Another question on Gravity

[Crewman47]

As it's semi unrelated to the other post I thought it best to make a seperate post to ask this.

Anyway earlier this morning I had the strangest thought come into my head and it was, what would happen if the force of gravity that keeps us all, and everything else, more or less fixed to the surface of the Earth were to suddenly do a complete 180 and reverse itself. Could there actually some force of nature (like maybe the Core spinning in reverse or something) that could cause gravity to actually reverse in one sudden move so like if you're in a location where there's a ceiling above you or you're outside, would you find yourself falling like a rock, so to speak, and smashed into the opposing surface, or, if your outside, heading for certain doom while approaching the Earth's atmosphere.

What do you think, any chance of something like this happening and what would it be like?

[All Seeing Eye]

Since gravity is created by mass exerting pressure on the fabric of space I doubt gravity could become reversed.

[Christopher]

Crewman47 wrote:

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Anyway earlier this morning I had the strangest thought come into my head and it was, what would happen if the force of gravity that keeps us all, and everything else, more or less fixed to the surface of the Earth were to suddenly do a complete 180 and reverse itself. Could there actually some force of nature (like maybe the Core spinning in reverse or something) that could cause gravity to actually reverse in one sudden move so like if you're in a location where there's a ceiling above you or you're outside, would you find yourself falling like a rock, so to speak, and smashed into the opposing surface, or, if your outside, heading for certain doom while approaching the Earth's atmosphere.

Gravity is not caused by the spin of the Earth's core, nor is it caused by "pressure on the fabric of space," which I think is an overly literal misreading of a common analogy for how gravity operates. Gravity is a force of attraction between masses. Any two particles with mass exert a weak gravitational attraction on one another. It's a very tiny effect, which is why you don't feel yourself pulled toward your desk or your refrigerator. But a very large concentration of mass, such as a planet, exerts a strong enough attraction to pull and hold other things against it. If anything, the rotation of the Earth slightly counteracts its gravitational pull by creating a centrifugal effect, though that's minuscule. (It is enough, though, to give the Earth a slight equatorial bulge as it spins.)

There is no known physical mechanism that could turn the attractive force between masses into a repulsive force. However, it is currently believed that the universe contains a "dark energy" that acts as a very faint repulsive force, and that it will grow stronger over trillions of years to come, until it reaches the point that it overwhelms gravity and causes galaxies and stars to fly apart and prevents new solid bodies from forming. But that wouldn't actually reverse gravity itself, just cancel it out with an opposing force (the same way that the thrust of a rocket cancels out gravity and exerts enough additional force to let a spaceship escape the Earth).

More simply, if a sufficiently huge mass were to be placed directly over you, it might be enough to cancel out the pull of the Earth's gravity beneath you. Since the Earth's mass acts as if it's all concentrated at the Earth's center, 6,377 km below you, then if the mass were, say, 6.4 meters above you, then by the inverse square law it would only have to have one millionth of one millionth of the Earth's mass, though that would still be enormous. The late Dr. Robert Forward wrote about this in some of his nonfiction, conjecturing ways that a large amount of matter could be compressed into a degenerate state (like white dwarf matter) and used for this kind of "antigravity" effect. Of course, it would have to be held up by an incredibly strong set of supports. I sure as hell wouldn't want to stand under it. Heck, the Earth's crust probably couldn't support it; it would sink straight through.

As for what would happen in the imaginary circumstance of the Earth's gravity reversing itself, well, naturally anything not securely fastened would fall out into space. The atmosphere and hydrosphere (water) would escape into space, leaving the planet barren and uninhabitable. Soil, sand, and the like would fall away too. How many structures remained would depend on how solidly they were built and secured to the ground; many would probably stay in place at first but gradually break and fall away because they were engineered with compression rather than tension in mind.

