General Relativity Theory

[Incendia]

I have recently has a thought but it might just be a highly simplified version of general relativity...Please explain GR to me without equations in the simplest way possible. A basic summary for it.

And don't use this diagram:

 

 

It makes no sense. Reasons why this diagram is misleading:

1. For it to make an indentation there would have to be something like gravity pulling the sphere down. There isn't as that would mean the entire universe would keep moving down until it hit whatever is the source. An effect like this would surely be visible or traceable in the movement of the stars and planets.

2. The sheet is space-time if I understand correctly. If distortions like that in space-time happen then it would mean the universe would have to be flat and level. This is clearly not the case. Why would it have to be level? In order to reach stars higher up then others space-time would have to curve for no apparent reason to reach them.

3. People and objects on the top part of the sphere would be free of time and space. Space-time is 4 or more dimensional so this makes no sense.

[How has no one noticed or spoke out about these problems in the diagram before?]

There may be more problems I haven't found but I know that this diagram is a wrong way to look at the universe and at space-time.

So...Thank-you for reading and thank-you again if you explain general relativity to me in a way that makes sense.

[ydoaPs]

Space and time are two very similar and connected ideas. Think of a state as a snapshot of the universe. Distance(space) is the separation of objects within a state. Duration(time) is the separation between states themselves. The magnitude of distance and duration are relative to your frame of reference and depend upon the energy density in that frame of reference.

[Incendia]

Thank-you...Now i'm pretty sure my thought is not general relativity...but if your explanation is true then where did that diagram come from? There doesn't seem to be a connection...

Also where did people get: Time slows down near high gravity: from it? Either I don't understand or your not correct or...

[ydoaPs]

The diagram is an attempt to show that energy alters the magnitude of distance. As for time 'slowing down', that is just saying that gravity alters the magnitude of duration.

[swansont]

The diagram shows one "plane" of the geometry, much like a typical graph only shows you the xy plane and ignores z. There's nothing special about the orientation, so there is no "level" or "higher up" or "top of the sphere" to worry about here — you are only looking at what happens to a single plane. The rubber sheet analogy is exactly that — an analogy. It's not the actual theory, so when you worry that gravity has to be present for this to work, you are taking the analogy too far: the effect is the same, not the cause. You aren't the first to run into these issues of interpretation.

 

In short: spacetime gets distorted when mass and/or energy are around. What we would normally think of as a plane has a different geometry to it. What's more, if we are in that geometry, we won't notice. What we think of as a straight line would be curved if viewed by someone who used a Cartesian geometry.

[Equilibrium]

The diagram isn't perfect because it's impossible for it to be shown in 4d because our eyes and mind can't perceive that. I think the diagrams ( i have seen tons of these) are just trying to represent how the indent or stretching of time and space creates gravity

[md65536]

Thank-you...Now i'm pretty sure my thought is not general relativity...but if your explanation is true then where did that diagram come from? There doesn't seem to be a connection...

Also where did people get: Time slows down near high gravity: from it? Either I don't understand or your not correct or...

Here's an example of how you can visualize time slowing down, using the diagram.

 

Imagine 2 trains traveling at the same speed on 2 different lines on the drawing, one which is curved more than the other. The train on the curved path will appear to take longer because on the drawing it has longer lines to travel along.

 

However, these lines represent straight lines in space, so (assuming no acceleration of the trains due to gravity) the train on the "curved" path in the drawing would appear to be moving slower across the same distance as the other train.

 

 

Similarly you can imagine a train spanning the long curve underneath that orange ball in the picture. Then picture that curve and the train mapped vertically onto a straight line, and it will be shorter than the curved train. This illustrates length contraction.

 

 

Yes, this diagram is not perfect and probably only makes sense if you already understand some basics of GR. The picture doesn't teach GR. One problem is that the vertical dimension (time?) doesn't represent the same thing as the horizontal dimensions (space), so the diagram illustrates a concept, not a visual observation.

Edited October 28, 2010 by md65536

[Incendia]

The magnitude of distance and duration are relative to your frame of reference and depend upon the energy density in that frame of reference.

 

What do you mean by frame of reference...

[ajb]

Please explain GR to me without equations in the simplest way possible. A basic summary for it.

