|Dec28-08, 10:10 PM||#69|
Effort to get us all on the same page (balloon analogy)
Google "wright balloon model". Ned Wright is a good teacher. his whole website is a useful resource. He usually has two balloon movies and its worth watching both.
All this stuff we are talking about is post-inflation expansion. If inflation happened it was by some exotic not-understood mechanism way early, like in the first second.
We are talking about stuff beginning at year 380,000 which is LONG past the end of inflation.
BTW there is an issue with arithmetic. If you have 13.7 billion years and you take away one million years, what do you have? You have 13.7 billion years.
That is, actually 13.699 but it rounds off to 13.7.
Likewise 13.7 billion minus 380,000 is still 13.7 billion. Even more true this time because 380,000 is less than a million.
So we are talking about an episode in history lasting from year 380,000 to year 13.7 billion, during which distances gradually increased only about 1000-fold, more precisely 1090-fold.
That period lasted about 13.7 billion years and I predict that if you watch the Ned Wright movies several times you will easily understand how at the end of 13.7 billion years a photon can find itself 46 billion lightyears from its point of origin.
Expansion makes the distance that the photon has already traveled grow like money you put in the bank, in your savings account, at a percentage rate. The rate actually changes over time but that is of secondary importance to what I'm saying.
You can see this happening in the movies. The photon travels a certain ways on its own, at the usual speed of light (say one millimeter per second on the balloon model). But because of expansion after a while it is a long long ways from where it started.
I think you are getting this, or have already gotten. It has nothing to do with inflation.
Positive and negative interference effects are something else, two beams of monochromatic light (both the same frequency) meeting on a projection screen. CMB is not monochromatic. It is a big mix of frequencies. Not to worry about interference.
Maybe inflation expanded some portion of the universe from the size of an atomic nucleus (say 10^-15 meter) to 100 million kilometers. That is the expansion factor the inflation scenario-makers typically attribute to an inflation episode. That still is not even the radius of the earth's orbit!
After inflation, what is now the observable universe (radius about 46 billion ly) is still not very large. Inflation, if it happened, would have increased size by a large factor, typically they use a figure of e^60. But if you start with something very small to begin with, a large factor doesn't mean the result is necessarily large in absolute terms.
I wouldn't bother trying to include inflation in your visual picture. Just start some time after the universe has attained some reasonable size----like for example on the order of 42 million ly.
So we have been receiving CMB radiation steadily for the whole 13.7 billion years. As time goes on, the glow emitted by more and more distant hot cloud comes in. Because the cloud was uniformly distributed. So the radiation would not have been sporadic.
|Dec30-08, 03:41 AM||#70|
I get that photons travelling at the speed of light can find themselves at a distance from their point of origin which, due to expansion, is further away than lightspeed alone could have achieved, and that they're destined to never exceed the speed of expansion, leading to an ultimately black and cold universe. What I was trying to do was point out challenges with the use of the balloon analogy.
Firstly, in offering a 2D construct in the form of the surface of a balloon, that surface can be misinterpreted as an expanding boundary to the universe, undermining all sorts of unbounded models. And then, of course, balloons don't expand forever; they burst, so, in looking at Wright's animation, or even just a static drawing, the balloon will (perhaps subliminally) be perceived as somehow finite in its expansion. And if expansion is finite, and light keeps travelling, light will eventually circle the balloon. I'm not saying such thoughts are of any use; quite the contrary, they merely muddy things.
Balloons tap into the layman's wealth of experience with birthday parties, sore lungs, and aching fingertips. It's why people look at the balloon as being the shape of the universe and then, quite logically and incorrectly, see the centre of the balloon as the centre of the universe. And I circle back to my earlier point that what is needed (what I need) is a proper analogy for the shape of space-time. Something that will let the balloon analogy be used purely to convey the concept of swelling distances between big things that are more or less at rest.
|Dec30-08, 05:12 AM||#71|
Those who take Ned Wrights tutorial as gospel will not take kindly to ditching his balloon model, even if some see its limitations.
I got short shrift when suggesting a more versatile model/analogy for which I was chastisd for calling a mechanism (though in my book even an expanding balloon is a mechanism).
If you take expanding foam as a more versatile analogy and you still want to think in 2D terms, simply take a slice through it; and the foam won't burst like a balloon!
|Dec30-08, 06:27 AM||#72|
I've no desire to ditch the balloon analogy. The stated objective of this thread is to: "...simply discuss the balloon analogy. Get clear on it. Find out any problems people have with it, if there are some." (refer quote below)
Maybe what we need to end up with is:
* a clear statement of what the analogy is (which several of the early posts have already done);
* a few pertinent elaborations (eg, someone already noted that inside the balloon was the past and outside the future)); and then
* qualification of the analogy by noting what it isn't (perhaps the top five misconceptions). Of course, the pursuit of precision necessitates no such thing, but you need to ask yourself: when drawing an analogy, do you want to be precise or do you want to be understood?
|Dec30-08, 07:32 AM||#73|
In your post you mention several real limits, even liabilities, of the balloon analogy. I certainly agree it has its drawbacks.
