Understanding Gravity: Exploring its Relationship with Space-Time and Mass

[timetravel_0]

I know that seems like a stupid question to ask. But I was watching a video on relativity and thought for a moment how the video didn't really explain gravity. Most examples that I see show a bowling ball on a trampoline. It is thought the bowling ball is a large object of mass(planet) and the trampoline is space-time. If you place a marble in the dip, it will fall towards the bowling ball - hence a small object falling within the gravitational field of a planet due to the curving of space-time. This example seems elegant, however its flawed because it is dependent on the gravitational pull of the earth.

Which brings me to the question, what is gravity? Sure, mass warps space time, much like a bowling ball warps a trampoline - only instead of one plane in one directions, it fully encompasses the object - which can be imagined to look much an air bubble in a bottle of hair gel. I understand how objects follow along lines called geodesics. But what I don't get is how an object succumbs to gravity because of the curving of these geodesics.

Now for the sake of understanding - let's set up an example and please ignore all variables that would inhibit the example for occurring - like logic.

Let say we had a switch that turns physics off(we want to set an experiment up that doesn't follow most rules of physics, but only a few to make it work). So we flip the switch off. Say you have two bullets and a revolver. One bullet is the sun, the other is the earth. You shoot the Earth bullet followed quickly by the sun bullet. Now say the sun is trailing behind the Earth at the same speed relative to one another. They remain at the current velocities in close proximity(remember physics is off... this is make believe at this point) Try to imagine them following behind one another, the Earth in front, and they are very close.

Now, flip the physics switch on. What happens? Does the Earth's velocity slow down and fall into the sun because of gravity? And if so, why? Why does it divert its path in a positive motion on the line its following to flow backwards on that line - just because the line is warped? I sure hope I'm making since. I just don't understand how warped space-time has anything to do with gravity. To me - it seems gravity is just another force, and that has no effect on space-time - that space-time warping is caused by mass and effects the flow of objects in space(such as an orbiting planet, and light, etc..) but gravity itself its not caused by the warping. It would make since for gravity to work much like electromagnetism - where its force has a reach(so to say) that extends past the atom(or object of mass) - wouldn't it make since for gravity to be just like that and not have anything to do with space-time?

I know this all sound stupid because I know there has to be some explanation.

 

[Nabeshin]

You understand that mass warps spacetime, and that freely falling objects follow geodesics in spacetime, so then how what are you missing from gravity? In GR all free particles move on straight lines, it's just that in the presence of mass they're not what we perceive to be "euclidian straight". This deviation from "euclidian straightness" is attributed to gravity. I find your whole example about turning physics off to be silly and would rather get right to the point...

 

[timetravel_0]

It is silly, but it presents a scenario that doesn't happen naturally. If two objects, one massive, the other small, were both following the same line at the same speed, and were close to each other - would the small object be pulled in? and if so, why?

Or better yet, if i throw an apple into the sky, why because of the curving of space does the apple fall back? I don't get that point. And what does this curve look like along a straight axis? I understand it in the concept of air in a bottle of gel. But we are within the bubble - how does the curve look from that vantage(from within the Earth's atmosphere.)

 

[Phrak]

Most of gravity is just warped time and behaves almost exactly as a potential field as Newton had in mind. Do you think you could find a you tube video of warped time that would make sense of this to laymen? Baring that, it would take some work and time starting with calculus, differential geometry and special relativity, then a class in general relativity (I left out a few).

 

[timetravel_0]

Baring that, it would take some work and time starting with calculus, differential geometry and special relativity, then a class in general relativity (I left out a few).

I just self study on my own time - don't have the money or time for formal education. Wish I did.

 

[DrGreg]

The "ball on the trampoline" picture can only represent the curvature of space, but to explain gravity requires the curvature of spacetime.

You might like to look at www.relativitet.se/spacetime1.html and see if that analogy makes more sense.

 

[Major_Energy]

Bottom line is, we don’t know much more than Newton, but recently we have found gravity has wavelike properties.


Unfortunately, one cannot turn physics off, but we can ignore effects of physics to simplify something. When one turns off Physics, you get Mathematics. You’ll see why later when we flip the switch. Anyway:

In your first example, you have three particles. One is shot at time t(earth) and then the Sun gets shot at t(sun). Then there is the Gun. We can write the time of the Sun shot as t(sun)=t(earth)+t(time between shots). Let’s say acceleration is instantaneous and at the muzzle it leaves with velocity v for each. These are your initial conditions. You have 3 physical things, the gun, the Earth, and the Sun.

