How is molecular hydrogen detected?

[JDoolin]

My textbook seems to give conflicting information on whether molecular hydrogen can or cannot be detected. On the one hand it says (p393) "Dark matter is not hydrogen gas (atomic or molecular), nor is it made up of ordinary stars. Given the amount of matter that must be accounted for, we would have been able to detect it with present-day equipment if it were in either of those forms."

However, it also says (p302) "Molecular hydrogen...does not emit or absorb radio radiation, so it cannot easily be used as a probe of cloud structure...Instead, astronomers use radio observations of other molecules, such as carbon monoxide, hydrogen cyanide, ammonia, water, and formaldehyde, to study the dark interiors of these dusty regions", i.e. they never actually see the hydrogen--they see the other molecules in the area, and assume the molecular hydrogen must also be there.

So on the one hand, they say "We'd be able to H₂ if it were there" and on the other hand they are saying "we can't see H₂ directly--we can only see the other molecules in its presence."

If they can't detect any radio emissions of molecular hydrogen, what spectrum ARE they using to locate it?

(Source- Astronomy-A Beginner's Guide to the Universe-Sixth Edition)

 

[cepheid]

It's true that most H2 is too cold for any of its radiative transitions to be excited, therefore we can't see it (I'm pretty sure that there are exceptions -- places where we can see warmer H2). For the most part, we need to use CO as a tracer for it. Certain empirical rules are used to determine the total amount of molecular gas (which is almost all H2) that is present based on the amount of CO emission. The accuracy of these techniques is debated, but I always got the impression that it was sort of a "factor of 2" type of problem. So the point is, when it comes to dark matter, even if you take into account that most H2 is unseen (at least in emission), anywhere where it's cold enough for there to be H2, it's also cold enough for there to be other molecules, and indeed, for there to be solid matter condensed out in the form of tiny microscopic grains, which astronomers call "dust". We can see the other molecules, and we can see dust. So, if H2 were to account for the missing mass attributed to dark matter, we would have see a LOT more emission from its visible tracers than we do see. We'd also have to explain why dynamical considerations require the DM to be everywhere in a spheroidal halo surrounding the galaxy, whereas molecular gas clearly cannot exist everywhere.

Besides all that, there are a host of other good observational reasons why DM has be non-baryonic (ie not made of ordinary atoms), not the least of which is that it doesn't interact with visible matter through any means other than the gravitational force, and it certainly doesn't absorb or emit light.

 

[JDoolin]

Well, I can see how the presence of Carbon Monoxide implies the presence of molecular hydrogen, but I don't see how the presence of molecular hydrogen implies Carbon Monoxide.

If I understand right, Carbon can only occur as a result of nuclear fission inside a star. So if you see carbon monoxide, you're seeing the emissions of a star, a red-giant or supernova explosion. But the hydrogen was there before the star formed, and it would have existed without any Carbon or heavier atoms.

 

[cepheid]

A couple of other points. I never answered your question of how H2 is detected in cases where it can be seen in emission. The intro to this paper talked about how the molecule's rotational transitions lead to emission in the mid-infrared (tens of microns):

http://arxiv.org/abs/1109.2544

The second point is that even if you can't see molecular hydrogen in emission, I'm pretty sure there are cases where you can see it in absorption (sillouhetted against luminous emission from nearby stars, and even seeing absorption line features from it in the spectra of other objects e.g. in the UV portion of stellar spectra). Granted, this may only allow you to see the densest clouds that happen to be in warmer surroundings (and haven't been fully dissociated by ionizing radiation), but at least it is an indication that it is there.

 

[cepheid]

Well, I can see how the presence of Carbon Monoxide implies the presence of molecular hydrogen, but I don't see how the presence of molecular hydrogen implies Carbon Monoxide.

If I understand right, Carbon can only occur as a result of nuclear fission inside a star. So if you see carbon monoxide, you're seeing the emissions of a star, a red-giant or supernova explosion. But the hydrogen was there before the star formed, and it would have existed without any Carbon or heavier atoms.

The ISM has been enriched with "metals" (elements heavier than helium) through billions of years (several generations) of star formation in our galaxy. So it's no longer true that these elements are localized only to supernova remnants or planetary nebulae (relics of dead stars). They've had time to spread out somewhat homogeneously. In fact, the molecular gas in the galaxy is spread out over a fairly wide area. It exists in a large ring between 3.5 kpc - 7.5 kpc from the galactic centre, in the galactic plane (although I understand that there is also some diffuse stuff at high galactic latitudes i.e. off the plane). We know this from tracing CO emission ;)

 

[JDoolin]

(Note: I have not read post 4 and 5 yet--criss-crossed communication.)

My real question here is whether it really is that clear that molecular hydrogen gas "cannot exist everywhere." Is it really 100% transparent to the radio waves? Precisely how much light-blocking power does it have, and at what frequencies? At what densities would it be possible to see through a billion light-years of the stuff as though it weren't even there?

The thing is, yeah, clearly, you'd think it was unlikely that a substance could be that transparent, but on the other hand, when you think about star formation, when you look at the lobes of a radio galaxy; or the bars on a bar-galaxy, it leads me to think there seems to be something out there; a gas that everything else is running into. And when you think about star formation, it seems like you need an initial bunch of stuff to start from, and we already know it was hydrogen gas.

So I'm thinking there must be a large portion of the stuff still out there that hasn't yet fallen into a clump to make stars.

 

[JDoolin]

The ISM has been enriched with "metals" (elements heavier than helium) through billions of years (several generations) of star formation in our galaxy. So it's no longer true that these elements are localized only to supernova remnants or planetary nebulae (relics of dead stars). They've had time to spread out somewhat homogeneously. In fact, the molecular gas in the galaxy is spread out over a fairly wide area. It exists in a large ring between 3.5 kpc - 7.5 kpc from the galactic centre, in the galactic plane (although I understand that there is also some diffuse stuff at high galactic latitudes i.e. off the plane). We know this from tracing CO emission ;)

The outer radius of this ring of detectable molecular gas is about where the sun orbits the galactic center. Now on the other hand, the part of the "galactic rotation curve" where the orbits are faster than expected due to dark matter starts around radius of 15 kpc and beyond.

Our galaxy is about 15 kpc in radius, though I'm looking at a "galactic rotation curve" in my text that extends out past 35 kpc. Its in that range of 15 to 35 kpc where the curve deviates heavily from keplerian motion, and indicates the presence of dark matter.

The Earth itself is a relic of a dead star. With an iron core, it was probably ejected from a type II supernova. Might it be possible that anything closer than 7.5 kpc to the center of the galaxy was a remnant of the same supernova? And more to the point--in the region from 15 to 35 kpc, there would be pure molecular hydrogen--so far unpolluted by supernova remnants.

 

[Chronos]

It appears your textbook is slightly misleading. Atomic hydrogen is easily detected via 21 cm band emissions. Molecular hydrogen is the more common, and stable species. It does not emit in the 21 cm band. It is normally detected by indirect means, as noted by cepheid.

 

[JDoolin]

So, just to reiterate... there is no known direct way to detect diffuse cold molecular hydrogen?

 

[Chronos]

Molecular hydrogen has a UV signature which is difficult to detect. It is readily absorbed and easily scattered.

 

[vociferous]

So, just to reiterate... there is no known direct way to detect diffuse cold molecular hydrogen?

It can be detected when gravitational potential energy causes it to coalesce and heat up. Any tiny variation in the density will cause the cloud to begin an isothermal and finally an adiabatic collapse.

Now, think about where all the dark matter is. Most of it is in the halo, exactly where there are very few stars. But how could there be very few stars if there are these huge, diffuse clouds of hydrogen? The hydrogen would have to be maintained in some kind of perfect density gradient that kept it from collapsing. Now, you suggest that the collapse is just extremely slow (on the order of 10 billion years). But this flies in the face of a multitude of globular clusters that are nearly as old as the Milky Way in the Halo. So why did those clouds of molecular hydrogen in the halo collapse but not this one? That sounds like special pleading to me. How does it sound to you?

 

[twofish-quant]

The main evidence for dark matter is that lots of things would break down if it turns out that dark matter were made of baryons.

Also I found this really interesting article...

http://arxiv.org/abs/1107.3314

 

[JDoolin]

It can be detected when gravitational potential energy causes it to coalesce and heat up. Any tiny variation in the density will cause the cloud to begin an isothermal and finally an adiabatic collapse.

Now, think about where all the dark matter is. Most of it is in the halo, exactly where there are very few stars. But how could there be very few stars if there are these huge, diffuse clouds of hydrogen? The hydrogen would have to be maintained in some kind of perfect density gradient that kept it from collapsing. Now, you suggest that the collapse is just extremely slow (on the order of 10 billion years). But this flies in the face of a multitude of globular clusters that are nearly as old as the Milky Way in the Halo. So why did those clouds of molecular hydrogen in the halo collapse but not this one? That sounds like special pleading to me. How does it sound to you?

Sorry I overlooked this response before.

I'm not entirely sure how to answer your question, but are you taking into account the changing density over time? Are you assuming that the local conditions were the same 10 billion years ago as they are now?

Consider that as we go back toward the Big Bang, each time you divide the age of the universe by two, you multiply the density by 8. If you agree with that reasoning, then consider, if the universe is 14 billion years old right now, at 7 billion years, it had 8 times its current density. At 3.5 billion years it had 64 times its current density.

The globular clusters formed sometime around at least 10 billion years ago, when the universe was at most 3.5 billion years old. Which would mean they formed when the gas was at least 60 times as dense as it is now. And since ALL the globular clusters are at least 10 billion years old, it suggests that they stopped forming, at a certain time, and my suggestion is that they stopped forming because the density of the universe dropped below some certain critical level.

Take that back another couple of steps. At 1.75 billion years, the universe would have had 64*8 = about 500 times its current density. At 900 million years, the universe would have had 500*8=4000 times its current density. At 450 million years, 32,000 times the density, etc, and you can keep going back in time and getting exponentially more and more density.

In this extremely dense environment, A supernova explosion, for instance, at that time could have a wildly different effect than a supernova explosion now, and could have made the perturbations that made our entire galaxy possible.

 

[Bobbywhy]

“Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is CO (carbon monoxide). The ratio between CO luminosity and H2 mass is thought to be constant, although there are reasons to doubt this assumption in observations of some other galaxies.”

http://en.wikipedia.org/wiki/Molecular_cloud

 

[JDoolin]

“Molecular hydrogen is difficult to detect by infrared and radio observations, so the molecule most often used to determine the presence of H2 is CO (carbon monoxide). The ratio between CO luminosity and H2 mass is thought to be constant, although there are reasons to doubt this assumption in observations of some other galaxies.”

http://en.wikipedia.org/wiki/Molecular_cloud

Right. I just think it is strange to ignore the possibility that there may be large amounts of H2 that is NOT accompanied by Carbon Monoxide. It seems to me, only that H2 which has interacted with supernovae and red giants should have any Carbon Monoxide in it.