One thing you made oblique reference to but didn't dwell on is the idea of being at rest relative to the CMB, or the matter that emitted it. Staying at the same longitude and latitude on the balloon surface provides something concrete corresponding to that. Helps assimilate the apparent paradox that things remain at rest while distances between them increase. I've highlighted a few things the balloon picture helps conceptualize.
In several instances I very much like your choice of words.
So now let's say we've learned all we can from the balloon model and it is time to move on. Where do we go? For some people, a reasonable next step would involve trying stuff with the cosmology calculators. Others might get more out of imagining another material analog. You may be familiar with one or more ways of picturing 3D expansion. Basically carrying over features of the 2D balloon model into 3D. One hears about rising bread dough--specifically raisin bread dough. A few happy souls proceed directly from the balloon to the Friedmann equations.
BTW have you googled "wikipedia friedmann equations"? Curiously, visualizing Alexander Friedmann as he was around 1922 can be a step towards acquaintance with his equations
I didn't see your latest post until just now. This is a valuable suggestion:
I haven't woken up properly. I'll get some coffee and think about what we could do next. The thread doesn't need to focus solely on that one analogy. I'm wondering if there is a kind of bridge---a way to segue to the scalefactor a(t) and the differential equations that describe how it grows. If space actually were finite, and actually were the 3D cousin of a 2D balloonsurface then in a certain sense a(t) would be proportional to or somehow related to the radius of curvature, the radius in an imaginary extra dimension. Or should we not go there? Desparate for coffee.
|Dec30-08, 12:00 PM||#74|
Just to be sure everybody realizes: we don't yet know whether space is finite or infinite volume. Any analogy has limitations and a critical flaw of the balloon picture is that it gives people the impression that we know space has a finite volume.
It might have, and space might be the 3D analog of the 2D balloon surface. Then if you could freeze expansion you could shine a lightray in any direction and after a long time it would circle around and come back.
But space might also be infinite volume and even, if you overlook minor local irregularities, it might correspond to conventional Euclidean space---the jargon term is "flat".
So there is a mental hurdle everyone has to hop over which is how to imagine infinite Euclidean 3D space expanding. Well it's not really much of a hurdle. It just means that the distances between stationary points are all increasing.
To approach it gradually first try to picture the 2D Euclidean plane expanding, with a grid on it showing points at rest with respect to CMB. So it is like graph paper with the squares constantly getting bigger.
The 2D Euclidean plane expanding is what you would see in the balloon model if the balloon was really vast, so big that the piece you were looking at seemed perfectly flat to you.
So the trick is to stay uncommitted mentally. Keep both images alive in your head. Because we don't know yet which one is closer to nature.
The finiteness issue is closely related to curvature. Anyone who is interested can keep an eye on the current state of knowledge, which changes as new astronomical data comes in.
(supernovae, galaxy and cluster surveys, CMB temperature map analysis...)
There is a nasty sign convention where what they tabulate and report is the negative of what intuitively corresponds to curvature. They report Omegak where if it is zero then we are in the flat Euclidean case and if it is negative then we are in the spherical, positive curved case, with finite volume. So the 2008 data gave a 95% confidence interval of [-0.0179, 0.0081]. (table 2 in http://arxiv.org/pdf/0803.0547 )
The unintuitive sign reversal is an historical accident, a kink in the notation. My personal accommodation is to think of a private "Omegacurv" = -Omegak. And then the 95% confidence interval for the private Omegacurv is [-0.0081, 0.0179].
Which is roughly [-0.01, 0.02]
So nature is somewhere in there, and future measurements will narrow it down some more (the Planck observatory is scheduled for launch in 2009) and if nature's number is zero then space is infinite volume and looks flat at large scale.
And if it's positive then we're in the positive-curved finite volume case. It still looks nearly flat, because the radius of curvature is so large, but it is nevertheless finite.
In neither case are there any edges or boundaries, the standard cosmo model is simple in that respect.
|Dec30-08, 03:06 PM||#75|
Thanks for the interesting thread.
