Top page (correct Bohr model including the two-electron atoms)
Special relativity is wrong ?
Supersymmetry and Modular invariance.
Conformal field theory and central charge are real ?
(Fig.1) Moving electrons "stop" by Higgs ??
As you know, it is reported that Higgs particle have been found in the accelerator.
Higgs particle (field) is said to fill all space, and act as "resistance" (= mass) for electrons, W bosons, and quarks.
But in the accelerator, trillions of collisions is said to be needed for generating a single Higgs particle.
( Can we say it actually exists at this extremely low probability ?? )
If Higgs acts as resistance to electrons, an electron moving at constant velocity easily stops by infinite Higgs, even when there are no other forces around it. ( This is strange. )
And Higgs mechanism has NO influence on the mass of proton, and photon.
As you know, the moving direction of photon is bent by the gravity.
Unfortunately, the present standard model can NOT answer these inconsistent phenomena at all.
(Fig.2) String theory has NO reality.
If you try to seek those reasons in the string theory, you will find the string theory can NOT give answers you want.
The relativistic quantum field theory such as standard model is very abstract "math", and has NO concrete images.
This "math" world causes the above problems of Fig.1.
( They hide the above inconsistencies in the "mathematical" world. )
And due to the very strict restriction of general relativity, the string theory is more abstract and unrealistic than the standard model.
The standard model can NOT predict anything of 20 parameters, furthermore, the string theory contains as much as 10500 different theories ( most of them are "unreal" theories ).
And the string theory has 26 dimensions and the superstring theory has 10 dimentions. ( These are impossible. )
This means the string theory, a final form of the present physics, is very unrealistic and has NO power to predict anything.
(Fig.3) What does the "failure" of string theory mean ?
Besides the strange string theory, the present quantum theory did NOT gain the approvals of great figures in the physics.
Einstein and Schrodinger resolutely opposed the unrealistic quantum mechanics.
And Dirac was very unsatisfied with the quantum electrodynamics (QED), which gives infinity.
And Feynman disliked the 10-dimensional string theory.
But other quantum gravity theories such as loop quantum gravity (LQG) can NOT unify the quantum mechanics and the general relativity.
( As much as 30 years have passed since the string theory was born, so NO other gravity theories would appear even in the future. )
So only the string theory is left. ( Though, of course, 10 dimension is impossible in this real world. )
In this very paradoxical situation, there is ONLY one choice left.
We have to return to the early quantum physics and correct them.
( Because the string theory completely depends on the quantum mechanics and relativity. )
As shown on top page, all these miserable situations were caused by the very complicated three-body problems in 1920s.
(Fig.4) No string theory → What's left ??
Some people are attacking the superstring theory and supersymmetry (SUSY).
( If supersymmetric particles do not exist, string theory becomes 26 dimensional and "tachyon" appears. )
But if they try to criticize the string theory, they should show other better theories which replace it.
Because all forces in the nature look obviously united and harmonize with each other
(Fig.4') Can you give up general relativity ?
Special relativity was said to succeed in making Maxwell's equation a covariant form.
So if the law of nature obeys the principle of relativity, the gravitational force needs to be expressed as a relativistically "covariant" form.
Though relativistic Maxwell's equation includes fatal paradoxes, as shown on this page.
Even if the vacuum of the outer space includes a few charged particles ( without "aether" ), they are NOT enough to control the very huge stars without new concept of gravity.
And if the general relativity is wrong, how do you explain about the time dilation of gravity and the light bending by the gravity ?
If you try to explain these things using the "ether" density difference around the stars, it means the special relativity itself is wrong.
As a result, All of Dirac equation, QED, and standard model are wrong, too.
( Though QED and particle physics completely depend on "virtual" particles which violate relativity. )
In the string theory, they use the wrong math of zeta function in calculating the vacuum energy.
(Fig.5-1) Zeta function.
At a glance, you can find the math of Fig.5-1 is wrong.
But the string theory uses this math to calculate the various important values.
(Eq.5-2) Grassmann number "c".
And as shown on this page, the comformal field theory in the string uses the artificial Grassmann number to determine the very important dimensions of our world.
The definition "1" of Fig.5-2 contradicts the definition "2" of Fig.5-2.
( If "1" is satisfied, "2" should be zero, too. But it is not zero. )
These definitions were introduced by our human beings, which do not mean the law of nature.