It seems to me that this explanation (the thought that the ratio of H2 to CO is constant) must be assuming that all of the H2 was emitted from stars. It completely ignores the possibility that there was H2 without carbon monoxide long before there was H2 with carbon monoxide, and that some, or even most of that pure H2 might remain.

 

[vociferous]

Sorry I overlooked this response before.

I'm not entirely sure how to answer your question, but are you taking into account the changing density over time? Are you assuming that the local conditions were the same 10 billion years ago as they are now?

I'm assuming that the Jean's Mass formula is still applicable.

Consider that as we go back toward the Big Bang, each time you divide the age of the universe by two, you multiply the density by 8. If you agree with that reasoning, then consider, if the universe is 14 billion years old right now, at 7 billion years, it had 8 times its current density. At 3.5 billion years it had 64 times its current density.

I am assuming that you are referring to the density of the universe, not an individual galaxy. While galaxy formation is still something of a mystery, I believe I am correct in stating that early in a galaxy's formation, it is in the process of overall increasing its density, not decreasing it. I do not really know how that might affect the density of molecular clouds, but you could certainly research it in the published literature.

Remember, the density of the universe is not necessarily linearly proportional to the density of early galaxies or the density of the regions where globular clusters formed. For instance, the density of the visible universe is still decreasing, but the density of the Milky way is constant.

The globular clusters formed sometime around at least 10 billion years ago, when the universe was at most 3.5 billion years old. Which would mean they formed when the gas was at least 60 times as dense as it is now. And since ALL the globular clusters are at least 10 billion years old, it suggests that they stopped forming, at a certain time, and my suggestion is that they stopped forming because the density of the universe dropped below some certain critical level.

It seems like a reasonable hypothesis. The question is, where is the evidence?

Take that back another couple of steps. At 1.75 billion years, the universe would have had 64*8 = about 500 times its current density. At 900 million years, the universe would have had 500*8=4000 times its current density. At 450 million years, 32,000 times the density, etc, and you can keep going back in time and getting exponentially more and more density.

Showing a correlation between density and formation of clusters does not actually support your hypothesis. You need to model how the clusters formed and how the density of the universe would affect their formation.

In this extremely dense environment, A supernova explosion, for instance, at that time could have a wildly different effect than a supernova explosion now, and could have made the perturbations that made our entire galaxy possible.

I believe others have theorized this in regards to current stellar evolution. You might want to research papers on supernova-induced star formation if you have not already.

 

[Chronos]

Twofish-Quant is our supernova expert, I'm certain he could shed light on this issue.

 

[twofish-quant]

Twofish-Quant is our supernova expert, I'm certain he could shed light on this issue.

Not much. This is an ISM question and not a supernova question. :-) :-)

One thing that I found rather surprising is that it turns out that early universe chemistry is incredibly complicated.

 

[JDoolin]

I'm assuming that the Jean's Mass formula is still applicable.
I am assuming that you are referring to the density of the universe, not an individual galaxy. While galaxy formation is still something of a mystery, I believe I am correct in stating that early in a galaxy's formation, it is in the process of overall increasing its density, not decreasing it. I do not really know how that might affect the density of molecular clouds, but you could certainly research it in the published literature.

Remember, the density of the universe is not necessarily linearly proportional to the density of early galaxies or the density of the regions where globular clusters formed. For instance, the density of the visible universe is still decreasing, but the density of the Milky way is constant.
It seems like a reasonable hypothesis. The question is, where is the evidence?
Showing a correlation between density and formation of clusters does not actually support your hypothesis. You need to model how the clusters formed and how the density of the universe would affect their formation.
I believe others have theorized this in regards to current stellar evolution. You might want to research papers on supernova-induced star formation if you have not already.

I bolded a few statements here; mainly I need to model how the clusters formed and how the density of the universe would affect their formation.

I don't have a quantitative model, but I can qualitatively describe three distinct stages--perhaps four.
Stage 1--Universe Age: Very young. Galaxy forming stage. Extremely high density. Perturbation caused by supernova results in a gravitational gradient sufficient to overcome outward Hubble-velocity.
Stage 2--Universe Age, Less than a billion years. Globular Cluster forming stage: Medium density. Perturbation caused by supernova results in clumping of matter into stars, but insufficient to overcome outward Hubble-velocity.
(Stage 3)--Universe Age--Current. Spiral forming stage. Superluminal jets fire into already swirling gasses, causing it to clump into stars.
Stage 4--Universe Age--Current. Diffuse stage. Supernova explosion is not sufficient to cause clumping into stars

I made a little video to see if I could make this clearer:
http://screencast.com/t/QxU3YaeWAkXM

I hope this makes clear some of the other differences between this model and your model.
(1) in my hypothesis, the overall density of the universe equal to the overall density of a galaxy or a globular cluster at any given time. The difference is not in density but in clumpiness.
(2) You are correct in saying that galaxy formation involves increasing the density; not decreasing it; but I'm looking for a phenomenon sufficient to reverse the Hubble flow, and clump, surrounded by a homogeneous distribution of matter. In your model, you have the distribution already starting out pre-clumped, and it becomes more clumped.
(3) I don't have any additional evidence. You're already aware of spiral galaxies, bar galaxies, Hubble's law, and globular clusters.

The only thing we disagree about is the level of clumpiness in the universe. You think that the universe is clumpy on the scale of galaxies, and clumpy on the scale of solar systems. I think that the universe is homogeneous on every scale right down to the cubic meter, but clumps up on the scale of stars, because of perturbations.

 

[twofish-quant]

FYI, I'm going to put on my boxing gloves. If you want to propose a serious astrophysical model, then that means that you want to get into the boxing ring and treated like a professional boxer. So I'm not going to pull punches.

I don't have a quantitative model, but I can qualitatively describe three distinct stages--perhaps four.

A qualitative model is useless since it's impossible to make predictions that are detailed enough to compare with observations. Now it doesn't have to be a complicated quantitative model, but you need to run some numbers.

One quick thing to calculate is that age of the universe at which the average density of the universe reaches densities that are typical of the interstellar medium. My guess is that it's going to end up before you have any stars at all.

What you need to be able to generate are *NUMBERS*. How many globular clusters do we expect to see? What's the density of galaxies? What's the distribution of bright matter and dark matter? What's the temperature of the gas? I want correlation functions, spectral predictions, etc. etc.

Extremely high density. Perturbation caused by supernova results in a gravitational gradient sufficient to overcome outward Hubble-velocity.

I don't think this is going to work since you are dealing with different scales. Supernova explosions happen on length scales of kiloparsecs when you already have large local gravitational fields that overwhelm the Hubble flow. If you are talking about supernova shock waves then the Hubble flow is going to be irrelevant.

Supernova bubbles are smaller than galaxies and can't affect Hubble flow. Supernova bubbles also have negligible gravational gradients. The shock wave is purely a gas pressure phenonmenon.

The other thing is were did the supernova come from? If you have supernova then you already have stellar formation, and if you have stellar formation, then things are already clumping.

(2) You are correct in saying that galaxy formation involves increasing the density; not decreasing it; but I'm looking for a phenomenon sufficient to reverse the Hubble flow, and clump, surrounded by a homogeneous distribution of matter. In your model, you have the distribution already starting out pre-clumped, and it becomes more clumped.

Jeans instability.

The only thing we disagree about is the level of clumpiness in the universe. You think that the universe is clumpy on the scale of galaxies, and clumpy on the scale of solar systems. I think that the universe is homogeneous on every scale right down to the cubic meter, but clumps up on the scale of stars, because of perturbations.

Well, you are wrong.

The matter correlation spectrum is pretty well established, and it pretty clearly shows that things clumped top down rather than bottom up. During the 1980's it was an extremely big debate between the hot dark matter people that argued that galaxies first formed and then clustered into superclusters, and the cold dark matter people that argued that the superclusters formed first.

The data supports the CDM people.

 

[JDoolin]

You bring up a good point. I would be happy to work on this professionally. In many ways it would be a lot easier than what I'm doing now. But right now my time is divided, and this is only a hobby.

But regarding pulling your punches, realize that I am skirting the edges of the rules of the forum. I have to be very, very careful what I say, and I may already have said too much. At any time the moderators decide that I am in disagreement with the scientific consensus, or that I'm arguing for a "personal theory," they can delete my post and give me an infraction for my troubles. So you don't have to pull your punches here, but I am not permitted to block your punches in any substantial way, unless I can do it within the context of the standard model.

Within those limitations, (with one hand tied behind my back) I have to ask...

I presume you mean that the data supported that the matter was cold. The matter was dark. And it was some kind of matter. What was it that convinced them that that cold dark matter was nonbaryonic?

 

[twofish-quant]

You bring up a good point. I would be happy to work on this professionally. In many ways it would be a lot easier than what I'm doing now. But right now my time is divided, and this is only a hobby.

This is why "doing science" takes so much time. It's easy for me to come up with new ideas, but to get to the point where I can put that idea in the boxing ring, and not have it get instantly killed takes lots of time and effort.

At any time the moderators decide that I am in disagreement with the scientific consensus, or that I'm arguing for a "personal theory," they can delete my post and give me an infraction for my troubles.

1) You can step back and ask what *is* the scientific consensus. Asking, so why can't supernova trigger galaxy formation and then listening to the answers is within the rules of the game.

2) The rules are not that it's within the scientific consensus but rather than personal theories are not allowed on the main forums. If you can go into the standard preprint or paper archives, and pull out a paper that defends a theory that's similar to the one that you personally like, then you can discuss that.

There are a ton of papers talking about oddball theories. If you come up with something and it's something that no one has uploaded to Los Alamos, then chances are that it's not really worth discussing.

In the case of galaxy formation there *is* no scientific consensus.

I presume you mean that the data supported that the matter was cold. The matter was dark. And it was some kind of matter. What was it that convinced them that that cold dark matter was nonbaryonic?

Baryons sound different.

http://en.wikipedia.org/wiki/Baryon_acoustic_oscillations

Basically baryons will conduct sound waves and non-baryonic material won't. The CMB and location of the galaxies "freezes" the sound waves at the start of the universe, and the fact that baryons will conduct sound and non-baryonic material won't means that you end up with clumps of matter at certain locations.

 

[twofish-quant]

One other thing. You'll have to do a bit of digging to find computer simulations of baryon-only universes. They date from the late-1980's when this was still under dispute.

 

[twofish-quant]

Here's a graph showing what the universe looks like versus what it would look like with just baryons.

http://www.astro.caltech.edu/~george/ay21/eaa/eaa-powspec.pdf

It sounds different.

If you look at the baryon only graph, you see lots of peaks. Those are standing waves. A baryon-only universe would conduct sound really, really well, so if you imagine a string that goes from one end of the observable universe to the other, and pluck it, you end up with very strong harmonics.

We don't see extremely strong harmonics, but we do some some harmonics, which says that the universe is this mixture of stuff that conducts sound very well with stuff that doesn't conduct sound very well.

