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Offline Chemistry4me

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« Reply #25 on: 05/01/2009 01:37:02 »
I'll go with Work & Energy Mr.S
 

Offline Bikerman

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« Reply #26 on: 05/01/2009 02:52:48 »
Ahh...I would have chosen GR but it seems to be off the curriculum. That leaves me with a lot of stuff I've already done to grad level...OK..how about Special Relativity? I could probably use a refresher...
 

Offline Mr. Scientist

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« Reply #27 on: 05/01/2009 17:18:29 »
General Relativity - Lesson Installation 1 of 3

One thing Einstein brought to the world, was his amazing conclusion of solving field equations that was describable as a spacetime geometry. The definition of a field equation, is one that describes a physical spacetime field where in the case of Einsteins equations, deal with gravity, which is an all pervading physical field which attracts all other gravitational radiating bodies in the universe.

To begin these lessons, we shall learn about one of Einsteins most famous equations, the Einstein tensor equation. Once we have covered the very basics of his formula, we will then consider the implications of it, through a worded essay.

Einstein’s Tensor Equation

The most important equation in Einstein’s field equations, is the field tensor equation, and is given as:

G_uv=T

Einstein began these equations from a simple equivalence:

G_(αβ)= T_(αβ)

*some times k will not be added, but it is usually more correct to add it

 G_(αβ)=kT_(αβ)

And this alone would explain that geometry was being involved in the description of spacetime. It said that particles are fluctuations of a gravitational field, and are themselves fluctuations of gravity. These fluctuations would bend and curve the space around them, not only caused by a generation of mass, but also the acceleration as it moved through the vacuum.

The right hand side of the equation G_(αβ)=T_(αβ) refers to the energy tensor, related to momentum, that naturally causes the space and time surrounding it to curve in on itself. In fact, in many ways, particles are tiny points that are visualized to be fluctuations that have curved in on themselves, so they can be seen as little creases in the very fabric of spacetime.

The provision of equations, also have about them, a conservation, just like the kind of conservation we may use in Kinetic Energy Equations, for example. We (in terms of physics jargon), that the tensor is covariantly conserved as a quantity in space and time, and we denote this conservation as:

▼βT^(αβ)= ▼βG^(αβ)

▼ Is the derivative, also known as the ‘’covariant derivative’’ is the same as the Einstein Tensor,

▼=G_uv

*Notice the lower and higher indices. They can be representable as traces in Einstein’s equations.

The constant k, is given a value of

K=8πG/c^4

These equations lead to a field equation that is most recognizable in physics education,
 
 G_(αβ)=(K=8πG/c^4)T_(αβ)

And in this one equation, if my memory serves me correctly, involves 10 differentiable equations. So there is quite a lot in this equation. In Einstein’s early resolution of the equations, he decided that it was necessary to believe the universe was static, but under closer observations of cosmological evolution, it became apparent that a cosmological constant divided Einstein’s thoughts to either a contracting universe or an expanding universe. It became obvious that it resolved to an expanding universe.

 G_(αβ)+Λg^(αβ)=(K=8πG/c^4)T_(αβ)

The cosmological constant ‘’Einstein’s biggest blunder’’ (a phrase he would coin that could be debatable), gave rise to an expanding universe, where an energy density was by a magnitude greater of 10^120, which would mean there was more energy predicted in the universe, than what can be observed – it is considered, understandably, one of the largest discrepancies known in physics today.

The Geometry of Spacetime

And so, what we learn from the Einstein Field equation, is that the right hand side of G_(αβ)=T_(αβ), described the geometry of spacetime. In fact, we learn through relativity, that this geometry is not just simply the three-dimensional presence of matter, but is also related to being distortions in spacetime itself. Because it is related to the momentum, it is also said that these distortions are equivalant to acceleration. So in a nutshell, matter is simply the same as the distortions, which is the same as acceleration; these are also the components of another entity; curvature.

