**Most common misunderstandings**
**about Special Relativity (SR)**

(Umberto Bartocci^{*})

**1 - Introduction**

**2 - What does " special" means?**

**3 - Sagnac effect**

**4 - The light’s speed for non-inertial observers**

**5 - The Principle of (Special) Relativity and
the "twins paradox"**

**6 - Roemer observations**

**7 - Bradley aberration**

**8 - Is it true that electromagnetism is relativistic?
That**

**"Classical Physics" is the "limit" of SR for low speeds?**

**1 - Introduction**

During its (rather brief) history, Physics has seen many
different theories challenging each other, in the attempt to solve some
of the riddles presented by natural phenomena. Between them, a *special*
place is occupied by SR, which, at this century’s beginning, proposed to
wipe out all discussions about aether’s (and light’s!) nature, with its
bold proposal to change the "usual" space-time structure. We have said
that SR must really be considered as "special", since, in the aforesaid
situation, advocates of the one or the other confronting parties have always
warmly debated, but never with that harshness which characterizes the criticism
towards SR. The reason for that is easily understandable, since SR forces
to abandon that *ordinary intuition* which, in a sense or in the other,
was always present in *both* opposing fields: remember for instance
the "struggle" between the supporters of Ptolemy and those of Copernicus,
or between the proponents the corpuscular nature of light against the defenders
of the wave-theoretical approach.

As a matter of fact, SR should more properly be regarded
as a kind of *revolution* with strong *conservative aspects*,
like for instance the proposal to choose as a *corner-stone* of the
"new" theory the "old"^{1} *Principle of Relativity*, joining
in such a way the Newton’s point of view of an "empty space" against Descartes’s
"plenum" - exactly as it went unmodified since XVIII century, during the
development of modern Mechanics.

This "conservative heart" of SR is even noticeable in
the metaphysical interpretation of the theory, that matches very well with
the *deanthropocentrization process* which, started with the birth
of modern science, found his climax with *Darwin’s revolution* (1859)^{2}.
It would have indeed been rather disturbing "modern philosophy", if man’s
ordinary categories of space and time, built only under evolution’s pressure
on the Earth’s surface, would have shown themselves useful even for a deeper
understanding of the largest universe’s structure. Thus, in some sense,
the opposition against SR has something to do with the wider fight between
*Tradition*
and *Modernity*, and it shares some characteristic of the reactions
to what is considered the Final Age of Moral Dissolution.

According to this conceptual framework, the present author
is not objectively indifferent, and he considers himself firmly rooted
in one party. For this reason, since the last 20 years, he has looked with
great interest at the activity of the opponents of relativity, and has
witnessed the resolute obstructionism of the "establishment" against them^{3}.
Nevertheless, he must also acknowledge that, sometimes, even referees defending
the "orthodox" point of view are not so wrong, since it happens that many
anti-relativistic papers are questionable, as they do either ignore the
confrontation with the relativistic approach, or do not show a good understanding
of it. This circumstance favours the actual holders of the "scientific
power", those who dictate the cultural strategies of Western Civilization,
allowing them to discard all issues about the *experimental* validity
of SR. Of course, there is no place for questioning the *logical*
validity of the theory, since it presents itself in the guise of a mathematical
theory (naturally, a mathematical theory with *physical significance*,
namely, endowed with a set of *codification and decodification rules*,
which allows to transform a physical situation into a mathematical one,
and conversely, but a mathematical theory anyhow), and as that one has
to confront it.

Thus this paper is born, with the purpose to collect the
most common errors of anti-relativistic physicists - in matters which are
sometimes misunderstood even by relativity supporters!, as we shall see
- and with the hope to contribute in such a way to make criticism against
SR grow stronger, and respected, with the purpose to finally restore the
dominion of (ordinary) rationality in science, but not only in it...

** Remark 1 -** Since the
aim of this paper is just to pursue "scientific truth", and

**2 - What does " special" means?**

Even if it would appear unbelievable, after almost one
century of relativity, the first point which needs to be examined, is concerning
**what**
SR really is. As a matter of fact, even during the conference it has been
said that SR is that part of relativity which takes under consideration
only *inertial systems* and *uniform motions*, and that one has
to introduce General Relativity (GR) is one wishes for instance analyse
Sagnac experiment, of course from a relativistic point of view! This opinion
is incorrect, as we shall show even in the next section, and we start here
our comments by recalling that GR can be defined as the theory of a general
*space-time*,
where by this term one simply means a Lorentz 4-dimensional connected time-oriented
manifold^{4}. Inside GR, SR is just the special case of a *flat*
space-time, and this means, from a *phyisical* point of view, of a
space-time in absence of gravitation, since in Einstein’s theory gravitation
is introduced as an effect of space-time *curvature*. This shows that,
as a physical theory, SR can be applied (successfully or not, this is another
matter!) when *gravitational* effects can be ignored (as well as *quantistic*
ones, but this is again another matter), and not just when uniform motion
are involved, and that is (almost) all. One should indeed add that, under
"mild" mathematical assumptions, there exists *only one* SR, according
to this point of view. As a matter of fact, one can prove that any two
*simply connected* and
*complete* flat space-times are *isometric*,
and then both isometric to the space **R ^{4}** with its canonical

Using these Lorentz coordinate systems, the physical phenomenology
pertinent to SR can be easily expressed: for instance the light’s speed
turns out to be isotropic and equal to the universal constant c (in this
mathematical framework, one puts often c=1) everywhere, namely for all
inertial observers, but one can also introduce *different* (and even
just *local*, that is to say, only defined on an *open portion*
of **M**) coordinate systems (from a physical point of view, *accelerated
observers*), and things can change very much, as we shall see in the
next sections: *but it will always be special relativity*!

** Remark 2 -** The fact
that one "practically" never has inertial frames, does not mean anything

**3 - Sagnac effect**

We have said that, when you ask what SR would predict
for observers which are not in uniform motion, you have to introduce coordinate
systems of **M** which are different from the Lorentz ones. We shall
now study as an example the famous *Sagnac experiment*, and the wrong
claim that it would disprove SR (or that it would necessarily require GR
in order to be explained from a relativistic point of view).

