Three Experiments Challenging Einsteins Relativistic

Mechanics and Traditional Electromagnetic Acceleration Theory

(variant 2)

Liangzao FAN
Senior Research Fellow, Chinese Academy of Science

fansixiong@yahoo.com.cn
 S.N.Pukhov, VlSU,
spuchov@mail.ru

www.electrosad.ru

 

Abstract

First Experiment: The speed of electrons accelerated by a Linac was measured in order to clarify whetherthe Linacs effective accelerating force depends upon the speed of electrons or not.
Second experiment:
High-speed electrons from a Linac bombarded a lead target and the increase of the targets temperature was measured.
Third experiment:
High-speed electrons from a Linac were injected perpendicularly into a homogeneous magnetic field and the radius of circular motion of the electrons under the action of the Lorentzian deflecting force was measured. Analyses of all the three experiments prove: (1) The accelerators efficiency decreases as the speed of electrons increases and the measured speed of electrons is far less than calculated according to the traditional electromagnetic acceleration theory. (2) Results of the experiments do not accord with Einsteins formulas of moving mass and kinetic energy but conform with the formulas in the New electrodynamics of moving bodies. (3) The third experiment proves that the effectiveness of the Lorentzian deflecting force also depends upon the speed of the deflected electrons.

 

 

1 Introduction

According to Einsteins relativistic mechanics, if an object with static mass m0 moves at speed V , then its moving mass is

 

 

and kinetic energy is Ek =( m m0) c2. Scientists have done experiments with high-speed electrons to examine these Einsteinian formulas. Most experiments were based on the traditional electromagnetic acceleration theory, which deems the electromagnetic force acting on moving electrons independent of the speed of electrons.

Some scientists feel doubtful about it.

To check these Einsteinian formulas and the traditional electromagnetic acceleration theory, we have applied high-speed electrons emitted from a linear accelerator (Linac) to do three kinds of experiments: [1][2]

(1) To measure the speed of accelerated electrons in order to calculate the kinetic energy gained by the electrons and compare it with the energy spent by the Linac.

(2) By use of high-speed electrons to bombard a lead target and to measure the targets temperature increase due to the kinetic energy of bombarding electrons.

(3) To inject high-speed electrons perpendicularly into a homogeneous magnetic field and measure the radius of circular motion of electrons under the action of the Lorentzian deflecting force.

All the three experiments were conducted on a femto-second Linac at Shanghai Institute of Applied Physics. The experiments provided clear data to check the traditional electromagnetic acceleration theory and the formulas of moving mass and kinetic energy. Analyzing the data from the three experiments, this paper proves:

(1) The actually effective force exerted by an accelerator on moving electrons depends upon the speed V of the electrons. There exists a "c -V phenomenon (or wind-sail phenomenon) so that the higher the electrons speed V , the less efficient the Linac is. Traditional electromagnetic acceleration theory is incorrect . The endless pursuit of accelerators power, including the construction of the costly European Large Hadron Collider (LHC), is a meaningless waste of money.

(2) In a homogeneous magnetic field, the effectiveness of the Lorentzian deflecting force, which acts on moving electrons, depends upon the speed V of electrons. There also exists a "c -V phenomenon and it is necessary to introduce a coefficient to match theoretical and experimental data.

(3) The results from all the three experiments do not accord with Einsteins formulas of moving mass and kinetic energy, but conform with the formulas in the New electrodynamics of moving bodies [3][4] ,

 

2 Experiment on the Acceleration of Electrons in a Homogeneous Electric Field

2.1 Method and Results of the Experiment

The front of electrons emitted from a Linac continues its linear and uniform motion through a straight tube with length of S 1.43[m]. Sensors were installed at both ends of a section of the tube to measure the entry time t1 and the exit time t2 of the electronic front into and out of the section. The speed gained by electrons due to the Linacs acceleration was calculated as V = S/(t2 t1)

The experimental results are shown in Table 1:

ble 1
Linacs working energy
E,
Mev
0.025 0.035 0.045 0.055 0.065
Measured speed of
electrons
V
0.313 c 0.369 c 0.412 c 0.449 c 0.480 c

 

2.2 Analysis

From Einsteins

 