The presence of matter entails the geometry of curvature in spacetime, where it will quite literally distort and derrange the spacetime within its vicinity and curve it within its presence. It is for this reason, that in 1919 Arthur Eddington was able to take a photograph of light being bend around the suns gravitational presence. This happens because light has momentum, and also its own gravity (whilst its gravity is very weak), it is still able to be influenced by gravity itself. The gravitational influence of light in the universe is far too weak (in fact, miniscule) to even have an influence in the evolution of the universal gravitational bodies, such as planets, stars to entire galaxies. Light may have had an effect on the gravitational evolution of bodies perhaps very early on in the universes history.

 

Offline Mr. Scientist

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« Reply #28 on: 05/01/2009 18:42:25 »
The second installation is coming soon. However, can i note, i have not numerically used General Relativity before, so i cannot inform you on how to do so. I have only studied the work myself.

Now, i must say, bringing in other topics on other subjects in this thread will be very confusing at best, with the amount of theories going to be reviewed. So, i will also start another thread, so there will be two threads dedicated to these subjects.

The other thread will focus on the Special relativistic equations, which i have numerically worked with. I hope will clear some of the possible confusion that coud arise when doing these things.
 

Offline yor_on

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« Reply #29 on: 05/01/2009 19:01:02 »
So if I got it right :)
You will create a separate thread for Special relativity.
and us reading your installments here wanting to discuss general relativity.
We will use this thread for that if I got you right.

So my first question then:)

You wrote "In fact, we learn through relativity, that this geometry is not just simply the three-dimensional presence of matter, but is also related to being distortions in spacetime itself. Because it is related to the momentum, it is also said that these distortions are equivalant to acceleration."
How do you see 'distortions in spacetime'?
Are you referring to mass influence on spacetime, or are you seeing it as something 'happening' in, for example, outer space to space itself by itself?
Not related to any 'normal' matter formations influence?

That is , do you see it as due to vacuums inbuilt energy?
« Last Edit: 05/01/2009 19:15:41 by yor_on »
 

Offline Mr. Scientist

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« Reply #30 on: 05/01/2009 19:44:56 »
I see these distortions like this:

Imagine a very beautiful woman on the beach, in the great sun belting on her sunkist face... she decides to have a presence made on the sand with her finger. She places her finger in the sand, and the sand reacts to her fingers presence. The sand will bend as she presses it into the harsh, corse silcone bits, and their distorted perimeter, is in fact the presence of her fineger which is made of matter istelf. This matter then, has caused a geometry in the sand, and this is analogous to the presence of matter in space. It distorts and derranges the sand around it, so the presence of matter has caused these distortions, and has caused the dent of geometry itself. The ability of matter to do this, is certainly also due to the energy is has, so yes.

 

Offline yor_on

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« Reply #31 on: 05/01/2009 22:33:57 »
Ok, more or less like I see it then:)
Although I'm starting to think that all space is matter:)
It's like a symmetry, you will get space if having matter.
241 sort of.

Which seems to fit with gravity being like some sort of 'field'.
But if that was true one could presume 'regions', far enough away so to speak, without a vacuum.
Even when allowing for a uniform inflation?
Not that I can 'imagine' it but it could be a possibility.

But then one might be expecting areas without 'light' coming towards us, if now light have to follow spacetime.

Spacetime won't let you see those other 'areas' as it will form itself into an 'enclosure, what is called a 'four vector four-dimensional real vector space, called Minkowski space' in special relativity, or a four-momentum (mass-energy and linear momentum) in general relativity'.
http://en.wikipedia.org/wiki/Four-vector


So I guess that thought was plain stupid.
Ah well, let's see where the journey takes me.
Carry on Mr S. ::))
 

Offline Bikerman

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« Reply #32 on: 05/01/2009 22:38:54 »
Errr...hang on a mo..
The analogy with sand is surely misleading. Sand is 'stuff'. The analogy indicates that spacetime is therefore 'stuff'. This leaves open the whole issue of the aether which Michelson-Morley was supposed to have buried.
Einstein himself said that spacetime could be regarded as an aether but ONLY a non-particulate aether in which there was no time dependent 'motion'. Thus the analogy seems to me to be misplaced....
« Last Edit: 05/01/2009 22:40:59 by Bikerman »
 

Offline chris

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« Reply #33 on: 05/01/2009 23:23:09 »
Where will these "lessons" be conducted?

