If this is true, then I think you have just resolved Olbers' paradox!

__________________
"Stupidity gets denser in a crowd" - Old Finnish saying. [My website and My BLOG] [Nimblebrain forums]

Bad choice of words (well, I did put it in quote marks).

How about "such bubbles would have more EM energy going into them than going out, if you count each photon crossing the boundary only once."

Of course, it's trivially true that, absent absorption inside a sphere, any sphere will be a net 'emitter' so long as it contains a souce anywhere inside it (all photons entering 'from outside' will also exit, absent absoption).

But this is an aspect of the OP's idea that I think we need to have him clarify, before we can consider it further, don't you agree?

Maybe the “bubble” idea was not a good way of explaining it…let’s talk some numbers.

The sun is radiating at some 4 x 10^26 watts (www.astronomynotes.com/starsun/s3.htm). There are about 100 billion suns in our galaxy, but most are not as big and bright as the sun. Let me make a very conservative estimate, and assume that there are “only” 1 billion sun-equivalent stars in the galaxy (if someone has a better number, please supply it!). Then the galaxy’s total power output is 4 x 10^35 watts. That is a lot of energy. Where is all that energy going? It is going “into space.” That is, the energy output of visible matter is powering the expansion.

Since all the numbers become “astronomical,” it is better to do the calculation on a per-kilogram basis. Our sun has a mass of roughly 2 x 10^30 kg (http://www.enchantedlearning.com/sub.../sunsize.shtml)
. So its energy output per kilogram is [4 x 10^26 watts]/[2 x 10^30 kg] = 2 x 10^-4 watts/kg, or 200 microwatts/kg. While the sun may be “typical,” it is not representative. For every kilogram of matter in a sun-like star radiating away energy, there may be 1,000 kg just sitting there, doing nothing. If we add in “dark matter” (questionable, but just to play it conservative), there is an additional factor of about 10 times as much non-radiant mass. So to get the power output per kilogram of the galaxy, I’ll divide the sun’s output by 10,000. Thus, the power output of the galaxy is estimated at 2 x 10^-8 watts/kg or 20 nanowatts/kg. Again, this is a very crude “guestimate,” and I welcome better numbers, but this will suffice for here and now. Finally, since I converted the expansion to an annual basis (#20), I’ll do the same for the energy output, so the estimate for the galaxy’s annual output is: [2 x 10^-8 watts/kg]*[3.15 x 10^7 sec/yr] = 0.63 joules/kg/yr.

Since j/kg/yr is not very intuitively helpful, we’ll change it to more familiar units. Star by converting to foot-pounds of energy per kg/yr: [0.63 j/kg/yr] * [0.73 ft-lb/joule] = 0.46 ft-lb/kg/yr. Now we get rid of the pounds & kilograms: [0.46 ft-lb/kg/yr] * [0.45 kg/lb] = 0.21 ft/yr, or about 2.5"/yr. In other words, the galaxy is radiating energy “as if” every bit of matter within it is “falling” 2.5 inches per year in earth’s gravitational field.

So there is one side of the equation: a rough estimate of the energy output of visible matter is 0.63 j/kg/yr, or -2.5 inches per year at the surface gravity of the earth.

There are two problems with Peter Wilson's idea:
1) it contains no new physics, so should not reach any conclusions that the current standard model is not already reaching, unless it can show that an error is being made in the standard analysis. No such argument is given.
2) it contains no useful numbers that would merit the conclusions. Despite prompting by Nereid, the response has only been to quantify the expansion as "very slow". What does that tell you? It takes an unbelievably small energy to rip apart a helium nucleus. Would you then care to rip apart one right now? The point is, the magnitude of numbers is not what matters, it is the comparison between numbers, or equivalently, the magnitude of ratios of numbers. What comparisons are offered in this analysis that could be used to judge whether expansion is "fast" or "slow"? The idea is not at all a bad idea. In fact, it's so good of an idea that it has already been included in the standard theory. Its impact, however, is negligible in the grand scheme-- photons are playing no currently important role in the dynamics of the universe for the last few billion years. This is all well understood, there are no new ideas being presented here, all that is happening is calculations are being suggested that have already been done. Been there, done that.

That is my point exactly! You do not need "new physics" to explain the expansion! The "standard model" presupposes an explosion, then uses GR to track how the explosion evolves. And the results look nothing like what we see! Hence, the flatness problem, the horizon problem, the singularity problem, the missing magnetic monopole problem, the ancient galaxy problem, the acceleration problem... The Big Bang model is a completely wrong on 6 of its 8 predictions. But instead of re-examining the initial hypothesis, one ad-hoc conjecture after another has been "piled on:" Inflation, dark energy, colliding branes in extra dimensions... None of these "theories" have a shred of observational evidence, except that they "save" the Big Bang theory!

This is not science. (www.cosmologystatement.org/) If a theory yields 6 completely wrong predictions (and the microwave background is only half-right...but that is another subject), then it is time to try another hypothesis.

The Big Bang model has tried to explain the present expansion in terms of a singular event in the past. This approach has completely failed. What I am saying is, look for an explanation in the present.

Presently, the moon’s orbit is expanding, because presently, the earth is spinning. Presently, the sun is expanding, because presently, nuclear reactions are taking place in its core. Presently, the Atlantic Ocean is expanding, because presently, geologic forces are at work beneath it. And presently, the universe is expanding, because presently, something is causing it to expand.

And that "something" could be any number of things, but radiant energy is one obvious source. I have estimated the quantity of radiant energy (two posts up). It is such a crude estimate, it could easily be off by 2 orders of magnitude (OOMs), either way. Do you agree that my number for the radiant energy is "in the ball park" (within 2 OOMs)? If not, what is it? If visible matter is not radiating energy at about 1 joule/kg/yr, then what is the rate?

I will quickly concede that the theory is inadequate...if the numbers are wrong. But before we can agree or disagree whether the numbers are right, we have to agree on what the numbers are.

"expansion" would be a much more suitable termOne of the many, common misunderstandings about the BB (see here for an attempt to set the public record straight)Before you get too carried away with these, don't you think it might be sensible idea to check them out? Maybe they're not the kind of 'problems' you seem to be claiming (e.g. 'singularity problem' - without a theory that unifies quantum theory and GR, this cannot go away)And which 6 (8) would they be?Oh my goodness, another collection of misunderstandings, errors, and plain nonsense. Please do read the webpage for which I provided a link earlier in this post.Oh dear, Peter Wilson, to what extent have you checked out the claims on that website? Would you be prepared to defend them, here in the ATM section of BAUT (under the BAUT rules)?

If you aren't prepared to defend the claims made there, why do you feel it is appropriate to repeat them here, in BAUT (a science-based discussion forum)? I'm serious; the number of BAUT members who post here with cases that amount to little more than "the concordance model MUST BE WRONG! {insert your favourite non-science/nonsense internet website here} said so!! I read what's on those sites AND THEY MUST, MUST BE RIGHT in what they write!!" is depressing (or perhaps it's the number who are utterly unable to defend such claims, when challenged to do so).Really? Please provide a link to a much-cited, peer-reviewed paper which makes such claims (not an internet popularisation).Oh good, you are making a clear assertion - so now we can attack your claim with glee and fervour (per the BAUT rules), and you will defend your claim?And if you would like to take the time to read up on GR, you will see that the 'expansive' capability of radiation is already included in the equations, when GR is applied to the universe as a whole.

Further, you will learn that there was once a 'radiation dominated era', but now it's a 'matter dominated era' (in modern cosmology, these terms are precisely defined, tested, and match good observational and experimental results very well).

If you'd like to continue with your idea, I'll happily continue to question you about it; in particular, about your estimates, how you derived them, how you think they apply, etc. Yes? No? Maybe (need more time to consider)?

Need more time & space, Thank you.