There are some things that confuse me about the expanding universe. For one thing, dark energy is talked about as being the mechanism to explain the acceleration of the expansion of the universe, but if there's one thing that I'm getting from the expansion of the universe, it's that it's independant of matter and does not interact with it. If this were not so, then the expansion would be limited to sub-luminal expansion rates since nothing can travel faster than light. It can expand faster then light because it works outside the physical geometry (and all the matter it contains) of the physical universe. So how can "energy" as we know it (the energy as defined by e=mc^2) be used to explain the expansion of non-physical space. A good analogy is to imagine being a ghost and trying to interact with physical reality by moving a plate across a table for witnesses to observe. It can't happen because of the un-connected nature between physical energy and the (non-physical)expanding universe. Or is dark-energy by definition something that is outside our physical universe?
The other thing that confuses me is how the wavelength of light can be affected by an expanding universe. According to quantum mechanics, light, once observed (as in a spectrograph while looking at red shift) collapses into photons. Not only that, but according to dual slit experiments that focus on delayed time anomolies, once observed, a wave not only collapses into a photon, but will suddenly always have been a photon throughout it's entire lifetime from the time it was released from it's source. Can an expanding universe have the ability to change the wavelength of a single photon? For a photon changing it's wavelength means changing it's energy, so this implies that an expanding universe has the ability to change the energy level of single photons. How is this explained?
All very strange stuff indeed.
BTW, I like the expanding ballon analogy better then the raising loaf of raison bread as the ballon easily demonstrates that nomatter where you are on the surface of the balloon, you can look in all directions and see the universe expand at the same rate from your point of view. Not so with the raising bread where looking toward the center of the bread will show a different rate of expansion then looking outward toward the surface of the bread. The balloon analogy is great!
|Dec31-08, 01:35 PM||#76|
BTW I'm curious to know what of this thread you may have read. Has it gotten too long? Do I need to summarize and restate what was said in the first 5 or 10 posts?
I'm not sure what you want explained. Whether I can explain depends on what it is. I think perhaps you are wondering how it is that "... an expanding universe [has] the ability to change the wavelength...?"
One way to think about it is it's just what happens with Maxwell's equations when the geometry is dynamic.
With a wave equation, each new cycle is determined by the E and B field geometry of the previous cycle, which has now been slightly extended. The effects of the slight expansion, the changing geometry, accumulate.
Expansion does not affect things that are bonded together like atoms in a crystal or a metal ruler, or which belong to bound systems like our solar system and local group of galaxies. But the wave crests of a wave propagating thru space are not bound together and they occur in the context of an an expanding geometry, so nothing prevents wavelengths from becoming extended.
There are other ways to think about how redshift happens, but they all amount to different ways of mathmatically parsing the same thing.
Just a side comment: conservation laws typically depend on the symmetries of a static geometry---one must be cautious about invoking them where they don't apply.
Probably the most important thing is it gives a visible analog to being at rest with respect to the CMB, or the expansion process itself. The dots representing clusters of galaxies stay at the same longitude and latitude, reminding us that they are stationary with respect to CMB. At rest with respect to the universe's expansion process, while distances between them nevertheless increase.
This is basically why the distances can increase at rates many times greater than c without anybody "traveling" faster than c.
Things at rest do not travel.
|Jan15-09, 05:51 AM||#77|
If my understanding is correct, GR speaks not of space or time but of spacetime. Is is spacetime which is expanding? If so, should not only distances be increasing, but also time intervals between events?
I have difficulty seeing the implications of this. And it is probably wrong but I'd like your help to explain to me my error. If any.
|Jan15-09, 09:51 PM||#78|
The observer's own personal clock, the proper time of that particular observer, gives one possible timeline and slicing of spacetime into spatial slices.
So GR does after all speak of space, and does speak of time. As experienced by some given observer.
Cosmology involves some additional simplifying assumptions---uniformity---sameness in all directions---that make GR boil down to a couple of simple equations which Alex Friedmann got first, around 1923, so they are called the two Friedmann equations. But they are really the Einstein equation of GR radically simplified by assuming a kind of democracy. We are not in a privileged location, there is no privileged direction, all locations and directions are more or less equal.
In GR geometry is dynamic, geometric relations change. But without cosmology's additional assumptions you don't always necessarily get an overall pattern of expansion. All kind of changes can be happening depending on the distribution and movement of matter. The picture is simpler if you go over to cosmology.
It is cosmology where you have this approximately uniform overall pattern of largescale distances increasing a certain percentage each year, or each million years. The pattern is called Hubble Law. It doesn't affect smallscale distances like within our galaxy or between us and neighbor galaxies. It only applies on really large scale. The percentage rate is currently 1/140 of a percent every million years.
If you are talking about a really big distance, an increase of 1/140 of a percent can be quite sizable.