 

and Ek =( m m0) c2 , we have

 

 

so that, having measured speed V , we can calculate the kinetic energy Ek gained by the electrons and the efficiency of the Linac as k/E

 

ble 2

Linacs working energy E ,Mev 0.025 0.035 0.045 0.055 0.065
Measured speed of electrons V 0.313 c 0.369 c 0.412 c 0.449 c 0.480 c
Kinetic energy of electrons k , ev 0.0270 0.0388 0.0498 0.0609 0.0715
Linacs efficiency k/E 108%% 111% 111% 111% 110%

 

It is surprisingly strange that the kinetic energies of accelerated electrons are more than the Linac can give them and the Linacs efficiencies are more than 100%! Obviously, both the Einsteinian relativistic mechanics and the traditional electromagnetic acceleration theory are questionable. In accordance with the New electrodynamics of moving bodies [3][4] , which is based solely on Galilean principle of relativity without Einsteins postulate of the constant speed of light and Loretnzs postulate of the length-contraction, if a static body (V 0 ) is accelerated to the speed of Vthen it obtains the kinetic energy Ek = mV2/2. On this formula we can get following results

 

ble 3

Linacs working energy E [Mev] 0.025 0.035 0.045 0.055 0.065
Measured speed of electrons V 0.313 c 0.369 c 0.412 c 0.449 c 0.480 c
Kinetic energy of electrons k, ev 0.025 0.0348 0.043 0.0515 0.059
Linacs efficiency k/E 100% 99,4% 96,4% 93,65% 90,6%

 

As the speed of the electrons increases, the Linacs efficiency decreases. This is understandable because the electromagnetic force cannot push electrons to reach the speed of light c which is the speed of electromagnetic action. This is similar to the case between wind-force and sailing-boat: A sailing-boats speed can never be equal to the winds speed. Because, as the boats speed approaches the winds speed, the winds effective force acting on the boats sail reduces sharply. A great amount of the windpower is wasted. In case of the electromagnetic acceleration, lets call it a c -V phenomenon.

 

3 Calorimetric Experiment with High-Speed Electrons Bombarding a Lead Target

3.1 Method and Results of the Experiment

High-speed electrons from a Linac bombarded a lead target. The Linacs working energy levels were set up at 6 MeV, 8MeV, 10MeV, 12MeV and 15MeV. The current strength of electrons was 1.26A with the impulse width of 5[ns] and frequency 5[Hz]. The electrons bombarded the target for 120[s], So, each bombardments cumulative time was only 120x 5x 10-9 x5 =3x 10-6 [s]. The cumulative electric charges receiveed by the target was 1.26x 3x 10-6 = 3.78x 10-6 [Coulomb]. Since 1[Coulomb] 6.2415x1018 electrons, so the target received 3.78x10-6 x6.2415x1018 2.36x1013 electrons. Since 1 [MeV] 1,60210-13[Joule], so each 1MeV of the 2,361013 electrons is equivalent to 2,3610131,602173310-13=3,78 [Joule]. The targets mass is 70[g]. Since the leads specific heat is 13 [J/g C], so 70 0.13 9.1[Joule] is needed for the lead targets temperature to increase 1C . The temperature is measured by a thermoelectric couple. The experiments equipment and the measured values of the lead targets temperature increase are shown below:

 


 
 

ble 4

Linacs working energy E [Mev] 6 8 10 12 15
measured temperature increase[C] 0,25 0,30 0,32 0,34 0,35

 

The targets temperature varies very little, although the Linacs working energy level changes widely.
 

3.2 Analysis

The traditional theory of electromagnetic acceleration maintains that the actually effective force exerted by an accelerator on an electron is independent of the electrons speed and all the accelerators working energy E becomes the electrons kinetic energy Ek , i.e., E k . If the electrons have actually received all the Linacs working energy ( E k ), then by use of the Einsteinian formula:

 

 

their speeds can be calculated as:

 

 

The kinetic energy E k of electrons causes the increase of the lead targets temperature. The increase of temperature can be calculated as

 

C

 

Given E k and by use of Einsteins (3.1) , the calculated values of the lead targets temperature increase are:

 

ble 5
Linacs working energy E [Mev] 6 8 10 12 15
Calculated speed of electrons V 0.9969c 0.9982c 0.9988c 0.9992c 0.9995c
Calculated temperature increase[ C] 2.52 3.36 4.20 5.04 6.35


The calculated values of the temperatures increase in the Table 5 are much bigger than the respective values measured in the Table 4. Moreover, the calculated values vary propotionally to the Linacs working energy, whereas the measured values vary little. This is because, on the one hand, when the speed of electrons approaches the speed of light, their kinetic energy did not increase as sharply as calculated by use of Einsteins formula:

 

 

On the other hand, the Linacs efficiency decreases sharply as the speed of electrons approaches the speed of light (i.e., the c -V phenomenon shown in 2) so that the electrons did not reach the speed as high as above calculated in the Table 5.

Lets take the c -V phenomenon into consideration. An accelerators work is to make its electromagnetic fields potential energy to become the electrons kinetic energy, i.e., to change the Linacs potential head into electrons velocity head: Fdx mvdv.

In the New electrodynamics of moving bodies is shown that when moving the charge along field efficient power F can be denominated

 

F=F0(1-V2/c2)

 

where V is the electrons speed and F0 is the accelerators nominal force of action. With provision for always existing when working the physical installing the losses to energ we have

 

F=F0(1- δ - V2/c2)dx=mvdv

or

     

 

The nominal work done by an accelerator consuming energy E is F0dx E, which accelerates an electron from υ 0 to υ = V

 

(3.2)

 

After integrating we get:

 

(3.3)

 

By use of (3.3) we can calculate the actual speed V of the electrons accelerated by the Linacs certain working energy E and consequently their kinetic energy,

The known [5] that in linear booster electrons by leaps and bounds, at energy 1-3 Mev, take the velocity close to velocities of the light. Degree of the approximation to velocities of the light is defined loss to energy electron in booster and, what follows from experiment on deflection electron to high energy in uniform magnetic field, forms value 0,997. With provision for that full energy electron stands out on dartboard we can also calculate the lead targets actual temperature increase as (Ek+mc2 )3,78/9.1[C],the Linacs wasted energy ΔE = E Ek and its efficiency k/E

 

ble 6

Linacs working energy E [Mev] 6 8 10 12 15
Calculated speed of electrons V 0.997 c 0.997 c 0.997 c 0.997 c 0.997 c
Kinetic energy of electrons k ev 0,254 0,254 0,254 0,254 0,254
Calculated temperature increase[ C] 0.32 0.32 0.32 0.32 0.32
Linacs wasted energy ΔE, 5,746 7,746 9,746 11,746 14,746
Linacs efficiency k/E 4,23% 3,2% 2,54% 2,12% 1,69%


 

The calculated values of the lead targets temperature increase vary little and match the varying trend of the measured values in the Table 4. Obviously, the classical mechanics together with the consideration of the "c -V phenomenon can explain why the lead targets temperature increases so little.

 

4 Experiment on the Deflection of High-Speed Electrons in a Homogeneous Magnetic Field

4.1 Method and Results of the Experiment

A stream of high-speed electrons from a Linac is perpendicularly injected through a rectilinear correcting tube made of 10cm thick lead-iron combination into a chamber with homogeneous magnetic field. To avoid any outside electromagnetic interference, the magnetic field is created by a permanent magnet, not by an electromagnet. The gap between two poles of the magnet is as narrow as just 2.5[cm] in order to make the magnetic field between the two poles as homogeneous as possible. Three series of experiments were done with three magnets of 0.121[tesla], 0.081[tesla] and 0.063[tesla] respectively. The Linacs working energy levels were set up at 4MeV, 6MeV, 9MeV, 12 MeV, 16MeV and 20 MeV. The experiments equipment is shown below:

 


In the Table 7 below are the measured radii of the circular track of electrons moving under the action of the Lorentz deflecting force:

 

ble 7

Linacs energy E [ ev] 4 6 9 12 16 20
0,121[tesla] Measured
radius
R [m]
~ 18 ~ 18 ~ 18 ~ 18 ~ 18 ~ 18
0,081 [tesla] Measured
radius
R [m]
~ 27 ~ 27 ~ 27 ~ 27 ~ 27 ~ 27
0,063[tesla] Measured
radius
R [m]
~ 35 ~ 35 ~ 35 ~ 35 ~ 35 ~ 35


