Help with GR

UrbanXrisis

So I'm reading this book on GR and I really dont understand the concept that gravity is not a force. If gravity is not a force, what's keeping us stuck to the earth? I understand that gravity warps the fabric of space but I cant transfer that thought to how warping spacetime keeps us on the ground.

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Ratzinger

in my humble, non-expert opinon it's like that

You are falling (like free-falling, like there is no gravity, remember equivalence principle) along a spacetime geodice formed by gravity and then you encounter forces (electromagnetic to be precise) when you hit the ground. When you jump and fall that's due to curved spacetime (the falling). You're falling along curved spacetime everytime.

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pervect

Staff Emeritus
UrbanXrisis said:
So I'm reading this book on GR and I really dont understand the concept that gravity is not a force. If gravity is not a force, what's keeping us stuck to the earth? I understand that gravity warps the fabric of space but I cant transfer that thought to how warping spacetime keeps us on the ground.
Does your book talk about geodesic deviation? That's really the key. Look at response # 10 in

for instance

Ratzinger

Einstein's happiest thought

in my humble, non-expert opinion, the key in understanding GR is the equivalence principle.. if you have a firm grasp of that, your problem is solved..and the good thing is you need no higher math (just like Einstein when he came up with it)

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pervect

Staff Emeritus
Ratzinger said:
in my humble, non-expert opinion, the key in understanding GR is the equivalence principle.. if you have a firm grasp of that, your problem is solved..and the good thing is you need no higher math (just like Einstein when he came up with it)
While the equivalence principle is certainly extremely important in GR, it doesn't really explain why curved space-time is equivalent to a force.
Geodesic deviation does explain why curved space-time acts like a force. There are both mathematical and non-mathematical treatments of the topic, though unfortunately I can't recommend a specific non-mathematical treatment. (I really wish I had one that I could recommend).

In the thread I cited, though, "Dodo" clearly got the point in response number 10 (without being an expert in the topic or using any math). Because of this I think his explanation should be quite accessible to other readers - and it's very short, though it may take a little bit of thought to follow.

The key point is that it is not space that is curved (as in many popular illustrations) - it is space-time that is curved.

I would suggest that this is a very good keyword / key concept for anyone interested in the topic of why curvature looks like a force to read up on.

hellfire

pervect said:
While the equivalence principle is certainly extremely important in GR, it doesn't really explain why curved space-time is equivalent to a force.
Geodesic deviation does explain why curved space-time acts like a force.
But the equivalence principle is a necessary condition for that, as you have to specify that particles on spacetime follow geodesics. Then, geodesic deviation will have an effect on them and will act as a force. Correct?

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Zanket

UrbanXrisis said:
So I'm reading this book on GR and I really dont understand the concept that gravity is not a force. If gravity is not a force, what's keeping us stuck to the earth?
A force pushes you in a way that you can feel. The push you now feel on your rump is not from gravity per se, but from a resistance to gravity. The force you feel is the electromagnetic force, from the Earth pushing upward to resist being squeezed to a point by gravity. Think of gravity as accelerating space. It accelerates toward centers of gravity. Because space itself is accelerating, when you fall you feel no force; you are carried along with the space.

UrbanXrisis

what is the difference between curved space and curved spacetime?

Zanket

Semantics, I'd say, given how many books seem to use "space" and "spacetime" interchangeably. As far as I can tell, "spacetime" is used to emphasize the interrelated nature of space and time. "Curved space" is technically incorrect terminology I think. "Curved spacetime" is synonymous with a nonuniform gravitational field. Someone else can probably answer better.

pervect

Staff Emeritus
hellfire said:
But the equivalence principle is a necessary condition for that, as you have to specify that particles on spacetime follow geodesics. Then, geodesic deviation will have an effect on them and will act as a force. Correct?
Yes, you definitely need to know that particles on space-time experiencing only gravitational forces follow geodesics to follow the argument. You also need the equivalence principle to convert geodesic deviation into an equivalent force.

dextercioby

Homework Helper
There's a wonderful chaper on geodesic deviation both in Newtonian physics & in GR in d'Inverno's book.I think he's inspired himself from MTW,like many others,actually.

Daniel.

pervect

Staff Emeritus
UrbanXrisis said:
what is the difference between curved space and curved spacetime?
Imagine that you draw a plot of position vs time on a sheet of paper. This is gvien the name a "space-time diagram".

Now, we usually draw space-time diagrams on a flat sheet of paper. This is called "flat-spacetime".

