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Abstract

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The object of this article is to present a new theory based on the introduction of a non-material medium which makes it possible to obtain a Preferred Frame of Reference (in the context of special relativity) or a Reference (in the context of general relativity), that is to say a dynamic medium of reference.

The theory of the dynamic medium of reference is an extension of Lorentz-Poincaré’s theory in the domain of gravitation in which instruments (clocks, rulers) are perturbed by gravitation and where only the measure of the speed of light always gives the same result.

The presence of a massive body creates a centripetal flux of the medium which has three fundamental effects:

• the dilatation of the period of material clocks,

• the contraction of the length of material rulers,

• the slowdown of light.

Thanks to the centripetal flux of the medium and these three effects, it is possible to find the correct expression of the deflection of a ray of light and the Shapiro delay.

The dynamic medium of reference allows to establish a gravitational transformation and to find the fundamental equations of movement for light and matter.

Hence, the theory of the dynamic medium of reference allows to find the main results of general relativity, but with important differences: the simultaneity is absolute, existence of the Preferred Frame of Reference, the physical reality is the universal present moment and not a global space-time (block-universe), light is slowed down by a gravitational field.

 

Keywords

General Relativity ; Preferred Frame of Reference ; Dynamic medium of reference ; Lorentz-Poincaré’s theory ; Simultaneity ; Speed of light

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1. Introduction

Up to now, general relativity is the best existing theory of gravitation and it provides very accurate values to many experiments and observations1,2,3.

 

Lorentz-Poincaré’s theory competes with Einstein’s special relativity.

Although contested by some, Lorentz’s theory is perfectly coherent. It has been defended by Henri Poincaré4 and Michel Lambert dedicates a whole chapter of 15 pages on Lorentz’s theory in his book5 showing that this theory is perfectly acceptable.

 

The present document is the presentation of a theory which is an extension of Lorentz-Poincaré’s theory in the domain of gravitation.

 

The proposed theory is based on the following concepts:

• Simultaneity is an absolute notion,

• Existence of a medium of reference,

• Existence of a reference time or privileged time, that is to say a universal present moment rather than a block-universe

• Centripetal flux of the medium created by a massive body,

• The contraction of rulers and the dilatation of the periods of the clocks are physical effects due to the movement of rulers and clocks with regard to the medium or due to the movement of the medium created by a massive body.

 

Several renowned scientists have defended or defend most of these concepts.

 

Of course Lorentz and Poincaré maintained their interpretation confronting Einstein’s special relativity.

John Bell also maintained the idea of returning to a pre-relativistic theory, close to Lorentz’s theory and the fact that the medium of propagation of light had been rejected based on erroneous arguments6,7.

 

Finally, in his book “Time Reborn”8, Lee Smolin claims the following arguments:

“The fact that it is always some moment in our perception, and that we experience that moment as one of a flow of moments, is not an illusion. It is the best clue we have to fundamental reality.

This means giving up the relativity of simultaneity and embracing its opposite: that there is a preferred global notion of time.”

 

All these arguments bring support to the theory which will be developed in the present paper.

 

After the present introduction, the second chapter describes the fundamental characteristics of this medium.

The third chapter provides three applications of the proposed theory corresponding to well-known tests of general relativity.

The fourth chapter gives the fundamental equations of movement in the theory of the dynamic medium of reference.

Lastly, the conclusion highlights the differences between this new theory and Einstein’s relativity.

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2. Theory of the dynamic medium of reference

2.1 Presentation of the dynamic medium of reference

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The proposed theory introduces a dynamic non-material medium which is present in the whole Universe.

The characteristics of this medium are:

• This medium enables one to deduce a Preferred Frame of Reference or rather a REFERENCE in the whole Universe and at all scales,

• This REFERENCE enables one to obtain a privileged time. The present moment is universal, that is to say the same in the whole Universe,

• This medium is also the medium of propagation of light,

• This medium verifies the principle of reciprocal action:

  • The medium is distorted by matter and energy like the space-time of general relativity,

  • The warping of this medium determines the trajectories of the particles (material particles and light particles).

The last two points explain that a ray of light is deflected by a massive body.

