Three Experiments Challenging Einstein’s Relativistic Mechanics and Traditional Electromagnetic Acceleration Theory
Senior Research Fellow, Chinese Academy of Science
First Experiment: The speed of electrons accelerated by a Linac was measured in order to clarify whether the Linac’s 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 target’s 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 accelerator’s 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 Einstein’s formulas of moving mass and kinetic energy but conform with the formulas in the newly developed Galilean relativistic mechanics. (3) The third experiment proves that the effectiveness of the Lorentzian deflecting force also depends upon the speed of the deflected electrons.
According to Einstein’s relativistic mechanics, if an object with static mass moves at speed , then its moving mass is and kinetic energy is . 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 emited from a linear accelerator (Linac) to do three kinds of experiments:
(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 target’s 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 of the electrons. There exists a “ phenomenon” (or “wind-sail phenomenon”) so that the higher the electron’s speed , the less efficient the Linac is. Traditional electromagnetic acceleration theory is incorrect . The endless pursuit of accelerator’s 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 of electrons. There also exists a “ 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 Einstein’s formulas of moving mass and kinetic energy, but conform with the formulas in the newly developed Galilean relativistic mechanics, which is based on the Galilean transformation and refutes Einstein’s Lorentz transformation.
§2 Experiment on the Acceleration of Electrons in a Homegeneous Electric Field
§2.1 Method and Results of the Experiment
The front of electrons emited from a Linac continues its linear and uniform motion through a straight tube with length of 1.43[m]. Sensors were installed at both ends of a section of the tube to measure the entry time and the exit time of the electronic front into and out of the section. The speed gained by electrons due to the Linac’s acceleration was calculated as . The experimental results are shown in Table 1:
From Einstein’s and , we have so that, having measured speed, we can calculate the kinetic energy gained by the electrons and the efficiency of the Linac as :
It is surprisingly strange that the kinetic energies of accelerated electrons are more than the Linac can give them and the Linac’s efficiencies are more than 100%! Even 100% efficiency is impossible, because it violates the second law of thermodynamics. Obviously, both the Einsteinian relativistic mechanics and the traditional electromagnetic acceleration theory are questionable.
According to the newly developed Galilean relativistic mechanics, which is based solely on the Galilean principle of relativity without Einstein’s postulate of the constant speed of light and Loretnz’s postulate of the length-contraction, if a static body () is accelerated to the speed of then it obtains kinetic energy . With this formula we can get the following results:
As the speed of the electrons increases, the Linac’s efficiency decreases. This is understandable because the electromagnetic force cannot push electrons to reach the speed of light which is the speed of electromagnetic action. This is similar to the case between wind-force and sailing-boat: A sailing-boat’s speed can never be equal to the wind’s speed. Because, as the boat’s speed approaches the wind’s speed, the wind’s effective force acting on the boat’s sail reduces sharply. A great amount of the windpower is wasted. In case of the electromagnetic acceleration, let’s call it a “ 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 Linac’s 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 bombardment’s cumulative time was only [s]. The cumulative electric charges receiveed by the target was [Coulomb]. Since 1[Coulomb]electrons, so the target received electrons. Since 1 [MeV][Joule], so each MeV of the electrons is equivalent to [Joule]. The target’s mass is 70[g]. Since the lead’s specific heat is [J/gC], so [Joule] is needed for the lead target’s temperature to increase C. The temperature is measured by a thermoelectric couple. The experiment’s equipment and the measured values of the lead target’s temperature increase are shown below:
The target’s temperature varies very little, although the Linac’s working energy level changes widely.
The traditional theory of electromagnetic acceleration maintains that the actually effective force exerted by an accelerator on an electron is independent of the electron’s speed and all the accelerator’s working energy becomes the electron’s kinetic energy , i.e., . If the electrons have actually received all the Linac’s working energy (), then by use of the Einsteinian formula their speeds can be calculated as: . （3.1）
The kinetic energy of electrons causes the increase of the lead target’s temperature. The increase of temperature can be calculated as .
