_{1}

^{*}

Based on
the space spherical symmetry of 3-dimensional and the translational symmetry of
time and the uncertainty principle, a 4-dimensional space-time cylinder model
of quarks and leptons is established. With this model, equations of the special
relativity can be extended more perfectly, thereby achieving a unity of the
special relativity and quantum mechanics in deeper level. New equations can not
only interpret issues explained by old equations but also solve several
important pending problems. For example, a formula to strictly calculate the coefficient ξ of Lorentz invariance violation (LIV)
is derived, to above 4 × 10^{19} eV UHECR protons the calculated |ξ| < 4.5 × 10^{-}^{30}, although
there is the LIV effect it is too weak to change the GZK cutoff, which is
consistent with observations of HiRes and Auger; Also, a relation formula
between the Hubble constant and several basic constants is derived, thus
theoretically calculated H_{0} = 70.937 km·s^{-1}·Mpc^{-1}, which is well consistent with the
final observation result of HST Key Project. In addition, an unusual effect
predicted by new equations can be experimentally tested in the electron storage
ring; a preliminary experiment result has hinted its signs of existence.

How to unify the relativity and the quantum mechanics? This is a great problem in physics across the centuries, which has been a concern. Popular view is that, since the establishment of quantum electrodynamics, the unification of special relativity and quantum mechanics has been completed, the remaining work is only to explore the issue of unification of general relativity and quantum mechanics. However, if broadened thinking, it can be found that above view is flawed.

As we all know, from the fundamental sense, the special relativity firstly is a measurement theory about time, space, energy, momentum and so on, i.e. it is a physical framework to theory to do principled rules for all measurement acts. On the other hand, we also know that measurements of these physical quantities must be subject to the insurmountable constraint of one natural law, that is, the Heisenberg uncertainty principle that reflected essential feature of quantum mechanics. So in this sense judgment, the special relativity as a clean measurement theory that utterly disregards uncertainty relation, can not be a complete theory. Thus if taking into account the universality constraint of the uncertainty principle, it is necessary to further improve the special relativity; only completing this work can truly achieve unifying relativity and quantum mechanics.

In fact people already realized that any perfect physical theory regarding space-time not only has the rational core of the relativity also must contain the uncertainty principle and treat it as one of fundamentals of the theory. However, what specific method should be taken to make the uncertainty principle naturally implant into the concept system of special relativity and keep that the overall structure of special relativity is not destroyed? For this problem, the physics must make satisfactory answer.

Now this paper presents a way to solve this problem. First, based upon the uncertainty principle, the time translational symmetry and the 3-dimensional space spherical symmetry, for the elementary particles of the level of quarks and leptons there established a cylinder model with 4-dimensional space-time (PSTC model). Then, used this model, we deduced a series of new equations that are compatible with old equations of special relativity and also fit for the uncertainty principle, thus achieve unifying special relativity and quantum mechanics in deeper level via a way different from the quantum electrodynamics.

New equations which reveal the concepts of space, time, mass, energy etc. have richer connotations, so that can help people to re-understand the essence of some physical phenomena and solve several pending important problems, such as: 1) The new mass equation directly shows the inevitable existence of the Lorentz invariance violation (LIV) and derives a strict formula to calculate the LIV coefficient^{19} eV UHECR protons, the calculation_{0} = 70.937 km∙s^{−1}∙Mpc^{−1}, which is well consistent with the final measuring result of the HST Key project [

According to an extraordinary effect prophesied by new equations, it is expected that in the electron storage ring RF cavity downstream direction there is an emission of unusual electrons of much higher than the beam energy. It is possible to test the new equations of special relativity by detecting those small probability unusual events. A preliminary experiment was done and its result hinted the signs of emission of super-high energy electrons. To this end I propose an experimental program and called for experimental physicists to exactly complete the interesting exploratory experiment.

This paper is organized as follows. Section 2 describes the cylinder model of intrinsic 4-dimensional space- time of particles. Section 3 gives new improved equations of special relativity. Section 4 describes that use new equations to solve several important problems. Section 5 proposes an experimental plan to test the prophecy of the new equation. Section 6 gives the conclusion.