(Fig.6) What is spin ??
As shown on this page, the spin is very strange.
If you seek the essential meanings of spin in the string theory, you can not find them.
The string theory only gives very abstract "math".
And "spinor", 720o rotation and anticommutation relation of fermions are the same as the usual quantum field theory.
So we cannot know about strange spin and the mysterious force which causes Pauli exclusion principle, even if we study the string theory.
The spin "2" of graviton is due to left and right-moving strings. But they say no more things.
This means spin itself is only "math" and NOT real.
(Fig.7) Why electron and positron fuse into photon ??
All versions of the string theory need to include closed ring.
In some version, open rings appear, which express electron and positron at both ends of photon.
But the string theory can not give more concrete mechanism about how an electron distinguishes a positron from other positive particles.
As shown on this page, the photon generated from the fusion of electron and positron, violates special relativity in all frames.
Some people say if the standard Higgs particle is found, we have nothing to study about the particle physics.
But as I said above, the present theory have NOT showed clear explanations about various things such as spin, virtual particles and antiparticle's properties.
They should show more concrete pictures about these basic things.
Like the ordinaty quantum field theory, the metric tensors gμν can be quantized, which expresses "gravitons".
(Eq.1)
But in general relativity, the derivative is more complicated like
(Eq.2)
In Eq.2, Christoffel symbol Γ is
(Eq.3)
This is very complicated.
The "complicated" Christoffel symbols and covariant derivatives cause various divergences in QFT.
( In QFT, the derivative means the momentum (= from infinity to infinity ) with the exponential function. )
If we try to eliminate various troublesome divergences, the new interaction appears (= Fig.8, right ).
This means "macroscopic" gravitational relation is also broken, when we try to renormalize it. This is a serious problem.
So in the general relativity, the renormalization method can not be used.
(Fig.8) General relativistic restriction in QFT breaks Einstein's gravity.
Basically, these divergences originates in the very strict relativistic restrictions of "symmetry".
To satisfy the Lorentz invariance (= Lorentz symmetry ), Lagrangian which generates the equation of motion must contain various "path integral" from infinity to infinity.
So at this point, the relativistic QFT loses reality.
( See also Relativity is wrong ?.)
(Fig.9) Lorentz symmetry is "impossible" in the real world !
Of course, the concept of "symmetry" is very important in the nature.
For example, the regular hexahedron of Fig.9 is symmetric.
But from the different viewpoints ( see Fig.9 two arrows ), this cube looks different.
So this is NOT symmetric according to the relativity.
"Sphere" is more symmetric than cube.
But from the observers moving at various velocities, this sphere is Lorentz contracted in one direction, which is NOT symmetric, either.
According to the relativity, we must deal with the time and space equally, which removes reality from the relativistic quantum field theory (QFT).
( It is impossible to express concrete objects in the world by the completely symmetric theories ! )
(Fig.10) Superstring theory aims ONLY at "mathematical" symmetries (NOT reality).
Under the very limited condition of the relativity, they created "gauge" symmetric theory to explain the standard model.
Because all we can do was to pay attention to "symmetry" in these "mathematical" jails.
So the present superstring theory is just aiming at the various mathematical symmetry. Of course, there are NO realities and clear images at all there.
(Fig.11) Superstring theory can eliminate divergence ?
As shown in Fig.11, the superstring theory uses "1" dimensional string ( 1 space + 1 time = 2 dimension ) instead of point particle.
In this string, we can manipulate the various math terms, variables and coefficients to remove divergences.
( Inside the point particle, we can not do these various manipulations. )
(Fig.12) Superstring is NOT a real string !
In the superstring theory, two (= 1+1) dimensional (= 1 space variable σ + 1 time variable τ ) worldsheet is moving through ten-dimensional ( 10D ) Minkowski background space-time.
Basically this space variable σ is from 0 to 2π, which expresses closed ring.
( In the open ring, the string is from 0 to π and can bind to other strings and membranes. )
The reason why they use this simple and strange 1+1-dimensional string is due to very strict relativistic symmetry.
But as you notice, this 1+1 dimensional string is NOT real.
As shown in Fig.12, the closed circle needs at least 2 space dimensions, for example ( x and y ) or ( r and θ ).
