Is the universe finite or infinite?

[marcus]

...
Actually I have seen curved models invoked many times, my point is that none of those models ever gave us the value, the bang for the buck, that the flat model does. Indeed those models can now be seen to be largely a source of unnecessary complication. Almost all cosmology textbooks, for example, start out with the three possible geometries, and go to great lengths describing their differences, only to throw it all away when they come to describing the currently favored model! It's so much wasted overhead...

Ah. This is where your personal attitude comes in. I remember in another thread you were urging that students not be exposed to the spatially curved versions of the model. You are campaigning for a kind of educational reform, in effect. Cosmology textbooks and curriculum should not WASTE STUDENT'S TIME by introducing the slightly curved case, or cases. It is "unnecessary complication"

The course outline, in effect, should focus exclusively on the flat case.

But not because flat is BELIEVED by any kind of mainstream majority or consensus.

Indeed to illustrate, in a central paper like the 2010 WMAP5 report by Komatsu et al they were keeping their options open and calculated up front with THREE versions of LCDM showing their results already on page 3 as I recall, Table 2, I think. A central paper with a dozen big name cosmologists reporting on a flagship project. Not fringe.

You are advocating a curriculum reform, to save "overhead", which would render students incapable of undertanding the options being kept open by core top professionals in the field.

It strikes me as a bit short sighted, a false "economy". It seems to have no logical basis, since we do not KNOW curvature is zero, and we may in future discover that it is on the positive or negative side of today's rather broad 95% confidence interval.

There is no logical basis for you to insist on this change in the course outline. It seems to have more to do with PERSONAL AESTHETIC.

I guess if we are going to talk at the level of personal aesthetics, prejudices etc. I will state my own, about what beginning cosmology students should be taught.

I would wish the course to present and explain the current confidence interval for Ω_k from the WMAP7 report (also Komatsu et al) and, assuming today's best estimate for the cosmological constant, describe the two basic kinds of universe contained in that confidence interval, both indefinitely expanding, one with slight positive curvature and the other with zero or slight negative. One model spatially finite (now and at the start of expansion) and the other infinite (now and at the start) or topologically rather intricate.

I'll go get that confidence interval for Ω_k Just google "komatsu wmap 7" and you get
http://arxiv.org/abs/1001.4538 and page 3 says:
−0.0133 < Ω_k < 0.0084

which means:
0.9916 < Ω < 1.0133

 

[Ken G]

Yes, thanks for that ViewsofMars. The take of that paper is that the observed curvature is consistent with a flat universe, which is of course all any observation could ever say. The authors of the paper take this observed fact and add an interpretation that this should be taken as evidence that the universe is Euclidean (i.e., actually perfectly flat), presumably because a Euclidean model is seen as a kind of conceptual watershed that should be given special attention if it is an allowed possibility. Probably that same conclusion could be framed in more uncontrovertibly scientific language by simply saying that these results call into question the usefulness of continuing to propagate non-flat models throughout the theoretical literature, and certainly more recent results further refine the confidence interval while reaching that same conclusion. None of this asserts that we should block out from our minds the possibility of curvature, it just means, as I said, the observations may be trying to tell us that we have reached a point of vanishing returns for continuing to carry around the mathematical excess baggage of nonzero curvature in the models, unless the question of curvature is explicitly the target of some investigation.

 

[Ken G]

Ah. This is where your personal attitude comes in. I remember in another thread you were urging that students not be exposed to the spatially curved versions of the model. You are campaigning for a kind of educational reform, in effect. Cosmology textbooks and curriculum should not WASTE STUDENT'S TIME by introducing the slightly curved case, or cases. It is "unnecessary complication"

Precisely. For some reason, you seem to disagree, though I can give you countless examples where we do precisely that in virtually every textbook, with no less justification. Let me choose a random example for illustrative purposes. A textbook wants to calculate the effect of the Moon on Earth tides. It's first step will be to choose a model for the Moon's gravity. Will the textbook:
a) cite a look-up table of precise measurements of the mass distribution of the Moon, or
b) treat the Moon as a sphere.
Seriously, I'm asking you-- which do you think that book is going to do? Surely you must be appalled if they choose (b), if they do it because they fear it would waste the student's time by using approach (a), right? You must say we cannot use a model that treats the Moon as a sphere, that would be blocking out of our minds any other possibility, while leaving our students incapable of understanding anything but spheres.

But it's just exactly the same issue with a model of cosmology. So why is everyone so happy to see a model of the Moon as just that (a model of the Moon), but suddenly when it's a cosmology model, we invoke some kind of religious devotion to the model? Such that it would be some kind of awful oversight to simply recognize that it's silly to do a bunch of extraneous math when a much simpler calculation will give us results well within the observational error bars? That's what I would like to know.

The course outline, in effect, should focus exclusively on the flat case.

Of course it should. The course outline is going to focus exclusively on the case where the speed of light is a constant in a vacuum, will it not? But that would be terrible, the idea that it would just waste the student's time to consider all the other possible ways that c might vary that are perfectly consistent with the observational constraints on the actual precision to which we can claim that c is constant in a vacuum.

Yes, I'm being a bit sarcastic, in response to yours, to demonstrate why your criticism is baseless. You simply put cosmology on a kind of pedastol for different treatment from every other subject you have ever seen in physics, when of course all we ever have anywhere in physics is observational constraints that are consistent with the idealizations in our models. Yet we make no apologies for not wasting student's time by including all those other possibilities in the course. But doing the exact same thing in cosmology, that would just be awful, you are saying.

Indeed to illustrate, in a central paper like the 2010 WMAP5 report by Komatsu et al they were keeping their options open and calculated up front with THREE versions of LCDM showing their results already on page 3 as I recall, Table 2, I think. A central paper with a dozen big name cosmologists reporting on a flagship project.

And what of it? It's hardly surprising that the flatness simplification must be examined closely before it is adopted, but it is inevitable that it will as the precision narrows more and more, as soon as we get tired of carrying around what is starting to seem like more and more useless baggage. We're already close enough that even if curvature is detected, the most commonly used model won't even use it, just as the most common treatments of gravity in astronomy still treat objects as spheres even when we have detected deviations. This is because models are designed to be simplifications, and they only need to be tailored to a reasonable accuracy target, never claims on the reality.

You are advocating a curriculum reform, to save "overhead", which would render students incapable of undertanding the options being kept open by core top professionals in the field.

And you see that as such a terrible thing? Why? Don't you realize we already do that all over the map? When is the last time you saw a cosmology book include the overhead of a rotating cosmology? Does that mean you think the observations have constrained the rotation of the universe to be zero? Of course not, it's exactly the same issue-- our observations are consistent with no rotation, so nobody bothers to waste the student's time by putting in all kinds of rotating cosmologies because they just have no reason to include all that unnecessary mathematical overhead. So you must be arguing this is a terrible choice that is rendering our students "incapable of understanding the options being kept open" by core top professionals who are working hard to observationally constrain the upper bounds on the rotation of our universe! So it's fine for rotation, but a terrible oversight for curvature? I have a good idea why you think that-- because curvature is ingrained in our cosmological upbringing, and rotation is not, by purely happenstance historical reasons. The ultimate irony would be if we never detect any curvature, but do someday detect a tiny rotation, and all the old cosmology textbooks get thrown in the garbage for spending all that time on curvature and completely ignoring rotation.

It seems to have no logical basis, since we do not KNOW curvature is zero, and we may in future discover that it is on the positive or negative side of today's rather broad 95% confidence interval.

It's not that broad, really it isn't.

There is no logical basis for you to insist on this change in the course outline. It seems to have more to do with PERSONAL AESTHETIC.

There is nothing "personal" in the aesthetic of removing extraneous mathematical baggage from our models, this is quite central to every chapter of every physics book everywhere in the world.

I'll go get that confidence interval for Ω_k Just google "komatsu wmap 7" and you get
http://arxiv.org/abs/1001.4538 and page 3 says:
−0.0133 < Ω_k < 0.0084

which means:
0.9916 < Ω < 1.0133

Like I say, really not that broad at all.

 

[marcus]

Physics is to a large extent the art of making the right simplifying assumptions (but not holding to one simplification exclusively) and choosing the right approximation (but not always the same) in order to calculate.

You gave the example of the tangent plane to a manifold. The tangent plane is a good approximation for some purposes. It is flat and infinite. It works fine for some things. But not for everything.

I happen to disagree with you about pedagogy in a beginning cosmo course, that's about all. I think you passionately overstate the case that students should be introduced at the start to no case except the infinite flat one. (Because nowadays for many calculations we use the flat approx.) I think they should meet the uncertainty up front and be prepared to read and understand mainstream calculations that use, say, the spatial finite endlessly expanding LCDM.

BTW that interval which you say is not broad has an upper limit of 1.0133 which means a radius of curvature of about 120 billion LY and a circumference of about 750 billion LY.

That would mean nothing in the whole wide universe is more than 380 billion LY from us. That strikes me as fairly close quarters given that the particle horizen, the most distant stuff we can see, is over 45 billion LY.

The upper limit of the 95% interval, IOW, says that the most distant stuff is less than a factor of 10 farther away than the stuff we can see.

I don't know if I'd WANT the upper limit to be larger than 1.0133
it would make things even tighter quarters, more closed in.

So you say the interval is not broad. To me it seems quite generous. And so we wait, and see if and how much the Planck observatory mission narrows it down.

Personally I think it is the wrong time to campaign for reforming the college course outline.

 

[Ken G]

Physics is to a large extent the art of making the right simplifying assumptions (but not holding to one simplification exclusively) and choosing the right approximation (but not always the same) in order to calculate.

Yes, I agree.

You gave the example of the tangent plane to a manifold. The tangent plane is a good approximation for some purposes. It is flat and infinite. It works fine for some things. But not for everything.

It has a simple mathematical form, easy to use in practice, and approximates well a manifold over some domain. That's a pretty good description of a flat cosmological model applied to observations of our universe, in the current state of affairs. So it doesn't have to work for everything, it just has to work for that thing.

I happen to disagree with you about pedagogy in a beginning cosmo course, that's about all. I think you passionately overstate the case that students should be introduced at the start to no case except the infinite flat one.

Do you think they should be introduced to rotating cosmology models, with all the equations and so forth? Why or why not?

BTW that interval which you say is not broad has an upper limit of 1.0133 which means a radius of curvature of about 120 billion LY and a circumference of about 750 billion LY.

That would mean nothing in the whole wide universe is more than 380 billion LY from us. That strikes me as fairly close quarters given that the particle horizen, the most distant stuff we can see, is over 45 billion LY.

It's a factor of 10 away from anything we can see, yes. That's why I say that we would never be able to use such a model to actually conclude that the universe was closed, it would never be observationally constrained as such. And then poof, there goes the whole main distinguishing feature of that model-- all that extra complexity and no payoff in terms of being able to say anything concrete about the universe's global geometry.

I don't know if I'd WANT the upper limit to be larger than 1.0133
it would make things even tighter quarters, more closed in.

Well, chances are, that upper limit will just keep dropping with time. It might not, but I'd bet good money it will. Anyway, if I'm right, eventually you will come around-- it's just a question of how long you will hold out! That's pretty much how I feel about the whole question-- everyone has to have a kind of personal limit where they finally decide the overhead just isn't worth it any more. I'm there now-- how much smaller does that upper limit need to be before you would go there too?

Personally I think it is the wrong time to campaign for reforming the college course outline.

Then we wait. I'm a patient man.

 

[twofish-quant]

That's the problem with a peak curvature that just happens to be what we can barely measure, why on Earth would life come along at just the time when it can barely measure the curvature?

The dark energy "cosmic coincidence problem" is a totally different problem. Inflation was never designed to fix that problem, and I think that's a different problem that irrelevant to inflation. Also, if you set flatness to zero, the "cosmic coincidence problem" also doesn't go away.

That's the "fine tuning problem" that you would be staring at if curvature is detected, and that's what would steal most of the wind from inflation's sails.

It wouldn't. The "flatness problem" is in fact a rather weak reason to support inflation. If we found that inflation didn't address the flatness problem then we'd still have the horizon problem and the CMB perturbations, which are far stronger pieces of evidence in support of inflation.

Exactly, and if curvature is detected, then we will have the fine tuning problem that dark energy is taking over at exactly the point when the curvature is barely detectable by intelligent life.

And if curvature isn't detected we have this fine tuning problem that dark energy is taking over at exactly the point at which we are making observations. Setting flatness to zero doesn't help you.

That's just the fine tuning that Weinberg argued is evidence for a multiverse, in relation to the amount of dark energy-- you would be in the exact same boat, but now in regard to curvature instead.

If you have two holes in a boat, that's not much worse than one.

In any case, it wouldn't affect the validity of inflation. The strongest evidence for inflation is that it predicts very well CMB fluctuations.

I agree completely, I don't think resorting to multiple universes is a fair way to make a theory seem palatable or plausible.

Except we have an example in which that happens. If you ask Steven Weinberg why he takes multiple universes and the anthropic principle seriously, the answer he will give is exoplanets.

Exoplanets provide an example of the anthropic principle in action. It turns out that solar systems with circular orbits are rare and hot Jupiters are common, but we didn't know about hot Jupiters because of the anthropic principle. If there were any hot Jupiters in our solar system, we wouldn't see them, because we wouldn't be here.

Also, exoplanets provide an example of how you can deduce something you can't observe. People first deduced the existence of exoplanets in the 1600's. They were only first observed in the 1990's, and they were detected using technology that was unimaginable in the 1600's. Weinberg would argue that trying to deduce the existence of multiple universes today is no difference than deducing the existence of exoplanets in the 1600's.

That's exactly why I claim any inflation proponent should be hoping we never detect curvature, and indeed, should probably even be confident we never will.