Einstein’s idea on space-time was to take the “physical object” as the premise. He said: “Space-time is not nec- essarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended” [

• When measuring such a particle, because the uncertain amount of the momentum and the energy can not be infinite, according to the Landau interpretation of the uncertainty principle, then the space uncertain amount and the time interval between twice measuring are impossible to zero. If abandoning the unreasonable infinity of the uncertain amount of momentum and energy, and taking a limited maximum value to replace them respectively, then the uncertain amount of space and the time interval will have the minimum value that are greater than zero. This indicates that in the actual observable sense the particles on this level should have a certain size.

• So-called the particle has “a certain size”, it means that the particle not only has a 3-dimensional space size, also has an intrinsic time size. Thus, according to the space-time unity of the special relativity, such a particle that has the nonzero and finite intrinsic scales of space-time should have an intrinsic 4-dimensional geometric shape.

• Taking into account when the particle is in rest, because there are the 3-dimensional space spherical symmetry and time translation symmetry, then the geometrical shape of particle should be a 4-dimensional cylinder that the timeline is taken as the rotational symmetry axis, and its axial height is the maximum value of the intrinsic time interval of particle.

• According to the above, the space and time of the 4-dimentional cylinder of particles must be the real physical space-time, rather than any formal mathematical space-time, such as the Minkowski space-time etc., so only Euclidean geometry is suitable for it.

• What particles are the final form that maintain the understandable time and space? According to the existing knowledge let us assume that they are particles of the quarks-leptons level. Of course, this is a mandatory assumption, of which correct or not need by testing its derived results later to judge.

Above these can be attributed to a basic postulate:

This [Postulate] gives the particles the cylinder model with intrinsic 4-dimensional space-time (for short PSTC model). In accordance with the requirements of [Postulate], when the particle is rest relative to the observer, its intrinsic time axis

Having a nonzero and finite intrinsic time height is the most important feature of the particles 4-dimensional space-time cylinder model. The time height concept comes from the Landau interpretation of the energy-time uncertainty relation [

Projection of the particle’s intrinsic 4-dimensional space-time cylinder on the t-u-t' plane (The velocity u of particle is along the x-axis direction of the coordinate system of observer)

measure, in the uncertainty relation

Here the so-called “apparent time height” (denoted by T) is a projection value of the particle 4-dimensional cylinder on the observer’s coordinate system time axis, according to [Corollary 1], T changes with speed u. The axial height of the particle 4-dimensional cylinder defined by the [Postulate] is called the particle’s intrinsic time height (denoted by

where

In addition, the calculating formula of the particle’s intrinsic time height will in Section 3.4.2 be deduced, now it is also written in advance:

(6) show that

Further use of (4) and (5) to calculate the diameter of electron:

On high-level composite particles as well as macroscopic objects, because they are the gathering of quarks and leptons in 3-dimensional space, so although their space scales can continue to amplify, their intrinsic time scale remains the intrinsic time height of elementary particles.

The intrinsic time-space ratio of particle is very large value, which shows the serious imbalance between the intrinsic time scale and intrinsic space scale, so saying geometry form of particle is the “4-dimensional cylinder”, rather is a very slender “4-dimensional thorn”.

The [Corollary 2] points out that the particle’s shape that is randomly observed at one moment is a 3-dimen- sional space cross-section of the particle’s 4-dimensional space-time cylinder in the coordinates-system of observer. Referring to

In

When

Similarly, when

According to

. The 3-dimensional space cross-sections of the 4-dimensional space-time cylinder of particles

, | , _{} | , | , | |
---|---|---|---|---|

Sphere with diameter D^{*} | ||||

Complete ellipsoid with major axis Λ_{1} and minor axis D^{*} | Ellipsoid zones with same height (=Λ_{2}), different end-plane diameters | |||

volume V of 3-dimensional space cross-sections can be gotten:

where

According to

1) If

2) If

where

3) If

4) If

5) If

6) If

To sum up, the differences as well as advantages of the PSTC model compared to other non-point particle models as follows:

1) The basis of establishment of PSTC model is realistic and reliable, it is based upon the spherical symmetry of 3-dimensional space, the translational symmetry of time, the space-time unity of relativity, the Heisenberg uncertainty principle, and its applying objects are quarks and leptons, which all are empirical facts and recognized principle, there are no additional imaginary content.

2) The PSTC model is simple, there is only 4-dimensional space-time, with no additional dimension.

3) For space-time, the PSTC model requires real physical space-time, i.e. Euclidean space-time, rather than any mathematical space-time, such as the Minkowski space-time etc. We know that the Minkowski geometry is one of expression forms of special relativity but has not the substantive contribution to the special relativity.

