Thread: Is the Sun and the Earth flat?

1. Is the Sun and the Earth flat?

OK ... so I saw this FB post today and it kind of made fun of people that still think the earth is flat or something ... to be honest didnt read it .... but it had me thinking ... is the earth and sun really flat and rather it is space time that is curved?

2. Re: Is the Sun and the Earth flat?

Well its thought the other way round, that space-time is flat. But I guess the definition of what is really flat and curved could depend on how many dimensions there really are.

3. Re: Is the Sun and the Earth flat?

Are you saying that space is topologically flat and 2 dimensional until it interacts with matter, curving space around it adding another dimension? So, the Sun would occupy a flat topology if not for the accumulative effect of each particle in it adding to the warping of space, curving the entire mass into a sphere. Since this happens at the quantum scale, you see the quantum oscillations of wave/particle matter warp space no matter the size of the object, explaining why any matter has mass and gravity.
This might also explain the interaction of the Higgs Boson and the Graviton, tying them into Relativity at the quantum scale.

I'd say, nope. That doesn't sound right.

4. Re: Is the Sun and the Earth flat?

Originally Posted by Neverfly
Are you saying that space is topologically flat and 2 dimensional until it interacts with matter, curving space around it adding another dimension? So, the Sun would occupy a flat topology if not for the accumulative effect of each particle in it adding to the warping of space, curving the entire mass into a sphere. Since this happens at the quantum scale, you see the quantum oscillations of wave/particle matter warp space no matter the size of the object, explaining why any matter has mass and gravity.
This might also explain the interaction of the Higgs Boson and the Graviton, tying them into Relativity at the quantum scale.

I'd say, nope. That doesn't sound right.
I realize wording was bad ... let me try again.

1) 3 spacial dimensions ... flat ... agreed?
2) however the space-time around objects are curved per GR. This is why light traveling in a straight line can curve around massive objects. agreed?
3) per GR space-time around a BH, the sun or the earth is curved somewhat proportionately with its mass
4) The closer to the center of the earth the more curvature there is as that is the part of the earth that has the least ( greatest??? ) gravitational potential.
5) No matter where I am on the surface of the earth the surface is at a tangent to the gradient of gravitational potential.
6) If I throw a rock straight, it will eventually fall to the surface of the earth even if I threw it hard enough that it took more that 1 circumference of the earth to hit the ground. ( except at extremely hight speeds it which case it could escape. )

7) who knows where I am going with this ... but this was my train of thought ... basically that for the same reason that planets follow a straight line in space revolve around the sun that the surface of the earth is similarly a straight plane?

5. Re: Is the Sun and the Earth flat?

Originally Posted by tom
1) 3 spacial dimensions ... flat ... agreed?
This is one of those Major Bones to Pick comes up with how words describe the math in laymans terms.
In this case, the word "Flat" needs some serious definition.
The universe is described as being "flat" but that does not necessarily mean that space is "flat."
Originally Posted by tom
2) however the space-time around objects are curved per GR. This is why light traveling in a straight line can curve around massive objects. agreed?
Agreed.
Originally Posted by tom
3) per GR space-time around a BH, the sun or the earth is curved somewhat proportionately with its mass
Agreed minus 'somewhat.'
Originally Posted by tom
4) The closer to the center of the earth the more curvature there is as that is the part of the earth that has the least ( greatest??? ) gravitational potential.
Tricky, there is curvature in multiple directions the closer you go to the center of the Earth (Imagine a magical drilling rig that can drill all the way to the center of the Earth.) You will have the curvature for the center of gravity of the Earth but also the curvature of the mass over your head, to the sides of you, etc.
Originally Posted by tom
5) No matter where I am on the surface of the earth the surface is at a tangent to the gradient of gravitational potential.
Agreed.
Originally Posted by tom
6) If I throw a rock straight, it will eventually fall to the surface of the earth even if I threw it hard enough that it took more that 1 circumference of the earth to hit the ground. ( except at extremely hight speeds it which case it could escape. )
Agreed.
Originally Posted by tom
7) who knows where I am going with this ... but this was my train of thought ... basically that for the same reason that planets follow a straight line in space revolve around the sun that the surface of the earth is similarly a straight plane?
Where you are going with it makes sense, considering that a straight line can be taken through a curve. In fact, that is what gravitational lensing is. It is great thinking.
However, the type of flat you are referring to is 2 dimensional. There really is no getting around that. Once you move your idea up into three dimensions, the curves would fold in on themselves, a bit like folding a tesseract into a hypercube. The Universe can be 3 dimensional and flat. But that does not mean that local space geometry is flat in the same way that you are considering here.
Because when curved, this type of "flatness" would push one dimension up into another dimension.

6. Re: Is the Sun and the Earth flat?

Originally Posted by tom
but this was my train of thought ...
Ah...
You think curvature is your ally.
I was born in the curvature. Molded by it.
I didn't see the flatness until I was a man.
And then it was just boring.

<slug>

7. Re: Is the Sun and the Earth flat?

Originally Posted by Neverfly
You will have the curvature for the center of gravity of the Earth but also the curvature of the mass over your head, to the sides of you, etc.
Yes ... that is why the gravitational force is the strongest on the surface, however the gravitational potential is the greatest at the center.

Originally Posted by Neverfly
Where you are going with it makes sense, considering that a straight line can be taken through a curve. In fact, that is what gravitational lensing is. It is great thinking.
However, the type of flat you are referring to is 2 dimensional. There really is no getting around that. Once you move your idea up into three dimensions, the curves would fold in on themselves, a bit like folding a tesseract into a hypercube. The Universe can be 3 dimensional and flat. But that does not mean that local space geometry is flat in the same way that you are considering here.
Because when curved, this type of "flatness" would push one dimension up into another dimension.
but it is 2d flatness in a real sense rather than a perceived sense. Like if I was dropped from an airplane I would think I was falling ... but if I was put in a room or an elevator that was falling I would realize I was just weightless. Like we look at us revolving around the sun ... but the earth is really just traveling in a continuously straight line.

8. Re: Is the Sun and the Earth flat?

Originally Posted by tom
Like we look at us revolving around the sun ... but the earth is really just traveling in a continuously straight line.
Or... you could really cook your noodle considering how the Earth is taking a straight line through a series of curves that make a sin wave. At no point does the Earth pass through the same Space it has before.

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