 

The measured values of radius R for the Linacs six different energy levels remain almost constant. The six small sesame-size spots merged together and appeared on the screen as a single big bean-size spot with its width of about 0.5[cm] so that there are about R ≈17.75 [cm], 26.75 [cm], 34.75[cm] at the low energy end of E 4 [Mev] and R ≈18.25 [cm], 27.25[cm], 35.25[cm] at the high energy end of E 20 [Mev].

 

4.2 Analysis

Traditional theory deems that the Lorentz force, which deflects an electron moving in a static homogeneous magnetic field, is irrelevant to the electrons speed V . If the strength of a static homogeneous magnetic field isB , then the theoretical Lorentz deflecting force is F0 eVB. The Lorentz deflecting force is balanced by the centrifugal force acting on an electron moving circularly due to the deflection. Therefore, the kinematic equation of the electrons circular motion is:

 

mV2/R = eVB or R = mV/ eB , [4.1]

 

where m is the electrons moving mass and R is the radius of the electrons circular track.

Einsteins formula

 

 

makes the equation (4.1) becoming:

 

 

or

 

[4.2]
 

The traditional electromagnetic acceleration theory maintains that all the Linacs working energy E istransferred to the accelerated electron and becomes the electrons kinetuic energy k E so that E E k . Asabove-mentioned in 3.2, the traditional electromagnetic acceleration theory and the Einsteinian relativisticmechanics together lead to the formula (3.1). By use of (3.1) we can calculate the electrons speed V andthen by use of (4.2) we can calculate the radius R of the electrons circular motion. The calculated values ofR are shown below:

 

ble 8

E, ev 4 6 9 12 16 20
V 0.9919c 0,9969c 0,9986c 0.9992 c 0.9995 c 0,9997c
0,121[tesla] R, cm 11.00 17,85 26,59 35,20 44,53 57,49
0,081[tesla] R, cm 16,43 26,66 39,72 52,58 66,52 85,88
0,063[tesla] R, cm 21,13 34,28 51,07 67,61 85,53 110,42


The calculated value of R increases almost propotionally to the Linacs working energy level E , which does not match the experiments results. Thus, both the traditional electromagnetic acceleration theory and the Einsteinian relativistic mechanics are questionable.

The above-mentioned calorimetric experiment with high-speed electrons bombarding a lead target has revealed a "c -V phenomenon (see 3.2). By use of the formula (3.3), which takes the "c -V phenomenon into consideration, we can calculate the speed V of electrons entering the magnetic field from the Linac.

On the other hand, in the New electrodynamics of moving bodies [3][4] is shown that when moving the charge in transverse magnetic field dependency interactions of the charge exists with field from its velocities under the law:

 


 

 

Considering this phenomena in (4,1) we get complying with (4.2) formula:

 

(4.3 )


As was it already noted, in linear booster electrons by leaps and bounds, at energy 1-3, take the velocity close to velocities of the light. Degree of the approximation to velocities of the light is defined loss to energy electron in booster and as can be seen from collation of the tables 7 and 8, in this instance velocity electron was within 0,997.

With provision for this on formula (4.3) we can calculate radius R :

ble 9
E, ev 4 6 9 12 16 20
V 0,997c 0,997c 0,997c 0,997c 0,997c 0,997c
0,121[tesla] R, cm 17,85 17,85 17,85 17,85 17,85 17,85
0,081[tesla] R, cm 26,66 26,66 26,66 26,66 26,66 26,66
0,063[tesla] R, cm 34,28 34,28 34,28 34,28 34,28 34,28

 

5 Questioning European Large Hadron Collider (LHC)

It was reported that the worlds most powerful colliderEuropean LHC succeeded in accelerating protons to the energy level of 3.5[Tev] and protons had obtained speed of

V ≈ 0.99999995c

Obviously, CERNs scientists stick to Einsteins relativistic mechanics and traditional electromagnetic acceleration theory in the calculation of the speed of their protons. Indeed, according to the formula (3.1), which comes from Einsteinsrelativistic mechanics and assumes the electromagmetic acceleration is 100% efficient, if E = 3.5[Tev], then V ≈ 0.99999995c which is only 15 > ms less than the speed of light.

