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Time for a paradigm shift in fundamental Physics?

The flat 3-D space component of Minkowskian spacetime in special relativity is isometric to Euclidean space but the 4-D spacetime is non-Euclidean. In general relativity, the 3-D space component of spacetime is non-Euclidean. In differential geometry, the metric tensor (or metric) of a manifold allows one to define distances and angles in an analogous way to the inner product of a Euclidean space, where the inner product is the vector dot product of Cartesian coordinates. Tensor mathematics is the heart of general relativity. For example, the Riemann curvature tensor describes the curvature of spacetime due to the presence of mass-energy.
 
the Riemann curvature tensor describes the curvature of spacetime due to the presence of mass-energy
How is mass-energy defined? Is this energy as in a moving body of mass? Does this also include heat-energy? Does the vibration of a body of mass make a difference to mass-energy? Does this also apply to rotating masses? In the case of moving masses, there is a vector component that may not be considered in the other forms of energy, would that be the difference in terms of curving space?

Thanks Asbo.

-Will
 
In general relativity, mass and energy are represented by the Einstein field equations, which relate the geometry of spacetime to the distribution of energy, momentum and stress within it.
(The density and flux of energy and momentum, rather than Newtonian mass, are the sources of gravitational fields. Mass is represented by its energy equivalent through E = mc².) Together with the geodesic equation, these equations can be used to predict the path of freely falling matter in curved spacetime.
 
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Because c is used as the symbol for the speed of light in vacuo by convention.

Another way of writing the equation to express the energy of a moving object is:

E = mc² = √((m°c²)² + (pc)²) = ɣm°c²

where m° is the rest mass, p = ɣm°v is momentum, v is velocity, and the Lorentz factor ɣ = 1/√(1-v²/c²).

For v <<c, E = m°c² + ½m°v², which is the classical limit.

The zero in m° should be a subscript but I can't work out how to express that using this website's coding.
 
It perhaps does look a bit odd to see a constant squared, but some constants are derived from other constants. For example, the dimensionless fine-structure constant α, which has the approximate value 1/137.0360, is defined as α = e²/2ε°hc, where e is the elementary charge, h is Planck's constant, c is the speed of light, and ε° is the permittivity of free space. The value of c is equal to √(1/ε°μ°), where μ° is the permeability of free space.
 
I will just state that my views on physics aren't orthodox. I don't believe virtual particles exist as usually described. I think physics lost its way when Richard Feynman and others of a similar mind started propagating nonsense that seems to give believable numbers - much like epicycles in early models of the solar system as I mentioned previously. But I can afford to be a heretic as I'm long outside academia. I suspect the particles termed 'virtual' actually exist in infinite alternate realities. I can't think of a way to test this hypothesis, so it's metaphysics, not science. I don't expect anyone to take me seriously. There will be a breakthrough one day, one way or another, and many text books will become historical records of discredited ideas - similar to what happened with phlogiston.
 
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Interesting developments in formulating a new theory of quantum theory called - I kid you not - almost quantum theory. It also makes testable predictions that would falsify it or traditional quantum theory (or both, I guess). In addition, almost quantum theory has a similar mathematical structure to the consistent histories formulation of quantum gravity, which would suggest that theory is also on the right track if almost quantum theory passes muster experimentally. Coming up with a workable theory of quantum gravity that doesn't contain embarrassing infinities has been a major hurdle for many decades now.

[1403.4621] Almost quantum correlations (arxiv.org)
Almost quantum correlations Nature Communications

Now I'm wondering how this theory fits with superdeterminism.
 
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