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Lord Antares

An issue I have with GR physics versus Newtonian physics

49 posts in this topic

Posted (edited)

Newton's law of universal gravitation states that F= g (m1 x m2)/r², i.e. a particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In Newton's view, there need to be two masses present for gravitation to take effect.

 

It has been proven by general relativity that gravitation occurs with just one mass present, as it is not a force which acts upon objects per se, but rather on the space in between them. This all makes sense and Newton's law still holds true, as any two masses will behave in accordance to his equation.

 

However, I have just one problem with Einstein's depiction of gravity. (problem as in ''I don't understand it'', not as in ''I'm trying to refute it'', to be clear).

If it is true that Newton's inverse square law extends indefinitely and the universe is constantly expanding, then one of the two statements must be true:

 

1) The gravitational force of every object is weakening, because it needs to extend the same amount of force over a larger area. The overall amount of gravitational force exerted by a mass stays the same, but is decreased within any given distance.

 

2) The mass of every object grows proportionally to the rate of expansion of the universe. This is the only way an object could exert the same amount of force over a distance, but is bizzare to consider.

 

These are the only two options I can think of. Neither of these would refute Newton's law in reality, because as the universe expands, the objects get further and further apart, and so the weakening in gravitational attraction would simply be explained by the increase in r.

Actually, I am not sure how the second case would affect Newton's law. I am trying to think about it, but this option is far-fetched anyway.

 

This problem only occurs when you talk about general relativity's concept of gravity. What do you think about this? What am I missing here?

All replies are appreciated.

Edited by Lord Antares
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Newton's law of universal gravitation states that F= g (m1 x m2)/r², i.e. a particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In Newton's view, there need to be two masses present for gravitation to take effect.

 

It has been proven by general relativity that gravitation occurs with just one mass present, as it is not a force which acts upon objects per se, but rather on the space in between them. This all makes sense and Newton's law still holds true, as any two masses will behave in accordance to his equation.

 

However, I have just one problem with Einstein's depiction of gravity. (problem as in ''I don't understand it'', not as in ''I'm trying to refute it'', to be clear).

If it is true that Newton's inverse square law extends indefinitely and the universe is constantly expanding, then one of the two statements must be true:

 

1) The gravitational force of every object is weakening, because it needs to extend the same amount of force over a larger area. The overall amount of gravitational force exerted by a mass stays the same, but is decreased within any given distance.

Why would it need to weaken? Is there an area or volume relationship you can cite? Newton's law tells you how force depends on distance. There's no conservation of force. If a new object entered out solar system and approached the sun, there would be an increase in the net attraction from the sun. That does not cause any contradiction with the law.

 

2) The mass of every object grows proportionally to the rate of expansion of the universe. This is the only way an object could exert the same amount of force over a distance, but is bizzare to consider.

Again, why would this need to be so?

 

These are the only two options I can think of. Neither of these would refute Newton's law in reality, because as the universe expands, the objects get further and further apart, and so the weakening in gravitational attraction would simply be explained by the increase in r.

Yes. Why does any other consideration have to be made?

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Your conclusion 1 is correct.

 

 

No, it's not. Explain how the attraction of the earth to the sun is affected by the expansion of the galaxy, and what evidence there is for it.

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Posted (edited)

I said that it has no effect on Newton's law and that it holds true. The attraction of TWO masses will change if they get further apart as a result of the expansion of the universe, but that is in unison with Newton's law because r has increased between the two.

 

I am saying that, as the universe expands, the force of gravitation of a mass has more and more reach every second. Simply put, it has more of the universe to cover. As the gravitational force is proportional to the mass of an object, and therefore limited by it, does that mean than it is constantly weakening as it needs to exert the same amount of force to a larger area? Or is the mass of everything increasing? This is what I'm asking.

 

OR are you saying that there need not be an increase in gravitational force for a larger space because it takes no force to bend space, only to pull objects together?

EDIT: It presents no questions to Newton's law so don't look there. It presents questions to general relativity.

Edited by Lord Antares
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Posted (edited)

The expansion of the universe has no influence on the strength of gravity in large scale clusters. Galaxies, galaxy clusters etc do not expand internally due to gravity.

 

Neither does stellar systems. So there is no increase in radius of these systems due to expansion.