 

[JDoolin]

(If this is hard to read, I could probably do another Jing video running through it... But maybe you could address any number of items where I appear to be confused. I just picked one of your links http://www.astro.caltech.edu/~george/ay21/eaa/eaa-powspec.pdf and started reading, to the best of my ability; trying to figure out what you're saying.)

So for this Power function P(k) is the Fourier transform of the correlation function. xi(r) and w(theta). Now as for spatial and angular correlation functions xi(r) and w(theta), are they looking at r=0 from our position, and theta =0 in some specific direction? Are they using the orientation of our galaxy, or are they using the orientation of the CMBR dipole?

However, the article also says dP = nbar^2(1+xi(r12))dV1 dV2

dP = \bar n^2(1+\xi(r_{12}))dV_1 dV_2

I'd have to review Fourier transformations; Is that an equivalent definition? Now the idea of a Fourier transform, if I'm not mistaken, is to take something from distance or time domain into a frequency domain. It turns a function which is graphed in terms of time or distance into a function which is graphed in terms of frequency, or wave number.

The correlation function is xi(r)-the spatial distribution or w(theta)-the angular distribution. Now, “the spatial two-point or autocorrelation function is defined as the excess probability, compared with that expected for random distribution, of finding a pair of galaxies at a separation r12.” By “random” do they mean a “uniform random distribution?” And by “probability of finding a pair of galaxies at a separation r12” are they saying, “Given a galaxy at point 1, what is the probability of finding a galaxy at r2” or are they working from a single origin, and expecting to find galaxies in a more-or-less spherical distribution? Another question--on the correlation function itself. I think of “sound” as a causality relation; not a correlation relation. Is this really a sound wave traveling through the universe now, or is it a correlation function that may or may not be due to a sound wave that went through the universe a long, long, long time ago when the universe was significantly denser?

It says that between .1 h^-1 and 10 h^-1 MegaParsec's the spatial correlation function is well described by a power law (5 h^-1/r)^1.8. Unfortunately, the article never tells us what h^-1 actually stands for. There's also not really any explanation for where that came from; though it reminds me of an inverse square law that you might get, either from gravitational effects, or intensity effects--anything that is proportional to the surface area of a sphere at a certain distance from an object or event.

Also, they quickly change their mind, and decide, instead that xi(r) = 1 over 2 Pi times the integral of dk * k^2 P(k) sin (kr) over kr. \xi(r) = \frac{1 }{2 \pi} \int{ dk * k^2 P(k) \frac{\sin(kr)}{kr}}.
I gather that is some kind of representation of an inverse Fourier transform, though I don't fully see the resemblance to the Fourier transformations on Wikipedia. It seems like they have k/r sin(kr) but are fixing it up so there's something that looks like the sinc function in there.

The article says the paradigm is that “small fluctuations in density are amplified by gravity.” That is a qualitative sort of statement, that could mean just about anything. The main thing I'm questioning is their concept of scale--what is a “small” fluctuation in density if you go back in time to where the mean density of the universe in the first nanosecond? A quantum fluctuation in the first nanosecond or microsecond of the universe will expand over the next 13.7 billion years into the entire visible part of the universe.

So yes, essentially that might be what they are saying when they say “one possible explanation being that they are quantum fluctuations boosted to macroscopic scales by INFLATION.” I just don't see why this is in doubt. Given a few carefully chosen, well-reasoned axioms, I would think that this conclusion is virtually inescapable.

Now, the primordial power spectrum, assumed to be P(k) proportional k^n, where n=1 is a popular choice... They've defined the Power spectrum so abstractly, I'm not sure which way is up, but is it a useful interpretation to say that this assumption claims that “sound” in the universe is present equally at all wavelengths? I don't think I have this right, but I'm also in great doubt as to the wisdom of transforming the map of the universe from a spatial description to a wave-number description at all. (By the way, on further thinking, I'm not sure the "popular choice" of assuming that P(k) ~ k really makes any sense. Why should there be any a priori assumption about the distribution of wavelengths of perturbations in the universe, and why would it be distributed in this way?)

My own feeling is that wave-number-based descriptions of the universe are deeply counter-intuitive. It would be rather like trying to find a Bessel function and Legendre Polynomials to describe the surface of the Earth. Of course, you CAN model the Earth this way, but why would you want to? Would it really have any predictive or explanatory power? Could you, from that mapping, then find a useful theory of plate tectonics, volcanism, oceans, etc?

A second difficulty I have with what appears to be the Standard Model, and this discussion of “sound” in general, is that to have what we commonly think of as sound, you need to have a region of gas that is more-or-less in the same inertial reference frame, and has a great enough density . It's not a question of whether it happened, but when. It sounds as though most people who support the standard model are under the impression that we should be able to see evidence of sound passing through the universe now.

I agree that they should be able to see some evidence of sound passing through the universe long ago. When the universe was one hour old, the particles 1 mile away from each other were moving apart at 1 mile per hour. Yes, in that environment, sound might travel quite well, except for a few caveats. (1) we're talking about a fluid so dense that ANY fluctuation is going to result in massive gravitational instability, and (2) We're talking about a fluid that probably doesn't interact in any way similar to the spring-like molecular interactions we're familiar with. And that region would grow in the next 13.7 billion years to a volume on the scale of galaxies and superclusters.

I'm still interested in seeing why they think that Baryonic matter could not have produced what we're seeing, but I think that argument applies only to the early universe when the density was great enough that sound would carry through the plasma.

I think there would have been a time in the universe where the density got low enough when baryons would begin to form (then sound would really begin to flow), and then a time in the universe where the density of those baryons got low enough to become almost a vacuum, and sound basically stopped.

So if I am understanding properly (a big if, at this point) they think that when Baryons formed, Nuclear interactions start becoming a push/pull interaction rather than just pulling; Hooke's Law would have begun to apply en-masse to all the particles, making the system begin carrying sound. But they see some evidence for sound but not enough evidence for sound, so they decided that most of the mass of the universe is nonbaryonic.

You may think I'm trying to construct a straw-man here. If I am, please forgive me. I still mean to just be asking... “What makes you think the dark matter in the universe must be nonbaryonic.” What you've told me is that if it were baryonic, the universe would ring like a bell. What I'm trying to do here is make my best attempt to guess what you mean. I think you must mean that the universe ONCE rang like a bell; when the density was much greater. I'm suggesting that the universe stopped ringing like a bell because it became too diffuse for sound waves to carry through diffuse molecular hydrogen. You seem to be saying that the universe should be ringing still now, except for the presence of nonbaryonic dark matter. Do I have that right?

 

[George Jones]

The rules are not that it's within the scientific consensus but rather than personal theories are not allowed on the main forums. If you can go into the standard preprint or paper archives, and pull out a paper that defends a theory that's similar to the one that you personally like, then you can discuss that.

Not necessarily. What the Rules actually say:

Scientific Discussion Guidelines

Generally, in the science discussion forums we do not allow the following:

• Discussion of theories that appear only on personal web sites, self-published books, etc.
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Generally, discussion topics should be traceable to standard textbooks or to peer-reviewed scientific literature. Usually, we accept references from journals that are listed here:

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Use the search feature to search for journals by words in their titles. If you have problems with the search feature, you can view the entire list here:

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In recent years, there has been an increasing number of "fringe" and Internet-only journals that appear to have lax reviewing standards. We do not generally accept references from such journals. Note that some of these fringe journals are listed in Thomson Reuters. Just because a journal is listed in Thomson Reuters does not mean it is acceptable.

References that appear only on http://www.arxiv.org/ (which is not peer-reviewed) are subject to review by the Mentors. We recognize that in some fields this is the accepted means of professional communication, but in other fields we prefer to wait until formal publication elsewhere.

Physics Forums is not intended as an alternative to the usual professional venues for discussion and review of new ideas, e.g. personal contacts, conferences, and peer review before publication. If you have a new theory or idea, this is not the place to look for feedback on it or help in developing it.

 

[twofish-quant]

Now as for spatial and angular correlation functions xi(r) and w(theta), are they looking at r=0 from our position, and theta =0 in some specific direction?

No. What you do is to look at r=0 for some random point in the sky and then calculate the power spectrum with respect to that random point. If the universe is isotropic and homogenous, then you should get the same power spectrum for any random point (and people have checked and we do).

Given a galaxy at point 1, what is the probability of finding a galaxy at r2” or are they working from a single origin, and expecting to find galaxies in a more-or-less spherical distribution?

If the universe is isotropic then if you start with any random galaxy, you should get the same numbers.

Is this really a sound wave traveling through the universe now, or is it a correlation function that may or may not be due to a sound wave that went through the universe a long, long, long time ago when the universe was significantly denser?

For CMB baryon oscillations, it's a snapshot of the universe as it was when CMB was emitted. For galaxy counts, the expanding universe ends up "freezing" the sound waves.

Unfortunately, the article never tells us what h^-1 actually stands for.

Hubble's constant. What happens is that when you do the calculation, everything scales to the Hubble constant, so you can just put at in as a variable, that way you don't have to worry about what it really is.

The article says the paradigm is that “small fluctuations in density are amplified by gravity.” That is a qualitative sort of statement, that could mean just about anything.

There are two free parameters in LCDM for this. One gives you the size of the initial fluctuation. The other one gives you the steepness of the fluctuations. You can fit that to the data.

his assumption claims that “sound” in the universe is present equally at all wavelengths? I don't think I have this right, but I'm also in great doubt as to the wisdom of transforming the map of the universe from a spatial description to a wave-number description at all.

It's just math. You have a differerntial equation in space. You can do a coordinate transform to do the math in wavelengths.

(By the way, on further thinking, I'm not sure the "popular choice" of assuming that P(k) ~ k really makes any sense. Why should there be any a priori assumption about the distribution of wavelengths of perturbations in the universe, and why would it be distributed in this way?)

That's where inflation comes in...

Inflation says that the universe underwent a period in which it was expanding exponentially exp(ax). So if you have random gaussian flucutations at quantum scales, and you ask what that does to the total spectrum, you get a power law spectrum.

This is why doing the numbers is important. Inflation is more than merely saying that the universe expanded, but once you get the exact numbers, you end up with the initial perturbation spectrum.

My own feeling is that wave-number-based descriptions of the universe are deeply counter-intuitive. It would be rather like trying to find a Bessel function and Legendre Polynomials to describe the surface of the Earth. Of course, you CAN model the Earth this way, but why would you want to? Would it really have any predictive or explanatory power?

Yes, it shows that the universe isn't all baryons, and that baryons cause peaks.

When the universe was one hour old, the particles 1 mile away from each other were moving apart at 1 mile per hour. Yes, in that environment, sound might travel quite well, except for a few caveats. (1) we're talking about a fluid so dense that ANY fluctuation is going to result in massive gravitational instability, and (2) We're talking about a fluid that probably doesn't interact in any way similar to the spring-like molecular interactions we're familiar with.

