Field equation interpretation

[Yoel]

What do you interpret from this equation. G μν(g αβ)+Λg μν= 8πG/C^4 T μν({φ i,θ i})
Spacetime geometry = Interference-driven stress-energy>>
I'm not looking for conformation. Just a little help n interpretation. Plz

 

[Ibix]

J.A. Wheeler described the Einstein field equation as "spacetime tells matter how to move, matter tells spacetime how to curve". As with all one-liners it's not really true, but it's not bad.

Roughly speaking, the left hand side describes spacetime curvature and the right hand side describes the stress-energy of all stuff (matter and radiation) in spacetime. I have no idea where you get "interference driven" from or what you think it means. It is no part of relativity.

 

[Orodruin]

J.A. Wheeler described the Einstein field equation as "spacetime tells matter how to move, matter tells spacetime how to curve". As with all one-liners it's not really true, but it's not bad.

To be a little more precise, the Einstein field equation is the latter part of that. The first part is the geodesic equation.

 

[PeterDonis]

Moderator's note: Thread moved to relativity forum.

 

[martinbn]

What do you interpret from this equation. G μν(g αβ)+Λg μν= 8πG/C^4 T μν({φ i,θ i})
Spacetime geometry = Interference-driven stress-energy>>
I'm not looking for conformation. Just a little help n interpretation. Plz

How do you interpret the other equations in physics? Can you give examples, so we can get an idea what you expect for an answer.

 

[Yoel]

J.A. Wheeler described the Einstein field equation as "spacetime tells matter how to move, matter tells spacetime how to curve". As with all one-liners it's not really true, but it's not bad.

Roughly speaking, the left hand side describes spacetime curvature and the right hand side describes the stress-energy of all stuff (matter and radiation) in spacetime. I have no idea where you get "interference driven" from or what you think it means. It is no part of relativity.

thanks for replying.. I was trying to see first if anyone could just give a new equation and it would be understood or would there be a need for additive description. also I was trying to make T μν = apply to something classical and quantum. I also understand that the equation could be way off..

 

[phyzguy]

thanks for replying.. I was trying to see first if anyone could just give a new equation and it would be understood or would there be a need for additive description. also I was trying to make T μν = apply to something classical and quantum. I also understand that the equation could be way off..

Why do we need a new equation when the Einstein field equations describe the large scale structure of the universe so well?

 

[Ibix]

also I was trying to make T μν = apply to something classical and quantum. I also understand that the equation could be way off..

General relativity is a purely classical theory. That is, the stress-energy tensor models classical matter and radiation fields. It isn't compatible with quantum sources of gravity.

How to make a theory of gravity that is both compatible with quantum sources and compatible with the large body of experimental evidence on gravity is an open question, and has been an active topic of research for several decades now.

 

[pervect]

I'm not sure what you're looking for, but I've always liked Baez & Bunn's "The meaning of Einstein's equation", https://arxiv.org/abs/gr-qc/0103044.

Note: to view the text of the article, chose the "view pdf" option on the right.

The title at least sounds like what you might be interested in. I'll quote the authors one sentence description of "the meaning of Einstein's equation" , though it's defintely NOT a substitute for reading the whole paper - think of it as a motivational teaser, not a complete exposition.

We promised to state Einstein’s equation in plain English, but have not done
so yet. Here it is:

Given a small ball of freely falling test particles initially at rest
with respect to each other, the rate at which it begins to shrink is
proportional to its volume times: the energy density at the center
of the ball, plus the pressure in the x direction at that point, plus
the pressure in the y direction, plus the pressure in the z direction.
One way to prove this is by using the Raychaudhuri equation...

In an appendix, the authors justify their statement that this single sentence is, in some sense, equivalent the full statement of Einstein's equations, but their argument requires some significant background knowledge.

Note that the authors omit discussing the cosmological constant (Lambda) in your formulation.

Also, I'll quote their section on "preliminaries", to give the reader some information on what the authors think is required as background (they may be a bit optimistic in how little they mention).

Before stating Einstein’s equation, we need a little preparation. We assume the
reader is somewhat familiar with special relativity — otherwise general relativity
will be too hard. But there are some big differences between special and general
relativity, which can cause immense confusion if neglected.

In special relativity, we cannot talk about absolute velocities, but only reative velocities.
For example, we cannot sensibly ask if a particle is at rest,
only whether it is at rest relative to another. The reason is that in this theory,
velocities are described as vectors in 4-dimensional spacetime. Switching to a
different inertial coordinate system can change which way these vectors point
relative to our coordinate axes, but not whether two of them point the same
way.

In general relativity, we cannot even talk about relative velocities, except for
two particles at the same point of spacetime — that is, at the same place at the
same instant. The reason is that in general relativity, we take very seriously the
notion that a vector is a little arrow sitting at a particular point in spacetime.
To compare vectors at different points of spacetime, we must carry one over to
the other. The process of carrying a vector along a path without turning or
stretching it is called ‘parallel transport’. When spacetime is curved, the result
of parallel transport from one point to another depends on the path taken! In
fact, this is the very definition of what it means for spacetime to be curved.
Thus it is ambiguous to ask whether two particles have the same velocity vector
unless they are at the same point of spacetime.
It is hard to imagine the curvature of 4-dimensional spacetime, but it is easy
to see it in a 2-dimensional surface, like a sphere.

Note: I attempted to credit both Baez and Bunn equally, but the Latex didn't really display well. Apologies for any confusion, they are listed as co-authors.

 

[cianfa72]

How do you interpret the other equations in physics? Can you give examples, so we can get an idea what you expect for an answer.

I believe the term interpret has to do with a mapping/correspondence between the mathematical model's concepts and the physical world.

For instance R. Penrose in his book The Road to Reality talks of 3 worlds and their mapping.