# THE END OF SPECIAL THEORY OF RELATIVITY

Petar Bosnić Petrus,

Langova 35, 10430 Samobor,

Croatia tel. ++385 1 3363 624 mob.: ++385 91 559 2793 and ++385 91 559 2741

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**Faster than light**

**CONICAL AND PARABOLOIDAL SUPERLUMINAL PARTICLE ACCELERATORS**

Enlarged and corrected article

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**Theoretical suppositions**

In the my previous work: **“How the velocity of light can be excedeed”, **I have shown that light is not a special // separate (or positive) physical entity and that velocity of light, *c*, is not the property of light itself but is, in fact, a vacuum or space **transference constant** – the ability or property of vacuum // space (non-mechanic, quantum medium, «luminiferous ether» – (Maxwell), to transfer electromagnetic impulses at precisely that and only at that speed.

Using the existing methods and accelerators I also have shown that it was not possible to accelerate the particles to a speed exceeding the velocity of light, *c*, in other words, that this is not possible, not due to the increase the particle mass, *m*, but because the acceleratory effect of force *F*, which affects the particle – and which is transferred exclusively at the velocity of light, *c*, – in relation to the particle, falls towards zero when at the velocity of the particle *v* is close to the velocity of light *c*.

This is the result one arrives at from further developing Einstein’s key equation of the Special theory of relativity and Einstein’s suggestions:

Einstein stated:

„Now if we call this force simply „the force acting upon the electron“, and maintain the equation – mass x acceleration = force – and if we also decide that the accelerations are to be measured in the stationary system K, we derive from the above equations

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* E. Enistein: THE PRINCIPLE OF RELATIVEITY

**On the electrodynamics of moving bodies**

§ 10, Slowly accelerated electron, page 63,

DOVER PUBLICATIONS INC 1952.

Once this equation is, at Einstein’s own suggestion, taken to its “pure” form suitable for interpretation, the following is obtained:

Equation by which is calculating value of longitudinal acceleration – acceleration along the coordinate X is:

Since by increasing the veocity of particle, *v, *value of force* F – *force acting upon the particle – therefore, value of that force we can not calculate by Newton’s eqation: *F = ma*. This Newton’s equation: *ma = F* have to be corrected by factor . From that correction is following

When the velocity of a particle, *v = c*, the **relative velocity**, *c _{rel}*, of dispersion and effect of the force

*F,*which accelerates the particle,

**in relation to the particle itself**, equal to zero, consequently, also its acceleration,

*a = 0*// also equals zero.

Therefore, if *v = c,*

* *

But the Theory of relativity interprets impossibility of further acceleration as a consequence of illusionary infinitive mass increasing:

**Attention!** Since the following equation by which is calculated value of mass

shows that value of mass of accelerated particle is decreasing and, finally, at *v =c,* falls to zero, we have to explain that paradoxical phenomenon. We, therefore, explain it by following fact:

Mass is inertia, and always equals to inertia:

However, when we say “mass”,we are in fact talking about particle’s inertial reaction to the force acting upon the particle and accelerate it. The higher is velocity of the particle the lower is the force accelerating it, and inertial reaction of the particle’s mass too. (Newton: 3 – reaction always equals to the action.) At the velocity *v = c *action of the force which accelerate particle falls to zero, as well as the inertial reaction of mass, *m* of the particle.In that sense,the value of the mass, *m*equals zero.

**Special notes**

I also have shown that a similar situation occurs with an object that is being accelerated by sound waves, and that in such a case the Lorentz transformation equations, by way of which the acceleration, caused by **force transferred by sound waves,** can be calculated extremely accurately, are also applicable. Therefore, it is not the increase of the particle mass, *m*, which is calculated using the Lorentz transformation equations (as was stated by Special Relativity), but rather the reduction of the acceleratory effect of force *F*. See equations (6), (7), (8).

Really increased impulse, *p, *i.e. its “mass”*, m, *is in fact energy which accelerator has invested in its acceleration and which was “condensed” in a field or “spatial aura” of the particle, and is not velocity transformed into mass.

Experimental experience got by usage large circular accelerators shows that particles, for a short time, actually achieves velocity of light. Long time of orbiting serves only to accumulate energy invested by accelerator. That accumulation or “condensation” of accelerator’s energy around the particle is not a problem, because veering waves around the particle is very easy (high velocity of particle, results in high degree of Doppler effect – relative value wave’s frequency, in regard to so high accelerated particle ≈ zero).

That accumulation of energy around the particle is possible only after the particle achieve velocity of light. Otherwise, if velocity of particle would be different (lower or higher) than velocity of light, it could not be possible to add energy of accelerator to a particles.