Given and by use of Einstein’s (3.1) , the calculated values of the lead target’s temperature increase are:
The calculated values of the temperature’s 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 Linac’s 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 Eintein’s formula . On the other hand, the Linac’s efficiency decreases sharply as the speed of electrons approaches the speed of light (i.e., the “ phenomenon” shown in §2) so that the electrons did not reach the speed as high as above calculated in the Table 5.
Let’s take the “ phenomenon” into consideration. An accelerator’s work is to make its electromagnetic field’s potential energy to become the electron’s kinetic energy, i.e., to change the Linac’s potential head into electron’s velocity head: . Due to the quadratic relationship betwee energy and force, an accelerator’s actual work done by its effective force can be expressed as , where is the electron’s speed and is the accelerator’s nominal force of action. Thus, we have :
The nominal work done by an accelerator consuming energy is , which accelerates an electron from to : . （3.2）
According to the Galilean relativistic mechanics, the formulas of moving mass is . Placing it into (3.2), we obtain:
By use of (3.3) we can calculate the actual speed of the electrons accelerated by the Linac’s certain working energy .
In the Galilean relativistic mechanics, if a particle moves at speed , then its moving mass possesses relativistic kinetic energy in relation to a static object. Therefore, we can also calculate the lead target’s actual temperature increase as [C], the Linac’s wasted energy and its efficiency :
^ of the measured values in the Table 4, although not exactly the same values. This is because the electric energy from the discharge of electrons in the lead target may add certain temperature to the target.
Obviously, the Galilean relativistic mechanics together with the consideration of the “ phenomenon” can explain why the lead target’s 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 Linac’s working energy levels were set up at 4MeV, 6MeV, 9MeV, 12 MeV, 16MeV and 20MeV. The experiment’s 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:
The measured values of radius for the Linac’s 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 [cm], [cm], [cm] at the low energy end of [Mev] and [cm], [cm], [cm] at the high energy end of [Mev].
Traditional theory deems that the Lorentz force, which deflects an electron moving in a static homogeneous magnetic field, is irrelevant to the electron’s speed . If the strength of a static homogeneous magnetic field is , then the theoretical Lorentz deflecting force is . 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 electron’s circular motion is:
or , （4.1）
where is the electron’s moving mass and is the radius of the electron’s circular track.
Einstein’s formula makes the equation (4.1) becoming:
or . （4.2）
The traditional electromagnetic acceleration theory maintains that all the Linac’s working energy is transferred to the accelerated electron and becomes the electron’s kinetuic energy so that . As above-mentioned in §3.2, the traditional electromagnetic acceleration theory and the Einsteinian relativistic mechanics together lead to the formula (3.1). By use of (3.1) we can calculate the electron’s speed and then by use of (4.2) we can calculate the radius of the electron’s circular motion. The calculated values of are shown below:
^ value of increases almost propotionally to the Linac’s working energy level , which does not match the experiment’s 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 “ phenomenon” (see §3.2). By use of the formula (3.3), which takes the “ phenomenon” into consideration, we can calculate the speed of electrons entering the magnetic field from the Linac. On the other hand, placing of the Galilean relativistic mechanics into (4.1), we obtain: or . （4.3）
By use of (3.3) and (4.3) we can calculate the electron’s actual speed and the radius :
The calculated values in the Table 9 are far smaller than those measured in the experiment. However, the varying trend of values is similar to the vaying trend of measured in the experiment.
The Lorentzian deflection is an interaction between a static magnetic field and a moving electron’s moving magnetic field. This is a force-force transaction, not an energy-energy transaction, because the kinetic energy of the electron in circular motion remains constant. Due to the same reason that a sailing-boat can never reach the speed of the wind, we may consider another kind of the “ phenomenon” in the action of a static magnetic field’s Lorentzian deflecting force on an electron moving circularly at constant speed .
However, the exact mechanism of this kind of magnetic interaction has not yet been clearly understood and is pending to be studied. We propose to match the theoretically calculated with the experimentally measured .
In case of 0.121[tesla], the calculated mean value of is 0.9735[cm] while the experimentally measured mean value of is 18[cm]. The gap is . In case of 0.081[tesla], the calculated mean value of is 1.4545[cm] while the measured mean value is 27[cm]. The gap is . In case of 0.063[tesla], the calculated mean value of is 1.87[cm] while the experimentally measured mean value is 35[cm]. The gap is . The matching coefficient changes very little as the electron’s speed changes from to .
