_{1}

^{*}

It is
proved in this paper that there are at least five situations in the interaction
theories of microparticle physics that the Lorentz transformations have no
invariabilities. 1) In the formula to calculate transition probabilities in
particle physics, the so-called invariability factor of phase space d^{3}p/E is not invariable actually
under the Lorentz transformations. Only in one-dimensional motion with u_{y} = u_{z} = 0, it is invariable. 2) The propagation function of
spinor field in quantum theory of field has no invariability of Lorentz
Transformation actually. What appears in the transformation is the sum of
Lorentz factors a_{μν}a_{λμ} ≠ δ_{νλ} when ν, λ = 1, 4, rather than a_{μν}a_{λμ} = δ_{νλ}. But in the current calculation, we take a_{μν}a_{λμ} = δ_{νλ}. The confusion of subscript’s position leads
to wrong result. 3) Though the motion equations of quantum fields and the
interaction Hamiltonian are unchanged under the Lorentz transformation, the
motion equation of perturbation which is used to calculate the transition
probability in the interaction representation has no invariability. 4) The
interactions between bound state’s particles have no Lorentz invariability. In
fact, the principle of relativity has no approximation if it holds. 5) The
calculation methods of high order perturbations normalization processes in
quantum theory of fields violate the invariability of Lorentz transformation. The
conclusions above are effective for strong, weak and electromagnetic
interactions and so on. Therefore, the principle of relativity does not hold in
the micro-particle’s interactions. On the other hand, the invariability
principle of light’s speed is still effective. So the formulas of special
relativity still hold, but we should consider them with absolute significances.

The Einstein’s special relativity is based on two foundational principles. One is the principle of relativity and another is the invariability of light’s speed. According to the principle of relativity, motion is a relative concept. We cannot determine whether a reference frame is moving in a uniform speed or at rest by physical experiments. Speaking more strictly, the forms of physical laws are unrelated to the choices of reference frames. To reach this aim, physical quantities should be covariant under Lorentz transformations.

Because most macro-physics involve low speed’s processes, special relativity is mainly used in micro-physics processes. Micro-physics includes relativity quantum theory of field and non-relativity quantum mechanics. Be- cause the motion equations and interactions Hamiltonians in quantum theory of field are considered invariable under Lorentz transformation, physicists believes that interaction processes of micro-particles satisfy the prin- ciple of relativity.

However, astronomic observations founded that the cosmic microwave background radiation (CMBR) was anisotropic in space distribution. If we take the reference frame in which CMBR is isotropic as an absolutely static reference frame, observations indicate that our solar system is moving in a speed about 390 Km/s along a certain direction in the coordinate system of celestial sphere. This velocity can be considered as the absolute velocity of solar system. In fact, Big Bang cosmology needs an absolutely static reference frame. We can think that all initial velocities of materials in the universe were caused by the accelerating processes in Big Bang. So physics is in a dilemma situation at present. Cosmology and relativity are inconsistent. This is a serious prob- lem.

In this paper, we prove that the principle of relativity is only a subjective and specious judgment under ma- croscopic and low speed’s conditions, just as Galileo’s intuitional experiments in a closed ship. Under micro- scopic and high speed’s conditions, the principle of relativity does not hold. In fact, the principle of relativity has never been accurately verified by experiments. Physicists have never carried out experiments in a reference frame with high enough speed to verify the correctness of relativity principle!

In the processes of micro-particle’s decays and collisions, the transition probabilities are considered having nothing to do reference frames. Quantum theory of field is constructed in this principle and the interaction theo- ries of micro-particles are considered satisfying the principle of relativity. However, in this paper, we carefully examines the motion equations and the interaction Hamiltonians of micro-particles in quantum theory of field and finds that at least in five situations the interaction theories of micro-particles have no invariability under Lorentz transformation.

