Theory of Gravitation

[skyfrog]

I have a huge book called "Gravitation" written by MISNER, THORNE and WHEELER, it seems that in this book English is not the major languange, math is.

I wonder if anybody have read this book, and if they could show me how to read it. I know it is silly question, but it is so thick I want to go through it quickly, no much time for this.

Okay, I know I started another cold topic, but Forrest are you interested ? In this forum you seem to be the only one who like math.

[WebPilot]

I have a huge book called "Gravitation" written by MISNER, THORNE and WHEELER, it seems that in this book English is not the major languange, math is.

I wonder if anybody have read this book, and if they could show me how to read it. I know it is silly question, but it is so thick I want to go through it quickly, no much time for this.

Okay, I know I started another cold topic, but Forrest are you interested ? In this forum you seem to be the only one who like math.

Hi Horace!

I never read the book, but the name, Misner, rings a bell.

Mathematics, after the hurdle of flash cards, always came easy to me. I guess it is because I have an abstract mind; I think in symbols. I at one time entertained the idea of becoming a physicist, but settled for engineering, instead.

Anyway, that's neither here nor there. Can you post some pics of the mathematics on the pages? Perhaps, I can identify it.

I hope it's not in tensor analysis.

-fde

PS Earlier this spring at a flea market, I picked up some interesting physics books. One was a 1st edition, 1962, by George Gamow (everybody knows him, right?) entitled, "Gravity". Cool book.

[skyfrog]

Hi Forrest,

Some PDEs and tensor

For example this Einstein curvature tensor

[WebPilot]

Hi Horace,

Yepper, my fears have materialized.

From:
http://mathworld.wolfram.com/Tensor.html

Tensors provide a natural and concise mathematical framework for formulating and solving problems in areas of physics such as elasticity, fluid mechanics, and general relativity.

So, whatever time you spend on learning this view of gravitation, you'll be able to read higher level books in fluid mechanics.

R. A. Sharipov wrote a 47 page textbook (it was preparing his undergrads for work in electromagnetism)
A Quick Introduction to Tensor Analysis
a pdf version can be downloaded here:
http://uk.arxiv.org/pdf/math.HO/0403252

His website is here:
http://www.geocities.com/r-sharipov/r4-b6.htm

I still like to read real books (softbacks and hardbacks), though.

If I remember correctly, there is a Schaum's Outline Series on tensor analysis. I have used these in the past to teach myself all kinds of subjects. The outlines give you theory, some worked out examples, then give you problems to work out on your own with the final answers in the back of the book. It's a great way to learn!

Yes, there are three:
1. Schaum's Outline of Theory and Problems of Vector Analysis and Introduction to Tensor Analysis
2. Schaum's Outline of Continuum Mechanics
3. Schaum's Outline of Tensor Calculus

For instance, here is a TOC of the 3rd:

Schaum's Outline of Tensor Calculus
Synopses & Reviews

Publisher Comments:
This lucid introduction for undergraduates and graduates proves fundamental for pactitioners of theoretical physics and certain areas of engineering, like aerodynamics and fluid mechanics, and exteremely valuable for mathematicians. This study guide teaches all the basics and efective problem-solving skills too.

Table of Contents

The Einstein Summation Convention.
Basic Linear Algebra for Tensors.
General Tensors.
Tensor Operations.
Tests for Tensor Character.
The Metric Tensor.
The Derivative of a Tensor.
Further Riemannian Geometry.
Riemannian Curvature.
Spaces of Zero Curvature.
Tensors in Differential Geometry.
Tensors in Mechanics.
Tensors in Special Relativity.
Tensors Without Coordinates.
Introduction to Tensor Manifolds.

Having mastered the above, you maybe ready to read your book.

If not, and you feel you want to pursue this further, then Google on the Einstein curvature tensor.

http://www.google.com/search?client=ope ... 8&oe=utf-8

I am already seeing lots of wiki-like sites, where it explains quite a bit of what you need to learn about the Ricci curvature and the Einstein manifold.

You're going to be spending quite a bit of time wading through this, though.

However,

. . . where there's the will, there's a way . . .

-fde

[skyfrog]

Hi Forrest,

Gee, thanks, I know you're the right person I should ask for help.

I have learned some tensor basics when in graduate school, but they are all gone, I need to refresh my brain with the info you provided.

[Mike Everman]

I have both of those books. Not exactly light reading, but the big book is very well done. I'm not a hardcore mathematician, so enjoy it more by osmosis. ;-)
Another great one is "The Riddle of Gravitation" by Peter G. Bergmann, one of Einstein's contemporaries. Very good read.

I enjoy pondering the "great riddle". Like perpetual motion, you don't have to believe it's possible to stretch your mind with "possible" mechanisms!

With gravitation, if you end up with "it Is, because it Exists", you're on the right track, I think. I believe current efforts to fold gravity into a Grand Unified Theory are doomed. It doesn't belong there, and one needn't beget the other, in my almost certainly ignorant opinion. Acceleration due to Gravity is an effect, not a mechanism. I'm sure of one thing, and that is that we are as able to know how it all began as an ant knows from where the picnic came.

