How exactly and WHY does matter affect space-time? [closed]

According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) are physically equivalent to a gravitational field of the same strength.

Refer: Einstein's thought experiment of a Physicist in an Accelerated Box.

I find that the 'How' part of this question is somewhat easy to understand Mathematically but hard to visualize physically and on the 'Why' part I am totally blank.

• Kids pester their parents with "why?" questions. Eventually their parents get flustered and say "because I said so!" Every theory in physics has a point where the answer to "why?" is "because the theory says so!" IN this case, that's the answer to your question. General relativity doesn't say why. Maybe string theory or quantum gravity will, but there will still be a point where the only possible answer to "why?" will be the parental response. – David Hammen Aug 20 '14 at 10:14
• The equivalence principle is an assumption rather than something that is derived. Are you asking why it seems a physically reasonable assumption? – John Rennie Aug 20 '14 at 10:15
• @DavidHammen: "Every theory in physics has a point where the answer to "why?" is "because the theory says so!' " This one seems to have reached this point quite early. – bright magus Aug 20 '14 at 11:41
• @brightmagus - Not nearly as quickly as did $F=GM_1M_2/r^2$. Why? Because Newton said so! – David Hammen Aug 20 '14 at 11:46
• We have some discussion about Why? already here. Also, at Philosophy, there's Why does the universe follow scientific laws?. When you already know How?. Why? is not a distinct physical question. – ACuriousMind Aug 20 '14 at 13:04

If you are asking about the mechanism that causes gravitation, it's mass. And energy. Why? General relativity doesn't say why. It says what happens.

If you are asking why Einstein chose to use the equivalence principle as a guiding concept in his development of general relativity, in a very real sense he had no other choice. There's a general concept that has driven the development of physics over the years: A new theory has to be consistent with an older theory in those regimes where the older theory is consistent with experimental results.

Here's the problem Einstein faced: Newtonian gravity was and still is an extremely accurate theory. It is also completely at odds with special relativity. How to reconcile those seemingly unreconcilable theories?

Moreover, simply adding a finite transmission speed to Newtonian gravity is demonstrably wrong. The solar system would be unstable; planets would spiral out in short order. That this is the case was known 100 years before Einstein developed general relativity. Einstein had to reconcile these unreconcilable theories, and he had to do so in a way that avoided the problem of a finite transmission speed being apparently very wrong.

The first part of the equivalence principle goes way back. It's an implicit part of Newtonian gravity, and Newton himself used experiments by Galileo to justify the equivalence of inertial and gravitational mass. This Galilean equivalence is the first part of Einstein's equivalence principle, but weakened with some carefully chosen weasel words. The weak equivalence principle talks about test objects, things you can carry. It does not address the acceleration of two supermassive black holes toward one another.

With regard to the inability of a physicist in a box to distinguish between whether the box is sitting still on the surface of a planet or being in an accelerating spacecraft, there's a very important weasel word in the formulation of that statement as well. The weasel word is locally. This rules out windows. It would be rather easy to distinguish the two situations if all the physicist had to do was look out the window.

That locally qualifier rules out a lot more than windows, however. The "GOCE satellite in a box" experiment could indeed distinguish between sitting still on the surface of a planet from being in an accelerating space craft. There's a solution: Make the box smaller. The micro-GOCE satellite wouldn't be able to tell the difference. Mathematically, locally means some volume that is not quite zero, but is very, very close to it.

The very careful ways in which Einstein phrased the various statements of the equivalence principle were key in the development of the theory of general relativity.