To increase particle’s “mass” at infinite largeness, is not possible by achieving velocity of light, than rather using infinite value of time in which accelerator would invest energy into the increasing “mass”, or rather impulse, *p* of the particle, i.e. its kinetic energy. This is possible only if, // after the particle achieves velocity of light.

**Method to achieve FTL velocities**

Since the largest known velocity of propagation of force is a speed of light, c, main question now is: how to achieve larger velocity of force propagation than that of light is.

To the: *a > 0 *(at particle’s velocity *v =c*)it is necessary that relative speed of light, i.e. relative speed of force propagation (in relation to the particle) (at its velocity *v = c*) have to be larger than zero.

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Before scientific explanation let’s consider, one analogical example.

Let as therefore suppose that we are observing a sailing ship which has the wind in its sails coming straight from behind, i.e. from the stern.

When the velocity of the sailing ship approaches the speed of the wind, the **relative** velocity of wind at which it hits the sails drops, and with it the force propelling the sailing ship forward is falling toward zero. In such a case a sailing ship does not, due to the resistance of water, reach even the velocity of the wind, but a somewhat lower speed.

A similar phenomenon occurs in existing accelerators, in which, the force affects particles also is coming straight from behind.

The reason for choosing the example of a sailing ship lies in its ability to demonstrate a fact of crucial significance for the particle acceleration physics, as the following short text will show. It illustrates the method for achieving superluminal velocities.

The following is the said text:

If a sailing ship, which we assume is offering low resistance to moving through water, if therefore, this sailing ship has wind blowing not from behind but from its side – at right angles in relation to the direction of its movement – then such a ship is going to achieve a speed several times higher than the speed of wind blowing into its sails.

Ships which are particularly suitable for achievement of such supravental velocities are the small, lightweight trimarans and catamarans, because they can (because of very low resistance) sail much times faster than the velocity of the wind propelling them forward. See the wonderfull video:

http://www.youtube.com/watch?v=GQ-gdqo35os

But let’s back to the particle physics.

**Conical superluminal accelerator**

In the contemporary common types of particle accelerator (linear and circular), the waves which accelerates a particle comes from behind – just like the wind into the sails of the above mentioned sailing ship – comes from its stern. That is why the particle cannot exceed the velocity of light.

However, if we were to bring that same wave to the side of the particle, then it could reach a velocity that would be many times greater than *c*.

Since a particle has no sails, no keel and no rudder which would redirect the force affecting it, we would have to bring the waves from all sides, and do so at an angle slightly over 90^{0} in relation to the direction of particle movement.

This can be achieved with a conical accelerator – a funnel-shaped accelerator. See **Picture 1**.

**Picture 1**: ax – axis of conical accelerator and trajectory of accelerated particles; 1 – wall of the conical accelerator; 2 – coils; 3 – electromagnetic waves; 4 – accelerated particle; 5 point of intersection of electromagnetic waves; 6 – standard accelerator tube or cathode tube; 7 – cisoidal cross-section of mantle resulting from the acceleration of particles to the speed exceeding the speed of light – Cherenkov effect.

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**Procedure**

A particle is first accelerated in a standard accelerator to a subluminal velocity close to the velocity *c* and then introduced into the funnel-shaped, or rather the conical, accelerator. Instead of a circular or linear accelerator, *6*, a more powerful cathode tube can be used.

The electromagnetic waves *3* – created by the coils *2* of the conical accelerator, *all of which are turned on at the same time* – moves transversally, i.e. **perpendicular // vertically in relation to the wall of the funnel**, *1* towards its axis *ax*. At the same time waves approaches both the particle it accelerates, *4* and axis *ax* along which the particle moves, at an angle somewhat greater than 90^{0} in relation to the movement direction of the particle. The intersection point of electromagnetic waves *5* which is located on axis *ax*, moves along the axis as many times faster as the axis *ax *is longer than the radius *r*. The particle is propelled and accelerated by the vector sum of all electromagnetic forces affecting it in the funnel (conical accelerator). The ultimate particle velocity *v* depends, as already said, on the ratio between axis *ax*, and radius *r* of the large aperture of the funnel. If axis *ax* is four times longer than radius *r* (as shown in our picture), then the particle velocity at the exit from the funnel will necessarily be four time faster than velocity *c*, due to the fact that the electromagnetic waves which accelerate it along axis *ax*, and the point of their intersection, *5*, must – in the same period of time in which, in their transversal motion, they cover the length of the radius *r* – cover a four times greater distance while moving along axis *ax* in an approximately longitudinal direction. Taken in general, ultimate particle velocity *v* is as many times higher than *c *the axis of the cone is longer than the radius *r*. In the conical accelerator shown in **Picture 1** that ratio is 4:1. With a higher ratio, for instance 5:1, the vector **sum** of forces affecting the particle would be smaller, which would have to be compensated for with a more powerful electromagnetic wave. And if the waves were strong enough, the ultimate velocity of the particle would be 5 times that of velocity *c*.