4) The PSTC model points out that the particles not only has a size of the space, in the time also has a non- zero and finite intrinsic “height”, the ratio of the time height T^{*} to the diameter D^{*},

5) The PSTC model can be used to develop the basic theory of physics, such as the development and improvement of special relativity.

Using the particle’s intrinsic 4-dimensional space-time cylinder model (PSTC model), a series of new more perfect equations corresponding to old equations of the special relativity are derived. The PSTC model is based on the uncertainty principle, so new equations have reflected the constraint of uncertainty principle. Taking into the applicability and the testability, we first focus on the new mass equation.

In accordance with [Postulate], “the amount of mass” included inside the particle of quarks and leptons etc. must uniformly be distributed in the intrinsic 4-dimensional space-time cylinder, and further in accordance with [Corollary 2], the particle’s shape observed at one moment is a 3-dimensional space cross-section of the 4-dimen- sional cylinder, so the mass m of particle is proportional to the volume V of 3-dimensional cross-section, that is

where, m_{0} denotes the rest mass of particle. Then (11) into (18) we obtain the more universal mass equation:

where on the speed

To this equation interpretations and in-depth discussions as follows:

[I] The mass m is not a single variable function of the speed u, it depend on both of the speed u and the random variable

[II] When

It can be seen that m_{R} depends singly on u. When _{R} and

Because the new equation eliminates the infinity, so the theoretical suppression of the physical particles moving at light speed will be eliminated. When

[III] Because generally m is a double variable function on u and

[IV] With reference to

Since Lorentz energy

The formula shows that the higher the particle’s speed u (i.e. the higher the Lorentz energy E_{R}), the greater the possibility appearing in HSLM state. Because

The probability of particle appearing in a neighborhood of

However the probability of particle in “normal state” of

Because there is always

[V] It can be seen in

when

(27) into (26) and using (21), to obtain

. The probability Ps of different E_{R} value electron appearing in HSLM state

In high energy cosmic ray | By artificial accelerated | In nuclear β decay | In hydrogen atom | |
---|---|---|---|---|

E_{R} (eV) | ~10^{16} | <10^{11} | ~10^{6} | <5.11 × 10^{5} + 13.6 |

P_{S} | ~10^{−}^{8} | <4 × 10^{−}^{14} | ~10^{−}^{19} | <10^{−}^{21} |

which shows that when a particle moving at the light speed, its energy changes proportional to the square of the sinusoidal of phase angle.

[VI] For the mass

The (29) shows:

1) The mean mass

2) In the “lower energy” state of

3) For composite particles and macroscopic objects, as long as the rest mass

4) The mass/energy of satisfying the conservation law are neither the

5) (29) multiplied (3) to obtain

That is, the product of the particle’s apparent time height T multiplied by the mean mass is a Lorentz invariant.

6) When

when

It should be noted, according to the PSTC model, only to the particles of level of quarks/leptons the speed

7) Putting the total mean energy

where

Compared with the old energy-momentum relationship

(34) than (36) multi-a

. LIV coefficients ξ corresponding to different speeds u

(Unknown) | Ultra-high energy cosmic ray protons | LHC accelerator protons | Slow neutrons in the reactor | Laser frozen atoms | (Unknown) | |
---|---|---|---|---|---|---|

u | c | ~ (1 − 10^{−22})∙c | ~ (1 − 10^{−8})∙c | ~ 10^{−5}∙c | ~ 10^{−11}∙c | c/Φ = 0.289 (Å/s) |

ξ | ~ −10^{−38} | ~ −10^{−30} | ~ −10^{−23} | ~ −10^{−15} | ~ −10^{−8} | −2 |

(37) suggests that people should re-understanding of the “stationary” concept, because such an extreme tiny speed ~0.289 (Å/s) has never been actually observed. About (29) and (34) we will do for a more in-depth discussion in Section 4.

By the

and inverse transforms

where

the time dilation

the “length contraction”

the velocity addition law

and

Defining

If time and space coordinates are transformed by (38) (39) (38’) (39’), the electromagnetic field are transformed by following (48), then in all inertial reference frames Maxwell’s equations still has the same form,

where

It can be seen that the new transform still kept the beautiful symmetry.

For the monochromatic plane wave

where k is in the

so in the new special relativity the phase angle of monochromatic plane wave is still a Lorentz invariant.

