[juggernot]

Up until a few months ago I thought gravity was simply an unexplainable force which pulled matter together. I've recently discovered that gravity is actually a bending in Space/Time caused by matter itself! I always wondered why black holes can trap light, because I thought that gravity could only affect matter and not energy. Apparently light always travels straight and it is Space/Time that bends. Awesome. This new revelation has opened up some new questions for me as I researched the topic.

-What is a geodesic?
-what is the 4th dimension?
-how are a geodesic and the 4th dimension related?
-What are gravity waves or gravity radiation?
-What is Frame Dragging?
I-f spinning objects affect space time differently, do they have greater 'gravitational pull'?

I'm sure that these answers will also result in more questions. If people feel that these questions warrant seperate topics, I will edit this post and make it so. Thanks in advance for your help.

Note: To fully understand this topic, I will need to know more about space/time, but I will save that for another thread. Right now I only really know the principle through analogies.

[modest]

Originally Posted by juggernot

Up until a few months ago I thought gravity was simply an unexplainable force which pulled matter together. I've recently discovered that gravity is actually a bending in Space/Time caused by matter itself!

There's a recent thread discussing the differences between Einstein's interpretation of curved spacetime vs. a quantum mechanical explanation using gravitons:

Gravitons and the bending of SpaceTime

Originally Posted by juggernot

I always wondered why black holes can trap light, because I thought that gravity could only affect matter and not energy.

According to General Relativity... Regardless of how much energy a particular beam of light has, it will follow a null geodesic through spacetime. If spacetime is flat (representing no source of gravity) then the geodesic is a straight line. If there is a source of gravity then spacetime is curved and the geodesic for which light follows is curved.

In the case of a black hole spacetime is curved such that all future pointing null geodesics behind the event horizon lead to the singularity.

Originally Posted by juggernot

-What is a geodesic?

In GR a geodesic is the path a body or particle will take when no force is acting on it. As such, it feels no acceleration.

Originally Posted by juggernot

-what is the 4th dimension?

In relativity, it is temporal. There are 3 spatial coordinates and 1 time coordinate on a curved manifold (4-dimensional Lorentzian manifold) which is most often called "spacetime".

Einstein's field equations describe the curvature of this spacetime given some distribution of energy and momentum (mass).

Originally Posted by juggernot

-how are a geodesic and the 4th dimension related?

The geodesic exists on the 4 dimensional Lorentzian manifold (explained in the link above) as a straight line between two spacetime events. The most common way to think of this is with a globe. A geodesic is some line segment of a great circle (such as a line of longitude). The surface of the globe is 2 dimensional and the geodesic is straight in that 2 dimensional setting. It is, however, curved in 3 dimensions and when the globe is flattened into a map the geodesic and the path of the particle it represents is curved.

A real world example would be earth orbiting the sun. The geodesic of earth's path is straight on the manifold, but the path is curved from our perspective.

Originally Posted by juggernot

-What are gravity waves or gravity radiation?

I don't know what gravity radiation would refer to (?graviton?), but gravitational waves in relativity are most cool. Wikipedia does them more justice than I'd be able.

Gravitational wave - Wikipedia, the free encyclopedia

Originally Posted by juggernot

-What is Frame Dragging?

Rotating massive bodies affect space and time by 'dragging' them with the rotation.

Frame-dragging - Wikipedia, the free encyclopedia

Originally Posted by juggernot

I-f spinning objects affect space time differently, do they have greater 'gravitational pull'?

I'll have to look into this... I'm not sure what would be expected.

~modest

[juggernot]

Thank you for your answer. I'd like to ask a follow up question if I may. So when a force does act on an object, such as magnetism or kinetic energy it is bumped into another geodesic path, correct? So when someone is skydiving they are simply following their geodesic path. However if someone jumps on a trampoline they move to another geodesic path. This path however, also points to earth because mass warps space time creating the effect we call gravity. If a geodesic refers to the path an object will take if no forces are acting on it, how does this work with the law: an object in motion will tend to stay in motion, at object at rest will tend to stay at rest. If no forces are acting on an object and it is at rest, is it still on a geodesic path?

[modest]

Originally Posted by juggernot

So when a force does act on an object, such as magnetism or kinetic energy it is bumped into another geodesic path, correct?

Yes. It’s usually said that a world line (or particle path) that is acted on by a force is not a geodesic. But, I think you’re talking about a world line that is following a geodesic then gets redirected by some kinetic or electrostatic interaction and gets set on a new geodesic. And, that’s right. I agree with the way you characterize it being “bumped into another geodesic path”.

Originally Posted by juggernot

So when someone is skydiving they are simply following their geodesic path.