Therefore, to match the theoretically calculated with the experimentally measured values, it is necessary to multiply the calculated values by times:
where , 18.6 and 18.7 for 0.121[tesla], 0.081[tesla] and 0.063[tesla] respectively. By use of the formula (4.4) we obtain:
^ values of in the Table 10 are 18[cm], 27[cm] and 35[cm] respectively.
§5 Questioning European Large Hadron Collider (LHC)
It was reported that the world’s most powerful collider—European LHC succeeded in accelerating protons to the energy level of [Tev] and protons had obtained speed of . Obviously, CERN’s scientists stick to Einstein’s 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 Einstein’s relativistic mechanics and assumes the electromagmetic acceleration is 100% efficient, if [Tev], then which is only less than the speed of light.
CERN’s scientists believe that, with , each proton has huge moving mass [Tev] and kinetic energy [Tev]. The cumulative energy of two colliding protons is [Tev]. The collision speed is according to Einstein’s law of addition of speeds. The collision may lead to some new physical findings mainly due to proton’s huge moving mass with huge energy.
However, according to our formula (3.3), which is based on the ^ and takes the “ phenomenon” into consideration, the protons were only accelerated to . A proton moving at such speed only has moving mass [Mev] and only possesses kinetic energy [Mev], far less than the LHC’s energy [Tev]. The LHC’s efficiency is only about . With increasing, the acceleration becomes less and less efficient because of the “ phenomenon”. It is not because a particle’s moving mass drastically increases as its speed approaches , according to Einstein’s 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: . The collision may lead to some new physical findings mainly because of the huge collision speed, not due to proton’s moving mass and kinetic energy which remain small.
CERN is going to double its LHC’s power to [Tev] to accelerate protons to (only about higher than in case of LHC’s energy [Tev] and only less than the speed of light.) so that , and . 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), LHC’s [Tev] energy can only accelerate protons to . At such a speed each proton has moving mass [Mev] and kinetic energy [Mev]. The results are almost the same as those in case of LHC’s energy [Tev]. This is because the “ phenomenon” lowers LHC’s efficiency further down to . The collision speed is . No matter how powerful a collider is, the collision speed will always be less than .
Disregarding the “ 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 LHC’s 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 LHC’s energy [Tev], the total kinetic energy of two precisely head-on colliding protons is only [Mev]. There won’t be any Big Bang or Birth of Universe.
(1) All the three experiments prove that the traditional electromagnetic acceleration theory and Einstein’s relativistic mechanics are misleading. Electromagnetic acceleration cannot push a charged partcle to . It is not because a particle’s moving mass drastically increases as its speed approaches so that the acceleration becomes harder and harder. It is because the “ phenomenon” makes the acceleration less and less efficient.
(2) Einstein’s relativistic mechanics can not explain the results from all the three experiments but the Galilean relativistic mechanics can.
(3) The Lorentzian deflecting force, which stems from the interaction between a static magnetic field and a moving electron’s moving magnetic field, depends upon the speed of the moving electron. It is successful to match the theoretically calculated data with the experimentally measured data by an almost constant coefficient . However, the precise mechanism of the Lorentzian deflecting force is pending to be studied.
(4) In order to examine the “ phenomenon” and to check which relativistic mechanics is true, Einsteinian or Galilean, we suggest physicists to repeat these experiments more accurately and by use of more powerful Linac.
 Ji Hao, “Calorimetric Experiment to Test the Mass-Speed Relationship”, China Sci-Tech Achievements, 2009(1)
 Ji Hao, “Experiment on the Motion of Electrons in a Homogeneous Magnetic Field”, China Sci-Tech Length and Breadth, 2009(6)
 Di Hua, “Inconsistencies in Einstein’s Formulation of Relativity Theory”, Hadronic Journal, Vol. 32, No.3, June 2009
 Di Hua, “Fundamental Revision of Einstein’s Relativity Theory —The Galilean Relativistic Mechanics with Variable Speed of Light”, Frontier Science, Volume 3, Number 4, 2009
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