Faster than light

CONICAL AND PARABOLOIDAL SUPERLUMINAL PARTICLE

ACCELERATORS

Corrected and enlarged article

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 to transfer electromagnetic impulses

at precisely that and only at that speed.

Using the existing methods and accelerators I have

also 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, - falls towards zero when at the

velocity of the particle v that 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 - equation related to this

subject-matter.

¡°Transverse mass = m/ 1 ¨C v2/c2¡± ¡° ¡±

(1)*

Once this equation is, at Einstein's own suggestion,

taken to its ¡°pure¡± form suitable for

interpretation, the following is obtained:

m = F/a, m/1-v27c2 = F/a...(2), m =

F(1-v2/c2)/a...(3), a =F(1-v2/c2)/m...(4)

, (2),

(3),

or rather .........(4).

See all eqations and figures at my site, by keywords:

petar bosnic petrus

When the velocity of a particle is v = c, the relative

velocity, crel, of dispersion and effect of the force

F, which accelerates the particle, is, in relation to

the particle itself, equal to zero. Consequently, its

acceleration is also a = 0 // also equals zero. For

the a > 0 it is necessary that the relative velocity

of light, crel, in relation to the particle, be higher

than zero.

I have also 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

________________

E. Einstein

On the electrodynamics of moving bodies

¡ì 10, Slowly accelerated electron.

particle mass, m, which is calculated using the

Lorentz transformation equations (as was stated by

Special Reativity), but rather the reduction of the

acceleratory effect of force F.

A similar phenomenon, which occurs in existing

accelerators, also affects a sailing ship which has

the wind in it 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.

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.

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.

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 significantly 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 catamarans, because they can (because of

very low resistance) sail much faster than the

velocity of the wind propelling them forward.

But let us return to the particle physics.

Conical supraluminal accelerator

In the common types of particle accelerator (linear or

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. Which is why the particle cannot achieve the

velocity of light, let alone exceed it.

However, if we were to bring that same wave to the

side of the particle, then it could reach a velocity

that would be several 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 900 in relation to the

direction of its movement.

This can be achieved with a conical accelerator ¨C a

funnel-shaped accelerator. See

Picture 1.

Figures at my main site: petar bosnic petrus com

Picture 1: ax - axis of conical accelerator and

trajectory of accelerated particles; 1 - wall of the

conical accelerator; 2 ¨C 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.

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 tansversally, i.e.

perpendiculary // 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 900 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.

Still one analogical explanation.

Please do imagine very smooth, but unshapred scissors

and try to cut a peace of steel file. You will not be

able to cut it. Smooth blades of scissors will pull

the steel file towards the its top (top of sccisors)

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 vawes 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.

***

The difference between the conical accelerator and

existing ones lies in its ability to make the relative

velocity of the electromagnetic waves crel ¨C 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. In standard

accelerators the relative velocity of waves, crel. is,

in relation to the highly accelerated particle, very

close to zero, crel @ 0. while in a conical

accelerator it is crel. > 0, several times over.

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 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 od

the density of magnetic field §¶ax will increase for

the value §¶0 x 2r ¦Ð . Where the §¶0 is density of

magnetic field onto the surface of coils; r is radius,

i.e. distance from coils to certain point onto the

axis ax.

§¶ax = §¶0∙2r¦Ð ( 5)

Bearing in mind a certain inertion 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 supraluminal 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

paraboloidal supraluminal 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 supraluminal 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 supraluminal 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

supraluminal velocity, the space maybe will transforme

ionized particles into neutral.

Additional technical solutions

Electrical, conical and paraboloidal supraluminal,

accelerators

Since the electrical field is spreaded in the same, or

similar manner as a magnetic field does (shovn by

picture 1), instead of magnetic accelarators, 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 tham.

Picture 3

Picture 3: ax - accelerator axis , 1 - wall of the

paraboloidal supraluminal accelerator charged by

positive electrical charge; 2. - tubes of a standard

accelerator or cathode tube; 3 ¨Caccelerated, positive

ion, particle.

How does it functions ?

Supraluminal electrical accelerators are turned on, or

charged by electricity, after the charged particle was

introduced into the space of conical or paraboloidal

acceletators. 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:

v :c = ax : r, v r = c ax (6)

v = c ax /r ...........(7)

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

would follow:

v = c 1,6m / 0,4mm (8)

v = 4c (9)

Maximal, theoretical possible velocity of particles at

this accelerator would be 4c

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, eg. 1 : 4 , acceleration of

particle will fall to zero close the velocity 4c.That

is in accordance with eqation based in Lorentz

transformation.

a = F(4 ¨Cv2/4c2)/m (10)

If we want to continue acceleration, or increase

velocity we can not do it by increasing the

accelerative force than rather by increasing ratio

between r and ax. If that ratio should be: eg. 1 : 7

the acceleration will fall to zero close to velocity

7c. In that case, (case of ratio 1 : 7) maximal

theoretically possible velocity also will be slightly

less than 7c

General equation is as follow:

a = F(n ¨Cv2/nc2) / m (11)

n is ratio betwen radius r and axis ax

If the n should be to large or ¡Þ, the acceleration

will be zero, because in that case the direction of

action of accelerating force would be perpendicular to

the line of particles movement.

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