Yep. Air resistance makes it not quite a geodesic, but the idea is correct... the worldline of an object in freefall is a geodesic.

Originally Posted by juggernot

However if someone jumps on a trampoline they move to another geodesic path. This path however, also points to earth because mass warps space time creating the effect we call gravity.

Yes. Earth’s escape velocity is 11.2 km/s. Excluding air pressure as a variable, we could say that any worldline with less than 11.2 km/s would intersect the ground.

Originally Posted by juggernot

If a geodesic refers to the path an object will take if no forces are acting on it, how does this work with the law: an object in motion will tend to stay in motion, at object at rest will tend to stay at rest. If no forces are acting on an object and it is at rest, is it still on a geodesic path?

Sure. Even if we consider something "at rest" in the three spatial dimensions, it still moves through time. In a spacetime diagram, this would be a worldline that points straight up, and it surely can be a geodesic.

These, by the way, are really good questions. When being introduced to this stuff, I bet a lot of people have a bit too much trouble with the basic ideas to get to things like you're bringing up. Impressive.

~modest

[juggernot]

I understand how gravity affects things spatially, but I have a question about how if affects time. My basic question is why does gravity cause things to accelerate. After all, if matter is causing space itself to bend, I undersand why gravity 'pulls' on us. However I don't understand why we accelerate towards an object and not just move at a constant rate. I have a theory about why this is, but I'm not sure if it is right. When space/time is bent by the earth, it curves my geodesic so that I will end up on Earths surface, however it also bends time so that I reach my geodesic destination sooner than I should? This would mean we experience time differently though, which would probably have other consequences, making this theory very unlikely. I also don't understand why there is a maximum falling speed. Even though the Earth is curving my Geodesic, I am also curving the Earths right? So does that mean that the maximum falling speed is different for every two bodies of mass? For instance I would fall slower on another planet? Or a whale would fall faster then me on earth?

For example, you said an object at rest spatially, but moving through time would be a worldline that points straight up. If no forces were to ever act on that object it would travel through infinite time, but no space. Can Space/Time be simply thought of as a grid then? With Y being Time and X being space? If we say that the normal space/time ratio is a 60 degree angle, then mass could cause space/time to bend so that it is a 30 degree angle, meaning that we traverse the same amount of space in less time. What about light, and the speed of light? For the speed of light to be the fastest possible speed that would mean it would be a 0 degree angle(covers an infinite amount of space in no time). But wouldn't that make the speed of light something we couldn't measure?

If whoever answers could attempt a visual explanation that would be great.

[modest]

Sorry this took me so long to answer.

Originally Posted by juggernot

If whoever answers could attempt a visual explanation that would be great.

Yes, I think that will help.

Originally Posted by juggernot

I understand how gravity affects things spatially, but I have a question about how if affects time. My basic question is why does gravity cause things to accelerate. After all, if matter is causing space itself to bend, I undersand why gravity 'pulls' on us. However I don't understand why we accelerate towards an object and not just move at a constant rate.

Very good question. Considering time as curved into our spatial dimensions by gravity will explain this. It’s not easy to describe, but show’s pretty well graphically.

The first example has no gravity - I guess I should say, it has no spacetime curvature. It is a flat spacetime grid. Moving up on the grid is moving forward in time. Moving left or right is moving through the spatial dimension. The green line represents the surface of a planet and the red line is our “free falling” observer.



Notice the two do not intersect. This is because spacetime is not curved and there is no gravity.

The next pic:



shows time curved into the spatial dimension by the mass of the planet. The green line is the surface of the planet. It is not a geodesic. It feels acceleration (notice how you feel acceleration right now on the surface of a planet). The red line is the freefalling observer which is a geodesic. It moves toward the surface of the planet - first slowly, then more rapidly. It does this following a geodesic on the grid, feeling no acceleration. Yet from the planet’s surface it appears to accelerate toward the planet, and intersect with the surface.

Originally Posted by juggernot

I also don't understand why there is a maximum falling speed. Even though the Earth is curving my Geodesic, I am also curving the Earths right? So does that mean that the maximum falling speed is different for every two bodies of mass? For instance I would fall slower on another planet? Or a whale would fall faster then me on earth?

The speed that you fall is determined by how curved spacetime is. A more massive planet will curve spacetime more and you will fall faster toward it. Ignoring Earth’s atmosphere (pretending it didn’t have one). We could consider an earthling falling some 50 meters height and hitting the surface of the earth. A mooninite falling 50 meters on the moon would fall with less speed toward the ground and would hit the ground of the moon slower than the earthling. This is because earth has more mass and curves spacetime more.