1) This isn't true. There is a well known criterion for when something will undergo gravitational instability called the Jeans instability. What you basically do is to calculate the speed of sound in a gas, and if the sound waves spread out the gas faster than gravity can compress it, there is no instability.

2) Fluids are fluids. One thing that happens with the big bang is that the densities pretty quickly go down to the level of things that we run into in daily life. One hour after the big bang, you have a gas of hydrogen/helium at conditions we can simulate with Earth based experiments.

What you've told me is that if it were baryonic, the universe would ring like a bell. What I'm trying to do here is make my best attempt to guess what you mean. I think you must mean that the universe ONCE rang like a bell; when the density was much greater. I'm suggesting that the universe stopped ringing like a bell because it became too diffuse for sound waves to carry through diffuse molecular hydrogen.

We are looking at a snapshot of what the universe looked like at the time the CMB was emitted and the galaxies first formed. At that point the pressure waves got "frozen" which gives us what we see today.

You seem to be saying that the universe should be ringing still now, except for the presence of nonbaryonic dark matter. Do I have that right?

No. What I'm saying is that observations of CMB and galaxy counts show what the universe was like at the time CMB got emitted and the galaxies started to form. That gives us a snapshot of the that moment, which is inconsistent with all baryons.

Now you could argue that there is some process that converts non-baryonic matter to baryonic matter, but then you look at the list of possible particle physics processes, and none of them fit. If you were arguing for a dark matter->baryon process happening at 10^-2 seconds after the BB, that would be easy. But we are now BB+300,000 years, you have hydrogen gas at 3000K, so if there were some dark matter->baryon conversion process, you should be able to see it in action on earth.

 

[JDoolin]

What is the standard model regarding Hubble's constant? Is it a true constant; i.e. it does not change over time, or is it changing? Is it the reciprocal to the age of the universe, or is it regarded to be an unchanging parameter?

Never mind, I think I found it on Wikipedia:

http://en.wikipedia.org/wiki/Hubble's_law#.E2.80.98Ultimate_fate.27_and_age_of_the_universe

And a little calculation.

If q were zero, and the integration constant is zero, then it is the reciprocal to the age of the universe.

 

[twofish-quant]

One of way of thinking of the standard model is that it's like piece of software. Cosmological Model 2012 is going to be different from Cosmological Model 1995 in the same way that Windows 8 is different from Windows 95 or Linux 3.4 is different from Linux 1.5.

As time passes, people will put in more bug fixes and features, and rip out old obsolete stuff. Right now the big work in Standard Model 2012 involves adding in a galaxy formation model and an inflation model. The perturbation model for the standard model is linear. What that means is that you do a Fourier transform of the perturbations and then assume that the interaction between the wavelengths is small enough to ignore. Once you have galaxies forming, things will definitively "go non-linear" and things will break.

 

[JDoolin]

One hour after the big bang, you have a gas of hydrogen/helium at conditions we can simulate with Earth based experiments.

Was this a mis-statement?

From what I understand, we believe that hydrogen and helium first formed at 30,000 years after the Big Bang. By my calculation ,

1 mile/hour * 13.7 billion years = 20 light-years

at one hour after the Big bang, there would have been all the matter now distributed in the nearest 20 light years (the mass of the nearest 20 or 30 solar systems) compressed into the space of a radius of one mile.

This would be like neutron-star like density. I don't think that matter at those densities can be simulated in a laboratory.

 

[twofish-quant]

From what I understand, we believe that hydrogen and helium first formed at 30,000 years after the Big Bang.

No. Hydrogen and helium first formed at three minutes after the BB.

At 34 minutes after time zero, the density of the universe was 10 times the density of water...

http://hyperphysics.phy-astr.gsu.edu/hbase/astro/bbang.html

there would have been all the matter now distributed in the nearest 20 light years compressed into the space of a radius of one mile.

There's something wrong in that calculation.

This would be like neutron-star like density, prevented from collapse only by the fact that there was no gravitational gradient--no net direction of gravitational pull. I don't think that matter at those densities can be simulated in a laboratory.

At three minutes after BB, we are at densities which we can simulate (albeit briefly) on the earth, and it's typical of the densities you find in the sun.

https://lasers.llnl.gov/programs/nic/icf/

Also, we can generate these sorts of temperatures/pressures in hydrogen bombs.

 

[JDoolin]

\frac{1 mile}{1 hour}* \left (13.7\times 10^9 years \right )*\frac{8760 hours}{year}*\frac{1 light-year}{5.8785\times10^{12} miles}=20.4 ly

I have checked the math now about ten times. Please check, and see if you see an error in the calculation.

 

[twofish-quant]

You might start out by explaining how you are setting up the calculation.

Where did you get one mile/hour and why are you multiplying it by the age of the universe.

Most calculations start with a(t), which is the relative size of the universe. You put in gravity and pressure and then you come up with an equation for a(t). In some limits you end up with some proportions that you can use for quick calculations.

Unfortunately, I don't have time to put together a set of intro cosmology lecture notes, although since you know basic calculus, you can definitely follow the dervivations of the basic cosmology equations. I'm sure that someone has done it already on the internet.

 

[JDoolin]

Thanks for your reply. I wasn't sure whether you actually saw an error in the calculation or you were disagreeing with my underlying assumption that the bulk matter of the universe is spreading out at constant speed.

I felt that I had justified that assumption in post #28; and thought that I was staying within the Standard Model. I now wonder whether the equation given hereq=-\left ( 1+\frac{\dot H}{H} \right )

is fully compatible with the equation given here: H=\frac{\dot a(t)}{a(t)}

There are basically two ways of looking at things. One is to expect that there would be a natural relationship between the velocities of distant objects, and their distance, which derives from the fact that they all originated at roughly the same place at the same time. That is essentially the meaning of the first equation.

Then there is another way of looking at things; to assume that things did NOT start out at the same place, but did start out at the same time, and that the natural relationship between redshifts and distance has to do with the scale factor, a(t) changing over time, and that is essentially the meaning of the second equation.

My calculation of 1 mile per hour times 13.7 billion years was coming from the first assumption, and I gather than Weinberg's calculation of a density 100 times greater than water after 3 minutes was coming from the second assumption.

I'll run out to the library, soon, and check out "The First Three Minutes" and see if I can find out why Mr. Weinberg's thought that the early density of the universe was so low.

To me, it appears that there are two different models for the universe, both actively in use by the astronomical community, as are summarized here:

http://en.wikipedia.org/wiki/Redshift#Redshift_formulae

One is for Minkowski spacetime, and the other is for the FLRW metric, and it refers to the cosmological scale factor. In my own reading, the reasoning behind gravitational redshift and velocity-based redshift is made fairly clear, and based on empirical data, and strong reasoning. Whereas the reasoning behind the FLRW metric generally begins with some hand-waving rationale based on a need for greater flexibility, like "What if the universe were spinning?" or "You can't have an expanding isotropic distribution that satisfies the cosmological principle."

I know in particular, since you quoted Weinberg, that he uses that latter argument in "The First Three Minutes" and he notably fails to apply the relativity of simultaneity. He makes some flawed argument about the density at point B as seen from A, versus the Density at point A as seen from B. I forget what figure it was in the book... I remember thinking to myself, there must be more than just this one mistake in the book.

I remember thinking at the time that I should really work my way through it, find a big collection of errors in Weinberg and others. The problem was that most of the book was much more hand-wavy than that diagram. So really, that one diagram, and his failure to apply the relativity of simultaneity--that was the only real error I saw in the whole book. Even so, if you want to quote Weinberg, it gives me the opportunity to mention that mistake. It is just one mistake, but I remember some quote from Einstein, when a whole lot of people were criticizing his theory, and pointing out lots and lots of mistakes.

You don't need lots and lots of mistakes--you just need one. If Weinberg's whole theory is based on his neglect of applying the relativity of simultaneity, then of course the whole theory falls. The only time you can really find an error in someone's reasoning is if they make their reasoning clear. And Weinberg made very clear that he was treating distant events as simultaneous in reference frames that are traveling away from each other at relativistic speeds.

Kudos to Weinberg here, though. It's incredibly rare for any proponent of the Standard Model to make their reasoning clear enough that you can find a flaw in it (or to be convinced by it, for that matter). Usually it's incredibly vague reasoning followed by page after page of dense tensor mathematics.

 

[twofish-quant]

One is to expect that there would be a natural relationship between the velocities of distant objects, and their distance, which derives from the fact that they all originated at roughly the same place at the same time. That is essentially the meaning of the first equation.

That's the wrong way of looking at it. The first equation doesn't describe anything. It's an equation that defines the deceleration parameter q.

My calculation of 1 mile per hour times 13.7 billion years was coming from the first assumption, and I gather than Weinberg's calculation of a density 100 times greater than water after 3 minutes was coming from the second assumption.

And the second way is the correct way of looking at things.

To me, it appears that there are two different models for the universe, both actively in use by the astronomical community, as are summarized here

Nope. Just one model, the second one. One thing about wikipedia is that it's a good resource, but I've often found it to be incorrect.

I remember thinking at the time that I should really work my way through it, find a big collection of errors in Weinberg and others.The problem was that most of the book was much more hand-wavy than that diagram.

You have to remember that Weinberg is writing for a general audience, and so he has to be hand-wavy in order not to bore people to death with equations. Also, often what appear to be errors in a popular work are simplifications. Finally, the first edition of that book was in 1977, and he wrote an updated addition in 1992, there are large parts of it that are out of date.

If you really want to do cosmology, you shouldn't start with his popular books. He's written some excellent textbooks that go through the equations in their full glory. The math isn't particularly difficult.

You don't need lots and lots of mistakes--you just need one. If Weinberg's whole theory is based on his neglect of applying the relativity of simultaneity, then of course the whole theory falls.

No it doesn't. Most "real world" theories aren't very brittle. If you make an assumption that turns out to be false, the theory still works as long as reality is "close enough" to the assumption.

The other thing is that it's usually a good idea to assume that people aren't idiots, and that maybe people have thought of an issue. For example, once you have a scale function, then you have a coordinate system and you can define simultaneity, so the principle of "no relativistic simultaneity" doesn't apply to cosmology calculations, because you've defined a fixed reference point which is the t=0 of the big bang.

The other thing is that if you have a conflict with a theoretical principle, you do the experiment and see what happens. It turns out that cosmology conflicts wildly with the principle of "no absolute reference frames". Oh well, that's what we observe. At that point you toss the theoretical principle.

And Weinberg made very clear that he was treating distant events as simultaneous in reference frames that are traveling away from each other at relativistic speeds.

Which you can do because you've defined a coordinate system based on the big bang. Once you've defined that coordinate system, then you can define simultaneous events and an absolute coordinate system.

There's no flaw. It happens that when talking about local stuff, you can use the "no simultaneity" principle to come up with a description of what happens, but it breaks down in cosmology.

Usually it's incredibly vague reasoning followed by page after page of dense tensor mathematics.