At this point we can ignore the effects of gravity if we like, but we can’t turn off physics because then we couldn’t describe the sun and Earth as particles, points, etc.

At low speeds (v<<c), we can figure out what happens classically easy enough. Anyway, back to your thought, we have two particles, that were shot out of a gun. We must establish our reference frame at this point. You have 3 things, so you have 3 points of view-so to speak, or reference frames. According to the Gun, it observes two particles moving in the x direction at a velocity v separated by a distance of v(m/s) * (t(earth)+t(sun))=d(earth and sun). The Earth sees the Sun behind it in the direction of –x [t(sun)-t(earth)] seconds behind it or the distance d(earth and sun) and sees the gun moving away at velocity v.

Basically, all observers agree, there is the Sun, then the Earth with some distance between them, both moving at the same velocity v away from the gun. If they go close to the speed of light, the OBSERVED time or distance may APPEAR different to one particle relative to another, (Special Relativity) but honestly in our example it doesn't really matter, so we still say v<<<c.

We can “flip on physics” as you mean it now, by saying now the initial conditions are where the Sun and the Earth are traveling at velocity v from the gun a distance d apart AND we suddenly “turn on” gravity. Well you can see the initial conditions of what we’re trying to figure out changed. We no longer care about the launches, etc, because now we are wondering what happens to two objects traveling at a velocity v in nothingness when we consider the effects of gravity.

So what happens? The Earth starts to accelerate to the Sun, or, starts moving toward the sun when before it was staying the same distance. The Sun would accelerate to the Earth also, but it would be very small (but finite) compared to the Earth accelerating to the Sun. So yes, the Earth slows down (decelerates) relative to the gun, or relative to the Earth: the Sun starts accelerating towards the Earth, or relative to the Sun, the Earth starts accelerating towards the Sun. I think what you mean is: relative to the Gun, (Our point of reference where their speed v comes from), the Earth starts decelerating noticeably towards the Sun, and if we measure carefully, we will find the Sun accelerated a little in the direction of the Earth. If we are very careful, we will notice both Sun and Earth decelerate a little due to the pull of the Gun (heh).

Why does this happen? Because of Newton’s Law of Universal Gravitation, or ( a quick google from wiki)

,
where:
• F is the magnitude of the gravitational force between the two point masses,
• G is the gravitational constant,
• m1 is the mass of the first point mass, (EARTH)
• m2 is the mass of the second point mass, and (SUN)
• r is the distance between the two point masses [v(m/s) * (t(earth)+t(sun))=d(earth and sun)]
Gravity is, as you put it, IS just another force, and as you have found is very similar to Electromagnatism. Consider Columbs Law:

Looks kinda familiar, doesn’t it! It is the same darn thing, the constant is different…. That’s all!

The whole warped space thing- remember that is A WAY of visualizing gravity. There is nothing different per se. Just a model, a way to visualize and calculate to a familiar physical analog. In our case, it is like looking down on a big marble and a small marble on a rubber sheet. The big marble makes a big dent, and the little marble doesn’t. The little marble goes to the big marble. One thing to remember tho, in this model, the assumption is that the gravity is pulling the marbles down toward the Earth on the rubber sheet you are looking at, which is often not mentioned………

But effective. Because now consider if those marbles are traveling really fast - and the rubber sheet starts bunching up in the the direction of travel... It creates a standing wavefront - of Gravity... whatever the rubber sheet, or Gravity actually "is." Right now we call that rubber sheet spacetime, and distortions to it, Gravity-or warped spacetime...

 

[Nabeshin]

The whole warped space thing- remember that is A WAY of visualizing gravity. There is nothing different per se. Just a model, a way to visualize and calculate to a familiar physical analog. In our case, it is like looking down on a big marble and a small marble on a rubber sheet. The big marble makes a big dent, and the little marble doesn’t. The little marble goes to the big marble. One thing to remember tho, in this model, the assumption is that the gravity is pulling the marbles down toward the Earth on the rubber sheet you are looking at, which is often not mentioned………

The whole rubber sheet thing is a visualization is right, but there certainly is a difference between GR and Newtonian gravity! In fact, almost all of its predictions are different! The rubber sheet analogy is flawed, yes, we all know this, but it does not mean GR is flawed!

Your point about gravity "pulling down the marbles into the rubber sheet", yeah, that's because it's just a silly picture, obviously not how GR actually works.

Also I really see no point to discussing gravitational waves at this point, doesn't quite seem relevant to the OP's query...

