# Thread: Expanding Space: Just say No - Part 1

1. Oh dear me.. do I dare jump in. Oh yes I do and just did. I am not understanding the reasoning behind this discussion.

Are you telling me that the accelerating expansion is not ? If that is so.

Then now I want for a maths alternate to what I have been told is so..

I have been looking at this for some hours and have failed to find or comprehend why the

'Finite but unbound' universe is in dispute..

All of the greater minds of the astrophysics world seem to agree more or less that the universe is expanding.

That it is still accelerating as it does this.

If I have missed some startling revelation or discovery.. would you bring me up to speed...

I feel I have missed the point somewhat..or. Can I play with the balloons. Have they all popped.. Hmmm...

2. I thought the point was that the choice of coordinate system does not affect any observations or theories but simply changes the pedagogy, and that in the OP's opinion the choice of a coordinate system that has expansion built in leads to lots of confusion. That it certainly does, but I'm not sure that's a good enough reason to ditch it. How many people think FTL galaxies are possible because of expanding space without realizing the converse: that those galaxies are only FTL when using expanding coordinates. I don't even see how this claim is against the mainstream.

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Originally Posted by caveman1917
The mass distribution is spherically symmetric about any point.
Yes, so the shell theorem applies about any point

Originally Posted by caveman1917
And likewise the shell theorem says that the object will experience a gravitational force of the same magnitude in the opposite direction due to the ball of mass centered on the point "behind the object" from our perspective, and thus the second derivative of the distance will be positive.
In the diagram you showed, point b will think of themselves as stationary, with a and c falling towards them.

Originally Posted by caveman1917
Adding both these accelerations together means that every point will have zero net acceleration, or in other words the second derivative of the distance equal to exactly zero.
There's a difference in that net acceleration implies a notion of absolute space, while second derivative of distance does not.

There is a problem in Newtonian Cosmology - see A paradox in Newtonian Gravitation Theorem II, in that the shell theorem says that matter will tend to collapse together, whilst Newton's argument is gravity will cancel out and the universe will be static. Norton points out that the response to this problem has often been to ignore it. I have to say that this rather surprised me, in that I thought that it was a well known problem. (It also surprised me that Norton didn't reference Boskovich's 1760 work which introduced a form of cosmological constant to deal with the problem)

In any case, there seem to be different views of what Newtonian gravity predicts. I have been taking one point of view which I think is by far the most logical, as it says that the behaviour of an infinite amount of matter is the limit of the behaviour of finite amounts of matter. But maybe I should have been more explicit in stating this.

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Originally Posted by Cougar
I'm not sure in what sense you mean that, but of course it is observations that have led us to this "expanding space" predicament. In around 1929 most everyone except Hubble ventured to conclude from Hubble's data that the Universe is expanding. Einstein said "Doh!" and the concept has been evolving over the last 80 years. It has even been noticed that the "expanding space" of the visible part of our Universe was slowing down over the first 5 billion years or so, but then the expansion slowly started "picking up speed." I'm not exactly sure what your model is, but I believe most physicists try to restrict themselves to what is or at least might be observed.
I have no objection to the expansion of the universe, in the sense of galaxies getting further apart What I object to is the notion that they are somehow being dragged along by space.

In fact expanding space isn't part of serious cosmological models, which use the equations of GR (well actually some of them use Newtonian gravity, because the difference is so slight). When I first encountered 'Expanding space' I thought that it must be one of those analogies that popular science writers used, but which shouldn't be taken at all seriously. It rather surprised me to find cosmologists defending the idea.

Originally Posted by Cougar
Then you have no argument, since by your reasoning, both QM and GR should be jettisoned because they're difficult and confusing. So that's a contradiction: We know those are good theories that shouldn't be jettisoned.
You haven't seen my arguments about QM and its interpretations yet. But GR, yes it's difficult, but it is conceptually straightforward.

Originally Posted by Cougar
What should be got rid of is the confusion, not the expanding space. This might be difficult at this point in history, with dark energy such a mystery. The observations that our theories have to match are coming in hot and heavy, so to speak. And the idea that there's some sort of materiality to space keeps getting supported by independent and complementary observations. Our understanding is evolving. Your solution seems like you want to go backwards, though. Back to the 1950s. There's a signpost up ahead....
It's very tempting to try to reinvent the aether - which is what I believe has happened with expanding space. But the aether implies that you can measure your velocity with respect to space, whilst physics is fairly definite that you can't. If you think of dark energy as built into the universe - as a cosmological constant - then it gives you no way to measure your velocity.