I have been trying to present my idea in a "conversational" mode, the basic format of this forum. But this "paint-by-number" approach is getting a little frustrating for me, and (obviously) for the reader as well. On the other hand, trying to present the whole idea at once is a little bit like a snake trying to swallow a pig. But I am going to have to do something like that, in order to get the whole idea "on the table," so it can be evaluated (digested?) in a fair and consistant manner.

So give me a day, or two, or four, to "put it all together," while keeping it reasonably brief. (That is the hard part: providing enouhg information to make it understandable, without "explaining it to death" and losing everyone in the process.)

ITMT...I estimated the magnitude of "light energy" in post #33, arriving at a figure of 1 j/kg/yr, or 2.5" of elevation per year @ earth's surface (+/- 2 OOMs). Perhaps you can tell me where I lost you, or which part you disagree with. I wish I could just Google it, and present a number that everyone agrees with (as I did with the mass and energy output of the sun), but cosmologists use parameters, not numbers. For the life of me, I have been utterly unable to figure out how to convert their parameters into numbers, so I have had to navigate my own way through the data, with the result that my calculation appears unfamiliar, and is (evidently) hard-to-follow.

Peter, the problem is not with the numbers, it is with the fact that you are using the same physics as is already being used in Big Bang calculations. As Nereid pointed out, the radiation is already in there. There's no need to reinvent the wheel here, just look at the calculations that already include radiation. They find that radiation is not playing any important role in the current behavior of the universe. If you are suggesting that these calculations, which have been checked and rechecked by people highly qualified to do such calculations, are incorrect, then you have to be able to say where they made their mistake before you ask us to do the same for you.

Okay, perhaps I should have qualified that with, “In its original incarnation…” And OK, I did exaggerated a wee-bit. But if we were keeping score:

In its original incarnation, BBT predicted chaotic expansion, like a core-collapse SN remnant. Instead, it is highly uniform. The Horizon problem. Strike-one. Iioi, BBT predicted that the expansion should either quickly fly apart to near-zero density, like a bomb going off in space, or matter should quickly fall back together, like the dreaded asteroid heading our way that we blast apart with a bomb, only to have it lump back together. Instead, the expansion is “perfectly balanced” between these “more likely” outcomes, like a pencil on end. The Flatness problem. Strike-two. The Singularity Problem: the SP is actually BBT's Ground Assumption. Every theory has to have a Ground Assumption. Technically, it is not a wrong prediction. Ball-one. The missing magnetic monopoles: only in some versions. Ball-two. The ancient galaxy problem: Well, they could have formed real quickly… It was a foul ball, in the stands, and the fan did interfer, but because the fan did not reach into the field-of-play, it is not fan interference. Count remains, 2-and-2. Iioi, BBT predicted the expansion should be slowing down. Instead, it is speeding up. Complete swing and a miss. Strike-three. Hit by dark energy, calls the ump, take a base.

And Pleeeese… The reference to the cosmology petition was not meant to say, “See this petition? Its signed by a bunch of people so it must be right!" The point is, I am not completely alone in thinking the theory should have been out on strike three. (And to encourage people to sign it. )

I am well aware that these “historic” deficiencies have been rectified in the current model. Talk.origins does an excellent job of summarizing the current thinking, and putting it “all in one place.” Thank you.

To quote, “When Einstein first tried to (apply GR to the whole universe), he found that it predicted the universe should either expand or contract.” This was pre-dark energy. If you think about that statement for a moment, you realize you could ask a contestant on the Cash Cab show: “Einstein’s theory of General Relativity predicts that the universe will either expand or contact. Which of these two options is the universe actually doing, expanding or contracting?” The clueless-contestant could flip a coin. Heads, its expanding…[coin-flip]…heads it is! Yeah! Got it right!

When the expansion was accepted as fact, it was quickly appreciated, likewise, that the expansion could be either speeding up or slowing down. Actually measuring which way it was changing was out of reach at the time, but people highly qualified to do such calculations set about calculating it. And it was unanimous. All twelve (someone once said, “Only twelve people in the world really understand GR”) agreed: tails, it should be slowing down. Final answer: the expansion should be slowing down. Then in 1998, Perlmutter et al made history by finally measuring which way it was going, and the observations said: heads again! (What are the odds? ) The expansion is speeding up!

I do not know where the pre-dark energy model went wrong, and I do not have to show that the present BBT is in error. All I know is the original modelers, “highly qualified to do such calculations,” had about six decades to check and recheck their math, before the measurement could actually be made, and they had a 50-50 chance of getting it right…and they got it wrong.

And I should read up on GR?

Let me draw an analogy here. When I was going to school (Berkeley —where else? and why would I specifically mention Perlmutter?—in the late 70s), I was taught in chemistry that the Casimir effect could be explained in terms of electrostatics, the same thing that holds a piece of dust to a vertical pane of glass. You just assume that electrical charge is not perfectly smoothly distributed around the molecules, and that it randomly fluctuates, and it follows from these two assumptions that dust will stick to the glass, and the plates in the Casimir experiment will be pulled together. Two completely different models--random charge fluctuation and virtual particles popping in and out of existance--yield the same result. What does this mean?

It means that if I were trying to shoot-down virtual particles (which I am not, but if I were trying to), and to prove that "electrostatics" was the correct explanation, I would have have to show where the virtual particle assumption is wrong. And I would have to justify the randomly-fluctuating-charge-distribution assumption as superior. Because if you examine the assumptions carefully, both are somewhat ad-hoc and arbitray, yet they both yield the correct answer. But such is not the presenet case. The "pros" had their chance (with not-bad odds), and they got it wrong.

What I do have to do is show that GR, in its original incarnation, sans dark energy, predicts that OUR universe, the one we have come to know and love, should expand. But that's not all. I must also show that the expansion should accelerate. Gotta' make both shots.

That I will do. In the next post. Unless there are more objections.

Since I cannot identify the error in the original prediction that had the expansion slowing down instead of speeding up, I suppose it is unfair to expect readers here to identify a mistake in my reasoning, unless I made a real blunder (has happened). But, the BAUT reader will have two models to choose from: The BBT, nicely outlined in talkorigins; and DEILE, to be summarized here, shortly, in a few days. The reader can then decide which theory "to buy."

Now does that seem fair?

The judges are re-tallying the score:
The things you are counting as failed predictions of the BBT are not predictions at all, they are aspects of the puzzle that the BBT does not explain. Thus they are to be viewed as incompletenesses of the theory, not errors in the theory. You can count them as flaws or problems, as any incompleteness would be, but that's more like having an olympic ice skater who does not include certain difficult jumps in her program, as opposed to jumps that she tried and ended up on her bumpty. When scientific theories fall on their bumpty, they are replaced. When they are incomplete, you just practice those difficult jumps a bit harder until you are ready to put them into your program and go for the gold.

In your baseball analogy, I'd put the BBT in the role of the pitching team, not the batters. The goal is to win the game, not pitch a perfect game. So when you are overmatched by the other team's heavy hitters, you intentionally walk them, and go after the ones you know you can get out. That's what BBT does-- it puts in a few intentional walks that after we develop a better changeup we can go after, but for now we'll just strike out the hitters we have in our back pocket.

Now, this is not an ideal state of affairs, but be patient. The changeup is coming. Or maybe we'll have to bring in a relief pitcher, who knows, but frankly there's nobody warming up in the bullpen at the moment. To sum it all up, I'll borrow from Winston Churchill: the BBT is the worst of all cosmology theories, except for all the rest.
Yes, that is right. Lots of luck, we have your Nobel prize waiting if you pull it off.

BAUT is based in Sweden?

Well, somebody has it waiting, that is-- I'm afraid my input will not be solicited.