 

Let me use "pseudoequations ".

 

General relativity says

 

[math]G = T[/math],

 

that is on the left we have the local geometry of spacetime and on the right we have the matter and fields (not the gravitational field) on spacetime. You should think of "G" as some measure of the curvature of the spacetime, which is a way of measuring how different it is from Minkowski spacetime.

 

 

If the spacetime contains no matter or fields then the spacetime is "Ricci flat", which is a looser measure of curvature that "G". Spacetimes can be Ricci flat and not Minkowski. So even with no matter or fields we can have non-trivial geometry.

 

What you want to understand is what is meant by curvature. The best place to start is in 2 dimensions. Why is the plane said to be flat? Why is the sphere said to be curved? What about a cylinder?

 

To understand this you need the notion of vectors and parallel transport. We can think of vectors as little arrows attached to a point on the surface. Parallel transport means move the vector along a path keeping the vector pointing in the same direction. That is you don't want to introduce any redirection of the vector other than that due to the path.

 

Now, take a vector and parallel transport it along a closed path. The angular difference in the original vector and the parallel transported vector is a measure of curvature.

 

So now do some "practical mathematics". Take a sheet of paper draw a simple closed path. Use your pencil as the vector. Carefully parallel transport it along this path, keep the paper flat. You will see that the pencil is in exactly the same position as when it started.

 

Now try the surface of a ball or balloon. You should see that the vector is rotated by 90 degrees.

 

For fun try it on the surface of a cylinder. This can also be thought of as a torus if we identify the ends. For example, try the cardboard in side a toilet roll.

 

In all the above examples the "spacetimes" are of constant curvature, that is they do not vary from point to point. However, this need not be the case and then one needs to think about the curvature as depending on the points.

 

In higher dimensions it takes a bit more work that this. However the basic idea is the same.

Edited October 28, 2010 by ajb

[Incendia]

Yes I understand the curvature of space-time part, But that isn't all of it is it? ydoaPs posted that space-time was relative to your frame of reference and depended on the energy density of that frame of reference...What does he mean by frame of reference?

[ajb]

What does he mean by frame of reference?

 

A choice of local coordinates.

Edited October 28, 2010 by ajb

[Incendia]

So space-time is relative to where you are and the energy density of that place?

[swansont]

So space-time is relative to where you are and the energy density of that place?

 

Yes.

[ajb]

So space-time is relative to where you are and the energy density of that place?

 

 

I am not sure exactly what you mean by this.

 

Anyway, the details of things will depend on where you are and how you choose the coordinates employed.

 

Technically this is where tensors come in to play. At a given point, any expression involving just tensors* will have the same form independent of the coordinates employed. Although the expressions themselves will be different in different coordinates they have a very nice transformation rule.

 

It is important to realise that the tensors themselves will depend on the choice of coordinate. Thus, they cannot have any real deep intrinsic meaning. One is more interested objects that do not depend on the choice of coordinates: the scalars.

 

This is vital when trying to understand curvature. Tensors that measure the curvature depend on the coordinates, scalar curvatures are independent of this and give an absolute measure of curvature. This is important when thinking about curvature singularities, for example.

 

* In more modern language I mean components of a tensor.

Edited October 28, 2010 by ajb

[Incendia]

I am not sure exactly what you mean by this.

 

Anyway, the details of things will depend on where you are and how you choose the coordinates employed.

 

Technically this is where tensors come in to play. At a given point, any expression involving just tensors* will have the same form independent of the coordinates employed. Although the expressions themselves will be different in different coordinates they have a very nice transformation rule.

 

It is important to realise that the tensors themselves will depend on the choice of coordinate. Thus, they cannot have any real deep intrinsic meaning. One is more interested objects that do not depend on the choice of coordinates: the scalars.

 

This is vital when trying to understand curvature. Tensors that measure the curvature depend on the coordinates, scalar curvatures are independent of this and give an absolute measure of curvature. This is important when thinking about curvature singularities, for example.

 

* In more modern language I mean components of a tensor.

 

 

I was happy with swansont's yes...

 

 

[between3and26characterslon]

I have recently has a thought but it might just be a highly simplified version of general relativity...Please explain GR to me without equations in the simplest way possible. A basic summary for it.