1) The so-called invariability factor of phase space

2) The propagation function of spinor field has no the invariability of Lorentz Transformation actually. What appears in the transformation is the sum of Lorentz factors

3) Though the motion equations of gauge fields and spinor fields and the interaction Hamiltonians are un- changed under Lorentz transformation, the motion equation of perturbation theory used to practically calculate the transition probabilities in interaction representation has no Lorentz invariability. In fact, even the most foundational normalization formulas of probability wave in quantum theory of field and quantum mechanics have no invariability of Lorentz transformation too. Unfortunately, these problems are neglected at present.

4) The interactions between bound state’s particles violate the invariability of Lorentz transformation. In fact, so-called relativity quantum theory of field only describes interaction processes in which particles are free at their initial and final states. The Hamiltonians of interactions are constructed by free particle’s wave functions. What are measured in experiments are free particles at final states. Because the wave functions and the products

However, in physics, more are the interactions between bound particles in which the wave functions, energies and momentums have no symmetries of free particles. We have

According to current understanding, relativity quantum theory of field describes unstable particles with high speed, and non-relativity approximate quantum mechanics describes stable particles with low speeds. This clas- sification is unsuitable for the principle of relativity principle. The principle of relativity has no approximation. If the principle of relativity is correct, it should also be effective for the micro-particles with low speeds. In fact, classical Newtonian theory also satisfies the principle of relativity. The motion equations of Newtonian mechanics are unchanged under the Galileo’s transformation. However, the motion equations and Hamiltonians of nonrelativity quantum mechanics cannot keep unchanged no matter under the Galileo’s transformation or the Lorentz’s transformation. This fact indicates that micro-particle physics has no relativity in essence! So called nonrelativities of motion equation and interaction Hamiltonians in quantum mechanics are not caused by the approximation methods of descriptions. The truth is that relativity does not exist in micro-physics at all!

5) The normalization processes of high order perturbations in quantum theory of fields violate the invariabili- ty of Lorentz transformation. We take the Lamb shift of hydrogen atomic energy levels as concrete example at first and then prove the conclusion generally.

The conclusions above are generally effective for strong, weak and electromagnetic interactions. Therefore, the principle of relativity does not hold in the fields of micro-particle’s interactions. However, the invariability principle of light’s speed is still effective. It means that the formulas of special relativity can still hold. But they should be explained with absolute significance.

In this way, the experiments of micro-particles and the observations of macro-cosmology become consistent and the contradiction between cosmology and special relativity can be eliminated thoroughly.

In particle physics, the basic formula to calculate the decay probability in particle physics is [

The basic formula to calculate the collision cross-sections is

In the formulas, the probability amplitude

Before proving it, we need to define the invariable quantity of Lorentz transformation. In Einstein’s special relativity, physical quantities are transformed in the forms of covariance. Suppose that there is a physical quan- tity

We take several examples commonly appearing in particle physics. Suppose that

The inversed transformation of (3) is

The Lorentz transformations of velocities are

So space-time coordinates

Substituting (5) in (6), we obtain the Lorentz transformations of momentum and energy

So

So

We can prove it easily. According to (6), we have

According to (7), we get

In particle physics, similar invariable quantities are

Meanwhile, we have

So the wave function of free particle is also the invariable quantities of Lorentz transformation with

The definition of

Transforming it to

So

If phase space factor is the invariable quantity of Lorentz transformation, it should satisfy

We will prove that (18) only holds in the situation of one-dimensional motion with

here

On the other hand, in general situations with

Comparing (22) with (19), we have

It is obvious that

We obtain

By using the Jacobi’s formula, we get

here

The up and down limits of integral signals about

In special relativity, we take

here

The others are zero. This result is very significant for our discussions below. It is proved that what appears in the Lorentz transformation of propagation functions of spinor fields is

The Dirac equation of free spinor field in

By transforming it to

It indicates that the covariant rule of differential operator

By introducing matrix

Suppose that there exists reversal matrix

It has been proved

we can write (31) as

(37) and (31) have the same form, so we say that the motion equation of free spinor field is invariable under the Lorentz transformation. On the other hand, it has been proved