We can, however, envision what happens if we drew space-time diagrams on a curved piece of paper. One way of envisioning curvature is to use the 2-d surface of a 3-d object, so we can imagine drawing our space-time diagrams on the surface of a sphere.

We can only actually do this physically for the simplest case, which is one space dimension and one time dimension. This gives us a two dimensional plot which we can then draw on the 2-dimensional surface of the sphere.

This may seem like a totally crazy idea, but when you follow through with it, you see that the result of drawing your space-time diagrams on a curved surface is that objects act like they have forces acting on them - they act just like they are being attracted by gravity.

On a flat sheet of paper, two people starting out with different velocities always move away from each other, getting further and further apart with time.

Exercise: draw the space-time diagram of two people with different velocities. (It's too hard to do it in ascii).

Now imagine drawing the same diagram on the surface of a sphere. Remember that "straight lines" on the surface of a sphere, geodesics, are "great circles".

(A diagram would be great here, wouldn't it? Too hard in ascii, though).

If you follow dodo's example in the link I mentioned above, a person following a "straight line" would follow a line of longitude on the sphere, starting (say) at the south pole and moving north.

Now we see an interesting result - two obsrevers, that start with the same velocity, do not continue to separate. They reach a maximum distance, and then start approaching each other!

It is very much as if the two obsevers were experiencing an attractive force. This idea, of geodesic deviation, shows how curvature can cause something that acts like a force.

Note that it's not just space that's curved. We've plotted a space-time diagram on a curved sheet of paper, so we say that space-time is curved.

UrbanXrisis

I understand this but I dont see where time comes into this. If space itself was curved as a sphere, wouldn't the two observers meet at the north pole as well?

pervect

Staff Emeritus
UrbanXrisis said:
I understand this but I dont see where time comes into this. If space itself was curved as a sphere, wouldn't the two observers meet at the north pole as well?
Yes, they would. But they wouldn't be tempted to explain their meeting by invoking an unseen force, it would be obvious to them that it was due to geometry.

Spatial curvature does exist, and it does cause the same effect of geodesic deviation. However, the geometry of space would have to be highly and obviously distorted for an object like the Earth to have a nearly circular orbit as its geodesic.

We do observe a very small amount of spatial distortion (which is why the length of the meter is different in outer space than it is on the surface of the Earth), but the pure spatial curvature terms are nowhere near large enough to cause the Earth's motion around the sun. The space-time curvature effects are highly dominant over the pure spatial curvature effects.

For objects moving at a very high velocity, the curvature of space *can* be important to it's total geodesic deviation. For instance, the pure spatial curvature effects explains why the deflection of light from a distant object in GR is twice as large as it is in Newtonian theory.

Anyway, if you look at Newtonian theory, that tries to explain everything with forces, it can't explain why space becomes warped near large masses (not a major effect, but noticable).

When you look at gravity as a curvature of space-time, you get the Newtonian gravity from the time-time component of the curvature, and you get the space warping effects as well. So the GR approach to gravity as a curvature of space-time it wraps up all the phenomena you need to explain in one nice, neat consistent package.

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UrbanXrisis

I guess what is really confusing to me is the difference between space and spacetime.

pervect said:
Imagine that you draw a plot of position vs time on a sheet of paper. This is gvien the name a "space-time diagram".

Now, we usually draw space-time diagrams on a flat sheet of paper. This is called "flat-spacetime".

We can, however, envision what happens if we drew space-time diagrams on a curved piece of paper. One way of envisioning curvature is to use the 2-d surface of a 3-d object, so we can imagine drawing our space-time diagrams on the surface of a sphere.

We can only actually do this physically for the simplest case, which is one space dimension and one time dimension. This gives us a two dimensional plot which we can then draw on the 2-dimensional surface of the sphere.

This may seem like a totally crazy idea, but when you follow through with it, you see that the result of drawing your space-time diagrams on a curved surface is that objects act like they have forces acting on them - they act just like they are being attracted by gravity.

On a flat sheet of paper, two people starting out with different velocities always move away from each other, getting further and further apart with time.

Exercise: draw the space-time diagram of two people with different velocities. (It's too hard to do it in ascii).

Now imagine drawing the same diagram on the surface of a sphere. Remember that "straight lines" on the surface of a sphere, geodesics, are "great circles".

(A diagram would be great here, wouldn't it? Too hard in ascii, though).

If you follow dodo's example in the link I mentioned above, a person following a "straight line" would follow a line of longitude on the sphere, starting (say) at the south pole and moving north.

Now we see an interesting result - two obsrevers, that start with the same velocity, do not continue to separate. They reach a maximum distance, and then start approaching each other!

