the Principle of Equivalence

[AntonioLao]

In 1907 Einstein started a road to reality for a goal of formulating the general theory of relativity. This theory was finalized in November 25, 1915. Within the interval of 8 years he conceived the mathematical principle of general covariance for all motions: uniform linear velocity and uniform nonlinear acceleration.

Uniform linear velocity was accomplished by special relativity. The general theory supposedly accomplished both motions. He received helps from his mathematician friend Marcel Grossmann on absolute differential calculus of tensor analysis (differential geometry and differential topology). In a sense, tensors are analysis situs or the highest branch of affine linear geometry called topology, in contrast to nonlinear fractal geometry of chaos theory. Topology studies continuous infinitesimal transformations which preserve local infinitesimal geometric properties: mapping parallel lines to parallel lines and finite points to finite points without creating new points or fusing existing points. This creation-annihilation invariance is absolutely necessary in order to have space-time quanta.

It is known from quantum field theories that creation and annihilation operators exist which transform fermions into bosons and vice versa. If fermions or bosons can be created or annihilated then they both cannot be the fundamental building blocks of the Universe. If mass and energy are not fundamental then what is? Obviously it must be the absolute vacuum of space-time. Fortunately these quanta of space-time are easily describable mathematically and physically as the square of energy in a theory of quantized space-time (TQS).

The possibility of TQS was foretold by the Principle of Equivalence which states succinctly that the Principle of General Covariance is only valid at the local infinitesimal domain of space-time where the square of energy holds its independence of both mass and time.

[mkirkpatrick]

Interesting thread Antonio,"Imagination is more important than knowledge"Quote,A Einstein,and another,"when you sit with a nice girl for two hours,it seems like two minutes,
when you sit on a hot stove for two minutes,it seems like two hours that's reativity"
Unquote.

regards michael.

[Lloyd Gillespie]

In 1907 Einstein started a road to reality for a goal of formulating the general theory of relativity. This theory was finalized in November 25, 1915. Within the interval of 8 years he conceived the mathematical principle of general covariance for all motions: uniform linear velocity and uniform nonlinear acceleration.

Uniform linear velocity was accomplished by special relativity. The general theory supposedly accomplished both motions. He received helps from his mathematician friend Marcel Grossmann on absolute differential calculus of tensor analysis (differential geometry and differential topology). In a sense, tensors are analysis situs or the highest branch of affine linear geometry called topology, in contrast to nonlinear fractal geometry of chaos theory. Topology studies continuous infinitesimal transformations which preserve local infinitesimal geometric properties: mapping parallel lines to parallel lines and finite points to finite points without creating new points or fusing existing points. This creation-annihilation invariance is absolutely necessary in order to have space-time quanta.

It is known from quantum field theories that creation and annihilation operators exist which transform fermions into bosons and vice versa. If fermions or bosons can be created or annihilated then they both cannot be the fundamental building blocks of the Universe. If mass and energy are not fundamental then what is? Obviously it must be the absolute vacuum of space-time. Fortunately these quanta of space-time are easily describable mathematically and physically as the square of energy in a theory of quantized space-time (TQS).

The possibility of TQS was foretold by the Principle of Equivalence which states succinctly that the Principle of General Covariance is only valid at the local infinitesimal domain of space-time where the square of energy holds its independence of both mass and time.

Fill in the missing infinitesimal link with absolute fundamental space substance, and you have the answer to TQS.

regards,

[Lloyd Gillespie]

In 1907 Einstein started a road to reality for a goal of formulating the general theory of relativity. This theory was finalized in November 25, 1915. Within the interval of 8 years he conceived the mathematical principle of general covariance for all motions: uniform linear velocity and uniform nonlinear acceleration.

