(1)GENERALIZED SPACE-TIME RELATIVITY
AND APPLICATION
(Author: Xia Xingguang)
[Abstract:] First, according to academic result of generalized space-time relativity, get the relevant formula of mass-energy. And then, use this formula to set up the calculate formula for the quiescent mass of photon, and give an example for calculation for the quiescent mass of the yellow photon. After that, bases on this mass formula, discuss the deflexion angle of beam when it get through the gravitation field of sun, have get the result same as chronometer observation. Thereby approved the photon has interior structure. Then, analyzed reason of inflation of μmeson’s moving life which is from the experiment evidence of some relations between microcosmic particle’s life and his energy. At last, bases on the inner structure mode of photon, explained the real reason of the read shift of spectrum in fixed star system, accordingly to deny the big-bang cosmology.
I FORWORD
We say, according to Einsteinian special theory of relativity, the relatively quiescent mass of photon is zero. Otherwise, it would get the absurdity result of “ photon has infinite relativity quiescent mass” from Einsteinian formula of mass –energy. But, from the ideas of philosophy, since the light is matter, so it should have catholicity of the matter. In view of knowledge for the nature in existence, among the commonness of matter, it always includes “quiescent mass” and “energy”, so the photon is also not exception. Regarding to the question of whether the photon has the quiescent mass, it puzzles the modern philosophy and physics all the time. At present, only generalized space-time relativity can solve this problem puzzled for long time.
In the theory of generalized space-time relativity, we consider: the concept of “free particle” has invariableness “relative velocity” from Newton mechanics cannot express the basic character of “mechanics quantity” in the mechanics system absolutely and correctly. So, must find out one “mass-energy formula” which different from Einstein’s special theory of relativity. Well then, how to set up such relationship bases on the generalized space-time relativity? This is the first question need to solve in this article. No doubt, this formula mush ensures: 1.Rationality in logic; 2.Rigors in derivation in mathematics; 3.Can explain the known phenomena reasonably in the application and forecast new phenomena.
On the other hand, in the past, the people consider at all times that the shortening phenomena “quiescent life” of mesonμ is the experiment evidence of correction of Einstein’s special theory of relativity and authenticity of “Lorentz contraction”. Actually, there is quite serious mistake. Because, if explain this phenomena by special theory of relativity, in any case, it cannot justify itself. Specially, physical structure of this phenomenon is different from the special theory of relativity. So we should not explain the theory result from special theory of relativity by this phenomenon. In another word, the existing physical experiment cannot provide the reliable evidence for Einstein’s special theory of relativity. Well then, how can we explain the phenomenon of “quiescent life shortening of mesonμ” ? This is our second question for discussion.
Besides, for big-bang cosmology, if explain the birth theory of universe according to this mode, it would get the fallacious logic consequence ---- now that observe from the earth, all the fixed star all over 360 degree have the “red shift”. Well then the earth would become the “original cradle ” of the explosion. But it is absolutely not! Not only for the earth, for the solar system, even Milky Way Galaxy, it is negligible in the great universe. How can be the center of explosion for the earth in such great universe? ! And also, the concept of Universe express the infinite space and time, all the limited fixed star system, is the part of Universe, not the Universe. So to explain the “red shift” phenomenon by Doppler’s effect, have the insurmountable logic mistake. How to understand, is another question.
II Impulse and Energy of Special Theory of Relativity
As we know, the content of principle of
minimums action quantum: for each mechanics system, there is “integral of action
quantum” (s), it has the “minimum value” for actual movement. So its
calculus of variations（δs）is zero, i.e.δs = 0. Actually, rigorously say, the
minimums action quantum only concludes: integral s only can has minimum value in the
integral section [a，b]. For the any length integral section（-∞，+∞）, only can
affirm that it has extremer, not minimums value. According to the classical special theory
of relativity, the integral must be invariable quantum to “Loranz transform” for
decision about action quantum integral of word point (origin is the
particle) without action of outside force.
