First, I am a rank novice in cosmology, very rank. However, I do see something that puzzles me. I put some numbers in an Excel spread sheet and I calculate that the early universe was far from homogeneous. I did a few limited searchs and did not find a discussion. Here is what I have written. I hope its not too long. Edit: What can I do to prevent the forums from removing all spacing in tabular data. My two tables are all run together. The CMBR (Cosmic Microwave Background Radiation) is said to be homogeneous and as a result our universe is also said to be homogeneous. The implication is that our early universe was homogeneous. The CMBR only appears to be homogenous now because it is approaching the limit of absolute zero. The current levels of CMBR shows that the universe was very heterogeneous. As we look at different parts of our universe we find differences in the CMBR, indicating differences in the temperature of the universe. And the significance of those differences are sometimes not given their true merit. If there were huge differences in the beginnings, some 15 billion years ago, and through however many of doublings in size, the expansion would cause the temperature differences to be reduced in proportion to the size. This is described by Charles’ law. Let’s look at a few calculations. In the below table the first column is the radius of a sphere of gas in meters, and to its right is the volume in cubic meters. The next column show how much the sphere expands from one row to the next. Each iteration increases the volume by a factor of eight. It’s a constant, but a good reminder. The fourth and fifth columns show the temperature of two spheres A and B. The two spheres begin with identical conditions except for the temperature. Sphere A starts at a temperature of one million Kevin while B is ten times hotter at ten million. When a volume of gas doubles in size, its temperature and pressure are both reduced to one half the original. In this table volume increases by a factor of eight so the temperature is reduced by that amount. The last column tracks temperature difference between A and B. Follow the chart down as the radius doubles and the temperature drops. Edit: These looked pretty good when editing, horible when displayed. I will try to make it look better. Code (Text): size volume in expansion A Temperature B Temperature Difference (meter ^3) factor 1 4.18879 1,000,000 10,000,000.0 9,000,000.0 2 33.51032 8 125,000.0 1,250,000.0 1,125,000.0 4 268.0826 8 15,625.0 156,250.0 140,625.0 8 2144.661 8 1,953.125 9,531.2 17,578.125 16 17157.28 8 244.140625 2,441.4 2,197.26562500 32 137258.3 8 30.51757813 305.17 274.65820313 64 1098066 8 3.81469727 38.14 34.33227539 128 8784530 8 0.47683716 4.76837158 4.29153442 256 70276238 8 0.05960464 0.59604645 0.53644180 512 5.62E+08 8 0.00745058 0.07450581 0.06705523 1024 4.5E+09 8 0.00093132 0.00931323 0.00838190 2048 3.6E+10 8 0.00011642 0.00116415 0.00104774 4096 2.88E+11 8 0.00001455 0.00014552 0.00013097 8192 2.3E+12 8 0.00000182 0.00001819 0.00001637 16384 1.84E+13 8 0.00000023 0.00000227 0.00000205 32768 1.47E+14 8 0.00000003 0.00000028 0.00000026 This model begins with a sphere of gas 1 meter in diameter that expands to 32 kilometers. The earth is about 13,000 kilometers in diameter. Our bubble is about two and a half times the diameter of earth. Tiny in terms of the universe. After only sixteen doublings in size, the difference between the two spheres is 0.00000026 degrees Kevin. That is only 0.26 times 1 one millionth of one degree. Sphere B started ten times hotter with a difference of nine million degrees, and in only sixteen doublings the temperature of B has closed in on that of A and moves to within about one fourth of one millionth of a degree of the temperature of A. In some 14 billion years of expansion our universe has