The experimental situation is well known. Suppose to think,
in an inertial frame in **M** (or from the point of view of an inertial
observer w , or, better, of a *field* of
them, as we shall see in the next section), of an "observer" a
placed on the border of a circular platform P (let us call it C, and R
its radius - of course with respect to - from now on: "wrt" - w
), and suppose that a sends two light’s rays
along C, in the two opposite directions. When P is still, the two rays
cover all the length of C, and come back simultaneously to a
after a time interval 2p R/c. Let us suppose
now that P, and then a , is rotating (and again,
wrt w ) with some angular speed v
. It is obvious then that, from w ’s point of
view, one light’s ray, the one which travels in the same sense of the rotation,
will arrive to a *delayed* of a time interval
2p R/c times b /(1-b
) (where we have put, as usual, b =v
R/c), while the second one will arrive *anticipated* of an analogous
time interval 2p R/c times b
/(1+b ). To make it short, we can introduce
the *ratio* k between the two time intervals *forwards* and *backwards*,
D
T_{I} = 2p R/c(1-b
) ³
D T_{B}
= 2p R/c(1+b ), and
see that SR, as besides any other "classical" theory (we can suppose for
instance w to be an "aether-frame", or some
other *absolute* frame), would predict an *effect*, the so-called
Sagnac effect, due to the rotation of P. Qualitatively, this means that
the two light’s rays do not arrive simultaneously to a
; quantitatively, that the effect is "measured" by the number k = (1+b
)/(1-b ) (k ³
1, and k = 1 if, and only if, v = 0). This k
coincides even with the analogous value computed by a
, using a ’s *proper time* (see next section),
since one would have then only to modify both numerator and denominator
of that fraction by the *same* factor.

So far, so good, but then somebody adds that SR is now
in "contradiction". If SR is true, he says, then even for the observer
a
, who is now supposed to move with the speed v = v
R wrt w , the light’s speed should always be
a *constant* equal to c, and then, from a
’s point of view, *no effect should be predicted at all*. In other
words, SR would predict a k > 1 effect for w
, but a k = 1 effect for a , which would indeed
be a patent contradiction.

Of course, the previous argument is wrong, since a
is *not* an inertial observer in **M**, and what would be the "light’s
speed" for a is matter to be wholly decided
with carefully rigorous definitions and computations. But then, in order
to avoid such complications, one gets further with naïve arguments,
saying that, even if a is not an inertial observer,
he would become such when R is "very large", and then the contradiction
in SR would still hold. In order to put this argument in a more precise,
and attractive, set-up, we go back to that value k, which is indeed a function
of R and v . We can suppose to let R increase
up on infinity, and to let v vary in such a
way that the product v R is a constant v. At
the limit, we would have the physical situation of a platform rotating
"very slowly", and of an observer a which could
not be considered other than an "inertial" one. This would, apparently!,
imply that SR is forced to predict a limit for k equal to 1 (no effect),
while k is actually defined, for *each* value of R!, as a *constant*,
definitively different from 1!

The simple solution to this objection is that SR predicts
indeed even at the limit an effect which is given always by the same constant
k¹ 1, without any contradiction, and that
the misunderstanding simply arises from a non complete mastery of how in
SR one has to introduce general coordinate systems, and concepts like the
light’s speed in these ones. We shall give a sketch of the situation in
the next section, but we end the present one saying that if a
could indeed be *locally* seen as an inertial observer, the same thing
cannot be said *globally*; that is to say, the whole of C would definitively
remain outside any inertial (and then global) coordinate system, even approximately.
Perhaps, it would be useful to remark that, if we think of the "observer"
a
as he was a "single man" lying on the platform, with his own clock, we
should distinctly realize that when this man is in one point p of the platform,
endowed with some vectorial velocity **v** wrt w
, then in this moment he belongs to an inertial system which is very different
from the inertial system to which the same man belongs when he is in the
*antipodal* point q of p, since in q he is endowed with the vectorial
velocity -**v** (always wrt w ). Claiming
that **v** and -**v** are "almost the same", is poor physics and
even worst mathematics, since it would simply mean that **v** is "almost
zero", which is indeed the only case of an "almost one" Sagnac effect!

** Remark 3 -** There seems
to be only one correct "limit argument" in this framework, which goes as
follows. Suppose beforehand that all P travels with an uniform motion wrt
w
, without any rotation, and call for instance
w
* the inertial system in which P is still (it is obvious that P would not
be any longer a "circular platform" wrt
w ,
if it is such wrt w *, just because of lenght’s
contraction). Then in w * there is no Sagnac
effect, and in force of the Principle of Special Relativity, there would
be no effect even in w , at least according
to SR. Suppose now to think of P placed in some "big" platform Q, say near
the border of Q, the centre of P far from the centre of Q, and at first
suppose that both P and Q are still wrt w .
In this case, you have no Sagnac effect at all on P. Then make just Q rotate,
dragging P "rigidly" with itself: there would be any Sagnac effect on P?
Yes, there would be one, and

**4 - The light’s speed for non-inertial observers**

Now we come, as announced, to the sketch of the question
(which is often misunderstood even by "orthodox physicists") of what is
in SR the light’s speed (in "empty space"!) wrt to a non inertial observer
- and let us point out that we shall often use the convention to put c
= 1, namely to use *geometrical unities*. First of all, let us recall
that by "observer", in a *general* space-time **S**, we must actually
mean a future-pointing (smooth) curve a (t
) : I® **S** (I an open interval of the
real line **R**), such that ds^{2}(a
’) < 0 (one says that a
is *time-like*). If ds^{2}(a ’)
= -1 for all t , then the parameter t
is called a *proper time* of a (and a
a *normalized observer*). Then, it must be clear that we cannot introduce
any conception of "light’s speed" with respect just to a *single*
observer. First of all, we need an *observer field*, namely a future-pointing
unit (which really means -1) vector field X, whose integral curves would
become "observers" (coordinatized by a proper time), according to the previous
definition^{6}. Then we must introduce, if it is possible, a coordinate
system of **S** *adapted* to X, by which we mean, if X is defined
on the open set U of **S**, a coordinate mapping of U such that:

1) the coordinate lines x^{i} = constant, i =
1,2,3, "coincide" with the integral lines of X (namely, in each point-event
p, the velocity of these trajectories, wrt to the parameter x^{4},
is parallel, and equi-oriented, with X(p));

2) the hypersurfaces x^{4} = constant are orthogonal^{7}
to X (and then, in particular, are *space-like*).

It is not always possible to find a coordinate system
adapted to an arbitrarily chosen observer field X, and we refer to O’Neill’s
textbook (Chap. 12) for details. For instance instead, given any inertial
(from a mathematical point of view, this simply means *geodesic*)
observer in Minkowski space-time **M**, it is always possible to uniquely
"extend" it to an inertial global (and complete) observer field X (all
X-observers are inertial), and to find, between the many adapted coordinate
systems to X, a Lorentz one.