For those who may have just joined the thread: So far, Peter has made the preposterous claim that dark energy is light energy, which, according to all the experts, is completely wrong, because according to their math, based on the equations of GR, light plays but a trivial role in the expansion of the universe today. He has shown that the value of H has been, shall we say “exaggerated,” by expressing it in kilometers per second (per megaparsec), instead of the usual APR, which would be 0.00000000073%. And he has “guessed” that the current radiant energy is 1 j/kg/yr, but no one is impressed, because the experts have already worked radiation into their equations, whatever its magnitude. Peter has babbled a little about infinity, saying nothing clearly wrong, but he has not used it to support his theory, either. The stakes? Same as every other “new theory” posted on BAUT: it either falls into the scrap-heap of the archive, never to be viewed or posted on again, unless some newbie suggests it, and the moderator has to explain: No, light-energy does not explain dark-energy, see here. Or, it wins a Nobel-prize. In simple terms, it’s a binary outcome.

That is pretty much where it stands now.

At this point, I would like to suggest a “virtual” office-pool, along these lines: 1) One person, one vote; one vote, one Euro. 2) Do not vote on whether you think the theory is right or wrong, because Peter has not yet explained it, and you cannot possibly have evaluated it yet. Wager on whether it will be accepted, not whether you accept it now. 3) The standings remain invisible until the pool closes, March 31. 4) A to-be-determined amount of time will be provided after April 1, in order to evaluate the theory, at which time Peter will be required to either present an actual explanation (AE), or we all assume it was a big AFJ. With BAUT having a virtual army of volunteer critical thinkers, evaluation of the AE, once provided, shouldn’t take long. 5) The kitty gets split equally among whoever is right.

The idea is that if the theory is wrong, and the majority are right, then nothing really changes, as usually happens. If 99 people bet it’s an AFJ, and one guy (me) is still thinking that it will be accepted, then I lose my Euro, and those who “got in on it” now have 1.01 Euro. It was a convoluted April Fools gag if there ever was one, but nothing ever came of it. Except ,01 Euro.

Ken G, does BAUT have the technology to set up a pool by such rules? (If not, see below.)

Here is the difficulty in explaining the theory: I believe Newton was deeply aware that his theory was flawed. He knew it worked in the solar system, but Newton let his mind wander, as he was wont to do, and thought about how it would work at infinity. And when he did that, he saw a paradox, which I will explain when I provide the AE, due on 1-4. Newton knew something wasn’t right, but couldn’t imagine how to resolve it, and his equations “worked,” so he just left them alone. But I believe he was “troubled” by the paradox, and that the instantaneous speed of the field-change (the “speed of gravity”), in his equations, in particular, bothered him.

About two centuries later (history is not my specialty, so don’t quote me on that), Einstein, using tools in mathematics which were completely unknown in Newton’s time, resolved the infinity-paradox, and also slowed-down the field-change, from infinite, to a pedestrian 1.0 (Cosmologists use parameters. In cosmological terms, c, the speed of light, 3 x 10^8 m/s, equals 1.0 .)

So early in the 20th century, Einstein resolved the problems with the Newtonian model, using math that only 12 people really understood. But he was frustrated, because he had to use this “fudge-factor,” the now-infamous Cosmological Constant (CC), in order to "make the model fit the observations.” Because with the instruments available at that time, the rate of expansion rate was thought to be zero. That 73 ppt/yr expansion rate we discussed earlier? That is the number they thought was zero. But when the observations finally came in, it wasn’t zero. It was close. But not zero. Einstein kicked himself. His original equations, sans the cosmological fudge-factor, had been correct after all! The universe does expand! But Einstein did not “blunder,” he was just doing his job: making a model that fit the observations! And the observations at the time had the expansion rate pegged at zero.

Okay, so where are we with all this? Well, until 1998, Einstein’s “GR Rev-2,” or as I prefer, “GR-Lite,” (no DE) was considered Gospel. Then after 1998, CCR burst upon the scene (Cosmological Constant Revival). Here we will just call it GR-Full-Body, although some of its backers prefer “GR-Original Recipe.” GR-FB includes dark energy, in a form yet-to-be-determined, and all that it entails. So there is no disagreement over the basic idea: General Relativity rules. The only bone of contention is this: Is General Relativity correct in its original form, Rev. 1, GR-FB? Or did Einstein get it right the second time, Rev. 2, GR-Lite? That is what the reader is wagering on. Experts say, GR-FB, Rev. 1. The dark-horse candidate (PI) Peter Wilson, says, No, GR-Lite, Rev. 2, is the correct answer.

I am assuming some readers will have difficulty understanding the AE, equations-and-all, once I present it. But I would like to point some things out that most readers will understand, in order to influence the wagering.

First, I am an engineer. And in order to become one, you have to go through this secret ritual, where you take the Engineer’s Creed, as an oath: Rev. 1 shall be better than Rev. 0, and Rev. 2 shall be better than Rev. 1. Granted, science is not engineering, but if you want to play it conservative, Rev 2 of a scientific theory is usually the odds-on favorite over Rev. 1. Keep in mind that while he was alive, GR-Lite was Einstein’s “final answer.” That can’t be too risky, can it? You can bet 1 Euro on ol’ Albert, no?

And let’s be clear on the numbers involved here. Remember the “excess precession” of Mercury’s orbit that Newtonian gravity could not explain? Remember how GR explained it? Let’s take a look at that number for a moment, which—if I am not misteken—is 46” (arc-seconds) per century. Which is 0.46”/yr. Which equals 0.0076’/yr. Which is the same as 0.000013 deg/yr. And if you consider the whole thing to be 360 degrees, the residual precession is 3.5 x 10^-7/yr, or 35 ppm/yr. Einstein used GR to explain a “residual effect” on the order of 35 ppm/yr. Keep in mind, the “residual” I have to explain using GR is smaller than that! And I have one whole j/kg/yr of light energy at my disposal. Again, using GR to explain a “residual effect” even smaller than 35 ppm/yr is not a long-shot, is it?

Furthermore: Recall that pre-CCR, the acceleration rate was assumed to be negative, not positive. How negative? Can anyone dig this up, say before March 31, what the actual magnitude of deceleration was supposed to be? In other words, I am going to pull a rabbit-out-of-my-hat of this size (www.myspace.com/4infinities) on 1-4. How big was that turkey that they failed to produce when the observations finally came in? If some one could come up with the magnitude of the negative answer (deceleration being considered negative) that the “experts” predicted, and compare it to the magnitude of the positive value of the observations which I must explain, this may influence the betting in a positive way (PI).

And so I do not receive any, “You never told us that!” kind of messages, let me reveal a certain “fact about my past:” I always knew expansion was accelerating. I just didn’t know why. How did I know? I cheated. Used a time-machine to look into the future, and see what the answer was. Think of it this way: Under shell # 1 was decelerating expansion; under shell # 2 was static expansion, no change; under shell # 3 was accelerating expansion. All the kings horses and all the king’s men placed their bets on shell # 1, deceleration. A few idiots bet on shell # 2. After 1998, however, people starting “coming out of the woodwork,” proclaiming: I knew it was GR-FB all along. I admit here I didn't "know all along:" I cheated. I peeked under the shells when nobody was looking. And we all know what that means: If he cheated once, chances are he'll cheat again.

And if the “pool” suggested above is beyond the technical/budgetary/time constraints of BAUT, how about a “traditional” on-line poll? Does the reader:

A) Like GR-Lite because it sounds great?
B) Like GR-Lite because it is less filling?
C) Prefer “original recipe” GR-FB?

Are there any further questions before we open the pool?

Peter, B lite please.

I can't speak for the forum, but my guess is that it would not want to be used for money changing hands. Why don't you just use an anonymous poll? The software can set up a poll for you, it's done a lot. (I've never done it, click on some options).
Newton didn't like action at a distance, and neither did Einstein, so that was a big motivator.

Without much work, a simple estimate is possible by taking the speed of light and dividing by the age of the universe, this is the scale of the acceleration in the non-exponential mode we find ourselves in, so that would be (negative) 10^(-9) m/s^2.

I'd like to apologize in particular for calling steady-state backers "idiots." Naming-calling is usually what you resort to when you know you have a losing hand. Sorry, I got carried away.