Therefore, it must be “scalar quantity function”. Besides, the function must be first
rank differential coefficient. For the world point, the space interval ds orαds, α is
proportion constant, is the only scalar quantity function we can consider. In this case, a
free world point’s action quantum integral (s) must be math form as follow:
(1)
in formula, ds is the “ line element ”of four-dimensional coordinate system, and the integral denotation∫ab is integral of “word line” which is along free particle moving contrail constructed between two special thing. The position of two points is word line a and b, they correspond two clock in the position of free particle. Viz. t1 correspond word point a, ----is a inception the time of day of resting clock, t2 correspond word point b, ----is a finally the time of day of moving clock, in the △t = t2 – t1 included necessaries lag time process （△t2）which is feed back moving information from finally point to moving inception in light speed; At same time, coefficient αis a special constant. (Refer to [1], Pages 29~33) Need especially emphatically is: the moving of free particle carrying out in the generalized space-time. Thereinto t1 is resting clock inception the time of day, t2 is moving clock finally the time of day. In the time process △t = t2 – t1,contained time process above meaning △t2, namely t =（t'+△t2）----this is different with Einstein theory. The free particle relative velocity that correspond with word point speed is（V = r/t），is not his absolute velocity（υ= r/ t'）.In addition, over here have demarcateα is a real number, but do not demarcate it must be a positive number.
Opposition, the classical《special theory of relativity》consider: integral formula∫abds has max. along a straight word line, and if along a bend word line the integral maybe is arbitrary smaller. So that, if the integral∫abds adopted a positive denotation; If adopted a minus the integral has mini. affirmatively along a straight word line. Thereby, put on a minus（–）subjectively in the front of integral∫abds and become –∫abds. The reason of the classical theory bring forward this request that is a understand error of classical theory for “alternation square”, viz. consider: there is an imaginary number coordinates, namelyτ= ict in the integral∫abds. But in the generalized space-time relativity, have dt≥dt’ always, this fact guarantee four-coordinates in the line element to be real number, so the alternation square ds2 = c2dt2–dr2 ≥0——viz. Time coordinates of resting system expanded. Thus, ∫abds has mini. Essentially. There for, we need not add a minus in the front of integral∫abds and that to make it become –∫abds, of course need not request the calculus of variationsδ∫abds = 0 of the integral∫abds. In fact, in the origin（O）of four-dimensional space coordinate system, the integral∫abds has mini. affirmatively, viz. ds = 0. It is obvious that, principle of minimums action quantum is not a integrant fundamental then theorize.
As know, this moving free particle’s action quantum integral can be changed to be integral to time, viz.
(2)
L is the Lagrange function in the mechanics system. Base on the basic transform formula of generalized space-time relativity
dt’ = (1 – V2/c2)1/2 dt
We can educe:
ds/c = dt’ = (1 – V2/c2)1/2 dt (3)
Put (3) in (1), educe:
(4)
We may write out Lagrange function from above
L =αc(1–V2/c2)1/2 (5)
Hereinbefore all the formula, have:
V 2 = (dx2 + dy2 + dz2)/dt2 (6)
Open up (5) to be power series, can get α= – mc, therefore get the expression of Lagrange function:
L = – mc2(1 – V2/c2)1/2 (7)
Follow the classical process of discussion (refer to [1], page 31—32), we can get the momentum of moving particle:
(8)
From
(9)
Can educe the classical result of classical special theory of relativity, viz.: a free particle energy expression:
E = mc2/(1 – V2/c2)1/2 (10)
III The impulse and energy of Generalized space-time relativity
As we know, in Einstein’s special theory of relativity,
nobody will consider the difference between relative velocity and absolute speed, so use
the relative velocity V directly. But according to the space-time ideas of 《Generalized
space-time relativity》: The energy in Mechanical system only has the relation with
absolute velocity of moving object, but not its relative velocity. Because, there is “feint”
in the time coordinates which form relative velocity, therefore: the “bigger” or “smaller”
of relative is not lie on the “bigger” or “smaller” of absolute velocity, but lies
on the distance “nearer” or “farer” between free particle with observer. Or, the
relative velocity consists of “subjective factor” of observer, so it cannot reflect
mechanics character of moving object in truth. Just base on this, we must bring in the
concept of absolute velocity. After bringing it in, use another formula of generalized
space-time relativity.
V = cυ/(c2 +υ2 )1/2 (11)
Put into formulas (8) and (10), to get the impulse of free particle:
P = mυ (12)
And his energy
E = mc (c2 +υ2 )1/2 (13)
then a absolute velocity of the free particle equal to velocity of light（c）, his impulse:
P = mc (14)
This result is accordant with common mechanics, but has some different with Einsteinian special theory of relativity.
