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Lord Antares

An issue I have with GR physics versus Newtonian physics

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No, I'm sorry, that was incorrect. It doesn't invalidate Newton's law but it means that every objects exerts an infinite value of graviational force.

 

As distance increases, gravitational force fades but some value, however small, is still present. Therefore, there is an infinite value of net gravitational force of any object for an infinite universe. As it directly depends on the mass of the object, that means that we get to infinitesimal values approaching infinity, no?

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No, I'm sorry, that was incorrect. It doesn't invalidate Newton's law but it means that every objects exerts an infinite value of graviational force.

 

As distance increases, gravitational force fades but some value, however small, is still present. Therefore, there is an infinite value of net gravitational force of any object for an infinite universe. As it directly depends on the mass of the object, that means that we get to infinitesimal values approaching infinity, no?

 

 

"Net gravitational force" (as you've used it) isn't a thing. There is no conservation law at play. There is no dilution or saturation effect from attracting multiple bodies. Gravity doesn't get "used up".

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No, I'm sorry, that was incorrect. It doesn't invalidate Newton's law but it means that every objects exerts an infinite value of graviational force.

 

As distance increases, gravitational force fades but some value, however small, is still present. Therefore, there is an infinite value of net gravitational force of any object for an infinite universe. As it directly depends on the mass of the object, that means that we get to infinitesimal values approaching infinity, no?

1)force is a vector with direction, so the very tiny forces would cancel out because they pull in all directions

2)infinite sums of small parts are not necessarily infinite e.g.

[math]\sum_{n=1}^\infty \frac{1}{2^n} = \frac{1}{2}+ \frac{1}{4}+ \frac{1}{8}+\cdots = 1[/math]

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No, I guess my terminology is incorrect. I meant to say overall force on all of the universe. Following Newton's equation, a finite amount of mass would have to exert an infinite amount of gravitational force.

 

EDIT: @Bender - your point two is interesting, I was actually wondering if this could be true, but this equation proves that it can. It would make sense in this case as well.

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That is not true at all, it's a strawman argument.

Whatever, it's clear from the other responses that you are not getting across properly what you are on about.

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This is a result of not being familiar with correct terminology and having to resort to linguistic elaborations.

It does not mean I am talking nonsense.

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No, I guess my terminology is incorrect. I meant to say overall force on all of the universe. Following Newton's equation, a finite amount of mass would have to exert an infinite amount of gravitational force.

Did you make a typo and meant to say "infinite" amount of mass?

Anyway, even an infinite amount of mass wouldn't exert an infinite force, because the distance is also infinite. Also, see point 1) I made.

Edited by Bender
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No, I guess my terminology is incorrect. I meant to say overall force on all of the universe. Following Newton's equation, a finite amount of mass would have to exert an infinite amount of gravitational force.

 

 

Newton demonstrated exactly the opposite: that if his theory were correct, then the universe would have to be infinite. If not, then there would be a centre of mass that everything would fall towards. If the universe is infinite, then the pull in all directions basically cancels out. (See also his Shell theorem.)

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Anyway, even an infinite amount of mass wouldn't exert an infinite force, because the distance is also infinite. Also, see point 1) I made.

 

 

It would depend on how the series converged.

 

But it's moot, because the force M exerts on m1 is not affected by the presence of a second mass, or a third, etc., etc. The force on mass mn is still given by GMmn/r^2

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If not, then there would be a centre of mass that everything would fall towards.

 

Yes, but this was before he knew that the universe is expanding. Doesn't this not hold true with this knowledge?

 

 

If the universe is infinite, then the pull in all directions basically cancels out.

 

I see. This is what Bender was trying to say as well, I believe. But this is true only with the assumption that there is an infinite amount of matter, as well as space. Because if there was a finite amount of matter in an infinite space, it would still fall towards the centre of mass, right?

Edited by Lord Antares
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Yes, but this was before he knew that the universe is expanding. Doesn't this not hold true with this knowledge?

 

 

There is mechanism for an expanding universe in Newton's theory.

 

 

 

But this is true only with the assumption that there is an infinite amount of matter, as well as space.

 

That is what we are talking about.

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I see. This is what Bender was trying to say as well, I believe. But this is true only with the assumption that there is an infinite amount of matter, as well as space. Because if there was a finite amount of matter in an infinite space, it would still fall towards the centre of mass, right?

More or less. For the pull to be equal in all directions, you would indeed need either an infinite universe or be in the CoG of a finite universe (that is not closed).

 

If you have a finite amount of matter in an infinite space, there are two options:

- it is distributed, which means in any finite portion of space there would be no mass

- it is located in a specific place, in which case the amount of space there is outside that place is irrelevant, and it might just as well be finite

 

Whether everything would be pulled to the CoG of a finite universe, depends on how fast the matter is moving outwards (at least, IIRC, but someone will surely correct it if it is wrong):

- too slow, and it will eventually collapse back to the CoG

- too fast, and it will continue to expand forever, because the force decreases faster than it can slow down the matter (in other words, some of the matter is moving faster than the escape velocity of the universe)

- just right: it will continue to expand, but always slower to go asymptotically to a fixed size.

 

Of course, it is all just a thought experiment, as we know none of this is actually the case in our universe.

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Because of the Shell theorem you can arbitrarily set any point as a CoG with regards to a homogeneous and isotropic matter distribution/ uniform

Edited by Mordred
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There is mechanism for an expanding universe in Newton's theory

 

I assume you mean to say that even with the expansion of the universe, everything would still gravitate towards the center of mass if the universe was finite. (according to Newton).

 

But as far as I understand it, more people think the universe is finite than infinite but we all consider his theory to be true. So how does that work?