Disagree. The physics of inflation are sufficiently complex that it's not that hard to create an inflationary model that produces large amounts of curvature. During the 1990's, it appeared that the universe was open, and there were a flurry of plausible scenarios in which you could naturally create universes with curvature of -0.7 look up "open inflation". People stopped doing that in 1998, but there was nothing physically wrong with those models, and if we find curvature then we can dust off those models.

The other thing is that inflationary models predict curvature. The universe is not flat, it's wrinkly. All you have to do is to set up inflation so that one of the "wrinkles" is larger than the Hubble distance, and bammm, you have a small amount of local curvature.

The problem with inflation is that the detailed physics is sufficiently unknown and complex that we can't rule out curved inflationary models. Look at what happened in the early 1990's, the observers thought that omega=0.3, and the theorists came up with models that produced omega=0.3. Contrast that with the reaction of theorists when people came up with FTL neutrinos. The reaction of the theorists was "do your measurements again, you did something wrong." Whereas, no cosmologist that I know of reacted to the 1990's CDM measurements with "you did your measurements wrong" and they didn't because the theory is just not firm enough to make that statement.

People stopped working on open inflation models once the data looked like omega is close to one. But if it turns out that we have our dark energy models wrong, then people will work on them again.

There's just no reason for the parameters of a working inflationary model to be so well perched at that arbitrary tipping point that would suddenly seem very special indeed.

Well there it is. Also this has nothing to do with inflation. The cosmic coincidence problem is there if you assume flatness. The fact that the cosmic coincidence problem exists (and I don't know why) is why I reject "this can't happen because it would mess up our simple theories" arguments.

I don't agree, I think that for the vast majority of ways to set up that universe, the curvature will remain way too small to detect, because the one-two punch of inflation and dark energy will insure that.

You are invoking multiverse arguments. Once you talk about "alternative ways of setting up a universe" you are invoking a multiverse argument. It's a philosophical problem. If you assert there is one universe, then you can't really talk about "alternative ways of setting up a universe."

In the vast majority of universes, we wouldn't see a dark energy omega that isn't either 0 or 1, but we see it and it's 0.7.

You have to really fine tune the combination of inflation and dark energy to both have a universe that inflates enough to be anything like what we see (and, dare I say it, to support life), but still leave a window for detectable curvature for a few billion years out of that vastly aging universe-- exactly when life comes along.

Not clear. If inflation and dark energy are connected then you can try to come up with a natural way of connecting the two.

And in any case, this problem doesn't go away if you get rid of curvature.

That's the problem I've been talking about, this bizarre "glimpse of curvature" phenomenon, which has no "natural" explanation at all, and would sorely tax the whole spirit of using inflation to recover a "natural" feel.

1) If there isn't an obvious natural explanation, then we look for one.

2) Even if we can't find one, then it doesn't kill inflation. There are enough pieces of evidence for inflation independent of flatness that if it turns out that it requires weird coincidences to have inflation work, then that is just the way the universe works.

 

[twofish-quant]

Such that it would be some kind of awful oversight to simply recognize that it's silly to do a bunch of extraneous math when a much simpler calculation will give us results well within the observational error bars? That's what I would like to know.

The problem with this is that it dumps out the reason for thinking that LCDM is the current model of the universe. Assuming the universe is flat is the "zeroth order" calculation. It's a Newtonian model of the universe, and people *do* use it for pedogogy. Adding curved space is a first order calculation, that gets you Friedmann-Walker metrics.

The thing about LCDM that makes is a spectacularly good model is that it makes very detailed and correct predictions about the distribution of matter in the universe (i.e. the first/second/third acoustic peaks) and those calculations are not simple ones. Without doing those calculations, there is no reason to trust LCDM.

One problem with teaching cosmology is that people don't realize that we are long past "spherical cows." Our current models are good enough so that we can make complex and detailed predictions about the early universe.

Yet we make no apologies for not wasting student's time by including all those other possibilities in the course. But doing the exact same thing in cosmology, that
would just be awful, you are saying.

Most introductory cosmology courses introduce the mathematics of cosmology through a Newtonian cosmology. You assume that the universe is flat, and then with simple math you can derive things like the Hubble relations.

The Newtonian cosmology is a perfectly good toy model that is great for teaching cosmology, but it is *NOT* LCDM. Comparing LCDM with Newtonian cosmology is like comparing a Boeing 747 with a paper airplane.

If you want to introduce cosmology through simple Newtonian models, that's great, but it's important to emphasize that this is *NOT* LCDM. LCDM contains all of the messy details that aren't in Newtonian cosmology.

It's hardly surprising that the flatness simplification must be examined closely before it is adopted, but it is inevitable that it will as the precision narrows more and more, as soon as we get tired of carrying around what is starting to seem like more and more useless baggage.

As precision increases, our models get more complicated.

We're already close enough that even if curvature is detected, the most commonly used model won't even use it, just as the most common treatments of gravity in astronomy still treat objects as spheres even when we have detected deviations.

Part of the reason I'm jumping up and down is that I don't think you understand what LCDM is.

LCDM contains curved space. Even if it turns out that we set the average curvature to zero, you still have a parameter in LCDM which measures the variation of that curvature. LCDM contains some detailed physics describing particle interactions, which let's you calculate acoustic peaks.

If you drop curvature, you still have a serviceable cosmological model, but it is *NOT* LCDM. It's something else. If you drop the interaction model, you end up with FLRW. If you drop curvature, you end up with Newtonian cosmology. People *do* use Newtonian cosmology for some rough calculations, but it's *NOT* LCDM.

When is the last time you saw a cosmology book include the overhead of a rotating cosmology?

When I was in graduate school? It's going to be in any course in GR.

Of course not, it's exactly the same issue-- our observations are consistent with no rotation, so nobody bothers to waste the student's time by putting in all kinds of rotating cosmologies because they just have no reason to include all that unnecessary mathematical overhead.

The danger is that you end up with students that think that they understand more than they do. Also, graduate courses are very different from undergraduate ones.

I have a good idea why you think that-- because curvature is ingrained in our cosmological upbringing, and rotation is not, by purely happenstance historical reasons. The ultimate irony would be if we never detect any curvature, but do someday detect a tiny rotation, and all the old cosmology textbooks get thrown in the garbage for spending all that time on curvature and completely ignoring rotation.

Cosmology changes very rapidly. Any textbook that is more than two years old is hopelessly out of date.

Also we do detect curvature. CMB background flucutations are the result of spatial curvature. Whether there is average *global* curvature, is another question.

There is nothing "personal" in the aesthetic of removing extraneous mathematical baggage from our models, this is quite central to every chapter of every physics book everywhere in the world.

If you want to do cosmology past the "toy model" Newtonian stage, you have to do GR. If you do GR, you have to include curvature.

My concern is that you need to present the material in a way that doesn't mislead students. I'm concerned because you *think* you understand what LCDM is and isn't, but you don't, and I'm trying to present the material in a way that doesn't lead to the misconceptions that you have. (Again, I apologize for being harsh, but it has to be said).

The issue is that the gravity model and curvature is probably the *least* mathematically messy parts of LCDM. The more messy parts are the parts dealing with particle interactions.

 

[twofish-quant]

Do you think they should be introduced to rotating cosmology models, with all the equations and so forth? Why or why not?

Who is they?

In any sort of graduate cosmology course that's theory based, then absolutely. If you want to do theoretical work in cosmology, you need to understand how to handle rotating frames.
The whole point of graduate physics courses is to train students to do complex math, so the more messy math, the better. It builds character.

For undergraduate courses, it's sufficient to mention why we think the universe isn't rotating. The Newtonian cosmology is something that's good to introduce in undergraduate courses, but when talking about the Newtonian cosmology, it's important to explain how that is similar and different from LCDM.

Whether to introduce the mathematics of GR depends on the level of the class.

For graduate students, I'm teaching them to fly a Boeing 747. For undergraduates, I can show them a paper airplane and take them on a tour of the 747.

Also for graduate students, it's really important to go through "failed" models and why they failed. For undergraduates, it's less important.

That's pretty much how I feel about the whole question-- everyone has to have a kind of personal limit where they finally decide the overhead just isn't worth it any more. I'm there now-- how much smaller does that upper limit need to be before you would go there too?

With LCDM you *need* curvature in order to calculate the CMB fluctuations and the location of the acoustic peaks.

 

[ViewsofMars]

The universe is not flat, it's wrinkly.

I thought I'd chime in with this comment of yours. Berkeley Lab had an interesting article Clocking an Accelerating Universe: First Results from BOSS dated March 30, 2012. Here's a quote from it:

“All the data collected by BOSS flows through a data-processing pipeline at Berkeley Lab,” says Stephen Bailey of the Physics Division, who describes himself as the “baby sitter of the pipeline.” Working with Schlegel at Berkeley Lab and Adam Bolton at the University of Utah, Bailey “turns the data into something we can use – catalogues of hundreds of thousands of galaxies, eventually well over a million, each identified by their two-dimensional positions in the sky and their redshifts.” The data are processed and stored on the Riemann computer cluster, operated by Berkeley Lab’s High-Performance Computing Services group.

The current crop of BOSS papers is based on less than a quarter of the data BOSS will continue to collect until the survey ends in 2014. So far, all lines of inquiry point toward the so-called “concordance model” of the universe: a “flat” (Euclidean) universe that bloomed from the big bang 13.7 billion years ago, a quarter of which is cold dark matter – plus a few percent visible, ordinary, baryonic matter (the stuff we’re made of). All the rest is thought to be dark energy in the form of Einstein’s cosmological constant: a small but irreducible energy of puzzling origin that’s continually stretching space itself.

But it’s way too soon to think that’s the end of the story, says Schlegel. “Based on the limited observations of dark energy we’ve made so far, the cosmological constant may be the simplest explanation, but in truth, the cosmological constant has not been tested at all. It’s consistent with the data, but we really have only a little bit of data. We’re just beginning to explore the times when dark energy turned on. If there are surprises lurking there, we expect to find them.”
http://newscenter.lbl.gov/news-releases/2012/03/30/boss-first-results/

 

[twofish-quant]

Yup, and one reason *not* to adopt flatness as a principle just yet is that the calculations of omega make assumptions about dark energy. If it turns out that dark energy is "something odd" then the numbers are going to change.

 

[Ken G]

The dark energy "cosmic coincidence problem" is a totally different problem. Inflation was never designed to fix that problem, and I think that's a different problem that irrelevant to inflation. Also, if you set flatness to zero, the "cosmic coincidence problem" also doesn't go away.

I'm not talking about dark energy, I'm talking about an analogous issue that is all about inflation and curvature. The curvature problem most definitely does go away if you have unobservable curvature, exactly the way the cosmic coincidence problem you are talking about would not have appeared had there been no dark energy.

It wouldn't. The "flatness problem" is in fact a rather weak reason to support inflation. If we found that inflation didn't address the flatness problem then we'd still have the horizon problem and the CMB perturbations, which are far stronger pieces of evidence in support of inflation.

Yes, that's a good point, it means that inflation has a lot of reasons to be here and probably isn't going away any time soon. Still, it would be a cool person in its armor to lose its "one stop shopping" flavor, and end up still having to address a fine tuning problem after all that.

If you have two holes in a boat, that's not much worse than one.

It is if you have two different boats!

In any case, it wouldn't affect the validity of inflation. The strongest evidence for inflation is that it predicts very well CMB fluctuations.

I don't dispute that, indeed that's exactly why I claim we should expect the flatness precision to only increase with more observations. The inflation phenomenon has good support, and should not lead to fine tuning problems like the "glimpse of curvature" conundrum, so that is the argument for expecting a flat model to continue to be excellent. A separate argument is that it is already known to be good enough for all but the most stringent accuracy needs.

Except we have an example in which that happens. If you ask Steven Weinberg why he takes multiple universes and the anthropic principle seriously, the answer he will give is exoplanets.

Exoplanets provide an example of the anthropic principle in action. It turns out that solar systems with circular orbits are rare and hot Jupiters are common, but we didn't know about hot Jupiters because of the anthropic principle. If there were any hot Jupiters in our solar system, we wouldn't see them, because we wouldn't be here.

There is a great deal of confusion about what the anthropic principle is. There is a weak version of it which is actually pretty obvious, and that is all that is being invoked by hot Jupiters. It's perfectly normal science to be able to observe some distribution, like planets, and have some special selection criterion, like life, which cuts the distribution in a highly non-generic way. That's quite a yawn, actually. But what makes it science is that we can indeed observe those hot Jupiters! Then there's a strong version, where we feel the need to invent a distribution of other universes that is completely untestable because the other universes cannot be observed, simply for the purposes of being able to feel better about fine tuning issues that nobody knows are even a problem in the first place.

Weinberg would argue that trying to deduce the existence of multiple universes today is no difference than deducing the existence of exoplanets in the 1600's.

And what that argument misses badly is that what makes exoplanets interesting is just one thing: they've actually been detected! Few people gave a hoot about the "deductions" of the 1960s, or the speculations of Bruno in the 1500s either for that matter. It's not even a remotely good analogy-- we saw stars out there, they look a lot like the Sun, it is perfectly natural to speculate that they might have planets around them. But if there was never any way to detect those planets, then the whole issue would never have been science at all.

Disagree. The physics of inflation are sufficiently complex that it's not that hard to create an inflationary model that produces large amounts of curvature. During the 1990's, it appeared that the universe was open, and there were a flurry of plausible scenarios in which you could naturally create universes with curvature of -0.7 look up "open inflation". People stopped doing that in 1998, but there was nothing physically wrong with those models, and if we find curvature then we can dust off those models.