From the day I left the relative warmth and safety of the womb and popped into "the real world," my life has been one continous change. Nothing has ever "stayed the same." So I just cannot imagine how anyone could possibly believe that the universe over-all "never changes." I can understand confustion about which direction the universe is changing (expansion speeding up or slowing down). Most of my life I have been "confused" about which directionit was going, but I have always felt certain that no matter the situation, eventually it will change. But as they say, "The more things change, the more they stay the same," so I guess the SSers have an argument.

So I will try to stick to explaining my theory, and not worry about the others, but I want me and the readers (I and the readers?) to have some fun along the way, and as I said, got a little carried away. I'll try to keep it "lite."

Thanks Peter-

I've read your theory, and I'm going over your calculations now. It doesn't seem to have any gross misstatements or errors as I can read it. I will check back in, when I've finished analyzing it. But so far, it's a plausible alternative, and pretty interesting!!

What is your background, if I may ask ?

Notice I said "virtual." I do not gamble (except for the occasional 2-bit office pool, and when the lotto jackpot goes over $300M), and do not want to encourage others to.

As for setting up the poll, I confess to being a bit of an idiot-savant. I understand why the universe is expanding, and why said expansion is accelerating, but I am still baffled by the blog. Careful readers will notice I haven't even figured out how to do a labeled-link (or whatever the technical term is). The speaker never sets up the podium and microphone; he or she always has help with such details. Can we have a volunteer, who knows more about The Blog than I do, set up the poll in a separate post? I think it is pretty clear what the options are: GR as-originally-published (with CC/DE), or GR as-later-amended, sans CC/DE.

Beautiful! That is exactly what I was after. Except it is in the wrong units. The acceleration is the same as the expansion, except it is different. In the Hubble relation, velocity is proportional to distance; in the acceleration relation, acceleration is proportional to velocity. But the units are the same. Interest is expressed as change-per number of starting units-per unit-time. 4% APR means 4 Euros per 100 Euros per year. As we have noted above, the expansion can most easily be expressed as change (73) per starting amount (1 trillion) per unit time (1 year), or 73 ppt/yr. Deceleration has to be in the same units: change in velocity (fill in the blank) per quantity of starting velocity (choice depends on the OOM of the phenomenon) per unit time (years in this case, for consistency). So I will assume you really meant it was approximately (negative) 10^-9/yr (1 ppb/yr), which is good enough for my purpose here , unless someone wants to argue your estimate, which they are of course free to do (see ATM Rules and Regulations).

So to sum up, here are the "basic numbers," so that the reader knows what I have to "shoot for," before placing his or her virtual wager. If you are going to bet on someone making a basketball shot, you have to know how far they are shooting from, correct? So here are the numbers, the 1st being subject to amendment, as already discussed:

Pre-1998 estimate of rate of change: - 1 x 10^-9/yr (- 1 ppb/yr)
Steady-State Model estimate: 0.0
Actual, observed rate of change: + 73 x 10^-12/yr (73 ppt/yr)

As you can see, the SSers were actually closer to the correct answer than the original BBT estimators, but they were still off by a little. And the actual, observed value that I have to explain is about 1 OOM less than the original estimate, although positive, not negative (the last part being the mysterious part that my AE will address).

I think that is enough information for everyone to make a responsible bet (if that is not any oxymoron), so with a little help , let the polling begin!

SSers bet on SS ... that's what SS does best.

That's even easier, you just divide out the c and get the inverse age of the universe. So it's -10^(-10)/yr. That this number came out close to what you quoted above is a coincidence of the fact that the speed of light in m/s is not that different from the number of seconds in a year.
That's not correct, the correct first number is more like 10^-10/yr, and note this is quite close to the third number. Furthermore, if you plot these numbers on a logarithmic scale, which is appropriate to do, you will see that the steady-state estimate is still off-the-scale wrong.

I agree entirely with Ken G's comments above...except to say you really cannot post both positive and negative numbers on a logarithmic scale.

I was unclear where the "coincidence" came from, but just figured go with it, and it would correct itself.

Certainly. I am an intelligent designer, more commonly referred to as an “engineer.”

As an engineer, calculations have never been my specialty. My approach is: be clear on what it is you are trying to accomplish; check the paper design over and over, make sure it looks right from every angle that you can possibly imagine; build a prototype, the infamous “Rev. 1;” test it, shake it down, figure out what is wrong (always something); fix those flaws in Rev. 2; and if all goes well, Rev. 2 can go into production. Of course, there is always room for improvement. But of these general steps in the engineering process, my specialty has always been the “figuring out what is wrong” part.

I developed an approach to “why is it not working” that always led to cracking even the toughest nut. And it is not the first approach, mind you, but the last: try to make the problem worse. Say the blessed thing is vibrating, and you’re stumped. You cannot figure out what is causing the vibration. So you ask yourself, How could I make it worse? What could I do to make it vibrate even more? Before long, you’ll have that thing shaking, and when you get it past vibration to down-right shaking, then you’ll understand what was making it vibrate. Try to do the opposite of what you are trying to accomplish.

So instead of trying to understand why our universe expands, we will build a model that doesn’t expand or contract. And when we do that, we can compare notes, and see what the difference is. And the difference between the static model and our universe will point to what is causing expansion in our universe.

Starting with Einstein’s key finding that the universe should expand or contract, we assume the role of an intelligent designer (theoretical physicist), and build a universe that does not expand or contract. We can do it on paper. Like a bridge, a universe with an expansion rate exactly equal to zero can be built, as long as certain “requirements” are met, which I will explain when I explain it.

And when our model is complete, nothing much will ever happen. It will not expand or contract, per the design specifications, but you will see that not much else of interest happens, either. Of note: one of the requirements is that it must be made entirely of dark matter. Another is that we must repeal the laws of GR, and use Newtonian gravity instead.

Since nothing ever happens in this universe, we will want to add something to get some action going. And that key ingredient will turn out to be radiant matter. Add radiant matter to our model, and interesting possibilities emerge. But there is a problem, Houston. The paradox Newton puzzled over. Suffice it to say, we have to put GR back into the model in order to make it work. A Newtonian model looks good on paper…but it won’t work in the real world, as you will see.

The reasoning goes like this: we create a model universe that neither expands nor contracts. We notice this static universe looks remarkably like ours, except for three key differences:
1) It contains no dark energy (sort of obvious)
2) It contains no radiant matter (not so obvious)
3) Newtonian gravity must prevail (even more subtle)
Finally, we put #2 & #3 back into the model, and Voila! Expansion! That is all you need. It expands all by itself, w/o DE. When I build the static model, which does nothing, you will see that when you add radiant matter to the model and apply GR, it expands.

So if the key difference between the static model and the expanding model is radiation, then it stands to reason that the radiation is “causing” the expansion! You do not have to know how to "do the calculation," all you have to notice is that the static model is without radiation, and that putting radiation back into said model causes it to expand. And since the static model does look so much like "the real" universe, it is enough to persuade me that radiation is the difference, hence "the cause." Now all that's left to do is persuade everyone else.

Lastly, I will try to show that the numbers come out right; I will try to show that the energy required to drive an expansion rate of 73 ppt/yr is less than the estimated 1 j/kg/yr of radiant energy that is available to drive it. As I said, calculations are not my specialty, but I will estimate the expansion energy, and argue that it is considerably less--more than 2 OOMs less, my estimated margin of error--than 1 j/kg/yr.

This strikes me as a very clever approach indeed, and should be very informative when applied to cosmology.
This is not sufficient, it won't work. The most important element is missing. The universe is not dynamical because of light, nor because of general relativity. Even a universe of pure dark matter and pure Newtonian gravity (even if that were possible) will still be dynamical. The key point is: gravity isn't stable on the largest scales. It falls victim to something called the "Jeans instability". This is a result of purely classical gravity, with no light and no GR. It says that a large enough gravitating system will fragment into dynamical pieces whose size depends on the density. Thus the same mechanism that gives you galaxies when you apply it to the inter-galactic medium will give you a dynamical universe when the cosmological principle is applied to the entire universe, for densities not that much less than the "critical density".