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I meant to say there is *no* mechanism for expansion in Newtonian gravity. So it is irrelevant.

 

It doesn't matter whether more people think the universe is finite or infinite - there is no evidence either way.

Edited by Strange
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If there is no mechanism, then that changes the perspective a lot. The expansion would negate this notion of everything falling towards the center of mass, I would think.

So Newton could be wrong, right?

 

I know it doesn't matter what people think. I was trying to make the following point:

you said his theory would only be correct if the universe was infinite. Most people consider his theory to be correct. Most people consider the universe to be finite. That is a contradiction.

Edited by Lord Antares
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Considering whether a model is correct is based on evidence. Opinion about the universe being infinite or finite is not.

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If there is no mechanism, then that changes the perspective a lot. The expansion would negate this notion of everything falling towards the center of mass, I would think.

So Newton could be wrong, right?

 

 

There can be no expansion if Newton is correct. Therefore you can't use expansion to argue against (or for) Newton's ideas.

 

 

 

you said his theory would only be correct if the universe was infinite.

 

No. Completely wrong.

 

If his theory were correct then the universe must be finite infinite.

 

 

 

Most people consider his theory to be correct. Most people consider the universe to be finite. That is a contradiction.

 

1. His theory is "wrong".

 

2. What evidence do you have that "most people consider the universe to be finite"?

 

3. As that belief is not based on any evidence it cannot conflict with science.

 

You might as well say that most people's favourite colour is red and this conflicts with the sky being blue. Opinions are not evidence. (Especially when I have no reason to believe that ,most people have this optinion.)

Edited by Strange
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There can be no expansion if Newton is correct. Therefore you can't use expansion to argue against (or for) Newton's ideas.

 

How so? If there can be no expansion if Newton is correct, then if there is expansion, I car argue against his ideas, surely.

 

 

No. Completely wrong.

 

If his theory were correct then the universe must be finite.

 

But I am only saying this because you said:

 

 

Newton demonstrated exactly the opposite: that if his theory were correct, then the universe would have to be infinite.

 

Stop confusing me. How am I supposed to communicate with you if you keep giving me conflicting information. Maybe you meant something else, but it is not clear to me at all.

 

 

1. His theory is "wrong".

 

2. What evidence do you have that "most people consider the universe to be finite"?

 

3. As that belief is not based on any evidence it cannot conflict with science.

 

You might as well say that most people's favourite colour is red and this conflicts with the sky being blue. Opinions are not evidence. (Especially when I have no reason to believe that ,most people have this optinion.)

 

No. That's a ridiculous analogy, especially because you misunderstood what I was trying to say. But it is irrelevant, since you are now saying that his theory is wrong.

 

The only thing that you are right about is that I don't have evidence for point number 2. I spoke from experience; I've heard/read that the universe is finite more times than not, but that is not evidence.

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How so? If there can be no expansion if Newton is correct, then if there is expansion, I car argue against his ideas, surely.

 

 

Indeed. And that is what Einstein did: show how Newton's theory doesn't work in all cases by coming up with a better one.

 

Stop confusing me. How am I supposed to communicate with you if you keep giving me conflicting information. Maybe you meant something else, but it is not clear to me at all.

 

I apologise. Another typo.

 

I meant to say: If his theory were correct then the universe must be infinite.

(Whereas you said "his theory would only be correct if the universe was infinite". This is a logical fallacy called "affirming the consequent".)

 

 

 

I spoke from experience; I've heard/read that the universe is finite more times than not, but that is not evidence.

 

I would guess I have heard about the same number of people insist it is finite and infinite. The evidence doesn't rule either out.

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I meant to say: If his theory were correct then the universe must be infinite.

(Whereas you said "his theory would only be correct if the universe was infinite". This is a logical fallacy called "affirming the consequent".)

 

I see what you mean. I didn't intend to say that, it was just a wrong choice of wording, I guess.

 

 

I would guess I have heard about the same number of people insist it is finite and infinite. The evidence doesn't rule either out.

 

One thing I really don't understand is how could the universe be infinite and expanding. The only way I can reconcile the expansion of the universe with an infinite universe is if the universe itself wasn't expanding, but if matter was simply getting further apart. But I would be completely baffled as to why this would be happening.

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I see what you mean. I didn't intend to say that, it was just a wrong choice of wording, I guess.

 

 

 

One thing I really don't understand is how could the universe be infinite and expanding. The only way I can reconcile the expansion of the universe with an infinite universe is if the universe itself wasn't expanding, but if matter was simply getting further apart. But I would be completely baffled as to why this would be happening.

Perhaps you are trying to visualise an outer edge to an infinite universe when you ought to just consider there is an increase in distance between cosmological groups that are not gravitationally bound; think locally rather than globally.

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Yes, that's what I meant when I said

 

The only way I can reconcile the expansion of the universe with an infinite universe is if the universe itself wasn't expanding, but if matter was simply getting further apart.

 

But why would this be happening?

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One thing I really don't understand is how could the universe be infinite and expanding. The only way I can reconcile the expansion of the universe with an infinite universe is if the universe itself wasn't expanding, but if matter was simply getting further apart.

 

 

That's about it. It may be easier to think of it as a decrease in density rather than expansion.

 

Here is an analogy: imagine the number line with all the integers going off to infinity (0, 1, 2, 3 ...). Now if you double all the numbers then they are twice as far apart (0, 2, 4, 6, ...) but the line still extends to infinity.

 

 

 

But I would be completely baffled as to why this would be happening.

 

John Baez's page has a good explanation. He explains it clearly enough that I think you can get something out of it even if the math goes completely over your head.

http://math.ucr.edu/home/baez/einstein/

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