doubled in size far more than 16 times. What are the results of that huge amount of increase in volume? From the Wiki page I checked: http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation The CMBR has a thermal black body spectrum at a temperature of 2.725 K, And elsewhere in that web page: The cosmic microwave background is isotropic to roughly one part in 100,000: the root mean square variations are only 18 µK Ponder this for a moment. In the first table sixteen doublings, a difference of nine million degrees, or ten to one, drops to a difference of only 0.00000026 K; or to scale it appropriately, 0.26 µK. That difference is about 692 times smaller than the differences in the CMBR. This is the result of only sixteen doublings, from a radius of 1 meter to only 32 kilometers. The earth has a radius of only 6, 378.1 kilometers. Some say the universe expanded from the size of a dime to its current size. Compare the two. A sphere the size of a dime is much smaller than a one meter sphere. And the size of our known universe far exceeds that of the earth. So our universe has expanded many times more than my little table of calculations. This tells us that the differences in temperature shortly after the big bang must have been on the order of billions of degrees. To have doubled in radius as many times as it has and still to retain temperatures differences of 18 µK, 692 times more than my example, indicates that the early universe was anything but homogeneous. From that same web page: The estimated age of the Universe is 13.75 billion years. However, because the Universe has continued expanding since that time, the comoving distance from the Earth to the edge of the observable universe is now at least 46.5 billion light years. That implies that it is roughly the same distance to the opposite side of our universe, so this measure will suffice as the radius of our known universe. Let’s run a few calculations by starting with a radius of 46.5 billion light years and see how many iterations are required to revert back to a radius about one meter. One light year is about 9.4605284E+15 meters. I put this data in an Excel worksheet and ran the numbers. The results are below. The first column is the iteration count, a count of halvings, while the second column begins with the radius of our observable universe. To reduce round off errors, the upper section of the table uses a radius expressed in light years starting with 46.5 billion. When the radius gets down to about one light year at iteration 36, the radius of our universe (in the table) shifts from light years to meters. After looking that those results, I put the RMS difference of the CMB in our current universe into a third column. For each halving of the radius, I multiplied the temperature by 8 per Charles’ law. At iteration 36 the radius of our known universe would have been on the order of 1.3 light years and the RMS temperature differences would have been 6.08472E+26. This is where the table shifts from light years to meters for the radius. At the 90th iteration the radius is reduced to bit smaller than one meter and the temperature difference is 3.5571E+75. That’s the RMS difference between the coolest and the hottest points. That is not the temperature of our universe when it was that size, but the difference between the coolest and hottest. The extreme coolest will differ from the extreme hottest by much more. After that I added a fourth column for the temperature. Beginning with 2.725 K the calculations end with a temperature of 6.46212E+80 K. Much more than just hot. I interpret this as indicating that the early universe not homogeneous. Run the numbers yourself and see what you get. Code (Text): Iteration Size in Temperature degrees K light years in K difference 1 4.6500E+10 0.000015 2.725 2 2.3250E+10 0.00012 21.8 3 