Thus the key things that require the universe to be dynamical are not light and GR, they are the cosmological principle and the density. To get a static universe you need the average density to be less than the critical density, and the lesser the better. You also need to get rid of the cosmological principle, and say that our universe is a part of some huge clump that is in stable equilibrium over the scale of the clump, like a giant galaxy of galaxies. You are right that if you had this, then adding radiant matter would monkey up the works and your galaxy of galaxies would also have to evolve. My point is that we observe a density on the order of the critical density (effectively equal to it, in fact), and we observe no evidence that the universe is not homogeneous on the largest scales, so we already have a dynamical universe at this point, even using classical gravity and no light at all. That is why light energy is not going to be the crucial issue in explaining the expansion of the universe, in a nutshell.
For the above reasons, the static model is not going to be static even before you add radiant matter and GR. But even if it were, how does adding either of these imply expansion? The point is, all you can conclude at some point along the way is that it can't be static. The things that force it to be dynamical are not necessarily causing the expansion. Consider a basketball in flight toward a hoop. The presence of gravity implies that the basketball cannot simply hang in the air, it must be dynamical, so it will either go through the hoop or it will be grabbed by another basketball player. Can we then say that gravity explains whether or not it will go through the hoop? Not by itself, no, because sometimes it does go through the hoop and sometimes it doesn't. A complete explanation requires inclusion of the shooter's hand motion. Indeed, what makes someone a great shooter is not their understanding of gravity, it is their ability to control that hand motion. Thus the expansion of the universe is not explained by light, or by gravity, it is explained by the initial condition. Our universe was prepared in a state of expansion, as if by some unseen 'shooter', and a very good shooter indeed-- that our universe is still in an interesting condition after almost 10^60 Planck times means that it is passing through an extremely small hoop indeed. There is presently no other explanation. The universe is not only a three-point shot, it is a buzzer-beating length-of-the-court prayer.
And by the same logic, since this is not the key difference, radiation is not causing the expansion. I believe you have been hoisted by your own petard.

But Ken G, you haven't even seen the drawing...

“The universe should expand or contract.” This is Einstein’s famous finding that was at odds with observations. And of course, it is wrong--his “greatest blunder.” So he worked into the equations the now infamous “Cosmological Constant,” to try to make the universe do neither.

“The universe” in the above context refers to any and all possible universes. The simplest universe—two particles—will expand or contract. They will either fly past each other off to infinity—expand—or fall towards each other—contract. (Orbiting counts as contraction because the pair will emit gravitational waves, and the orbit will decay). From the simplest to the most complexest of the infinite possibilities, every starting configuration will end up in one bin or the other. A coin will land heads or tails, and a universe will expand or contract.

So if GR says every starting configuration will expand or contract, how is it possible to build a model universe that is static?

Same way we stand a pencil on its pointed end. Start with a granite slab; a room with no air movement; no vibrations; no thermal gradients; throw out QM (no “random” disturbances); balance the pencil with infinite precision, and it will stand on its pointed end. Building a static universe is similar: it can be done, provided we allow some “kind of artificial” conditions. Some, as we shall see, however, are perfectly natural.

A static model can be built as long as it is:
1) Infinite
2) Homogeneous
3) Isotropic
4) Ruled by Newtonian gravity, not GR
5) Composed entirely of “dark matter”

Reviewing these requirements briefly: to be stable, the universe must be infinite in extent, otherwise it will have a “center of gravity.” If it has a C-of-G, it will be either “hot,” i.e. expanding, like the bomb going off in space; or “cold,” like the dreaded asteroid that falls back together. One or the other. The only way for it to not have a C-of-G is for it to be infinite. The only way to “keep it from falling in on itself” is to make “it” infinite.

The need for homogeneity and isotropy are related to this idea: keeping everything “balanced.”

Newtonian gravity (NG) is specified only in so far as the matter cannot emit gravitational waves. The matter’s “darkness,” the last requirement, must be absolute. If an infinite, homogenous, isotropic universe, composed entirely of dark matter obeying NG could be built, it would neither expand nor contract.

Why does it not expand? Well, it takes energy to expand, to move things apart. And there is no source of energy. There is no dark energy (obviously), nor is there any radiant energy. So it cannot expand.

Why does it not contract? This is the crux of the whole matter: It cannot contract, because in order to contract, it must lose energy. The grid is infinite, and for it to contract, it must lose energy. And the particles cannot lose energy by radiation, because as we have already said, they are dark. This last point is subtle, and is entirely missing from the main stream accounting.

1) No gravitational system can contract without losing energy.
2) No gravitational system can contract without losing angular momentum.

The earth does not fall into the sun, because it cannot radiate away gravitational energy/angular momentum very efficiently. The sun does not fall into the black hole in the center of the galaxy, likewise. Dusty clouds of gas, on the other hand, can radiate away energy relatively efficiently, and in “only” a hundred millions years radiate away enough energy to collapse to the point of thermonuclear ignition. Only those systems which can radiate away energy and angular momentum can contract.

A meteoroid can pin-ball its way through the solar system for billions of years, but it never really “falls” until one day it skims earth’s atmosphere, lighting up the night sky for a moment. And in that glorious moment of lighting up the sky, it radiates away enough energy “to fall.” Ultimately, all its starting energy (wrt earth) is radiated away as heat or light. But until it finds a way to lose energy (running into earth will do), it never “falls.” If a system cannot lose gravitational energy and angular momentum, it cannot contract.

But dark matter has no way to lose energy…by definition. Therefore, nothing ever happens in this model. The dark matter—whatever it is composed of—can be moving this way and that. It can have any temperature; can have elastic collisions, like molecules in the air. Air is “dark” in the casual-sense, i.e. neither absorbs nor emits visible light. If the air you are breathing extended to infinity in all directions--same temperature, pressure and composition--and it was dark in the strictest sense, and there was nothing else in the universe, it would just sit there. It would not expand. It would not contract. Nothing would happen.

There. We did it. We built a model universe that neither expands nor contracts. We had to meet the requirements listed above, but we did it.

The top panel of Figure 1 shows such a model, only one cube of which is shown. (Suggestion: print it.) It represents infinity by picturing one cube of an infinite number, repeating in all directions without end (post # 24). The dark matter is represented by black dots (tee-he). The outline of the cube is a “tracer” to keep track of things. The model just sits there. Whatever its temperature, pressure, composition and density, as long as these are the same everywhere, it just sits there. Forever. The true Steady State model: the rate-of-change is 0.0.

The bottom panel of Figure 1 shows what happens when you add radiant matter and GR back into the model: it contracts and expands. [Have to switch gears here: now the black dots represent radiant matter; the dark matter is still there—it just cannot be seen...because its dark!] Because “there is light,” matter can radiate away energy. It may start out homogenous, but over time it grows clumpier and clumpier.

Exactly.

The particles in the bottom panel are in a lower energy state than at the start. They have slid “down hill.” Having contracted under their own mutual gravitation, they have radiated away gravitational energy. But where has this energy gone? You might answer: The energy has been radiated into space. Which is true…literally. Remember, every cube off to infinity is also radiating away energy as the matter within it clumps. So there is energy coming and going, from everywhere, to everywhere. When you balance the books, the total energy entering and leaving each cube is the same. The total energy never changes. So as “local” particles lose energy by falling into clumps, the distant clumps gain energy by moving apart. Expansion is a reaction to contraction.

If space cannot expand, then the energy has nowhere to go. This is the paradox Newton puzzled over. Like Einstein, Newton assumed the universe was static, and in his imagination, he built a model like the top panel of Figure 1…infinite in extent. Then he imagined that it would “fracture” into innumerable clumps, such as the stars we see populating the heavens. In order for matter to go from a distributed state to a compact one, it must lose energy, as pointed out above. But where would the energy go? Newton could not imagine. He knew the universe would have to be infinite to keep from falling in on itself, but he also knew that if the universe was infinite, there would be energy coming from everywhere, and going everywhere, in equal proportion, so there could be no net change.