Using above those results we can design two ideal experiments respectively to evaluate the particle’s intrinsic time-space ratio

The new mass equation indicates that when ^{19} times of the rest neutron, which equals ~3 × 10^{14} years and greatly exceeds the universe age ~1.38 × 10^{10} years, so the “observer” can still do the second measurement of the two neutrons system. Clearly, the time interval

to get in twice measurements the minimum value of the uncertain energy

However, what is the specific form of energy corresponding

In addition, for the expression of the universe age, we require an in-depth analysis. Two neutrons predecessors, i.e. quarks and so on primordial particles, were from a same cosmic singularity starting, the big bang caused they fly at the light speed at that time. If the subsequent expansion of the universe is roughly uniform and isotropic, today’s “observer” and the two neutrons must be on those locations of the great circle shown in

As is known, at different periods the universe expansion speed is variable, so the universe age

(53) (54) into (52), to ultimately get

Schematic diagram of the ideal experiment of “two-neutrons”

All factors of the (55) right side have the known exact value, so

It can be seen that

Finally it must be noted that the particle that fits this ideal experiment only is the neutron and not any other particles, for the following reasons: So far all astronomical observations and experimental facts show that the weak gravitational source substances satisfying Newton’s gravitation law have all the structural unit with the nucleons as main component, so the real and stable “basic gravitational charge” must be nucleons. In addition, in order to avoid electromagnetic interaction so only the neutron is chosen.

We can design another ideal experiment to deduce the formula (6) calculating the particle intrinsic time height. Let us imagine that an observer is measuring the energy of a slow-moving free-particle, such as an electron. He can choose an appropriate way to satisfy always the particle speed

which correspond to once occur in

About this issue, the new special relativity gives three levels theoretical results which consistent with observations of HiRes and Auger: First, pointed up the existence of Lorentz invariance violation is inevitable and the LIV coefficient ^{19} eV UHECR protons the calculated

The people have known that the higher than 10^{18} eV UHECRs, in propagating from the extragalactic sources to the Earth, interact with CMB photons to result in a decline of their energy and flux and finally cause the spectrum suppression at (3 - 6) × 10^{19} eV, that is the GZK cutoff predicted by Greisen, Zatsepin and Kuzmin in 1960s [

Thus, if the coefficient absolute value ^{−}^{23} enough to eliminate the GZK cutoff. However, in 2008, the HiRes Collaboration announced to confirm the GZK cutoff with a ^{19} eV with a 6σ standard deviations [

Here let us use the new Equation (34) of the special relativity to solve this problem. Although (34) and the Coleman-Glashow formula (57) both have the same form (I even deliberately use the same symbol

1) (34) is derived out from a basic Equation (29) of the new special relativity, so the occurring of

2) The LIV coefficient

3) (29) points out, for all kinds of particle the physical quantity with common upper limit is just the speed i.e. the light speed c (not other physical quantities, e.g., energy). When_{0} there are different maximal attainable energies (and not different maximal attainable speeds).

4) (35) shows, the higher the speed u, the smaller (and not the larger!) the coefficient absolute

5) When

In the energy region

For the UHECR spectrum ankle region protons and ^{56}Fe, we use (58’) to specifically calculate the LIV coefficient values and list to

To above 4 × 10^{19} eV protons, the calculated

. Values of LIV coefficient of different energy UHECR protons and ^{56}Fe

Energy E_{R} (×10^{19} eV) | 0.5 | 1 | 3 | 4 | 6 | 8 | 10 | 20 | |
---|---|---|---|---|---|---|---|---|---|

Proton (×10^{-}^{30}) | 36.2 | 18.1 | 6.0 | 4.5 | 3.0 | 2.3 | 1.8 | 0.9 | |

^{56}Fe (×10^{-}^{28}) | 20.3 | 10.1 | 3.4 | 2.5 | 1.7 | 1.3 | 1.0 | 0.5 |

On the other hand, we know that events beyond GZK energy were also really recorded in cosmic ray observation, in order to explain this phenomenon, it is necessary to use the basic Equation (19-1). As described above, (34) is derived from (29), and (29) is derived from (19). The mass of composite particles is usually embodied as the mean mass