(I am thinking that our Second Life auditorium might be a good venue...)

Chris
 

Offline yor_on

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« Reply #34 on: 05/01/2009 23:28:22 »
Bikerman, you're right:)

Still, if vacuum is something containing energy (looking at BEC and radiation).
And if so called 'stopped light is something truly 'vanishing' inside that BEC but still somehow 'imprinted' on the BEC.
So that it come back as moving light again, when one stops the lasers interference (as I've understood it)?

It doesn't make a aether, but it seems to be something else than a 'nothing', do you agree.
To me it seems more like having some hidden dimensional field giving us both matter and what we call space?

And now its definitely time for me to go to bed, huh:)


 

Offline Soul Surfer

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« Reply #35 on: 05/01/2009 23:39:44 »
Chris I don't think these "lessons" a good idea.  MR Scientist just copies and pastes stuff from other science websites and sometimes adds bits himself and these are not always accurate.  The stuff he has just posted is not properly understandable unless you already have a good grasp of tensor calculus in the particular notation used(this is the really difficult bit) and hence is not really imparting useful knowledge to anyone.
 

Offline Bikerman

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« Reply #36 on: 06/01/2009 01:42:28 »
Chris I don't think these "lessons" a good idea.  MR Scientist just copies and pastes stuff from other science websites and sometimes adds bits himself and these are not always accurate.  The stuff he has just posted is not properly understandable unless you already have a good grasp of tensor calculus in the particular notation used(this is the really difficult bit) and hence is not really imparting useful knowledge to anyone.
I have to reluctantly agree. My maths has always been my weak point in science (a MAJOR drawback) though it is something I'm currently addressing in my spare time (mainly by working through 'The Road To Reality - Penrose'. I'm still currently working my way through Hamiltonians/Lagrangians :-)
 

Offline Mr. Scientist

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« Reply #37 on: 06/01/2009 02:50:44 »
Oh no, when apprecication is not taken, is when one must give up.

I give up.
 

Offline Mr. Scientist

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« Reply #38 on: 06/01/2009 02:52:55 »
In fact today, i learn i have no place here, if one is not willing to ask a question, without prejudice, and without cause or just making of me to be fool of the science or ''remedial'' explanations i bring to my audiance.

It must now, seem clear that the one who came to teach, is nothing but a fool.


edited: You lot jumped on some wagon without explanation or guidance. Does one like me who has a lot to show, may have more luck with talking to his big toe?
« Last Edit: 06/01/2009 02:56:07 by Mr. Scientist »
 

Offline Madidus_Scientia

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« Reply #39 on: 06/01/2009 06:21:48 »
Quote
You lot jumped on some wagon without explanation or guidance. Does one like me who has a lot to show, may have more luck with talking to his big toe?

Did you not expect the people of a science forum to have critical thinking skills? Twice in this thread alone, you have taken great offence to people questioning what you've said. If you say something questionable, you will be questioned on it. WELCOME TO SCIENCE
 

Offline Bikerman

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« Reply #40 on: 06/01/2009 10:37:01 »
I'm sorry you feel like that Mr Scientist, but speaking as one who has devoted a large part of his life to teaching, I can tell you that you had better get used to being questioned if you are serious about teaching.

I did not insult you or in any way 'have a go' - I simply agreed that your explanation of GR was formulaic and would only be of use to those with an existing grasp of tensor mathematics.
I also pointed out that your 'sand' analogy was flawed and very likely to confuse the issue by reintroducing a notion that modern physics has dispensed with.
If you have a problem with either of those observations then I would suggest that you really need to reconsider teaching as an option, since both points were made reasonably, civilly and in the spirit of constructive criticism.

