TWIN PARADOX-------[ Return home ]


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A) Logical introduction.

In the logic lecture it has been proved that the principle of relativity as a logical statement, independantly of his physical truthness is connected in such a way to the Lorentz' transformations in the 1905 paper of Einstein, that it may be physically false even if the Lorentz' transformations are true.

That means that the physical analysis by the Lorentz' transformations alone of the twin B travel may not lead to physical absurdities, but that an other physical analysis in using the principle of relativity may lead to a physical non-sense which is the definitive proof that the " principle of relativity " is physically false, without affecting the validity of the Lorentz' transformations alone.

The purpose of this article is to definitely show this fact, in order to close one century of dialogs of the deafs about the reality of the twin paradox or antinomy.

This is additionally confirmed by the fact that a lot of experiments are in agreement with the Lorentz' transformations alone and also that I have been able to detect the ether-wind.

B) Preliminary agreement.

If we suppose that the clocks in a frame are really synchronized, it is clear that a change of the setting of the clocks is going to change all the physical measurements, like lengths, velocities, time periods of physical phenomenons in motion.

For example if a body has the velocity V before a change of the setting of the clocks like (for example): t1(x) = t(x)+x where t1(x) is the new time and t(x) the old one, we have V= dx/dt(x) and V1= dx/dt1(x)= [dx/dt(x)][dt(x)/dt1(x)]=[dx/dt(x)][1-dx/dt1(x)].

That is to say: V1=V[1-V1] or V1=V/[1-V] which is different of V.

The same way, the lengths in motion or the time dilations observed are changed, by a change of the settings of the clocks.

But there, there is a big philosophical problem to know if the way we synchronize the clocks is not going to delude us about the way nature works.

As a matter of fact, the way Einstein has decided to synchronize his clocks in a frame before to study the physical world may lead to a lot of artifacts if the clocks are not really physically synchronized.

We must note here that Einstein and his apotles consider the clocks as being really synchronized in all their works because they don't hezitate to affirm that there is a mutual " time dilation " or a mutual " length contraction ".

What is their proofs of that, without being able to affirm that distant clocks are really synchronized ?

The agreement I ask to the reader is that when we measure a length in an Einsteinian frame, it is a true length and we speak of true velocities and time dilations.

But I have to say here that if you don't agree with that, the theory of relativity is a non-sense and is thus useless as a physical theory. Because in physics, we need to know what we speak about.

C) The twin paradox

According to the above agreement, we make the hypothesis that in the frame K, the clocks are really synchronized and that an absolute time t exists for that frame (when we are inside it) in order to know of what we speak about like good " relativists ".

The time Lorentz' transformation between the frame K (see figure above) and the moving frame K' is: t= [t'+vx'/cc]/sqrt(1-bb) with b=v/c.

That means that the time t'(o') of the clock in O' is connected mathematically to the time t by the formula t= t'(O')/sqrt(1-bb).

But for a clock in x' in K', its time is connected to the unique time t by the formula:

t= [t'(x')+vx'/cc]/sqrt(1-bb).

Thus now, by elimination of the unique time t between the two equations, we see that the clocks in K' are not synchronized according to t'(x')=t'(o')-vx'/cc, in contradiction with the principle of relativity which affirms that the clocks are really synchronized.

Here, there is thus, already, an antinomy which permits to conclude that the principle of relativity is not compatible with the Lorentz' transformations.

But nevertheless I continue to show below that the " relativistic " twin B travel is impossible, that is to say : illogical.

For that I have to consider also that as the time Lorentz' transformation between the frame K ( see figure above) and the frame K '' is t=[t''-vx''/cc]/sqrt(1-bb), the lack of synchronism in K'' is : t''(x'')=t''(o'')+vx''/cc also in contradiction with the principle of relativity. (Please note here that the velocity v and thus b is the same for K' and K '' because it is the situation that I have chosen to study easily the twin paradox)

The most important thing here is to memorize the two formulas of the lack of synchronism obtained and which will be used later.

D) Twin A analysis.

When the twin B jumps at t = 0 in the frame K' in O', the absolute Einsteinian time of the frame K (agreement !) which is t is connected to the time of twin B by the formula above: t=t'(o')/sqrt(1-bb).

That means that from the departure to the place where Twin B jumps on K '' at x0'', we have delta-t1 = [delta-t'1(o')]/sqrt(1-bb). ( where 1 stand for positive way travel).