The planet itself would remain largely intact, I think, because the electromagnetic forces that bind it are immensely stronger than gravitational forces. However, considering that the crust of the Earth is a set of overlapping plates floating on a bed of liquid magma, I suppose it's possible that if those plates suddenly found themselves on the "underside" (gravitationally speaking) of that liquid, they might simply fall away into space, breaking apart into chunks. The magma would also spill out into space, leaving the solid core. That would expand somewhat because it wouldn't be under gravitational compression anymore.

And if that core continued to exert an antigravitational field, I imagine it would accelerate out of Solar orbit and wander off into the galaxy, eventually being repelled away from the galaxy and into intergalactic space.

[Shaw]

Christopher wrote:

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...nor is it caused by "pressure on the fabric of space," which I think is an overly literal misreading of a common analogy for how gravity operates.

Well, there is also the problem of people assuming that the analogy is not as literal as it actually is. And as pictures are at the heart of the misunderstanding, lets avoid them for this discussion and just look at the math.

Lets start with an example of the differential equation for arc length in the Cartesian plane.

This form most likely looks very familiar but what is missing is the metric,

which is trivial and so often not mentioned. But when working out the geometry on a surface it does become of great importance as the metric defines the intrinsic characteristics of the surface. In Classical Differential Geometry we are given the First Fundamental Form of a surface (parametrized by u and v) as

but for us it is best illustrated in a more generic form like this

(Note: I'm not going to define E, F or G here as they aren't germane to this discussion)

Now for Minkowski Space-Time this expression expands to include three spatial dimensions and one time dimension,

which can be reparametrized in polar coordinates as

In General Relativity the metric is not static throughout space-time, it is effected by mass-energy. So if we put a mass M at the origin of the above representation what we get is

So what this shows is that intrinsic characteristics of space-time (defined by the metric) are a function of mass-energy. The study of differentiable manifolds all stems from the intrinsic geometry being defined by the manifold's metric... including things like the intrinsic curvature and covariant derivative.

So yes, gravity is geometry... but at the same time it acts like a force. After all, what is the curvature of space-time effecting but the inertial reference frames. The curvature acts like acceleration, acceleration requires force, the curvature seems like a force.

So just like light has properties that are both wave-like and particle-like, gravitation has properties that are both geometry-like and force-like. And because of this you really shouldn't discount either aspect.

[Christopher]

^^But that's hardly "pressure." It's also way too complicated to be worth bringing into a basic-level discussion like this. It wouldn't help the original poster understand the answers to his questions.

[Shaw]

Christopher wrote:

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^^But that's hardly "pressure."

True, but the geometric analogy part is well founded.

It's also way too complicated to be worth bringing into a basic-level discussion like this. It wouldn't help the original poster understand the answers to his questions.

I wasn't trying to make it complicated, I was hoping that seeing the same geometric tools evolve from Euclidean geometry to their form in General Relativity would help illustrate the geometric foundations in a similar way to the visual illustrations normally used.

It wasn't meant to be complex, it was an approach I had been considering for a long time and thought I would test it out on you guys. I just thought it would be generalized enough for a discussion like this, but maybe there really is no substitute for the time tested 2D surface examples.

[Crewman47]

I was actually going to post earlier and say that I actually understood what Christopher said in his post so much so that I could see what was he describing but what Shaw said wass so complex that my head nearly exploded. To me all it looked like was just a bunch of numbers with letters and squiqqly lines put in them. No offense to Shaw but I was looking more for a lamens version.

[Ronald Held]

Shaw, how did you get those equations into a post so cleanly?

[Verteron]

I think that the only thing I could conceive of that would cause something so dramatic would be the arrival of decent sized singularity (or, indeed, a rogue body of any kind) arriving in the solar system at high speed, say, >0.9c or so, perhaps having been ejected from the galactic core by some tumultuous interaction with our galaxy's very own black heart or something equally as malevolent.

Of course, that's highly unlikely, and wouldn't be instant, and would pass as quickly as it came (and, I might add, would only reverse the pull for one half of the Earth), and I suspect there might be catastrophic consequences for Earth's orbit around the Sun in such a circumstance.

