What Is Einstein's Geometric Model of Gravitation?

[Seraph404]

I'm putting this here since I'm a high school student who has only completed two years (pre-AP and AP) of introductory physics. If it's misplaced, then I apologize for the inconvenience.

So, I've been reviewing for the upcoming AP test, and I just finished re-reading in my textbook the chapter on Gravitation. I noticed there's a portion we didn't cover in class: it involved Einstein's geometric model of gravitation. I read it and then looked for additional resouces on the Internet to help me understand it better, but everything I've found seems to say the same thing.

I read about Einstein's thought experiment on gravity and acceleration being one in the same and that this somehow lead him to conclude that gravity isn't really a force but a phenomenon caused by "curvature in the space-time continuum", which is total greek to me. Gravitation was never completely clear to me in the first place. We learned in school that Newton concluded the tendency of bodies to move toward each other, but we never discussed the reason for this "tendency". Basically, I can calculate the force of attraction between two bodies given a frame of reference, but I have no idea why this calculation works, much less Einstein's model.

When I first read about it, I thought curvature just meant the path an object travels due to gravitation; instead, from what I've read, curvature seems to replace Newton's idea of gravitation altogether with the notion that space is made of some kind of material with little paths along which bodies travel. I don't see how space can literally be a fabric or a material.

And then I read something about quantum gravity where atoms attract other atoms in the universe and how scientists don't understand this phenomenom. Why shouldn't this occur? I mean, what is it about the behavior of atoms that indicates they shouldn't exert an attractive force on other atoms?

I know I lack a great deal of foundation in this area of physics, but a concise explanation with simple diction and maybe even a couple links to some external references will go a long way with me.

 

[Mentz114]

Hi Seraph,
gravity is tough to understand. Newton's gravity is a straightforward potential theory - the force is the gradient of the potential. There is an implicit assumption in this theory that the gravitational source ( gravitational mass) is identical to the inertial mass ( resistance to acceleration). As to 'why' masses attract each other, we're no closer than Newton was to understanding that.
If you want to understand general relativity, you must get well acquainted with special relativity, where four-vectors are used to characterize states and motions. In SR you meet the concept of the metric, or line element. General relativity works by putting the gravity into the metric, and trajectories are calculated geometrically without resort to forces.

There are many resources on the web to study GR, but a decent introductory book is best.

M

 

[Bose]

Hello Seraph,

Einstein asked himself this question when he was 16 year old: "what happen if I chase a beam of light and catch up with it?" You should follow him instead of asking a lot of useless questions like the following:

We learned in school that Newton concluded the tendency of bodies to move toward each other, but we never discussed the reason for this "tendency". Basically, I can calculate the force of attraction between two bodies given a frame of reference, but I have no idea why this calculation works .

You can ask the same question why general relativity works?
No one knows why it works.

 

[matheinste]

Hello Seraph404.

There are no useless questions but many useless answers.

Natheinste.

 

[Bose]

Hello Seraph404.

There are no useless questions but many useless answers.

Natheinste.

That's right. Yours is definitely one of many useless answers

 

[Mentz114]

I said earlier -

Newton's gravity is a straightforward potential theory - the force is the gradient of the potential.

but it is not strictly true. Newton's gravity differs from EM theory in that it is the acceleration, not the force which is the gradient of the potential. Which is fairly important in understanding gravity.

 

[Usaf Moji]

Hi Seraph,

I don't think your question is useless...certainly, it isn't any more useless than the question Einstein asked himself when he was 16.

In my humble opinion, the best place to start learning about relativity is from Einstein's book, appropriately titled "Relativity". Ironically, it's easier to understand than most of the Coles Notes type of relativity books/papers. And since you'd be getting it straight from the horse's mouth (not to say that Einstein was a horse )), you'd be getting the most accurate version of it.

 

[Bose]

We learned in school that Newton concluded the tendency of bodies to move toward each other, but we never discussed the reason for this "tendency". Basically, I can calculate the force of attraction between two bodies given a frame of reference, but I have no idea why this calculation works.

I think it's fair to say that even Newton didn't know why his theory work. We now know the reason since it's a slow speed and low gravitation approximation of Einstein's relativity theory. But the next question is why Einstein's relativity theory works? This we don't know.
It's important to understand how it works and make prediction that match experiment

 

[jtbell]

We learned in school that Newton concluded the tendency of bodies to move toward each other, but we never discussed the reason for this "tendency". Basically, I can calculate the force of attraction between two bodies given a frame of reference, but I have no idea why this calculation works, much less Einstein's model.

Every single theory in physics, no matter how successful, has something "unexplained" at its root, that we have to take as postulates that are simply "given." Sometimes we come up with a new theory that "explains" an older theory, (as Einstein's general relativity "explains" and improves on Newtonian gravity) but the new theory itself always starts with new postulates...

 

[Seraph404]

Hm, I see. What's wrong with "atomic" or quantum gravitation? What makes the small any different from the large?

Also, I've been watching clips on youtube about curvature, and I've found that the example with the sun suddenly not existing really helped me understand an aspect of the flaw in Newton's theory.

Still, I don't understand the flexible grid used to represent curvature in space. Is it just a coordinate system where you can plot points, or what? I mean, in pre-cal last year, we did some plotting in three demesions. Is it just another system like that with one more dimension? And how does it expand and contract like a trampoline? I'm told that it does, but I don't understand if they're being literal or just using a fancy metaphor to replace a chalkboard of math. It's really hard for me to think of time and space as a substance.