These are spatial distances that are increasing. The cosmic microwave background allows us to define a kind of standard observer's perspective, and an idea of being at rest. So in cosmology there is a standard idea of time. Hubble Law says distances between stationary objects increase with the passage of that standard time. It is understood we are talking space distances.
Keep in mind that when people say "space expands" that is a verbal shorthand, a partly misleading way to put Hubble Law in words. What they are really talking about is some mathematics, a simple pattern of increasing largescale distances. It is the distances that are expanding. The expansion is not in a substance, but in geometry. In relationships.
GR teaches us that geometric relationships are dynamic and there is no reason to assume they are always the static orthodox ones of Euclid. Euclidean geometry is just one possible outcome allowed by GR, approximated in the limit when there is almost no matter in the universe. GR is the reason why Euclidean geometry (that maybe you learn in 10th grade) works, or almost works. It is the reason why, at this time in our history, the angles of a triangle add up to 180 degrees, or so close you can't tell the difference.
|Feb4-09, 02:05 AM||#79|
- However in very small scale like our body or atomic scale, it is different. Its expansion is extremely small in size and the distance of constituent components like molecules or atoms stays the same because the dominant physical law, electromagnetic and quantum physics, moves all back to stable position, so the tiny expansion is canceled out immediately. Thanks.
|Feb4-09, 05:34 AM||#80|
since gravity is curved spacetime geometry. Does that mean a triangle outside the earths gravity would have angles that add up to 180 degrees, but they would add up to something other than 180 degrees in a strong gravitational field? would it be more or less than 180?
if you had a very long line segment rather than a triangle, would it be continuously getting longer in length because of the universe's expansion? In other words, is the expansion of the universe only a change in distance between galaxies or is it an actual change in the geometry of spacetime in the same sense that a gravitational field is a change in that geometry?
|Feb5-09, 02:57 AM||#81|
- In expanding universe the light wave length becomes longer. But a solid long ruler does not expand, because the ruler follows 2 main physical laws at the same time, the expansion and electric binding force to keep its shape, therefore as soon as there is an expansion it contracts back to original stable state resulting in no change of shape.
|Feb5-09, 07:08 AM||#82|
actually I had something more abstract in mind, the geometry of space time rather than gravitational lensing or physical rulers.
|Feb23-09, 03:56 PM||#83|
Also if what you say is true then red shift would be impossible as the recession speed the light gains would prevent the waveform from lengthening into the red end of the spectrum.
Please explain, I'm quite confused by this.
|Feb26-09, 11:18 AM||#84|
No one can explain this to me?
|Feb26-09, 01:14 PM||#85|
sorry, I didn't see your post until just now.
There are two Einstein Relativities. The 1905 one was SR (special) and the later extension to include curved and dynamically changing geometry is the 1915 (general) one.
Every man-made mathematical theory has limits to its applicability and cannot be pushed too far. As a student when you learn the math model of something you are also told the limits---how far you can trust its predictions, where it blows up and fails to compute meaningful numbers, or starts to diverge from reality.
A major fault of pop-sci journalism is it often fails to make this clear.
The 1905 special only applies locally in situations that are approximately uncurved and approximately non-expanding. It is only perfectly right in situations that dont exist, namely where space is perfectly uncurved, or flat, triangles always add up to 180 degrees, parallel lines...etc. etc. and that simply is never true. And locally means temporarily too, since we are talking spacetime.
Basically, 1915 general trumps 1905 special. But as a rule nature deviates from static flat geometry so slightly and slowly that 1905 works admirably well! It is only over very long distances and time periods that deviation is pronouced enough to be intrusive.
Be sure you have watched Wright's balloon model, the animated film. Better watch several times.
A galaxy (the white spiral whirls) is at rest with respect to the microwave background if it stays at the same longitude latitude on the balloon. All the galaxies are at rest. The distances between them increase.
We have this rule that information cannot travel faster than c.
Think about two galaxies, both sitting still relative to background, and the distance between them increasing. Neither is going anywhere, no information is being transmitted from one place to another, by the mere fact that the distance between is increasing.
Neither of the galaxies could overtake and pass a photon!
The speed law only applies to motion within a given approximately flat frame of reference, where SR applies.
So two things can sit still, and the distance between them can be increasing at 4 or 5 times the speed of light, and nobody is breaking any rules.
You can see that in the balloon animation. The wiggles that change color and have lengtheningwavelengths represent photons. They move at a standard speed like one millimeter per second. But if you watch alertly you will see that after a photon has left the neighborhood of some galaxy the separation between it and the galaxy will begin to grow faster than c, and after a while will be several times c. It's remoteness is increasing several times the rate it can travel on its own.
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