But let us suppose to take from now on such a "nice" field
X, and then ask what the light’s speed could possibly be wrt X, namely
wrt to any coordinate system adapted to X. It is clear that the "usual
definition" speed = space/time cannot work any longer without some specifications,
since there would be problems in giving correct definitions both for numerator
than for denominator of that fraction^{8}. For instance, the difference
between the final and the initial *coordinate time* x^{4}
of a light’s travel would *not* have a *physical meaning*; not
even would have a physical meaning the difference between the final and
the initial *proper times* of the travel, since the X-observers would
in general not be *synchronized*. What one could think of, is to see
whether is it possible to choose adapted coordinates which are *properly
synchronized*, that is to say, such that the coordinate time x^{4}
acts as proper time for all X- observers, but this is impossible, unless
the field is *geodesic* and *irrotational*! This implies for
instance in SR, that only inertial observers are "good" in this sense,
and that there is no hope to introduce such good coordinate systems in
Minkowski space-time for *accelerated observers*.

Anyway, one can say something even in this case. For instance,
one can introduce at least an *instantaneous light’s speed*, taking
into account the "splitting" of the metric form ds^{2}, according
to the natural decomposition induced by X(p) on any tangent space T_{p}(**M**)
(for each point-event pÎ U). Indeed, under
our actual hypotheses, we have, all along the light’s path, ds^{2}
= ds ^{2}+g_{44}dT^{2}
= 0 (we put T = x^{4}, and call ds ^{2}
the *spatial component* of ds^{2}, ds
^{2}
= g_{ij}dx^{i}dx^{j}, i,j = 1,2,3), which implies
that the instantaneous light’s speed, ds /dT,
would be - in this system, and wrt to the coordinate time T - equal to

Ö -g_{44}, and
this value, as a matter of fact, could be almost *everything* (of
course, even greater than 1 - see for instance O’Neill’s textbook, pp.
181-183). But one can make use of the proper time of the X-observer defined
by X(p), and we can get in this case ds /dt
= 1. This shows that, under suitable definitions of space and time, it
will always possible to *define* the instantaneous light’s speed (in
the "empty space"), *in presence or in absence of gravitation*, always
equal to the universal constant c - but let us repeat once again that this
time "t " could possibly *not* coincide
with any coordinate time. "Doing in such a way, one extends to any possible
physical reference frame what in SR was confined only to inertial systems"^{9}.

We have thus seen that, in some sense, one could say that
the "light’s speed" is always equal to c, in any coordinate system (both
in SR and in GR), and this would seem to be a point in favour of people
asserting that Sagnac experiment would disprove SR. But this is not true,
since the previous definition *does not* imply that the ratio = space/difference
of proper time wrt to a *single* observer, in the case of a *closed*
light’s path, is necessarily equal to c! In other words, coming back to
Sagnac set-up, even if the light’s speed can be instantaneously measured
as c wrt to *any* observer on the platform’s border, this will *not*
imply that the *average light’s speed*, as measured by one single
observer, when light comes back to him along a closed path, is a constant
- and it is not difficult to understand it, when one realizes that all
proper times of the observers of the "observer field" are not synchronized
between them.

One could give many examples of this situation, even in
SR, showing that this average light’s speed could be even greater than
c, and be time depending (in the sense that an accelerated observer in
SR could measure this speed along a closed path in some moment, and then
do it again in another moment, using the "same" closed path - a path of
the same spatial length - in such a way to obtain in some cases two *different*
results - of course, this would not be the case for an uniform circular
motion), but we hope that just what has been said until now would make
the reader at least understand that one should be more *careful* before
making physical assertions about relativity. Anyway, we shall now briefly
discuss a paradigmatic example (from O’Neill’s quoted textbook, pp. 181-183).

** Example -** Let us introduce
a simplified 2-dimensional Minkowski space-time

But, as we have said, this "speed" has not a great physical
meaning, since the coordinate time t* coincides with a proper time *only*
for the observer a : for instance, as far as
a
_{L} is concerning, the coordinate time t* is *no longer*
a proper time (but for L=0), since: ds^{2}((gL+1)sinh(gt*), (gL+1)cosh(gt*))
=

-(gL+1)^{2}. It is now obvious that, if we define
the instantaneous photon’s speed, when the photon reaches a
_{L},
not as the previous value dx*/dt*, but as the value dx*/dt
_{L},
where t _{L} is a proper time for a
_{L}, then we shall get dx*/dt
_{L}
= 1, as asserted. On the other hand, we have already remarked that it is
impossible to find a coordinate time which could act as a proper time for
*all* observers in this non inertial system!

If we want to learn more from this example, we can send
a photon from a to a
_{L},
and then back, and try to compute the value 2L/D
t
, where D t is the
elapsed proper time interval wrt a , in such
a way to obtain a value for this average light’s speed (which is also called
*radar speed*). An easy computation shows that 2L/D
t
is independent of t (but dependent of L, and
this is rather paradoxical indeed), as it is equal to gL/log(1+gL). Remark
that the "limit" of this expression, as g ®
0, is exactly 1, and that this value can be as well *greater than 1 (c)*.

This shows that the average light’s speed, *in SR*,
wrt to an accelerated observer, **needs not to be a constant, and can
even be greater than c**.

We conclude this long digression saying that, if one makes
this same computation exchanging rôles between a
and a _{L}, one would obtain the value
gL/(1+gL)log(1+gL), which is different from the previous one (one will
find "symmetry" only using the coordinate time t*, instead of the proper
time t _{L}). Moreover, if one sends
a photon from x*=0 to x*=L, and then back, and makes the same operation
wrt x*=0 and x*=-L (0< L<
g^{-1}), then he would get two *different* values for the
average light’s speed, namely gL/log(1+gL) and gL/log(1-gL). All this shows
the existence of obvious *optical anisotropies* in the accelerated
system, which would consent to these observers to realize that they *are
not inertial*, without any violation of the Principle of Special Relativity.

For this same reason, it appears even **hopeless**
try to persuade relativistic physicists to give up the theory, just pointing
out at **small** "anti-relativistic" effects which can be found (or
have already been found) in experiments performed in a terrestrial laboratory:
these could always be ascribed to the Earth’s diurnal rotation, or to some
other non-inertial feature of the aforesaid system^{10}!

