The Essential General Relativity

[josephpalazzo]

Just published a new blog on The Essential General Relativity. I wanted to condense a 400 page textbook on the subject in a 1 page blog. I know, that is totally crazy, but I think I managed it.


Comments would be greatly appreciated as I can edit it to make it better.

[AllPurposeAtheist]

Wow, and I thought 4th grade math was hard. :shock:

[aitm]

While that is all interesting and educational stuff....how do you get all those funky symbols from the keyboard? Where the fuck is an upside down triangle found? I mean GODDAMIT this is important shit.

[Jason78]

All I need now is a beginners guide to calculus, so that I can understand the maths presented.

[barbarian]

So does this mean that when we start the conversation of "the essential general relativity" you have to talk about spacetime and then what about the spacetime in past directions.

(15) G?? = 8?Gc-4T?? - Equation (A)

Knowing that it must yield in weak gravity field and low velocity, Newton's equation

Are you saying that inflation is truly internal? Or, is this condensed blog a drop back to the singularity theory?

Further matters in space-time geometry: f(R,T,R??T??) gravity

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the model are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of models the matter energy-momentum tensor is generally not conserved, and this non-conservation determines the appearance of an extra-force acting on the particles in motion in the gravitational field. The Newtonian limit of the model is also considered, and an explicit expression for the extra-acceleration which depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability, and obtain the stability conditions of the model with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the model are investigated for both the conservative and non-conservative cases, and several classes of analytical solutions are obtained.

[josephpalazzo]

So does this mean that when we start the conversation of "the essential general relativity" you have to talk about spacetime and then what about the spacetime in past directions.

(15) G?? = 8?Gc-4T?? - Equation (A)

Knowing that it must yield in weak gravity field and low velocity, Newton's equation

Are you saying that inflation is truly internal? Or, is this condensed blog a drop back to the singularity theory?

The blog is about how Einstein developped his field equations between 1905 and 1915 literally from scratch. Inflation was developped in the 1970's. And singularity is only a concern when you apply GR to cosmology - that was developped later on by people like Lemaitre, Friedman, Robertson and Walker.





Further matters in space-time geometry: f(R,T,R??T??) gravity

We consider a gravitational model in which matter is non-minimally coupled to geometry, with the effective Lagrangian of the gravitational field being given by an arbitrary function of the Ricci scalar, the trace of the matter energy-momentum tensor, and the contraction of the Ricci tensor with the matter energy-momentum tensor. The field equations of the model are obtained in the metric formalism, and the equation of motion of a massive test particle is derived. In this type of models the matter energy-momentum tensor is generally not conserved, and this non-conservation determines the appearance of an extra-force acting on the particles in motion in the gravitational field. The Newtonian limit of the model is also considered, and an explicit expression for the extra-acceleration which depends on the matter density is obtained in the small velocity limit for dust particles. We also analyze in detail the so-called Dolgov-Kawasaki instability, and obtain the stability conditions of the model with respect to local perturbations. A particular class of gravitational field equations can be obtained by imposing the conservation of the energy-momentum tensor. We derive the corresponding field equations for the conservative case by using a Lagrange multiplier method, from a gravitational action that explicitly contains an independent parameter multiplying the divergence of the energy-momentum tensor. The cosmological implications of the model are investigated for both the conservative and non-conservative cases, and several classes of analytical solutions are obtained.

Yes, there are many of those on the web that cover this topic, but my blog is simple, historical, without compromising too much on the math, and my main goal was to show that GR's development was a mix of brilliant insights and a few lucky guesses. It was far from being a straight line from start to the goal line.

[josephpalazzo]

While that is all interesting and educational stuff....how do you get all those funky symbols from the keyboard? Where the fuck is an upside down triangle found? I mean GODDAMIT this is important shit.

Much easier then you think: Google 'nabla'. :P

[josephpalazzo]

All I need now is a beginners guide to calculus, so that I can understand the maths presented.

Calculus For Dummies

[josephpalazzo]

It's never too late.;-)

[Solitary]

Just published a new blog on The Essential General Relativity. I wanted to condense a 400 page textbook on the subject in a 1 page blog. I know, that is totally crazy, but I think I managed it.


Comments would be greatly appreciated as I can edit it to make it better.

If E has to decrease, then the frequency f must also decrease, or its wavelength increase. This is known as the gravitational redshift. What does this say about the red shift showing that space-time is expanding. Couldn't it because light coming from farther away is losing energy from gravitation causing the red shift and not acceleration? Solitary

[josephpalazzo]

Just published a new blog on The Essential General Relativity. I wanted to condense a 400 page textbook on the subject in a 1 page blog. I know, that is totally crazy, but I think I managed it.


Comments would be greatly appreciated as I can edit it to make it better.

If E has to decrease, then the frequency f must also decrease, or its wavelength increase. This is known as the gravitational redshift. What does this say about the red shift showing that space-time is expanding. Couldn't it because light coming from farther away is losing energy from gravitation causing the red shift and not acceleration? Solitary

You've just invoked the Equivalence Principle. For all purposes, one cannot tell the difference between an acceleration going one way from a pull of gravity the other way. So in this case you can't tell if the gravitational redshift of a light coming from a far away galaxy is due to gravity of that galaxy on light or it's due to the acceleration of the universe.

[Solitary]

Just published a new blog on The Essential General Relativity. I wanted to condense a 400 page textbook on the subject in a 1 page blog. I know, that is totally crazy, but I think I managed it.