Uniform linear velocity was accomplished by special relativity. The general theory supposedly accomplished both motions. He received helps from his mathematician friend Marcel Grossmann on absolute differential calculus of tensor analysis (differential geometry and differential topology). In a sense, tensors are analysis situs or the highest branch of affine linear geometry called topology, in contrast to nonlinear fractal geometry of chaos theory. Topology studies continuous infinitesimal transformations which preserve local infinitesimal geometric properties: mapping parallel lines to parallel lines and finite points to finite points without creating new points or fusing existing points. This creation-annihilation invariance is absolutely necessary in order to have space-time quanta.

It is known from quantum field theories that creation and annihilation operators exist which transform fermions into bosons and vice versa. If fermions or bosons can be created or annihilated then they both cannot be the fundamental building blocks of the Universe. If mass and energy are not fundamental then what is? Obviously it must be the absolute vacuum of space-time. Fortunately these quanta of space-time are easily describable mathematically and physically as the square of energy in a theory of quantized space-time (TQS).

The possibility of TQS was foretold by the Principle of Equivalence which states succinctly that the Principle of General Covariance is only valid at the local infinitesimal domain of space-time where the square of energy holds its independence of both mass and time.

Antonio, I'm wondering if you're familiar with the "mass gap" literature. How does this fit into the above?

Here's a post I posted elsewhere. How does it fit?
First, thank-you BottomLander...

The article mentioned below is: With Realizations of a Hierarchy of Oyibo-Einstein Relativities: http://www.math.buffalo.edu/mad/phys...GUTreview1.pdf
It's also sub-titled: Discovery of the Theory of Everything and the Fundamental Building Block of Quantum Theory.

In answer to your question Dipayankar, string theory is the newest gauge theory of a long line of strung together gauge theories. It's mathematics and language use have value in developing better understandings of a new sub-quantum language, that must be created, and understood, to understand the ergodicity of all gauge theories, less their false semantical axiomatic unions, of the present. Here's a deffinition of ergodicity:
http://dictionary.reference.com/browse/ergodicity IMO, the overall physical dynamics of string theory itself, is far too far fetched, to be valuably accepted or used. However; omitting its physical predictions, its math and language have theory value, in extending our analytic ideas of the universe. Extra dimensions are not required to explain the hydrodynamic state changing fluid dynamics of the universe, but one problem that must be overcome is the mass gap listed here: http://en.wikipedia.org/wiki/Yang%E2...e_and_mass_gap IMO, and with BottonLander's post agreeing with me, as well as Alexander Zazerskiy's merged fluid dynamics of the electron, with electrodynamics, I see the ability of merging all valid gauge theory ideas and maths, into one hydrodynamic changing state fluid dynamics, and its changing state fluid field dynamics, into a completed "real mass" understanding of the entire universe...

If we unite the true ergodicity of all systems' thought, inside the one system, of the hydrodynamics of fluid[viscous and non-viscous] dynamics, we can successfully solve the true mass gap. And BTW, this is worth $1,000,000 from the Clay Institute: http://en.wikipedia.org/wiki/Clay_Mathematics_Institute I think it may be worth the try...

Regards,
Lloyd

[michellemfry]

You can be a lone survivor on an island, never heard of Einstien, and still instinctively feel relativity. Personal time, as opposed to absolute time, and warped space based on nearness to a mass, as opposed to flat forever square in all directions. It is how the universe holds you, each and every one of you, close and dear.

[Lloyd Gillespie]

You can be a lone survivor on an island, never heard of Einstien, and still instinctively feel relativity. Personal time, as opposed to absolute time, and warped space based on nearness to a mass, as opposed to flat forever square in all directions. It is how the universe holds you, each and every one of you, close and dear.

I don't buy it Michell, your feeling is only relative to your own self-emotions...

regards,

[dleviwing]

The concepts of Relativity stated by Antonio, refer mainly to Special Relativity and thus is a subjective function of the perception of motion. (space-time geometry) The 1915 covariance is the General Relativity version that accounts for the influence of mass and also acceleration and thus the equivalence principle.

The quantum field theory mentioned is one of the problems of calling a measured quantity an entity. (mass and energy) The building block is a fundamental substance, not a measurement.