1.1625E+10 0.00096 174.4 4 5.8125E+09 0.00768 1395.2 5 2.9063E+09 0.06144 11161.6 6 1.4531E+09 0.49152 89292.8 7 7.2656E+08 3.93216 714342.4 8 3.6328E+08 31.45728 5714739.2 9 1.8164E+08 251.65824 4757139.2 10 9.0820E+07 2013.26592 365743308.8 11 4.5410E+07 16106.12736 2925946470 12 2.2705E+07 128849.0189 23407571763 13 1.1353E+07 1030792.151 1.87261E+11 14 5.6763E+06 8246337.208 1.49808E+12 15 2.8381E+06 65970697.67 1.19847E+13 16 1419067.383 527765581.3 9.58774E+13 17 709533.6914 4222124651 7.67019E+14 18 354766.8457 33776997205 6.13615E+15 19 177383.4229 2.70216E+11 4.90892E+16 20 88691.71143 2.16173E+12 3.92714E+17 21 44345.85571 1.72938E+13 3.14171E+18 22 22172.92786 1.38351E+14 2.51337E+19 23 11086.46393 1.1068E+15 2.0107E+20 24 5543.231964 8.85444E+15 1.60856E+21 25 2771.615982 7.08355E+16 1.28684E+22 26 1385.807991 5.66684E+17 1.02948E+23 27 692.9039955 4.53347E+18 8.23581E+23 28 346.4519978 3.62678E+19 6.58865E+24 29 173.2259989 2.90142E+20 5.27092E+25 30 86.61299944 2.32114E+21 4.21673E+26 31 43.30649972 1.85691E+22 3.37339E+27 32 21.65324986 1.48553E+23 2.69871E+28 33 10.82662493 1.18842E+24 2.15897E+29 34 5.413312465 9.50738E+24 1.72717E+30 35 2.706656232 7.6059E+25 1.38174E+31 36 1.353328116 6.08472E+26 1.10539E+32 Convert this iteration from light years to meters. 36 1.28E+16 6.0847E+26 1.10539E+32 37 6.40E+15 4.8678E+27 8.84313E+32 38 3.20E+15 3.8942E+28 7.0745E+33 39 1.60E+15 3.1154E+29 5.6596E+34 40 8.00E+14 2.4923E+30 4.52768E+35 41 4.00E+14 1.9938E+31 3.62215E+36 42 2.00E+14 1.5951E+32 2.89772E+37 43 1.00E+14 1.2761E+33 2.31817E+38 44 5.00E+13 1.0208E+34 1.85454E+39 45 2.50E+13 8.1668E+34 1.48363E+40 46 1.25E+13 6.5334E+35 1.1869E+41 47 6.25E+12 5.2267E+36 9.49524E+41 48 3.13E+12 4.1814E+37 7.59619E+42 49 1.56E+12 3.3451E+38 6.07695E+43 50 7.81E+11 2.6761E+39 4.86156E+44 51 3.91E+11 2.1409E+40 3.88925E+45 52 1.95E+11 1.7127E+41 3.1114E+46 53 9.77E+10 1.3702E+42 2.48912E+47 54 4.88E+10 1.0961E+43 1.9913E+48 55 2.44E+10 8.7690E+43 1.59304E+49 56 1.22E+10 7.0152E+44 1.27443E+50 57 6.11E+09 5.6122E+45 1.01954E+51 58 3.05E+09 4.4897E+46 8.15635E+51 59 1.53E+09 3.5918E+47 6.52508E+52 60 7.63E+08 2.8734E+48 5.22006E+53 61 3.82E+08 2.2987E+49 4.17605E+54 62 1.91E+08 1.8390E+50 3.34084E+55 63 9.54E+07 1.4712E+51 2.67267E+56 64 4.77E+07 1.1770E+52 2.13814E+57 65 2.38E+07 9.4157E+52 1.71051E+58 66 1.19E+07 7.5325E+53 1.36841E+59 67 5.96E+06 6.0260E+54 1.09473E+60 68 2.98E+06 4.8208E+55 8.75781E+60 69 1.49E+06 3.8567E+56 7.00625E+61 70 7.45E+05 3.0853E+57 5.605E+62 71 3.73E+05 2.4683E+58 4.484E+63 72 1.86E+05 1.9746E+59 3.5872E+64 73 9.32E+04 1.5797E+60 2.86976E+65 74 4.66E+04 1.2637E+61 2.29581E+66 75 2.33E+04 1.0110E+62 1.83665E+67 76 1.16E+04 8.0880E+62 1.46932E+68 77 5.82E+03 6.4704E+63 1.17545E+69 78 2.91E+03 5.1763E+64 9.40363E+69 79 1.46E+03 4.1410E+65 7.5229E+70 80 7.28E+02 3.3128E+66 6.01832E+71 81 3.64E+02 2.6503E+67 4.81466E+72 82 1.82E+02 2.1202E+68 3.85173E+73 83 9.10E+01 1.6962E+69 3.08138E+74 84 4.55E+01 1.3569E+70 2.46511E+75 85 2.27E+01 1.0856E+71 1.97208E+76 86 1.14E+01 8.6844E+71 1.57767E+77 87 5.69E+00 6.9475E+72 1.26213E+78 88 2.84E+00 5.5580E+73 1.00971E+79 89 1.42E+00 4.4464E+74 8.07766E+79 90 7.11E-01 3.5571E+75 6.46212E+80
There's a lot more physics involved than Charles's law. For one thing, Charles's law would only apply to, say, molecular hydrogen gas, but during the time period you're talking about, there are many different states of matter. There is a huge amount of physics that goes into this kind of thing, and there are specialists who do it full-time as a scientific specialty. Their calculations include all kinds of things that you haven't taken into account, including general relativity. If you're interested in learning more about this kind of thing at a nontechnical level, there's a wonderful book called The First Three Minutes, by Weinberg.