So if a thing is moving at the constant velocity along the line of σ (= uniform linear motion ), it does NOT generate "centrifugal force" in the worldsheet.
But from the viewpoint of the background Minkowski spacetime, this circular motion causes centrifugal force, so if there are no external force, this object is flying away to different dimension !
So this string theory includes self-contradiction from the beginning, which is explained later.
(Eq.4) Mathematical trick.
As shown in Eq.4, if we define artificial 1-dimensional ring, the infinite space integral of Eq.4 left can be expressed as simple 2π ( Eq.4 right ).
And in the conformal field theory ( this page ), the space integral of 1-dimensional ring can be considered as complex integral of closed curve.
So only for the mathematical reason, this 1+1 dimensional string was chosen.
(Eq.5)
(Eq.6)
In QFT, we often integrate the exponential function with respect to some variables from minus infinity to infinity to satisfy Lorentz symmetry.
As shown in Eq.5 and Eq.6, when x is just equal to y, this value (= delta function ) becomes divergent.
when x is different from y, "oscillation" of the exponential function makes them zero.
(Fig.13) Lattice gauge theory.
To avoid divergence, "lattice gauge theory" was born.
As shown on this page (Eq.5-46), Dirac Lagrangian includes the interaction term between electrons (= ψ ) and photon (= A ).
In Fig.13, electrons are at lattice points, and the photons (= vector potential A ) are the bonding lines between them.
Of course, Fig.13 model is NOT symmetric in every directions, as shown in Fig.9.
So the intervals need to be infinitesimal later.
In lattice theory, Dirac Lagrangian momentum (= derivative ) term is expressed as
(Eq.8)
where "d" means the unit interval between lattice points.
Eq.8 is a symmetric form in the "n" direction.
In the four-dimensional world, each lattice point is expressed as
(Eq.9)
Photons (= A ) which link the two electrons are
(Eq.10)
The opposite direction becomes minus.
So the interaction term between photons and electrons are
(Eq.11)
The sum of Eq.8 and Eq.11 includes
(Eq.12)
Under the gauge transformation of
(Eq.13)
the equations need to be invariant.
Lattice version of Eq.13 is
(Eq.14)
Usng the relation of Eq.10, the opposite direction is
(Eq.15)
When the interval "d" is small,
(Eq.16)
Substituting Eq.14 and Eq.15 into Eq.12, and using the relation of Eq.16, the gauge θ(r) at the "r" point is just canceled out like
(Eq.17)
But the gauges at the both ends ( r+e and r-e ) of Eq.14 and Eq.15 are left.
To erase all these gauges, we consider some loops and link both ends.
(Eq.18)
In the loop state of Eq.18, all gauges θ are just canceled out, which means "gauge invariance".
(Fig.14) Loop quantum
Here we think about the minimum loop like Fig.14.
( Of course, this loop is gauge invariance. )
The vector potentials of the lower and upper lines are
(Eq.19)
where the upper ( Eq.19 right ) and lower ( Eq.19 left ) are opposite.
Expanding the exponential functions of Eq.19,
(Eq.20)
Calculating the left and right lines of Fig.14 in the same way and combining them, we get
(Eq.21)
The " d2 " terms of Eq.21 vanish by integration of action.
( The total differential becomes zero in the action. )
The " d4 " term is left after integrating it with respect to 4D-spacetime.
This term means photon Lagrangian. ( See also this page )
(Fig.15) Loop quantum gravity
In the loop quantum gravity, things can move only in one dimensional loop.
( Though this real world obviously consists of 3 dimensional space. )
So in all spaces without loops, there are no concepts such as "space" coordinate of x, y and z, as shown in Fig.15.
Generalized coordinate transformation of general relativity resembles gauge transformation.
Under the infinitesimal coordinate transformation of
(Eq.22)
The vector changes like
(Eq.23)
So Eq.23 resembles the gauge transformation (Eq.13) of
(Eq.13)
This means the loop is invariant under gauge and coordinate transformation of general relativity, as shown in Eq.18 and Eq.23.
In the loop quantum gravity, the next variables are used
(Eq.24)
But in the loop quantum gravity, the metric tensor is 3 × 3 (= only space ).
This is a little strange.
And the loop is expressed as ( like Eq.18 )
(Eq.25)
(Fig.16) Loop quantum gravity is real ?
In the loop quantum gravity, the background spacetime contains nothing.