It is very much as if the two obsevers were experiencing an attractive force. This idea, of geodesic deviation, shows how curvature can cause something that acts like a force.

Note that it's not just space that's curved. We've plotted a space-time diagram on a curved sheet of paper, so we say that space-time is curved.
This to me sounds like a description of curving space. I dont think I get the description of what is meant by saying spacetime.

pervect

Staff Emeritus
UrbanXrisis said:
I guess what is really confusing to me is the difference between space and spacetime.

This to me sounds like a description of curving space. I dont think I get the description of what is meant by saying spacetime.
If you can envision curving time directly, more power to you. What I am describing is a process whereby you first visualize time as a spatial dimension because you are plot space-vs time on a graph, and then you imagine putting this graph on a spatially curved surface. This is a visual aid, basically.

Also not that curvature is a rather interesting phenomena, in that you can't really have a curved line. (You can imagine drawing a curved line on a plane, but the inhabitants of any point on the line don't know that it's curved and don't care - it has no intrinsic curvature). You need at least two dimensions before you can have intrinsic curvature at all.

Thus the simplest example of curved space-time is one space and one time dimension - you can't have a curved time dimension by itself, this makes no more sense than the curved line did.

It's possible to treat the curvature entirely mathematically, in fact that's how it's actually done.

One point I haven't mentioned specifically is how the concept of space-time came about. It came about when people noticed that an interval between two points that was a purely spatial separation according to one observer becomes an interval that is separated in both space and time according to another observer. Thus space and time can "mix together" as one viewpoint changes. This means that they have to be treated as a unified entity, not as two separate quantities.

UrbanXrisis

pervect said:
If you can envision curving time directly, more power to you. What I am describing is a process whereby you first visualize time as a spatial dimension because you are plot space-vs time on a graph, and then you imagine putting this graph on a spatially curved surface. This is a visual aid, basically.
Are you saying that on this http://home.earthlink.net/~urban-xrisis/phy003.jpg [Broken], an object moves along this graph means that they are moving thought time and space? So to represent this means that you need to plot both time and space on the graph right?

pervect said:
It came about when people noticed that an interval between two points that was a purely spatial separation according to one observer becomes an interval that is separated in both space and time according to another observer. Thus space and time can "mix together" as one viewpoint changes. This means that they have to be treated as a unified entity, not as two separate quantities.
Are you saying that an object cant just travel just thought time, or just thought space but need to be seen as both spacetime? Hence, the space vs time graph cant be drawn as a space vs space graph.

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pervect

Staff Emeritus
UrbanXrisis said:
Are you saying that on this http://home.earthlink.net/~urban-xrisis/phy003.jpg [Broken], an object moves along this graph means that they are moving thought time and space? So to represent this means that you need to plot both time and space on the graph right?
A line on the graph represents the motion of a specific object - a line with a constant position coordinate indicates an object that is not moving, for example.

Are you saying that an object cant just travel just thought time, or just thought space but need to be seen as both spacetime? Hence, the space vs time graph cant be drawn as a space vs space graph.
I'm saying a couple of things. The first thing I'm saying is that simultaneity is relative. Two points which occur "at the same time" according to one observer do not occur "at the same time" according to another, moving observer.

This comes from special relativity - it shows up when we figure out how to draw a space-time graph from a different perspective. One can say that thiis shows up when we figure out how a space-time diagram transforms under a change in observer.

The mathematical name for the transform used is the "Lorentz transform", this described how a space-time graph is transformed from a stationary observer to a moving one.

The second thing I'm saying is a conseqeunce of the first. This is that because time and space can mix together, we cannot rigidly separate time from space. Time and space can inter-convert under some circumstances, strange as this may seem. Again, this comes from special relativity, not general relativity.

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pmb_phy

UrbanXrisis said:
So I'm reading this book on GR and I really dont understand the concept that gravity is not a force. If gravity is not a force, what's keeping us stuck to the earth? I understand that gravity warps the fabric of space but I cant transfer that thought to how warping spacetime keeps us on the ground.

There are forces of two main types amd those two;

They are
(1) Strong force
(2) Weak force
(3) electric force
(4) gravitational force
(5)

I forgot the last one - the paricles ae overest.

Pete

UrbanXrisis

pmb_phy said:

There are forces of two main types amd those two;

They are
(1) Strong force
(2) Weak force
(3) electric force
(4) gravitational force
(5)

I forgot the last one - the paricles ae overest.

Pete
well... why does my book claim that gravity is not necessarily a force? Such as geodesic deviation as pervect pointed out?

and why is there a 5th force? I thought that scientists never could verify it thought multiple experiments

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