ＴＨＯＵＧＨＴ ＥＸＰＥＲＩＭＥＮＴＳ ＷＨＩＣＨ
ＤＩＳＰＲＯＶＥ ＳＰＥＣＩＡＬ ＲＥＬＡＴＩＶＩＴＹ

　In this paper, we present two spaces in different states by simple thought experiments, and in the process of detecting the difference between those two spaces, indicate contradiction of special relativity.
　Further, we explain the difference between them by introducing an unknown physical quantity: a depth velocity vector.

.INTRODUCTION

　To disprove special relativity, which is established as the perfect theory, we present two thought experiments and think about them. But before that we suppose ‘the principle of constancy of light speed', which has two meanings:

　Now, standing on the supposition above, we consider thought experiments below.

　[Thought experiment 1]
　We suppose the universe only with the ideal heavenly body M(a perfect globe with uniform density) and consider the spread of the light emitting from the resting source on it. In this case, it is thought the source is at rest with the center of gravity of the universe, and that the space is isotropic.
　Therefore, the time must be ‘absolutely simultaneous' when the light from reaches the reflective mirrors A and B on M. (equally distant from )
　Next，we imagine a ‘rocket a' whose inside is vacuum is running above the heavenly body M at the uniform velocity (see Fig．1a)
　And we suppose the light source standing in the center of the rocket a emits the light when passes before ．When the observer standing at see this situation， reaches the mirror A（rear）faster than the mirror B（front）because the speed of and is equal from the principle of constancy of light speed �T．
　Then，we suppose a heavenly body M−exactly the same as M−is moving parallel to the moving direction of a rocket（ axis）at the velocity of ．The rocket is called ‘rocket b'.(see Fig．1b)
　　

　The distance between b and M, b and M is equal, and the space is symmetrical. Let us consider the moment when the light sources (, , ) of the three objects (M, M, the rocket b) accord with axis, which is perpendicular to axis. However, is a velocity of M measured by an observer on M. If measured by an observer in the rocket b, is a motion of M at the uniform velocity . Therefore, from the theory of relativity,

　When the light is emitted from the source in b to reflective mirrors A(rear) and B(front), is interpreted as ‘isotropic spread’ by the observer in b. In addition, if the situation is seen from observers on M() and M (), the arrival of at A and B must be interpreted as ‘absolutely simultaneous'. This means the vacuum around M are distorted because of addition of the mass of M, and the action spreads through the space as a wave and changes the spacetime in b.
　According to the theory of relativity adopting ‘principle of relativity' as a supposition, it is impossible to detect by an experiment the difference between the state of the spaces in a and b. But this paper presents a thought experiment which will detect the difference between these two spaces in ‘Thought experiment 2' in the next chapter.

．INDICATION OF CONTRADICTION OF SPECIAL RELATIVITY AND INTRODUCTION OF AN UNKNOWN PHYSICAL QUANTITY : A DEPTH VELOCITY VECTOR

　To detect by an experiment the difference between the spaces in the rocket a and b presented in the introduction, we consider a thought experiment below.

　[Thought experiment 2]
　Let us consider the condition where the rocket a is at rest along the axis on the heavenly body M in Fig.1a, and another rocket a in a is at rest.(see Fig.2)

　In the center of the rockets a and a the light sources and are set, which share the axis with the light source , installed on the origin of the - axis on M. At the six points on M, in a and a, twelve clocks of the same kind are placed at equal distance ＝±L/2 from the light sources, the clocks which work exactly at the same tempo when at rest: one clock is placed at each end on M, two clocks at each end in a and three clocks at each end in a. The clock placed at the point ＝−L/2 on is expressed as which means ‘the lock at the eft side of the light source’, while the one placed at the point =L/2 is expressed as meaning ‘the lock at the ight side of the source’. In the same way, the four clocks in a are expressed as , , , . And the six clocks in a are expressed as , , , , , .
　Then we set three pairs of clocks ( and , and , and ) using the way of clock settings which was used by Einstein when he constructed special relativity.
　In this case, M is at rest relative to the center of the gravity and is regarded as ‘the absolute rest frame’. And the spreads of the lights , and emitted from the three sources which are at rest on M are thought to be isotropic relative to the observer .
　Therefore, those six clocks can be said to agree with one another in the absolute sense.
　The next clock setting is about and in the rocket a, which begins to move at the uniform velocity relative to M, and about and in the rocket a , which is still at rest in a.(see Fig.3)