In addition, foundation the objectivity principal, we have got:
1/V2 = 1/c2 +1/υ2
(Refer to, §9, page 68). From above formula and (13) we may see, then υ<<c, 1/c2 →0, ending have V≈υ.
E ≈ mc2/(1–V2/c2)1/2， (15)
----This is in reason kernel of Einstein’s matter-energy formula.
At one time, we may expandedness formula (13) according to power series:
E ≈ mc2(1+V2/2c2 -υ2/8c2 + …) (16)
can see from formula （16）, then the absolute velocityυ→0, ----the face to face quiescence between moving coordinate and resting coordinate----and than have
E ≈ mc2 (17)
thenυ→c----moving coordinate and resting coordinate connect all together, and in the absolute velocity c movement depart from start point, ----adopt front two items of formula（16）, have get:
E ≈ mc2 + m c2/2≈3m c2/2 (18)
Under the prevalent condition, have: ：0 ≤υ ≤ c. In case we adopt front two items of formula（16）,to get:
E ≈ mc2 + mυ2/2 (19)
This is to say, in general condition, the gross energy consist of two parts: one is the quiescence energy of microcosmic particle; another is kinetic energy of moving object in Newton’s mechanics. Thus it can be seen, Einstein’s special theory of relativity is same as Newton’s mechanics, which are all the approximately tenable relative truth in the special condition, but cannot austerely come into existence in general condition!
IV The formula and its application of quiescence mass of photon
From the mass- energy formula of Generalized space-time relativity
E = mc (c2 +υ2 )1/2 (20)
Can see, when the absolute velocity υ= c, get:
(21)
According to the photon energy formula 
, we can get the formula of “mass” of
photon:
(22)
in the formula, 
is the Planck constant 
, ω is light wave frequency. Here, we make: 
, so the formula
above can be change as:
m0 =ηω
(23)
Thereinto, η is constant, by the calculation: η=5.2123 x 10-48 g·s; ω is the circle frequency of photon, the unit is Hz（s-1）.
We can use one sample to prove the correction of this formula. For example, the frequency scope of visible light is 1014 —1015 Hz（Hertz）. So we can get the “quiescence mass” of photon in visible light from formula (23) is about: 10-34 —10-33g. Now as the yellow light for example (frequency is 5.0812 x 1014Hz), we can get the quiescence mass of photon is 2.6485 x 10-33g from this formula. As we knew, the quiescence mass of electron is about 9.1085 x 10-28g, so we can get photon’s quiescence mass is about one three millionth of electron’s quiescence mass.
V The experiment evidence for photon quiescence mass
Correct or not for a new theory is not only un-contradiction logically, but also has the correctness in the derivation of math, more important is whether it can explain the existing phenomenon, and predict new thing or not. Here we will prove the correctness of formula about photon’s relative quiescence mass through the fact known. Accordingly to prove the correctness of generalized space-time relativity indirectly.
The calculating process about “photon has the quiescence mass not be equal to zero” is as follows: firstly find out the “theory value” through generalized space-time relativity. And then put it into relevant formula to prove by calculation of “deflexion angle” of beam near the sun. Suppose a Newton particle, mass is m, moving by low speed in the pole coordinates r,φ plate. Bases on Newton’s mechanics, the integral of energy is:
(1/2)r’2 +(1/2)r2φ’2 - GM/r = E/m (24)
(Refer to [3]，Pages 25~27). In formula, φ’ is the angle velocity of Newton particle, M is the mass of star (Sun) which make the particle deflected, E is the energy of Newton particle, m is quiescence mass, G is gravitation constant.
Bases on “Kepler law”, the integral of Angle momentum A is:
A = mr2φ’ (25)
Just as we know, along with the increasing of moving velocity of Newton particle, its relative quiescence mass will be reducing gradually. According to the formula “relative quiescence mass of photon” from generalized space-time relativity, if the velocity of particle is equal to light speed （c）, its “relative quiescence mass” change to be:
(26)
And the angle momentum at this time:
A c = m0r2φc’ (27)
Should be rφc’= c in the perihelion. Therefore, the angle momentum of photon in this point is Ac = m0Rc. To meet the formula (24), should have Ac≡A (i.e. Angle momentum conversation law), so have:
m0r2φc’ ≡ mr2φ’
or
m0Rc≡mr2φ’ (28)
and then get from (26):
or
(29)
R is the distance from center of mass of Sun to the perihelion. We can eliminate time derivative in formulas above.