** Remark 4 -** The "optical
anisotropies" (and other peculiarities) displayed in the previous example
are of the same kind which can be found in presence a gravitational field,
in force of the so-called

** Remark 5 -** The example
above could be used even to point out another common misunderstanding concerning
"terminology", which consists of the belief that the "essence" of SR relies
in the assertion that any "velocity" cannot be other than "relative" (which
is true), and then going from this statement to the belief that an "apparent
relative velocity" wrt to some observer (just introduced as an ordinary
"difference" between

** Remark 6 -** One should
say that, in some sense, the misunderstandings about the use of accelerated
systems in SR (and the Sagnac case is one of these) are rooted in a misinterpretation
of the meaning of the "special" Principle of Relativity,

** Remark 7 -** I am fully
aware that some of my readers will dislike all these "mathematical details",
and even this rather paradoxical Physics - in which for instance a constant
instantaneous speed does

**5 - The "Principle of (Special) Relativity" and the
"twins**

**paradox"**

Between the arguments connected to SR which still today
enjoy a great popularity, one must indeed include *time dilation*,
which is commonly described as one the most noticeable consequences of
the theory. One of the most known formulation of this phenomenon is the
so called *twins paradox*, which was introduced by the French physicist
Paul Langevin in 1911^{12}. The essence of the paradox, and its
"explanation", are contained in almost all relativity textbooks, but we
take advantage of the set-up given in the previous section in order to
describe the situation in a rather unusual fashion.

We consider the same 2-dimensional Minkowski space-time**
M** as before, and the same coordinate system (x,t) inherent to an inertial
observer w (we suppose that w
is exactly x = 0). For each L>g^{-1}>0, we introduce the following
uniformly accelerated normalized observer a
:

x = L-g^{-1}cosh(gt
), t = g^{-1}sinh(gt ).

While w remains still in this
system, a "shares" with him the point-event
e_{1} = (0,-Ö (L^{2}-g^{-2}))
- the intersection between the line x = 0 and the hyperbolic branch (x-L)^{2}-t^{2}
= g^{-2}, x<L, t(e_{1})<0; then he goes away from
w
in the direction of the increasing x, until he reaches the (spatial) point
L-g^{-1}, in the time

Ö (L^{2}-g^{-2}).
Afterwards, he comes back approaching w , and
meets him again in the point-event e_{2 }= (0,Ö
(L^{2}-g^{-2})), the other intersection between the line
x = 0 and the aforesaid hyperbolic branch.

When one compares the elapsed proper times, both for w
and a , between these two point-events, one
easily discovers that: D t
w
= t(e_{2})-t(e_{1}) =

2Ö (L^{2}-g^{-2});
D
t a = t
a (e_{2})-t
a
(e_{1}) = 2g^{-1}sinh^{-1}(Ö
(g^{2}L^{2}-1)), which implies

D t
w
> D
t
a . Namely, when
a
and w meet again,
a
finds w *older* than him (putting for instance
L=1, and for a large g, D
t
w is almost equal to 2, while D
t a is infinitesimal).

If one introduces the equation dt
a
= Ö (1-va
^{2})dt,
which connects the infinitesimal proper time dt
a
with the infinitesimal coordinate time dt, and integrates dt
a on the portion of the hyperbolic branch going
from e_{1} to e_{2}, one gets, of course, the same result
as before, but the formula

D t
a
= INT (dt a ) = INT
(Ö (1-va
^{2})dt)

has now the advantage to emphasize the dependence of the
*twins
effect* on the speed va , besides than on
the length of the a ’s trajectory.

This can sound "strange" indeed, and undoubtedly far from
the ordinary conception of "time"; but this is SR, and one must accept
this result as one of the consequences of the relativistic conception of
Nature. Thus, why some people says that this argument reveals an *inner
contradiction* of this theory?

Perhaps the most famous form of this objection is the
one advanced by Herbert Dingle, under the logical appearance of a *syllogism*:

1 - According to the postulate of relativity, if two bodies (for example, two identical clocks) separate and re-unite, there is no observable phenomenon that will show in an absolute sense that one rather than the other has moved.

2 - If on re-union one clock were retarded *by a quantity
depending on their relative motion*, and the other not, that phenomenon
would show that the first has moved and not the second.

3 - Hence, if the postulate of relativity is true, the
clocks must be retarded equally or not at all: in either case, their readings
will agree on re-union if they agreed at separation^{13}.

But, as we have just seen, assertion 3 is plainly false,
and then there must be something wrong either in assertion 1 or in assertion
2. The simple solution of this "riddle" is that the "postulate of relativity",
either special or general, does not state that presumed *complete symmetry*
between the two clocks^{14}. The misunderstanding is rooted in
the belief that, if a moves away from w
and then re-unites, then, from a ’s point of
view, it is w instead the one which movea, and
then re-unites, *exactly in the same symmetric way*. This is not true,
because of the very different paths which the two observers are travelling
in space-time: one is geodesic, the other *definitively not*^{15}.

One can hope to persuade irreducible critics showing what is the motion of w from a ’s point of view. Acting as before, we can introduce non-Lorentz coordinates (x ,t ), connected with (x,t) by the transformation:

x = Ö
((x-L)^{2}-t^{2})-g^{-1}, t
= g^{-1}tgh^{-1}(t/(L-x)),

whose inverse is:

x = -(x +g^{-1})cosh(gt
)+L, t = (x +g^{-1})sinh(gt
).

x <0 represents the internal portion of the hyperbolic branch under consideration, while t is a ’s proper time (a is actually described by x = 0).

Then w ’s motion, as "seen" by a , is:

x = 0 = -(x +g^{-1})cosh(gt
)+L ® x cosh(gt
) = L-g^{-1}cosh(gt ) ®

x = L/cosh(gt
)-g^{-1}.

This parameter t is *not*
w
’s proper time. If we want to know dt
w
, namely dt, in the new coordinates (x ,t
), we must *directly* compute:

dt = (¶ t/¶
x
)dx +(¶ t/¶
t )dt = (gL/cosh^{2}(gt
))dt ,

which shows that dt *is not equal* to Ö
(1-vw ^{2})dt, where vw
is the speed of w in the new coordinates (this
speed is given by dx /dt
= -gLsinh(gt )/cosh^{2}(gt
))^{16}.

It is necessary to explicitely compute the integral dt
= (gL/cosh^{2}(gt
))dt , from e_{1} to e_{2},
in order to be persuaded that one gets the same value D
t
w = t(e_{2})-t(e_{1}) = 2Ö
(L^{2}-g^{-2}), which was obtained before? Namely, as w
travels from e_{1} to e_{2}, he takes a time, wrt a
, which is *bigger* than the corresponding D
t
a , and not *smaller*, with a complete
*asymmetry* as to the previous case. No "twins effect" from a
’s point of view: w is moving wrt a
, but he does not become "younger".

