__* * * Important * * *__
New important articles have been written in the research of Neo-classical Theory of Relativity, in addition to the first document of NCTR (2010 - 2013) presented on this site. The new articles are:

February 9, 2017: "The Nineteen Postulates of Einstein's Special Relativity Theory" - TheNineteenPostulatesOfEinsteinsSpecialRelativity.pdf

March 17, 2016: "The core mathematical error of Einstein's Special Relativity Theory" - CoreMathematicalErrorOfSpecialRelativity.pdf

October 26, 2015: "Einstein's variable speed of light and his enforced wrong synchronization method" - EinsteinsVariableSpeedOfLight.pdf

February 12, 2016: "Einstein's Time Dilation concept proved false by Time Sharing methods" - EinsteinsTimeDilationProvedFalseByTimeSharingMethods.pdf

Introduction to the Neo-classical Theory of Relativity

The Neo-classical Theory of Relativity (NCTR) uses concepts of Classical Mechanics and Classical Electromagnetism to describe the relativity of inertial motion better than it is described in the Special Theory of Relativity (STR) conceived by Albert Einstein in 1905.

The Neo-classical Theory of Relativity reveals the conceptual errors of Einstein’s Special Theory of Relativity and also explains why the STR doesn’t have a valid experimental basis.

Also NCTR confirms the works of several physicists of the last century which showed that the absolute nature of space and the absolute frame of reference are valid concepts which can be proved experimentally and used practically.

This is the second edition of the document which presents the Neo-classical Theory of Relativity, featuring a reorganized and more clear presentation in comparison to the first edition (May 2010). The goal of this reorganization was to restructure and to detail better the critical aspects that invalidate Einstein’s theory, and to describe further a Classical foundation for a new theory of space, time and motion.

This edition also contains more cross-references, more graphical representations which now include several animated simulations, in order to relate properly all the aspects discussed here. The format and the quality of this presentation will be evolving in the future in the next editions of this document.

Our thorough analysis of Einstein’s Special Theory of Relativity (STR) revealed so far four groups of conceptual errors:

In the beginning of the first document of the Special Theory of Relativity (STR) Einstein postulated that the velocity of light is a constant value which is independent of the state of motion of the emitting body:

“[…] light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.” [1]

We will explain here why that first postulate of STR is incorrect:

The motion of the observer is very important because the observer is the one who measures the velocity of light in a certain reference frame, and his motion influences that measurement. The inertial motion of an observer of a photon can be:

- towards the photon on the same straight line with the photon’s motion, or
- away from the photon on the same straight line with the photon’s motion, or
- away out of the path of the photon; this case is equivalent to the "Aberration of Light".

Let’s set up imaginary experiments which reveal the motion and the path of light as perceived in two reference frames, for each of the cases a, b and c mentioned above. We will also use animated simulation of such experiments to represent them even better.

We set the first reference frame to be stationary. However, this frame will be conceptually different from the stationary frame used by Einstein in STR, as we need to specify clear attributes to the meaning of the word “stationary” to show why it is special and different from other reference frames:

A stationary reference frame means here a frame in which:

- the velocity of light has a measured value of c , constant in any direction;
- the "Aberration of Light" is zero in any direction for any observer which is at rest within this frame.

(That means the distance between the observer and the path of any photon is a constant;

or, in other words, the observer is not in motion, relative to any ray of light.)

We set the second reference frame as an inertial frame which moves linearly with a velocity v away from the stationary frame. We will name this second frame 'the mobile reference frame'.

In an imaginary experiment, let’s assign the stationary frame to a platform of a railroad station, and the mobile frame to a car which passes by the platform moving uniformly and linearly with a constant velocity v .

Case a.) – the observer moves towards the photon, on the same line:

We mount a light source on the car at one end, and a light source on the platform as in Figure a-1 here. We arrange an ideal double switch which will turn both light sources on, in the moment they pass by each other. Also we arrange that each source will emit one photon in the direction opposite and parallel to the direction in which the car moves.

For an animated simulation of this case please see the video at: http://youtu.be/aZ0-JBq7IlA .

Once the double switch is activated as in Figure a-2, we observe the motions of the two photons:

- the photon emitted from the car; and
- the photon emitted from the platform.

As the photons are generated in the same moment and oriented in the same direction, their motions are parallel.

Also, in a time unit both photons travel together the same distance measured in a particular reference frame.

Let’s consider the motion of the photons until the photon in the mobile frame reaches the wall mounted at the end of the car, as we see in Figure a-3.