**Special note**

Conical accelerator is able to accelerate only those particles which have entered in its conical space before “switching on” its coils.

**The second analogical explanation**

Please do imagine very smooth, but blunt scissors and try to cut a piece of steel file. You will not be able to cut it. Smooth blades of scissors will pull the steel file towards to its top (top of scissors) by velocity several times larger than is the velocity of movement of the blades itself.

In this example, the blades of scissors are representing the electromagnetic waves of accelerator and its velocity. Steel file is representing charged particle. The charged particle will behaviour just as steel file. This accelerator functions as an electromagnetic scissors.

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**Stil one important analogical example**

Let us suppose that we have one big and empty ball. In addition, let we suppose that the ball can swim, but, since it is not too light, it can’t climb on the top of big oceanic wave. In such case the wave will push the ball **by same velocity and same direction of its movement**.

In contemporary accelerators, electromagnetic waves, in the same way are pushing subatomic particles.

But let us further suppose that, instead of that ball we have surfboard and wave surfer on it. Wave surfers are surfing **along** the big oceanic waves and are moving in different direction and **much time faster than** **waves.**

Why this example is important?

This example is very good because the means of acceleration of mentioned ball, surfers and particles are **waves**.

Water waves, of motionless sea water, transfers mechanical impulses by constant or unchangeable velocity and are pushing ball or surfers.

Motionless space of the accelerator (vacuum), transfers electromagnetic impulses by electromagnetic waves, also by constant, unchangeable velocity.

Velocity of ball, surfers and particles depends on direction of its movement in regards to waves. If they are moving **along** the waves, its velocity can be much times larger than the velocity of waves is.

*In conical and paraboloidal accelerators, particles are “surfing” along the electromagnetic waves, just like surfers on big water waves.*

The difference between the conical accelerator and existing ones lies in its ability to make the relative velocity of the electromagnetic waves *c _{rel}* – for particles which move at the velocity of light or greater – several times greater than the velocity of the particles themselves,

*v*, thus enabling their acceleration above the speed of light. At a contemporary accelerators, the relative velocity of waves,

*c*– in relation to the highly accelerated particle – is very close to zero,

_{rel}.*c*

_{rel }*@*0. While in a conical accelerator it can be, many times larger.

The electromagnetic field of a conical accelerator need not be of enormously great power or density since, due to its specific shape, the density of electromagnetic wave – similar to those in nuclear fusion reactors – concentrates and increases the closer it gets to axis *ax*, and consequently, when close to the axis of the electromagnetic field it increases to an very high density. At every point of axis *ax* value of the density of magnetic field *Ф _{ax }*will increase for the value

*Ф*x

_{0}/mm*2r π*. Where the

*Ф*is density of magnetic field onto the surface of coils; r is radius, i.e. distance from coils to certain point onto the axis

_{0 }*ax*.

Bearing in mind a certain inertia of the particles it would be necessary, in order to achieve velocities many times greater than the velocity of light, to accelerate them with a battery or row of conical accelerators, the first of which would accelerate the particle to a speed only twice as fast as the speed of light, the second three or four times, the third four, five or six times, and so on.

**Paraboloidal superluminal accelerator**

The same effect could be achieved by an accelerator whose axial cross-section that would not be strictly conical and rectiliniar, as the one already shown, but more like a parabola, i.e. similar to a parabolic concave mirror. (See picture 2.) With such an accelerator the ratio between axis *ax* and radius *r* would be continually increasing from the entry into the accelerator to the exit from it – the large aperture of the cone. The velocity of the electromagnetic waves along axis *ax* would increase at the same rate in relation to speed *c* – from a ratio of, for instance, 2:1 to 10:1.or 20:1 In these relations the figure 1 denotes the length of radius *r* and the velocity of light *c*, while figures 2, 10 and 20 denotes the length of the axis *ax* and the number of times the velocity of the wave traveling along axis *ax* exceeds its transversal velocity *c*.

**Picture 2.**

**Picture 2:** *ax**–* accelerator axis , 1 – wall of the parabolic superluminal accelerator; 2. – tubes of a standard accelerator or cathode tube.