In quantum theory of field, by considering the interaction between electromagnetic field and spinor field, the motion equation in

Here ℋ(x) is the Hamiltonian of interaction. According to the covariant rule of vector in special relativity, simi- lar to

We write out the concrete results

The reversed transformation of (41) is

It is similar to

The motion equation (39) of non-free spinor particle contains the item

So the motion equation of non-free spinor particle is Lorentz invariable. Similarly, considering (35), (36), (38) and (41), we get

The Hamiltonian of electromagnetic interaction is also invariable under Lorentz transformation.

However, in quantum theory of field, we calculate particle’s transition probabilities in interaction representation. The basic equation of perturbation used practically is [

In fact, the probability amplitude

Using (48) to do calculation, the transition probability is certainly different from that based on (47). In fact, even for the most foundational normalization formula of probability wave in quantum theory of field and quantum mechanics, there is no invariability of Lorentz transformation with

Unfortunately, these problems are neglected at present.

In quantum theory of field, the operators of scalar fields can be written as

Their commutation relations are

As mentioned before,

According to (17),

In quantum theory of field, the operators of spinor fields can be written as

The commutation relations are

Here

By transforming them to moving reference frame, according to (36) and (38), we have

here

(61) becomes

Similarly, the transformation of (58) is

However, in the current quantum mechanics of field, we take

The commutation relations of spinor fields have no Lorentz symmetry too. The propagation function of spinor field is defined as

Here

Set

According to (63) and (64), the Lorentz transformation of spinor field is

Therefore, the propagation function of spinor field has no invariability of Lorentz transformation too.

The first order process describes particle’s decay in quantum theory of field. In the formula (1),

The transition probability of second order collision process is described by (2). Because the propagation func- tion of spinor field has no invariability of Lorentz transformation, the probability amplitude

the transition probability amplitude is [

here

and so do for

According to present classification, the theories of micro-physics are divided into relativity quantum theory of field and non-relativity approximated quantum mechanics. Quantum theory of field describes unstable particles with high moving speed, mainly used in the interaction processes between elementary particles which are free at their initial and final states. The interaction Hamiltonians can be constructed by using the wave functions of free particles. As shown in (14) and (15), the wave function of free particle is invariable under Lorentz transformation. The amplitudes of transition probabilities can also be represented by the products of four-dimensional energy momentums of free particles just

However, fundamental particles physics is only a branch of physics. These particles are created in laboratory and then decay immediately. So quantum theory of field can only dealt a small part of physics which has no closed relation with real world. What closely connected to practical world is the interaction between bound par- ticles, for example, atoms emitting photos, superconductors and condensed matter and so on. In these problems, the interaction Hamiltonians cannot be constructed by free particle’s wave functions. For non-free particles, we have

Non-relativity quantum mechanics describe stable particles with low moving speed. However, the principle of relativity has no approximation. It is either tenable or not tenable. If it is tenable, it should hold for the particles moving in low speeds. In fact, the principle of relativity is considered to be tenable in classical Newtonian me- chanics. The formulas of the Newtonian mechanics are considered unchanged under the Galileo’s transformation. The motion equations of non-relativity quantum mechanics cannot keep unchanged under the Lorentz transfor- mation. Can it be invariable under the Galileo’s transformation? The answer is neglected. For example, the Schrodinger’s equation is

It is not invariable no matter for the Lorentz transformation or the Galileo’s transformation. So generally speaking, quantum theories of common micro-physics have no relativity. So-called the non-relativity of bound particle’s motion equations is not due to the approximate description methods we used. The essence is that they have no relativity at all!

We take electron’s scatting in eternal field, fine structure of hydrogen atomic energy level and light’s emission and absorption in bound atoms as examples to prove this conclusion below. The free particle’s Dirac equation of quantum mechanics is based on special relativity and invariable under Lorentz transformation. However, it becomes non-relativity when it is used to describe the energy levels of bound hydrogen atoms.