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Originally Posted by astromark
Are you telling me that the accelerating expansion is not ?
No, I happy that the expansion is accelerating (the second time derivative of distances between galaxies is positive)

Originally Posted by astromark
'Finite but unbound' universe is in dispute..
The evidence favours an open universe rather than a closed (hyperspherical) universe. This means an infinite universe, although I prefer to interpret this as a potential infinity - there's no point in speculating about the boundary of the universe - rather than philosophising about actual infinities.

Originally Posted by astromark
Can I play with the balloons. Have they all popped.. Hmmm...
Maybe balloons have their uses in understanding a closed universe - but even then thinking that matter gets dragged along on the surface is wrong.

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Originally Posted by worzel
I thought the point was that the choice of coordinate system does not affect any observations or theories but simply changes the pedagogy, and that in the OP's opinion the choice of a coordinate system that has expansion built in leads to lots of confusion. That it certainly does, but I'm not sure that's a good enough reason to ditch it.
Indeed, using comoving coordinates is generally the best way to do calculations - the problem is when people believe in the fictitious effects they introduce

Originally Posted by worzel
How many people think FTL galaxies are possible because of expanding space without realizing the converse: that those galaxies are only FTL when using expanding coordinates. I don't even see how this claim is against the mainstream.
The thing is that if you look at the bottom of this page then you'll see lots of threads about expanding space and you'll notice the confusion it causes. the trouble is that a lot of the explanations trying to resolve the confusion are wrong too. But if I waded in and started claiming that published papers contain mistakes then I would presumably be criticised for introducing my 'personal theory' (at least that's what happened on PhysicsForums)

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Originally Posted by quantropy
In the diagram you showed, point b will think of themselves as stationary, with a and c falling towards them.
You keep repeating that they will fall towards eachother yet show no argument whatsoever as to why that should be so, other than cherry-picking the acceleration you want. I can use the same argument to get the result that they will be repelled from eachother (or any other result for that matter).

The only meaningful results that you can get this way is either that Gauss' law (and its implication - newtonian gravity) cannot be used to answer the question, or if you really want it to answer the question that the answer is zero net acceleration, which you get by a symmetry argument.

There's a difference in that net acceleration implies a notion of absolute space, while second derivative of distance does not.
How so?

There is a problem in Newtonian Cosmology - see A paradox in Newtonian Gravitation Theorem II, in that the shell theorem says that matter will tend to collapse together, whilst Newton's argument is gravity will cancel out and the universe will be static.
Even in that paper it is not argued that the shell theorem says matter will collapse, what is argued is that an application of the shell theorem is inconsistent, which is itself a flawed argument. There is no problem in newtonian cosmology, only a problem in how (and whether) to apply it to this question.

Your argument is akin to (not just akin to, in fact, it is an instance of) the following

When shown that you can just as well use this form of argument to get

you simply reject this out of hand because it is not the result you want. Yet there is no a priori reason to prefer one over the other.

The newtonian gravitational force on a test particle is the vector sum (in this case an integral to be strict) of the force by each mass element on that particle. You're cherry-picking the result you want by grouping those mass elements in such way as to get you that result, just like one can group the terms in the above series in any way one wants to get the result one wants.

That is simply not a valid argument.

the behaviour of an infinite amount of matter is the limit of the behaviour of finite amounts of matter.
Please show this rigorously in the appropriate mathematical detail, that statement is incorrect.
Last edited by caveman1917; 2012-Mar-27 at 10:15 PM.

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Originally Posted by quantropy
Norton points out that the response to this problem has often been to ignore it. I have to say that this rather surprised me, in that I thought that it was a well known problem.
It's of course possible that a philosopher spotted a glaring(!) inconsistency in newtonian gravity that has somehow been missed (or "ignored" as he calls it) by numerous working physicists and mathematicians over the past 300 years, however such a claim should put up a big red flag.