Anyway - I will leave you to think about it - I'm off for an interview for a lecturing post :-)
 

Offline yor_on

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« Reply #41 on: 06/01/2009 11:11:47 »
Well Mr S.

I still think you should present your installments :)

Bikerman is a cool dude :) as they say in the States.
And he's not really out to 'brand' anything or anyone.

If you have, what you are satisfied with, explaining spacetime, do post it.
Differ between what you know is "main frame science" and 'other views'.
Just as you did before.

There is no stigma to not 'knowing it all', not even Newton, nor Einstein, believed that they had it all.


-----

(Although Newton was kind of 'prickly' at times, wasn't he?:)
« Last Edit: 06/01/2009 11:46:01 by yor_on »
 

Offline Mr. Scientist

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« Reply #42 on: 06/01/2009 12:23:49 »
He's not the problem.

The one who is saying these lessons are a bad idea, does not have two brain cells to rub together. It is true, i have taken my work from previous sites, but it is still my work. I would have understood his lame comments if i had pleigarised the work, or copied it without permisssion. I only brought the work here, because i have had comments in the past that it helped them understand physics, or it was written well; but i will not see how taking my work for those purposes is by any means, not good, as Soul Surfer said. What's worse, is that i really did honestly take my time out to write this stuff, and that should be appreciated. Criticism is fine, as i once said. But being ignorant towrds someone without proof is bad in itself.
 

Offline Madidus_Scientia

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« Reply #43 on: 06/01/2009 13:20:51 »
Quote
Criticism is fine, as i once said. But being ignorant towrds someone without proof is bad in itself.

The people who have criticised you have shown the opposite of ignorance, they have exercised critical thinking skills and have questioned your logic. If they were ignorant, they would have blindly taken what you said to be truth. You are the one being ignorant toward those who question you.
 

Offline syhprum

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« Reply #44 on: 06/01/2009 14:50:49 »
After reading the excellent article on how the negative mass of the gravitational field was derived that lightarrow direted us to
http://www.negative-mass.com/
I was somewhat disappointed by Mr Scientist efforts that really dropped us into the deep end of a pool of tensors explaining little on the way.
 

Offline Mr. Scientist

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« Reply #45 on: 06/01/2009 16:23:49 »
Quote
Criticism is fine, as i once said. But being ignorant towrds someone without proof is bad in itself.

The people who have criticised you have shown the opposite of ignorance, they have exercised critical thinking skills and have questioned your logic. If they were ignorant, they would have blindly taken what you said to be truth. You are the one being ignorant toward those who question you.


well, that's interesting, because I see it completely differently. As i said, there is criticism, and then there is just ignorance, and in this case, the ignorance was directed to impune my work, and me.

I can take criticism, but not if it has behind it bad intentions.
 

Offline Mr. Scientist

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« Reply #46 on: 06/01/2009 16:28:37 »
After reading the excellent article on how the negative mass of the gravitational field was derived that lightarrow direted us to
http://www.negative-mass.com/
I was somewhat disappointed by Mr Scientist efforts that really dropped us into the deep end of a pool of tensors explaining little on the way.

I did warn the reader it would be hard. Whilst it might have felt i let you jump into the deep end, i did warn the reader of these facts first-hand.
 

Offline Seany

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« Reply #47 on: 06/01/2009 16:38:15 »
*Lifts hand up like a nice child to ask a question* ;D
 

Offline Mr. Scientist

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« Reply #48 on: 06/01/2009 16:41:08 »
please ask.
 

Offline Seany

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« Reply #49 on: 06/01/2009 16:47:11 »
Can we start the lessons again?
I am sure people will be more careful this time.
And we appreciate your time which you've taken to write this!

And please stay with us here! :)
 

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« Reply #49 on: 06/01/2009 16:47:11 »

 

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