This means there are no concepts such as "time" and "space" in the background world !
So only loops exist in the "nothing" world.
( In the superstring theory, the background world exists as 10-D Minkowski spacetime, which is different from this loop quantum gravity. )
In this very limited space, the invariance under coordinate transformation can be treated like gauce invariance.
Combining these loops, it becomes "spin network".
The problems are these strange and special loops can not be used in the ordinary QED and gauge theory.
General relativistic condition is the strongest, so if we consider general relativity, this theory doesn't satisfy ordinary quantum theory.
And it is difficult to accept the idea that this world is made only of these loops ( including time and space ).
The background Minkowski spacetime of D dimensions ( D=10 ) is expressed as
(Eq.26)
XI mean the coordinates of the background.
The background spacetime is also called "target space ".
where we use (-1, 1, 1 ..) version of D-dimensional metric tensor,
(Eq.27)
The state of the string is expressed as two-dimensional ( 2 = 1 space + 1 time ) variables of
(Eq.28)
where τ means "time" variable and σ means 1-dimensional (= 1-D) space variable.
Of course, this state is very difficult to imagine.
As shown on this page, the metric tensor in the general relativity can be changed into usual Minkowski metric tensor (= η ) under some coordinate transformation.
(Eq.29)
(Eq.30)
From Eq.29 and Eq.30, considering each determinant (= determinant × determinant × ... ),
(Eq.31)
where we use the Minkowski metric tensor determinant = -1.
So the determinant g(x) of the generalized metric tensor is
(Eq.32)
From Eq.32, we get
(Eq.33)
Eq.33 is scalar action integral under general relativity.
The action S (= integral of scalar Lagrangian ) of the string is
(Eq.34)
where hαβ is two-dimensional metric tensor
Eq.34 includes a pair of metric tensor × tensor in each world ( 2D and background ).
So this action is scalar, which doesn't change under coordinate transformation of general relativity.
The variation of the metric tensor h is
(Eq.35)
where we use the relation of
(Eq.35')
See also this page (Eq.74-Eq.77).
Using Eq.35, the variation of the action Eq.34 with respect to the metric tensor h is
(Eq.36)
When the variation of action (Eq.36) is zero ( δS = 0 ), it means the equation of motion.
So the equation of motion is
(Eq.37)
If we define the tensor G (with respect to α β ) like
(Eq.38)
The determinants of both sides in Eq.37 become
(Eq.39)
The square value in the last term of Eq.39 is scalar constant.
So in the determinant, this costant becomes a square.
From Eq.39, we get
(Eq.40)
So the action of Eq.34 is equal to the left side of Eq.40.
Under some coordinate transformation, the metric tensor h can be 2-D Minkowski like
(Eq.41)
Basically, the space coordinate (= σ ) of Eq.28 is from 0 to 2π
( If this range is from -∞ to ∞, we can actually see this very long string. )
So one rotation goes back to the original configuration.
Here we think about a "real" closed ring.
From the viewpoint of the backgound, this closed ring which is rotating at the angular frequency ω is
(Eq.42)
See also Fig.12. Other XI are not supposed to be functions of ( τ σ ).
When the metric tensor is Eq.41, the action S of Eq.40 ( right side ) is
(Eq.43)
Substituting Eq.43 into the next Euler-Lagrange equation,
(Eq.44)
When I = 1, substituting Eq.42 into the equation of motion (= Eq.44 ),
(Eq.45)
where "dot" means the partial derivative with respect to τ
When the the circular radius R is constant, we get the solution of
(Eq.46)
Eq.46 is strange. When ω is not 1, the acceleration of R is NOT zero, which contradicts the constant radius R.
This means this superstring includes self-contradiction, and this string is NOT real.
This contradiction originates in the 1+1 dimensional circular-ring, as I said above.
The action of Eq.40 (right side) is invariant under the following transformation (= Weyl symmetry ).
(Eq.47)
where
(Eq.48)
So
(Eq.49)
see also Eq.39.
Eq.47 means the very abstract string of Eq.40 does not have the concept of "scale".
So this general relativistic world is only "mathematical" thing.
As shown in Eq.43, when the metric tensor h is an ordinary Minkowski tensor, the action is
(Eq.50)
Here we make the time and space variables more symmetric by the transformation of
(Eq.51)
The equation of motion of Eq.44 can be expressed using the new variables of Eq.51 like
(Eq.52)
The solution of Eq.52 is
(Eq.53)
where σ+ means rotation around to the left (= L ).