Hello Ben, Oh, I am certain there is far more that I imagine, let alone understand. Still, given the differences in the CMBR, imagine a giant pair of hands crushing the universe back down to a relatively small size. Little differences will become huge differences. Before running out and buying another book, is there a simple explanation of the concept of why this thought is wrong?
Let me guess. Charles law relates T and V and constant pressure. Where do you get constant gas pressure in an expanding universe? ============================= Also your basic data seems to be about the CMB homogeneity. CMB temperature doesn't say much about temp of clouds of gas in today's U. You haven't got much of a handle on gas. I think you should stick with LIGHT in your analysis because you have some information about that at present. You should work back in time and keep track of the homogeneity and inhomogeneity of the light. Anyway that's what I'd suggest. ============================= In any case Charles Law is no good. Don't have constant pressure, so can't use that. Or so it seems to me.
You're making the assumption here that the CMBR becomes more homogeneous with time. This is not the case. The CMBR is a (slightly fuzzy*) image of the first time our universe became transparent. The inhomogeneities that existed at that time are accurately-represented in this image. All that the expansion of the universe does is extend the wavelength of this light. It doesn't change the ratios in temperature at different parts of the sky. So when we look at the CMBR and see an image that is uniform to one part in 100,000, then we know that our early universe was, indeed, uniform in temperature to one part in 100,000. This claim makes no sense to me, being directly involved in CMB research. The differences in temperature from place to place on the sky are basically the entire field of CMB research, because they provide us with an extremely sensitive test of the physics that happened before the emission of the CMB. The CMB, for example, is the most sensitive estimate of the ratio of normal matter to dark matter, and when combined with nearby estimates of the expansion rate provides an extremely accurate measurement of the spatial curvature. These inhomogeneities are studied in exquisite detail. Two problems here. First, Charles' Law is only valid for a gas under constant pressure, which the early universe was not. Second, Charles' law does not include the gravity between the molecules in the gas. It turns out that this self gravity is the most important aspect in determining how the universe becomes more inhomogeneous with time. Anyway, I'll leave it at that for the time being. *On why the CMB is slightly fuzzy, it's fuzzy because our universe did not become transparent instantly. So instead of looking at a clear image of a hard surface, it's more likely we're looking at a cloudy surface with some depth to it. This depth tends to smooth out the small-scale fluctuations, but it does so in a very predictable way, and we have to take it into account to understand the physics of the early universe.
Marcue wrote: In any case Charles Law is no good. Don't have constant pressure, so can't use that. Or so it seems to me. And Chalnoth wrote: Two problems here. First, Charles' Law is only valid for a gas under constant pressure Wikipedia says here: http://en.wikipedia.org/wiki/Combined_gas_law I should have mentioned Boyles and Gay-Lussac’s, and possibly others. Charles references constant pressure, Boyles references constant temperature, and in the expanding universe few things were constant. Each law is like a model. All models are wrong, many are useful. Recognizing my lack of knowledge in the area, still, nothing said has refuted my basic premise. When the universe was half its current size, the temperature was twice the current value. And the differences would be twice their current value. And I don't claim this to be fact. But please consider the concept.