I do believe that one day we'll "bend" one of the conservation laws so that we can flit around like starship Enterprise. That will be Something, huh?

[skyfrog]

Hi Mike,

Thanks, just searched the amazon.com, yes they have "The Riddle of Gravitation" listed. Should start from easier books I think.

Gravitation is a mystery, how can it reach distance of light years away, without a medium ? did they find gravitation wave yet ? We should pay attention to these scientific topics even though we are not scientists.

If we could understand what gravition really is, maybe we can find a way to block the passage of gravitation wave and get a free floats in the air ? Hehehe pardon me, this is not science but science fiction.

[Bruno Ogorelec]

how can it reach distance of light years away, without a medium ?

Horace, why would it need a medium? Consider medium as an indicator. It lights up, telling you that something has happened, but does not necessarily take part in the process. If you consider it a field, there is no medium involved.

That was my point in the aborted debate on the action-reaction topic. I should have persisted and argued it out, but the older I am, the less urge I have to push the tilted upright and the crooked straight. Maybe I revert to it when I replenish my batteries.

[Mark]

http://redshift.vif.com/BookBlurbs/Push ... tm#Preface
http://redshift.vif.com/BookBlurbs/PushingGravity.htm

[Bruno Ogorelec]

I'm sure of one thing, and that is that we are as able to know how it all began as an ant knows from where the picnic came.

Mike, thank you for this. It is an apt and profound metaphor. I first encountered it in an SF novel by the Strugatsky brothers, 'The Roadside Picnic', and it hit me like a hammer.

[Mark]

In this movie the husband proclaims God does not bother with microbes, the husband was a naturalist/school teacher. It's just a line I remember from the movie.
Mark
http://images.amazon.com/images/P/B0000 ... ZZZZZZ.jpg

[Mike Everman]

I'm sure of one thing, and that is that we are as able to know how it all began as an ant knows from where the picnic came.

Mike, thank you for this. It is an apt and profound metaphor. I first encountered it in an SF novel by the Strugatsky brothers, 'The Roadside Picnic', and it hit me like a hammer.

Shoot, and I was so proud of that one! Must have read it somewhere.

[Bruno Ogorelec]

Shoot, and I was so proud of that one! Must have read it somewhere.

Not necessarily. You are a thinking man. You could have come up with the paradigm yourself, thinking about the vastness of the unknown.

Another SF writer, Algis Budrys, used the same paradigm in his novel, Rogue Moon, after the Strugatskis. I asked him about it once and he swore he head never even heard of their Roadside Picnic. I believe him; he was an honorable man and the Strugatskis have not been exactly popular in the US, especially not in the 1960s when Budrys wrote his novel.

I think you might like both novels. Both propose the discovery of big artificial objects of unfathomable purpose. Men try to examine and explore the objects, meeting great dangers in the process, suffering fatalities etc. Bit by painful bit they collect information about the mysterious objects, map the safe paths and safe patterns of behavior but even after years of examination they are nowhere near even a coherent theory on their purpose or origin.

In both novels, one of the central ideas is that the thing may actually have been something completely unimportant, a bit of refuse left behind on the side of the road (as it were) by a civilization vastly more advanced than mankind. Men are examining it and mapping it and studying it hard, but it remains as far from their understanding as the bits and pieces left behind by human picnickers are to the ants that find them in the grass by the road.

A disturbing idea. God knows how pround the ants are of their own understanding of the Universe. They may well think they are on the brink of putting together the Theory That Explains It All.

The Strugatski novel was filmed by the late Andrey Tarkowski as 'Stalker'. The movie is avalable on DVD from http://www.russiandvd.com/store/product ... =&lang=eng.

The Budrys book is out of print but available secondhand from a number of bookstores in the US. I may have a copy signed by the author somewhere but would not like to part with it.

[skyfrog]

how can it reach distance of light years away, without a medium ?

Horace, why would it need a medium? Consider medium as an indicator. It lights up, telling you that something has happened, but does not necessarily take part in the process. If you consider it a field, there is no medium involved.

My question was stressed on "light years away". Newtonian model of gravitation taught us gravity is a field, governed by :

Gravitational force = (G * m1 * m2) / (d2)

And it says the propagation of gravity needs no time, instantaneously. But what we are interested is, does gravity travel at the speed of light? and here is an answer :

http://science.howstuffworks.com/framed ... ion-6.html

Einsteinian gravitational theory answered YES to this question, but where's the proof ?

A related question is, if a huge mass is converted into energy, for instance via nuclear explosion or fusion, how long it will take for a object of light year away to sense the mass has disappeared ?

[Bruno Ogorelec]

if a huge mass is converted into energy, for instance via nuclear explosion or fusion, how long it will take for a object of light year away to sense the mass has disappeared ?

A nice question. My gut feeling is that the 'sense' is instantaneous but my gut feelings are not a very good indicator of the state of the Universe.

I see a field connecting a system and it is this field that detects the change. The field is one. News does not have to travel from anywhere to anywhere else. It is or it isn't.

I see gravity as such a field, but again it is a gut feeling. I'd have problems envisioning the Universe if gravity traveled at light speed.