　Since these two pairs of clocks are set in the same way, we consider the clock setting of and .
　Let us consider the case in which an observer , who is at rest on the heavenly body M, measures the time required for the light emitted from the source to reach . When measures the distance between and , which is L/2 in the rocket, it is 　() because the rocket a contracts in the moving direction at the rate of . Therefore, by 's clock, the time required for to reach is　

　On the other hand, the time required for to reach is

　But, the clock ticks at the rate of : 1, compared with 's clock. Thus, from and , observes the time difference required for to reach and ,

　That is, is sec. fast compared with .
　The same is true with the time difference between and . What we have to notice, however, is it is when measures the time that and disagree with each other. For the observer in the rocket a, these two clocks agree with each other. can not discuss the absolute time difference between them as it is.
　Then, as a next operation, a time adjustment is made so that and agree, which usually do not.
　In addition, the same adjustment is made about .(Of course we do not really have to make the clocks agree. Calculational adjustment is enough)
　When observes this situation, , and agree with one another, while is sec. fast. Therefore, when the observer in the rocket a () compares with , the latter is sec. fast. This agrees with the prediction of special relativity.
　When the same clock setting and time adjustment are made about and in the rocket a the observer will find that is sec. fast comparing with.
　Next, we make a clock setting about and when the rocket a in the rocket a begins to move at the uniform velocity '. (see Fig.4)

　Now, we regard the velocity of a observed by as , and when observes the time difference between and ,

　as is clear from the previous consideration.
　[From the theory of relativity, ]
　 Then, as a next operation, a time adjustment is made in order to make agree with and .

　In addition, the same adjustment is made about .
　When this situation is observed by , , , and agree with one another. But is sec. fast, and is sec. fast relative to these four clocks.
　Consequently, when the observer in the rocket a compares with , the former is

　fast relative to the latter. This result contradicts the prediction of special relativity.
　According to the supposition of ‘the principle of relativity’, which was used when special relativity was constructed, inertia1 frames moving relatively are equal and so the laws of physics must be the same in every inertial frame.　Thus, if the time difference between and in the rocket a (moving at the uniform velocity above the heavenly body M ) is sec., the time difference between and in the rocket a (moving at the uniform velocity in the rocket a) must be sec.
　But the thought experiment in this paper does not produce such an result.
　By the way, let us consider the clock settings of the four clocks in a rocket b which is in the rocket b in Fig.1b : , , and . (See Fig.5)

　The distance between , and , is L. The light source is at the center.
　 and are set when the rocket b is at rest in the rocket b. In this case, the light (emitted from the source in b) isotropically spreads a priori, and so we can say that and agree with each other in the absolute sense.
　Next, a clock setting about and in the rocket b moving at the uniform velocity in the rocket b.(see Fig.6)

　When the observer in b () tells the time difference between these two clocks, is sec. fast relative to , as is clear from the previous consideration.
　So, to make agree with , a certain time adjustment " is made. And the same adjustment " is made about .
　When observes this situation, , and agree with one another, while is sec. fast relative to them.
　Consequently, as a matter of course, when the observer in the rocket b compares with , the latter is sec. fast relative to the former.
　This result agrees with the prediction of special relativity.
　As for the time difference Eq.( 5) between and , which is compared in the same way, however, the prediction does not agree with that.
　The correspondence of clock settings between these four clocks (, , , ) and the clocks(, , , ) in the rocket a is as follows:

　From ‘Thought experiment 2’, we have presented the way to detect the difference of physical state between the inside space of the rocket a (see Fig.1a) and the rocket b. (see Fig.1b)
　Now, what makes the time difference between and disagree with the prediction of special relativity?
　To explain the cause, we only have to think the space in the rocket a is moving at ‘a certain velocity ’ relative to some frame of reference.
　However. ‘the absolute rest space’ does not exist in the real physical space. So it is impossible to regard ‘a certain velocity' as a velocity relative to such a frame of reference.
　Then, this paper supposes that the physical space has a double layer.
　That is, we suppose an imaginary rest space − a depth rest space − in the depth of the real physical space, and suppose that the space in the rocket a, in which the spread of light is thought anisotropic, is moving at the velocity relative to a depth rest space. In this case, we define that the space in the rocket a has a depth velocity vector . (see Appendix)
　On the other hand, the space in the rocket b, in which the spread of light is thought isotropic, does not have a depth velocity vector.
　However, a depth rest space is not a real space. It is an imaginary one which is introduced in order to describe ‘the extent of the space dragging effect by mass' with an unknown physical quantity : a depth velocity vector. If we suppose the light spreads isotropically relative to each point in this rest space, we can understand the speed of light does not depend on the velocity of the light source. As for a depth velocity vector, the physical space itself does not have it. It is a vector whose start point is a depth rest space and the end is the real physical space.
　Now, let us calculate the magnitude of a depth velocity vector introduced in the consideration above.
　In this paper, the magnitude is calculated from the time difference between and ( sec.) predicted by special relativity, and Eq.( 5 ) predicted in this paper. Generally speaking, however., the direction of a vector is not clear. So the component of its direction of axis is regarded as (>0).
　In addition, we define as below :

　The case we deal with is >0, so omit the minus solution,，

　Now, we can get the component of a depth velocity vector in axis. If the same experiment is made about the direction of axis and axis, we can get the magnitude of , and .
　Therefore, we can get the magnitude of a depth velocity vector by synthesizing the components of these three directions.

．A NEW POINT OF VIEW WHICH TRANSCENDS SPECIAL RELATIVITY

　In this chapter we discuss some errors in special relativity and correct them.