Except for one thing-- they will of course be vastly finely tuned! So there goes the hope that inflation models will seem generic or inevitable. What's more, doesn't it bother you at all the "all things to all people" aspects of inflationary theory that you keep alluding to? If we need flatness, poof, inflation explains it. If we need curvature, poof, inflation explains it. If we need the model to seem generic, poof, inflation will make it all seem generic. If we need to explain some finely tuned result (like barely detectable curvature), poof, inflation does that too. Now, there's nothing wrong with a versatile theory, but I think we need a little truth in advertising-- I feel like putting my hand on my wallet when people start telling me all the conflicting advantages of these "all things to all people" inflationary theories.

other thing is that inflationary models predict curvature. The universe is not flat, it's wrinkly. All you have to do is to set up inflation so that one of the "wrinkles" is larger than the Hubble distance, and bammm, you have a small amount of local curvature.

Sure, but note that's also exactly why I've claimed that detecting curvature would not imply anything about the global geometry of the universe! Note this is the whole fallacy of placing so much importance on detecting some tiny curvature, it doesn't matter much at all unless you think it constrains what exists way beyond what you can actually observe.

Whereas, no cosmologist that I know of reacted to the 1990's CDM measurements with "you did your measurements wrong" and they didn't because the theory is just not firm enough to make that statement.

Well, the cosmologists I knew in the 1990's very much did suspect that the observation was wrong, or more correctly, misinterpreted. Certainly it was a perfectly standard statement at the time that non-flatness was a big headache for inflation, and many inflation proponents were quite clearly saying that they suspected something wrong with the non-flat interpretation. Ironically, those who stuck to their guns had a lot less backpedalling to do later on when dark energy came around.

The fact that the cosmic coincidence problem exists (and I don't know why) is why I reject "this can't happen because it would mess up our simple theories" arguments.

I agree there, I think fine tuning is not nearly as much of a weakness of a theory as multiverse thinking is. I never think a theory can dictate to reality, it is always the other way around. But fine tuning is something you do not expect to see if you haven't already seen it, that's the whole point about the flatness issue. If I'm playing poker, I never expect my opponent to have 4 aces. But if he is betting the roof, and I don't think he's bluffing, only then do I need to adjust my expectations, and I do so without requiring the existence of a multiverse of other poker games in which I am winning!

You are invoking multiverse arguments. Once you talk about "alternative ways of setting up a universe" you are invoking a multiverse argument.

No, there is a huge difference, summed up in the analogy I just made. When you are playing poker, of course you imagine a range of possible deals, but when you get evidence that the deal you are in has very unusual properties, you just accept that at face value, and discard the vast numbers of hypothetical deals that don't fit the facts-- a multiverse argument is something different, it is the argument that "if my deal is special, then there has to actually be a bunch of generic deals somewhere else, but I couldn't exist in them so I'm in this one." It is purely a way to "feel better" about being in a very unusual deal, and it is strictly for people who want the laws of physics to make the universe seem inevitable or generic. Anyone who is just fine with an amazingly special universe has no use for a multiverse, but they still have every use for imagining a "range of deals" when addressing what is not already known to be unusual. That's the key difference.

Not clear. If inflation and dark energy are connected then you can try to come up with a natural way of connecting the two.

That's true, it would seem necessary in fact, if both curvature and dark energy seemed to come out very special. If we did detect curvature, and were then face to face with the "glimpse of curvature" conundrum (but we should not expect this, as it is not something that is already known to hold), I think we could make a strong case that we would need to kill both those birds with the same stone-- we'd need to connect inflation and dark energy to seek one explanation instead of two.

And in any case, this problem doesn't go away if you get rid of curvature.

No, but we already know we have that problem (or the Nobel committee thinks we already know that), whereas we do not already know we have a curvature problem. That's a crucial distinction. If you already know one opponent has a very unusual hand, you still expect the other opponent not to.

2) Even if we can't find one, then it doesn't kill inflation. There are enough pieces of evidence for inflation independent of flatness that if it turns out that it requires weird coincidences to have inflation work, then that is just the way the universe works.

I agree, I'm not arguing that inflation will be killed. Indeed, I'm arguing that inflation is probably pretty good, and that is the basis why we should expect curvature to remain undetected, just as we should expect rotation to remain undetected. I see no evidence those issues should be treated so vastly differently as they are.

 

[Ken G]

Who is they?

Advanced undergraduates would be a fine test bed for what I'm suggesting. Possibly also graduate courses in cosmology, it depends on whether or not the instructor has some particular reason to want to address rotation. I'd wager that most graduate, and virtually all undergraduate, cosmology courses say little or nothing about rotating models, but the vast majority go into great detail about the various curvature possibilities. Just why is that? I argue it's purely an accident of history, and is high time to correct. Certainly any course is not going to be able to cover everything, so you pick and choose what areas give you the greatest "bang for your buck." If you stick to flat models, it does not at all mean, as was suggested, that the students will be hopelessly crippled for thinking about anything else, what it means is that you can spend your energy instead on digging deeper into some other area, perhaps inflationary models, that has much more promise of being something important, and not just a minor correction in the second decimal place.

With LCDM you *need* curvature in order to calculate the CMB fluctuations and the location of the acoustic peaks.

Of course, but you don't need global curvature in your model to do that. Indeed, mixing global curvature with the local curvature that affects CMB fluctuations is exactly the kind of extraneous detail that obscures the important concepts, rather than brings them out-- unless one favors the "black box" school of education, where you just teach students to put everything but the kitchen sink into the computer, and see what comes out, without any real understanding entering the student's brain.

 

[Ken G]

I thought I'd chime in with this comment of yours. Berkeley Lab had an interesting article Clocking an Accelerating Universe: First Results from BOSS dated March 30, 2012. Here's a quote from it:

Yes, "the concordance model", I forgot about that tidbit of jargon. That is what I have been referring to as the "consensus best model", but whoever coined "concordance" is a PR genius! Thanks for showing abstracts of concordance model papers that quite clearly demonstrate that the concordance model is a flat model with a cosmological principle, i.e., an infinite model of the universe. Indeed I would personally not go so far as to take that as evidence that the universe is actually infinite-- anyone who does may extrapolate too much (infinitely too much?) to suggest that!

 

[ViewsofMars]

Thank you Ken. twofish-quant, and Marcus

As far as dark energy this is what I recently read:

How can we solve the mystery of dark energy?

Observations of light emitted near the horizon of the universe reveal that everything seems to be flying apart with increasing velocity. Big Bang cosmology attributes this to “dark energy” that fills the entire universe— an amazing phenomenon! Is the Big Bang model too simple? Should Einstein’s equations be modified? Is there an unknown fundamental force? As the answers emerge, I expect that in the next decade physicists will solve the mystery of dark energy.

Wilfried Buchmueller, DESY, Germany
http://www.interactions.org/beacons/twenty-first-century-questions

I must say that I absolutely love discussions about the universe.

 

[twofish-quant]

I'm not talking about dark energy, I'm talking about an analogous issue that is all about inflation and curvature. The curvature problem most definitely does go away if you have unobservable curvature, exactly the way the cosmic coincidence problem you are talking about would not have appeared had there been no dark energy.

But we have dark energy. That's why I don't buy this "let's assume that we won't observe this because it will lead to a weird coincidence" logic. We've already seen it fail once.

Then there's a strong version, where we feel the need to invent a distribution of other universes that is completely untestable because the other universes cannot be observed, simply for the purposes of being able to feel better about fine tuning issues that nobody knows are even a problem in the first place.

It's not untestable. The idea behind anthropic principle is that you can use this to estimate parameters that you haven't observed yet. If someone comes up with an anthropic argument for the mass of the electron to thirty digits, and they start matching, that's good evidence that we've got something.

Few people gave a hoot about the "deductions" of the 1960s, or the speculations of Bruno in the 1500s either for that matter. It's not even a remotely good analogy-- we saw stars out there, they look a lot like the Sun, it is perfectly natural to speculate that they might have planets around them. But if there was never any way to detect those planets, then the whole issue would never have been science at all.

We don't know that there isn't a way of detecting exoplanets or multiverses until you think about it for a long time. The problem with your definition of science is that it means that in 1590, Bruno should have given up thinking about exoplanets, because they are unobservable by the technology of the 16th century.

What's more, doesn't it bother you at all the "all things to all people" aspects of inflationary theory that you keep alluding to? If we need flatness, poof, inflation explains it. If we need curvature, poof, inflation explains it. If we need the model to seem generic, poof, inflation will make it all seem generic. If we need to explain some finely tuned result (like barely detectable curvature), poof, inflation does that too. Now, there's nothing wrong with a versatile theory, but I think we need a little truth in advertising-- I feel like putting my hand on my wallet when people start telling me all the conflicting advantages of these "all things to all people" inflationary theories.

As I mentioned before flatness is a very weak argument in favor of inflation. The two strong ones are CMB power spectrum and the horizon problem.

In some cases the theory is stronger the the observations. For example, when FTL neutrinos were observed people were pretty sure that the observations were wrong since the theory is strong. Inflation has some strong parts and some weak parts. The parts regarding flatness are one of the weaker parts. That means that if it turns out tomorrow that someone claims that we messed up dark energy, and omega=0.1, I'm more likely to redo inflation to fit the observations than to assume someone messed up the observations.

Note this is the whole fallacy of placing so much importance on detecting some tiny curvature, it doesn't matter much at all unless you think it constrains what exists way beyond what you can actually observe.

It matters quite a bit because changing curvature also changes the calculated power spectrum which also changes things like galaxy formation. It also eliminates possible inflation scenarios.

It's also important just to get the science right.

Well, the cosmologists I knew in the 1990's very much did suspect that the observation was wrong, or more correctly, misinterpreted.

Name three.

No, there is a huge difference, summed up in the analogy I just made. When you are playing poker, of course you imagine a range of possible deals, but when you get evidence that the deal you are in has very unusual properties, you just accept that at face value, and discard the vast numbers of hypothetical deals that don't fit the facts

I don't. If I flip a coin 50 times and it comes up heads, I don't just accept that.

I agree, I'm not arguing that inflation will be killed. Indeed, I'm arguing that inflation is probably pretty good, and that is the basis why we should expect curvature to remain undetected, just as we should expect rotation to remain undetected. I see no evidence those issues should be treated so vastly differently as they are.

I'm arguing that inflation is good for some things. Bad at others. Curvature is one of the things that 's bad at, so if we detect curvature, then it's not hard to tweak the model to explain why.

As far as why they are treated differently. LCDM contains a model for curvature variation so that if you do LCDM, you have to include curvature.

 

[twofish-quant]

I'd wager that most graduate, and virtually all undergraduate, cosmology courses say little or nothing about rotating models, but the vast majority go into great detail about the various curvature possibilities. Just why is that?

Because the heart of LCDM involves calculating density perturbations, and without going into GR models (which include curvature) you can't do that.

I argue it's purely an accident of history, and is high time to correct.

History is important. You have to go through the history of cosmology models to point out what didn't work. Any decent course either graduate or undergraduate has got to mention steady state and tired light.

If you stick to flat models, it does not at all mean, as was suggested, that the students will be hopelessly crippled for thinking about anything else

I think they would. They'll be stuck in a Newtonian world, and you need to go into GR.

What it means is that you can spend your energy instead on digging deeper into some other area, perhaps inflationary models, that has much more promise of being something important, and not just a minor correction in the second decimal place.Of course, but you don't need global curvature in your model to do that.

You need GR, which means that you need curvature.

The sequence is

Newtonian -> FLRW -> LCDM

Indeed, mixing global curvature with the local curvature that affects CMB fluctuations is exactly the kind of extraneous detail that obscures the important concepts, rather than brings them out

No it doesn't. It's the same theory of gravity. It's also not extraneous detail. It's the heart of LCDM. The global curvature affects the growth rate of local perturbations

http://arxiv.org/pdf/1106.0627.pdf

Unless one favors the "black box" school of education, where you just teach students to put everything but the kitchen sink into the computer, and see what comes out, without any real understanding entering the student's brain.

For non-major undergraduates, computers are useful, because they can illustrate what happens when you vary the parameters.

 

[twofish-quant]

Right, most likely they believe almost as many different things as their are cosmologists, and indeed they are welcome to hold any personal beliefs they wish, but believing it wouldn't make it science.

One thing that's grating on the nerves is that you are talking to several theorists and trying to advance your view of science as somehow gospel. Why should your definition of science be better than mine or Steven Weinberg's?

There is a tendency to use the euphemism "speculative" to mean crank, and "mainstream" to mean "non-crank" but this will not work in this situation. The anthropic principle and multiverse concept is an important part of mainstream cosmology. I dislike it, but that's my personal opinion (and Max Tegmark has come up with some clever ways of addressing my issues).

But there is also a clear consensus on what is currently regarded as the best model, the model that is often heard in a sentence with "precision cosmology", and it is a model with no reason to include any curvature, so it doesn't. There's always the interplay between consensus and contrariness in science, and nowhere did I ever say that there is only one cosmological model that ever gets looked at-- I said there is one widely regarded best model, and Nobel prizes have been awarded.

And you have several people with experience with cosmology telling you that you are wrong.

The reason that you have to use a flat LCDM model is that if you don't fix curvature then you can't get information on the time evolution of dark energy. Flat LCDM models are essential if you want to study the evolution of dark matter, but using a flat LCDM doesn't mean that someone thinks that the universe is in fact, flat.

What happens if you allow any curvature uncertainty is that you can't pull out some numbers that you'd like to get.

Edit: let me rephrase that, I'm not trying to tell cosmologists how to do their business

It comes across that way.

Part of what I'm trying to tell you is that there is a reason why cosmologists make the assumptions that they do, and they are good reasons. I'm being somewhat harsh because you keep making statements about what cosmologists do that are false.

I'm pointing out that we may very well be approaching a time when we need to give very serious consideration to treating the flatness of our models as a physical principle.

And several things have to happen before that point is reached.

1) we have to understand what dark energy is. First of all, in order to get omega = 1, we are making several assumptions about the nature of dark energy. If those assumptions are wrong, then the omega=1 calculation falls apart. Also, if the nature of dark energy changes as a result of a phase transition, that will change the value of omega.