That's because people start with the physical principle and then work out the mathematical consequences of the principle. When you come up with physical principles, you just guess and hope you get lucky. You then work out the mathematical consequences of your guess, compare with observations. They may match. They may not. Repeat.

Sometimes the principle that you come up with happens to work in some situations but breaks in others. The idea that there are no preferred reference frames happens to work nicely in electrodynamics. It fails when you try to do cosmology with it, when there happens to be a absolute reference frame.

 

[JDoolin]

I really appreciate your clarity, here, when you say in cosmology, "there happens to be a absolute reference frame." In my experience, reading texts on the subject, they often give lip-service to the idea of figuring out a way to handle things with "no preferred reference frame," but then they are generally starting with an assumption of an absolute reference frame, and naturally, ending with the conclusion of an absolute reference frame.

The notable exceptions to this are Milne and Epstein, who start with Hubble's Law, and end with a conclusion of no preferred reference frame.

When you tell me that "once you've defined a coordinate system based on the big bang...you can define simultaneous events and an absolute coordinate system" you are saying that simultaneous has an arbitrary mathematical meaning, and has nothing to do with our own perceptions of time. The meaning of simultaneous as referenced from the big bang is an entirely different meaning of the word simultaneous.

However, in Weinberg's example, he does not restrict himself to the "arbitrary mathematical meaning" of simultaneous. He uses the common conception of the meaning of "simultaneous" which is two things that happen at the same time relative to specific observer, observing a specific set of events.

Weinberg tries to make "simultaneous" do a double-duty. Certainly in mathematics you have the option of defining variables any way you want. However, when you go back and reason, using the results of the calculations, you MUST keep the definition you originally used.

Now twofish-quant, I want to ask you, a question here, because you have given two defenses for Weinberg's mistake, and I think we deserve some clarity on which you regard as the proper defense. One, you said that Weinberg was writing for a general audience, so he should be given some lee-way in saying things that are [strike]not true[/strike] hand-wavy. Second, you seem to agree with Weinberg that all definitions of simultaneity are equivalent, and that once you've defined a mathematical quantity to mean time, you can use it for any purpose you desire. So are you saying that it is okay for him to make this mistake, since it's intended for popular reading, or are you saying that it is not a mistake?

(Edit-on second reading, I realize that you are absolutely clear. You do not see this mistake of confusing proper time and coordinate time. I'm saying you need to be aware of the distinction; whether you are dealing with the scales of Cosmology or the scales of Gedanken train experiments, you need to be aware of the distinction.)
What I would like to see is to have the two theories placed side-to-side, and really compared to the physical data, in much the same way that Copernicus's ideas and Ptolemy's ideas were compared by Galileo. You have A.E. Milne, Lewis Carroll Epstein, (and me, of course) on the one side--saying there are no preferred reference frames in cosmology, while most of the rest of the consensus seems to be on the other; agreeing with twofish-quant, here.

Peebles gave a somewhat accurate explanation in Principles of Modern Cosmology, as he said that Milne's "approach to using the Cosmological Principle to come up with a model for the universe is no longer considered interesting."

What I see now, though, is a lot of people who have not really taken the time to thoroughly understand Milne and Epstein. Their work has already been judged by cursory reading, as uninteresting or perhaps flawed. However, I have never seen anything resembling a legitimate criticism of their ideas. For instance, whereas Milne and Epstein go to some lengths to distinguish between coordinate time and proper time, and understanding that they are different things, you have Weinberg clearly confusing the two, and most criticisms of Milne and Epstein all seem based on the critic's failure to distingush the difference between proper time and coordinate time, and really understand the kinematic universe.

 

[twofish-quant]

They are generally starting with an assumption of an absolute reference frame, and naturally, ending with the conclusion of an absolute reference frame.

No way around this. Once you start with a universe that is

1) dynamically evolving
2) isotropic
3) homogenous

Then mathematically you *can't* avoid an absolute reference frame. Now it so happens that we live in a universe which is dynamically evolving, isotropic, and homogenous.

This is one of those "blame God, I don't make the rules" situations.

The notable exceptions to this are Milne and Epstein, who start with Hubble's Law, and end with a conclusion of no preferred reference frame.

Sure, and they also end up with a model that doesn't look like the universe that we see. Again, blame God.

you are saying that simultaneous has an arbitrary mathematical meaning, and has nothing to do with our own perceptions of time. The meaning of simultaneous as referenced from the big bang is an entirely different meaning of the word simultaneous.

Simultaneous has an exact mathematical meaning. A space time event with identical time coordinates. Relativity is based on the idea that you can assign T coordinates any which way and there is no "natural" best way of doing it.

He uses the common conception of the meaning of "simultaneous" which is two things that happen at the same time relative to specific observer, observing a specific set of events.

I don't think he means that at all. One problem is that he is writing a popular work, and you have to deal with the ambiguities and limits of the English language. It's pretty clear from his graduate textbooks that he understands what is going on.

Weinberg tries to make "simultaneous" do a double-duty.

That's because he is writing books in English and not math.

Second, you seem to agree with Weinberg that all definitions of simultaneity are equivalent, and that once you've defined a mathematical quantity to mean time, you can use it for any purpose you desire. So are you saying that it is okay for him to make this mistake, since it's intended for popular reading, or are you saying that it is not a mistake?

I'm saying that the English language is not the preferred communications mechanism for expressing these sorts of thoughts, so if you write a book in English, it's like doing surgery with boxing gloves. You will end up with a mess, and Weinberg does as well as anyone can be expected trying to write something using ordinary English.

Based on his graduate textbooks, I think that Weinberg understands the situation.

What I would like to see is to have the two theories placed side-to-side, and really compared to the physical data, in much the same way that Copernicus's ideas and Ptolemy's ideas were compared by Galileo. You have A.E. Milne, Lewis Carroll Epstein, (and me, of course) on the one side--saying there are no preferred reference frames in cosmology, while most of the rest of the consensus seems to be on the other

CMB defines a preferred reference frame.

Let's see... From big bang we can get

1) CMB fluctuation calculations
2) Galaxy count spectrum
3) predictions of elemental abundances
4) various other age related predictions (i.e. no evolved red dwarfs,
no low mass white dwarfs, globular cluster ages)

So what can we get from Milne?

The problem is that there is *so much* stuff you get from big bang, that trying to get evidence for anything else is like trying to get evidence for a flat earth. There's no contest.

What I see now, though, is a lot of people who have not really taken the time to thoroughly understand Milne and Epstein. Their work has already been judged by cursory reading, as uninteresting or perhaps flawed. However, I have never seen anything resembling a legitimate criticism of their ideas.

It doesn't match what we see. That's all that matters.

With big bang, I can get the size of the third acoustic peak. I can pull one rabbit after another out of the hat.

Can you name even *one* rabbit, that gets pulled out of Milne?

 

[vociferous]

Unfortunately, I don't have time to put together a set of intro cosmology lecture notes, although since you know basic calculus, you can definitely follow the dervivations of the basic cosmology equations. I'm sure that someone has done it already on the internet.

Introduction to Cosmology by Ryden was what I used and it is pretty easy to follow.

 

[twofish-quant]

The big problem with the Milne cosmology is that it assumes an empty universe. If you set density=0, you get the Milne cosmology, and a lot of the symmetries of Milne are precisely because the universe is empty. Empty universe means no gravity means the Hubble constant is constant. If you compress nothing you get nothing. So if density=0, then you go back in time, and no matter how much the universe shrinks, density=0, and there is no big bang. No big bang means that there is no preferred reference frame.

The trouble with all of these symmetries is that they break the moment you add anything to the universe. No matter how small the density is now, if it's not zero, then if you go into the past, it will increase and eventually go off to infinity in finite time.

So it's not correct. It's still interesting

Milne is useful as a baseline to plot supernova results

http://www.astro.ucla.edu/~wright/sne_cosmology.html

(empty universe means Milne)

Since the universe could be decelerating or accelerating, it's useful to plot things relative to a "constant" universe.

There's also this sort paper which it typical of "nutty theory papers"

http://arxiv.org/pdf/0903.2446v1.pdf

It's nutty because it says that if you assume that the universe is a mix of equal matter and anti-matter and if anti-matter also has anti-gravity, then you end up with a Milne universe in which looks like our own. That's interesting. The only problems are

1) we don't see any anti-matter in the universe
2) our best guess is that anti-matter doesn't have anti-gravity

But it's useful to know that if you assume these two *crazy things* that everything will work out. That way we know who to give free trips to Stockholm if it turns out that anti-matter behaves weird when we actually test its gravitational effects.

One final thing is that a lot gets resolved with better data. With one years of supernova data, you could argue that it's close enough to the Milne cosmology for a match, but you can't argue this any more with better data.

http://arxiv.org/pdf/astro-ph/0503690.pdf

 

[JDoolin]

We seem to be in some disagreement over what Milne's Model actually is.

The general properties of Milne's model is
(1) It is a "Big Bang" in the literal sense.
(2) It is isotropic but nonhomogeneous. The density goes up toward infinity as you look toward the edges, due to Lorentz contraction and time dilation.
(3) It is a kinematic model. There is no "stretching of space" but rather, the universe is expanding by objects actually moving away from each other.
(4) It makes use of the Relativity of Simultaneity in order to demonstrate that the above two features are mathematically possible and self-consistent.
(5) Any deviation from homogeneity would not be noticeable in the universe within 12 billion light-years.
(6) I don't feel that Milne took into account the possibility of a secondary acceleration, which might result in a local "young" universe (high Hubble constant) and a more distant "old" universe (low Hubble Constant). Also, when I hear that people have disproved Milne's model based on the observation of supernovae, I want to know exactly what that supernovae data said.

Real world theories aren't very brittle. But straw-men are. If Milne claimed that his model of the universe was an "empty model" then of course, we'd have to reject the model, based on our observation that the universe is not empty. But that's a straw-man. Milne never claimed such a thing. What he claimed was that the universe was balanced, so there was no net force in any direction. He did not claim that it was empty.

(7) Milne's model is literally an infinite number of particles in a finite space. He made this pretty clear. I'm not entirely sure I agree with him that it has to be, but I recall him putting some effort into justifying this reasoning--based on the fact that if it weren't infinite, it couldn't be isotropic. If you want to claim that Milne's model is empty, you need to square that somehow with Milne's own claim that his model had an infinite amount of mass. I realize that it has become popular to say that Milne's model is empty, but I don't see anyone actually making that case, or anyone getting Milne to agree that is the case.

Most "real world" theories aren't very brittle. If you make an assumption that turns out to be false, the theory still works as long as reality is "close enough" to the assumption.

The main thing is that when you are testing a theory, there are a couple of degrees of freedom. One is in the possible nature of events of the universe itself. Another is in the flexibility of and complexity of the theory.