Einstein resolved the paradox by allowing space itself to bend and stretch.

The total energy content of the universe in Figure 1 does not change as it evolves from homogenous to clumpy (top to bottom). What changes is how the energy is distributed. Locally, matter loses energy as it falls downhill into the clumps. Relative to other clumps, however, matter gains energy, going up-hill. The net change is zero. Energy is conserved. Conservation of energy is what “causes” expansion in General Relativity. This has been overlooked again and again to the point of nausea. The talk.origins paper mentions that, “the universe should expand or contract,” but not why any particular universe, say ours, should expand. Do not even bother checking other sources, because no other source mentions the "why" part, either. The "why" part is here. The reason our universe expands is Conservation of Energy. The more bizarre tenets of the theory—that space itself can bend and stretch—are what allow it, but the more mundane principle of energy conservation is what drives it. Space expands in GR in such a way that the total energy content of the universe is constant.

And this is why the expansion is perfectly flat. Like a balloon, which expands in exact proportion to the volume of helium being pumped into it, the universe expands at a rate proportional to the radiant energy driving it.

The earth-moon system makes a perfect analogy. If the earth were not spinning (earth & moon tidally locked, like Pluto & Charon), it would not expand. The spinning earth is the source of energy driving the expansion. The earth-moon system does not expand so fast that the moon will fly off to infinity (“open” in BBT parlance), nor is it expanding so slowly that it will fall back to earth (“closed”). Its expansion is “flat,” perfectly poised betwixt the two. The reason it is “flat” is that it expands at the rate it is being driven. Like the static model above, which neither expands nor contracts (with neither a source of energy nor a means to lose energy), if the earth were not spinning, the earth-moon system would be “static,” or in a “Steady-State.” But it is the earth’s rotation that supplies energy, causing the system to expand at 100 ppt/yr.

Likewise, if there were no radiant energy in the universe, it would not expand, like the static model above. And in analogy with the earth-moon system, the expansion is “perfectly flat,” because it is expanding at the rate it is being driven. “Conservation of helium” is what makes a balloon expands at the rate helium is pumped into it. Conservation of Energy is what makes the universe expand at the observed rate of 73 ppt/yr.

Figure 2 shows the Big Picture: the source of the energy driving the expansion, and the reason the expansion accelerates. The curved line represents the generalized potential-energy vs distance curve of a gravitational field. The vertical scale is in energy per-unit-mass, i.e. joules/kilogram. Or, as expressed in post # 33, “inches of elevation in earth’s gravitational field at sea-level.” This is the most intuitive way to picture gravitational potential energy: up and down. You have more energy on the 2nd floor than on the 1st, and the difference is proportional to the change in elevation.

On the left-hand side, at a distance of less than 5 Mpc and off the vertical scale downward, lies everything within the cube shown in Figure 1. This is the source of the energy. Notice that it is almost bottomless. The total amount of energy per kilogram is not infinite, but the curve goes a long, long, long…long ways down. The bottom is something like 10,000,000,000,000,000 inches down! There is net “slippage” down the hill, at some rate, which I estimated at 2.5 inches per year. So within 5 Mpc, everything is “falling together,” but at 2.5 inches per year, this “fall” is going to take a looooooooooooooong time to "bottom out."

At any rate, as we saw in post # 55, the Crux of the Matter is this: gravitational systems can only contract at the rate they are able to radiate away energy. Therefore, the net radiation represents the net contraction. Within the 5 Mpc distance, expansion and contraction can always be found side-by-side: the core of the sun contracts, its outer envelope expands; the orbits of low-earth satellites contract, the orbits of high satellites (above GESO) expand; the core of a core-collapse SN contracts, its outer envelope expands; massive stars tend to “sink” (contract) to the center of globular clusters, while low-mass stars tend to get flung off (expand). Nonetheless, when you balance the books, the net effect is always contraction. Things are going down hill.

In the middle of Figure 2 and to the right, beyond 5 Mpc, there is net expansion. Matter is going “up” hill, not down. Figure 2 graphically illustrates three key points: First, beyond 5 Mpc, all matter is gaining energy at the same rate. Things that are farther recede faster, but because the energy curve is flatter, the actual rate-of-energy change is everywhere the same. Second, it shows the “why” of acceleration. Receding galaxies recede faster and faster with time, but all this means is they “have to go faster and faster just to stay in place” (i.e. gain energy at a constant rate). Lastly, it shows that the Hubble “constant” is a measure of the rate of energy gain. In other words, both galaxies pictured (and all galaxies beyond 5 Mpc) are gaining energy at the same rate, and H tells us what this rate is. The value of H says how fast remote galaxies are going “up the hill.”

Figure 2 also illustrates the Infinity Principle, (IP) discussed in post #24, from another angle. Beyond 1 Bly, the universe looks very uniform and isotropic (the Hubble Deep Field North looks just like the Deep Field South). If, at vast distances, “everything looks the same,” then we should expect that, at vast distances, “everything is the same.” Figure 2 shows how. Remoter and remoter galaxies recede faster and faster, but because the curve gets flatter and flatter, the rate of energy gain is “everywhere the same,” as the IP tells us it should be.

So the Big Picture in our universe is that within every roughly 5 Mpc cube of space, there is a net contraction, as shown in Figure 1 . This “rate of fall” (contraction) is evidenced by the rate at which matter radiates energy “into space.” Beyond 5 Mpc, there is net expansion, and the “rate of rise” is constant everywhere, as shown in Figure 2. This duality (local contraction/cosmic expansion) is impossible to picture in Newtonian space-time coordinates, but in GR, the duality is a natural outcome, just as the wave/particle duality is a natural outcome of QM.

So in the Big Picture, our universe is:

1) Infinite
2) Isotropic ("flat") on large scales
3) Composed of both dark and radiant matter
4) Ruled by General Relativity
5) Contracting locally
6) Expanding cosmically (and "flatly")

The premise of this thread, DEILE, is that the energy released by phenomenon #5, contraction, is greater than the energy required to drive phenomenon #6, expansion. And if the contraction energy is greater than the expansion energy, there is no need to postulate “dark energy” to drive it. If matter within 5 Mpc is “falling” at 2.5 in/yr, and matter beyond 5 Mpc is “rising” at less than 2.5 in/yr, then DE is not needed to “balance the books.”

“When Einstein first tried to (model the whole universe), he found that (GR) predicted the universe should either expand or contract.” [talk.origins] Call it Einstein’s subtlest error.

In hindsight, I don’t know how he missed it. Seems so obvious when you look back. And yet, I have tried to understand Einstein’s equations of General Relativity, and many others’ manipulations of them. It’s Greek to me. I understand them in the sense of, “some change on the LHS is equal to some change on the RHS.” And I understand that the equations take into account the basic conservation laws (linear and angular momentum; mass and energy, speed-of-light, etc), and that the “tensor-matrix algebra,” or whatever it is, somehow resolves the problems of infinite space alluded to in post 33, and illustrated in Figures 1 & 2 in the above post. But as far as what all those symbols mean…I haven’t a clue.

But whatever one is to make of the equations, we now know the above statement is incorrect. The universe does not do one or the other. It expands and contracts. It is not an either/or; not a one-or-the-other. It is a both. A duality. Like the wave-particle duality of light. Like the nature/nurture duality of human behavior. It is both. The universe is falling together at local scales, and falling apart in the all-in-all. It is true that every possible finite universe will expand or contract. But an infinite universe does both. Somehow, Einstein missed this, and to this day the duality remains “un-appreciated.”

If “the theory is correct,” then you can put the numbers in, and the equations will tell you that in an infinite, isotropic, radiant universe, space will expand at such-and-such a rate. Sans dark energy.