In this case the resolution is simple, Norton doesn't seem to understand that not every integral (or series) has to converge. His argument is of no more substance than to say that mathematics is inconsistent because the series above can give two different answers. The resolution is of course that the series (or the necessary integrals for a direct application of newtonian gravity on the problem he brings up) simply doesn't converge at all.

It's akin to using classical mechanics to find the center of mass of an infinitely long (constant density) thin rod. You can also get any answer you want since at every point you'll have "as much stuff on the left as on the right", so every point can be said to be the center of mass. Does this mean that classical mechanics is inconsistent? Of course not, it means that the integral doesn't converge. Basically the argument that "the stuff on the left cancels the stuff on the right" is wrong when they are both infinite, substracting infinity from infinity is indetermined. However even more wrong than to say that classical mechanics is inconsistent would be to say that classical mechanics predicts the center of mass is well-determined to be at the origin, which is basically your argument with Gauss' law getting you the acceleration you want.

ETA: perhaps this example of the center of mass of an infinite rod makes it easier to see the relation to the error about convergence of series because it is in one dimension (though the error is the same with applying Gauss' law as quantropy does in three dimensions). Please refer to the schematic below

Suppose we want to see whether the center of mass is at point o. So we mentally divide up the rod in segments (where the length of each segment is inverse with its distance from o, just so the factor of r will cancel in the sum). Again this is really an integral rather than a simple sum, but this is probably easier to see.

When we then take the needed sum we immediately get (because the length and thus mass of each element is inverse to its distance), when normalizing, taking the first element on the right, then the first on the left, then the second on the right, then the second on the left and so on
Last edited by caveman1917; 2012-Mar-28 at 03:39 PM.

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Originally Posted by caveman1917
You keep repeating that they will fall towards eachother yet show no argument whatsoever as to why that should be so, other than cherry-picking the acceleration you want. I can use the same argument to get the result that they will be repelled from eachother (or any other result for that matter).
Maybe if you gerrymander some weird shape you can - but even that I find hard to believe. If you take two points of matter distance x apart within a homogenous sphere of density ρ then , whatever the size of the sphere or the position of its centre. So however you let the size go to infinity, that it the result you will get.

Originally Posted by caveman1917
It's of course possible that a philosopher spotted a glaring(!) inconsistency in newtonian gravity that has somehow been missed (or "ignored" as he calls it) by numerous working physicists and mathematicians over the past 300 years, however such a claim should put up a big red flag.
But people did notice it - it was pointed out to Newton, then Boskovich in 1760 decided it was necessary to add a repulsive force at large distances to counteract the problem of matter collapsing together, and then again in the 1890s. I 'joined the dots' and assumed that it was a problem that people have worried about from the start.

Originally Posted by caveman1917
It's akin to using classical mechanics to find the center of mass of an infinitely long (constant density) thin rod. You can also get any answer you want since at every point you'll have "as much stuff on the left as on the right", so every point can be said to be the center of mass. Does this mean that classical mechanics is inconsistent? Of course not, it means that the integral doesn't converge. Basically the argument that "the stuff on the left cancels the stuff on the right" is wrong when they are both infinite, substracting infinity from infinity is indetermined. However even more wrong than to say that classical mechanics is inconsistent would be to say that classical mechanics predicts the center of mass is well-determined to be at the origin, which is basically your argument with Gauss' law getting you the acceleration you want.
The moral I draw from this is not that it doesn't matter if integrals don't converge, but to take examples involving infinitely large systems with a pinch of salt. The trouble is that Newton's cancellation argument relies on an infinite system. It is just as much adding up the series 1-1+1-1+1... and it has the further problem that the acceleration of an apple towards the ground is now ∞ + 9.8m/s² - ∞. What is needed is some notion of locality. That is what the shell theorem, and the restriction to relative rather than absolute accelerations gives you. You can get the absolute acceleration to be anything you want - so what, it's not a quantity that can be measured.

