Though the Sun is gone, I have a light. -Kurt Cobain
Last time we visited dark energy, we discussed its initial discovery. This came about from the fact that supernovae observed with a certain redshift (i.e., moving away from us) appear to be systematically fainter than we were able to explain.
But we weren't satisfied with simply saying that there must be dark energy. We asked a lot of critical questions about why these supernovae might appear so faint.
First off, we asked the question, "Could these supernovae from far away be different than the type Ia supernovae we have today?"
Unfortunately, the answer is a resounding no. So long as atoms work exactly the same way, they require the same pressure to collapse at all points, times, and places in the Universe. The process of forming a Type Ia Supernova -- having a white dwarf accrete mass until the core collapses and it explodes -- should be independent of location and time.
Well, if the supernovae are constant, could the environments that they form in be different than the environments today? Of course they could. So, is there any way to make them appear fainter without them actually being fainter, and without having to resort to dark energy? Sure, you might say, block some of that light! All you need is some dust, like so.
What a simple idea, right? Problem solved?
Not so fast. Dust, in real life, is made up of real particles (atoms, molecules, grains, etc.), with real sizes. This means they affect light differently at different wavelengths. Not just red, green, and blue, but X-rays, ultraviolet, infrared, and more. We don't see this light dimmed more in one spectral band than any other; it's dimmed equally at all wavelengths!
So, real dust is out. But what if we invented some new type of dust that absorbed light the same at all wavelengths? We can give it a name: grey dust. We have no idea what would cause it, but it's a lot more believable that there's some new kind of dust out there than there is a whole new type of energy pervading the Universe.
Well, if this grey dust were there, then the light from distant supernovae would simply continue to appear dimmer and dimmer the farther away they were. Whereas, if the Universe had dark energy, the supernovae should start to appear relatively brighter beyond a certain distance. Take a look at the graph below to compare some different theories with the data.
As you can see, grey dust (the top line) is as inconsistent as a Universe with only normal matter (bottom line) when compared to the data.
So you can't simply blame it on a trick of the light. In fact, if we look at the most modern supernova data, it clearly favors dark energy significantly over even a flat, low-density Universe.
Other "light-blocking" schemes, such as photon-axion oscillations, suffer from the same problem; they don't give the right turn-over as shown above. If we've got the right laws of gravity, there's pretty much no way around dark energy.
But we don't like relying on only one source of data. Supernovae are nice, but what happens when we look at all the other evidence? Does that tell us there must be dark energy too, or could it be that the supernova data just cannot be trusted? Seems like a job for part 4, and so I'll see you then!
Awesome post again, I find your Dark Energy/Dark Matter posts collect all my scattered data and compile it into one coherent picture. Awesome information.
For the next series, can we have black holes? :) Do black holes have anything to do with dark matter - for example, could they form from dark matter or is there some reason to believe that the matter we are familiar with could collapse into a black hole without invoking the dark side?
Starts With A Bang is my favourite blog. Well, apart from FUP :D.
Look forward to the next part.
Grey dust actually is a good fit to the supernova data IF the physical density of the dust is constant. A bit contrived, but this is just the behavior of the axion-oscillation model: a constant fraction lost for each unit of cosmic time. This loss function applied in an Einstein - de Sitter Universe gives the "Evolving SNe" curve on http://www.astro.ucla.edu/~wright/dDM-vs-z-29Dec06.gif
which is on the same web page (
http://www.astro.ucla.edu/~wright/sne_cosmology.html ) where you got my other plot. The evolving SNe model was and still is a slightly better fit to the supernova data than the flat LCDM model but the preponderance of the evidence including CMB, BAO, cluster M/L ratios, etc favors LCDM.
Nice summary Ethan.
Ethan says, " Whereas, if the Universe had dark energy, the supernovae should start to appear relatively brighter beyond a certain distance. Take a look at the graph below to compare some different theories with the data."
So, what would a "3-sphere" theory of our visible universe predict? It would predict that beyond a certain point 6.5 Billion lightyears to be exact (i.e. 1/2 of the largest observable distance of 13 billion lightyears, the equator so to speak of our 3-sphere visible universe); light from an Ia supernova would begin to increase in brightness.