An infinite, isotropic, radiant universe w/o DE will expand. Period. The real universe certainly appears infinite and isotropic, and because it is radiant, we can see it contracting locally, and expanding globally. Not one or the other. Both. The statement, “The universe is expanding,” completely misses the mark; paints the completely wrong picture. The universe is both falling together and falling apart. And if “the theory is correct,” it will tell you how fast things can be expected to fall apart, based on how fast they’re falling together.

If the rate of expansion predicted by GR is less than 73 ppt/yr, then DE can be invoked to explain the “excess.” But if the model does not predict net-expansion at some rate, the model cannot be correct. How is that? The net effect on a “local” scale (< 5 Mpc) is everywhere negative; therefore, the net effect on the cosmic scale has to be positive. If one side of the scale goes down, the other must go up. It’s that simple.

If the rate of expansion due to radiant energy predicted by GR is 1 ppt/yr, then Okay, I’m wrong. Light plays no significant role. But if the model predicts a negative rate-of-change, as it did prior to 1998, the model is not right. The theory of GR may be correct, but the model must be in error. Prior to 1998, there was no dark energy, only radiant energy. Nonetheless, radiant energy is “more than zero.” In an infinite, isotropic universe, radiant energy “greater than zero” is enough to cause expansion to some degree, whether it is 1 ppt/yr or 73.

I don’t know where in the forest of equations they took a wrong turn, but the modelers lost sight of this axiom. Newton saw there was a “problem” with his equations at infinity, but he was unable to imagine the solution. Einstein figured it out, or so I’ve been led to believe. Yet Einstein approached the problem from a completely different angle—that “the laws of physics must be the same, even in differing frames of reference.” He seems to have been so focused on this "equivalency principle" that he missed the fact that our universe is fundamentally Dualistic.

The universe is not expanding or contracting. It is not doing one or the other. It is doing both. At the same time. With no hands. Radiant energy accounts entirely for the contracting side of the equation; and radiant energy accounts for some, if not all, of the expanding side.

And that’s the way it is.

This isn't right. Most of the matter that is contracting is apparently matter that emits little or no light, so it has a way to contract without emitting light. It just didn't contract without limit-- it contracted only so far, due to the Jeans instability, but eventually the Jeans limit stabilizes when the matter "virializes". This takes a free-fall time. So the point is, at some point the free-fall time was faster than the Hubble time at the scale of the Jeans instability in the dark matter, and that's what gave us galaxies. We just had to wait for the regular matter to slide down into the dark matter potential wells. It's true that the regular matter, being able to emit light, didn't stop there-- it kept contracting into stars. But most of the light in the universe is not starlight, it is the background radiation that was emitted before there was very much in the way of contraction going on. To say that the creation of stars by a tiny component of the universe's energy density is somehow responsible for the vast expansion of all the rest is just never going work out mathematically. Expansion is an initial condition in our universe, and acceleration of expansion is a recent turn of events. Contraction is happening on very different time and mass scales, and the connections between them are tenuous at best. It's not a bad idea, it just won't work, and the physics behind it is already in the models.

Technically, that is correct. The “way” it contracts is by weakly “coupling” to visible matter. It gets “dragged along,” or ensnared, in the process of visible matter contracting. Because the coupling is so weak, however, it remains diffuse.

That is one theory’s history.

DEILE is not about history. I was never good at history… It is about the instantaneous rate-of-change. The earth-moon system is presently expanding, and this expansion can be entirely explained in terms of present parameters. Ditto for the universe. This is where DEILE differs from standard cosmology. BBT is about explaining the present in terms of the past, and has become Ptolemaic in the process. DEILE is about explaining the present in terms of the present, and is therefore simple and elegant.

The moon’s orbit is expanding at the rate that earth’s rotational energy is “coupled” to the moon. The universe is expanding at the rate radiant energy is “coupled” to matter. The power-output of the earth is the rate its rotation is slowing down. The power output of visible matter is the rate it is contracting. Therefore, the instantaneous rate of expansion is directly related to the instantaneous rate of contraction. That is DEILE in a nutshell.

In terms of numbers, that is correct. Microwave photons far out-number visible ones. But in terms of power, it is the other way around. Stars positively roar compared to the whisper of the CMB. And how do you know there was not very much contraction going on? Because that assumption is built into the BBT. But DEILE is not weighed down by that assumption, because its “starting assumptions” are not the same as the BBT’s.

Could be. I guess we’ll find out April 1 when I (hopefully) present the math. (The calculation is turning out to be tougher than I thought. )

…the BBT. In DEILE, expansion is a natural consequence of on-going contraction, not an initial condition.

Thanks

We have been over this (post 39). In BBT, expansion was an initial condition, as you point out above, and was supposed to slow down. It is not. It is speeding up. The model was and is fundamentally flawed.

DEILE succeeds by anchoring itself in the present, not in the past. Its starting assumptions are the present conditions. And the laws of physics (“I don’t make the laws…” ) say that given the present state-of-affairs, and the present rate-of-contraction, the universe should undergo finite, positive, on-going expansion.

The expansion estimate will just about wrap up the present presentation of DEILE. In one sentence: The on-going expansion of the universe on cosmic scales is a natural, to-be-expected consequence of the on-going contraction occurring on local scales.

Figure 1 provides a charaterization of local contraction; Figure 2 shows the "big picture," and why the expansion is accelerating.

In post 33, I provided my OOM contraction energy estimate: 1 j/kg/yr, or – 2.5”/yr in earth’s gravitational field at sea-level (+/- 2 OOMs). This is the power available to drive expansion. To put this number in perspective, consider the moon, which as noted earlier, is receding from earth at about 100 ppt/yr, proportionally the same OOM as the expansion of the universe. That is to say, rather slowly.

Consider that the expansion of the moon’s orbit is driven by the spinning earth. The rate the earth loses energy as its spins down is a hushed murmur compared to the jet-engine roar of stars burning nuclear fuel. So we should expect that the energy involved in the earth-moon system would be considerably less than the output of stars.

In terms of distance, the moon recedes at about + 1.5”/yr. To convert distance to energy, recall that the earth’s gravitational field is much weaker at the moon’s distance. In rough terms, the moon is 60 times farther (2 OOMs) from the center-of-the-earth than we are at sea-level. Because the field decreases as the square of the distance, there is 3600 times less energy-per-distance traveled than at sea-level. So in terms of energy gain, the 1.5 in/yr recession velocity of the moon corresponds to only 0.0005 in/yr at sea level.

The moon is gaining energy at a rate 3 - 4 OOMs less than the estimated power-output of visible matter. By roughly “sizing up” the situation, we could expect the moon to be gaining energy at a rate considerably less than the stars lose it. It should be smaller, and it is. Check.

The earth-moon system is a two-body affair, of course, while the expansion of the universe involves an infinite number of bodies. The calculation is a little more difficult. This is where the “tensor-matrix algebra” comes in, I believe. Nonetheless, the two-body system and the infinite-body system share some characteristics, which we can use to get a feel for the answer.

First, in both the two-body system and the infinite-body universe, the rate of expansion determines the power. That is, if the moon were receding at twice the rate it is, it would be gaining energy at twice the rate it is. The same applies to the infinite-body universe: if the expansion rate, H, were twice its value, stuff would be gaining energy at twice the rate, other things being equal.

Secondly, the power of expansion for both the two-body system and infinite-body universe depends on the density. For the two-body system, density is the total mass divided by the volume encircled by the orbiting bodies. If the moon and earth together had half the mass they do, but were in the same orbit, the system would have half the density. And if the moon’s orbit was expanding at the same rate, the energy gain per-kilogram would be half what it is. And the same is true for an infinite-body universe: as its density decreases, less energy is required to expand it at the same rate.

Lastly, recall that the starting assumption for the two-body system is that the 2nd body is in a stable orbit around the 1st, and we are considering only the rate-of-change. In the two-body system, centripetal force counterbalances the gravitational force, such that there is no net change without input or loss of energy (and angular momentum). In the infinite-body universe, bodies on opposite sides provide the countervailing force, instead of centripetal force. Provided the infinite-body universe is isotropic, which our universe appears to be at large scales, the infinite-body universe will behave the same way, i.e. neither expand nor contract without input or loss of energy (post 52).