But now according to the the time lorentz' transformation t=[t''(x0'')-vx0''/cc]/sqrt(1-bb) which applies for the place where twin B has reached, we have also:

delta-t2= [delta-t''2(x0'')]/sqrt(1-bb).

And thus: [delta-t1+delta-t2]=[delta-t'1(o')+delta-t''2(x0'')]/sqrt(1-bb)

That means that TWIN B is younger than TWIN A or ageA > age B.

E) Twin B analysis.

When Twin B has jumped in K' (o'), and as the time Lorentz' transformations is

t'=[t-vx/cc]/sqrt(1-bb) towards the frame K, here if we continue to admit the validity of the principle of relativity and thus that the clocks are really synchronized (agreement above!) in spite of the fact that Twin A analysis says that there were already a problem with the PoR, we have t'=t(o)/sqrt(1-bb) (because x=cte=0 for twin A)and thus delta-t'1(o')=delta-t1/sqrt(1-bb).

Now twin B is in K''(x0''), and as the time Lorentz' transformation is

t''=[t-vx/cc]/sqrt(1-bb) we have delta-t''2(x0'')=delta-t2/sqrt(1-bb)

and finally: [deltat'1(o')+delta-t''2(x0'')]=[delta-t1+delta-t2]/sqrt(1-bb)

or AgeB > Age A exactly the contrary as above: Age a > Age B

A very fine antinomy !!!

F) Back to logic.

In the logic lecture it has been proved that the principle of relativity as a logical statement is connected only by a logically weak implication thruth table to the lorentz' transformations, and thus that the principle of relativity may be physically false.Thus, the fact that we have obtained a physical absurdity with the ages of the twins is fully possible in the logical structure of the 1905 paper of Einstein.

But this physical result of the obvious falsety of the logical statement:

[Age A> Age B] and [Age A < Age B] permits to obtain an important result from the science logic alone.

The twin paradox reasoning is the following:

[PoR and LTE] implies [logical statement never physically true=C]

But in the truth table of the logical connection:

__A_B_C_[A_and_B]_implies_C

1)_0_0_0__0__0__0___1___0

2)_0_0_1__0__0__0___1___1

3)_0_1_0__0__0__1___1___0

4)_0_1_1__0__0__1___1___1

5)_1_0_0__1__0__0___1___0

6)_1_0_1__1__0__0___1___1

7)_1_1_0__1__1__1___0___0

8)_1_1_1__1__1__1___1___1

We see that, as the logical statement c( the paradoxe) is not physically true, the only possible lines of physical truthness are: 1), 3), 5) with the following possibilities for the PoR and LTE truth values:

PoR LTE

0--------0

0--------1

1--------0

And that means that either the Lorentz' transformations are not true or the PoR or both. But as the LTE are true because they in agreement with a lot of experiment:

the conclusion is :  THE PRINCIPLE OF RELATIVITY IS NOT TRUE .

G) Additional proof

We have obtained above with the Lorentz' transformations, in contradiction with the principle of relativity that the clocks in K' and in K'' are not synchronized according to:

t'(x')=t'(o')-vx'/cc and t''(x'')=t''(o'')+vx''/cc if they are really synchronized in K.

But that means in K' that along the X' axis, the twinA (in motion in that frame) meets

clocks in K'not synchronized and thus that the time difference between these clocks is not the time difference of the time difference of the watch of twin B.

In fact we have: dt'(o') =dt'(x')+[v/cc].[dx'/dt'(x')]dt'(x').

But as the twin A travel in the negative way in the frame K' where the twin B is, we have dx'/dt'(x') = -v and thus dt'(o')=[1-bb]dt'(x').

The same way we obtain for the frame K'', that dt''(x0'')=[1-bb]dt''(x'')

And thus the result of the twin b analysis:

[deltat'1(o')+delta-t''2(x0'')]=[delta-t1+delta-t2]/sqrt(1-bb) becomes while corrected:

[delta-t'1(o')+delta-t''2(x0'')]=[sqrt(1-bb)] [delta-t1+delta-t2] in agreement with his brother (twinA analysis).

This result prove that there is not the slightest error of reasoning in the way my twin paradox has been derived.

Conclusion: the Lorentz' transformations are directly in contradiction with the principle of relativity. If we neglect this direct contradiction, we obtain the twin paradox.

If we solve the paradox with this direct contraction result [ t'(x')=t'(o')-vx'/cc], the paradoxes disappear but that means that the direct contraction exists.

In both cases there is a logicalproblem.

Conclusion Einstein is really wrong.

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