When measuring the achieved velocity of a particle one should bear in mind the existence of theoretical indications whereby a pure vacuum could, with regard to the superluminal particles, behave as a diamagnetic medium and therefore decelerate them. Ionized particle would cause a change in the density of a magnetic field – precisely because of the superluminal speed – *exclusively in the space behind the accelerated particle.* The particle moving faster than light would also cause the Cherenkov cone-effect, i.e. conical mantle of “compressed vacuum”, while due to the

**acceleration**of a particle the axial cross-section would not be strictly conical – as demonstrated to date by experiments based on the Cherenkov theory – but would instead be more of a cisoidal shape elongated along axis

*ax*.

**Theoretical possibility**

After leaving the field of accelerator, at the *superluminal velocity*, the space maybe will transform ionized particles into neutral, because it can’t transfer electrical neither magnetic field faster than the velocity *c *is. In addition, because of the same reason, particle moving faster than light could not manifest its electrical or magnetic qualities in the space in front of itself. It could be very important and useful in collision of heavy ions and nuclear fusion.

**Additional technical solutions**

**Electrical, conical and paraboloidal superluminal, accelerators**

Since the electrical field is spreading in the same, or similar manner as a magnetic field does (shown by picture 1), instead of magnetic accelerators, provided with coils, we are enabled to use electrical accelerators at which the mass of walls, 1 is charged by positive or negative electricity charge or power, as shown by the figure 3. In this, electrical type of accelerators we can also use paraboloidal and conical shape of accelerator and a battery or row of it.

**Picture 3**

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**Picture 3**: *ax –* accelerator axis 1 – wall of the paraboloidal superluminal accelerator charged by positive electrical charge; 2. – tube of a common accelerator or cathode tube; 3 –accelerated, positive ion, particle.

### How does it functions ?

Superluminal electrical accelerators are turned on, or charged by electricity, after the charged particle was introduced into the space of conical or paraboloidal accelerators. They are accelerating the particles by repulsive force along the axis *ax. *Negative charged particles, eg. Electrons are accelerated by negative charge of accelerator.

**Maximal velocity**

The largest theoretically possible velocity of accelerated particles at the certain conical or paraboloidal accelerator depends on the ratio between radius *r* and axis *ax*. We can calculate it by the relation:

If that ratio should be 1,6*m : *0,4*m*, i.e 4 : 1, than would follow:

Maximal, theoretical possible velocity of particles enabled by such accelerator would be 4*c.*

General equation to calculate maximal, theoretically possible velocity of particles given by any conical or paraboloidal accelerator should be:

at which *v* is velocity of particles, *n* is ratio between radius *r* and axis *ax* and *c* is velocity of light.

**At which velocity an acceleration of the particle is falling to zero?**

It depends of the ratio between the radius *r *and axis* ax* If the ratio is, e.g. 1: 4 , acceleration of particle will fall to zero at the velocityof particle, *v = 4c.*That is in accordance with equation based in Lorentz transformation.

If we want to continue acceleration, or increase velocity of particle we can not do it by increasing the accelerative force than rather by increasing ratio between *r* and *ax*. If that ratio should be: e.g. 1 : 7, the acceleration of particles will fall to zero close to velocity *7c. *In that case, (case of ratio 1 : 7) maximal theoretically possible velocity also will be slightly, negligible less than *7c*

General equation is as follow:

The *n *is ratio betweenradius* r *and axis* ax*

If the *n* should be to large or ∞, the acceleration will be zero, because in that case the accelerating force would be perpendicular to the line of particles movement.

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The highest theoretically possible speed that some conical or paraboloidal accelerator could give to particles can be calculated from the value of sin. angle *α* – the angle made or closed by walls of that accelerator, *1* and axis *ax.* It can be calculated by equation:

Symbol *c* also denominates the radius *r, *since that radius also shows transversal direction of spreading of electromagnetic waves. The same thing also can be denominated by symbol, i.e. number*1, *which, in this case denominates velocity of light too. The angle *α*, as just was stated, is an angle made or closed by walls of accelerator, *1* and axis *ax*.

Accelerator, E.g. which could have value of the angle *α* only 0^{0}10`, i.e. only ten angular minutes, in accordance to the following equation, could give to a particles maximal velocity of: 103.060.538 km/sec. or 343*c.*

,

or, *v* = 343c

During the second half of the 20 th century, it was possible to build an accelerator whose cone was two arc or angular seconds, 0, 2 ”. The accelerator would be about 30 m long, and it could accelerate particles to speeds of one parsec / sec, that is, about 103 million times greater than the speed of light. Clearly, this accelerator could be used only in the vacuum of space, and could serve as a communicator, weapon, or repulsive motor. for superluminal space ships.

To the technology of today is not any problem to build such accelerator. But accelerator whose angle of cone would be only a particle of angular seconds – which could give much larger velocity to particles (Ten or twenty or more bilions times faster than light – kiloparsecs or megaparsecs per second) … it… maybe… could be a problem.. maybe??