 

The presence of a massive body creates a flux of the medium (centripetal that is to say directed towards the center of gravity of the massive body)

of speed                                                                                           (1)

and acceleration                                                                                   (2)

where r refers to the distance to the center of gravity of the massive body.

 

In the theory of the dynamic medium of reference, the factor       (3)

plays a role quite equivalent to the factor :                              (4)

• The material rulers are contracted by the factor g(V) due to their movement with regard to the dynamic medium of reference and they are contracted by the factor K(r) due to a gravitational field (centripetal movement of the medium created by a massive body),

• The material clocks have their period dilated by a factor g(V) due to their movement with regard to the dynamic medium of reference and they have their period dilated by the factor K(r) due to a gravitational field (centripetal movement of the medium created by a massive body).

 

However, there is a great difference between the two cases:

• In the case of the movement of a material ruler or clock, it is the movement of the ruler or the clock with regard to the Preferred Frame of Reference which creates the effect. The medium is not distorted.

• In the case of a gravitational field created by a massive body, the medium undergoes a centripetal flux increasing when one gets closer to the massive body. This flux, as a result, physically alters the length of the material rulers and the period of the material clocks. Another important point: as the medium is being physically altered by the presence of the massive body, this alteration plays the role of the curvature of space-time of general relativity.

 

In the case of a gravitational field, for a fix referential with regard to the massive body, the Preferred Frame of Reference moves at the same speed as a laboratory in free fall .

 

The material clocks and the material rulers are then physically affected with the factor  which gives the factor of general relativity:

.                                                                                            (5)

 

This parallel between special relativity and gravitation is very important and justifies the claim that, for all dynamic phenomena in a gravitational field, the part due to the temporal effect is exactly the same as the part due to the spatial effect.

This is due to the fact that in special relativity, the factor used for the temporal part (clocks) is the same as the one used in the spatial part (rulers).

 

Remark: the centripetal flux of the medium is linked to the fundamental notion of the free fall referential of general relativity.

This concept of free fall referential is so essential that it is systematically used by Clifford Will in his book “Was Einstein right?”2 to explain the following phenomena in the presence of a gravitational field:

• Shifting of the clocks (chapter 3),

• Shifting towards the red (redshift) of the light (chapter 3),

• Deflection of the light (chapter 4),

• Shapiro delay (chapter 6).

 

Also, in their book “Relativité Générale”, Julien Grain and Aurélien Barrau often use the free fall referential9:

“In a free fall referential, the correct laws must be the ones satisfying special relativity.”

“From a geometric point of view, geodetics are the shorter lines between events of space-time. Physically, they are the trajectories of the test-masses in free fall.”

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2.2 Material clock in a gravitational field

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As a result of what we have seen in part 2.1, a material clock, of period T0 when situated very far from all gravitational fields, undergoes a dilatation of its period of a factor K(r) when situated at the distance r from the center of gravity of a massive body, in such a way that its period is equal to:

   with   .                                                                       (6)

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2.3 Material ruler in a gravitational field

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Likewise, a material ruler, of length L0 when situated very far from all gravitational fields, undergoes a contraction of a factor K(r) when it is situated at the distance r from the center of gravity of a massive body, in such a way that its length is equal to:

    with   .                                                              (7)

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2.4 Speed of light in presence of a gravitational field

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2.4.1 Speed of light for a radial trajectory

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From the two previous points, we can deduce the fundamental result:

The speed of light varies according to the distance from the center of gravity of a massive body.

 

Indeed, very far from the massive body, the speed of light is:

.                                                                                                                   (8)

On the other hand, at the distance r from the center of gravity of the massive body, when light follows a radial trajectory, the speed of light actually has the following expression with regard to a referential linked to the massive body:

.                                                                        (9)

 

In the frame of radial trajectories, we can deduce an index of refraction of the medium due to gravitation:

.                                                                                          (10)

 

Light is therefore slower close to a massive body than very far from it.

 

This notable result allows one to find a good approximation of the Shapiro delay due to a massive body.

 

Another major point is that the measure of the speed of light results in the same value whatever distance we are from a massive body.