2) we have to understand inflation better than we do. The omega=1 result can be achieved if you let inflation run for a large number of e-foldings, but we have to understand what starts and stops inflation.

3) we have to push the limits on omega to below what they are.

Note this still does not represent a claim that the universe is actually flat, any more than relativity is a claim that the photon is exactly massless, it is merely a recognition of the value in adopting a particular mathematical simplification in our best models.

That doesn't work.

Relativity and electroweak *is* a claim that the photon is *exactly* massless. If there are any differences from zero mass, then electroweak theory and much of relativity is wrong.

The point of physics is to make claims on the nature of the universe. I see no reason to claim that the universe if flat, unless and until we actually think that it is flat. We can be wrong, but making incorrect assertions is what pushes science further.

 

[twofish-quant]

Quoting myself:

One thing that's grating on the nerves is that you are talking to several theorists and trying to advance your view of science as somehow gospel. Why should your definition of science be better than mine or Steven Weinberg's?

This may have sounded harsher than it was intended, but it's in fact a serious question. One thing that is a reality is that "anthropic arguments" and "multiverse" are taken quite seriously in high energy physics and cosmology. So in arguing that those arguments are invalid and "not science" is arguing against the "scientific mainstream" on this issue.

Now what?

The reason I dislike anthropic arguments is that they involve sociological assumptions. You assume that with situation X, intelligent life could not evolve. How do you know that in situation, intelligence is impossible?

However, Max Tegmark has come up with a clever way around that issue. Instead of "counting" universes in which there is intelligent life, he counts universes in which stars form or galaxies form, which let's him take human beings out of the anthropic equation. Saying that under condition X, intelligent life is not possible is a statement I'm not willing to make. Saying that under condition X, stable self-gravitating objects are impossible, is.

 

[twofish-quant]

One other thing, I'm a fan of going to the original papers. Here is the paper for BOSS

http://arxiv.org/pdf/1203.6594v1.pdf

Something to point out is that they put their data through six different parameterization, and then they explain why they do it.

The reason why is this

http://arxiv.org/pdf/0802.4407v2.pdf

Essentially, you can get very impressive looking numbers if you assume that the cosmological constant is constant. However, once you assume that dark matter changes then it becomes difficult to tell what is evolving dark energy and what is curvature.

Since the BOSS people are observationalists, they run their data through several models.

One reason I think this is worth looking at is that we have no clue what dark matter is, and if it turns out that it is evolving, that gets rid of the cosmic coincidence problem.

Other practical point is that the minimum curvature that we can measure is 10^-4 to 10^-5. Remember that in LCDM, the universe is not flat. It's wrinkly. If global curvature goes below 10^-5, then it gets lost in the wrinkles.

 

[ViewsofMars]

[snip]
The reason that you have to use a flat LCDM model is that if you don't fix curvature then you can't get information on the time evolution of dark energy. Flat LCDM models are essential if you want to study the evolution of dark matter, but using a flat LCDM doesn't mean that someone thinks that the universe is in fact, flat.

[snip]
The point of physics is to make claims on the nature of the universe. I see no reason to claim that the universe if flat, unless and until we actually think that it is flat. We can be wrong, but making incorrect assertions is what pushes science further.

Twofish-quant, on the previous two pages we discussed a flat universe. I was wondering what you think about the comments by NASA Official: Dr. Edward J. Wollack
Page Updated: Monday, 04-02-2012- WAMP:

The Universe Content: the Ingredients

There are three ingredients in this universe: normal matter (or atoms), cold dark matter, and dark energy.

Atoms: The amount of ordinary matter (atoms) in your universe, the stuff you see around you: tables, chairs, planets, stars, etc. Expressed as a percentage of the "critical density".
Cold Dark Matter: The amount of cold dark matter in your universe, as a percentage of the critical density. Cold dark matter can not be seen or felt, and has not been detected in the laboratory, but it does exert a gravitational pull.
Dark energy: The amount of dark energy in your universe, as a percentage of the "critical density". Unlike dark matter, dark energy exerts gravitational push (a form of anti-gravity) that is causing the expansion of the universe to accelerate or speed up.

Note that the three ingredients can add up to more than or less than 100%. The sum is compared to a quantity that determines the Flatness of the universe. A "flat" universe is said to be at "critical density", having 100% of the matter and energy needed to be "flat". Euclidean geometry describes a flat universe, but non-Euclidean geometries are needed for the alternatives. If the ingredients add up to more than 100%, then the universe has positive curvature and said to be "closed". This means that it curves around on itself (like the surface of a ball), and that if you go in one direction long enough, you'll get back to where you started. If the ingredients add up to less than 100%, then the universe has negative curvature and is called "open". This is the type of curvature that you'd find (in 2 dimensions) on the surface of a horse's saddle, or a potato chip. In that case, space is curved, but it doesn't wrap back around on itself. (Footnote: Mathematicians can probably come up with pathological models where positively curved universes don't wrap around on themselves, and negatively curved ones do, by cutting and pasting various parts of the universe together. We just describe the simplest cases here.)

The Age of the universe is controlled by the amount of the ingredients and the flatness of the universe. By viewing the scale of the universe now, and using Einstein's General Relativity equations to compute the time, under these conditions, needed to reverse the universe to "zero" size, we have the age calculated for us.
http://map.gsfc.nasa.gov/resources/camb_tool/index.html

 

[twofish-quant]

Twofish-quant, on the previous two pages we discussed a flat universe. I was wondering what you think about the comments by NASA Official: Dr. Edward J. Wollack
Page Updated: Monday, 04-02-2012- WAMP:

I think he is doing a wonderful job of trying to simplify some very complicated topics.

A lot of the problems come in when you try to take something very complicated and then try to simplify things for popular consumption. If I have one or two pages to talk about cosmology, I'm not going to go into the messy details, because 99% of the people that read the press releases don't care about the messy details. He is trying to use some metaphors for what is going on. Those metaphors are somewhat inaccurate, but it's hard, maybe impossible to show the accurate version without a ton of greek symbols that will cause 99% of the readers to fall asleep. He is leaving out some important details, but putting in all of the details would give you a 100 page textbook, and most people reading it will fall asleep.

Press releases and popular websites are inherently misleading because they don't tell the full story, and they don't tell the full story because you can't tell the full story in two pages, and most people reading the sites don't care about the full story. That's why I like web links to original papers. Even if you can't totally understand everything in the papers, you can figure out some things that aren't obvious from press releases.

For example, one thing that becomes obvious when reading the BOSS paper is that getting good data is hard work. There are at least thirty pages listing all of the corrections that they made and justifying all of their decisions.

 

[twofish-quant]

Also, let me explain the problem with dark energy evolution and curvature.

Imagine a plot of possible dark energy evolution and curvature fits to data. It turns out that this looks like a long diagonal ellipse.

Now let's pretend that I assume that there is zero curvature. I slice the ellipse vertically at zero, and I get a very small error in DE evolution. Now let's pretend I assume that there is no dark energy evolution. I slice the ellipse horizontally at zero, and I get a very small error in curvature.

If I just look at the two errors, I can (incorrectly) assume that because I get a small error in curvature assuming zero DE evolution and a small error in dark energy evolution assuming zero curvature that both numbers are zero.

In fact the errors work out so that this isn't the case. The errors are huge, but it's just because of the way that I slice the error that it comes out small.

All of the quoted numbers that say that the universe is flat assume that dark energy is not changing, and since we have no clue what dark energy is, that's not a great assumption.

Again, if you look at the original WMAP and BOSS papers, it's obvious that everyone is aware of this problem, and trying to fix it. People don't mention it in popular summaries, not out of malice, but because you only have one page to explain something, so you have to leave out some messy details, and most people that read these sites really don't care.

 

[ViewsofMars]

Thanks! I'm an avid reader. I have a large library in my home. I'm especially fond of rare books. My computer has a large volume of of good stuff too.

So I can find the WAMP data through the Legacy Archive for Microwave Background Data Analysis (LAMBDA) at http://larnbda.gsfc.nasa.gov . (1.)

1. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20080032973_2008031489.pdf

I'll look at the BOSS papers. I'll get back to you on the Dark Energy.

My previous post from NASA stated, "The Age of the universe is controlled by the amount of the ingredients and the flatness of the universe." If I understand you correctly then the flatness of the universe is no longer necessary in determining the age of the universe. Is that correct? If so, please tell me how you would calculate the age of the universe. Thanks. I'm having fun.

 

[Ken G]

All of the quoted numbers that say that the universe is flat assume that dark energy is not changing, and since we have no clue what dark energy is, that's not a great assumption.

This language seems to completely overlook the reality of what models are in physics. We just don't make claims on reality when we make models, we make claims on the models (that they adequately describe the current observations of reality). We have no idea if a photon is massless, if c is constant, if dark energy is constant, if the universe is infinite, if curvature is zero. That's not the point at all. The point is to ask, can we adequately understand our current knowledge of reality using a model that uses massless photons, constant c, constant dark energy, and an infinite universe with zero curvature. That is the question that physics asks. And for the data we now have, the answer to that question is, "yes." Will that still be the answer 100 years from now? Probably not! But we have no idea which in that list will be the source of the "no", all we have, all we ever had, have, or will have, is the current best model.

 

[Ken G]

There is a tendency to use the euphemism "speculative" to mean crank, and "mainstream" to mean "non-crank" but this will not work in this situation.

I mean ther terms "speculative" and "mainstream" in exactly the way the words are used in astronomy. Had I meant "crank", I would have said so.

The anthropic principle and multiverse concept is an important part of mainstream cosmology.

I don't agree. Yes there is a group of cosmologists who like to make anthropic arguments and refer to the multiverse, but that certainly does not make it part of the bulk of mainstream consensus that astronomers can comfortably refer to as "our current best understanding". What makes something mainstream is that a working astronomer could stand in front of an audience and say "we have observations that support the following view of things", without feeling like they had stepped well outside the realm of what can be empirically justified. You seem to be arguing that you could do that with a model of our universe that includes vastly many other universes we cannot see, but you could not do that with a model of the universe that was flat and infinite, since you have claimed the former is mainstream and the latter is not, whle I have claimed the opposite-- based on the actual observations that we have actually done, which is also why we see that kind of argument on the WMAP website and so forth (where we do not find multiverse arguments). I don't know any astromers who could comfortably stand in front of an audience and say that our best understanding is that our inverse is one of a gajillion unobservable ones, but I know plenty who would be perfectly comfortable saying our current best model of the universe is flat.

And you have several people with experience with cosmology telling you that you are wrong.

Actually, no. What I have is basically one person changing my words into things I did not say (like claiming that I equate speculation with crankism, or claiming that I said most cosmologists "assume" the universe is flat, either of which I would have actually said had I meant that), while failing to assail any of the core logic of my argument.

The reason that you have to use a flat LCDM model is that if you don't fix curvature then you can't get information on the time evolution of dark energy. Flat LCDM models are essential if you want to study the evolution of dark matter, but using a flat LCDM doesn't mean that someone thinks that the universe is in fact, flat.

Thank you for repeating a point I have made myself countless times in this discusson!

What happens if you allow any curvature uncertainty is that you can't pull out some numbers that you'd like to get.

Yup. Which is all part of the art in physics of "creating the best current model." Like I said, over and over.

Part of what I'm trying to tell you is that there is a reason why cosmologists make the assumptions that they do, and they are good reasons.

No kidding. Really?

I'm being somewhat harsh because you keep making statements about what cosmologists do that are false.

Name one. I mean, one that I really said, not these absurd mischaracterizations.

1) we have to understand what dark energy is. First of all, in order to get omega = 1, we are making several assumptions about the nature of dark energy. If those assumptions are wrong, then the omega=1 calculation falls apart. Also, if the nature of dark energy changes as a result of a phase transition, that will change the value of omega.

No kidding! Goodness man, this is just how science works. We make our best models, based on what works. Then we do observations, and what works changes, so we change our best model. Are you now telling me that our best models can change based on new information? Is this supposed to come as some kind of surprise to me? You think that if we do the things on your list, that then we will be able to say we finally know that omega actually is 1? No, we won't be able to say that, we never get to say that. We never get to say that omega is actually 1, we never get to say that c is actually constant, we never get to say that protons never decay or that photons are exactly massles. All we get to do, all we ever get to do, is make the idealizations that work, given the current state of the observational data.

And when we do that in cosmology, we arrive at a flat universe, and it's OK to recognize that. This is all I have been saying, put away all the silly things you claim I have said.

Relativity and electroweak *is* a claim that the photon is *exactly* massless.

Wrong, that's ridiculous. Why on Earth would physicists ever need to claim any model is exact? Are they fools, even after all these many centuries of doing physics?

If there are any differences from zero mass, then electroweak theory and much of relativity is wrong.

Obviously. Like that's never happened!

The point of physics is to make claims on the nature of the universe. I see no reason to claim that the universe if flat, unless and until we actually think that it is flat.

So you think that claim becomes true when we think it is? If I think something is true about the universe, I can claim it, but if I'm skepical that it's true, I cannot, so I have to stop being a scientist when I form an opinion of how things are? If you take that approach, then you must either think that the whole enterprise of physics is hopeless (because the claims we make on the universe invariably get overturned later on), or else you have fallen into the all-too-common fallacy of thinking that our own current version is actually the correct one, despite all the clear evidence that this simply does not happen in physics.

Let me suggest a more workable option. We recognize that it doesn't make a hill of beans of difference what we personally "think is true" about the universe, what matters is the models we make, the simplifications this involves, the understanding this wins for us, and the observational data we can understand using those models. That's what physics is, would you not say?

 

[twofish-quant]

This language seems to completely overlook the reality of what models are in physics. We just don't make claims on reality when we make models, we make claims on the models (that they adequately describe the current observations of reality).

