Fundamental truths taught in Einsteiniana's schizophrenic world:

1. The principle of constancy of the speed of light is true because
the speed of light is constant by definition. Moreover, in a
gravitational field, the speed of light is both variable and
constant:

http://math.ucr.edu/home/baez/physic..._of_light.html
Steve Carlip: "Is c, the speed of light in vacuum, constant? At the
1983 Conference Generale des Poids et Mesures, the following SI
(Systeme International) definition of the metre was adopted: The metre
is the length of the path travelled by light in vacuum during a time
interval of 1/299 792 458 of a second. This defines the speed of light
in vacuum to be exactly 299,792,458 m/s. This provides a very short
answer to the question "Is c constant": Yes, c is constant by
definition! (...) Einstein went on to discover a more general theory
of relativity which explained gravity in terms of curved spacetime,
and he talked about the speed of light changing in this new theory. In
the 1920 book "Relativity: the special and general theory" he wrote:
". . . according to the general theory of relativity, the law of the
constancy of the velocity of light in vacuo, which constitutes one of
the two fundamental assumptions in the special theory of relativity
[. . .] cannot claim any unlimited validity. A curvature of rays of
light can only take place when the velocity of propagation of light
varies with position." Since Einstein talks of velocity (a vector
quantity: speed with direction) rather than speed alone, it is not
clear that he meant the speed will change, but the reference to
special relativity suggests that he did mean so. This interpretation
is perfectly valid and makes good physical sense, but a more modern
interpretation is that the speed of light is constant in general
relativity."

2. As soon as the observer starts moving towards the light source, the
approaching light automatically decreases its wavelength so as to
present itself to the observer with a constant speed, in perfect
accordance with Einstein's 1905 constant-speed-of-light postulate:

http://www.pitt.edu/~jdnorton/teachi...ang/index.html
John Norton: "Here's a light wave and an observer. If the observer
were to hurry towards the source of the light, the observer would now
pass wavecrests more frequently than the resting observer. That would
mean that moving observer would find the frequency of the light to
have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE
BETWEEN CRESTS - TO HAVE DECREASED)."

3. The relativity theory cannot be false (more precisely, it is the
only possible theory in Einsteiniana's schizophrenic world) because
"it is impossible to detect a movement at constant speed":

http://www.crm.umontreal.ca/~durand/club-math-2011.pdf
Stéphane Durand: "Puis nous expliquerons pourquoi la théorie de la
relativité ne peut pas être fausse (du moins, dans notre univers).
Plus précisément, dans un univers où il est impossible de détecter un
mouvement à vitesse constante (comme c'est le cas dans le nôtre), la
théorie de la relativité est la seule possible; avec comme cas limite
la physique galiléenne."

4. An arbitrarily long object can be trapped inside an arbitrarily
short container; the object does not undergo any physical compression:

http://www.quebecscience.qc.ca/Revolutions
Stéphane Durand: "Pour mieux comprendre le phénomène de ralentissement
du temps, il est préférable d'aborder un autre phénomène tout aussi
paradoxal: la contraction des longueurs. Car la vitesse affecte non
seulement l'écoulement du temps, mais aussi la longueur des objets.
Ainsi, une fusée en mouvement apparaît plus courte que lorsqu'elle est
au repos. Là aussi, plus la vitesse est grande, plus la contraction
est importante. Et, comme pour le temps, les effets ne deviennent
considérables qu'à des vitesses proches de celle de la lumière. Dans
la vie de tous les jours, cette contraction est imperceptible.
Cependant, si une fusée de 100 m passait devant nous à une vitesse
proche de celle de la lumière, elle pourrait sembler ne mesurer que 50
m, ou même moins. Bien sûr, la question qui vient tout de suite à
l'esprit est: «Cette contraction n'est-elle qu'une illusion?» Il
semble tout à fait incroyable que le simple mouvement puisse comprimer
un objet aussi rigide qu'une fusée. Et pourtant, la contraction est
réelle... mais SANS COMPRESSION physique de l'objet! Ainsi, une fusée
de 100 m passant à toute vitesse dans un tunnel de 60 m pourrait être
entièrement contenue dans ce tunnel pendant une fraction de seconde,
durant laquelle il serait possible de fermer des portes aux deux
bouts! La fusée est donc réellement plus courte. Pourtant, il n'y a
PAS DE COMPRESSION matérielle ou physique de l'engin."