Indeed, if we own a ruler of length L and a clock of period T, in such a way that the light covers the length of the ruler in a period of the clock, whatever the strength of the gravitational field we measure:

.                                                                                                                                  (11)

 

In fact, whether we are very far from all massive bodies (absence of gravitational field) or very close to the surface of a massive body, the light covers the length of the same ruler during the period of the same clock.

The measure provides an identical result of the speed of light, so apparently that light has a constant speed.

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2.4.2 Speed of light in the general case

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The expression of the speed of light found in the previous section is only valid for a radial trajectory.

 

For any kind of trajectory of light, the expression of speed is more complex and we are going to establish it.

 

The speed vector of light must be decomposed along two components which don’t follow the same rule because the rulers are contracted by the factor K(r) only when they are disposed along a radial of the massive body.

 

The radial component can be written:

            .                                         (12)

The ortho radial component can be written:

.                                                (13)

where     and                                                                          (14)

Morover we have:  .                                                                       (15)

 

We name  the angle between the vector  and the speed vector of light .

The vecteur  represents the speed vector of light if there wasn’t any massive body.

 

We can write:

     which gives us:             (16)

 

We also have:

                                                       (17)

 

Thus we obtain the modulus of the speed vector of light:

   which can also be written:

 

  or even: .       (18)

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2.5 The three fundamental effects of the theory of the dynamic medium of reference

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The three fundamental effects due to gravitation predicted by the theory of the dynamic medium of reference are the following:

• (1a) dilatation of the period of the clocks: ,

• (1b) contraction of the length of the rulers: ,

• (2) distortion of the dynamic medium of reference: the gravitation creates centripetal flux of speed .

 

The two first effects have been noted (1a) and (1b) because:

• They are quite equivalent to the dilatation of durations and contraction of lengths of special relativity,

• For the light, the two cumulated effects imply the effect (1c): diminution of the speed of light in a gravitational field according to the rule .

 

The third effect (2) is specific to the domain of gravitation. Thus it is an additional effect compared to special relativity (which corresponds to a non distorted medium).

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2.6 New postulates of the theory of the dynamic medium of reference

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In the context of the theory of the dynamic medium of reference, the two Einstein’s postulates become:

 

1) The measure of the speed of light is constant in all referentials and in all directions, including in the presence of a gravitational field.

This implies that all instruments, in particular the material clocks and the material rulers undergo physical effects due to their movement or the presence of a gravitational field in order to ensure a constant measure of the speed of light.

 

2) All the inertial/Galilean referentials are equivalent for the expression of physical laws AND there is a Preferred Frame of Reference or medium of reference in which the light really propagates at the speed c0 and the material clocks and rulers don’t undergo any physical effect of dilatation of their period or contraction of their length. This Preferred Frame of Reference or medium of reference makes it possible to define an absolute simultaneity and a privileged time everywhere in the Universe.

 

Important remark: in this theory, it is not question to come back to an absolute time as in Newton’s theory where all the clocks of the Universe beat in unison whatever their speed and whatever the gravitational field.

By contrast this theory proposes that all the material clocks (of same building) in all the parts of the Universe beat at exactly the same rhythm if and only if they are immobile with regard to the dynamic medium of reference. All these clocks provide the universal time of reference.

 

2.7 Discussion on the principle of equivalence

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This part presents three objectives:

• To show that the principle of equivalence such as stated by Einstein in 1907 and 1911 can be used in the frame of Lorentz-Poincaré’s theory in order to extend it to the domain of gravitation,

• To provide a new formulation of the principle of equivalence in the frame of the theory of the dynamic medium of reference and to show that it is sufficient to postulate the existence of the dynamic medium of reference to demonstrate the principle of equivalence,

• To show that the formulation of the principle of equivalence in the frame of the theory of the dynamic medium of reference allows to establish that the inertia force due to a variation of the speed vector of a material object is fundamentally of the same nature that the gravitational force.