And σ- means rotation around to the right (= R ).
In the string theory, the constant Ts is related to "mass" per unit energy (= H )
(Eq.54)
From Eq.53, we define the solution as
(Eq.55)
Using the new variables of Eq.51, Hamiltonian can be separated like
(Eq.56)
Here we prove Eq.56.
From Eq.50, we obtain the Hamiltonian H of
(Eq.57)
From Eq.51 and Eq.55,
(Eq.58)
So Eq.56 ( "I" term ) is
(Eq.59)
This is equal to Eq.57.
When the string satisfies the boundary condition of
(Eq.60)
The solutions become
(Eq.61)
When the operators satisfy the commutation relations of
(Eq.62)
As shown in Eq.62, de Broglie like relation is also valid in the string theory.
So the string theory can NOT answer more fundamental mechanisms inside the quantum physics.
It only imitates the same math.
a+ of Eq.62 means creation operator. Using the number operator of
(Eq.63)
(Eq.64)
So "mηIJ" is added by the creation operator.
This means I,J = 0,0, this creation operator creates "minus" energy (= minus number ), which is NOT real.
This unreal zero component quantum operator originates in the relativistic covariance.
From Eq.61, we have
(Eq.65)
(Eq.56) Hamiltonian.
Substituting Eq.65 into Eq.56, left-moving Hamiltonian is
(Eq.66)
where 2π is
(Eq.67)
In Eq.66, when m is not equal to n, it becomes zero using the boundary condition of 2π
(Eq.68)
From Eq.54
(Eq.69)
Using commutation relation of Eq.62 and Eq.69, Hamiltonian of Eq.66 is ( only I=J cases are left ),
(Eq.70)
where we use
(Eq.71)
In the same way,
(Eq.72)
As shown in Eq.64, when I,J = 0,0, the generated energy (=number) becomes "minus".
(Eq.73)
To avoid this serious situation, this unreal value of zero component needs to be cancelled out by another 1 component.
So the remaining Hamiltonian ( of D-dimension ) is
(Eq.74)
This means (D-2) components are left.
So η of Hamiltonian (Eq.70) is "1", as follows,
(Eq.75)
From Eq.75, all vacuum energy of D-2 components becomes divergent like
(Eq.76)
The vacuum energy of fermion is minus.
So later this divergent is eliminated by "R" sector fermion.
"NS" sector fermion is half-integer, which can not cancel the vacuum energy.
( These rules are artificial things, and NOT natural ones. )
If we try to cancel this infinity "artificially", this theory does NOT satisfy relativistic symmetry.
To satisfy symmetry, we use the "mathematical" trick of zeta function of
(Eq.77)
Of course, Eq.77 is wrong. But string theory uses this wrong math to keep symmetry.
Next we prove Eq.77.
We define G(β) as
(Eq.78)
So
(Eq.79)
From Eq.79 and Eq.78,
(Eq.80)
Of course, when β is zero, R = -1, which doesn't converge.
From Eq.77,
(Eq.81)
When s=-1 Eq.81 is just equal to Eq.78.
(Eq.82)
As a result, we get
(Eq.83)
From Eq.77 and Eq.83, the vacuum energy of Eq.76 becomes
(Eq.84)
From Eq.54, the mass of the string is
(Eq.85)
(Eq.86)
when D dimension is more than 2, this string includes tachyon (= a square of mass is negative ).
When one particle is created in each left and right string ( to keep symmetry, left= right ), the mass becomes
(Eq.87)
To explain the zero mass of bosons, the dimension needs to be 26.
So when the string does not satisfy "supersymmetry" (= boson = fermion ), the string theory becomes 26 dimensions with tachyon !
( Unfortunately, there are no concrete and real images here. )
See also Central charge and critical dimensions are real ?
(Fig.17) Gravitational tensor field
To keep symmetric, the excited energies need to be equal in left-moving and right-moving strings.
And the first excited pair of particles with zero mass in Eq.87 means tensor fields (= gravitons ).
According to their interpretation, left-moving + right-moving = spin "2".
Only one of them means spin "1". But these are only mathematical definitions.