It is not easy to understand the permanence, and the "fortune",
of such *pseudo-arguments*, which every now and then spring up again,
even in the following form of a "proof" *per absurdum*: the Principle
of Relativity implies that some phenomenon (time dilation) cannot be true;
this phenomenon is experimentally confirmed; *ergo*, the Principle
of Relativity cannot be true^{17}! I suppose that this conclusion
is very likely physically correct (see the final section of this paper),
but unfortunately it will not be so easy to prove it!!

In conclusion, *if* the time dilation is a real natural
phenomenon, then "classical physicists" must find a way to explain it (perhaps
an effect of an absolute velocity wrt to the aether?!), but they should
stop to believe that the twins paradox have an antinomic value inside SR.

** Remark 8 -** We have
avoided to comment in this paper "critics" of the kind: in relativity c+v
must be equal to c, but this is "clearly" impossible if v ¹
0 (as Einstein would have changed Algebra’s law!), but there is an "analogous"
argument which I have seen many times in action, and then I wish to dedicate
a few lines to it. With the previous notations, let us suppose that a
is an inertial observer too (different from w
, and meeting him in the point-event (0,0)). The a
’s speed wrt w is some v ¹
0, the w ’s speed wrt a
is -v, everything is all right. But dt a
= (Ö (1-v

(Ö (1-v^{2}))dt
a
(w ’), and these two rigorous formulations would
have not allowed such a misunderstanding^{18}!

**6 - Roemer observations**

I shall discuss now the wrong claim^{19} that
SR would not be able to explain Roemer observations (1675).

Let us synthetically recall the situation. In an (inertial)
reference frame R centred in the Sun, suppose that the period of a Jupiter’s
(J) moon (M) is equal to T. Suppose to observe this period from the Earth
(E), when our planet is *going away* from J, in a position in which
the Earth’s orbital velocity is (almost) parallel to the line EJ. Let t_{0}
be an *instant* in which M appears from Jupiter’s shadow, and L be
the distance between J and E *in this very moment*. It is obvious
that one shall start to observe M from E in the time t_{0}+x, where
x = (L+vx)/c (since E has moved away from J, with speed v, during the time
x, and one can suppose J, which is much slower than E, approximately stationary
during all these observations). From this equation, one gets cx = L+vx,
and then x = L/(c-v).

In the same way, when M appears again, in the instant
t_{0}+T, one shall see it from E after a time interval y such that

y = (L+vT+vy)/c,

from which one gets y = (L+vT)/(c-v).

The period T’ of M, as seen from E in this configuration, will be then not equal to T, but rather to:

(t_{0}+T+y)-(t_{0}+x) = T+(L+vT)/(c-v)-L/(c-v)
= T+vT/(c-v) = cT/(c-v),

that is to say:

T’ = T/(1-b ) (where, as usual, b =v/c).

Suppose then to do the same observation 6 months later,
when one can approximatively say that Jupiter is still in the same position
as before, but now the Earth is *approaching* J, with the same speed
v (and velocity **v** once again almost parallel to the line EJ).

One can argue as before, and get for the new period T",
seen from E in this position:

T" = T/(1+b ),

whence it follows:

D T = T’-T" = 2b
T/(1-b ^{2}),

which allowed Roemer to estimate c, knowing v and T (which is the period of M which appears from E in the two positions in which the Earth’s orbital velocity is approximately orthogonal to the line EJ), and after carefully measuring T’ and T".

As one can see, in the previous argument one makes no
use at all of any *composition of velocities*. Moreover, the effect
which has been described is exactly the same thing as a *Doppler effect*,
since one is in front of a *cyclic* phenomenon, which is seen from
a moving observer, in the first case moving away from the source, and in
the second one approaching the source (of course, this does not mean that
the phenomenon which one is actually appreciating is an optical Doppler
effect, namely a "shift" in the frequency of the light coming from Jupiter’s
moon^{20}!).

What is the relativistic description of this same phenomenon?
Almost exactly identical as before, since we have the same inertial reference
frame R in which we can do all computations we need. Is there any difference
between the relativistic and the classical approach? Yes, there is one,
since all the values which we have previously calculated, are referred
to R, and this mean for instance that T’ is not exactly the period of M
as seen from E, when it is in the first position we have considered, since
the observer moving with E belongs to a different (almost) inertial reference
frame R’, moving with a scalar velocity v with respect to R. In order to
deduce the *relativistic values* of the (predicted) periods as really
measured from E, one has simply to apply a Lorentz transformation, and
then get, instead of the previous T’, the value T’Ö
(1-b ^{2}), which is the simple effect
of the relativistic *time dilation*. In the same way, one has to take,
in the second position, the value T"Ö (1-b
^{2}),
instead of T" (E belongs now to a *third* inertial reference frame,
moving with speed -v with respect to R!), and at last one gets *the relativistic
Roemer effect*

D T_{r} = T’Ö
(1-b ^{2}) - T"Ö
(1-b ^{2}).

This is equal to the *classical Roemer effect* D
T_{c} previously calculated, but for the factor Ö
(1-b ^{2}), which gives a *very small*
difference (as a matter of fact, a difference only up to b
^{3}):

D T_{r} = D
T_{c}Ö (1-b
^{2})
= 2b TÖ (1-b
^{2})/(1-b
^{2}) =

= 2b T/Ö
(1-b ^{2}) »
2b T(1+b ^{2}/2)
= 2b T+b ^{3}T

D T_{c} = 2b
T/(1-b ^{2}) »
2b T(1+b ^{2})
= 2b T+2b ^{3}T.

In conclusion, both SR and "classical theory" *qualitatively*
predict the same effect, with a *quantitative* difference which is
impossible to experimentally detect, and that is all...

** Remark 9 -** Of course
in SR one can also do computations directly in the two different reference
frames R’ and R"! In this case, it is J which, in the first case, moves

** Remark 10 -** Talking
about

T’ = T/(1-b ) »
T(1+b ).

**7 - Bradley aberration**

As in the previous section, the annual displacement of
a star due to Earth’s motion around the Sun, was quite well explained using
classical concepts^{21}, which allowed to estimate light’s speed
c, once known the orbital Earth’s speed v, or, conversely, to estimate
v (or, which is the same, the value of one Astronomical Unity), once known
c.