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2.7.1 Use of the principle of equivalence in the frame of Lorentz-Poincaré’s theory

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The equivalence principle10 allows us to state that a material clock undergoes exactly the same effect in the two following cases:

• The clock moves with an acceleration G and with the speed V with regard to the Preferred Frame of Reference. According to Lorentz-Poincaré’s theory, the material clock undergoes a physical, real dilatation of its period,

• The clock is fixed with regard to a massive body of mass M creating a gravitational field of acceleration G. According to the proposed interpretation, which is an extension of Lorentz-Poincaré’s theory in the domain of gravitation, the material clock undergoes a physical, real dilatation of its period.

 

First, we are going to show that an object moving at the speed   with regard to a referential R (r indicates the distance from the origin O of the referential R to the position of the object) undergoes an acceleration  (the signs are given with regard to a unit vector  going from the origin O towards the position of the object).

 

Starting from the speed  , the acceleration can be written:

.

 

So we can state the following important result:

For a clock moving with the speed  with regard to the Preferred Frame of Reference PFR, this clock undergoes the acceleration .

 

According to Lorentz-Poincaré’s theory, this material clock undergoes a physical dilatation of its period according to the formula:

 with .                                                (19)

T0 indicates the period that the clock would have if it was immobile with regard to the Preferred Frame of Reference.

The equivalence principle10 allows us to claim that this clock undergoes the same effect being in presence of a massive body of mass M creating a gravitational field of acceleration , that is to say that its period undergoes a physical dilatation according to the formula:

 with .                                                               (20)

T0 indicates the period that the clock would have in the absence of gravitational field.

 

 

The equivalence principle10 allows us to state that a material ruler undergoes exactly the same effect in the two following cases:

• The ruler moves with an acceleration G and with the speed V with regard to the Preferred Frame of Reference. According to Lorentz-Poincaré’s theory, the material ruler undergoes a physical, real contraction of its length,

• The ruler is fixed with regard to a massive body of mass M creating a gravitational field of acceleration G. According to the proposed interpretation, which is an extension of Lorentz-Poincaré’s theory in the domain of gravitation, the material ruler undergoes a physical, real contraction of its length.

 

We can state the following important result:

For a ruler moving with the speed  with regard to the Preferred Frame of Reference PFR, this ruler undergoes the acceleration .

 

According to Lorentz-Poincaré’s theory, this material ruler undergoes a physical contraction of its length according to the formula:

 with .                                              (21)

L0 indicates the length that the ruler would have if it was immobile with regard to the Preferred Frame of Reference.

The equivalence principle10 allows us to claim that this ruler undergoes the same effect being in presence of a massive body of mass M creating a gravitational field of acceleration , that is to say that its length undergoes a physical contraction according to the formula:

 with .                                                             (22)

L0 indicates the length that the ruler would have in the absence of gravitational field.

 

Conclusion: the principle of equivalence such as stated by Einstein in 1907 and 1911 is sufficient to establish the laws concerning the clocks and the rulers in a gravitational field and so to establish the speed of light in a gravitational field and finally to extend the Lorentz-Poincaré’s theory to the domain of gravitation.

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2.7.2 New formulation of the principle of equivalence in the theory of the dynamic medium of reference

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In the frame of the theory of the dynamic medium of reference the principle of equivalence is formulated in terms of speed and not acceleration and the two following statements are naturally equivalent:

• The effects on material clocks and rulers are due to their movement with regard to the medium of reference,

• The effects on material clocks and rulers in the presence of a massive body are due to the movement of the medium with regard to the massive body and so with regard to the clocks and the rulers.

 

This formulation is a justification of the principle of equivalence because it is obvious that the relative movement of the clocks and the rulers with regard to the medium is equivalent to the relative movement of the medium with regard to the clocks and the rulers.

 

In every case, it is the relative movement (speed) of the material clock and ruler with regard to the medium (which is the reference) which creates the effects (dilatation of the period of the material clock and contraction of the length of the material ruler).

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2.7.3 Inertia force

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In the theory of the dynamic medium of reference the force of gravitation is due to the movement of the medium created by a massive body, which means that the force of gravitation is due to a variation of the speed vector of a material body with regard to the medium.

Thanks to the principle of equivalence established in the frame of the dynamic medium of reference, it is possible to state that, without gravitation field, all modification of the speed vector of a material object with regard to the medium of reference creates a force: it is the inertia force.

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