 

Expansion has nothing to do with the differences between GR and Newtons laws. The main difference between the two is GR realized the equivalence principle. In GR gravity is modelled by freefall motion.

http://www.einstein-online.info/spotlights/equivalence_principle

 

Objects in freefall follow spacetime geodesics. They experience no force as a result.

Edited by Mordred
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I know this but isn't there another difference?
In Newtionian physics, gravity strictly needs to be btween at least two masses.

 

In general relativity, one mass is enough to create distortion of spacetime, no?

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In Newton physics a single objects exerts a potential force. That force is simply not acting upon another object. The potential is still there.

 

As you recall in freefall the mass of the falling object factors out. Two objects of different masses will freefall at the same rate.

 

GR already accounts for this by stepping right into freefall motion

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I know this but isn't there another difference?

In Newtionian physics, gravity strictly needs to be btween at least two masses.

 

In general relativity, one mass is enough to create distortion of spacetime, no?

 

 

You can talk of the gravitational field of a single mass with Newtonian physics.

As the gravitational force is proportional to the mass of an object, and therefore limited by it, does that mean than it is constantly weakening as it needs to exert the same amount of force to a larger area? Or is the mass of everything increasing? This is what I'm asking.

 

No. It's always going to be GMm/r^2. If m and r are the same for the remote object, the force is the same. There is no "dilution" from having more volume, or by introducing a new object.

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GR goes to more depth than Newtonian gravity and explains WHY there is an acceleration between the two masses.

They are following curved space-time !

 

Gravity's plot is an asymptotic potential well which approaches zero at large distances.

At these distances ( galactic cluster size ) the trivial negative gravitational potential is easily overcome by an also exceedingly small positive potential. It is this net positive potential which leads ti expansion at these distances.

For all smaller distances, the gravitational potential is much greater, and the positive expansion potential is so negligible as to have no effect.

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You can talk of the gravitational field of a single mass with Newtonian physics.

 

No. It's always going to be GMm/r^2. If m and r are the same for the remote object, the force is the same. There is no "dilution" from having more volume, or by introducing a new object.

 

 

But does it imply that the gravitational filed does exert force even if there isn't another mass nearby? I thought it was just a field in which gravity would act in such and such way IF there was another mass.

 

Also, can you answer post #5? I know you are very knowledgeable but both you and Mordred, I think, missed what I was getting at.

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I know this but isn't there another difference?

In Newtionian physics, gravity strictly needs to be btween at least two masses.

 

 

The force is between two masses. But, for example, the acceleration due to gravity at the surface of the Earth is due to mass of the Earth alone.

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Yes, but the object that accelerates on earth (such as a human) is also a mass. This acceleration wouldn't mean anything if there wasn't a mass to accelerate.

 

I think I thought of an example to illustrate my question, seeing how it doesn't seem to be clear enough. I will post it a bit later, since I have to go now.

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Yes, but the object that accelerates on earth (such as a human) is also a mass. This acceleration wouldn't mean anything if there wasn't a mass to accelerate.

 

The acceleration could be measured with a vanishingly small mass (which is how you can calculate the effect of Newtonian gravity on something massless like light).

 

And, you could argue that the curvature of spacetime could only be measured by using a second mass.

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And, you could argue that the curvature of spacetime could only be measured by using a second mass.

 

 

Not neccessarily. Shining a beam of light would do.

I will draw some illustrations and post them later in the evening.

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Posted (edited)

A beam of light would indeed show several differences between Newton and GR as light is treated differently between the two. I will wait to see your example before going further.

Edited by Mordred
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Not neccessarily. Shining a beam of light would do.

I will draw some illustrations and post them later in the evening.

 

 

And the same can be said of Newtonian gravity.

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But does it imply that the gravitational filed does exert force even if there isn't another mass nearby? I thought it was just a field in which gravity would act in such and such way IF there was another mass.

 

Also, can you answer post #5? I know you are very knowledgeable but both you and Mordred, I think, missed what I was getting at.

 

 

Neither treatment says anything about a force existing if there is no mass nearby. In GR, it's not a force. So it can't require more force in a larger universe.

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Neither treatment says anything about a force existing if there is no mass nearby. In GR, it's not a force. So it can't require more force in a larger universe.

It seems to me that he doesn't understand that gravity overwhelms the expansion where it is sufficiently strong.