As usual, the possibility to explain aberration using
"ordinary" composition of velocities, even in the case in which one of
these is the velocity of light, induces some people to believe that SR
cannot explain this phenomenon, or must "strain the truth" in order to
do it. This is of course not true, even if many modern textbooks do not
give indeed an account of aberration which can be considered completely
correct. For instance, the well known Italian physicist Piero Caldirola
honestly acknowledges: "The study of such phenomenon is given in all textbooks
... But having ascertained that the discussion that usually is given for
the [relativistic] computation of the aberration is not quite correct ...
we believe useful to briefly exhibit here the relativistic treatment of
this phenomenon..."^{22}.

The starting point for understanding *relativistic aberration*
is to carefully distinguish between __speed__ (*scalar* velocity)
and __velocity__ (*vectorial* velocity), which in some language
is not possible - for instance, in Italian we have just one word, "velocità",
like in German one has only "geschwindigkeit". With this specification,
SR second postulate prescribes the *light’s speed* to be independent
of the motion of the source (in any inertial frame), but **not** the
*light’s
velocity*, which in fact *can depend* on the velocity of the source.

As a simple example, let us take a photon’s path, travelling
backwards along the y-axis (the photon is supposed to start at time t =
0 from some undetermined distance L>0):

f : x = 0, y = L-ct, z = 0

(velocity (0,-c,0), speed c).

If you imagine the "usual" observer travelling along x-axis
with some uniform velocity (v,0,0), endowed with a coordinate system (x’,y’,z’),
then you must use in SR a Lorentz transformation in order to connect coordinates
(x,y,z) and coordinates (x’,y’,z’):

x = (x’+vt’)/Ö (1-b
^{2}),
y = y’, z = z’, t = (t’+vx’/c^{2})/Ö
(1-b ^{2}),

and the motion of f becomes, in these new coordinates:

x = 0 ® (x’+vt’) = 0 ® x’ = -vt’,

y = L-ct ® y’ = L - c(t’+vx’/c^{2})/Ö
(1-b ^{2}) ®
y’ = L-ct’Ö (1-b
^{2}),

z = 0 ® z’ = 0.

These equations show that, in the new coordinates, the
*photon’s
velocity* is

(-v,-cÖ (1-b
^{2}),0)
(of course, the *photon’s speed* is always c, since

v^{2}+c^{2}(1-b
^{2})
= c^{2}!), which clearly *does depend* on the velocity of
the source (in the system (x’,y’,z’), this is obviously equal to (-v,0,0))^{23}.

This is the reason for relativistic aberration, since
the light coming from the source will be received by the "moving observer"
shifted under an angle q such that

tg(q ) = v/cÖ
(1-b ^{2}) = b
/Ö (1-b ^{2})
»
b (up to higher order terms in b
)^{24},

and that is (almost) all.

** Remark 11 -** When one
studies astronomical aberration from the relativistic point of view, one
can take the solar system as a

** Remark 12 -** It is paradoxical
(for people to whom this section is intended) to underline that it is not
so much aberration to be a problem for SR, rather than it is aberration
to be a problem for (some) aether theory! As a matter of fact, at first
sight it would seem that aberration would prove that Earth is really moving
"through the aether", and then it is a widespread opinion that this phenomenon
would show that Stokes "aether dragged" theory

**8 - Is it true that electromagnetism is relativistic?
That**

**"Classical Physics" is the "limit" of SR for low speeds?**

Until now, this paper could appear a kind of "mémoire
en défense" of SR, rather than a critical analysis of it, as his
author would have preferred. Thus in this last section we shall discuss
some other common convictions concerning SR, which appear no better founded
than the others we have hitherto examined, and which will hopefully point
out the very *heart* of relativity, the only one which anti-relativistic
physicists (or philosophers) should try to "attack".

As a matter of fact, there is an important *epistemological*
aspect of SR which is often not appraised as instead it would deserve:
namely, its (partial) *conventionality*, which truly removes the theory
from the strict realm of an experimental science. This conventional nature
of SR is clearly manifested in its second postulate, which one can interpret
rather as a methodological suggestion for coordinatizating space-time (that
is to say, for synchronizing distant clocks), than as an experimental *datum*.
Since it appears that one has to perform this task before measuring any
velocity, here it is that one could propose to conventionally assume the
light’s speed to be isotropic, and synchronize clocks in such a way that
this characteristic will obviously be experimentally confirmed. Of course,
this does not exhaust the content of the II postulate, since for instance
it excludes, on a presumed experimental basis, the so-called *ballistic
hypothesis*, but this is certainly "enough", thus inducing most physicists
to believe that any alleged experimental confutation of SR is defective
under this aspect. As we have already said in footnote 8, anti-relativistic
physicists often try to avoid such objections using concepts as "rigid
rods" and so on (with whose help introduce *surreptitious simultaneity*,
and as it were "invariant" concepts which are not), but all the same do
not succeed in getting that attention which they demand. If this is in
some sense true, it is even true that SR consists of *two* postulates,
and that in fact it is this first postulate which appears as a good conceptual
foundation even for the second one, granting it trustfulness, even if there
is not a *strict* implication relationship between the two^{28}.
This shows that it should be the first one the most questioned on the experimental
ground, but that notwithstanding, unfortunately, the anti-relativistic
criticism does mostly concern the second^{29}.

As a matter of fact, the Principle of Relativity only
seems commonplace when we forget about the peculiarity of asserting "no
matter what is your reference frame" for light phenomena: in principle,
it would instead be reasonable to claim that light *does* have a preferred
reference frame (like sound), and only very strong evidence should impose
the contrary viewpoint. What evidence was available to Einstein (and, as
for that matter, to us nowadays)? Apart from the "unsuccessful attempts
do discover any motion of the Earth relatively to the light-medium", so
sparingly referred to, he lead the main emphasis on the well known *induction*
phenomenon. But is it really true, as he affirmed in the first lines of
his 1905 paper, that electromagnetic phenomenology is not affected by uniform
motions? Have we enough experimental evidence to this regard? The example
that he pointed out (which was not really founded on an experimental ground,
as it was nothing more than an *exercise* in Maxwell Theory - MT),
indeed predicts identity of the two inductions, but this could have been
*accidental*.
Apart the fact, ignored by most textboks, that there exist different electromagnetic
theories challenging each other, and that it is not so clear that Maxwell’s
approach will definitively *prevail* against all the others, even
in MT, *classically interpreted* (namely, without introducing *a
priori* length contractions and time dilations)
**symmetry is not the
norm**, and that of the induction is more an *exception*, than a
*rule*. This "classically interpreted" MT is not relativistic in essence^{30},
and relativity can spring up in it only when relativistic ingredients are
inserted in it *in advance*. We cannot here but send the interested
reader to the already quoted U. Bartocci & M. Mamone Capria’s paper
(which has been used in this section without explicit references), in which
it is clearly shown also that the validity of the Principle of Relativity
in electromagnetism could be checked with **low-speed experiments**,
and this is once again in disagreement with which one generally believes^{31}.
The reason for this "misunderstanding" is quite evident: in the fundamental
relativistic equation **F** = d/dt(m**v**), it is true that for low
speeds the right-hand side of this equation is "almost equal" to the classical
one, but the most important point is concerning the left-hand side, namely
the expression of the forces. There are forces which are predictable in
some theories, and not in others, for instance there are electromagnetic
forces which arise in classical MT from a uniform motion, and which obviously
do not arise in SR, *and then the final word in this field must just
be left to direct experiments*^{32}.