Suppose that the external field is static electric field with form

ℋ

(74) is not the Lorentz invariable quantity. Based on it, it is proved in quantum theory of field that the effective scatting section is [

The transition probability amplitude is

here

By transforming (77) to moving reference frame, we have

So (78) is not the Lorentz invariable quantity. In addition, phase space factor is not unchanged, so (75) has no relativity.

It is obvious that the energy levels of hydrogen atom cannot be calculated by quantum theory of field, though it can be used to calculate the high order revision (Lams shift). By considering relativity quantum mechanics, the motion equation of an electron in hydrogen atom is

here

However,

After transformation, the potential is related to speed and time. It is impossible for us to obtain the energy le- vels if we do calculation in

In the radiant process of common material, interaction between electromagnetic wave and bound electron in atom is involved. Suppose that electromagnetic wave transits along

here free plane wave

The operator is acted on the wave function of bound electron and the bound wave function is not Lorentz in- variable. The result has no symmetry of Lorentz transformation. Similarly, (82) is not invariable under the Gali- leo’s coordinate transformations. No mater from what angle, the processes of light’s emission and absorption have no relativity too.

In fact, for most practical problems of micro-physics, we cannot use the method of relativity quantum theory of field to deal with. We can only calculate them by non-relativity quantum mechanics. Under the conditions of low speeds, these methods are very effective. We cannot say they are imprecise. More important is that these problems have no the symmetries of Lorentz transformation in essence, we cannot impose relativity on them.

The high order perturbation processes of quantum theory of fields contain infinite and need to be renormalized. The normalization may introduce the symmetry violation of Lorentz transformation. At first, we take the Lamb shift of hydrogen atom’s energy levels as examples. By the normalization calculation, the Lamb shift is [

here

By transforming it to moving reference frame, we get

New wave function depends on time and relative speed without Lorentz invariability. Operators

In the normalization processes of high order perturbations, following integrals are involved

here

So

However, the direct calculation of (87) is difficult. In order to complete the integrals, we need to move the original point of coordinate, then introduce transformation

we get

In this way, for same simple situations, (87) can be integrated. For example

Let

So

The probability amplitude of mass normalization is [

By introducing

The probability amplitude of mass normalization has no invariability of Lorentz transformation.

The probability amplitude of vacuum polarization is [

here

By taking several simplifications, including

we obtain

Let

Similarly, because

The amplitude of third order vertex angle process is [

Set

Similarly,

The normalization of the third order vertex angle process is not invariable under Lorentz transformation.

It notes that this kind of symmetry violation is caused by the calculation method of integral transformation

In summary, three basic normalizations processes of electromagnetic interaction violate the symmetry of Lo- rentz transformation. The conclusion is also suitable for other interaction theories.

By the analysis above, we see that the principle of relativity cannot hold in the interaction theories of micro- particles at all! But why physicists did not find this problem up to now? This question is worthy of our thought.

When Einstein put forward special relativity in 1905, science community has not yet reached common under- standing about whether or not atoms exist, not to mention quantum mechanics and elementary particle physics. It was the matter after relativity was accepted widely when it was applied in elementary particle physics. Phy- sicists believed relativity was correct, so that Lorentz symmetry violation in micro-physics was neglected con- sciously or unconsciously. Speaking in other words, the problems of Lorentz symmetry violations in micropar- ticle physics were handled vaguely. However, as long as we get to the bottom of matter, the problems still emerge from the water.

In special relativity, the invariability principle of light’s speed and the principle of relativity are independent each other. But in some situations, they are connected. The Lorentz formula is deduced based on the invariability principle of light’s speed. According to the principle of relativity, the Lorentz formula has relative significance only. Meanwhile, the principle of relativity declares that the forms of physical motion equations do not change with reference frames. To reach this aim, physical quantities should be transformed in covariant forms. As shown in (41) and (42), covariance is for general physical quantities and Lorentz transformation is for space-time coordi- nate. Both are different concepts, but we often do not distinguish them.