And don't use this diagram:

 

 

It makes no sense. Reasons why this diagram is misleading:

1. For it to make an indentation there would have to be something like gravity pulling the sphere down. There isn't as that would mean the entire universe would keep moving down until it hit whatever is the source. An effect like this would surely be visible or traceable in the movement of the stars and planets.

2. The sheet is space-time if I understand correctly. If distortions like that in space-time happen then it would mean the universe would have to be flat and level. This is clearly not the case. Why would it have to be level? In order to reach stars higher up then others space-time would have to curve for no apparent reason to reach them.

3. People and objects on the top part of the sphere would be free of time and space. Space-time is 4 or more dimensional so this makes no sense.

[How has no one noticed or spoke out about these problems in the diagram before?]

There may be more problems I haven't found but I know that this diagram is a wrong way to look at the universe and at space-time.

So...Thank-you for reading and thank-you again if you explain general relativity to me in a way that makes sense.

 

 

Frames of reference;

 

If you're on a train are you moving or not? If the train was running on perfectly flat and smooth rails, was not accelerating or braking, was not turning and the windows were covered you would not know you were moving. If you put something on the table in front of you it would stay there and not move even though the train is speeding along the tracks so this object is moving relative to the ground outside but stationary relative to the train.

 

The ground outside is one frame of refference and inside the train is another frame of refference so when you talk about the velocity of an object you have to relate it to a frame of refference.

 

A frame of refference is an imaginary grid consisting of x, y and z coordinates which you use to describe the motion of objects.

 

That Diagram;

 

Imagine you are in a box floating in space so there is no gravity, if you are either not moving, or moving at constant speed in a straight line you will float freely in this box and have no concept of up or down. If there was a tiny hole in this box (you're in a space suit) with a lazer shining through it the laser light would describe a straight line to the other side of the box.

 

Rule 1; light travells in straight lines

 

If a space ship came along an gave this box a shove it would accelerate momentarily and then reach a constant speed again. You inside the box would see one of the sides approaching and you would bump into it. It would in turn shove you and so now you have the same speed as the box again and are back to floating around inside it.

 

If the space ship were to hook up to the box and give it a tow and accelerate at a constant rate one of the sides of the box would come up to meet you but his time you would feel it constantly pushing you and you would be able to stand up on what you might now consider the floor.

 

Rule 2; being stationary in a gravitational field or being in an accelerating box are the same thing.

 

If a laser were to shine through the tiny hole in an accelerating box the light would describe not a straight line but a curve accross the box before hitting the other side.

 

So now we have a conflict light travels in straigt lines but gravity bends it even though light does not have mass so gravity can not bend it.

 

The Answer;

 

Light travels in straight lines relative to spacetime, gravity bends spacetime and therefore light appears to bend. The diagram shows how mass warps spacetime and how it would affect the trajectory of anything passing through it. It's a 2d plane of a 3d distortion in 4d space, it's a bit like taking a cross section so you can see what's going on.

 

 

no equations and the simplest way I can

[Incendia]

So the final answer is: Space-time is relative to an area and the energy density of that area. Gravity bends space-time and appears to bend light but light in fact travels in straight lines relative to space-time. Is that all? Yes. Good. A moderator can lock this or this thread can be left alone or can be stickied/pinned as a reference to other who want to learn what it is.

[ydoaPs]

What do you mean by frame of reference...

As ajb said, a frame of reference is a choice of local co-ordinates. I'll demonstrate with an example that should give an idea of what frame of reference means and that show that energy is relative to the frame of reference.

 

Imagine a universe in which all that exists are three balls(one red, one blue, and one yellow). Each ball has a mass of 1kg. The red and blue balls are at rest with respect to each other, but are moving with respect to the yellow ball. From a reference frame in which the yellow ball is at rest, the red ball and the blue ball are moving at 100m/s and thus have kinetic energy. Now, let's move our reference frame to one in which the blue ball is at rest. The red ball is at rest relative to the blue ball, so has no kinetic energy(and neither does the blue ball). The yellow ball, however, is moving at 100 m/s and thus has kinetic energy. The red ball has more energy in the reference frame of the yellow ball than it does in the reference frame of the blue ball.