When you want to make observations of the universe, you man occasionally need to stretch a little bit to get things to work. I recall a simple conservation of momentum experiment recently that I did in a lab where it appeared that every trial seemed to indicate that in fact the momentum was increasing! We did not make the theory try to fit the data though. We tried to figure out what had gone wrong with the data. Perhaps we could have conjectured that it was ghosts or dark energy, but we eventually settled on the mundane idea that our surface was slanted, and went back and found indeed, there was a 2 or 3 degree angle that we hadn't detected before; significant enough to affect the experiment.

We didn't go back and change the theory based on the data; we tried to figure out how to make the data fit the theory. But in order to do that, you need to have a fairly deep understanding of the theory, and what all might go wrong.

When people tell me that the "data didn't match Milne's Model" though, I'm not at all convinced that they went through that extra step, where they try to figure out WHY the data didn't fit. If you have no expectation that it would work in the first place, you're not likely to try to figure out "what went wrong."

I have this feeling that most people are not interested enough in Milne's model to look at the data, and check possible explanations for what went wrong. If you have people who are so biased that they cannot even acknowledge the possibility of a kinematic Big Bang, then I cannot believe that they would have the technical competency to model the data based on a theory of a kinematic Big Bang. This isn't a matter of intelligence, but of pragmatism. If you've been told something is impossible, and you believe it is impossible, why would you spend time trying to get it to work?

 

[Chronos]

... Milne's model is literally an infinite number of particles in a finite space. He made this pretty clear.

That is a rather unique interpretation. Can you clarify, or better yet, provide supporting references?

 

[JDoolin]

That is a rather unique interpretation. Can you clarify, or better yet, provide supporting references?

Just one. "Relativity, Gravitation, and World Structure" by A.E. Milne. I can't give you the pages where he goes into detail (because I don't have a copy of the book), but I can point to the list of 17 properties of his model. The infinite number of particles, here, appears as property number 8.

From http://en.wikipedia.org/wiki/Talk:Milne_model#List_of_properties_of_the_Milne_Density_Distribution

In section 112, "Properties of the 'hydrodynamic' or simple kinematic system," Milne lists these seventeen properities of the system. (Except for 14-16, these are exact quotes.)

1. "The system is described in the same way by the same formula (36) by any observer situated on any particle of the system, using his own coordinates, in flat space constructed out of his own clock measures."
2. "The system is spherically symmetrical round any particle of the system, in the experience of the observer attached to that particle."
3. "The particle-density is locally homogeneous near any given particle-observer O of the system, in O's reckoning. Departures from homogeneity are of the second order in r/ct."
4. "The particle density, in the reckoning of any particle-observer O, at any given epoch t, increases outwards."
5. "Near O, at any fixed distance, the particle-density decreases at a rate inversely proportional to the cube of the time."
6. "The system is contained at any epoch t within a finite expanding sphere centred round any particle-observer O, of radius r=ct where t is the age of the system in O's reckoning. The radius of this sphere increases with the speed of light."
7. "As the distance r tends to ct, i.e. for points nearer and nearer the expanding light-sphere, the particle-density tends to infinity."
8. "The total number of particles in the system is infinite."
9. "The members of the system form at any epoch t in the experience of any particle-observer O an open set of points of which every point of the expanding sphere r=ct is a limiting point. Every particle of the system is completely surrounded by other particles. No particle stands on the 'edge' of the system."
10. "Every particle of the system is in uniform radial motion outward from any arbitrary particle O of the system, and the acceleration of every particle in the system is zero. But the acceleration of a freely projected particle, other than the given particles, is not zero."
11. "The domain occupied by the system, though finite in volume, has all the properties of infinite space, since its boundary is for all time entirely inaccessible by any hypothetical observer traveling with a speed not exceeding the speed of light."
12. "The velocities of different particles at anyone epoch are proportional to the distances of the particles from any assigned particle taken as origin, and tend to the velocity of light as the distance tends to ct."
13. "If the particles are supposed to be luminous, then the luminosity near the expanding boundary approaches zero, since the particles are receding with nearly the speed of light (see Note 7)"
14. describes the phenomenon of desynchronization (more commonly known now as the relativity of simultaneity)
15. gives the relativistic doppler shift equation
16. says that the age of the universe at any given event is indefinite, the system has "no definite age or radius at any assigned event, the age t and radius ct depending on the epoch assigned to the event, which depends in turn on the observer making the assignment."
17. "A particle-observer O at the moment of experiencing an event E2 at himself is at a much later stage of his own experience, reckoned in his own time-scale, than P is in his (P's) time-scale at the event E1 at P which O is then observing."

 

[twofish-quant]

If Milne claimed that his model of the universe was an "empty model" then of course, we'd have to reject the model, based on our observation that the universe is not empty. But that's a straw-man. Milne never claimed such a thing.

Milne himself never claimed such a thing, but it follows from general relativity. If Milne's original model was correct then it means that gravity works absolutely nothing like general relativity. GR only gives you Milne's model if gravity doesn't exist. Milne ignores gravity. If you claim that GR is wrong, that just digs your hole deeper.

Also, you can calculate the recessional velocities from Milne's model and it looks nothing at all like what we actually see.

What he claimed was that the universe was balanced, so there was no net force in any direction. He did not claim that it was empty.

And his claims are inconsistent with the way that we know gravity works. If you have purely attractive forces you can't have a stable configuration with no net force.

When people tell me that the "data didn't match Milne's Model" though, I'm not at all convinced that they went through that extra step, where they try to figure out WHY the data didn't fit

Have you considered the possibility that it's because Milne is wrong? The theory is decades years old, people have tried to make it fit, but it just doesn't. At some point, you just have to face the possibility that the universe just doesn't work that way.

I have this feeling that most people are not interested enough in Milne's model to look at the data, and check possible explanations for what went wrong.

No. They've looked at the possible explanations, the most obvious one is that Milne is just wrong. You look at the velocities of the galaxies and they don't match. The only way that it will work with something that resembles GR is if you assume an empty universe. If you have matter and then insist on the Milne model, then you have to throw out any theory of gravity that looks Newtonian.

If you have some specific idea of what people have missed, then you can publish it. But that involves more than "just having a feeling."

Personally, I really want *you* to try to fit the data with Milne's model. The reason I want *you* to try to do it, is that I suspect that if you try very hard, and then figure out that it just doesn't work, that's the only way of convincing you that people aren't being idiots here.

When people tell me that the "data didn't match Milne's Model" though, I'm not at all convinced that they went through that extra step, where they try to figure out WHY the data didn't fit.

Because the simplest conclusion is that Milne is wrong. I don't think that people are biased *against* Milne, but what you are asking for is for people to be biased *for* Milne, and no one is. If I take galaxy recessional velocities, and they don't match the Milne model, they why should I *try* to make it fit rather than just throw out the Milne model.

In the case of the standard model, there is a reason to try to make it fit. The standard model explains a lot of things, and so when there is data that conflicts with it, then you don't want to throw out all of the things for which it fits. So you take a hammer and try to bend the model and the data until you get something that works.

In the case of Milne, there is *no* reason that I can think of that you should even try to just toss out the model.

This isn't a matter of intelligence, but of pragmatism. If you've been told something is impossible, and you believe it is impossible, why would you spend time trying to get it to work?

1) The truth will win out. The thing about data is that if the data supports you then eventually you will stumble on the truth.

2) This might sound rude, but put up or shut up. The data for galactic expansion is out there, and if you can figure out how to get it to match Milne's model, then feel free to have a go at it. The reason that I want you to try is that having you try to figure out what could have gone wrong and failing is the only way I think I can convince you that cosmologists aren't idiots or particularly closed minded.

If you claim that people are closed-minded, but then *you* spend a decade trying to get things to work and can't, what does that mean?

 

[twofish-quant]

Also, the gravity model is wrong. Milne is assuming "balanced forces" -> "no acceleration" and even in the Newtonian universe that's wrong.

 

[JDoolin]

Let me make it absolutely clear that I am not in any way claiming to be open-minded. No, I don't think there's any problem with people not being open minded enough. It's quite the opposite problem. So when I tell you that Milne's model had an infinite amount of mass in a finite volume, your reaction is, "No it doesn't. If that were true, smart people would have noticed." But where? Where do I find a single source that acknowledges what Milne actually said?

When I multiply 1 mile per hour times 13.7 billion years, your reaction is that "If that made any sense, smart people would have figured it out." But where? Where do I find that.

And when I say that balanced forces implies no acceleration, I am fairly precisely quoting Newton's Second Law.

\vec a = \frac{\sum\vec F}{m}

I have read that people argue (including Einstein, if I'm not mistaken) that force should be calculated by some kind of Gaussian surface, and if you want to make that argument... Do you know what argument I am talking about? In any case, I have read it over a couple of times, and not been able to make any sense of it. The possibilities are that I missed something, or that it really doesn't make any sense. Wish I could give you a link, but it is one of those things that I've only read in books from the library, and I don't think that I've ever seen it online. I'd like to have that discussion, because I think it is fundamental to the premise behind General Relativity, but it really doesn't make any sense at all. (Edit: I put this in another post below.)

Also, another thing I've noticed about all books on General Relativity is that they tend to skip over the idea of a kinematically expanding universe without mentioning it. Instead, they begin with the assumption of a commoving set of matter. I've also noticed that whenever I bring this up in discussions, I find myself in exactly the same arguments. Usually an irrational person will decide to take the opportunity to criticize me and misinterpret what I am saying.

I am willing to acknowledge the possibility that I'm wrong. I've made some terrific blunders over the years, and some of them have been quite embarrassing. But in the end, when I recognized I was wrong, it was because either someone pointed out the error in my thinking, or I realized the error of my thinking. I have never been convinced that I was wrong by someone telling me that I am not intelligent enough to understand, or that I haven't worked hard enough, nor have I ever been convinced that Milne was wrong by someone misrepresenting his model, or misrepresenting what I am saying.

You know, when I was learning about Rindler Coordinates, for instance, I had a lot of misconceptions, and learned a great deal from people who understood it. But when I talk to people who understand the central argument behind General Relativity, I find that they are utterly unable to convey that understanding to me, and almost always resort to saying "If you were right, don't you think that someone would have noticed by now?" or "I don't have time to explain basic calculus to you right now." or "If your theory is right, show me the data." But in the meantime, no one has ever offered me a look at the data. Nobody has ever offered me a derivation of the Einstein Field Equations. Nobody has ever offered to explain basic calculus to me. I am naturally agnostic. All those things might exist. But in ten years of looking, I have not found it.

On the other hand, you just gave me a paper that said that Milne's model was only off by a factor of 2 sigma. In my own opinion, this kind of result SCREAMS that you need to go back and give the Milne Model another chance. Yes, I'd be very interested in seeing the data involved in that paper, because I strongly suspect that the reason for it being off by 2 sigma is because they SPECIFICALLY SAID in the paper they were not accounting for any secondary acceleration.

