Comments on: Demystifying Einstein’s Field Equations on General Relativity

By: Anonymous

Anonymous — Sun, 21 Aug 2011 05:45:00 +0000

Nice to hear back from you. Yes, a lot of the core universal truth requires a more of an analytical mind to understand it rather than math equations. The core of Buddhist preachings and the Advaita philosophy have a lot in common with quantum world. Good luck for your knowledge exploration. Sure, will try to answer you questions based on whatever knowledge I have on the subject.

By: Anonymous

Anonymous — Sun, 21 Aug 2011 05:42:00 +0000

You are right, the stress energy tensor is the actual source of the gravitational field. It has a non-zero value only INSIDE the matter in question, it deals with matter density, momentum, stress – all of which play an active role in the resulting gravitational field which in turn cause the space-time curvature.

By: Francis Ferrara

Francis Ferrara — Fri, 19 Aug 2011 19:26:00 +0000

I recognize that the LHS of the field eq. is well understood and the differential non-Euclidean geometries of Riemann and Gauss are more than 125 years old(I just don’t know them except very very superficially). But the RHS of the equation is what I have absolutely no idea about, What is a “stress-momentum-energy” array [T_ij( )] for matter? Is it related to the motion(its acceleration) of the matter in any way? If It is then I can see that the spinning disk thought experiment might imply that mass energy cause the geometry of spacetime to curve(the g_ij( ) to be affected).

By: Francis Ferrara

Francis Ferrara — Fri, 19 Aug 2011 18:59:00 +0000

Dear Mr.Gurudev
I wrote to you some last year when I was looking at Wheelers book “Journey into Gravity and Spacetime” along with E.F.Taylors new book on “Exploring Black Holes” but I found your article “Demystifying the Einstein Field Equations” easier to follow. Since last year I have been looking into Buddhism and find that all of science pales in comparison to Buddhas Dharma(4 Noble TRUTHS and no-Self). Yhe idea of emptiness as the lack of identity seems to go to far for me(but who knows!). Well in any case I will try to get up to speed about GR again by reading your article and what I asked you and your answers.
I will try to put what you say in your article and what you say in your answers into some kind of picture for myself and then send it to you.
Yours truly
Francis Ferrara

By: Gurudev

Gurudev — Mon, 07 Feb 2011 10:35:59 +0000

Yes I agree with you on this. Einstein was a great genius who could think beyond dimensions and it was as if he understood the mind of God during creation! This is evident by the facts that even though he himself didnt believe it initially, his theory predicted Big bang, black holes etc. Einstein stands apart from rest of the mass in that experiments were done later (infact are being done even today) to test the predictions of his theory where as the theory itself was created mostly out of his own thoughts (thought experiments). Almost all other physicists based their theories largely on already available experimental data.

Also almost all theories are for that matter creative ordering of observational data and human predictions, because nature itself doesnt have any boundaries in terms of its laws. Nature doesnt differentiate between physics, chemistry, DNA, black holes – it is we for our understanding have created all these braches, we have physics, we have chemistry, we have biology – but then since nature itself draws no such hard boundaries, we also then have bio-physics, bio-chemistry, physio-chemistry to also study the laws sitting in the boundaries drawn by us. And yes discovery of new science is definitely an art which requires creativity else we could have programmed Robots to discover new laws of science

By: francis Ferrara

francis Ferrara — Sun, 06 Feb 2011 20:20:58 +0000

Dear Mr. Gurudev
I have really enjoyed this disscussion with you about Einsteins fiels eq. and GR in its overall structure, but I think that the theory is more about the human creativity of Mr.Einstein(his philosophy,experiences,distrust of authority and that inexplicable thing that artists and scientists all have) rather that the theory being inferred and distilled out of observations. Observations may have given him clues but Putting them together was a work of art by an artist.
Francis

By: Gurudev

Gurudev — Sun, 06 Feb 2011 19:28:30 +0000

space-time and mass-energy are related because they are different manifestations of the same entity – the pre big-bang soup from which space-time as well as mass-energy were created. Imagine an empty space-time without mass-energy, well you cant imagine that, because there is nothing that ticks (time runs inside mass ie inside quantum particles), and without mass-energy there is nothing to measure in space, to measure distance you need reference points ie mass. If we have a universe where there is only space-time and no mass-energy, then where did the mass-energy of that universe which existed in its big bang singularity disappear? My very own thought is that space-time is just another manifestation of mass-energy and is probably even the source of the mysterious dark-energy. After all everything is finally an outcome of energy, and so should be space-time I guess. I guess our understanding of the actual nature of space-time is still limited and is prejudiced by what we observe in the observable universe.

For instance, how can we be sure that there isn’t an even larger portion of our observable universe which is moving away from us beyond the speed of light? If regions beyond the observable universe are expanding at a rate greater than the speed of light, then no light (ie information) will ever reach us from such regions of the universe, nor will there be any observable impacts of gravity from such regions.

By: Gurudev

Gurudev — Sun, 06 Feb 2011 19:19:17 +0000

Yes, even the mass which is following a geodesic gives its own contribution in manipulating the curvature because of its mass, and hence to keep equations simple we consider “negligible” mass or point mass whose effects are so small that they can be ignored while studying the effects of a given mass like say Sun or Earth. But yes, in practice every mass makes its contribution to the curvature. If we study the effect of Earth on moon, its not just that of earth, but also of the mass of moon itself, which is not negligible compared to that of Earth!

Acceleration is related to mass-energy distribution because it is in the first place CAUSED by the mass-energy distribution. If there was no mass-energy, then there would be no curvature, and hence no acceleration at all. Consider an magnet which deviates the path of charged particles moving in its vicinity causing their velocity to change ie causing acceleration. Now if this magnet (similar to mass-energy) was absent, then the charged particle would never have had deviated from its flight path (ie it would not have had acceleration)!

By: Gurudev

Gurudev — Sun, 06 Feb 2011 18:45:11 +0000

Yes you are absolutely right that this fictitious force is actually due to inertia and is caused because of the resistance to natural trajectory. This is also the reason as you said that we dont feel this force in geodesic motion. Many a times it looks like physicists unnecessarily complicate things by creating different avatars of the same effect. Things which could be explained in simple terms are given complex names and complex definitions

By: Gurudev

Gurudev — Sun, 06 Feb 2011 18:41:29 +0000

Yes you are right. What relativity or newtonian mechanics tells is about what is observed. It does not tell us HOW that what is observed takes place. Like Newton said Sun attracts Earth, but HOW does Sun attract Earth, what exactly is the medium of this action was not described by Newton. He only reported what he observed. Similarly Einstein further refined it and came to the conclusion that space-time is curved. But he could not define WHAT EXACTLY is the medium for this, what exactly is curved? Humanity as a whole is trying to solve the mystery of Universe, one step at a time, first report observations, create a law, see if it passes or fails, apply the law (semiconductors, electronics, computers etc) and in parallel try to understand HOW it works (string theory?)