**FOOTNOTES**

^{*} **Dipartimento di Matematica Università, Via Vanvitelli
1, 06100 Perugia - Italy (bartocci@dipmat.unipg.it). **The author wishes
to thank most heartily the Cartesian philosopher and good friend Rocco
Vittorio Macrì, for very stimulating discussions, and Prof. Giancarlo
Cavalleri, for his friendly revision of a preliminary version of this paper.

^{1} As it is well known, the conviction that an *uniform
motion* does not affect any "physical phenomenology" was already perfectly
exposed by Galileo in his celebrated "ship’s argument", but we can find
the same conviction (using moreover the same argument!) in Giordano Bruno,
Johannes Rheticus, Nicholas Krebs,... and even in ancient science (Lucretius,
Seneca,...). But does this principle really express some essential "natural
truth", or is it just a theoretical expedient, which was brushed up during
the great debate about the Copernican system, in order to give some reason
for the unperceived *Earth’s motion*? This historical utilization
has still today psychological influence ("Eppur si muove"), for instance
in the interpretation of the famous Michelson-Morley or Trouton-Noble experiments,
which tried to look at the elusive "absolute velocity" of a terrestrial
laboratory. Could one say instead: "Eppur *non* si muove"?! On the
contrary, this principle very likely holds just approximately in Mechanics,
and its extension to optical and electromagnetic phenomena appears the
more arbitrary the less it is supported by suitable *direct* experimental
evidence.

^{2} Of course, when we make use here of the term "conservative",
we intend just to emphasize the continuity’s relationship between SR and
the "modern science" of the last 4 or 5 centuries, and not to mean that
SR is really conservative in a most proper sense.

^{3} One can find many evidences of this obstructionism in the
famous dissident physicist Stefan Marinov’s publications.

^{4} As a good reference textbook one can quote B. O’Neill’s
*Semi-riemannian
geometry* (Academic Press, 1983).

^{5} The *Lorentz group* is a (large) subgroup of Poincaré
group, consisting of those transformations which fix the point-event (0,0,0,0)
(homogeneous isometries).

^{6} Of course, it is quite clear that the extension from one
single observer to a "continuous infinity" of them is far from being *unique*,
and that this extension is very often decided by the "physical problem"
one is trying to adapt to the theory. Anyway, there is always a *local*
unique extension, which uses as a "coordinate time" an extension of the
proper time of the primitive observer (we shall very soon see an application
of this concept).

^{7} This assumption is not strictly necessary, but we are trying
to make things the simplest as possible.

^{8} One example is given by the question known as the *Ehrenfest
paradox*: what would be the "length" of the platform’s border C as "measured"
by the observer a ? The "radius" of C should
not change, but the border of P should experience length contraction. Would
that means that the value of p would change
on the rotating system? This is not really a "problem" for SR, in which
one talks just of transformations between "measured values", and could
always assert that some global measure is *not defined*; but this
could be a problem for some "relativistic aether theory", like for instance
Lorentz theory, in which *true* Lorentz-Fitzgerald contractions are
predicted. It is this kind of problems that naïve anti-relativistic
physicists try often to avoid, by means of introducing in their arguments
"rigid" bodies as trains, spaceships, platforms, and so on (on this point,
see also the final section).

^{9} From C. Cattaneo’s *Introduzione alla teoria einsteiniana
della gravitazione*, Roma, 1961, p. 158.

^{10} As for that matter, according to SR, even the fact that
the Earth is not inertial in its motion around the Sun, should indeed be
experimentally detected! (and in fact it is so, see the next section 7,
concerning *aberration*). Going further in this direction, we would
enter into the realm of a *Physics of precision*, in which one is
compelled to compare very small effects, and this does not seem the best
strategy to fight the theory - even because physicists know very well what
the *real* value of experiments is, at a very near to zero quantitative
level. As Einstein once said, or at least one says so: nobody believes
in a theory, but its promoter, all believe in experiments, but their performers
(we could remark that: all *declare* to believe in experiments)...

^{11} This could be perhaps the reason for another common misinterpretation
of the "relativity principle", in its different degrees of generalizations,
which confuses this principle with the *relative motion principle*.
We shall not make a comparison of these two principles in this paper, sending
the interested reader to: U. Bartocci, M. Mamone Capria, "Symmetries and
Asymmetries in Classical and Relativistic Electrodynamics", *Foundations
of Physics*, 21, 7, 1991, pp. 787-801.

^{12} "L’évolution de l’espace et du temps", *Scientia*,
Vol. 10, 1911, pp. 31-54. Nevertheless, Einstein himself had already paid
attention to this "phenomenon" in his first fundamental relativistic essay
(1905), and in a subsequent paper (1911).

^{13} From H. Dingle’s *Science at the Crossroads*, Martin
Brian & O’Keeffe, London, 1972, p. 190.

^{14} This obvious comment was immediately put forward to Dingle
by W.H. McCrea (*ibidem*, pp. 190 and 240-245): "In Professor Dingle’s
letter, his statement (1) is demonstrably false".

^{15} Sometimes, "critics" try to avoid this difficulty considering
a motion the "most possible inertial", introducing a polygonal path (a
*broken*
geodesic): but this is still non geodesic, even is made up with geodesic
components!

^{16} The infinitesimal proper time interval is defined (only
for trajectories with ds^{2} < 0)
as dt = Ö (-ds^{2}),
and, from this expression, the well known relation follows immediately,
*but
only in a Lorentz coordinate system*: dt
= Ö (-ds^{2}) = Ö
(-dx^{2}+dt^{2}) = (Ö (-v^{2}+1))dt.