Do I think that it is possible that I figured out something that none of these other guys figured out? Yes. Do I regard that as highly unlikely? Somewhat. But not any more unlikely than getting struck by lightning, or winning a lottery. I've stumbled upon an idea, mostly due to some luck and quite a lot of hard work. (Most people do not set about understanding special relativity in the way that I did--independently by designing a public website--demonstrating the principles of Special Relativity via visualizing it with Flash software. I had some opportunities that other people don't have. Getting a chance to sit and think for 8 to 12 hours a day for many months. Most people only get the opportunity to think about this stuff for one semester, and their grade and their career is on the line.) It's possible that it's wrong, and it's possible that it's right.

I have heard many people claim that "you can learn all you need to know about special relativity in two weeks." I know that I am not smart enough to have learned what I know about special relativity in two weeks. It probably took me about two years to really get the gist of it. And only after I got the gist of it did I learn the mathematical shortcuts you can take using hyperbolic geometry. I've gotten two Masters degrees SINCE I got the basic gist of Special Relativity. When you learn it in school, most people learn the math first, and pretty much skip over the implications.

But I think what you're not understanding here is that what I have in mind is not an experimentally based theory. It's a geometrically based theory. I am every bit as sure of hyperbolic rotational geometry as I am of trigonometric rotational geometry. The common consensus among General Relativity experts is that you can just TURN OFF hyperbolic geometry at large distances, while inexplicably, rotational geometry still applies. But it's a twisted argument, because upon further analysis, they simply refuse to accept the premise that things are actually moving apart at relativistic speeds, and therefore, they can a priori reject the premise that they even need to learn hyperbolic geometry.

Yes, it is extremely surprising to me that in 10 years I have not found anyone "in charge" that seems to take this seriously, and can only find Milne and Epstein. But that's all I've found. Nobody is seriously taking Milne as a real theoretical model. Instead, they are treating it as a null hypothesis, which they can reject using purely statistical methods.

Obviously Milne had a few misconceptions here and there, but whereas the "standard model" is allowed to evolve as new data appears, people reject the Milne model based on an unrealistically strict interpretation (that there wouldn't be secondary acceleration) or unrealistically strict misinterpretation (that Milne thought there should be stars going out forever in all directions, that Milne derived an empty universe)

As far as looking at the data, I've tried that before, but I would need some serious one-on-one help in getting a hold of the right data to look at, and organizing it in the format that I need, and I would need the time and resources to do it. Last time I managed to get hold of some data, it had already been converted into lambda-CDM coordinates or something like that, and if that could be converted back into something I could use; i.e. redshift-luminosity comparisons, and identification of object types. I am fully aware of the great number of educated guesses are made in assigning the redshift-luminosity distances to various objects in the universe. I'm not sure of how many of those educated guesses are made AFTER applying the assumptions of the FLRW metric. What I would need is data that came from before these assumptions were applied.

And frankly, I would also probably need some education to understand exactly how, for instance, the Cephied variable stars distance-luminosity relationship works, and exactly how estimates of distance are made for the most distant galaxies. How they determine the black-body spectrum for these things. In order to convince me that I'm wrong about this, I would need to understand precisely what the data you are using actually says. I don't really have the background to do what you want me to do, and in the next twenty years, I might find time to learn it all and get it all done, and show beyond a shadow of any doubt, either that Milne was right, or Milne was wrong.

But if it is possible, I'd like to not spend the next twenty years trying to fix one mistake, all by myself. It's either Milne's mistake, or Einstein's mistake. I want people to acknowledge that this is an actual disagreement between the two. If people just say Milne was modeling "empty space" then it just covers up the fact that he genuinely disagreed with Einstein, and he genuinely disagreed with Eddington.

With Copernicus and Ptolemy, you have Galileo coming along and pointing out "Hey, these two ideas are different. Only one of them can be correct. Which one is right?" With Milne and Eddington, I'm just saying "Hey, these two ideas are different. Only one of them can be correct. Which one is right?"

I'm pretty well convinced that Milne was right and Eddington was wrong. I'm perfectly willing to acknowledge that might be a mistake. However, right at this point, I'm not looking around for someone to prove me wrong. What I'm looking for is for someone to acknowledge that Milne's model is not empty. That Milne had a fundamental disagreement with the nature of the universe. That his model is self consistent. (Because I get people going back and forth--sometimes they argue that Milne's model is not self-consistent. Other times they argue that it is not in agreement with the data. It's either neither, one, or both, but when somebody argues that it's not consistent with the data AFTER they've already claimed it's not self-consistent, I am left in doubt that they are arguing in good faith, because there is no point in comparing an internally inconsistent model to data.)

Then once we acknowledge that we have two models, i.e. two hypotheses, the same level of care must be taken to fit the data to both models.

Large numbers of people have been working in good faith, trying to put the data into the Standard model for 70 years, and during that time, they have played with a large number of parameters to get the data to fit.

I see no evidence of anyone doing the same with Milne's model. The general attitude is "We don't need to. It's wrong." And there are lots of reasons given to claim that Milne's model is wrong. But I don't need LOTS of reasons to claim Milne's model is wrong. I need just one. One convincing argument would outweigh any number of unconvincing arguments.

In any case, if you're trying to humiliate me by saying that I have been stubborn about this for ten years of looking, and I still haven't admitted that I'm wrong, I take that with a grain of salt. Yes, unfortunately, this question has been a main motivator of the last ten years of my life, during which time, I got two MS degrees, one in physics, and one in math, during which time I could find no one who agreed with me, or was willing to discuss this with me. And many many people who said that they did not have any expertise in the field, or were too busy, or were not interested, or thought it was a waste of time. I've been called stubborn, and you're not the first person to assume I must not be that bright. And I can't vouch for myself; maybe I'm not that bright.

What I haven't seen is any argument to show that I'm wrong, or that Milne was wrong. All I've seen are straw-men, appeals to consensus, appeals to "data" in general, but never to any specific data, and criticisms of me and/or Milne.

 

[JDoolin]

Also, the gravity model is wrong. Milne is assuming "balanced forces" -> "no acceleration" and even in the Newtonian universe that's wrong.

You may well have located the flaw in Milne's argument, or Einstein's. If you can justify that with more than just a statement. but carefully reason it out.

Because I completely disagree with you. Newton's second law states that \vec a=\frac{\sum \vec F}{m}If that sum of forces is zero; i.e. there is a balance, then there is no net acceleration.

You're claim is that this is a false statement, even in a Newtonian Universe. But isn't a Newtonian Universe described by Newton's Laws? If I am understanding you properly, you are saying that In a Newtonian Universe, Newton's second law is false. Is that correct?

Do you have some other reasoning, perhaps based on an application of Gauss's Law? I'm asking that because I'm pretty sure that I've seen such an argument made by none other than Einstein himself. However, I don't remember where I saw it; some book I've long since returned to the library (in frustration).

 

[twofish-quant]

Newton's second law states that


\vec a=\frac{\sum \vec F}{m}


If that sum of forces is zero; i.e. there is a balance, then there is no net acceleration.

That's not correct. Newton's second law is

\vec F = \frac{d\vec{p}}{dt}

In situations where you have constant mass, it reduces to F=ma, but we are talking here about a situation in which masses are moving around, and in that situation you have to use the second version.

If you are using Newtonian physics, then the easiest way of dealing with the problem is by conservation of energy. You figure out the kinetic and potential energies. The total is constant, if you change the potential energy, then the kinetic energies changes.

http://www.ast.cam.ac.uk/~pettini/Physical%20Cosmology/lecture02.pdf

The only way you can have constant kinetic energy in a universe which approximates Newtonian physics is if you have constant potential energy, and in the absence of other forces, constant potential energy means an empty universe.

But isn't a Newtonian Universe described by Newton's Laws? If I am understanding you properly, you are saying that In a Newtonian Universe, Newton's second law is false. Is that correct?

I'm saying that you are not using the correct form of Newton's second law. The version you are using won't work for things with non-constant mass distributions (like rockets).

 

[JDoolin]

http://www.ast.cam.ac.uk/~pettini/Physical%20Cosmology/lecture02.pdf

Ah, yes, thank you for that article. This was exactly the argument that I was thinking of. I've seen this argument in books, but I had never found it online. I was calling it "Gauss Law" but it is "Birkhoff's Theorem."

While I am essentially in agreement with Birkhoff's theorem, the article you reference is making a major error in its application, (and if I am not mistaken, Einstein made this same mistake, and was perhaps its originator.) If you are calculating the forces on particles A, B, C, and D, it is completely inappropriate for you to draw a circle around an arbitrary observer O, and then treat all of the mass in that circle as though it were a point mass at point O.

It would make much more sense to account for the masses near the objects A, B, C, D, respectively, to calculate the forces that are acting upon them.

(The other major error in the article is equation 2.3... Failure to apply time dilation and the relativity of simultaneity.)

 

[twofish-quant]

When I multiply 1 mile per hour times 13.7 billion years, your reaction is that "If that made any sense, smart people would have figured it out." But where? Where do I find that.

A well stocked research library should have the answer to that. The internet helps, but the trouble here is that a lot of this stuff comes from "pre-internet" age when you actually have to go through the world of dead trees.

If you want to find out the reason "so why don't people believe X" you usually have to do some digging. The problem is that there are *so many* rejected theories, that to find out why a theory was rejected, you have to do quite a bit of digging.

There are people who get Ph.D.'s in science history looking over this sort of thing. Since you only have eight years to do a Ph.D., most people in looking over failed theories don't spend that much time investigating *why* they failed.

I'd like to have that discussion, because I think it is fundamental to the premise behind General Relativity, but it really doesn't make any sense at all.

There is a ton of evidence behind GR, so if you have some logic that leads to you conclude that GR is wrong, then it's much more likely that there is something wrong with that logic than with GR.

Also, another thing I've noticed about all books on General Relativity is that they tend to skip over the idea of a kinematically expanding universe without mentioning it. Instead, they begin with the assumption of a commoving set of matter. I've also noticed that whenever I bring this up in discussions, I find myself in exactly the same arguments.

Because that's what fits what we see. You have about five hundred pages to write a textbook, and most people are interested in models that match observations. If you want to start mentioning "failed theories" that's enough material to fill another ten textbooks. And it's sort of pointless since once you understand the "standard model" you can figure out for yourself why the other models have problems.

I am willing to acknowledge the possibility that I'm wrong. I've made some terrific blunders over the years, and some of them have been quite embarrassing.

You can avoid being wrong, by not making assertions, and by saying "I don't know". One thing that I don't quite understand is why you seem fixated on the correctness of the Milne model. You can get the same sort of answers by asking "so what is wrong with the Milne model that people don't use it?"

The problem is you seem to be assuming that people don't have very good reasons for rejecting Milne.

But when I talk to people who understand the central argument behind General Relativity, I find that they are utterly unable to convey that understanding to me, and almost always resort to saying "If you were right, don't you think that someone would have noticed by now?" or "I don't have time to explain basic calculus to you right now." or "If your theory is right, show me the data." But in the meantime, no one has ever offered me a look at the data. Nobody has ever offered me a derivation of the Einstein Field Equations. Nobody has ever offered to explain basic calculus to me. I am naturally agnostic. All those things might exist. But in ten years of looking, I have not found it.