So now let me look at Ethan's graph. It looks like the point beyond which relative brightness of Ia supernova increases is at Z = .6. How do I translate that into lightyears? Google search finds the answer at:
where we see that Z = .6 is 6.5 lightyears.
Wow. Thanks Ethan for this insight.
Hold on, Thomas - the universe is 13bn years old alright (+.72bn), but the largest observable distance is much more than that (space itself can move away from a point at >c).
I'm not sure what you're implying - that z=.6 is evidence for a finite spherical universe? I don't follow, or it doesn't.
I don't understand how you get 6.5 (probably billions?) lightyears from the site you linked to.
I recommend Ned Wright's Cosmology Calculator:
That provides a comoving distance of about 7.2 billion light years for z = 0.6.
Additionally, I don't understand your claim that in the "3-sphere" theory, light from a SN should begin to increase in brightness at "1/2 of the largest observable distance". Could you please clarify that?
Oh, and as DaveH already pointed out: 13 billion light years isn't the "largest observable distance", actually.
Great series on dark energy Ethan, much appreciated.
A (really) silly question: On these graphs of distance against velocity, they show that the further away things are the faster they are moving away. But since further away also means further back in time, doesn't that mean that things were moving faster the further back in time we look and that things are moving away slower the closer in time (or distance) we get to now? A curve going upwards just means things were moving even faster back in time, that seems to mean the opposite of accelerating to me?
ok I knew it was a silly question, just remembered that the expansion is caused by space expanding as the light travels through it and not by motion, so the curve going upwards means the longer light travels through expanding space the more it gets redshifted and hence the faster space is expanding, so it is indeed accelerating.
I guess the next question is how do we separate the effects of redshift from relative motion and how big of an effect is it on redshift?
and scratch that too, just found the answer digging in your past blog posts (hey i'm new here!): http://scienceblogs.com/startswithabang/2009/08/redshift_and_distance_i…
"If we've got the right laws of gravity, there's pretty much no way around dark energy." What about http://arxiv.org/abs/0909.3853 ... of course, not compelling yet... but what kind of modified gravities actually do predict this gravitational slip? Pretty much all of them, and thus also TeVeS and the Generalized Einstein-aether theories... also called "relativistic MOND" theories... Is Ethan running into circles or willingfully ingnoring (or dismissing) new informations or results (or just being stupid) by dismissing these theories alltogether in his previous posts about MOND? Moooron :D
Of course, not compelling yet.
There was an interesting (and sober) discussion of that paper over at Cosmic Variance a couple of weeks ago.
From the above data chart, it looks that Z = .6 is no more precise than plus/minus = .1 or maybe even =.2; thus it makes no difference whether the exact conversion from Z = .6 is 6.5 or 7.2 billion light years because the precision in light years is probably plus/minus = 2 lightyears. But I'll be glad to accept your 7.2 billion light year estimate and then to be more exact I'll use 13.7 billion lightyears as the largest "observed" distance in our visible universe. So then 1/2 or 13.7 is 6.8 lightyears which is in pretty good agreement with 7.2 light years which has a precision of maybe plus or minus maybe 2 lightyears.
The largest "observed" time is 13.7 Billion years and thus the largest "observed" distance is 13.7 Billion lightyears. I personally, see no compelling scientific reason to speculate beyond the "observed" 13.7 billion light years for our "visible universe". Whether there might be some galaxy at 25 Billion lightyears away, that by definition (i.e. assumptions and theory) can never be "observed", is like saying that pink elephants dance in trees at night when humans are asleep and all recoding devices are turned off. I limit myself to the largest "observed" distance and to "observed" behavior of elephants; unless of course there is compelling reason to hpothesize "elephants dancing in trees" such as tusk marks 50 feet high and broken branches.
I suggest that you start with wiki's discussion about 3-sphere. This will confuse but it is a necessary preliminary. Next and this is harder; you must practice visualizing a 3-sphere.