If we compare the paths traveled by the two photons, as observed from within each of the two different reference frames (the stationary frame, and respectively the mobile frame), we observe that those paths do not have equal lengths, as we see in Figure a-4, and also in the video aforementioned:

Let’s consider the time interval between these 2 events:

- t0 : the moment the photons get emitted.
- t1 : the moment the photons reach the other end of the car. (Please read section 3.3. to see how we can detect that

event in both frames)

Following the same reasoning that Einstein thought in STR, section “§ 2. On the Relativity of Lengths and Times” [1], we find that the distances traveled by the photons in both frames, between t0 and t1 are:

In the stationary frame (the platform’s frame) the distance Ds traveled by the photons is:

In the mobile frame (the car’s frame) the distance Dm traveled by the photons is:

According to Classical Mechanics, the velocity of light cm-opposite measured in the mobile frame, when the direction of frame’s motion is opposite to the direction of light, is:

which means: cm-opposite ≠ c

The velocity of light cm measured in the mobile frame is not equal to the velocity of light c measured in the stationary frame.

As we will demonstrate in the next sections, it is correct and practical to share the same length units and time units between the two reference frames, and that means in different reference frames we will measure and observe different values for the velocity of light.

In short for this case, we can simply notice that the distance between the rails can be used as a common length unit between the stationary frame and the mobile frame. Also here, the time interval t1 – t0 (between the events t1 and t0) can be used as a common time unit between the two reference frames.

Case b.) – the observer moves away from the photon:

We apply a similar reasoning as in the case a.) , and as the car and the photon move on the same direction, we find that the velocity of light measured on the mobile frame is:

And so in this case, the conclusion is again that: cm-same ≠ c .

For an animated simulation of the cases a.) and b.) see the video at: http://youtu.be/XZ9hPwoTyC0

Surprisingly, Einstein himself used the same reasoning and the same equations (as in the cases a.) and b.) here) to show that the clocks in the mobile frame cannot be synchronized. We will explain in the section 1.2.2. why his conclusion about synchronization is wrong. With that provision, for the case here we notice that Einstein ignored his own definition of velocity:

He wrote (in “§ 2. On the Relativity of Lengths and Times” [1]):

And then his equations were:

and

Notice how the velocities of light cm , measured by Einstein’s reasoning, have respectively the same values with the velocities of light cm measured in our cases a.) and b.) mentioned above:

and

with the same conclusion which we found above, that:

cm-same ≠ c and cm-opposite ≠ c

Therefore Einstein ignored the fact that the measured velocity of light is not a constant across different reference frames.

We will explain in the section 1.2.4. why Einstein ignored that fact, and also we will note it in the section 1.3. as one of the contradictions of his theory.

Case c.) – the observer moves away out of the path of the photon:

In this case we adjust the sources of light so they emit the photons on a direction perpendicular to the direction of car’s motion, as in Figure c-1 and the video at: http://youtu.be/wo2F_b-kSsM :

The sources are turned on simultaneously when a double switch is activated as they pass by each other, and at that moment each of them emits one photon - as represented in Figure c-2 :

Once emitted, the photons move independently from the emitters (the sources of light) and independently from the observers who are attached to the stationary frame and respectively to the mobile frame. The observers (represented as targets in Figure c-3 and Figure c-4) are placed so the line segments between them and the sources are perpendicular to the direction of the car’s motion.

In the stationary frame the photon moves on the segment between the source and the target which are attached to the stationary frame, and that is because by definition there is no aberration of light in the stationary frame.

In the mobile frame (the car) it appears that the photon moves away from the segment between the source and the target which are attached to the frame. What actually happens is that the car moves out of the way of the photon, and so the observer on the car does not receive the photon as intended.

In Figure c-4 we can also see that the paths of the photons observed in the two frames are unparallel and that they have different lengths.

If the two paths would be translated so that the destination points of the photons would coincide, then the two paths would be the sides of a right triangle. The path Pm on the mobile frame would be the hypotenuse of that triangle, and that means it is longer than the path Ps on the stationary frame. If we consider the time interval ΔT between the emission of the photons and the reception of the photons on the other side across the car, then the measured velocities of light in the two frames are:

In the stationary frame:

In the mobile frame:

As Pm > Ps it is clear that cm > cs , and again we observe that cm ≠ c .

Based on all the related experiments, on our simulations and also on the phenomenon of aberration of light [6] , we can affirm that the motion of light is not only independent from the emitting body; it is also independent from the observer. Therefore a correct postulate on the motion of light should read:

The motion of light in vacuum is independent from the emitter and from any observer located in any inertial reference frame.

The velocity of light has a measured value which is independent from the emitter, and which is dependent on the motion of the observer who measures it.