1) That's because people are busy and they have better things to do.

2) Also what you are looking for may not exist. If you are looking for a philosophical justification for GR, then that just doesn't exist. People believe that GR works because it is consistent with enough experiments so we are pretty sure that the true theory of gravity is something like GR.

There are a lot of papers online about the experiment tests in support of GR. I'm pretty sure that you can find them in Annual Reviews of Astronomy and Astrophysics and that you can find them for yourself if you have access to a university research library.

3) The other thing is that people don't know these sorts of things off the top of their heads. If you want me to tell you what the experimental constraints of GR are then I would have to spend several hours/days researching GR.

On the other hand, you just gave me a paper that said that Milne's model was only off by a factor of 2 sigma. In my own opinion, this kind of result SCREAMS that you need to go back and give the Milne Model another chance.

It's 2 sigma today. It will be five sigma tomorrow. These are the results of supernova observations and as time passes the observational constraints get tighter, and tightening observations is something that lots of people are working on.

If people take more data and it looks like that points are moving toward the Milne zero line, then yes people will take a look at things. If you look at the papers in arxiv.org, there *was* some interest in Milne way back when the data was more noisy than it is now, but it's moving the wrong way.

And the problem with that graph is that it gets chopped off at low z. If you look at the trend line once you get past the "interesting" part, it goes into massive deceleration.

Yes, I'd be very interested in seeing the data involved in that paper, because I strongly suspect that the reason for it being off by 2 sigma is because they SPECIFICALLY SAID in the paper they were not accounting for any secondary acceleration.

There are references in that paper, and you can use google.

However, lack of secondary acceleration is not going to help you much. You look at the data, and there is a pretty clear trend. If it was noisy, then you'd have random scatter across zero.

There are also statistical tests that you can do (KS test) to test fitness to a particular model. The two sigma figure is two sigma against any deceleration. If you try to do a statistical test to a specific model (zero acceleration), I think you'll get a much high rejection.

And that's supernova data. Once you get past that, then you have WMAP CMB results.

Do I think that it is possible that I figured out something that none of these other guys figured out? Yes.

Honestly... No...

If you look at the original data, people are *very* careful at data reduction. When the original results came out some colleagues spend a few weeks trying to crush the results, and we couldn't. This wasn't a surprise. The groups involved were very careful and they had people try to crush the results before they published.

Do I regard that as highly unlikely? Somewhat. But not any more unlikely than getting struck by lightning, or winning a lottery.

False analogy. Since this isn't a matter of luck.

You are talking about beating a chess master without any training in chess or beating a heavy weight fighter without having any boxing training.

The *only* reason you think that you have a chance is because you haven't even *read* any of the original papers.

That's why I'm telling you to "put up or shut up." If you read the original papers and you can think of something that they haven't thought of, then we can talk. Otherwise, there really is nothing to discuss.

Getting a chance to sit and think for 8 to 12 hours a day for many months. Most people only get the opportunity to think about this stuff for one semester, and their grade and their career is on the line.) It's possible that it's wrong, and it's possible that it's right.

Look. The people that do this for a living spend *years* thinking about this stuff. Now sometimes, people look at the data for too long, so they need an outside perspective, but people get that. If you have say a biostatistician look at the papers and they conclude that the statistics are bogus, that's cool and useful.

But I think what you're not understanding here is that what I have in mind is not an experimentally based theory.

I think I understand quite well.

If it's not experimental, then it's not physics, and if it's pure math, then you need to be talking to someone other than me since I'm not that interested in pure math.

Yes, it is extremely surprising to me that in 10 years I have not found anyone "in charge" that seems to take this seriously, and can only find Milne and Epstein. But that's all I've found. Nobody is seriously taking Milne as a real theoretical model. Instead, they are treating it as a null hypothesis, which they can reject using purely statistical methods.

No physicist takes it seriously because *IT DOESN'T MATCH OBSERVATIONS*. Milne says there was no big bang. We see a big bang. Milne is wrong. Life goes on.

Obviously Milne had a few misconceptions here and there, but whereas the "standard model" is allowed to evolve as new data appears, people reject the Milne model based on an unrealistically strict interpretation (that there wouldn't be secondary acceleration) or unrealistically strict misinterpretation (that Milne thought there should be stars going out forever in all directions, that Milne derived an empty universe)

That's because the "standard model" isn't a specific model. The "standard model" is a phrase for "whatever model is fits the data right now." If it turns out that the data supports Milne, then the Milne model will become the "standard model." If you look at the standard model-2012 it is *VERY* different than standard model-1992. Standard model-1992 is *very clearly* WRONG. You reject old models, name the flavor of the day, the standard model, and life goes on. The king is dead, long live the king.

Think of it like Windows. Windows 8 is different from Windows 95.

When people talk about the Milne model, they are talking about a *specific* model and in that situation the rules are that you specify it strictly.

As far as looking at the data, I've tried that before, but I would need some serious one-on-one help in getting a hold of the right data to look at, and organizing it in the format that I need, and I would need the time and resources to do it.

Science is hard. Also, if you are trying to "prove the Milne model correct" then no one is going to help you. In order to get anyone to help you, you have to set things up so that you get something useful out if (surprise, surprise), Milne is wrong.

So suppose Milne is wrong, what's your backup?

I am fully aware of the great number of educated guesses are made in assigning the redshift-luminosity distances to various objects in the universe. I'm not sure of how many of those educated guesses are made AFTER applying the assumptions of the FLRW metric.

You can go to the original papers. I can't see where they made *any* assumptions that FLRW is correct. Redshift you read from the spectra. Luminosity distance you get from the brightness.

In order to convince me that I'm wrong about this, I would need to understand precisely what the data you are using actually says. I don't really have the background to do what you want me to do, and in the next twenty years, I might find time to learn it all and get it all done, and show beyond a shadow of any doubt, either that Milne was right, or Milne was wrong.

And with all of that effort, you could have actually done something more useful. You need to explain to my why you are so fixated with Milne. With 20 years of effort you *might* convince yourself what everyone else has been convinced of for the last fifty years.

Or you might actually discovery something new with galaxy formation, or exoplanets.

And then there is just waiting of new data to come in. If you think that there is a deep flaw in the way that supernova data is being processed, then you can just wait for someone to trip over that flaw. In the mean time, you could get something useful done with things that people really think are holes.

It's either Milne's mistake, or Einstein's mistake. I want people to acknowledge that this is an actual disagreement between the two. If people just say Milne was modeling "empty space" then it just covers up the fact that he genuinely disagreed with Einstein, and he genuinely disagreed with Eddington.

In that case you can do research in science history. I'm more interested in science history than most people, but frankly, I don't see much point in figuring out who was "right". If it turns out that people are using the "Milne model" to mean something that Milne himself would have found bizarre or even objectionable, that's an interesting historical footnote, but it's not terribly important for the things that I'm interested in.

With Copernicus and Ptolemy, you have Galileo coming along and pointing out "Hey, these two ideas are different. Only one of them can be correct. Which one is right?" With Milne and Eddington, I'm just saying "Hey, these two ideas are different. Only one of them can be correct. Which one is right?"

Or maybe they are both wrong (i.e. Copernicus thought that planets travel in circles, they don't). Or maybe they both figured out pieces of the puzzle.

It's interesting science history, but honestly, I don't see the relevance to science.

I'm pretty well convinced that Milne was right and Eddington was wrong.

And I don't understand the basis for that belief.

What I'm looking for is for someone to acknowledge that Milne's model is not empty.

And you can look for someone to tell you that up is down, and black is white.

Whether Milne himself believed that his model requires an empty universe is an interesting historical footnote, but if he thought that he could have an non-empty universe that wasn't decelerating. Well, he was just wrong. If you have any sort of gravitational model that resembles Newtonian gravity, then this just will not work, and if Milne thought it would, then he was wrong.

Large numbers of people have been working in good faith, trying to put the data into the Standard model for 70 years, and during that time, they have played with a large number of parameters to get the data to fit.

And when the data doesn't find, then change the model, and call whatever the new model is the "standard model." If we observed zero deceleration, then the Milne model would be the standard model. If it turned out that the CMB was from distant stellar sources than steady state would be the standard model. If the skies light up, and we see "The Universe is 6000 year old, signed GOD" then the book of Genesis would be the standard model.

I see no evidence of anyone doing the same with Milne's model. The general attitude is "We don't need to. It's wrong." And there are lots of reasons given to claim that Milne's model is wrong. But I don't need LOTS of reasons to claim Milne's model is wrong. I need just one. One convincing argument would outweigh any number of unconvincing arguments.

I've been giving them to you.

Yes, unfortunately, this question has been a main motivator of the last ten years of my life, during which time, I got two MS degrees, one in physics, and one in math, during which time I could find no one who agreed with me, or was willing to discuss this with me.

You can get more people to discuss things if it looks like you are asking a question.

What I haven't seen is any argument to show that I'm wrong, or that Milne was wrong. All I've seen are straw-men, appeals to consensus, appeals to "data" in general, but never to any specific data, and criticisms of me and/or Milne.

Sigh.

All I've been doing here is giving you arguments. You are free to reject those arguments, but if you *ignore* those arguments then people will just give up talking with you. I posted a link to the supernova results. If you take a look at them and say "well maybe Milne was wrong" then we might be getting somewhere. If you take a look at them and say "MILNE IS GOD AND CAN'T BE WRONG" then I might as well be arguing with young Earth creationists.

Also, you can't expect people to help you. One thing that you have to learn if you want to be a productive physicist is to be your own worst critic. If you start out with "MILNE IS WRONG, CONVINCE ME OTHERWISE" then you are going to get nowhere. You have to start trying to prove yourself wrong. If you lack the ability to convince yourself that you are wrong, then people have better things to do than to talk with you.

The other thing is that I think you are wasting your own time. In all of the time you spent on defending Milne, you could have done some productive work in something else.

There is an exciting wonderful world out there that you are not seeing. I have only the vaguest idea of what "Standard Model Version 2020" will look like, but it's going to have a lot of cool features and fix a lot of bugs that are in "Standard Model Version 2012". There are going to be surprises, and there is lots of interesting work to be done. Even "Standard Model 2013" is likely to have cool new features and bug fixes. (Standard Model 2013 Now with Higgs fields!)

So that's exciting, but the sad thing is that by digging yourself in a hole, you aren't seeing any of this. "Standard Model 2012" is missing a model of galaxy formation, it produces crap numbers when things go non-linear, and there are a lot of bugs with it. Given all of this exciting stuff, why should I chain myself to this argument that should have been resolved fifty years ago.

 

[JDoolin]

As I pointed out, attacks on me and my character, and appeals to consensus really don't convince me that you're right. I see my post #48 got stuck on the previous page. Please don't overlook it.