I'm making a claim on reality when I make my models. They might turn out to be incorrect claims, but they are claims nevertheless.

We have no idea if a photon is massless, if c is constant, if dark energy is constant, if the universe is infinite, if curvature is zero. That's not the point at all.

That's exactly the point.

We have experimental data that puts tolerances on those values. We then make physical theories that make statements about reality. Electroweak theory says that the photon is massless. Relativity says that c is constant. It could very well be that the standard model of cosmology in 2020 says that curvature is exactly zero.

Those are claims. If it turns out that the photon has mass, then electroweak theory is wrong. The standard electroweak theory in 1974 stated that the neutrino had zero mass. That turns out to be wrong. The standard cosmological model in 1995 stated that the cosmological constant was zero. That's also wrong. We make progress by making claims, and if those claims turn out to be false, then GREAT!

The point is to ask, can we adequately understand our current knowledge of reality using a model that uses massless photons, constant c, constant dark energy, and an infinite universe with zero curvature.

The point of a theory is to go *beyond* current knowledge. Once you claim that the neutrino has zero mass, you can calculate the solar neutrino flux, and then you find that it's not what you think it was.

And for the data we now have, the answer to that question is, "yes."

It's actually no. There are lots of things about the universe that don't make sense. LCDM falls apart once you start calculating power spectrum at galactic scales. Also, there's always a lot of noise in observations.

But we have no idea which in that list will be the source of the "no", all we have, all we ever had, have, or will have, is the current best model.

And any model is afraid to be wrong isn't very good.

 

[Ken G]

But we have dark energy. That's why I don't buy this "let's assume that we won't observe this because it will lead to a weird coincidence" logic. We've already seen it fail once.

I know this debate is getting long, but this particular point is very important, so I must point out the logical fallacy in this argument. This is exactly the same as if we were playing poker against two opponents, and information had emerged that one of our opponents has a hand that fits into a highly unlikely class of poker hands. Now we make our best analysis of the other opponent's hand, and you say "we can't assume they have one of the more likely types of hands that fits with the data we have, because we already saw that fail once when we discovered the other opponent had an unlikely hand." No, we always expect a generic outcome, and getting a non-generic outcome once does not lead us to expect a non-generic outcome for something else, unless we expect some correlation between the outcomes. So your argument here is only logically accurate if there is some reason to expect a connection between the surprise that dark energy is just beginning to take over the large-scale dynamics of the universe, and that there would be barely observable curvature.

Now, should we expect such a connection? There is no evidence to suggest it. What we are doing is taking all the models we could imagine that have arbitrary amounts of dark energy and arbitrary post-inflation curvature, and we are throwing away all of them that are not consistent with the rather special amount of dark energy that we have observed we need. Then we analyze the surviving class of models, and ask, what is now the generic expectation for this class? Throwing away the models that are inconsistent with the dark energy requirements means we have models whose post-inflation curvature starts out very small, rapidly grows, and then begins to level off more recently. Going forward, the leveling off should turn over into falling curvature, or has already made that turn. Now we have the question, are models where the curvature just peaks up into what we can barely observe the generic class we should expect, or do they still seem highly non-generic, given the dark energy requirements we already have and any connections we expect between that and the post-inflation curvature?

I have argued the answer to that is "the latter," and not a single thing you've said contradicts that. Indeed, if we did observe curvature, it would be perfectly natural to immediately begin scrambling to find the connection between the amount of dark energy, and the very special post-inflation curvature, that made these seemingly independent "specialnesses" both occur together. Have I claimed that couldn't happen? Of course not, I've claimed we have no reason to expect that to happen, so we should not expect that to happen. It would be quite exciting if it did, so certainly we should look for it, we just shouldn't expect to find it, unless there is something very significant missing from our understanding of inflation.

In some cases the theory is stronger the the observations. For example, when FTL neutrinos were observed people were pretty sure that the observations were wrong since the theory is strong.

Again, I would argue this is just not the correct connection between theory and observation in physics. The real reason people are skeptical of FTL neutrinos is that something going > c flies against a vast number of observations that we can understand with a theory that says things can't do that. The theory is nothing but a proxy for our understanding of that weight of observational evidence, that is all that is meant by "the theory is strong." So this is not at all a case of theory getting "ahead of observation", that is simply impossible in an empirical science. Instead, it is a case of a huge body of observations, unified and represented by a theoretical proxy, getting ahead of a single rather hard to interpret observation.

But as Einstein said, a single observation can indeed overturn an entire theory. It is all a matter of how certain we can be that the conclusions of that observation are correct, and there was not some subtle experimental error. We don't overturn our understanding of a vast number of experiments because of one uncertain and unconfirmed result, that doesn't mean the theory is "ahead of" the observations. We should certainly have gotten past the idea that a theory should be right because it sounds right to us!

 

[twofish-quant]

Yes there is a group of cosmologists who like to make anthropic arguments and refer to the multiverse, but that certainly does not make it part of the bulk of mainstream consensus that astronomers can comfortably refer to as "our current best understanding".

If someone tries to get a paper into Astrophysical Journal with young Earth creationist arguments, then it's not science, and I can trash that paper. Anthropic arguments are sufficiently well accepted that you can write journal articles about them and have them pass peer review. If you don't believe me, go into the standard research databases and key in "anthropic."

It's a legitimate argument.

There's a difference between "mainstream" and "mainstream consensus." If we get ourselves into two or three different models which people scream at each other with, that's "mainstream" but it's not consensus.

And there is no consensus that omega=1.

What makes something mainstream is that a working astronomer could stand in front of an audience and say "we have observations that support the following view of things", without feeling like they had stepped well outside the realm of what can be empirically justified.

You are trying to teach astronomy to astronomers, and cosmology to cosmologists.

Part of the reason I'm rather harsh toward you is because you keep doing that. It's fine if you make up your own philosophical rules, but once you start trying to argue that cosmologists should do this and shouldn't do that or astronomers should do this and shouldn't do that, then you need to realize that most scientists don't follow those rules.

Also, Stephen Hawking goes way out of things that are empirically justified. My beef with him isn't that he does that, my beef with him is that he does it and doesn't tell people he is doing that.

You seem to be arguing that you could do that with a model of our universe that includes vastly many other universes we cannot see, but you could not do that with a model of the universe that was flat and infinite, since you have claimed the former is mainstream and the latter is not

I'm claiming that your definition of "mainstream" is not a good one, and it's certainly not the one that I use. By "mainstream" I'm referring to arguments that are commonly used in writing theory papers, and assumptions that can be used within theory papers without having to justify them.

I don't know any astromers who could comfortably stand in front of an audience and say that our best understanding is that our inverse is one of a gajillion unobservable ones, but I know plenty who would be perfectly comfortable saying our current best model of the universe is flat.

Steven Weinberg, Max Tegmark, Alan Guth just to name three.

Also you have this other habit of claiming sources without citing them. There's nothing wrong with being a minority opinion, and my claim is that you have philosophical beliefs that most astrophysicists don't share. Nothing wrong with that.

No kidding. Really? Name one. I mean, one that I really said, not these absurd mischaracterizations.

Well you seem to think that anything that is not observable is not scientific.

Goodness man, this is just how science works.

You are doing it again. Lecturing scientists about how science works.

We make our best models, based on what works.

No. You come up with random models without any clue if they will work or not. You then use observations to cross models off the list.

You think that if we do the things on your list, that then we will be able to say we finally know that omega actually is 1?

No. We see where we are at that point.

We never get to say that omega is actually 1, we never get to say that c is actually constant, we never get to say that protons never decay or that photons are exactly massles.

Yes we do. I make the claim that c is constant and photons are exactly massless. I can change my mind latter, but I make the claim now. If it turns out that omega is exactly one, then we start looking for symmetry mechanisms that would set omega to exactly one.

Wrong, that's ridiculous. Why on Earth would physicists ever need to claim any model is exact? Are they fools, even after all these many centuries of doing physics?

Because claiming that something is exact makes it easy to falsify. If I make the claim that photons are *exactly* massless or that omega is *exactly* one, that means that it's easy to come up with experiments to show that the model is wrong. If I come up with "waffle" statements, then it's harder to falsify things.

The goal of a theorist is not to be right. The goal of a theorist is to come up with something that is testable. A theory that says that the photon is *exactly* massless is much easier to test than one that has no predictions. Same with the speed of light.

The current theories of physics say that all electrons have *exactly* the same charge, and that particles and anti-particles have *exactly* the same mass. This means that you have models that are testable and falsifiable.

My big beef with string theory is that it hasn't come up with exact predictions. Even *stupid* predictions are better than no predictions.

So you think that claim becomes true when we think it is? If I think something is true about the universe, I can claim it, but if I'm skepical that it's true, I cannot? I have to stop being a scientist when I form an opinion of how things are?

There's too much psychology here. In my experience, one thing that makes a good theorist is not to have too many opinions about what is true or not. The job of a theorist isn't to "come up with true theories." The job of a theorist is go come up with theories and then have observationalists shoot them down.

For example, I can write a theory paper about the consequences of a universe with omega being *exactly* one. It doesn't mean that I think omega is one, I'm doing a what-if. Just because I claim that omega is one in a theory paper, doesn't mean that I believe it, since the point of a theory paper is to figure out consequences of assumptions.

If you take that approach, then you must either think that the whole enterprise of physics is hopeless (because the claims we make on the universe invariably get overturned later on)

Onward and upward.

We recognize that it doesn't make a hill of beans of difference what we personally "think is true" about the universe, what matters is the models we make, the simplifications this involves, the understanding this wins for us, and the observational data we can understand using those models. That's what physics is.

What's interesting is going *beyond* current observational data. Physics is not just about "understanding observational data." A lot of it involves understanding things that we haven't observed.

I'd have less problem with your statements if you say "this is what I think physics is." Saying that "this is what physics is" or "this is what science is" implies that people who don't share your philosophical beliefs aren't doing science or aren't doing physics.

There is a lot of philosophical variation between physicists.

 

[twofish-quant]

I know this debate is getting long, but this particular point is very important, so I must point out the logical fallacy in this argument. No, we always expect a generic outcome, and getting a non-generic outcome once does not lead us to expect a non-generic outcome for something else, unless we expect some correlation between the outcomes.

In fact it does if you do Bayesian analysis. If you have a fair coin, and you flip it 50 times, and it always comes out heads, then the odds of the next flip coming out heads is 50:50. The trouble is that if you have even the slightly reason to suspect that the coin is unfair then it changes things considerably.

So your argument here is only logically accurate if there is some reason to expect a connection between the surprise that dark energy is just beginning to take over the large-scale dynamics of the universe, and that there would be barely observable curvature.

And there is reason to think there might be some connection.

There is no evidence to suggest it.

I'm a theorist. I come up with new ideas which connect the two.

Also observationally dark energy and curvature are very closely connected and it can be hard to separate the two.

The theory is nothing but a proxy for our understanding of that weight of observational evidence, that is all that is meant by "the theory is strong."

Strongly disagree. The thing about the theory is that you can tell "how bad things get" if the observation was correct.

But as Einstein said, a single observation can indeed overturn an entire theory. It is all a matter of how certain we can be that the conclusions of that observation are correct, and there was not some subtle experimental error.

But it's circular. Part of what makes you suspect that there is some experimental error is if you get weird results. If the observation was on something we didn't think we understood, then we wouldn't spend as much effort looking for experimental error.

 

[Ken G]

In fact it does if you do Bayesian analysis. If you have a fair coin, and you flip it 50 times, and it always comes out heads, then the odds of the next flip coming out heads is 50:50. The trouble is that if you have even the slightly reason to suspect that the coin is unfair then it changes things considerably.

Which is exactly why I said "unless we expect some correlation between the outcomes." In the coin analogy, we obviously should, if we use the same coin, and we should not, if we use a different kind of coin. You have not offered any reason to expect that the presence of dark energy, and whatever is the post-inflation curvature, have any reason to be thought of as the "same coin." The only inflation theory I've seen that connects the two is "quintessence", but even that only connects the sources of dark energy and inflation, it doesn't have any reason to connect the magnitudes of an order-unity dark energy contribution with a barely-measurable curvature.

And there is reason to think there might be some connection.

Which is...? We can only judge the strength of this claim on how well you can justify that reason.

Also observationally dark energy and curvature are very closely connected and it can be hard to separate the two.

Any theory that invokes two unknown variables will make it hard to observationally separate their values, that is not an argument that a non-generic outcome for one of the variables is evidence for a non-generic value (after accounting for our prior knowledge of the first) for the other. We should still expect the curvature to be generic, unless we have some specific aspect of the theory that suggests a connection between their values. I have not yet heard you give an argument that a 0.7 dark energy term in Omega suggests a non-generic curvature result that would make curvature measurable.

But it's circular. Part of what makes you suspect that there is some experimental error is if you get weird results.

But here "weird" means "in contradiction with the way we understand all the other good observations we have done", not "in contradiction with our opinions of how we think the universe ought to work." The former is a perfectly valid way to contrast different bodies of observations and their relative uncertainties, the latter is a fallacy we have fallen into so many times we should really know better by now. But you are right when you object that I am actually describing a particular viewpoint about what science is or should be, and it is decidedly Popplerian, I just think this is so clearly the correct way to frame science that I'm not constantly prefacing it with "in my opinion". The point is I'm presenting an argument by evidence for why we regard those observations as weird, and it's not because the theory is "ahead" of observation, it is because the theory is supported by other observations.

 

[twofish-quant]

You have not offered any reason to expect that the presence of dark energy, and whatever is the post-inflation curvature, have any reason to be thought of as the "same coin."

Dark energy causes curvature. But that's beside the point.

The point is that you are using a heuristic principle (i.e. observations producing coincidences should be rejected) that's known to have failed in one situation, and so there isn't any reason I can see that I should agree to using that principle in another situation.