Thank you all for the positive feedback. I guess it would be a good idea to check out Einstein's books. I probably won't understand any of it though; however I think the more math I take, the more this stuff will make sense to me. I can't see how physics works without the math. I mean, I'm not very intuitive.

By the way, do normal colleges offer this kind of stuff or would you have to go to a fancy school like MIT? What are the course names I should look for?

 

[Usaf Moji]

It's really hard for me to think of time and space as a substance.

In the preface of Einstein's book, Relativity, Einstein wrote (this isn't an exact quote, I'm just paraphrasing) that there is no such thing as empty spacetime - rather, objects extend along the dimensions of space and time. In this sense, spacetime isn't a substance, it's just an intrinsic property of matter/energy.

 

[Bose]

Hm, I see. What's wrong with "atomic" or quantum gravitation? What makes the small any different from the large?

Also, I've been watching clips on youtube about curvature, and I've found that the example with the sun suddenly not existing really helped me understand an aspect of the flaw in Newton's theory.

Still, I don't understand the flexible grid used to represent curvature in space. Is it just a coordinate system where you can plot points, or what? I mean, in pre-cal last year, we did some plotting in three demesions. Is it just another system like that with one more dimension? And how does it expand and contract like a trampoline? I'm told that it does, but I don't understand if they're being literal or just using a fancy metaphor to replace a chalkboard of math. It's really hard for me to think of time and space as a substance.

Thank you all for the positive feedback. I guess it would be a good idea to check out Einstein's books. I probably won't understand any of it though; however I think the more math I take, the more this stuff will make sense to me. I can't see how physics works without the math. I mean, I'm not very intuitive.

By the way, do normal colleges offer this kind of stuff or would you have to go to a fancy school like MIT? What are the course names I should look for?

Here's a very popular book by Schutz: Gravity from the Ground Up
An accessible introduction to astronomy and general relativity, requiring only high-school level mathematics.

http://books.google.com/books?id=jR3S1ValtgYC&printsec=frontcover

 

[Mentz114]

Seraph,

And how does it expand and contract like a trampoline? I'm told that it does, but I don't understand if they're being literal or just using a fancy metaphor to replace a chalkboard of math.

It is a bad metaphor, you're right about that. The 'curvature' in GR is intrinsic, and is defined by derivatives of the metric coefficients.

 

[Bose]

Still, I don't understand the flexible grid used to represent curvature in space.

Now, it's very important to realize that it's the curvature in time, not the curvature in space, that cause gravity. In the solar system, the curvature in space is very small, that's why it takes 100 year's observation to notice something wrong with Mercury's orbit.

As Schutz indicates in his book: Gravity from the Ground Up
"All of Newtonian gravity is simply the curvature of time"

http://books.google.com/books?id=jR...g=5TKhI47cSM3Qgo-u-jzOIDnWvlc&hl=en#PPA232,M1

 

[pmb_phy]

I read about Einstein's thought experiment on gravity and acceleration being one in the same and that this somehow lead him to conclude that gravity isn't really a force but a phenomenon caused by "curvature in the space-time continuum", which is total greek to me.

I can tell you this; that idea didn't come from Einstein. It seems to have originated with Max Von Laue. Einstein never intended the gravitational force to be viewed as a so-called "pseudo-force" but that those "pseudo-force"s should be considered as "real" as the gravitational force. And Einstein never definded gravity such that it was a curvature in spacetime. Only tidal forces are related to spacetime curvature and tidal forces are not the same thing as gravitational forces. They are defined differently and you can have non-zero gravitational forces in the absense of spacetime curvature.

Gravitation was never completely clear to me in the first place. We learned in school that Newton concluded the tendency of bodies to move toward each other, but we never discussed the reason for this "tendency".

To be precise Newton's gravity represents the tendency of particles with non-zero mass to accelerate towards each other. Objects can move toward each other in the absence of all forces.

Basically, I can calculate the force of attraction between two bodies given a frame of reference, but I have no idea why this calculation works, much less Einstein's model.

Neither Newtonian nor Einstein's theories of gravity can explain "why" there is an attraction. All they are able to do is to describe the phenomena, each in different ways, General Relativity being the more accurate theory.

When I first read about it, I thought curvature just meant the path an object travels due to gravitation; ...

Actually Einstein used the term "curvature" in his first book on relativity to mean exactly that.

instead, from what I've read, curvature seems to replace Newton's idea of gravitation altogether with the notion that space is made of some kind of material with little paths along which bodies travel. I don't see how space can literally be a fabric or a material.

Its a mistake to think of space as being made of a material. That would represent a misinterpretation of general relativity and curved spacetime. Spacetime curvature is more of a mathematical thing than it is a physical thing. The reason for this is that the mathematical representation has a geometrical analogy with the curved surfaces that we are familiar with.

And then I read something about quantum gravity ..

Since there is no universally accepted theory of quantum gravity I recommend that you

I know I lack a great deal of foundation in this area of physics, but a concise explanaton with simple diction and maybe even a couple links to some external references will go a long way with me.

I'll send you some references in PM so check your PM when you have a chance. I'll try to get to it later tonight.

Best wishes

Pete