The backgound tensors (= XIJ and gIJ ) can be expressed using 2-D string left and right-moving strings.
When this tensors bind to energy-momentum tensor (=TIJ) to form scalar, this means the gravity acting on the mass.
When the metric tensor (= g ) in the background spacetime is a function of 2-D string variables, this means curved spacetime.
So this corresponds to the case in which the photon is bent by the graviational time dilation.
And when the background functions form "antisymmetric tensor", this means photon field.
Unfortunately, these are only math and NOT real, and they can NOT show us concrete and clear images about the gravitons and other particles.
These mathematical world causes inconsistency as shown in Fig.1.
So it is about time we go back to "real" and "physical" world, I think.
To erase "tachyon", and reduce "dimensions", string theory needs to include symmetric "fermions".
To distinguish bosons and fermions, we need to define periodic boundary condition (= R sector ) and antiperiodic boundary conditions (= NS sector ).
NS+R and R+NS show fermion's nature, NS+NS and R+R show boson-like nature.
( So the superstring theory includes various "unreal" force's particles. )
The action of boson + fermion is ( as I said above, only I=J > 1 cases ( D-2 dimensions ) are left )
(Eq.88)
The masses of them are equal to each other.
And if we choose some supersymmetry transformation like this page,
we can prove Eq.88 is supersymmetry.
So supersymmetric particle is caused by the condition that Lagrangians of bosons and fermions are packed into one action S.
( There are no "real" images here. )
Fermion's expansion in NS sector is
(Eq.89)
This is related to half-integer angular momentum.
So even the final basic form of the superstring can not explain what half-integer spin really is.
Because as I said, spin itself is unrealistic thing.
And fermions satisfy the anticommutation relation of
(Eq.90)
Eq.90 means the origin of anticommutation (= Pauli exclusion principle ) remains a riddle even in the superstring theory.
And the superstring theory uses real number ( not † ), so when r is minus s, the right side of Eq.90 is not zero.
From Eq.88, the fermion's part of the action S is
(Eq.91)
where
(Eq.92)
These fermions are supposed to be "real" (Grassmann) numbers.
Using two-dimensional gamma matrices of Eq.88, the action of Eq.91 becomes
(Eq.93)
The canonical momentums are
(Eq.94)
By the definition, Hamiltonian is
(Eq.95)
From Eq.89
(Eq.96)
Using Eq.89, Eq.90 (= anticommutation ), Eq.95 Eq.96, and integrate Hamiltonian density, we get Hamiltonian of
(Eq.97)
The vacuum energy of Eq.97 is opposite to the boson of E.75.
The sum of the vacuum energies of Eq.75 and Eq.97 becomes
(Eq.98)
where we use Eq.78- Eq.80.
So the left-moving vacuum energy becomes
(Eq.99)
Eq.99 includes tachyon.
To eliminate tachyon, supersymmetry and some artificial manipulations are needed.
The first-excited state mass (only left-moving ) is
(Eq.100)
Eq.100 means the existence of zero-mass particle needs 10-dimensions !
But unfortunately, these are only "math", and do you think these mathematical tricks are real world ??
To eliminate "tachyon", superstring theory needs supersymmetry.
( See Supersymmetry and Modular invariance. )
It seems that superstring theory precisely eliminates various anomalies to keep symmetry.
But there are many "mathematical" assumptions in this theory.
According to this book ( The Trouble with Physics, Lee Smolin ), there are too many geometric structure of the extra dimensions in the superstring theory.
This means the present string theory (and 11-D M theory ) can NOT predict the experimental results at all.
Furthermore, there seem to be too many strange forces which do not really exist.
So there have been a lot of researchers who gave up string theory until now.
But if any new theory which can replace the superstring theory does not appear, all they can chose was the string theory as unifying theory.
This is a main reason why the "strange" and unreal string theory survives until now.
But to correct this state in physics ( + quantum chemistry and molecular biology ), we have to go back as far as to Bohr model, as shown in top page.
Now any supersymmetric particles have not been found.
What I am worrying about now is the possibility that the researcher's intentions may change the experimental results, as shown in faster-than-light neutrino.
So it is possible that we will hear the news that "unreal" supersymmetric particles are found.
( Because if supersymmetrc particles do not exist, unification theory is impossible, as long as quantum mechanics and relativity are right. )
2012/7/18 updated. Feel free to link to this site.