Or maybe not. If you really believe that "reject coincidences" is a good principle, then it seems to me that you should conclude that there is curvature + dark energy evolution. If in fact there is a small amount of curvature and also some dark energy evolution, then that would get rid of the cosmic coincidence problem, and not generate any new coincidences that I can see.

Any theory that invokes two unknown variables will make it hard to observationally separate their values

That's not true. It just happens that the mathematics of the situation is such that current observations of the cosmological constant create this problem. There are ways around that problem.

But here "weird" means "in contradiction with the way we understand all the other good observations we have done", not "in contradiction with our opinions of how we think the universe ought to work." The former is a perfectly valid way to contrast different bodies of observations and their relative uncertainties, the latter is a fallacy we have fallen into so many times we should really know better by now.

There's an element of creativity and luck in doing theory. If someone comes up with useful theory, I really don't care how they do it. One thing that is interesting is that some of the most creative theorists also happen to be stubborn and pig-headed. Penrose, Newton, and Einstein for example.

In the case of "doing theory" there's no shame in coming up with a dozen silly ideas if you happen to come up with one that happens to have legs. The point of a theorist is not to be right. It's to be interesting. There's no way with pure thought to know if you are right or not. But with thought, you can come up with stuff that the observers might be able to figure out.

But you are right when you object that I am actually describing a particular viewpoint about what science is or should be, and it is decidedly Popplerian, I just think this is so clearly the correct way to frame science that I'm not constantly prefacing it with "in my opinion".

And part of the reason I'm arguing with you is that it's not.

There are some things that Popper IMHO got wrong. One is that there is nothing within the Popperian view for levels of certainty. There's also the problem that Popper has problems in situations where you have a model that's probabilistic (quantum mechanics). You also have problems when you deal with one time events (like the Great Depression or the Big Bang).

The point is I'm presenting an argument by evidence for why we regard those observations as weird, and it's not because the theory is "ahead" of observation, it is because the theory is supported byother observations.

But a lot of those other observations are theory dependent.

The other thing is that there are very few observations of neutrinos, that's why they were doing that experiment in the first place. So there really are few observational reasons for arguing that "neutrinos will be different." Same for gravity waves. No one has observed a gravity wave. But we think that 1) they exist and 2) they travel at light speed. If the first experiments say that they are traveling faster than light, my reaction would be that they did their experiments wrong, not withstanding the fact that no one has ever observed a gravity wave.

 

[ViewsofMars]

The goal of a theorist is not to be right. The goal of a theorist is to come up with something that is testable.

I noted that you are a theorist on the previous page. I'd like you to answer my question found on the previous page (#73).

"We should stand firm and insist that genuine science is based on observational testing of plausible hypotheses. There is nothing wrong with physically motivated philosophical explanation: but it must be labeled for what it is. Overall: theory must be subject to experimental and/or observational test; this is the central feature of science." George F R Ellis, November 21, 2008, "Dark matter and dark energy proposals: maintaining cosmology as a true science?"
http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.3529v1.pdf

In the case of "doing theory" there's no shame in coming up with a dozen silly ideas if you happen to come up with one that happens to have legs. The point of a theorist is not to be right. It's to be interesting. There's no way with pure thought to know if you are right or not. But with thought, you can come up with stuff that the observers might be able to figure out.

I'm interested in talking about science. Your comment leaves me drifting out in space with no spacecraft .

 

[marcus]

Nice quotes, VoM. I'll take them out of the context of your post #82 to have them accessible for mulling over.

Twofish: "The goal of a theorist is not to be right. The goal of a theorist is to come up with something that is testable."
https://www.physicsforums.com/showthread.php?p=3944684#post3944684

George Ellis: "We should stand firm and insist that genuine science is based on observational testing of plausible hypotheses. There is nothing wrong with physically motivated philosophical explanation: but it must be labeled for what it is. Overall: theory must be subject to experimental and/or observational test; this is the central feature of science." George F R Ellis, November 21, 2008, "Dark matter and dark energy proposals: maintaining cosmology as a true science?"
http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.3529v1.pdf

Twofish: "The point of a theorist is not to be right. It's to be interesting. There's no way with pure thought to know if you are right or not. But with thought, you can come up with stuff that the observers might be able to figure out."
https://www.physicsforums.com/showthread.php?p=3944798#post3944798

These strike me as very well chosen quotes. I'm not engaged in the discussion at least at present, but I'd like to mull them over and perhaps keep them handy. Here, for reference, is your post which afforded context.

I noted that you are a theorist on the previous page. I'd like you to answer my question found on the previous page (#73).
I'm interested in talking about science. Your comment leaves me drifting out in space with no spacecraft .

 

[Ken G]

Dark energy causes curvature. But that's beside the point.

Actually, dark energy reduces curvature, so it does not cause it. We must not confuse the two meanings of curvature-- GR curvature, which is invariant, and spatial curvature, which is coordinate dependent everywhere but in cosmology (where we have the cosmological principle which picks out a very clear splitting between space and time). Dark energy reduces spatial curvature, and so does inflation-- they act on whatever spatial curvature is handed to us by our initial conditions. My point is that they reduce spatial curvature in unrelated ways-- or at least, no one has any theory to say why they should be related in the kind of special way that would be required to get a double-special value of both. That's pretty much my whole point.

The point is that you are using a heuristic principle (i.e. observations producing coincidences should be rejected) that's known to have failed in one situation, and so there isn't any reason I can see that I should agree to using that principle in another situation.

Then I'll play poker with you any time-- since you've probably seen highly unlikely poker hands, and are therefore unable to expect my hand to be generic.

Or maybe not. If you really believe that "reject coincidences" is a good principle, then it seems to me that you should conclude that there is curvature + dark energy evolution. If in fact there is a small amount of curvature and also some dark energy evolution, then that would get rid of the cosmic coincidence problem, and not generate any new coincidences that I can see.

If I thought that was true, I would completely agree, but I don't see what you are basing that on. There's no value in turning two problems into one if you think you only had one problem in the first place.

 

[twofish-quant]

Actually, dark energy reduces curvature, so it does not cause it.

Depends on the type of energy.

Dark energy reduces spatial curvature, and so does inflation-- they act on whatever spatial curvature is handed to us by our initial conditions. My point is that they reduce spatial curvature in unrelated ways

1) You don't know that.
2) It's not crazy to think that the DE and inflation are part of the same quantum field. In that cause, the theorist would think about this and try to figure out something interesting.

At least, no one has any theory to say why they should be related in the kind of special way that would be required to get a double-special value of both. That's pretty much my whole point.

I'm a theorist. The job of a theorist is to come up with theories. If there isn't a theory, then you make one up.

I don't know if you want to be a theorist, but one advice is that if you come up with an idea, then you should take it to it's logical conclusion. You've advanced the idea that "any theory that creates a cosmic coincidence should be rejected." Something that would be a useful paper would be to take that idea to it's logical conclusion and argue that the idea that we are seeing zero curvature and zero DE evolution is *wrong*.

Then I'll play poker with you any time-- since you've probably seen highly unlikely poker hands, and are therefore unable to expect my hand to be generic.

Let's play logic chess.

I'm just trying to get you to take your claims to their logical conclusions. If you are arguing that "any theory that creates a cosmic coincidence *MUST* be wrong" and if you accept the standard interpretation of current observations, then logically you have a problem. You need to either reject your principle as a logical principle, or you must reject current observations.

If it's not a logical principle, then I don't see why it should apply to inflation. You can weaken your statement so it's a heuristic and not a logical principle, which is fine, You can also question current interpretations, which shows a lot of chutzpah, but it's cool if you turn out to be right (and if you aren't a jerk about it, no one will care if it's wrong).

If I thought that was true, I would completely agree, but I don't see what you are basing that on. There's no value in turning two problems into one if you think you only had one problem in the first place.

1) Remember that the purpose of being a theorist is not to be right, but to be interesting, and being interesting often involves figuring out non-trivial consequences of ideas. I don't buy the "non-coincidence principle" because I know of one violation, but what if it's not a violation?

2) You are the person that quotes Popper. If you have *one* problem, that should falsify the principle, shouldn't it? However, it could be that the mathematics of the situation causes both problems to cancel out.

3) The whole *point* of much of science is to turn multiple problems into a single problem. It turns out that it makes the problem easier.

 

[twofish-quant]

"Overall: theory must be subject to experimental and/or observational test; this is the central feature of science." George F R Ellis, November 21, 2008, "Dark matter and dark energy proposals: maintaining cosmology as a true science?"
http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.3529v1.pdf

Sure, but that's different from saying that we must have observational confirmation *right now*. Also for someone that is demanding large amounts of experimental and testable evidence, he seems prone to making statements like "The multiverse idea is not provable either by observation, or as an implication of well established physics."

It also turns out to be less of a problem than it appears. What will happen if something isn't provable is that people will end up with different ideas, and in the end people will "agree to disagree." If you can't come up with a compelling argument as to what exists in the multiverse, then some people will think it's gumdrops and other people will think it's Coca-Cola, and in the end people will just give up fighting over it.

One thing that it sort of weird is that the citation that "The multiverse idea is not provable either by observation, or as an implication of well established physics." is a citation to someone that *isn't* a scientist, whereas the link to people that have tried to use the anthropic principle are to practicising theorists.

Ellis: It is dangerous to weaken the grounds of scientific proof in order to include multiverses under the mantle of ‘tested science’ for there are many other theories
standing in the wings that would also like to claim that mantle.

On the other hand, it's equally dangerous to limit what we define as "science" so strongly that it excludes natural phenomenon that are amenable to logical deduction, and limit "evidence" in a way that biases what can be studied. You end up with higher levels of non-sense.

If we reject Marxism and Freudian psychoanalysis as being outside the bounds of science, that's not very far from saying that science has nothing useful to say about human societies or the human mind, and that opens the door up to even worse silliness. One of the reason that I think Popper's statements that Marxism is unfalsifiable is wrong is that much of Marxism was falsified but it took several tens of million dead to do it. If we could have figured out that it wasn't going to work in 1925, then it would have saved us a lot of trouble. Past is past, but I do worry a lot about going to work and operating under economic assumptions that will prove disastrously wrong.

I'm interested in talking about science. Your comment leaves me drifting out in space with no spacecraft .

Science is hard.

 

[Ken G]

2) It's not crazy to think that the DE and inflation are part of the same quantum field. In that cause, the theorist would think about this and try to figure out something interesting.

Of course they can be part of the same field, I already mentioned the "quintessence" idea. But the point is, simply making them part of the same field does not give any reason to synchronize the time when dark energy takes over with the time that life appears and with a brief period of measurable curvature. Even if it's one field, that's still two surprising coincidences associated with that field, not one. My point is that we already know one of those surprising properties to be true, but we should still expect the other surprise to not be true, hence the word "surprise."

You've advanced the idea that "any theory that creates a cosmic coincidence should be rejected."

Where did I say any such thing? Not at all, what I've said over and over is that no theory should ever be rejected for any reason other than it did not agree with experiment, or it can be replaced by something simpler and make the same predictions. What I also said is that a theory that creates a cosmic coincidence should be expected to fail. That means it is making a "risky prediction", that means it is a valid theory (but one that should still be expected to fail). I never said any theory that gives measurable curvature should be rejected prior to measuring the curvature, I said that a theory that finds it more likely that there will not be detectable curvature than that there will be is placed in a bad position if curvature is detected, expressly because we should then look instead for a theory that made the "risky prediction" that curvature should be detected. The problem with inflation is that it is not one theory, it is a factory of theories, so no matter what is observed, there is somewhere in that factory a version that gets it right. That's not the meaning of "risky predictions"!

Something that would be a useful paper would be to take that idea to it's logical conclusion and argue that the idea that we are seeing zero curvature and zero DE evolution is *wrong*.

I agree that it would be a useful paper to anticipate curvature detection and offer an explanation for the double-coincidence. Such a paper does make a risky prediction-- it says "this theory predicts a double coincidence, in a way that unifies the double coincidence into a single principle (rather than jury-rigging a generic model to get that outcome), so if that is what is observed, this theory should be considered the best way to understand it." Note that is not the same as saying "here I have a theory with enough free parameters to accommodate whether or not curvature is detected, so I can make either outcome seem natural with the appropriate parameter choice." That's not making a risky prediction, that's preparing for a rationalization.

I'm just trying to get you to take your claims to their logical conclusions.

To do that, logically, you have to start with my actual claims. It's best to stick to what I said and not dubious reconstructions.

2) You are the person that quotes Popper. If you have *one* problem, that should falsify the principle, shouldn't it? However, it could be that the mathematics of the situation causes both problems to cancel out.

Now it seems you are applying the practice of dubious reconstruction to Popper as well!

 

[twofish-quant]

Of course they can be part of the same field, I already mentioned the "quintessence" idea. But the point is, simply making them part of the same field does not give any reason to synchronize the time when dark energy takes over with the time that life appears and with a brief period of measurable curvature.

I haven't done the math in detail, but if you assume that dark energy doesn't have a constant equation of state and that there is non-zero curvature, then the coincidence disappears. Depending on how the EOS evolves you can set thing up so that curvature is a generic feature of the universe, and they EOS evolves in such a what that it *doesn't* suddenly switch on.

But getting to the broader point about "how theorists really do theory." A lot of it involves "playing" with ideas. You stated an interesting principle which is that "all theories that create a cosmic coincidence should be rejected". OK. Let's accept that principle and see where that gets it. Can you tweak the EOS and curvature so that there *isn't* a coincidence?

If there isn't a reason then let's *invent* one. The problem with Popper's ideas of how science works is that a lot of good theory involves asking *what if*.

Even if it's one field, that's still two surprising coincidences associated with that field, not one.