A 2-sphere can be imagined as the 2-dimensional surface of for example a globe like our Earth. A 2-sphere is a 2-dimensional surface (i.e. area) with no boundary. You can travel on it in any direction (within its 2-dimensions) and never reach an edge; yet it is a finite spatial area unlike a Euclidean plane which is an infinite spatial area.
A 3-sphere can be imagined by analogy as a 3-dimensional volume with no boundary. You can travel on it in any combination of 3 dimensions and never reach an edge; yet a 3-sphere is of finite volume. Whereas a 3-Dimensional Euclidean space has infinite volume (and areas and distances).
Now, if our "visible universe" is a 3-sphere as Einstein and Hubble asserted; then light travels along 3-sphere great circles (analogous to the great circles of our 2-sphere Earth). Now in such a 3-sphere "visible universe", great circles are the "straight lines" along which light travels. For all practical purposes in the Milky Way galaxy such 3-sphere "straight lines" can be thought of as Euclidean straight lines; just as for all practical purposes for travel in any major Earth city, Euclidean geometry is perfectly accurate and 2-sphere geometry is unnecessary.
Now to explain my 1/2 the largest distance. Let's for simplicity of visualization consider our "visible universe" not to be a 3-sphere but a 2-sphere (i.e. a big beach ball without a north or south pole). Put a dot labeled "Earth" on the beach ball for Earth. Then on the opposite side of the beach ball for the largest distance from Earth put a dot labeled "Largest distance". Now in this 2-sphere-model-of-our-"visible universe" light travels in 2-sphere-straight-lines (i.e along great circles). In this 2-sphere-visible universe" the most distant "observed" 2-dimensional star or galaxy is very close to the dot labeled "Largest distance". And if this "largest distance" is 13.7 billion light years; then the circumference of this 2-sphere-visible universe is 27.4 billion light years. Now at half this largest distance of 13.7 billion lightyears we can draw a "relative" equator (relative to Earth).
Now you have to visualize this or do some horrendous calculations. I choose to visualization. If a star is inside the "relative equator" of our 2-sphere-model-of-our-"visible-universe" then the light brightness will get dimmer and dimmer as it travels to the dot labeled "Earth". (I'm ignoring dimmining due to dust etc.) However, if the star is beyond the "relative equator" then the light from that star will get dimmer and dimmer until it has traveled 1/2 or 13.7 billion light years (i.e. to it's "relative equator"); at which point it will get brighter and brighter for the rest of its journey to the point labeled "Earth" because of what I will call "3-sphere" geometric lensing. But of course we have to remember that brightness is not only due to distance but also dust etc of the interveneing space and as well there are limits to the redshifting of light in a finite 2-sphere-model-universe just like there are limits to the wavelengths of sound produced by hitting a finite sized string or drum. Of course, this model is only a static model; it's much harder to visualize a dynamic 2-sphere model.
Now if you have visualized this 2-sphere-model-of-our-"visible-universe"; then you are ready to visualize a 3-sphere-model-of-our-"visible-universe". It'll take a while but if you play around you will begin to understand the similarities and the difference between concepts and ideas in a 2-sphere-model universe and a 3-sphere-model-universe.
By the way, visualizing a 3-sphere is relatively easy but tricky compared to the mathematics is horrendous; which is why astronomers and cosmologist use the Euclidean assumption for their model of our "visible universe". Similarly, the 2-sphere mathematics on the surface of the Earth is horrendous. If I ask what is the area of a triangle (of great circles) formed by Tokyo, Rio de Janeiro and Paris; it's a challenging problem to get an exact mathematical answer (though Archimedes solved similar difficult problems without our modern algebra).
I won't say any more.
Thomas, I think you should try to start to personally see a scientific reason why the age of the universe in light years is not the radius.
@Thomas: Thanks, I know what a 3-sphere is, your explanation wasn't necessary.
1) Why do you keep assuming that in a universe which is 13.7 billion years old, the largest visible distance is 13.7 billion light years? As you have been told several times now, that is wrong! Wrong due to the simply fact that the universe itself expanded since the light left that stars - and the expansion of the universe can (and has) exceed light speed. Hey, even the figure of 6.8 (or 7.2) billion light years you use is *based* on the same math which says that the largest visible distance is much more than 13.7 billion years! Go again to the cosmology calculator and compare the "light travel time" with the "comoving distance"...