And so the PERCENTAGE inhomogeneity would be the same! There you go. I was thinking earlier if I should point that out, but the presentation with Charles Law got in the way. What you say here is true. When distances were half, the temperature of the light was twice. Likewise the fluctuations (approx.) so same percentagewise uniformity. this does not disprove homogeneity! This can be educational to think about. Notice that you are not talking about GAS or dustclouds etc etc. All you are talking about is LIGHT. The temperature of the light. That is what increases in proportion to redshift (actually z+1, redshift plus one). There is some physics involved, that is special to light and a few other things. Clouds of gas, dust, stellar blow-off plasma, intergalactic medium, do NOT have to be the same temperature as the background light. It's not a pure equilibrium equalized-out situation. But in any case, now we do have the homogeneity of the light! It is uniform today to one part in 100,000. So it would be uniform back in year 380,000 to one part in 100,000.
It wouldn't have helped, unfortunately. These laws still ignore the gravitational attraction between the molecules in the gas. This gravitational attraction is completely irrelevant for experiments we do here on Earth, so it is no wonder that we don't include its effects for empirical gas laws built upon experiments done here. But when you are dealing with the formation of structure in the early universe, you cannot come close to the right answer without taking gravity into account, because the formation of structure is all about gravity. And by the way, in order to get the right answer, you also have to take dark matter into account. And dark matter feels no pressure, so it certainly doesn't behave like an ideal gas.
First, I was misconstruing the CMB thinking of it as a measure of temperature. But still, CMB is measured in degrees Kelvin. And that is a measure of temperature. And wasn't the CMB much hotter as we look back closer to the big bang?
Expansion cools the light while it is traveling towards us. The CMB light that we see today is the thermal glow emitted at a temperature of about 3000 Kelvin. So in a sense the answer to your question is yes. The light filling the universe WAS much hotter as we look back. If we look back to year 380,000 when the CMB light was emitted and started on its way to us, the temperature of the light was 3000 K. Just as you suggested, much hotter. But the point of the 1915 theory of gravity (as dynamically changing geometry) is that the wavelengths of the light are extended by the same factor as the largescale distances. Geometry is a living active thing. So, during the time that the light has been traveling to us, since year 380,000, largescale distances (between stuff not held together by attraction) have expanded by a factor of 1090, and also the wavelengths of the traveling light have lengthened out by the same factor. Longer wavelength light is cooler. So the temp of the light WAS 3000 when emitted and it is NOW 3000/1090 K, or about 2.75 Kelvin.
I continue to say that the small differences present today indicate that when the universe was much smaller the differences were much greater. That would mean that there were huge differences from one part of the universe to another. In turn that means that something must account for the huge differences.
bkelly, I think what you are saying is that the ratio of the CMB temperature variation to the 2.7K must remain the same all the way back to last scattering. It seems reasonable to me.
Saying it in another way, to verify we are on the same page, the ratio of high to low presently found now will be held the same as we run the universe in reverse back to the beginning. If so then yes. Here is another perspective on this idea. As the universe expands and cools, the temperature approaches an absolute limit that cannot be crossed, 0 degrees K or absolute zero. Regardless of any and all differences at the start, everything approaches the same limit. The temperatures are all converging on absolute zero. So of course they are now uniform. And after 15 billion years of cooling and convergance on that limit, every little bit of differernce implies huge differences all those billions of years ago. That was the concept of the first table of temperatures in the OP.
Yes, a fixed fractional variation [itex]\Delta T/T[/itex] does correspond to a large additive variation [itex]\Delta T[/itex] at early times when T was large. Although your use of ideal-gas laws to analyze all this was incorrect, it is certainly true that [itex]\Delta T[/itex] values were much larger in the early universe. I think what you've failed to put across to us is why you think it's a big deal that [itex]\Delta T[/itex] values were much larger in the early universe. So are you basically saying that you're surprised by the empirical fact that the initial conditions of the universe were a certain way? We don't have any known physical laws that dictate the initial conditions of the universe, so I don't see any reason to think that this is really much of a scientific issue. Some people do feel that it's odd, and requires explanation, that the universe started out in a state of less than maximal entropy. We have a FAQ entry about this: https://www.physicsforums.com/showthread.php?t=509650 But we don't have any known physical laws that dictate that the universe should have been in a state of maximal entropy.