I'm asking if the math is such that the coincidences cancel each other out. So you assume that dark energy *always* evolves, and that cosmic curvature *always* exists. At which point you no longer have a coincidence because an observer will *usually* see dark energy and cosmic curvature

What I also said is that a theory that creates a cosmic coincidence should be expected to fail.

Therefore LCDM with zero curvature and constant DE should therefore be expected to fail because it creates a cosmic coincidence. If you change the model so that you have a non-zero curvature and a non-constant DE, then (and I need to check the math) the concidence disappears.

That means it is making a "risky prediction", that means it is a valid theory (but one that should still be expected to fail).

That makes zero sense. If a theory fails, then how can it be *valid*. If LCDM with zero curvature and constant DE is wrong, then it's wrong. if it's not wrong, then it's not wrong. If you argue for "no cosmic coincidence" then it's wrong.

The problem with inflation is that it is not one theory, it is a factory of theories, so no matter what is observed, there is somewhere in that factory a version that gets it right. That's not the meaning of "risky predictions"!

But there is a *reason* for this.

The two big predictions of inflation that seem to hold true are the horizon problem and the CMB background fluctuations. *If* you believe that FTL signaling is impossible *and* you believe that the big bang is more or less accurate, then you *MUST* believe that something like inflation happened.

People have looked for alternative explanations that explain the horizon problem and those either involve some sort of faster than light signaling *or* complete rejection of the big bang.

If you reject FTL signalling *AND* you don't reject big bang completely, then this wipes out any non-inflationary theory that anyone has suggested in the last thirty years. At that point, what you can do is to create a "factory" for generating inflationary theories, and then you end up with several hundred different scenarios, and then you start looking for other things that allow you to cross out scenarios.

Now it's *possible* that we may have missed something, but the longer things go on without anyone able to suggest anything new, the more likely we are that we didn't miss anything, and if you have any ideas on how to deal with the horizon problem without inflation, I'm open to suggestions.

Also, if you can "parameterize" ignorance than that's good. The thing about LCDM is that it reduces our ignorance about the universe to 12 numbers. The good thing about the standard model is that it reduces our ignorance of the universe to 24 numbers. If you are in a situation were you can list "all possible theories that are not in contradiction to known facts" then you are in good shape.

Note that is not the same as saying "here I have a theory with enough free parameters to accommodate whether or not curvature is detected, so I can make either outcome seem natural with the appropriate parameter choice." That's not making a risky prediction, that's preparing for a rationalization.

And yet another reason why I think Popper is all wrong. If you can't explain then at least you can describe.

If you can get to the point where you can describe a situation with a number of parameters, you are doing really, really well. We can do this with the big bang. We *can't* do this with supernova or accretion disk jets or galaxy formation. (This is a problem since the early measurements of the universe *assumed* that type SNIa's have constant luminosity. We have *zero* theoretical reasons to explain why that is. Also a lot of the galaxy distances come across because of Tully-Fisher, and we don't know why that works.)

So if you are in a situation where you can describe the whole world with twenty parameters, you are doing really, really good.

Here's something to try. Try to come up with a model with ten numbers that can describe your day tomorrow, in which that anything that can happen is described by those ten numbers and anything that can't happen is outside the scope of those numbers.

It's actually quite hard.

To do that, logically, you have to start with my actual claims. It's best to stick to what I said and not dubious reconstructions.

This isn't about you.

If you didn't make the claim that "models with cosmic coincidences should be rejected" then you should have, because it's an interesting claim, that you can get a theory paper out of it.

A lot of what theorists to involves "playing" with ideas. You actually came up with an interesting idea, but rather than developing it, you are backing away from it, which seems odd. If you aren't going to develop the claim, then I will.

I'm trying to understand the universe. This involves creating ideas and throwing them at each other. If you aren't willing to develop a particular idea, then someone else needs to.

Something to remember is that the goal isn't to "win the argument" or to "be correct." The goal is to find truth. If I have a new idea and go to one of my colleagues, they are going to automatically and reflexively take the opposing side because that's how physics works.

One thing that happens in graduate school to a lot of students is that student argues with advisor. Advisor comes up with counterarguments. Student starts backing down, and then advisor takes student to task, because they could have used other arguments and shouldn't have backed down.

One other trick is that pretty much any adviser will do is to vehemently argue something that they don't really believe in. It's a useful trick because students will tend naturely to try to please their advisers by copying them, but if you are in a situation where you don't know what your adviser believes, that doesn't work. Just because someone strongly argues for proposition A doesn't mean that they are emotionally attached to it. They could just be playing with an idea.

 

[twofish-quant]

Also, I'm willing to wait X number of years for data on string theory. The trouble comes in when there are public policy issues where you can't wait and you can't falsify. Global warming comes to mind. There isn't a practical way of experimentally falsifying global warming without risking the destruction of the planet, but the fact that we can't practically *experimentally* falsify global warming doesn't make it "non-science."

The closest you can do without burning down the planet is to run "what-if" computer simulations that take known physical principles and extrapolate them to show that yes, if we don't do X and Y, the planet will be destroyed. But if this is philosophically *valid* to make statements about "alternative Earth's" then I don't see why statements about multiverses are inherently non-scientific.

It's also possible to take these ideas too far. For example, Imre Lakatos extended a lot of Popper's ideas, but he ultimately came to the conclusion that sociology and Darwinism were not science.

 

[Ken G]

I haven't done the math in detail, but if you assume that dark energy doesn't have a constant equation of state and that there is non-zero curvature, then the coincidence disappears. Depending on how the EOS evolves you can set thing up so that curvature is a generic feature of the universe, and they EOS evolves in such a what that it *doesn't* suddenly switch on.

And that's exactly what I'm talking about-- that's precisely the kind of alternative to standard inflation models that I referred to at the outset when I pointed out that curvature detection would constitute evidence for the the need of that kind of alternative! I'm glad we have finally reached agreement.

That makes zero sense. If a theory fails, then how can it be *valid*.

First of all, you have changed my words once again. I said that a theory can be valid and expected to fail at the same time. And indeed, that is actually a very nice feature of a good candidate theory.

The scientific "validity" of a theory could be several things, depending on the purpose of the theory. Some theories are designed to help us build new technology, but these are highly mature theories, and these are only "valid" if they have a huge preponderence of evidence in their favor. There is little issue in determining which theories of this type are valid, they have become part of a trusted scientific analysis scheme. However, immature, or candidate, theories have a totally different criterion for being "valid", and this is the only place where we need input from philosophers like Popper to help us determine what our standard of "validity" should be.

The Popper insight here is that for a candidate theory to be a valid candidate theory, it must make "risky" predictions, which are (by definition) predictions that seem to have a high likelihood of failure-- so if they don't fail, it is grounds for graduating the candidate theory to a trusted theory. The quintessential example of this is special relativity, which predicts that in the Sagnac experiment, airplanes traveling different speeds between the same events should measure different elapsed times. That is a risky prediction for relativity to make, because no one in their right mind who was skeptical of relativity would expect that prediction to be successful. That is precisely what "falsifiability" means in Popper's scheme, not the caricature you imagine.

The two big predictions of inflation that seem to hold true are the horizon problem and the CMB background fluctuations. *If* you believe that FTL signaling is impossible *and* you believe that the big bang is more or less accurate, then you *MUST* believe that something like inflation happened.

In either this thread, or the other we are debating, I pointed to the distinction between the inflation phenomenon (everything you just mentioned), and a particular theory of inflation (scalar potentials, slow roll, etc.). There is wide mainstream consensus that the inflation phenomenon is most likely necessary to understand our observations. What we are talking about here is specific elements of any particular theory, like eternal inflation and the multiverse, and whether these theories are numerous enough to "stack the deck" such that they are bound to succeed-- rather than facing legitimate risks of failure. If I roll a die, and have 6 different theories that predict each of the 6 outcomes, that's not a "risky" prediction, and so I cannot attribute "success" to the one that happens to prove true in that single case.

And yet another reason why I think Popper is all wrong. If you can't explain then at least you can describe.

Sounds like something Adler or Freud or Marx might have said, word for word. This is exactly why Popper is not wrong.

Here's something to try. Try to come up with a model with ten numbers that can describe your day tomorrow, in which that anything that can happen is described by those ten numbers and anything that can't happen is outside the scope of those numbers.

It's actually quite hard.

I've no doubt. And the reason has a lot to do with the number of fundementally independent facts I need to explain about my day tomorrow. But in cosmology, just how many fundamentally independent facts do we need to explain? And how many variables will we allow ourselves to have to explain them? That's exactly why it is essential to be able to make risky predictions-- any attempt to predict n independent results with m parameters is going to be very risky indeed, if m << n, but presents no risks at all if n=m.

If you didn't make the claim that "models with cosmic coincidences should be rejected" then you should have, because it's an interesting claim, that you can get a theory paper out of it.

Please find the place where I said that quote. Then ask yourself: if you really had a logical position to stand on, why would it be so important for you to constantly change my argument?

One thing that happens in graduate school to a lot of students is that student argues with advisor. Advisor comes up with counterarguments. Student starts backing down, and then advisor takes student to task, because they could have used other arguments and shouldn't have backed down.

Actually I know all about graduate school. But I agree with your basic point-- a good argument involves sticking to one's guns, and so even though neither of us "pull our punches", the reason we are still involved in this discussion is we believe some mutual understanding can emerge between the lines of what appears to be a simple debate.

Just because someone strongly argues for proposition A doesn't mean that they are emotionally attached to it. They could just be playing with an idea.

Yes, and they might find themselves arguing the opposite point tomorrow, or next year. They may even forget why! It's just the value of discourse.

 

[twofish-quant]

I said that a theory can be valid and expected to fail at the same time. And indeed, that is actually a very nice feature of a good candidate theory.

I think the terminology is off. Without any sort of experiment data, it's not a theory, it's a hypothesis. If it's hypothesis with strong predictive value, then it is a "well-posed" hypothesis.

It's important to get the definitions right. There is a big difference between a "valid theory" and a "well-posed hypothesis". "Valid theories" are not expected to fail, but "well posed hypotheses" can.

The scientific "validity" of a theory could be several things, depending on the purpose of the theory.

"Validity" has a specific meaning in science, which is rather different than the meaning in mathematics.

http://en.wikipedia.org/wiki/Validity_(statistics)

The Popper insight here is that for a candidate theory to be a valid candidate theory, it must make "risky" predictions, which are (by definition) predictions that seem to have a high likelihood of failure

Disagree. I think that it is *good* for a theory to make risky predictions, but if you can't do it then you make the best with what you have. Also, there are useful models that *don't* make risky predictions or any predictions at all.

What we are talking about here is specific elements of any particular theory, like eternal inflation and the multiverse, and whether these theories are numerous enough to "stack the deck" such that they are bound to succeed-- rather than facing legitimate risks of failure. If I roll a die, and have 6 different theories that predict each of the 6 outcomes, that's not a "risky" prediction, and so I cannot attribute "success" to the one that happens to prove true in that single case.

But this is a perfectly correct way of doing science. I know that there are six possible alternatives, I create a different model for each of the six scenarios, and once I know what the answer is, I eliminate five of them.

If I roll the dice, and it turns into a butterfly and flies away, then at that point I know that I'm outside of my initial model assumptions.

I've no doubt. And the reason has a lot to do with the number of fundementally independent facts I need to explain about my day tomorrow. But in cosmology, just how many fundamentally independent facts do we need to explain?

galaxy distributions
nucelosynthesis numbers
CMB radiation characteristics
observations of galactic evolution
observations of chemical evolution

Each one probably involves thousands of individual facts.

That's exactly why it is essential to be able to make risky predictions-- any attempt to predict n independent results with m parameters is going to be very risky indeed, if m << n, but presents no risks at all if n=m.

In the case of cosmology, m is twelve and n is in the tens (maybe hundreds) of thousands. If it turns out that we have to turn m from twelve to fifteen, it's not a big deal.

One problem that I have with the way that cosmology is taught is that it doesn't quite go through how much data we have.

Please find the place where I said that quote. Then ask yourself: if you really had a logical position to stand on, why would it be so important for you to constantly change my argument?

You didn't. My point is that you should have.

Also, I'm not *intentionally* trying to change arguments. Communications is difficult. Also, "arguments by psychology" don't work that well.

 

[Ken G]

I think the terminology is off. Without any sort of experiment data, it's not a theory, it's a hypothesis.

Who said anything about there not being any experimental data? I said if the theory is a good candidate theory, it makes predictions we would expect to fail (unless we are already inclined to accept the theory, in which case it is not a candidate theory any more). The classic example was general relativity, which certainly did have data to support it, but also made predictions that no one expected to be true unless they already favored the theory. That's the quintessential example of a good candidate theory, which with further verification graduated to a just-plain-old good theory.

"Valid theories" are not expected to fail, but "well posed hypotheses" can.

My use of the word "valid" in regard to a candidate theory is quite different from how the word would be used for a mature and well-accepted theory. I am saying "valid" in the sense of achieving the goals we have for a candidate theory, to wit, a theory that is consistent with what is already known, yet also makes risky predictions that we would tend to disbelieve if we were skeptical of the theory. That's a valid candidate theory, in that it meets our goals for it.

Disagree. I think that it is *good* for a theory to make risky predictions, but if you can't do it then you make the best with what you have. Also, there are useful models that *don't* make risky predictions or any predictions at all.

Well, I realize you don't agree with Popper, but I haven't seen much in the way of justification for your position. Popper, and I, are talking about trying to judge when a theory can be regarded as science, so the issue arises when an idea is still rather speculative. For mature theories that have already been tested in a wide array of legitimately falsifiable venues, and have had their domain of reliablity clearly spelled out,we have no issue and no need for Popper's falsifiability criterion. Popper would know that as well, only caricatures of his views would overlook that.

