## How is molecular hydrogen detected?

 Quote by JDoolin 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first edition of that book was in 1977, and he wrote an updated addition in 1992, there are large parts of it that are out of date.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.

 Blog Entries: 4 Recognitions: Gold Member 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 not true 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.

 Quote by JDoolin 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?

 Quote by twofish-quant 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.

 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

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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?

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 Quote by JDoolin ... 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?

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 Quote by Chronos 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:Mi...y_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.)"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." "The system is spherically symmetrical round any particle of the system, in the experience of the observer attached to that particle." "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." "The particle density, in the reckoning of any particle-observer O, at any given epoch t, increases outwards." "Near O, at any fixed distance, the particle-density decreases at a rate inversely proportional to the cube of the time." "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." "As the distance r tends to ct, i.e. for points nearer and nearer the expanding light-sphere, the particle-density tends to infinity." "The total number of particles in the system is infinite." "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." "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." "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 travelling with a speed not exceeding the speed of light." "The velocities of different particles at any one 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." "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)" describes the phenomenon of desynchronization (more commonly known now as the relativity of simultaneity) gives the relativistic doppler shift equation 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." "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."

 Quote by JDoolin 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?

 Also, the gravity model is wrong. Milne is assuming "balanced forces" -> "no acceleration" and even in the Newtonian universe that's wrong.
 Blog Entries: 4 Recognitions: Gold Member 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.

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 Quote by twofish-quant 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).

 Quote by JDoolin 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/Ph.../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).

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 Quote by twofish-quant
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.)

 Quote by JDoolin 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.

 Blog Entries: 4 Recognitions: Gold Member 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.

 Quote by JDoolin 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.
Why? That's how the universe behaves.

The problem here is that you are trying to do philosophy rather than physics.

 (The other major error in the article is equation 2.3... Failure to apply time dilation and the relativity of simultaneity.)
This is a Newtonian model. In it we are assuming that the speed of light is infinite and there is no time dilation. If we add time dilation and relativity, then we can't do anything Newtonian and we have to go to full blown GR. If you add the speed of light and time dilation to a Newtonian model, then what you end up with is likely to be inconsistent and wrong (it's a fun physics problem.)

The assumption here is that the "real theory of gravity" is "close enough" to Newtonian that we can do everything using Newtonian physics. You can show that this is true if the velocities involved are less than the speed of light. The problem with using GR is that then be becomes very hard to visualize.

In the real world, we don't know what the "true model" of gravity is. We *do* know that under most situations it looks like Newtonian gravity and under every situation that we've been able to measure, it looks like GR. So rather than apply an unknown model that's impossible to visualize, you take the observation that things are "close to Newtonian" do the problem and then work backward to argue that the difference between Newtonian and the actual situation isn't important to the conclusions.