5. An arbitrarily long object can be trapped inside an arbitrarily
short container; the object does undergo physical compression:

http://math.ucr.edu/home/baez/physic...barn_pole.html
"These are the props. You own a barn, 40m long, with automatic doors
at either end, that can be opened and closed simultaneously by a
switch. You also have a pole, 80m long, which of course won't fit in
the barn. Now someone takes the pole and tries to run (at nearly the
speed of light) through the barn with the pole horizontal. Special
Relativity (SR) says that a moving object is contracted in the
direction of motion: this is called the Lorentz Contraction. So, if
the pole is set in motion lengthwise, then it will contract in the
reference frame of a stationary observer.....So, as the pole passes
through the barn, there is an instant when it is completely within the
barn. At that instant, you close both doors simultaneously, with your
switch. Of course, you open them again pretty quickly, but at least
momentarily you had the contracted pole shut up in your barn. The
runner emerges from the far door unscathed.....If the doors are kept
shut the rod will obviously smash into the barn door at one end. If
the door withstands this the leading end of the rod will come to rest
in the frame of reference of the stationary observer. There can be no
such thing as a rigid rod in relativity so the trailing end will not
stop immediately and the rod will be compressed beyond the amount it
was Lorentz contracted. If it does not explode under the strain and it
is sufficiently elastic it will come to rest and start to spring back
to its natural shape but since it is too big for the barn the other
end is now going to crash into the back door and the rod will be
trapped IN A COMPRESSED STATE inside the barn."

6. Time is not an illusion:

http://www.humanamente.eu/PDF/Issue13_Paper_Norton.pdf
John Norton: "It is common to dismiss the passage of time as illusory
since its passage has not been captured within modern physical
theories. I argue that this is a mistake. Other than the awkward fact
that it does not appear in our physics, there is no indication that
the passage of time is an illusion. (...) The passage of time is a
real, objective fact that obtains in the world independently of us.
How, you may wonder, could we think anything else? One possibility is
that we might think that the passage of time is some sort of illusion,
an artifact of the peculiar way that our brains interact with the
world. Indeed that is just what you might think if you have spent a
lot of time reading modern physics. Following from the work of
Einstein, Minkowski and many more, physics has given a wonderfully
powerful conception of space and time. Relativity theory, in its most
perspicacious form, melds space and time together to form a four-
dimensional spacetime. The study of motion in space and all other
processes that unfold in them merely reduce to the study of an odd
sort of geometry that prevails in spacetime. In many ways, time turns
out to be just like space. In this spacetime geometry, there are
differences between space and time. But a difference that somehow
captures the passage of time is not to be found. There is no passage
of time."

7. Time is an illusion after all:

http://www.pitt.edu/~jdnorton/teachi...sim/index.html
John Norton: "In a relativistic (i.e. Minkowski) spacetime, the
relativity of simultaneity tells us that there are many ways to do
this; there is no unique, preferred unstacking. In this sense, space
and time get fused together and this fusion is the real novelty of the
spacetime approach in relativity theory. This novelty is surely what
Hermann Minkowski had in mind when he wrote in the introduction to his
famous lecture "Space and Time" of 1908: "The views of space and time
which I wish to lay before you have sprung from the soil of
experimental physics and therein lies their strength. They are
radical. Henceforth space by itself and time by itself, are doomed to
fade away into mere shadows, and only a kind of union of the two will
preserve an independent reality."

Pentcho Valev