But this is a perfectly correct way of doing science. I know that there are six possible alternatives, I create a different model for each of the six scenarios, and once I know what the answer is, I eliminate five of them.

That is fine under only one circumstance-- after you eliminate five and settle on #6, you must be left with a theory that actually makes predictions that could, or even should, be wrong. That's arriving at a "good candidate theory." It doesn't matter much what path you took to get to it, it must have that attribute. But if, instead, you have 6 possible outcomes to a single experiment, and design 6 theories that explain each one, and settle on whichever worked, and then have exhausted any predictive potential of that theory because you have no new falsifiability for it, then you are not making a scientific theory, you are doing rationalization of your own view. It's a bit like studying the end of your nose instead of nature. That is what Popper was trying to say, and indeed did say, quite famously.

In the case of cosmology, m is twelve and n is in the tens (maybe hundreds) of thousands.

But that data is far from independent. Let's take for example the CMB. If we count all the bits of data that has been taken on the CMB, the result would be astronomical, no pun intended. But when we see that the spectrum is thermal, suddenly the amount of independent information there drops drastically. We have the temperature, and the fluctuation spectrum. Again, the fluctuation spectrum has a huge number of bits, but when you analyze them, you see a few humps, and those few humps are all that anyone is trying to fit with current cosmological models. So they are fitting one T, and several humps, and they are doing it with a few parameters. It's quite unclear how to tell if the degrees of freedom in the data are more than the parameters used, once you establish the basic idea that you have a thermal spectrum coming from recombination, and how that has "covered the tracks" of what came before. This is the fundamental distinction, alluded to above, between a general "phenomenon" (like a thermal fireball, or an era of inflation), versus a "theory" (which attempts to explain the phenomenon, not just rationalize it).

You didn't. My point is that you should have.

Well I'm afraid that is a perfectly absurd mode of discourse. I must have missed the section of logic that goes "proof by telling other people what they should have said, and then refuting it." Baloney.

Also, I'm not *intentionally* trying to change arguments. Communications is difficult.

I can accept that-- I withdraw any claim you are doing it on purpose.

 

[twofish-quant]

I said if the theory is a good candidate theory, it makes predictions we would expect to fail (unless we are already inclined to accept the theory, in which case it is not a candidate theory any more).

The technical term for "candidate theory" is "hypothesis." You can make up your own terminology, but it just gets confusing for everyone.

I am saying "valid" in the sense of achieving the goals we have for a candidate theory, to wit, a theory that is consistent with what is already known, yet also makes risky predictions that we would tend to disbelieve if we were skeptical of the theory.

Again. "Valid" has a specific meaning among scientists. You can invent your own terminology, but it just makes things more confusing.

Well, I realize you don't agree with Popper, but I haven't seen much in the way of justification for your position.

It works? Through a lot of trial and error we've come up with cultural practices that seem to be able to say meaningful things about the universe.

For mature theories that have already been tested in a wide array of legitimately falsifiable venues, and have had their domain of reliablity clearly spelled out,we have no issue and no need for Popper's falsifiability criterion.

Then there is yet one more thing that I disagree with Popper with. Mature theories can be wrong. The amount of evidence to overturn a mature theory is higher, but they still can be wrong.

But if, instead, you have 6 possible outcomes to a single experiment, and design 6 theories that explain each one, and settle on whichever worked, and then have exhausted any predictive potential of that theory because you have no new falsifiability for it, then you are not making a scientific theory, you are doing rationalization of your own view.

Disagree. I have a problem if I come up with one theory, and it can "explain" any outcome. However if I design six different theories, and then pick the one that works, that's fine. I don't see why it's necessary to create "new" falsifiability.

But when we see that the spectrum is thermal, suddenly the amount of independent information there drops drastically.

No it doesn't, because the fact that it's thermal is still "indepdendent."

It's quite unclear how to tell if the degrees of freedom in the data are more than the parameters used, once you establish the basic idea that you have a thermal spectrum coming from recombination, and how that has "covered the tracks" of what came before. This is the fundamental distinction, alluded to above, between a general

It's actually quite clear. There are statistical tests that determine how far something is likely to produce a given curve "by chance."

Well I'm afraid that is a perfectly absurd mode of discourse.

It's not. I'm trying to illustrate how theoretical discourse works among physicists. Someone comes up with a good idea. Then you toss it against the wall to see if it breaks. You came up with an interesting idea. At that point, one of us argues for the idea. The other one argues against the idea (it doesn't matter who does it), and if it survives, then it might be interesting enough to share with other people.

I must have missed the section of logic that goes "proof by telling other people what they should have said, and then refuting it." Baloney.

Except that I'm not refuting it. I'm trying to explain why I don't agree the way that you are going about science. In the course of talking about things, you came up with an interesting idea. Rather than go and develop that idea, you gave it up. That's a shame.

My point is that this is not a good way of doing theory. If you come up with a thousand rules that prevent you from exploring ideas, that's not a good way of doing science. So far most of this discussion has been able metaphysics, and the discussion *shouldn't* be about philosophy, because if you are talking too much about philosophy, that's a sign that you aren't talking about physics.

 

[Ken G]

Then there is yet one more thing that I disagree with Popper with. Mature theories can be wrong. The amount of evidence to overturn a mature theory is higher, but they still can be wrong.

No one disagrees with that, and I have no idea why you think Popper would.

However if I design six different theories, and then pick the one that works, that's fine. I don't see why it's necessary to create "new" falsifiability.

That's what you don't get about Popper. If you design six theories, flexible enough to cover all possibilities, and one of them succeeds so you pick it, then you are doing rationalization of that outcome. What you are missing is any reason to think your theory got it right by anything but pure dumb luck. That's why Popper requires risky predictions. It's the same as if I asked a thousand people to come up with numerological schemes that follow some general prescription but include a range of possible parameters, to predict my birthday, and one of them succeeded. I'd have no reason at all to attach any importance whatever to that numerological scheme. But if I only asked one person, and they made the "risky prediction" that I was born a certain day, and sure enough I was, then I'd have to give their approach some attention!

Except that I'm not refuting it. I'm trying to explain why I don't agree the way that you are going about science. In the course of talking about things, you came up with an interesting idea. Rather than go and develop that idea, you gave it up.

OK I think we crossed wires somehow there. I may have misinterpreted what you were saying-- I don't think we should reject any cosmological schemes that require cosmic coincidences, because it would simply mean that the scheme was incomplete. It could still be right! Indeed, a scheme that requires a cosmological coincidence is an excellent result if it is testable (like Kepler's ellipses), because it is then very easy to tell if it is on to something or not (it makes a "risky" prediction, that other orbits, by some cosmic coincidence, will also be ellipses). Even better would be a scheme that makes the same risky prediction, and offers a reason to think of it as something other than a coincidence (like Newton's inverse-square gravity). So we don't reject theories that look like they require coincidences, but we expect them to be wrong unless there is some deeper theory that we are missing. The greatest excitement of all is when a prediction that requires what seems to be a cosmic coincidence tests out successfully. Note this is rather the opposite of the spirit of the multiverse approach to cosmology, which is looking more and more like a factory that is rigged to make sure nothing ever seems like a cosmic coincidence, yet without pinning itself down to any risky predictions, so you have no chance of judging what is actually a good theory that points to some deeper truth we have been missing.

My point is that this is not a good way of doing theory. If you come up with a thousand rules that prevent you from exploring ideas, that's not a good way of doing science.

Popper's criteria are not rules to prevent you from exploring, they are rules to keep you from fooling yourself that you are exploring-- when you really aren't.

 

[Eric333]

there's probably some element of "space" that is expanding from the Big Bang, but the void which that space resides in (i.e., which it is expanding into) must be infinite.

Eric

 

[Drakkith]

there's probably some element of "space" that is expanding from the Big Bang, but the void which that space resides in (i.e., which it is expanding into) must be infinite.

Eric

Space is not expanding into any pre-existing space or void.

 

[twofish-quant]

That's what you don't get about Popper.

I think that I do get Popper. I just disagree with him.

If you design six theories, flexible enough to cover all possibilities, and one of them succeeds so you pick it, then you are doing rationalization of that outcome. What you are missing is any reason to think your theory got it right by anything but pure dumb luck.

The reason is deductive logic. For example, I claim that because mints are green, the sky is blue. However, someone else can argue equally well that because mints are green, the sky is pink, or orange, or magenta. In order to make a scientific argument, I have to present a chain of logic that starts out with a set or premises, and logically to a conclusion, so that no one can question the conclusion if the premises are correct.

If I've done that, then there is something there more than "dumb luck."

And sometimes just presenting the change of logic is scientific progress. For example, accretion disk jets. We are pretty sure we know the premises (i.e. the scientific laws that operate with accretion disk jets). We know the result (i.e. accretion disk jets exist). What we don't have is the logical chain of reasoning that connects the rules with the result. Now if someone could present that chain of reasoning, that would be a scientific theory, not withstanding that it hasn't demonstrated anything new.

In the case of the early universe, there a lot more wiggle room because the premises are unclear, but as we know more, there will (hopefully) be less flexibility both in the premises and in the observations.

This is the problem with "God does it" arguments. I can argue that God created the sky blue. Fine, so why didn't he want pink skies? In some religions you can constraint the actions of God through motivational arguments (i.e. God loves you therefore...) But even that doesn't constrain things when it comes to the natural world. I don't see why a loving God would prefer blue skies over pink ones. Therefore why is the sky blue and not pink is a scientific question and not a theological one.

That's why Popper requires risky predictions. It's the same as if I asked a thousand people to come up with numerological schemes that follow some general prescription but include a range of possible parameters, to predict my birthday, and one of them succeeded. I'd have no reason at all to attach any importance whatever to that numerological scheme.

But if instead of matching one number with one number, you match one with fifty, then you have something useful. For example, you come up a formula someone correctly figures out your age *and* height, that would be useful, because you go from age to height.

I may have misinterpreted what you were saying-- I don't think we should reject any cosmological schemes that require cosmic coincidences, because it would simply mean that the scheme was incomplete.

The main job of theoretical physicists is to come up with logical chains, and sometimes you don't have the whole chain. The reason I brought this up is that the statement "reject any cosmological schemes that require a coincidence" is a perfectly good premise, and one thing that a theorist should do is to ask, assume this is true, then what logically follows. If you come up with something non-obvious (i.e. "rejecting cosmological schemes that require a coincidence" -> "cosmological constant numbers have been misinterpreted"), this is something that you want to share with people.

So we don't reject theories that look like they require coincidences, but we expect them to be wrong unless there is some deeper theory that we are missing.

You shouldn't expect anything. The problem that I have with the way that you are thinking is that you are trying to do physics theory by assuming philosophical principles, and that it's a good way of going about things, not the least of which is that we will probably never agree on what those principles are. You say "Popper says this" and I say "so what, he's wrong" then what?

Science involves a lot of people, and the job of a theorist *isn't* to figure out if a theory is true or not. The job is to come up with logical chains and deductive facts, and then through them into the pot for people to make some use of.

And that's where the "anthropic project" has been useful. For example, one "deductive fact" which is non-obvious is that the existence of stable matter is very sensitive to dimensionality and the fine structure constant, whereas it's not sensitive to the cosmological constant. That's interesting.

The greatest excitement of all is when a prediction that requires what seems to be a cosmic coincidence tests out successfully. Note this is rather the opposite of the spirit of the multiverse approach to cosmology, which is looking more and more like a factory that is rigged to make sure nothing ever seems like a cosmic coincidence, yet without pinning itself down to any risky predictions, so you have no chance of judging what is actually a good theory that points to some deeper truth we have been missing.

But you can't tell the universe what to do. The "multiverse approach to cosmology" is no different than the approach scientists take to most problems, and it's what Thomas Kuhn calls 'ordinary science." You have a set of premises, and your job is to make the observations fit the premises. You'd *like* to make a "risky prediction" but you go into your model and it turns out that it doesn't make any predictions that aren't trivially wrong.

Doing "revolutionary science" requires the universe to cooperate, and you can't make the universe do that. As far what constitutes a good theory, there are heuristic criterion, and as for "deeper truths" if you take enough data and make enough models you'll stumble onto the truth by accident.

You can't *plan* to make risky predictions, because any predictions you can plan for aren't risky.

Popper's criteria are not rules to prevent you from exploring, they are rules to keep you from fooling yourself that you are exploring-- when you really aren't.

They don't do a good job of that.

There are some tricks that people use to deal with the psychology and cognitive bias aspects of doing science. One is to do what I was trying to do with with the "coincidence principle". You flip a coin, and then have one person advocate an idea and then someone else tear it down, and then you blow a whistle and have people switch places.

The other thing is to make heavy use of mathematics to make unambiguous predictions. We can disagree whether inflation is true, but it's got a mathematical model so it's not possible to dispute whether it lead to conclusion X or not.

And if you can't explain, at least you can classify and observe. It's an important fact that all supernova Ia have the same absolute magnitude. We have no clue why. Pointing out that supernova Ia is a statement and not a model, and if you think the only valid scientific inquiry involves making falsifiable models, it's not science which is an absurd conclusion.

 

[Chronos]

... your job is to make the observations fit the premises.

That is where MOND came from ... My apologies, I couldn't resist.

 

[phinds]

there's probably some element of "space" that is expanding from the Big Bang, but the void which that space resides in (i.e., which it is expanding into) must be infinite.

Eric

You completely misunderstand cosmology and the structure of the universe. The universe isn't expanding "into" anything. That idea is nonsense.

 

[Alex-NL]

On a related note: can Hawking radiation cross the "boundary" from what's beyond it into our visible bubble? Afaik the phase velocity of the Schrödinger wave isn't limited to c.

If so and if the magnitude of this effect could be measured, it could theoretically be possible to calculate the size of the universe beyond our visible bubble with the assumption that the universe has a roughly equal mass-energy density at very large scales.