(30)
Hereby, we can rewrite (24) to be:
(1/2)(dr/dφ)2(R2c2/2r4)+(1/2)(R2c2/2r2)-GM/r = E/m. (31)
Bring u = 1/r, into above formula, can get:
(1/2)(du/dφ)2(R2c2/2)+(1/2)(R2c2/2)u2 -GMu = E/m. (32)
Get the derivate for above formula, and transpose to get:
d2u/dφ2 + u = 2GM/c2 R2 (33)
Refer to the relevant discussion in [3]. Can get at last:
δ≈2GM/c2 R (34)
Therefore get the deflexion angle:
α= 2δ≈4GM/c2 R (35)
This result is same as the result （1.75"）
from Einstein’s general theory of relativity completely. And also tally with the
chronometer observation result（1.70"） in 1952. (Refer to [4], page 282).
Recently, somebody proved further through accurate observation that: the value should be
1.775"（±0.019"）. therefore proved, the photon has the relative quiescence
mass（m0） which not be equal to zero certainly. In the past, the result of
“deflexion angle” got from using photon energy
, and photon mass m = E/c2 from “mass-energy”
conversation law bases on Newton mechanics is only half of correct value.
According to Einstein’s general theory of relativity, the academic deflexion angle is 1.75", close to real observed result. So the people believe: the general theory of relativity is absolute right, and Newton mechanic is not applicable anymore. But from my opinion, this is exactly big mistake of modern physics. Actually, the reason of “warp” through the calculation by Newton mechanics is not because of its inapplicability in this case, but because of mistake of the adoption for photon quiescence mass in the calculating process. It can prove by this result: Einstein’s general theory of relativity is only approximate tenable theory in partial, un-symmetrical gravitation field, but not the unique accurate gravitation theory in modern physics.
VI Analysis of velocity and life of μ meson
We have known from the laboratory, the observer who keep relative quiescence with μ meson (in moving coordinate K’) can get the “quiescent life” ofμmeson t’= (2.09±0.03)x10-6s. ----Obviously, from the point of view of “rest coordinate”, it is moving life. Because, the “life” is the durative “time process” from the birth of μ meson to the disintegration to one electron and two neutrinos.
In addition, we have known from the observation about the existence of μ meson, most of them produced from the collision of “high energy nucleon—nucleon” are the top of aerosphere ( about 10 km from the earth), and move towards to the earth at the velocity of 0.955c or more. (Refer to [3], page 49). If the observer from the earth consider that the μ meson’s maximums relative velocity is 0.995c, and suppose the earth is in the “resting coordinate” (K). that is, as known, the relative velocity is V = 0.995c（c =2.9979x1010cm/s） and quiescent life of μ meson is t’ = (2.09±0.03)x10-6s between moving coordinate（K’）and resting coordinate（K）.Therefore, base on the “velocity transform formula” of generalized space-time relativity, the absolute velocity ofμ meson which keep relative with moving coordinate is:
υ= V/(1- V2/c2)1/2 (36)
Put the value of V to above formula, we can get
υ=0.995c/(1-0.9952)1/2= 9.96246 c (37)
here we blow up the relative velocity（V）of resting coordinate and moving coordinate for 10 times.
Underside we cipher out the observation result of μ meson’s life（t）, and the relative velocity（V）has been got by looker-on of resting coordinate（K）----earth.
t = t’/(1- V2/c2)1/2 (38)
Put their values into above formula to get:
t = (2.09x10-6)/(1-0.9952)1/2 =20.9262 x10-6 (s) (39)
All appearance, under fool observer measure μmeson’s life is 10 times bigger thanμmeson’s life of moving coordinate and more.