　1. According to special relativity, the relation between ‘the rest frame’ and ‘the motion frame’ in Lorentz transformation is mathematically equal and commutable, and the same is true with that between ‘the orthogonal coordinates' and ‘the oblique coordinates’ in Mincowski diagram.
　In this paper, however, we are of the opinion that mathematical equality does not necessarily agree with physical equality. We give the position of ‘the rest frame’ to a depth rest space and to a physical space without a depth velocity vector. And we regard the space or the frame of reference moving relative to these ‘rest frames’ as ‘a motion frame’. In addition, we tentatively make Lorentz ‘rest frame’ correspond with Mincowski's ‘orthogonal coordinates’ and Lorentz ‘motion frame’ with Minkowski's ‘oblique coordinates’.
　Considering these correspondences above, there are different reasons for the space contraction and the time dilation between frames of references visually moving one another at a uniform speed. That is, though the contraction of a ruler in ‘the motion frame’ relative to ‘the rest frame’ is true contraction (contraction ), the contraction of a ruler in ‘the rest frame’ relative to ‘the motion frame’ occurs for another reason. Here, we regard ‘the rest frame’ as the rocket b and ‘the motion frame’ as the rocket b, then measure the contraction of ‘the rest frame’ in two ways as below:
　�@ An observer in the rocket b () starts the stopwatch when he passes the front of the ruler with the length L along axis of the rocket b and measures the interval until he reaches the rear of the ruler. Since the proper time of the rocket b passes more slowly than that of the rocket b, the time needed for to pass the both ends of the ruler in the rocket b shortens at the rate of () in comparison with that supposed by classical physics before the construction of the theory of relativity. Thus, the observer concludes that the ruler in the rocket b contracts at the rate of . This contraction is caused by the time dilation in the rocket b.(contraction )
　�A Two observers (at the left end) and (at the right end) are at each end of the ruler with the length L in the rocket b, and there is one clock at each end. These two observers read the ruler set along axis in the rocket b at the same time in the rocket b defined operationally by Einstein.
　By comparing the length of the ruler in the rocket b with that in the rocket b, the length of the ruler in the rocket b is calculated. The two observers in the rocket b read the length from the ruler in the rocket b. Then they get the value : L as a ratio of their ruler and the one in the rocket b.
　From this, the observers in the rocket b conclude that the ruler in the rocket b has contracted at the rate of . (contraction )
　That is, this contraction is caused by the true contraction of the ruler in the rocket b as ‘a motion frame' (contraction ), and by the relativity of simultaneity of the clock in the rocket b defined operationally by Einstein.
　Next, let us consider tile time dilation in ‘a motion frame’.
　The a priori relation between the times which pass in the rocket b as ‘a rest frame’ and in the rocket b as ‘a motion frame’ is .
　By the way, the light spreads isotropically relative to every point in a depth rest space. But the observer in ‘a motion frame’ judges that the light spreads isotropically relative to his own frame because he thinks of himself as ‘a rest frame’ on the ground of ‘the principle of relativity’. Therefore he concludes the reason for the time dilation of the arrival of the light is that the clock in the other frame (Lorentz ‘rest frame’) ticks more slowly.
　But this time dilation is only apparent ;　we can understand this well by using Mincowski diagram.
　Considering all the things above, we can explain the twin paradox clearly because we can discuss the a priori time dilation.
　2. In the thought experiment Fig.1b, we see that as the distance between the heavenly body M and M is getting infinite, the influence of the mass of the one on the space around the other is getting ignorable. These two spaces are getting closer to the state without a depth velocity vector, and depth rest spaces around M and M come to aquire the relative velocity approximately equal to that of the two heavenly bodies.()
　Thus, a depth rest space is not ‘an absolute rest frame' imagined by Newton.
　However, we can regard it as ‘a rest frame' which Lorentz meant. So we can call it ‘a relative absolute frame of reference’, though this name appears to be contradictory.
　3. Let us consider the situation where the two distant points A and B in the space without a depth velocity vector (Lorentz ‘rest frame') are moving at a uniform speed. In this situation, the light emitted from the source on B spreads isotropically relative to all the points of a depth rest space around it.
　Thus, when the observer on A telemeters the spread, he sometimes observes super light speed which is different from the light velocity as the physical constant. For example, in Fig.1b, when the observers on M and M measure the light speed around M and M, they get the value ±.
　However, this does not mean the speed of light depends on the velocity of the source, or that an object which passes light exists.
　Even if the super light speed is found in telemetry, the situation is not contradictory to ‘the principle of constancy of light speed ,’. That is because when the light spreads to the point of the observer on A the light spreads isotropically relative to a depth rest space of that point.
　At present, there is no reason for setting a limit to relative velocities between each point of depth rest spaces. What exists is a limiting value of relative velocity between a moving object and a depth rest space in the physical space around the object.

．CONCLUSION

　In this paper, we have presented thought experiments which give different results from those predicted by special relativity.
　To explain the state of such a space, we have supposed a rest space in the depth of the physical space, predicted the existence of a depth velocity vector, and have succeeded in presenting a formula to get the magnitude of it.

APPENDIX

　In publishing the theses, we append a note as follows.
　I am of the opinion that, of ‘the depth rest space’ and ‘the depth velocity vector’, the more essential is latter. The former is a concept, whereas the latter is a physical quantity i.e., reality.
　According to quantum electrodynamics, the vacuum transmitting electric force is thought to be a space which is dense with pairs of virtual particles and antiparticles, which we can not observe.
　And according to uncertainty principle, these virtual particles always shake without stopping, even in the lowest energy state.
　Therefore, it would be valid to consider that ‘the depth velocity vector’, which is physical quantity is the mean value of the relative velocity between the light source as a macroscopic object and countless virtual particles constituting the vacuum around the space occupied by the light source.

ACKNOWLEDGMENT

　I am very grateful to Takahiro Yasui for putting this paper into English.