Now let us imagine that a group of beyond the GZK energy protons from an extragalactic source which is more distant than the mean free path fly to the Earth. In this process, a very few of protons could appear in certain HSLM state in some time. Because at the HSLM state the energy and the relative cross-section are both smaller than the normal values, therefore the possibility that the HSLM protons interact with the CMB photons will be smaller than of the normal protons, thereby they can propagate farther than the normal mean free path. If arriving Earth before restored to the normal

2002, J. Magueijo and L. Smolin modified Einstein’s special relativity and proposed the “doubly special relativity (DSR)”, of which one of four basic principles is the observer independence of the Planck energy [

Considering a particle at a velocity u moves along the x axis of an inertial frame

As a special case, we use (31) and (55) to calculate the maximum value of the mean mass of neutron

where,

In addition, we prove that an important formula of DSR can be derived by (29). According to (20-1), letting the Lorentz mass

When

At the same speed the mass ratio

According to (59), the Planck mass

It is interesting, the DSR also has such a similar formula [

Now it has been seen that the DSR’s one basic principle and a similar to (63) result all can be proved by the new special relativity. However, this does not mean that my new special relativity and the DSR are the same thing, in essence they are different in not only the theoretical fundamentals but also some typical results. For example, the new special relativity has proved that the Planck energy cannot serve as the common upper limit of the energy of all kinds of particles, and indicate that of importance is not the Planck energy but the parameter

(32) (33) show that there is a specific speed

Because in the real universe this expansion is inevitable, so even though there is no any external forces, but the electron moving at

where,

Noting (65) is a derived result of the Schrodinger equation, and the energy operator in Schrodinger equation is of corresponding the classical mechanics, so there must be

By (32) and (64)-(67) thus obtaining another

According to the magnitude of the “today”

Here it must be noted that the particle that fits above ideal experiment only is the electron and not any other particles, for the following reasons: 1) According to the PSTC model, only to the particles of quarks/leptons level the speed uq can be defined, so composite particles are rejected; 2) Particles must be in the free state, so only the leptons can be selected; 3) Because neutrinos are always in the oscillation so also are rejected; 4) The life of

Combining (69) with (55), a relationship between the Hubble constant and several basic constants is obtained:

All factors of (70) right side have known accurate values, so we can use this formula to exactly calculated

^{−}^{1}∙Mpc^{−}^{1} (71)

(32) (70) into (64) calculated a_{q} = 1.26 × 10^{4} km, so our theoretical value is the “near-place” Hubble constant.

Generally believed that the Hubble law is an empirical law and the Hubble constant is obtained by astronomical observations. However, the theoretical result (70) is derived from a non-point model of microscopic particles, in its deductive process the Hubble law is used but does not involve any astronomically observed quantity (such as the redshift, the luminosity), which indicates that the theoretical value (71) is completely independent to astronomical observation, so its comparison with the measuring value of Hubble constant is a persuasive way to test the new special relativity. It is noted that after long efforts the enough credible observed values of the Hubble constant have been obtained, such as the final measurement result of Hubble space telescope key project [_{0} = 72(71) ± 4 ± 7 km∙s^{−}^{1}∙Mpc^{−}^{1}, the exciting is my theoretically calculated value is well consistent with this observed value.

Dirac long noted, there are two approximately equal non-dimensional large numbers,

N_{1} is the ratio of the universe Hubble radius to the electron classical radius, N_{2} is the ratio of the static electricity force to the gravitation between proton and electron. In addition there are a series of large pure numbers, which are roughly equal with integer powers of

or

where

The Dirac large numbers problem as a mystery to the people left a deep impression, however, so far on this problem did not achieve breakthroughs. Why exists such a mysterious numbers relation (73)? What is the elusive basic fact hiding at behind those large numbers? Dirac had reward to seek answers the questions has not been deciphered.

It is interesting that in our new special relativity there is also a dimensionless large number of approximately

The ratio of the Hubble radius to the electron classical radius

^{}

The ratio of the static electricity force to the gravitation between proton and electron

^{}

The ratio of the electron classical radius to the Planck length

The ratio of the Planck length to the Schwartzchild radius of proton

The ratio of the Hubble radius to the Schwartzchild radius of proton

where

Based on the above analysis it can be considered that the Dirac large numbers principle is a secondary effect, the important thing that hides at behind the relevance of large numbers is the particle’s intrinsic space-time feature described by parameter