 

One reference frame thus has KE of 100J while the other has KE of 200J. Which is correct? Both. Energy is dependent on the reference frame and is not invariant between frames.

[Incendia]

So it depends on where your looking from?

 

I'm only just starting my first GCSEs, I doubt I should know this or have to know this...I am merely interested so excuse me for not really understanding that well...

So is this right: [The bracketed may not be necessary...point out if it is: The amount of] space-time is relative to where you are looking from and the energy density of where you are looking from. Gravity bends space-time causing light to appear curved by the light is travelling in straight lines relative to space-time.

[Myuncle]

Now after this thread you will be under the illusion that GR makes sense, but 10 years later you will understand that you were just fooling yourself...

[ydoaPs]

Now after this thread you will be under the illusion that GR makes sense, but 10 years later you will understand that you were just fooling yourself...

o.O

[IM Egdall]

I find the explanation in Nigel Caulder's book, Einstein's Universe helpful in explaining how general relativity works. Maybe it is a simplification, but I think it gives a real feeling for the concept. Take an apple falling towards the surface of the Earth for example.

 

The Earth's mass/energy causes the space around it to stretch (iin the radial direction). And this stretching gets greater and greater as the apple approaches the ground. The apple just released from a tree moves in the direct of stretching space.

 

Now the Earth's mass/energy also affects time. It makes time run slower and slower as the apple approaches the ground. This means that (from the point of view or reference frame of a far away observer) a clock will run slower and slower the closer it gets to the Earth. So as the apple moves ,all its atoms and molecules slow down more and more. To make up for this reduced internal energy of motion, the apple accelerates. In other words, it goes faster and faster towards the ground so its overall energy of motion makes up for this reduced internal energy of motion. In this way, the law of energy conservation is maintained.

 

In summary:

 

- an apple falls towards the ground (rather than upward or sideways or in other direction) because of the stretching of space as it approaches the ground; and

- the apple accelerates as it moves downward due to the slowing of time and to obey conservation of energy.

Edited October 29, 2010 by I ME

[swansont]

 

Now the Earth's mass/energy also affects time. It makes time run slower and slower as the apple approaches the ground. This means that (from the point of view or reference frame of a far away observer) a clock will run slower and slower the closer it gets to the Earth. So as the apple moves ,all its atoms and molecules slow down more and more. To make up for this reduced internal energy of motion, the apple accelerates. In other words, it goes faster and faster towards the ground so its overall energy of motion makes up for this reduced internal energy of motion. In this way, the law of energy conservation is maintained.

 

 

Near the earth's surface, the slowing of time is given by gh/c^2, while the change in energy is mgh. How do you equate the two?

[IM Egdall]

Near the earth's surface, the slowing of time is given by gh/c^2, while the change in energy is mgh. How do you equate the two?

 

Good question! I looked up the reference again (Nigel Caulder, Einstein's Universe, p. 82-83.) and it says:

 

"Atoms, atomic clocks and light all vibrate slowly in regions of stronger gravity. Because of the link between energy and frequency, they possess less energy than they would in space, a long way from the source of gravity. An apple consists of atoms and possesses less energy when lying on the ground than it has when on the tree. Its rest-energy, in the sense of Einstein's equation E = mc^2 is reduced."

 

Caulder points out that the quantity which remains unchanged in general relativity is actually "the scalar product of the tangent vector with the Killing vector".

 

So I took E=mc^2 and tried to apply it to your question.

 

Let E be the rest energy

 

Rearranging E=mc^2, we get m = E/c^2.

 

As you note, the change in energy near the earth's surface is mgh

 

So substituting gives mgh = E/c^2 gh = Egh / c^2

 

As you also note, the slowing of time near the earth's surface is this same gh/c^2 factor.

 

Is it this simple?

[ydoaPs]

Let E be the rest energy

 

Rearranging E=mc^2, we get m = E/c^2.

 

As you note, the change in energy near the earth's surface is mgh

 

So substituting gives mgh = E/c^2 gh = Egh / c^2

 

As you also note, the slowing of time near the earth's surface is this same gh/c^2 factor.

 

Is it this simple?

Egh/c^2≠gh/c^2

 

Also, E²=(mc²)²+(pc)²

 

E=mc² is a special case in which the system being studied is at rest with respect to your chosen reference frame.