larger each year. Just how it is, no contradiction.
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There are still lots of questions about Hubble expansion law. It involves distances now and the rate they are increasing now. Likewise at some earlier moment in time, or later. How is that "now" instant defined? How are distances defined? (Imagine stopping the expansion process everywhere at once, at a definite instant to make it possible to measure distances without them changing while you measure them. How is "everywhere at once" defined?) We use the idea of observers at CMB rest. There's an FAQ about that in the FAQ section.
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Still lots of questions that can and should be asked. But I hope that some readers will try using the google calculator, watch the balloon animation observantly, and experiment with one of the online redshift calculators. Jorrie's for instance:
http://www.einsteins-theory-of-relat...ocalc_2010.htm

marcus

I'm not sure it is a silly question. I'm not an expert on the very brief inflation era that is widely supposed to have occurred. It's still speculative and there are a variety of scenarios.
One type model that is gaining attention involves a BOUNCE. In the main model of this type you get a brief period of faster than exponential growth of distances. Normally what is called "inflation" by cosmologists is exponential and slightly slower growth.

a(t) = e^Ht with H either steady or slowly declining.

In stark contrast to this, in socalled Loop cosmology you get this but with H increasing very rapidly to extremely high (Planck scale) values and because this is faster than the unsual exponential growth called inflation it is called "superinflation" by Loop cosmolgy researchers. I don't remember hearing the term "hyperinflation" in cosmology.

For me it is completely speculative what conditions could have been like and what could have been happening at such extremely high densities. In Loop cosmology, according to their equation model, gravity becomes repellent at near Planck density, which is what causes the bounce. It is a quantum gravity effect. Quantum nature doesn't like to be pinned down too tightly, so resists extremely dense compression.

One option is not to try to understand the very beginning of expansion but only start thinking about it a few blinks after it started. Wait until there is more agreement among the real experts before trying to understand. sorry so unhelpful.

BTW CCWilson, I'm curious to know. Have you done any of these things?
Watched the wright balloon animation
http://www.astro.ucla.edu/~wright/Balloon2.html
Experimented with the cosmology calculator
http://www.einsteins-theory-of-relat...ocalc_2010.htm
Read the LineweaverDavis SciAm article
http://www.mso.anu.edu.au/~charley/p...DavisSciAm.pdf
I'd be curious to know any impressions, what you may have learned etc.

CCWilson

Marcus, I had previously done the calculator and animation.

The problem with the cosmology calculator is that the terms - the omegas and the Hubble constant and even some of the calculated results - were unfamiliar or unclear to me, so it wan't that helpful. Would be much improved for laypeople with instructions and definitions.

The balloon animation was kind of interesting but not compelling. I'm not sure it added to my understanding, but I already had a fair grasp of it, having ruminated on the balloon analogy before, which was tremendously helpful; I'd have been lost in trying to understand universe expansion without it. One problem for me with the animation's redshift changes was that we are not outside the sphere watching the whole thing, our two-dimensional selves are presumably somewhere on the balloon skin, in which case the redshift for us should not be the same for all the galaxies and other sources of photons, right?

I just now went through the "Misconceptions about the Big Bang" and thought it was great. I learned some new things. One is that the red shift is not Doppler but related to expansion of space, which sort of makes sense. Question: When Hubble noticed the red shift, from which he deduced that the universe was expanding, was he aware that it was not, strictly speaking, the Doppler effect? In fact, was he aware at first that it indicated expansion of space time, or did he think it meant that galaxies were moving away from each other within a three dimensional universe?

Also, it made clearer the concept of how some galaxies can be moving away from us faster than the speed of light. The idea that we can see some of those galaxies moving away from us faster than the speed of light, I'm still working on that one.

These ideas are a lot for anybody to get our minds around, especially laymen. But the more you read such articles and think about them, the more sense they make. Are there people who can actually think in four dimensions, or do even you smarties have to rely on balloon analogies and such, and are resigned to doing the mathematical calculations without having a clear visualization in your minds?