^{17} With the real paradoxical consequence, from a *logical*
point of view, that the principle of relativity would be able to predict
a true natural phenomenon, but this fact, instead of being considered a
point in favour of the theory, would on the contrary prove that the theory
is wrong!

^{18} If we call, as usual, (x’,t’) the Lorentz coordinates
inherent to a , we would have indeed dt = dt
w
and dt’ = dt a .
From the Lorentz transformation x = (x’+vt’)/Ö
(1-v^{2}), t = (t’+vx’/c^{2})/Ö
(1-v^{2}) (with the actual notations b
= v/c = v), we would have for instance dt = (¶
t/¶ x’)dx’+(¶
t/¶ t’)dt’ = v/Ö
(1-v^{2})dx’ + (1/Ö (1-v^{2}))dt’,
which implies the previous equation dt = dt
w
= (Ö (1-(-v)^{2}))dt
a
= (Ö (1-v^{2}))dt’
*only*
if x’ = -vt’, dx’ = -vdt’ (which is indeed the motion of w
wrt a ), and that is all.

^{19} It would have been perhaps just enough to say that, if
this was true, then relativity would have not been born at all!

^{20} Of course, even this kind of Doppler effect should have
to manifest itself, but it would be very small indeed...

^{21} But one often forgets that the original "simple" Bradley’s
explanation (1728) required the *corpuscular* nature of light (as
Bradley belonged to the "Newtonian" party!), and that one had to wait till
1804, before Young succeeded in giving a wave-theoretical explanation!
(see for instance E.T. Whittaker’s *History of the Theories of Aether
and Electricity*, Dublin University Press Series, 1910, Chap. IV, p.
115).

^{22} "Applications and experimental verifications of Special
Relativity", at p. 395 of the volume dedicated to the *50 years of relativity*,
Sansoni, Firenze, 1955.

^{23} This phenomenon could perhaps be
the conceptual ground for some experiment aimed to compare SR predictions
with analogous aether-theoretic expectations, since one could suppose that
it would be natural, in an aether-frame, to have *total independence*
of light’s velocity of the velocity of the source. One could think for
instance to use the circular platform of section 3 for sending a light’s
ray from a directional laser source, placed in the border of the platform,
towards the centre, and then to check whether this ray arrives exactly
in this point, or it is instead "dragged" from the velocity, as SR would
predict!

^{24} And since b is of course "very
small", one can directly approximate q »
b
, as it is usual.

^{25} The *radial* velocity would be responsible instead
for the relevant part of the *Doppler effect*, which is known, in
the general case, as the *red-shift*.

^{26} With this term one could designate *any* aether theory
which claims that the relative velocity aether-Earth is equal to zero -
at least at Earth’s surface, and possibly not taking into account the Earth’s
diurnal rotation velocity - even if in the *Descartes-Leibniz vortex
theory* it would be better to speak instead of a "dragging aether" theory!

^{27} "Esperimenti di ottica classica ed etere - Experiments
of classical optics and aether", *Scientia*, Vol. 111, 1976, pp. 667-673.
By kind courtesy of Prof. G. Cavalleri, we hereafter quote this remark:
"However, Stokes aether is unable of explaining the *transversal*
property of electromagnetic waves. On the contrary, Stokes-Planck compressible
aether would imply the existence of *longitudinal* electromagnetic
waves. That is why we can exclude the theory of an irrotational, compressible
aether, as said at the end of the previous reference".

^{28} By the way, if one accepts the validity of Maxwell electromagnetism
(in inertial frames), then the *invariance* of light’s speed (in these
same frames!) directly follows from Maxwell equations *plus* principle
of relativity.

^{29} In general, it appears that people is willing to readily
accept the first SR postulate (in force of the *historical suggestions*
pointed out in the previous footnote 1?!), while being critical on the
second, which is admittedly counter-intuitive, and difficult to "understand".

^{30} It should be made indeed very clear for instance that
the *finite speed of propagation* is not an exclusive character of
the relativistic point of view, but simply of Maxwell equations, which,
as we have said, can as well been used in a "classical" context. As for
that matter, anyway, the prediction of the retardation in the interactions
is quite typical of an "aether theory", rather than of a theory which does
not introduce such a concept, since then the effects are transmitted through
the *underlying medium*, and the characteristic speed c can be for
instance interpreted as a function of some of its *physical* properties.
In other words, instantaneous actions at a distance are much more coherent
with the *Newtonian* point of view of an "empty space", rather than
with the *Cartesian* one, and this shows once more that SR is really
a sort of an unpleasant hybrid between these two.

^{31} With some important exception: this circumstance was emphasized
for instance in A.P. French’s known textbook, p. 259 (*Special Relativity*,
MIT Press, 1968). The point is that the actual "history of Physics" is
prejudiced by some *evolutionistic postulate*, according to which
there are no confutations of "old" theories (for instance, Newtonian *versus*
relativistic Mechanics), but just simple improvements in the degree of
approximation ("Principle of Correspondence"), or extensions of the phenomenology.
Of course, this point of view is rather questionable, and we could refer
the interested reader to the important M. Mamone Capria’s studies: "The
Theory of Relativity and the Principle of Correspondence", *Physics Essays*,
8, 1994, pp. 78-81; "La crisi delle concezioni ordinarie di spazio e di
tempo: la teoria della relatività", in *La costruzione dell’immagine
scientifica del mondo*, La Città del Sole, Napoli, 1999, pp.
265-416; "Newtonian Physics and General Relativity: Reflections on Scientific
Change", in *La scienza e i vortici del dubbio*, Proceedings of the
International Conference "Cartesio e la scienza", Università di
Perugia, 1996.

^{32} In the quoted Bartocci-Mamone Capria’s paper, an experiment
is proposed, which has been recently performed by the Italian physicist
Fabio Cardone, in L’Aquila’s laboratories. The experiment has put in evidence
some "anisotropy" of difficult interpretation, but was undoubtedly coherent
with all the until now "unsuccessful attempts to discover any motion of
the Earth relatively to the light-medium" (and let us quote another kind
remark of Prof. G. Cavalleri: "All the extremely accurate electronics on
space ships, satellites, shuttles, etc., show that the aether drag is *not*
present"). This fact points once again at the possibility that the relative
velocity Earth-aether, at Earth’s surface, is zero, or very near to zero
(on this argument see also the previous footnote 26). In order to find
decisive elements in favour, or contrary, to SR, one should stop to emphasize
the certainly successful but *indirect* consequences of the theory,
and start, at long last, to perform experiments in **two** different
reference frames, one in real uniform motion with respect to the other.