Christopher -- I'm interested to flesh out your ideas about magnetic attraction being able to hold together the core if gravity suddenly went away or was reversed. Obviously EM is a far stronger force than gravity, but I'm not sure whether such an idea makes sense in my head. I'm going to see if I can come up with some reasonable back of envelope calculations (have been re-reading my textbooks, Mr. Shaw ) about this...

[Shaw]

Crewman47 wrote:

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I was actually going to post earlier and say that I actually understood what Christopher said in his post so much so that I could see what was he describing but what Shaw said wass so complex that my head nearly exploded. To me all it looked like was just a bunch of numbers with letters and squiqqly lines put in them. No offense to Shaw but I was looking more for a lamens version.

Well, Like I said, I was always wondering if this approach would work and really the only way to find out was to give it a try.

Ronald Held wrote:

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Shaw, how did you get those equations into a post so cleanly?

After writing out the equations I saved them as a PDF and brought them into Photoshop. From there I reversed the color (turning the black letters white) saved them as individual PNG images which preserved the transparency behind the letters.

Verteron wrote:

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(have been re-reading my textbooks, Mr. Shaw )

Not to get too far off the subject, but there are a ton of nice (if old) text books over at archive.org. While (for me) nothing can replace an actual book in hand for studying, it is great to be able to have an extensive library (as PDF articles and books) all available on my laptop rather than attempting to carry the paper versions around with me. For most both the OCR text and page images are included in the PDF so they are searchable documents (which is also quite helpful).

Just wanted to point out that resource.

[Zachary Smith]

So . . . erm . . . What is the "fabric" of space/time MADE of?

[Shaw]

Zachary Smith wrote:

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So . . . erm . . . What is the "fabric" of space/time MADE of?

Space-time is rather elemental... And asking what it is made of doesn't solve the issue and you could ask whatever it is made of is made of.

What is time made of? What is the distance between any two points in space made of?

Most people think of these things as pre-existing, so when talking about the expansion of the universe, people often picture the universe expanding into a pre-existing volume when in actuality it is volume itself which is changing.

It is like asking where the big bang happened. By definition, you are standing where it happened... but then again, so am I. Because everywhere was there. The big bang is more impressive when you start considering that it (by definition) was the beginning of the distance between any two points and the start of intervals of time between events.


It is interesting to think that the same type of issues we have today with grasping the nature of space-time aren't that different from the conceptual issues that people were having at the end of the 19th century with inertial reference frames. The nature of the universe around us isn't ever going to come easy, the more we learn the more we find out that we don't really know. And at every step we have to rise to the challenge of understanding what we are presented with.


Sorry for diverging from the question there... I find this whole area of study both beautiful and inspiring.

[Christopher]

Zachary Smith wrote:

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So . . . erm . . . What is the "fabric" of space/time MADE of?

Metaphor. Spacetime isn't a fabric of any kind; we just find it convenient to use a stretchable fabric as an analogy for describing the way that topological relationships between objects within spacetime are affected by movement, mass, and energy.

[Geoff]

Verteron wrote:

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I think that the only thing I could conceive of that would cause something so dramatic would be the arrival of decent sized singularity (or, indeed, a rogue body of any kind) arriving in the solar system at high speed, say, >0.9c or so, perhaps having been ejected from the galactic core by some tumultuous interaction with our galaxy's very own black heart or something equally as malevolent.

I reckon the result would look something like this.

[NCC621]

#4:

LOL! You seem to be either:

1. Showing off, or

2. Demonstrating that even smart people can be surprisingly dumb. How dumb do you have to be to fail to explain your terms clearly to your audience? Hawking understands that blinding his audience with equations is mere obfuscation or technobabble, that without explanation, it fails to illuminate.

Based on the amount of effort you've expended with Photoshop to make a pretty presentation, I vote for #1.