CERNs scientists believe that, with V ≈ 0.99999995c, each proton has huge moving mass

 

ev
 

[ ev ] and kinetic energy Ek= 3,5[ev].

The cumulative energy of two colliding protons is 2E=7[ev]. The collision speed is - 0.9999999999995C according to Einsteins law of addition of speeds. The collision may lead to some new physical findings mainly due to protons huge moving mass with huge energy.

However according to our formula (3.3), which is founded on classical mechanics and takes the "c -V phenomenon into consideration, the protons were speed before smaller velocities. Moreover if even proton moves at the speed of C he possesses the kinetic energy, equal only 469,13 [MeV], far less than the LHCs energy E = 3.5[Tev]. The LHCs efficiency is only about 0.013%

 

With V increasing, the acceleration becomes less and less efficient because of the "c -V phenomenon. It is not because a particles moving mass drastically increases as its speed approaches c , according to Einsteins relativistic mechanics, so that the acceleration becomes harder and harder.

Nevertheless, according to the Galilean law of addition of speeds, the collision speed is high:

 

V + V =(2- δ) C ≈2C.

 

The collision may lead to some new physical findings mainly because of the huge collision speed, not due to protons moving mass and kinetic energy which remain small.

CERN is going to double its LHCs power to [Tev] to accelerate protons to V = 0.999999991c (only about 12.3 m/s higher than in case of LHCs energy E = 3.5 [Tev] and only 2.7m/s less than the speed of light) so that Vsum~ C, m ≈ ∞ Ek≈ ∞.

Mainstream scientists guess such collisions may cause a Big Bang and help them to know some scenario at the Birth of Universe.

However, according to our formula (3.3), LHCs 7 [Tev] energy can only accelerate protons to

 

V≈(1- δ/2) C

 

The results are almost the same as those in case of LHCs energy E 3.5[Tev]. This is because the c -V phenomenon lowers LHCs efficiency further down to 0.0065%

The collision speed is

 

V + V = 2(1-δ/2) C 2C.

 

No matter how powerful a collider is, the collision speed will always be less than 2c.

Disregarding the "c -V phenomenon, the costly LHC has been wasting a great amount of energy and money to do ineffective work. Indeed, what CERN ought to do is not to double the LHCs power but to increase the current density of its proton stream. Because, not any kind of collision of two protons may cause new physical phenomena. Oblique collisions are ineffective. Only precise head-on collisions, the probability of which is extremely small, are effective and deadly needed for finding new physical phenomena.

Yet, with LHCs energy 7 [Tev], the total kinetic energy of two precisely head-on colliding protons is only

 

2Ek≈ 938,26 [ ev]

 

There wont be any Big Bang or Birth of Universe.

 

6 Conclusions

(1) All the three experiments prove that the traditional electromagnetic acceleration theory and Einsteins relativistic mechanics are misleading. Electromagnetic acceleration cannot push a charged particle to Vc. It is not because a particles moving mass drastically increases as its speed approaches c so that the acceleration becomes harder and harder. It is because the "c -V phenomenon makes the acceleration less and less efficient.

(2) Einsteins relativistic mechanics can not explain the results from all the three experiments but the Classical mechanics with the New electrodynamics of moving bodies can.

(3) The Lorentzian deflecting force, which stems from the interaction between a static magnetic field and a moving electrons moving magnetic field, depends upon the speed of the moving electron.

(4) In order to examine the "c -V phenomenon we suggest physicists to repeat these experiments more accurately and by use of more wide speed electrons.

 

Literature

[1] Ji Hao, Calorimetric Experiment to Test the Mass-Speed Relationship, China Sci-Tech Achievements, 2009(1)

[2] Ji Hao, Experiment on the Motion of Electrons in a Homogeneous Magnetic Field, China Sci-Tech Length and Breadth,2009(6)

[3] .., , . 9,06,1993.,N1582-B93.

[4] .., , , 1994.

[5] .., , .349,., , 1975.

 

 

 

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