2) What is this "3 sphere geometric lensing" you mentioned?
I've never heard of that, and it is unclear to me how that is supposed to work. If you want to claim that light gets brighter because all of the geodesics coming from a light source converge again at the point of the observer, then you are in principle right - but that effect happens for *every* distance - not just distances "beyond the equator"!
Really great imformation, I found this blog on physics.org and think its really good :D
To my way of thinking, the approximate radius of our "visible universe" is 13.7 Billion light years; and the "apparent age of our visible universe" is 13.7 Billion years. These are distinct ideas.
Regarding only the second one, the "apparent age of our visible universe", two Columbia University physicists independently reviewed my calculation showing that Einstein's "gravitational redshift is suffienct to account for Hubble's law", both agreed that there was no apparent error in my calculation or reasoning; but each was hesitant to reach my conclusion since their physics expertise was not astronomy. After being denied criticism by the professional physics and astronomy community on several other such occasions (all on this one simple calculation); I decided to write a scholarly yet readable work titled A Crtique of Pure Physics. If someone would break this idea or my other various ideas, I'd be quite pleased to learn and understand such and such reasons. Page 36 to 39 shows the simple calculation that a first year physics student can follow; yet professional physicist will not comment upon. It is the only calculation in my book. Feel free to follow my name to link to my book (fully viewable online) and/or contact me via my email link.
I do not want to take advantage of the hospitality of Ethan's blog with my un-peer reviewed theories. I am not a professional physicist. On Ethan's blog, I simply want to appropriately to be part of a physics dialogue that interests me. And yes my focus is often a critique of physics and cosmology theories, most often because of what I consider unwarranted extraordinary assumptions.
Thomas, I agree - here is not the best place for us to present speculative fringe science. It can only lead to misleading confusion, since your theory would not get the exhaustive treatment it deserves. So we'll hopefully move on now I'm absolutely clear that your apparent insight was in fact based on an alternative interpretation of cosmology.
Back on topic, Ethan's discussion of the other evidence (WMAP data etc) for dark energy should be interesting.
I briefly looked at your calculation - not at the whole thing, but at the assumptions which go into it. I see two problems:
1) You say that the radius of the observable universe is 13.7 billion light years. As has been pointed out several times, this is wrong in an expanding universe. However, you seem to use a non-expanding universe in your model, hence I'll grant you that point.
2)You use Newton's law of gravitation. But that is only right for spherically symmetric situations in flat space, whereas the universe a) possibly is not flat, and more important, b) has a uniform density distribution. It is easy to show that for a uniform density, the forces of gravity completely cancel out (for every mass pulling you into one direction, there is another mass which pulls you into the other direction!). And since there is no net gravitational force, red shift can't be explained by gravitational red shift.
If you are interested in further discussion, you can contact me at (name used here) at feuerbacher minus web point de.
The goal of the project, reports the paper, is to "investigate whether it is feasible and, if so, to encourage other hospitals nationwide to follow.
What is intriguing about these instances is that they come from people who are usually very circumspect and subtle about their condescension and contempt and worried that they should at least show some respect for the majority of Americans.
How many jobs were funded by the stimulus bill? The question is: How many jobs would have been funded if that same money had been put to other uses?
If creating jobs were that easy, the government could simply tax the country into endless prosperity.
While the result is tragic, if the Williards are voting against their economic interests, then how did they have that kind of money to invest in the first place?
He said that while it might look as if the commission wasn't concerned about the culture of cost cutting at BP, it will address that broader corporate problem in the future. Monday was more about what immediately led to the disaster.
I've read your books and articles through the years, and now to see that the implementation of the EHR is a national priority must be as gratifying for you as it is daunting for us in health education and patient advocacy. Thanks for the leadership! I will be checking this website often.
I was shocked too see these facts which were hidden in our universe
grate work keep it up..!
Great Blog, but not sure why you would quote some idiot who
popped himself off (cobain) as having some kind of innate
insight on anything at all?? Am I missing some kind of profound
lesson here ?