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. In GR, it's not a force. So it can't require more force in a larger universe.

 

Yes, you are correct. This got me into a very lengthy train of thought and I had some interesting questions and conundrums. However, they would be too long to post and would take too much effort from you to explain so I refrained from posting. What I will ask, though, is this:

 

I was going to draw a ball on two different cloths which are held by the edges. The ball would curve the smaller cloth more and the bigger cloth less because it would have to disperse the same amount of gravitational force on a bigger area. But this cannot work for space because it would invalidate Newton's law. So my question is why does it work for a ball and a cloth, and not a planet and space if the same force is involved? What is the difference? I realize that it is not technically a force so, numerically, it wouldn't have to provide more force for a larger universe as you correctly pointed out, but the principle is still very similar.

Is it because space is massless and the cloth is not? That would make sense.

 

 

It seems to me that he doesn't understand that gravity overwhelms the expansion where it is sufficiently strong.

 

Nowhere in my posts did I imply the contrary. Explain how you deduced that.

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Nowhere in my posts did I imply the contrary. Explain how you deduced that.

My understanding of what you wrote is that you don't realise that gravitationally-bound objects stay that way.

 

 

If it is true that Newton's inverse square law extends indefinitely and the universe is constantly expanding, then one of the two statements must be true:

1) The gravitational force of every object is weakening, because it needs to extend the same amount of force over a larger area. The overall amount of gravitational force exerted by a mass stays the same, but is decreased within any given distance.
2) The mass of every object grows proportionally to the rate of expansion of the universe. This is the only way an object could exert the same amount of force over a distance, but is bizzare to consider.
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Also, can you answer post #5? I know you are very knowledgeable but both you and Mordred, I think, missed what I was getting at.

 

With regard to post#5 I agree that the OP has been misunderstood.

 

 

 

 

You can talk of the gravitational field of a single mass with Newtonian physics.

 

No. It's always going to be GMm/r^2. If m and r are the same for the remote object, the force is the same. There is no "dilution" from having more volume, or by introducing a new object.

 

I also think that Lord Antares has misunderstandings of his own so the replies are not wrong, just at cross purposes.

 

This quote for swans states the general Newtonian formula, but the response does not address what LA is trying to say, since he is proposing that r in general is getting larger, for two general bodies.

 

Assuming G does not change over time.

 

So yes, if and as astronomic bodies move further apart, the net force on each will diminish.

 

This is entirely consistent with a geometrical interpretation that the larger the radius of a circle the flatter the circumference.

 

But it does not mean that the effect we call gravity is 'weakening' in an Asimovian sense.

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I was going to draw a ball on two different cloths which are held by the edges. The ball would curve the smaller cloth more and the bigger cloth less because it would have to disperse the same amount of gravitational force on a bigger area. But this cannot work for space because it would invalidate Newton's law. So my question is why does it work for a ball and a cloth, and not a planet and space if the same force is involved? What is the difference? I realize that it is not technically a force so, numerically, it wouldn't have to provide more force for a larger universe as you correctly pointed out, but the principle is still very similar.

Is it because space is massless and the cloth is not? That would make sense.

 

 

Cloth is a physical substance, and the entire piece of cloth is involved in exerting a force. Two things that are not true of gravity.

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My understanding of what you wrote is that you don't realise that gravitationally-bound objects stay that way.

 

That is not true at all, it's a strawman argument. I was simply assuming that it weakens very slightly, not that it completely overcomes the gravitational force.

Also, you will note that this thread is a simple question from someone who is not so knowledgeable towards the people who are. It is not a theory or assertion of any kind.

 

 

/cut

 

Thank you. Of course I have misunderstandings of my own but I did not want to give up on the answer simply because my question was misunderstood.

What you wrote is what I was saying, but I made the blunder of thinking that space was physical. And so if it was, Newton's law wouldn't hold true for space because in the process of expanding and distributing the gravitational force equally, it would have to be weakened in te same distance as before expansion. That was my whole point. But space isn't physical nor does it have mass, so it doesn't have to follow this logic.

 

Which brings me to another question: If Newton's law is true, then space can't be infinite, right?

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Which brings me to another question: If Newton's law is true, then space can't be infinite, right?

 

 

I don't see how that follows.

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