However, two objects of different mass on the moon will fall at the same speed. If both are dropped from the same height, they will hit the ground at the same time. I believe an astronaut did this with a feather and a hammer. Because there’s no atmosphere they both fell at the same speed. Both follow the same geodesic toward the ground. Both accelerate equally toward it.

Originally Posted by juggernot

Can Space/Time be simply thought of as a grid then? With Y being Time and X being space?

Yes, it’s not quite as simple as it sounds, but what you describe is a Minkowski diagram of spacetime.

Originally Posted by juggernot

If we say that the normal space/time ratio is a 60 degree angle, then mass could cause space/time to bend so that it is a 30 degree angle, meaning that we traverse the same amount of space in less time. What about light, and the speed of light? For the speed of light to be the fastest possible speed that would mean it would be a 0 degree angle(covers an infinite amount of space in no time). But wouldn't that make the speed of light something we couldn't measure?

Here you've steered us into special relativity. On a spacetime diagram, nothing can move faster than light. If light moves one unit of space per one unit of time, then it looks like this:



Light is massless, and it is the fastest moving thing. This means all mass will have a steeper worldline on the diagram than light:



This is a ridiculously sparse explanation I'm giving you, so I encourage you to check out wikipedia's articles on special relativity and Minkowski diagram

And this is also a wonderful little applet to play with,

http://www.adamtoons.de/physics/relativity.swf

I will be here for any questions as best as I can answer them and I apologize again for letting your post fall through the cracks and taking so long to answer.

~modest

[Pluto]

G'day from the land of ozzzzzzz

Hello Modest, I'm learning just by reading your response.

Thank You.

======================================

[ChunTzu]

Originally Posted by juggernot

what is the 4th dimension?

I really hope I'm not bastardizing this but I'm going to attempt a brief explanation of another interpretation of the 4th dimension, which is not altogether related to you question of gravity, I just want to put it out there to chew on. Maybe somebody more qualified can back me up, here. I'm not a scientist, just an enthusiast...

According to Hyperspace Theory (as explained by Michio Kaku in Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension, really easy to find on Amazon, etc), the 4th dimension is not made up of time or spacetime, but is actually the next spatial dimension above the 3rd spatial dimension. In a more macro view, the universe is actually made up of 10 dimensions that were split into 6 and 4 as a result of the Big Bang. The 6 dimension universe shrank to such an infinitesimal size that it can no longer be detected while we reside in the alternate 4 dimensional universe.

The 4th spatial dimension should be thought of in the context of the human grasp of 1D (x dimension, a straight line) , 2D (i.e. x & y dimension, folding a piece of paper), and 3D (i.e. x, y, & z dimension, folding a piece of paper into a cube). Control of the 4th dimension can more easily be understood in a simile: imagine a person (existing in 3D space) peels stickers off a piece of paper (existing in 2D space); now imagine a being of some kind in 4D space peeling stickers off a 3D piece of paper. As I understand it, there's no proof of anything in 4D space being detected though there has been projections of 4 dimensional shadows from unseen objects.

The existence of multiple spatial dimensions numbering greater than the tried and true 3 folds into one of the proposed greater calculations for the Theory of Everything. The idea, here, being that each higher dimension would effectively give us more "room" to figure out the laws and formulas of the dimensions "below" it, which are most importantly assumed to be simpler and more compact. Therefore, if humans ever harnessed the power to achieve existence in something like the 10th dimension, we could possibly have one calculation which could explain every single thing in our known 3D universe, thus the Theory of Everything. This would undoubtedly touch upon your question, "what is gravity?" while possibly giving us an avenue to control it.

This is, interestingly, rumored to be what Einstein was trying to figure out for the last 30 years of his life, after his presentation of the Theory of Relativity. Papers full of notes of this wispy "all-encompassing, universal view", which he himself did not fully understand at the time, were left on his desk after his death.

That's as accurate and brief as I can make it. Corrections are welcome because this stuff is fascinating to me and I want to be right.



P.S. I haven't read this entire site and can't speak for its credibility but there are some more resources related to multiple spatial dimensions available here.

[ChunTzu]

Ah ha! I knew something had to be around here: Hyperspace on Hypography

[truth_united]

juggernot

what is the 4th dimension?

As explained by modest, 4th dimension is time. Further, gravity is a direct consequence of interaction between the 3 dimensions of space, the 4th dimension of time, and the matter existing within this space-time.

Theoretically, we can have even more dimensions but our human capabilities would perhaps be limited in perceiving them. One can only wonder what other phenomena would be a consequence of interactions between these other unknown dimensions and the known 4 dimensions!

truth_united