We now look at how a radiant two-body system behaves. Take the solar-system. Technically, it’s a multi-body system, but for the OOM est., the two-body model is a good approximation. The power output of the sun is roughly 4 x 10^26 watts (post 33). This radiation produces a net outward force of about 70 trillion pounds. But how “efficiently” does this 70 trillion lb-f of outward pressure “couple” to the two-body system under consideration?

The efficiency of coupling, or coupling-parameter (CP), depends on the albedo of the 2nd body, and its surface-to-mass ratio (for larger than molecular-scale systems). The coupling-parameter is defined this way: (energy available)*CP = energy gained. 0.0 < CP < 1.0. Since albedo makes only a small contribution, and we are after OOM estimates, we will ignore it here, and say that the CP depends on the surface-to-mass ratio (STM). For sub-micron sized dust-particles, STM is over 1,000 m^2/kg, and coupling is significant. For planetary-sized objects, it is close to zero. (earth: est. 2 x 10^-11 m^2/kg). While STM in the solar system varies over a range of 15 + OOMs, it is always a positive number.

What this means is that sub-micron dust gets “coupled” efficiently to the solar wind and expanded right out of the solar system on the order of years (think comet tails); 10-micron-sized dust gets expelled on the order of centuries; 100um dust is driven out in millennia, etc. For a Jupiter-sized body, however, the sun will burn out before expelling it. The point is, the sun has plenty of expansion energy available, but the “coupling” of this energy to bodies in orbit is very small, except for the very smallest.

Interestingly, for a body of a given STM, the expansion velocity does not depend on the distance from the source. Suppose the radiation pressure from the sun is pushing an asteroid-belt asteroid of a given STM outward at 1 m/yr, and there is a Kuiper-belt object with the same STM, only 10 times more distant. Ten times farther away, solar radiation pressure is 100 times weaker, due to the inverse-square law. But the gravitational field is also 100 times less, for the same reason. Because the driving force—radiation pressure—and the opposing force—gravitation—decrease in exactly the same proportion with distance, the net effect does not change with distance. The KBO of the same STM will also recede at 1 m/yr. In the general 2-body radiant system, expansion velocity does not change with distance.

In summary: a radiant, two-body system expands at a rate that depends on the radiant power of the system, and the “Coupling-Parameter” of the 2nd body, which depends primarily on its area-to-mass ratio. Recession velocity for a given STM does not change with distance.

Now we turn to the infinite-body radiant system: the universe. First, consider the “Coupling-Parameter” of the universe. It is not “close to 1.0” for small objects, and “close to 0.0” for large ones, as we found in the two-body system. Instead, the CP of the universe is some average of everything. This is because, “in the big picture,” it does not matter that dust, e.g, is coupled to radiation more efficiently than larger objects. From 10 Mpc away, the gas, dust, planets and stars of a galaxy all appear to move together, under their local mutual gravitational grip. So the CP of the universe is “some average” of all and everything combined. I have no idea what the CP of the universe is, suffice it to say, it must be very small; not zero, but very close to zero. Say, 10^-12.

As to the effect of distance: In the two-body radiant system, we saw that expansion velocity is constant with distance. When you go from 2-bodies in 2-dimensions, to an infinite number in 3-dimensions, the expansion velocity increases with distance, instead of remaining constant. When you add one dimension, velocity multiplies by one dimension. Another way to look at it is to picture the 3D infinite system as a bunch of 2-body systems “added up.” So instead of recession velocity being constant, it keeps “adding up,” that is, it increases with distance. In other words, Hubble’s law: expansion proportional to distance.

As noted above, expansion energy is proportional to density. The density of the universe is about 3 x 10^-27 kg/m^3. source The density of earth-moon system is about 0.1 kg/m^3. The earth-moon system is expanding at roughly 100 ppt/yr, “the same” OOM as the universe. The universe is 26 OOMs less dense than the earth-moon system, however. Making a wild guess, I would say the expansion energy of the universe at-large is 26 OOMs less than in the energy involved in the earth-moon system, i.e. about 10^(-29) j/kg/yr.

This seems impossibly small. But when I look at the numbers, it seems the answer must be very small, whatever it is. The density of the universe is said to be something like 1 hydrogen atom per cubic meter. Over the course of a year, the distance between each atom increases from 1.0m to 1.000000000073m. How much force is there between hydrogen atoms 1 meter apart? How much energy can it take to move them apart by 10^-10 per year? It has to be a small number, whatever it is.

Summarizing the parameters that are known with confidence:
1) Expansion rate of universe: 73 ppt/yr
2) Expansion rate of earth-moon system: same OOM as universe
3) Energy of expansion of earth-moon system: <0.001 j/kg/yr
4) Density of earth-moon system: 0.1 kg/m^3
5) Density of universe: 3 x 10^-27 kg/m^3

Maybe my math is off a little. To hedge, I’ll split the difference. I’ll add 9 OOMs to the energy estimate, and knock 8 OOMs off the CP guess. Final estimates:

1) Power output, P, of visible matter: 1 j/kg/yr
2) Coupling parameter (CP): 10^(-20)
3) Resulting power of expansion (P*CP): 10^(-20) j/kg/yr
4) Resulting expansion rate, H:10^(-10)/yr

In layman’s terms: Density of the universe is not mathematically zero, but close to it. Expansio rate is almost zero. Energy of expansion is almost zero. Energy available to drive expansion? 1.0 (j/kg/yr). Conclusion? Expansion easily explained in terms of radiant energy available.

According to The Mainstream, however:

1. The expansion energy is immense, and can only be accounted for by dark energy.
2. The quantity of DE required to explain the expansion is so large it makes up 74% of the universe.
3. Radiant energy plays no significant roll in expansion.



How could my back-of-the-envelope calculation be so different? The infinite-body system is not an exact analog of the two-body system. Maybe energy in the infinite body goes at the square-root of density, instead of linearly. That would bring it up from 10^(-29) to 10^(-15) j/kg/yr. GR complexifies things, and maybe that changes it by an OOM or two. Maybe I have to multiply it by the age of the universe, 10^10 years. That is still only 10^(-3) j/kg. It’s a mystery to me.

When I look at the numbers, everything seems to add up. Thin universe; slowly contracting; expanding even more slowly. Just another ordinary universe. No Inflation. No Dark Energy. No elephant in the chicken coop. :yawn: Just a thin soup—3 x 10^(-27) kg/m^3 thin—on a budget of 1 j/kg/yr, becoming even thinner, at a sub-glacial 10^(-10) per year. Really, not much happening…well, Old-man Rigley died last year.

But the mainstream insists, No, it doesn’t add up. You’ve got the math all wrong, and don’t understand GR. In a 2-body system, sure, radiation pressure causes expansion. But in GR, in an infinite universe, positive pressure produces contraction, not expansion. Here, post 7 Only DE, which produces negative pressure, can overcome the positive pressure of radiation.

According to TM, the universe is crazy. In the beginning, there was this huge explosion. Crazy. But that didn’t work. Bangless BBT So we added inflation. Crazy. But it worked. For a while. Then we found the expansion was accelerating. Crazy. Dark energy was added to explain that, but it takes a lot of it. Crazy. The universe is crazy, and if you think otherwise…

I don’t know. Maybe it is. The expansion seems rational to me. 73 ppt/yr? It’s like almost nothing is happening. What is wrong with this picture? I can’t tell. I’ve gone over the numbers again and again. Extremely thin universe; contracting locally at a moderate clip; radiating energy as it does so; resulting in infinitesimal expansion over-all. Looks right on paper. Everything appears in order, exactly as it should be. All I can say in conclusion is that if TM is right on all this, and the universe is crazy after all…at least I got something to blame it on!