Comments would be greatly appreciated as I can edit it to make it better.

If E has to decrease, then the frequency f must also decrease, or its wavelength increase. This is known as the gravitational redshift. What does this say about the red shift showing that space-time is expanding. Couldn't it because light coming from farther away is losing energy from gravitation causing the red shift and not acceleration? Solitary

You've just invoked the Equivalence Principle. For all purposes, one cannot tell the difference between an acceleration going one way from a pull of gravity the other way. So in this case you can't tell if the gravitational redshift of a light coming from a far away galaxy is due to gravity of that galaxy on light or it's due to the acceleration of the universe.

Thank you! This is one reason I don't buy the Big Bang "Creation" Theory, because cosmologists assume the red shift is from the expansion and acceleration of space-time, and not from gravity. Solitary

[likebutNotTheSame]

Thanks for the summary.

Reality is hard to understand. If it where easy would we all be in this mess that the world is?

I takes MORE than simple calculus, it takes 4 dimensional tensors, with the understanding of gradients and MORE to have even a chance to perceive what Einstein proposed, not as KNOWING, but as MAYBE (Yeah, he was HONEST about it)

The bar to TRUE UNDERSTANDING is difficult. Oops, I've never known TRUE UNDERSTANDING, so maybe this is words for others. STUPID OTHERS who KNOW PURE, PERFECT, COMPLETE.

So, what should this dude have said that might have been relevant to all those STRUGGLING around him to MAKE THIS WORLD BETTER?
(other questions? Your questions are not mine. I care for SURVIVAL, FOR MORE, not survival for the few)

Black Whole... some say a monster of horror, I say pivotal expression of order.

Photons... are real things, and have mass. I say, they are resonant, potential differences or FREE energy, needed by all life. VITAL/NECESSARY for all LIFE TO GROW AND CHANGE.

Space is curved they say, I SAY IT IS WARPED and strange... Others LONG to understand what lies beyond, when we have only time to not consider the MESSED UP, INSANE, POISONOUS EXISTENCE that is LIFE.

That which is around, abounds, exists.

What matters. What WE DO. What we CHOOSE.

YOU MUST STRUGGLE FOR BETTER AS YOU ARE.

Don't you adore LIFE, all those like, different from you but LIFE. Don't you LOVE and ADORE them and long for a better existence than I have known for them? I LONG FOR THEM TO KNOW A BETTER STRUGGLE THAN MINE, and MY WILL AND STRUGGLE MATTERS. I MATTER. I AM MATTER. I AM JOHN. I CHANGE, to adore those who are adorable better.

I AM NOT A SONG. (although I sing, and Pure One is my harmony... the Pure One is never counted on to be there, the Pure One is only perceived, never UNDERSTOUND---hah, welcome? You fools, the Pure One needs no welcome. The Pure One is in all, with all, through all. Without the Pure One, YOU ARE NOTHING. What is something? The Pure One.

I am NOT unique.

I am not PERFECT/PURE/STUPID... these three things go together.

In the beginning there was... It's over. I KNOW WORDS, I KNOW SHALLOW ICONIC IDEAS, I KNOW STUPID LIES.

I know... what came before and humanity is soooo tiered of your bs and lies.

We are no longer humble and starving for you expression, WE PERCEIVE YOU and  KNOW YOU ARE FOOLS.

[josephpalazzo]

If E has to decrease, then the frequency f must also decrease, or its wavelength increase. This is known as the gravitational redshift. What does this say about the red shift showing that space-time is expanding. Couldn't it because light coming from farther away is losing energy from gravitation causing the red shift and not acceleration? Solitary

You've just invoked the Equivalence Principle. For all purposes, one cannot tell the difference between an acceleration going one way from a pull of gravity the other way. So in this case you can't tell if the gravitational redshift of a light coming from a far away galaxy is due to gravity of that galaxy on light or it's due to the acceleration of the universe.

Thank you! This is one reason I don't buy the Big Bang "Creation" Theory, because cosmologists assume the red shift is from the expansion and acceleration of space-time, and not from gravity. Solitary

It's not the cosmologists who have made that assumption. It's Einstein. If you go back to my blog, you will see equation (2),

2) (?f/f)gravity = -(?f/f)doppler = -?v/c

That is crucial in developping the whole theory of General Relativity. Cosmologists are just using what Einstein assumed. If that is wrong, then the whole of theory of GR collapses. Unfortunately for the detractors of GR, Einstein correctly made some predictions that turned out to be empirically verified.

And lastly, there is no "creation" in the Big Bang Theory. That is made up by theists who are desperate in justifying their belief in a deity.

[Solitary]

That may be so, but it could be correct and he was wrong, and why cosmology and a unified theory are at a stand still. When I say wrong, I mean like Newton was.  I believe hawking's is on the right track with cosmology now and no one is listening. There are so many things in physics we still don't understand like what is a photo really like, or space-time that are fundamental to physics. We know that electrons and positrons make something positive or negatively charged, but what makes them have properties of electrons and positrons? It's like, when does H20 become wet? We live in a very strange world, but that is the very reason it is so interesting to me. It seems to me that mathematics will make it all understandable eventually if we survive long enough. It's going to take a genius of abstract thinking using new information about the world we live in. We know so little, and taking the easy way out is holding science back like it always has. Keep up the good work, and maybe you could be the one. :shock:  Seriously. Solitary