According to generalized space-time, using above theory result, we may cipher out: looker-on and observer have got singly distance ofμmeson’s stepping from his birth to disintegration in the aerosphere. For example, for looker-on at the earth (resting coordinate), μmeson stepping distance is:
S = Vt = 0.995 x 2.9979 x 1010 x 20.9262 x 10-6 = 6242.098（m） （40）
and that the observer toμmeson face to face quiescence (moving coordinate) say, μmeson stepping distance is:
S’=υt’=9.96246 x 2.9979 x 1010 x 2.09 x 10-6 =6242.090（m） （41）
It is obvious that, theμmeson from birth
to disintegration in position of 10km aerosphere, stepping distance (S and S’) for two
observers on the K and K’ are identical. This calculate result explains: μmeson
stepping distance “neither expand nor constriction.”
But, remarkable: this result is the cost by scarification of “light absolute velocity”
is the terminal velocity in the universe, so it cannot be accepted absolutely! Therefore,
in spite of we can get the same result as generalized space-time relativity from the
experiment, it does not mean it is logical. So, how to explain this phenomenon? We will
analyze it in Part G. In order to compare in the following analysis, here let us introduce
the classical explanation first.
VII New explanation about change of theμmeson’s life
Regarding to the classical explanation of this phenomenon, refer to the bookmaking of Rossi and Hall、Swann and so on（see also [3]，page 49）.According to their explanation, because μmeson life explosion observing from earth, the observer can detect the existence of μmeson in the sky about 4 km high. At the same time, the observer moving with μ meson feels that the journey of μ meson shorten accordingly. Obviously, this is different from the view of special theory of relativity.
According to the special theory of relativity: the observer moving with μ meson should find the contraction of μ meson’s life. But, if consider the quiescent life [t’ = (2.09±0.03) x 10-6s] as the value after contraction, so, even μmeson’s velocity equal to light velocity, the distance it move by its whole life can not be over 600m; or, we consider the quiescent life [t’ = (2.09±0.03) x 10-6s] as the value before contraction, so even the velocity of μ meson is same as light speed, the distance move for its whole life can not be over 60m. Obviously, no matter how to explain the quiescent life of μ meson, the observer from the earth can not find μ meson in the sky 4 km high. Therefore, there are self-contradiction in the all explanation,
If accept according to the explanation of classical: 6 km in resting coordinates is equal to 600m in moving coordinates, or 60m, this is just believe, “time and space is not exist impersonality, but is perceptual intuition of human.” At the result, come back to the view of space-time of relativism, namely, to the subjective idealism. So this classical explanation has the self-contradiction.
Through the analysis, we can see that,
there is indivisibility relation between the contradiction in this question and the
observing way to this phenomenon for《universe radial physics》. Concretely say, in the
observation of universe radial physics, the observer is not following and recording
certain μmeson throughout from the birth in the 10km height to the death in the 4km
height, but to understand it from the general thinking way, consider that: from the height
10km to 4km, can find the trace of μmeson. It is to say, that in this thickness layer,
have the μ meson. In this case, for the abominable consideration, we suppose that the
maximum velocity ofμmeson inborn from the collision of high energy universe radial with
atmosphere molecule is equal to light velocity, then according to the quiescent life to
calculate, the μmeson found in the 4km height, only can be produced in the 4.6km height.
No other than understanding it like this, we can explain it reasonably. So the probability
for the discovery of μ meson in the 4km height, is mean the “birth probability” of μ
meson in the 4.6km height. Of course, there is self-contradiction in this explanation. So
we give out another explanation: the life of μ mesons with different energy, so, when the
collision of “high energy particle – particle” in different energy universe radial
happen, the μ meson inborn has different energy accordingly, so their life is different.
So their journey in their life would be different because of different energy. In this
case, only, the people can discover the existence of μ meson in 4km height sky.
Actually, the conclusion of different life forμmeson with different energy has already been proved by the experiment. But the people who agree special theory of relativity consider that: this phenomenon is the evidence of time coordinates expansion in the resting system; not mean: for the same kind of particle, more energy, longer life. Obviously, this is mistake assume as a matter of course in the classical explanation.
VIII photon aging and fixed star spectral red shift
It not only proves that the correction of “photon quiescent mass formula” of generalized space-time relativity, but also provides a clear picture of photon structure. Accordingly, we strongly believe that: photon also has the structure inside. Just as the result, the relation among gross mass m, moving mass mc and “relative quiescent mass (gravitation mass) m0:
m = m c + m0 (42)
bases on the photon quiescent mass formula m0 =ηω, we can get the result that, the quiescent mass （m0）only is 70.71% of gross mass. And the rest 29.29% is relative moving mass （m c）. When we calculate the deflexion of photon near the perihelion, the moving mass（m c）does not contribute to the deflexion angle. That is mean the moving mass is not working on the deflexion angle. So, the moving mass must exist in energy form.
