The Lorentz transformation,  Minkowski space.
===========.
The Galilean transformation belongs to each inertial frame.
The Galilean transformation fails to preserve Maxwell's equations.
Why the Galilean transformation useless in the Maxwell's equations?
Because Maxwell's equations ( Lorentz transformations)
don’t belong to inertial frames.
Because Maxwell's equations ( Lorentz transformations)
 belong to another reference frame. Which?
What are Lorentz transformations?
Of course, now everybody thinks that difference between
 these two math equations (conceptions) lies only in
 speed’s distinction.
Such understanding leads to all kinds of confusions.
#
What is Lorentz transformation?
The Lorentz transformation describes transformation
 of all particle’s physical parameters in the time of transition
from one inertial frame to some kind of another reference frame.
Is this ‘another reference frame’ inertial?
No. Why?
In 1905 Poincare wrote that the Lorentz transformation creates
 math group, which conforms of arise turning- point in the space,
 which we call now 4D Minkowski space.
Again.
The Lorentz transformation describes the event in Minkowski space.
This math group describes rotation ( something that has three
 dimensions parameters) in the 4D Minkowski space.
The Lorentz transformation describes only the transformations
( rotation) of particle in the 4D Minkowski space.
#
Many physicists, including George FitzGerald, Joseph Larmor,
 Hendrik Lorentz and Woldemar Voigt, had been discussing
the physics behind these equations since 1887.
 Larmor and Lorentz, who believed the luminiferous ether hypothesis,
were seeking the transformation under which Maxwell's equations
were invariant when transformed from the ether to a moving frame.

http://en.wikipedia.org/wiki/Lorentz_transformation
#
In this rotation Maxwell's equations ( Lorentz transformations)
 change the homogenous and isotropic structure of Aether.
Maxwell's equations ( Lorentz transformations) create new
spherical reference frame.
#
Early in 1889, Oliver Heaviside had shown from Maxwell's equations
 that the electric field surrounding a spherical distribution of
charge
should cease to have spherical symmetry once the charge is in motion
 relative to the ether.

http://en.wikipedia.org/wiki/Lorentz_transformation
#
Of course, only I as a layman, can think that Lorentz
 transformation which creates math group in 4D Minkowski
space describes the behavior of real particle- photon/ electron.
In the books is written that this is only math trick, which
philosophically absurd and doesn’t have any real physical sense.
#
Now consider that Minkowski space is a good description in an
 infinitesimally small region surrounding any point
( barring gravitational singularities).
The structure of Minkowski space doesn’t have gravity.

http://en.wikipedia.org/wiki/Minkowski_space
#
In my opinion the Universe ( as a whole) doesn’t have gravity.
 The detected material mass of the  matter in the Universe is so small
(the average density of all substance in the Universe is approximately
  p=10^-30 g/sm^3) that it  cannot ‘close’ the Universe into sphere
and
 therefore our Universe  as whole is ‘open’, flat , endless Vacuum.

Therefore the 4D Minkowski metric is applied to the Universe as a
whole.
And the General Relativity only applies in a local flat 4D Minkowski
space.
=========.
Best wishes.
Israel Sadovnik  Socratus
 ===============.

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