Then along came Einstein who after 1905 had to make gravity consistent with relativity. He already had worked out a consistent theory of an inverse square force - electromagnetism - but that would predict the wrong results for gravity (the Earth would fall into the Sun). So his problem was to invent something which agreed much more closely with Newtonian gravity. Where did he start? With the Equivalence Principle, essentially the statement that as far as gravity is concerned, only relative accelerations are significant. So he was aiming for a theory that was close to Newtonian gravity, but insisted that only relative accelerations mattered (and so was denied Newton's dubious cancellation argument), and he deduced that the universe would tend to collapse - so he introduced a repulsive term, just as Boskovich had done over 150 years before.
Last edited by quantropy; 2012-Mar-29 at 07:29 AM. Reason: Missed out gravitational constant G

10. I am not going to say no as long as a mathematical construct which includes expanding space enables useful calculations when interpreting observations.

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Originally Posted by quantropy
Maybe if you gerrymander some weird shape you can - but even that I find hard to believe.
Not some weird shape, a sphere. I even drew a diagram in post 29 that should make it clear. You argued that point b should have an acceleration to the left, i used your own argument to argue that it has zero net acceleration. One could of course also use that argument to argue that point b should have an acceleration to the right (or anything one wants). As far as i can tell you did not counter that argument other than to repeat "they will approach eachother". And you have now also not countered that argument other than to appeal to "some weird shape" that is clearly not being used.

If you take two points of matter distance x apart within a homogenous sphere of density ρ then , whatever the size of the sphere or the position of its centre. So however you let the size go to infinity, that it the result you will get.
Again, that is not correct. I will make this a direct request:
CM1: Please prove that assertion, in the appropriate mathematical detail, directly from newton's law of gravity.

That expanding space can cause confusion i agree with. However proposing to replace that heuristic with one based on flawed mathematics does not seem to help.

With the Equivalence Principle, essentially the statement that as far as gravity is concerned, only relative accelerations are significant.
That is not what the equivalence principle states. Also, you seem to have a non-standard use of the terms relative acceleration, absolute acceleration and the second derivative of distance. Could you clearly define your use of these terms?

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Originally Posted by caveman1917
Not some weird shape, a sphere. I even drew a diagram in post 29 that should make it clear. You argued that point b should have an acceleration to the left, i used your own argument to argue that it has zero net acceleration. One could of course also use that argument to argue that point b should have an acceleration to the right (or anything one wants). As far as i can tell you did not counter that argument other than to repeat "they will approach eachother". And you have now also not countered that argument other than to appeal to "some weird shape" that is clearly not being used.
If you are just considering the matter in the diagram then a and c will be accelerated towards the centre of mass b. The second time derivative of the distances ab and bc will be negative.

Originally Posted by caveman1917
Again, that is not correct. I will make this a direct request:
CM1: Please prove that assertion, in the appropriate mathematical detail, directly from newton's law of gravity.
Take two points in A and B in a sphere of uniform density. Take the origin of coordinates at the centre of the sphere, and let the positions of A and B be represented by the vectors a and b. Let a=|a| and b=|b|. In these coordinates A will experience a force due to the sphere centred at the origin with radius a, as if its mass (), were concentrated at the origin, and no force due to the matter outside this sphere (shell theorem). Hence it will experience an acceleration of towards the centre, so as a vector the acceleration will be . Likewise the acceleration of point B will be . Hence the acceleration of B relative to A, will be . So an observer at A will see all other matter in the sphere accelerating towards A with the acceleration proportional to the distance.

We'll go on imagining that there is no Dark Energy, so that the deceleration parameter is positive. Consider a range of gravitational systems: An apple falling to Earth, the moon in orbit around the Earth, the behaviour of the solar system, the behaviour of the galaxy and the behaviour of a large sphere of galaxies. My claim is then that the behaviour can be described well enough for a qualitative understanding by Newtonian gravity. This involves imaging to the system under consideration to be isolated from the rest of the universe, but this is done in virtually all parts of science. My arguments involving the shell theorem and the equivalence principle show that the justification in this case is in fact far stronger than in other parts of science. And the proof of the pudding is in the eating, it will describe the behaviour, in the case of the sphere of galaxies just as much as for the other systems. Your claim is that one case is invalid, based on an argument involving an infinite amount of matter and how you can get its effect to cancel out. If you tried to make a similar claim in any other part of science then I can't see you being taken seriously.

Imagine now that the redshifts had been discovered before relativity. Would that have caused people to think that the Newtonian model didn't work? Of course not, galaxies receding from us poses no problem for Newtonian physics. Some people might have carried on believing in the cancellation argument (as Milne did), others might think it should be dropped as it was no longer needed for a static universe. Then later, if the deceleration parameter was found to be positive, then the second group would claim success. At no point would anyone think that any modification to the basics of Newtonian gravity was needed.