In Section 3.1 [III], it has been pointed out, the new mass equation predicts that there is a unusual “high speed-low mass (HSLM) effect” in motion of particles. The HSLM effect is very weak, however, in the electron storage rings with high current and long time running we could still observe abnormal phenomenon caused by it, that is, an emission of super-high energy electrons much higher than the beam energy in the RF cavity downstream direction. By detecting such small probability abnormal events we can test the new mass equation. In the NSRL800MeV electron storage ring, I used the lead plates-X films detector to cumulatively detect for a long time, preliminary experiment results hinted the signs of existence of super-high energy electrons [

According to (19.1), at a same speed, the mass m of HSLM electron in

1) Strength: Using (19-1) (23’) (24) (15) it can be proved that numbers of super-high energy electrons may appear per hour

where, _{R} (MeV) denotes the energy of beam; U (MV) denotes the accelerating voltage; I (mA) denotes the average current intensity; E_{0} (MeV) is the rest energy of electron; e (C) is the electron charge. So in

In existing electron storage rings, calculated N_{21} values are all very small, such as, if E_{R} = 2000 MeV, U = 1.5 MV, I = 500 mA, about average 1 hour appearing 1 event of super-high energy electrons of

2) Energy-positional distribution: Shown in

where r is the normal bending radius of beam in the bending magnetic field; a is the length of first bending magnetic field; b is the distance between the exit end of first magnetic field and the absorber.

New equations expect that in the electron storage ring RF cavity downstream direction there are small probability events of emission of unusual electrons whose energies are much higher than the beam energy

The super-high electrons occurring in electron storage rings are very rare, but it is still feasible to detect such small probability events by existing experimental techniques, which because:

1) Electron storage rings have higher current and can run continuously for a long time, so to facilitate the long-term search and cumulative record. And, to many electron storage rings, in the RF cavity downstream direction occurring super-high energy electrons, the beam pipeline of synchrotron radiation are not installed and the vacuum chamber is only closed by the blind end, which facilitate the placement of detector.

2) The sampling electromagnetic calorimeter can be used as a detector, and such detectors are mature technologies. Because the copper blind-end is very thick, the super-high energy electron injects in which will occur electromagnetic cascade shower, so the detector will in fact accept such the secondary particles shower. To the sampling electromagnetic calorimeter, the copper blind-end is equivalent to its front-side absorber. Of course, it is best to place the detector to inside of the vacuum chamber of storage ring. In addition, taking into the residual gas bremsstrahlung along the straight section axis is a main interference, so in order to reduce its impact, the detector should be appropriately off-axis placed.

Could the special relativity and the quantum mechanics unify at deeper level via a way different from the quantum electrodynamics? This is a potential big problem which should not be overlooked; In recent years, about whether existing the Lorentz invariance violation has become a hot topic of extensive discussions; Since the superstring theory driven, the way using a non-point particle model to replace the concept of mass point to seek developments of theory has been widely accepted. Under this context, therefore, it is imperative to try to use the basic principles of quantum mechanics, especially the uncertainty principle to further improve the special relativity. This paper is in this direction an independent research and useful contribution.

This work is first based upon the space spherical symmetry of 3-dimensional and the translational symmetry of time, and the uncertainty principle, to establish a 4-dimensional space-time cylinder model of the quarks and leptons. Then, we use this model to deduce a series of new equations that are compatible with old equations of special relativity and also satisfy the uncertainty principle, thereby achieve unifying special relativity and quantum mechanics in basic concepts. New equations which reveal the concepts of space, time, mass, energy etc. have richer connotations, so that can help people to re-understand the essence of some physical phenomena and solve several pending important problems. The results derived by new equations show:

1) The mass is a binary function of speed u and another dimensionless variable

2) When

3) The violation of Lorentz invariance is inevitable and the LIV coefficient ^{19} eV UHECR protons, the calculated

4) It is proved that the Planck energy is a Lorentz invariant, so there is certainly “the observer independence of Planck energy”. However it is also proved that the Planck energy isn’t the common upper limit of energy of all kinds of particles.

5) A relation formula between the Hubble constant and several basic constants is derived, thus the theoretical value H_{0} = 70.937 km∙s^{−}^{1}∙Mpc^{−}^{1} is obtained, which is well consistent with the final result of observation of HST key project. The mystery of Dirac large numbers can be clarified too by this relation formula.

6) An unusual effect is predicted, and accordingly expected that in the electron storage ring RF cavity downstream direction there is an emission of rare unusual electrons of much higher than the beam energy. New equations can be tested by searching for such small probability events.