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light in the tunnel
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
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
Only an extremely massive object would have such an effect and the Earth isn't massive enough. So no.
Hammer
it would look flat only if you looked from a non 3+1 dimension
light in the tunnel
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
QUOTE (light in the tunnel+Aug 15 2009, 09:29 AM)
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?

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
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
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
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.
danshawen
Newton's law of gravitation very much depends on the direction of "down" being always toward the center of mass, as if all of the mass of an object were concentrated at that point. [Moderator: Incorrect.

"Like the moon being made of green cheese?" This is a pretty pedestrian bit of classical physics, not fantasy. But that is the kind of wisecrack moderators (and formerly trolls) typically will make about perfectly legitimate physics questions like this one.

First, if the Earth were flat (like a coin), it could not remain so for very long, and part of the reason for that is that there would be an anisotropy in the gravitational field for the flattened earth, which would have a tendency to collapse the mass back to spherical unless it were made of something like neutronium (the stuff of burned-out neutron stars, unique among shapes of celestial bodies, is surmised to be cubical). [Moderator: Incorrect.

From the edge, a flattened Earth would have much greater gravity than on the surface of a sphere of equivalent mass. From one of the flat surfaces (above or below), there would be increased gravity near the edges, tending to pull anything loose onto the edge. Gravity at the dead center of one of the surfaces would be negligible, like being at the center of a spherical Earth. This consideration is one reason that center of mass was so important to Newton's theory of gravitation. The fact that even Newton's math has a singularity (infinite gravitational force) at the dead center of a spherical mass such as the Earth, independent of the mass or whatever falls into it, is an obviously errant anomaly that should be a lesson to young theoreticians who may believe that their mathematical descriptions of physics is infallible. It isn't, not by a long shot.

Only some arrangement like Larry Niven's ring world, or Arthur C. Clarke's Rama could counter the tendency of a very large non-spherical structure to collapse, by spinning it so as to counterbalance the force of gravity that would cause it to collapse to a more spherical shape..

It isn't just gravity that behaves in this anisotropic manner. While machining parts for the Manhattan Project, considerable effort was spent calculating critical masses of various shapes of fissionable cores for nuclear weaponry. This had to be done by roomfuls of young women using comptometers, pencil and paper, because calculators and computers were not yet practical. A single errant neutron entering the wrong shape core at just the right angle could have quickly gone critical, with disastrous consequences for anyone nearby when it occurred.
danshawen
Source:

Wikipedia
"Newton's law of universal gravitation"

"...are attracted as if all their mass were concentrated at their centers"

I'm not saying that Newton's law of gravitation is correct. It has been replaced by General Relativity, of course.

I'm also not saying that smaller worlds are round, or even that the Earth is perfectly round (it isn't, besides which, it's also spinning, and that also affects its shape).

The question, as I interpreted it, was whether a coin-shaped mass the same as the Earth, that was not spinning, would be able to retain that shape, being of similar mass and composition. How would you have answered it? Could it remain coin shaped? How long? I try to stay away from most materials science, since I'm no expert.

Better?, or am I totally missing the point here?

Thanks.

pmb61
QUOTE (danshawen+)

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?

No.

QUOTE (danshawen+)

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.

Youíve made a common misconception. If youíre on a large at surface far away from the edges and since youíre a small person compared to the size of the earth then the gravitational field will be approximately uniform and a uniform gravitational field has zero spacetime curvature.

QUOTE (danshawen+)

Could gravity bend space time in a way that a flat plane reconnects with itself in some places, but continues further in others? 

No.

QUOTE (danshawen+)

In other words, if the Earth was a flat plane, could modeling it as a sphere ..

Thatís a contradiction.
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