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Originally Posted by quantropy
If you are just considering the matter in the diagram then a and c will be accelerated towards the centre of mass b. The second time derivative of the distances ab and bc will be negative.
I was, as you were, considering an infinite homogenous mass distribution. Point a is considered as the origin and thus as stationary. Because by the diagram b experiences no net acceleration, the second time derivative of the distance between a and b is zero. That is the argument.

and no force due to the matter outside this sphere (shell theorem)
For reference here is your statement where i bolded the part i take issue with:
Originally Posted by quantropy
If you take two points of matter distance x apart within a homogenous sphere of density ρ then , whatever the size of the sphere or the position of its centre. So however you let the size go to infinity, that it the result you will get.
What i am asking you to prove (by direct request), in the appropriate mathematical detail, is that there is "no force due to the matter outside this sphere" in the limit to infinity.

Your claim is that one case is invalid, based on an argument involving an infinite amount of matter and how you can get its effect to cancel out. If you tried to make a similar claim in any other part of science then I can't see you being taken seriously.
What i am trying to achieve is to get you to acknowledge the hidden corollaries in your proposed replacement of the heuristic of expanding space.

They are:
1. The universe is finite (and not finite but unbounded in the GR sense, but finite in the sense that we have an homogeneous universe and beyond that there is empty space)
2. The universe is spherical (and again not spherical in the GR-curvature sense, but spherical in that it is quite simply a spherical mass)
3. The universe has a clear edge, where at one point you have the mass of universe which suddenly stops and beyond that you have empty space

Given those corollaries, do you really think it is better we tell people that our universe is like that rather than tell them that space is expanding?

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Originally Posted by caveman1917
I was, as you were, considering an infinite homogenous mass distribution. Point a is considered as the origin and thus as stationary. Because by the diagram b experiences no net acceleration, the second time derivative of the distance between a and b is zero. That is the argument.
I was considering a finite mass distribution for which I let the size tend to infinity. You draw a finite mass distribution, but then claim that you're actually considering an infinite mass distribution all the time. I think that you've been confusing things enough. You were adamant that the only way to apply Newtonian gravity to an infinite mass distribution was to use Newton's cancellation argument and so disagree with general relativity. I had got the idea that the use of the shell theorem to deduce a negative second time derivative of distances was fairly well known, but I'm not a professional cosmologist and so couldn't really be sure of what people thought. Norton said that the contradiction between these has been generally ignored. How could I resolve this?

Well I've done some searching, and it seems that a lot of cosmology courses have something like http://www.astronomy.ohio-state.edu/...682/notes4.pdf in which it is shown how to derive the Friedmann Equation using Newtonian gravity. They use the Shell theorem (Newton’s “iron-sphere” theorem) exactly as I did, and Newton's cancellation argument isn't mentioned at all. Essentially it's been dropped which is why the contradiction is never mentioned.

I also found the following paper Why Newton's gravity is practically reliable in the large-scale cosmological simulations
confirming what I had thought, that professional cosmologists actually use Newtonian gravity a lot, and yet we're constantly told that we can't possibly understand cosmology in terms of Newtonian gravity.

Originally Posted by caveman1917
What i am trying to achieve is to get you to acknowledge the hidden corollaries in your proposed replacement of the heuristic of expanding space.

They are:
1. The universe is finite (and not finite but unbounded in the GR sense, but finite in the sense that we have an homogeneous universe and beyond that there is empty space)
2. The universe is spherical (and again not spherical in the GR-curvature sense, but spherical in that it is quite simply a spherical mass)
3. The universe has a clear edge, where at one point you have the mass of universe which suddenly stops and beyond that you have empty space
This doesn't seem to have any relation to what we have been talking about. Nothing I say implies that the universe is finite

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Originally Posted by quantropy
You draw a finite mass distribution, but then claim that you're actually considering an infinite mass distribution all the time.
So i've misled you by not drawing an infinite mass distribution? How exactly does one draw an infinite mass distribution?

