How is molecular hydrogen detected?

Now I am a trained listener and a professional public speaker (Toastmasters International=28 years) but, unfortunately, I never could figure out what message you were trying to communicate in each of those four modules. Perhaps your written script could be revised to be more coherent and to clearly address the point you want to make. The point is I couldn't find the point.

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).

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.)

Here's another way of thinking of it.....

I have point A. You can argue that all of the forces are balanced at point A, so it doesn't accelerate.

I have point B. You can argue that all of the forces are balanced at point B, so it doesn't accelerate.

AHA!!! You say, the universe must then be non-accelerating!!!!

But that doesn't work. If I start with point A as my origin, and then look at point B, I find that there is a force at point B pulling it toward point A. But wait, I just showed that the forces are balanced if I take point B as the origin? What gives?

The issue here is that the forces at point B when viewed from point A are *different* from the forces at point B when viewed from point B, because when you change coordinate systems then the forces change. But how can that be? Don't forces stay the same when you change between inertial coordinate systems?

Yes, but from point A's point of view, point B is not an inertial coordinate system, it's accelerating, and because it's accelerating, when you switch between point A and point B, the forces change. From point B's point of view, it's an inertial coordinate system, and A is accelerating. So when you switch between A and B, you have to change the forces to take into account the fact that the coordinate systems are non-inertial.

From A's point of view, there is a force on B pulling B toward A, and there is zero forces at A. Now when you switch to B's point of view, you are a non-inertial reference frame from A's point of view. To make it inertial, you have to subtract the forces that are acting on it. That causes the forces at B from B's point of view to go to zero, and then causes the A to go from zero force to the opposite of what was the force that A sees acting on B.

So if you take any point as the origin, you will see a force of zero for that point, but you will see non-zero forces for points other than the origin.

Now then you see how the universe works. We don't have any infinite clouds, but we have clouds that are "practically" infinite. You take something like the interstellar medium with a one light year cube, and then take a piece that is much, much smaller, and see how you calculate gravity.

Thank you for giving further explanation here.

I still think that ignoring the relativity of simultaneity is a flaw, but I also realize now that I was misunderstanding Einstein's argument.

He was literally saying that the force on a distant particle is an observer dependent quantity, while time is an observer independent quantity. That seems amazing to me, and I will have to think about it further.

And if you do your bookkeeping right, you come up with the same answer. The important thing is to keep track of what reference frame you are in so that you can account for non-inertial effects correctly.

Thank you. But actually, I encourage you to question that! Don't take my word for it; go and actually read "Relativity, Gravitation, and World Structure," if you can find the time.

I'd like to understand why people argue with me over this.

The Milne model seems to be misrepresented everywhere I look

The type of homogeneity assumed in the FLRW metric is an infinite homogeneous distribution of matter.

But at those distances, 10, 20, 30 billion light-years, we possibly can't see anything as dim as a galaxy anyway.

You need to be able to point at something that tells me clearly that there is no increase in density at the extreme periphery of the visible universe, and I have strong doubts that we have observations that are that good.

Also from Milne's Model, there should be a directional difference in the distribution of galaxies. I would expect an asymmetry in the distribution of galaxies that fairly precisely matched the asymmetry in the dipole anisotropy of the CMBR.

Now, if none of these expectations are happening, then perhaps we can reject Milne's model based on comparing hypotheses to data. But as long as Milne's model is being rejected because it is a zero-mass model, then we're not rejecting Milne's model. We're rejecting a straw-man.

I meant to ask, precisely what bookkeeping is done, so that you all get the same non-zero answer?

I think the circle needs to be drawn to encompass a large volume around the object. At least, make the circle large enough to encompass the masses that are in the object's immediate vicinity.

With this sort of bookkeeping, all observers would, indeed, agree that the force on the object would be the same. But the "same value" that everyone would come up with, would be zero.

The younger universe means we should have less galaxies.

While I agree cosmology is still largely a matter of conjecture, it is a conjecture based on observational evidence. Once you leave the realm of observational evidence you enter the realm of metaphysics.

My apologies for refering to you as James, Jonathan. I perceive your error as one of philosophy, not science - e.g., I agree with twofish. Cosmology is a conjecture founded on observation. While I agree cosmology is still largely a matter of conjecture, it is a conjecture based on observational evidence. Once you leave the realm of observational evidence you enter the realm of metaphysics.

The problem is that you are doing philosophy rather than physics. You are treating isotropy and homogenity as if they were mathematical axioms when they aren't.

Once you start with the premise that the universe is isotropic and homogenous, then at large distances things are going to be flying away from each other at > c, and Lorenz transformation will break down.