 

[timetravel_0]

I was sitting around pondering all this, and was trying to understand how space(space-time) is warped/curved. I couldn't grasp it. However - I was thinking about how gravity effect time and the closer you are to the gravitational field, the slower time goes. Let me first state that my reasoning behind all this is that my mind for some reason wants to eliminate the idea that gravity curves space, or mass curves space, or whatever. I want to think of gravity as merely a force and its effect on time - not space. Maybe... I don't know yet. I'm still working through it all in my head. I was drawing up a diagram that shows how time(or space-time) is not curved, but rather a the frame is shortened when near a gravitational field.

[PLAIN]http://portal.nfitpros.com/time.png

Let me first say this example is highly exaggerated for simplicity. And probably wrong... I just think to much for my own good... but I thought I'd share my thoughts anyway. Feel free to comment and correct me. :)

In this example if two observers were in the "1sec/1000km" frame of space. Anywhere in that frame of space-time they both would agree(to some degree) on 1 second ticking on there watch. However, those in the "1sec/100,000km" would have a much wider space of agreement compared to those in the 1000km group. If the two groups were to compare times, the 1000km group's watches would have elapsed 10 times as much as the 100,000km group.

This example explains the bend in light around a gravitational field. Because light travels a constant distance over time, when it approaches a gravitational field it must curve its path to compensate for the lack of distance available in the time frame. Though this effect is very small, the view of space is slightly distorted from the POV from Earth than it is in deep space free from a gravitational field. Furthermore, if you were to venture into a black hole and look out into space, the closer you got to the singularity - the more stretched out space would look. It would almost be like looking through a telescope.

Ok... These are just my mental observations - I've never taken a class in physics or anything. I'm just some self-taught freak. Maybe the bending in light it caused by frame dragging... I don't know. Its late and I'm tired... So the floor is open to comment, criticize, and correct. I don't think I'm right... I just think to much.

 

[Passionflower]

I don't know yet. I'm still working through it all in my head. I was drawing up a diagram that shows how time(or space-time) is not curved, but rather a the frame is shortened when near a gravitational field.

That is pretty close to an example of curvature.

This example explains the bend in light around a gravitational field. Because light travels a constant distance over time, when it approaches a gravitational field it must curve its path to compensate for the lack of distance available in the time frame. Though this effect is very small, the view of space is slightly distorted from the POV from Earth than it is in deep space free from a gravitational field.

Again this is not very far from what actually happens in GR, however the space curvature is only half of the actual effect, the other half you could think of "regular gravity".

Ok... These are just my mental observations - I've never taken a class in physics or anything. I'm just some self-taught freak.

Kudos for your creativity and imagination.

However, if you really want to get ahead in understanding GR you need to get familiar with the mathematical language first. There were many very smart people before you who kind of figured it all out. As soon as you understand the mathematical language you know it as well. But, and this is not to discourage you from being creative and imaginative, don't try to reinvent the wheel.

 

[Phrak]

The "ball on the trampoline" picture can only represent the curvature of space, but to explain gravity requires the curvature of spacetime.

You might like to look at www.relativitet.se/spacetime1.html and see if that analogy makes more sense.

That's very clever. Is the surface a 3D embedment of time and radius? Apparently it is valid for radial trajectories without a circumferential component.

 

[DrGreg]

That's very clever. Is the surface a 3D embedment of time and radius? Apparently it is valid for radial trajectories without a circumferential component.

Correct.

Unfortunately we humans can only visualise three dimensions, so if we want to envisage a surface embedded in 3D space, the surface can only have two dimensions, in this case time and radius.

 

[Ich]

The motion of an upwards-thrown apple is determined by the shape of the spacetime together with the law of straight lines.

I don't like this description. Most of the motion is due to coordinate choice, which has generally nothing to do with the "shape of spacetime".
In this example, the embedding would correspond to a cone instead of an intrinsically curved surface. Of course, if one calls the extrinsic curvature of the embedding of the two dimensions the "shape of spacetime", everything is formally correct again. But misleading, IMHO.

 

[Geigerclick]

I still find the best way to understand gravity is through the SET. It tells you everything we really know about a given region, and the interaction of energy, momentum, mass and spacetime, and the feedback between them. Anything else is imagery that is approximate, and misleading.

 

[DrGreg]

I still find the best way to understand gravity is through the SET. It tells you everything we really know about a given region, and the interaction of energy, momentum, mass and spacetime, and the feedback between them. Anything else is imagery that is approximate, and misleading.

What is SET?

 

[Count Iblis]

Gravity is what you get if you demand covariance under general coordinate transformations.

 

[Geigerclick]

What is SET?

Stress Energy Tensor