Part of what kicked off my flurry of posts is watching Morgan Freeman narrate "Through the Wormhole." I have watched several of them and find them sometimes, and mostly, fascinating, but also sometimes rather simplistic. Problem is, I am in between competency levels. I played an important part of building a portable system that tracked rocket launches giving the launch team an independent method of monitoring the launch and being able to destruct an errant launch. I am more aware than average Joe. On the other hand, I do not have the real math skills to truly understand the deep concepts currently being explored. In particular, one scientist in this wormhole episode spoke of the homogeneity of the early universe and (as I recall but may have concluded by implication) the theoretical problems in that early universe developing into what we see know. I have no method asking about alternatives such as the concept of this thread. From what I see the early universe was not homogeneous at all. So here, per this discussion, is what I see as an obvious indicator that the universe was anything but homogenous. And I believe that somewhere out there is a relatively simple explanation. It may be backed up by many complex theories, but should be explainable simply.
I see. When you hear statements that the universe is homogeneous, that's a relative statement, not an absolute one. It's also a description of [itex]\Delta T/T[/itex], not [itex]\Delta T[/itex]. We observe that the CMB's [itex]\Delta T/T[/itex] is about 10^{-4} now, and I think that means that the [itex]\Delta T/T[/itex] of the universe has been about 10^{-4} since some very early time. As far as I know, there is no physical theory that is capable of saying what this number should be, and in particular there is no physical theory that says it has to be zero, so that the nonzero value requires some new mechanism. We simply don't have any known physical principles that constrain the initial conditions of the universe. It's very cool that you've got an itch to learn about this stuff and are willing to make an effort in order to figure it out. If you want to learn more, I'd suggest you switch from getting your information from the TV and start getting it from books. There are a lot of good popular-level books on cosmology and physics. Some possibilities: Weinberg, The First Three Minutes Takeuchi, An Illustrated Guide to Relativity Gardner, Relativity Simply Explained
It is that thought that because of quantum fluctuations, the early universe was inhomogeneous. Expansion of the universe (including inflation) blew up these quantum fluctuations into the very small temperature variations we observe in the cosmic microwave background, and then into the clusters and superclusters of galaxies that we observe today. The universe expanded by a (linear) factor of (about) [itex]10^{30}[/itex] during inflation and another factor of (about) [itex]10^{30}[/itex] between the end of inflation and now. This means that structure on the order of the Planck length at the start of inflation has now expanded to [tex]10^{-35}m \times 10^{60} = 10^{25} m = 10^9 light-years[/tex] This is fascinating stuff. For more details and unanswered questions, see https://www.physicsforums.com/showthread.php?p=1810866#post1810866.
George, you're making a lot of strong affirmative statements here, but my understanding as a nonspecialist is that inflation still lacks strong empirical confirmation (although it has made some correct predictions), and it also has severe, possibly insoluble, theoretical issues. The other thing that makes me a little uneasy about your post is that it could give the impression that there is some kind of ab initio calculation using inflation that can predict that the inhomogeneity of the CMB should have its observed value of about 10^{-4}. AFAIK that isn't the case, is it?
Well, how "confirmed" it is depends upon your point of view. The primary confirmation is that of a nearly scale-invariant spectrum of CMB fluctuations. There are other potential explanations for these, but inflation remains the simplest by far, in particular because it doesn't depend upon most of the details of beyond standard model physics (other explanations tend to assume a particular theory, such as loop quantum cosmology or string theory). As for its problems, well, I'm pretty sure it doesn't have any in general. Some particular inflation models have severe issues, but not all. One thing to recognize here is that inflation is not one model, but an entire class of models.