As known, the photon is the electromagnetic field itself. So it is not difficult to image, the structure mode maybe as the picture as follow: Namely: there is “core” formed by dense “quiescent mass” in the center, there is one “continuous electromagnetic field” distributing on the limited “space” around the “core”. Actually, this kind of structure mode is not unique character of Photon. From small elementary particle to large fixed star system, they all have similar structure mode. ---- The phenomenon “gravitation field” around any star has already be recognized by people. Although, not find the quiescent mass of photon by the experiment, we already got that neutrino’s mass is not zero already by experiment. It provides indirect evidence for the photon quiescent mass, because neutrino’s velocity is almost same as light speed. Since neutrino has the quiescent mass, it is unbelievable that photon has no quiescent mass. Ulterior say, if photon has the “quiescent mass”, then it must has the inside structure, and it would be divisible.
There out, the energy can attenuate gradually during the diffusion in the space. In this way, red shift problem has come back to the traditional explanation about the photon “aging mode”. ---- If the attenuation form of photon aging is quantisation, and tends to become zero at the infinite, then it only changes the frequency, not diffusion velocity. And then, measurement for distance of star system from us by the radial from the star system will cause the phenomenon of red shift observed by astronomer Hubble. So it is not difficult to understand that to deny “universe expanding” by the explanation of photon aging mode naturally. At the same time, use this mode; we can understand the chronometer observation of Australian scientific research group about “light velocity maybe not a constant” easily.
According to the report, after abundant research of Australian research group, announced that the light velocity maybe not constant. They found, the light of quasar 12 billion light-year away from earth absorb mistake mode photon on the trip to earth. But according to modern physical theory, light cannot absorb this kind of photon at all. There are only two possibilities to make this difference: the changing of electron charge, or the changing of photon speed. The last conclusion is that photon has changed. (Haitian)----（refer to《Sina》main page----science and technology age----the masses science and technology, Aug. 2001）. For this phenomenon, it is easy to find out if accept “photon has structure inside”: it cannot express that the velocity slowing down during the diffusion, but the change of structure inside because of quantisation aging of energy. Just because of this change found by Australian physical worker, so it would support the explanation about red shift “aging explanation” interiorly. In another word, it provides the experiment evidence for the fixed star’s red shift “aging explanation” from different point of view.
Of course, it is not going to deny the universe theory completely, not deny the isotropy in the big scale, and deny the possibility of explosion caused by gravitation collapse of some fixed star system. It denies “Universe birth theory” due to the big-bang, deny the absurdity view of considering “earth” (or any star) to be the center of explosion.
IX Conclusion
The discussion above proves, when the absolute velocity is less then light speed, from the view of generalized space-time relativity, not only transit to the mass-energy formula of special theory of relativity, but also to the movement law of Newton mechanics. So in the mistake view of space-time, the special theory of relativity can achieve such splendent scholarship. Obviously, the formula about relative quiescent mass of photon is the physical question, which Einstein’s special theory of relativity cannot solve. Specially, the result indicates: The order of magnitude for the relative quiescent mass of all kind of visible light is under 1/million. That is why the people cannot measure the quiescent mass until now. Here, we prove through the calculation result for the deflexion angle when beam near Sun: photon does have the relative quiescent mass not equal to zero. Specially, the result from Newton mechanics and Kepler law proves: Einstein’s general theory of relativity is not unique correct space-time theory for researching the movement in the gravitation field.
Nay, the discussion also express: movingμmeson
has the experiment phenomenon of increasing of moving life. Any way, it cannot be the
experiment evidence of special theory of relativity and Lorentz contraction. Besides,
because photon has the quiescent mass, which is not equal to zero, so it would appear the
attenuation of energy. Just because this procedure is “quantisation”, so it only
changes the frequency, not speed. So the frequency red shift appears. In despite of the
red shift can be caused by Einstein effect and Doppler effect, but the red shift
phenomenon from Hubble is not resulted from great explosion. So the great explosion
universe birth and Ptolemy’s “theory of earth center” is not different essentially!
It would bring the modern physics to the old belief way at last if insist on this view.
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