If The Earth Were Flat . . .

light in the tunnel

15th August 2009 - 02:56 AM

The topic title and description basically sum up my question.

Start with the (assumed to be false) belief that the Earth is flat (avoid questions about where it ends, what happens when you get to the edge and so forth).

Now, assuming that gravity bends light or that space-time is curved (however you like to talk about it), would the earth appear to become more spherical as an observer moves to higher altitudes?

It seems that the convex appearance of an actually-flat surface could be the result of gradual space-time curvature viewed in a larger context, where more area and thus mass/gravitation are viewed within a smaller perspectival-frame.

Now imagine if the world was flat, what could explain (other than spherical shape) the appearance from various orbital paths that it reconnects with itself in places that appear to have already gone by? Could gravity bend space time in a way that a flat plane reconnects with itself in some places, but continues further in others?

In other words, if the Earth was a flat plane, could modeling it as a sphere effectively obscure the points at which the plane continues to areas not represented on the surface of the sphere? What if the plane extended infinitely in all directions? Would it then be possible for gravity to hold an orbiting satellite in such a pattern that it continues to trace the same path, revisiting the same ground-points repeatedly? If that was the case, what would it take to get out of that orbital path and explore other parts of the infinite plane?

Call it science fiction all you want, but please don't insult and . . . if you are clever enough with science, please try to explore the hypotheticals in scientific terms as this helps develop the fiction further and stimulates human imaginations.

AlexG

15th August 2009 - 03:44 AM

Let us start with the assumption that the moon is made of green cheese.

Could the visible cratering we see be do to the action of mice?

AlphaNumeric

15th August 2009 - 09:07 AM

Only an extremely massive object would have such an effect and the Earth isn't massive enough. So no.

Hammer

15th August 2009 - 11:07 AM

it would look flat only if you looked from a non 3+1 dimension

light in the tunnel

15th August 2009 - 02:29 PM

QUOTE (AlphaNumeric+Aug 15 2009, 09:07 AM)

Only an extremely massive object would have such an effect and the Earth isn't massive enough. So no.

How massive does an object have to be to bend space-time/light? Is there a rate of bend that correlates mass/gravitation with space-curvature?

How much mass/gravity has to be present to generate sufficient space-time curvature to make a plane appear spherical?

flyingbuttressman

15th August 2009 - 03:50 PM

QUOTE (light in the tunnel+Aug 15 2009, 09:29 AM)

You are seriously wearing down my patience. It seems as if you are approaching physics for the first time, yet you casually assume that you are magically smarter than everyone else, including those who have done actual work in the field of physics. Hmmm, let's see... I'm sure there's a word for it.... Hubris! That's it!

To answer your question, every object bends space-time a little, but only very massive objects can produce gravitational fields strong enough to create an optical effect. We can see our own sun bend the light that passes by it, and neutron stars can produce even more weird effects.

For your second question, I'm not going to answer it. Based on the OP, you are asking the dumbest question in the book. You don't get an answer.

light in the tunnel

15th August 2009 - 07:31 PM

QUOTE (flyingbuttressman+Aug 15 2009, 03:50 PM)

To answer your question, every object bends space-time a little, but only very massive objects can produce gravitational fields strong enough to create an optical effect. We can see our own sun bend the light that passes by it, and neutron stars can produce even more weird effects.

So would it be hubristic naivete to say that the space-time curvature produced by the sun's mass creates a relatively consistent area of space time among the planets of the solar system?

In other words, if an object with the mass of the Earth would stand alone, far away from any other massive object, would it bend space-time to a level of curvature more significant than it does in it's current position within the curvature of space-time caused by the more massive sun?

Would the same be true for the moon, i.e. if it was in orbit with the Earth without the sun or anything else around, its effect on space-time curvature would be subsumed within that produced by the larger mass, in this case the Earth?

From another perspective, would it be the case that black holes orbiting each other (from a distance far enough to avoid collapsing into one another) bend space-time more gradually than a single black hole far away from any other masses?

In other words, is space-time curvature relative to the mass/gravitation of nearby massive bodies? Or is it an absolute relationship between distance (measured in absolute terms, i.e. meters) and mass-density/gravity measured in absolute terms? So, for example, does a body the size and mass of the sun always produce the same amount of space-time curvature regardless of the presence of other neighboring masses?

AlexG

15th August 2009 - 09:19 PM

QUOTE

So, for example, does a body the size and mass of the sun always produce the same amount of space-time curvature regardless of the presence of other neighboring masses?

Yes. Other neighboring masses also produce curvature, but the curvature caused by a body of a given mass and size (i.e., it's gravitational field) is the same regardless of other masses..

light in the tunnel

15th August 2009 - 11:56 PM

Can red-shift and blue-shift be caused by relative expansion and compression of space-time or only by motion?

Does the term, "space-time" imply that space-compression is impossible because it would entail a proportionate amount of time-compression, which would essentially mean that light is traveling the same distance as a function of its travel-time?

When space-time curves, around the sun for example, such that photons from the same stream split directions and end up being visible as two distinct images of a distant source (I believe this was observed in some important experiment), Is the amount of space-time curvature of one path relative to the other measurable in standard geometrical length of curved lines? If so, does that mean that the light that took the more curved path will be slightly behind its counterpart that took the less curved one?

I could probably keep going, but I'm actually trying to find out where I derail, if possible, and resume "on the rails" with my understanding.

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