Besides, in order to keep the motion equation of spinor field unchanged, we should introduce spinor trans- formation. However, as shown in (36), spinor transformation is not covariant. That is to say, in order to make the motion equation of quantum mechanics unchanged, covariance is not enough. The problem is very complex ac- tually. It is proved in this paper that even though spinor transformation is considered, the interaction theories of micro-particles have yet no relativity.

On the other hand, the invariability principle of light’s speed has obtained a lot of verifications, especially in the experiments of high energy accelerators. For example, the experiment to measure light’s speed in the process that high energy proton decays into meson and photon in CERN in 1964. However, the principle of relativity is only a kind of belief without really strict verification. Because common experiments only involve low speed motions, similar to Galileo, modern physicists make their judgments according to common experiments. They belies that the principle of relativity is alright.

So the real situations may be that the effectiveness of the invariability principle of light’s speed coves the in- effectiveness of the principle of relativity. In fact, up to now days, physicists have never made practical mea- surements in the moving reference frame with high enough speed to verify the principle of relativity. The Mi- chelson interference experiment seems to prove that the absolute motion of the earth cannot be measured. How- ever, in relativity, we use the invariability of light’s speed to explain the Michelson interference experiment. In this meaning, the Michelson interference experiment only verifies the invariability principle of light’s speed, without verifying the principle of relativity.

Ironically, many pioneers of relativity including Michelson, Lorentz, Poincare and March and so on did not accept Einstein’s relativity. What they opposed was the principle of relativity, rather than the invariability prin- ciple of light’s speed. The reason was that the principle of relativity leads to various logic paradoxes. In fact, it is the problem of experiment whether or not the invariability principle of light’s speed can hold. If there is no the principle of relativity, we can still reach the Lorentz transformation based on the invariability principle of light’s speed. In this case, the Lorentz transformation becomes absolute, just as Lorentz himself considered it. All for- mulas of special relativity are still effective, but become absolute ones. The effects of special relativity also be- come absolute ones.

However, it is mainly a logic problem whether or not the principle of relativity is tenable. So it is easy to cause arguments. Since Einstein established special relativity one hundred years ago, criticism has never stopped. The arguments are so violent and last so long time that it is unwonted in the history of science. The arguments are concentrated on the space-time paradox problems just as length paradox and time paradox which are often specious. Correctness and mistakes are mixed together so that it is difficult to obtain correct judgment. Because these problems do not belong to the main stream of physical research at present time, physicists do not pay at- tention to them again.

A dramatic change appeared in 1960’s when CMBR was founded. The isotropy of CMBR provided a choice of absolutely static reference frame for physics. The principle of relativity is not a problem of logic again. It be- came a problem which can be verified through experiments and observation of astronomy. In fact, the Sagnac effect found in 1912 had indicated that the relativity of motion was impossible. The time comparison experi- ments of microwave communications through satellite between Xian and Tokay achieved in 2001 also revealed the same conclusion [

On the other hand, all arguments about relativity principle such as space-time paradox, Sagnac effect, and the isotropy of CMBR are macro-phenomena. But macrocosm is composed of micro-particles. If the physical laws of micro-particles have relativity, physicists have reason to believe the principle of relativity. But if the physical laws of micro-particles have no invariability under the Lorentz transformations, physicists have no reason to stick to the relativity principle of motion again.

The proofs in this paper are clear and certain without any speciousness. So there is only a way for physics. That is to give up the principle of relativity but reserve the invariability principle of light’s speed. In this way, all formulas of special relativity can be reserved but we need to explain them in absolute forms. The author will discuss this problem later.

About three hundred years ago, Newton established classical mechanics. Newton thought that absolute space existed, but he did not know where it was. Modern cosmology found absolute reference frame for physics. Par- ticle physics will also provide its judgment for absolute motion. Both macro-physics and microphysics reach united conclusion again.