Besides, you already agreed that the diagram intended to show an infinite mass distribution in your response to that post containing the diagram:
Originally Posted by quantropy
Originally Posted by caveman1917
The mass distribution is spherically symmetric about any point.
Yes, so the shell theorem applies about any point
For a finite distribution the answer should've been no.

I was considering a finite mass distribution for which I let the size tend to infinity.
Again, incorrectly. You keep asserting that this works when you let the size tend to infinity, yet never prove this. So i will reiterate my request:
Originally Posted by caveman1917
What i am asking you to prove (by direct request), in the appropriate mathematical detail, is that there is "no force due to the matter outside this sphere" in the limit to infinity.
There are countless examples of integrals that diverge in the limit to infinity, for example the center of mass of a thin rod, or for a real easy one:
that will always give 0 for a finite "a", yet diverges in the limit to infinity.

You continuously assert that the shell theorem does work when you let the size tend to infinity, so prove it.

Well I've done some searching, and it seems that a lot of cosmology courses have something like http://www.astronomy.ohio-state.edu/...682/notes4.pdf in which it is shown how to derive the Friedmann Equation using Newtonian gravity
for a finite, isolated sphere of mass.

I also found the following paper Why Newton's gravity is practically reliable in the large-scale cosmological simulations
confirming what I had thought, that professional cosmologists actually use Newtonian gravity a lot, and yet we're constantly told that we can't possibly understand cosmology in terms of Newtonian gravity.
Because professional cosmologists know that this practical approximation only holds for a finite universe, which they are of course not bothered by since they are just using this for easier calculations, not to explain to a layman how large scale cosmology works. For that they use the picture of expanding space.

This doesn't seem to have any relation to what we have been talking about. Nothing I say implies that the universe is finite
This directly follows from your use of newtonian gravity to describe large scale cosmology.

16. It is wrong to chase the dogs tail. Its his tail. Let him have it.. right or wrong regardless..

I am trying to say it's not my business to attempt to change a point of view in convergence with mine.

This subject has become a argument of unknowns.. I will try to make clear..

and be patient, I am not so good at that..

You all know I like, because it makes good sense to me. That 'Finite' can be used so long as the understanding is

that only in respect of the proposed fact that the universe at some time past was so very small

as can be said to have been a singlearity. That it expanded and is still.. From that beginning point.. The BB.

and that any thing that was within must therefore have been finite.

Then the word unbound is added for the fact observed that this expansion is eternal and eccelorating still.

So this discussion seem to me to be going no where.. (or in fact everywhere..)

In the above postings I see a point about expansion.. and voids being expanded into and thus a outside of the universe..

To that I would say. NO... My, and I think the understanding of 'most' is that there is no space to expand into..

That it might be better to try and think of it as a expanding mass.. just getting bigger..

all those parts that are not otherwise bound by other forces..

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As of lately, it has been my interpretation of the facts existing so far, that space is neither expanding or contracting but moving, and in many directions. Also, one question, if space is expanding and all objects are supposedly moving away from each other, then why would the next galaxy over, Andromeda, be on a collision course with our Milky Way?

It is just my opinion that our science is still so primitive and too many intracacies and variables are involved. No math equation will measure such a great amount of objects moving in so many different directions all with different mass, speed, trajectories, and with all the different forces involved as gravity, electromagnetism, solar winds, and cosmic rays...

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Originally Posted by Kalopin
As of lately, it has been my interpretation of the facts existing so far, that space is neither expanding or contracting but moving, and in many directions. ...
If it is moving, what is it moving relative to? Further, how do you account for the fact that the majority of galaxies seem to be moving away from us - a situation best explained by expansion?

Originally Posted by Kalopin
Also, one question, if space is expanding and all objects are supposedly moving away from each other, then why would the next galaxy over, Andromeda, be on a collision course with our Milky Way?
Because locally gravitationally effects overcome the general expansion. Analogy: we may both be on a plane headed for Moscow, but we can readily walk down the aisle towards each other.

Originally Posted by Kalopin
It is just my opinion that our science is still so primitive and too many intracacies and variables are involved. No math equation will measure such a great amount of objects moving in so many different directions all with different mass, speed, trajectories, and with all the different forces involved as gravity, electromagnetism, solar winds, and cosmic rays...
So your argument is that if we cannot set up an equation to describe what is happening then it cannot be happening? I trust you see the illogic in that.

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