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RAJAN DOGRA

**APPARENT
LACK OF SYMMETRY IN STELLAR
ABERRATION AND EUCLIDEAN SPACE TIME**

**ABSTRACT :- **

( 1)
**INTRODUCTION:-**

It is known
that the earth completes a full circumference around the Sun every year.
Consequently, since the Earth-Sun radius (R_{e}) is well known,
it is easy to determine the earth tangential velocity (V_{t})
required to complete the circumference in twelve months (T seconds).
We have:

**2 **p
(R

Equation (4) predicts that the average translational velocity V of the earth around the Sun is 29.79 Km/s. Of course, the earth velocity vector changes continuously in direction and completes a full cycle during a one year period while the earth circles the Sun.

On
Figure A [26], an observer on Earth detects the photons emitted by a
stationary star S, located in a direction perpendicular to the Earth
velocity V_{t}. The star is located at such a large distance
from the earth that the parallax caused by the orbit diameter around
the Sun is completely negligible. Only the transverse velocity matters
here. *The stationary
star S is emitting photons in all directions. The Earth and the telescope
are moving upward at a velocity V . The telescope must make an angle **q**
with respect to the real direction of the arriving photons in order
to collect them at its focus.*

_{t}), explains why a telescope on Earth
(see Fig. A) must be pointing at the angle q , with respect to the Earth-star direction,
to be able to point at the star. Figure A shows that while the photons
move in straight line toward the Earth, they will always remain in the
axis of an inclined telescope, since it is moving sideways with the
Earth. The angle q is
equal to:

_{t})/c [EQUATIO** **
N 5]

^{2}/c^{2})^{0.5} ------(2)

** **

**(2) MECHANISM
OF ABERRATION :**

**
Consider a starlight photon in** S'** at point P in the x' -**
y'** plane with x**'** and** y'** coordinates as c sin** q'**
and c cos** q',
**respectively.** This photon would be observed simultaneously in
S and S' when O and O' coincide at t = t' = 0. Due to stellar aberration
[37] the observer O sees the incoming direction of the starlight photon
along line O'P' at t = t' = 0 such that PP' = m and point P' coincides the point P
at t' = -1. This coincidence of P and P' is possible only in classical
time concept, t = t', and not in Einstein’s new time concept, t = b
(t' + m
x' / c^{2}) where b = 1/ (1 - m^{2}/c^{2})^{0.5}.
The problem lies in the fact that the stellar aberration as outlined
above can be explained only in classical time concept with which the
principle of constancy of light speed in S and S' is incompatible. It
is this incompatibility that lead Einstein to establish new time concept
[38]. Our endeavour is to find a time concept that explains stellar
aberration as well as principle of constancy of light speed in S and
S’.

^{*}(In [39] Einstein defined the concept of moving length as “By means of stationary clocks set up in the stationary system and synchronizing in accordance with Einstein’s definition of simultaneity, the observer ascertains at what points of stationary system the two ends of the rod to be measured are located at a definite time. The distance between these two points, measured by the measuring rod already employed which in this case is at rest, is also a length which may be designated the length of the rod. The length to be discovered by the above operation, we will call the length of the (moving) rod in stationary system.) in Fig. 1 to substantiate the preceding
statement. In objective reality there are only rest lengths OP and O'P'
of S'. This means that the coinciding of O and O' at t = t' = 0 is accompanied
by dislocation of initial point P of starlight photon to the point P'
in S. In other words, the length OP at t'
*=* -1 is a moving length which moves to position O'P' at t'
= 0 in Fig. 1. But the principle of constancy of light speed in S and
S' demands that the moving length OP must be Lorentz contracted along
the direction of motion of S so that the rest length OP in S' reveals
itself as a dilated value rather than a contracted value in S. Moreover,
the dislocation of initial point P of starlight photon to point P' in
S implies that the relativity of simultaneity acquires meaning only
when the spatial and temporal axes coincide each other in S and S'.

^{2}/c^{2})^{0.5}.
This is the relativistic formula for the aberration of starlight which
was already deduced by Einstein in his first paper [40].

** **
The formula for the angle of aberration, instead of being tan q
= m/c,
then becomes sinq
= m/c
when q’
= 0. The relativistic formula agrees with the classical formula for
quantities of first order in case of relative transverse velocity between
star and earth. Further, Let assuming that Fig. 2 represents. Fig.1
at time instant t’ = +1 such that q’ = 0. Additionally, there is present
at origin O of earth frame S a small horizontal plane mirror in x-z
plane that reflects the incoming star light photon at

t’ = t = 0. In accordance with laws of reflection the starlight photon
is reflected at angle sin q = m / c along OP in earth frame S and
at normal along O’P = c in frame S’ because of normal incidence in S’.
After reflection the earth becomes moving source that has emitted reflected
starlight photon at t = t’= 0. It is quite obvious that the direction
OP of outgoing reflected starlight photon in earth frame S is apparent
direction (as incoming starlight photon direction was apparent in S)
and the direction O’P of outgoing reflected starlight photon in frame
S’ is true direction. This implies that the earth frame S as moving
source with transverse velocity emits the reflected star-light photon
without any aberration. Consequently, the apparent lack of symmetry
(described in section 1 of this paper) in stellar aberration, when the
star is moving at transverse velocity, can be explained on the basis
of above discussion. The fact, that Einstein’s theory fails to explain
this lack of symmetry in aberration, implies that something is wrong
with Einstein’s theory. Let us see what new conclusions can be drawn
about relativity from the above discussion of stellar aberration that
explains apparent lack of symmetry in aberration.

**(3)
CONCLUSION (1) :**

^{2}/c^{2})^{0.5}.
This clearly establishes that the rest length OS in S' does reveal itself
as a dilated value in moving frame S in Fig. 1 rather than a contracted
value. Further, in Fig. 1 the point P is the origin of temporal axis
O'P in S' and of temporal axis OP in S for the starlight photon at P.
Due to stellar aberration the physical existence of these temporal axes
in S and S' can be experimentally proved in the form of apparent and
true star positions observed simultaneously in S and S' when O and O'
coincide at t = t' = 0 and observe the starlight photon previously at
point P. This implies that (a) the distinction between space and time
disappears completely. (b) there is no difference between time direction
[41] and space direction, (c) time should be measured in imaginary numbers
rather than real ones. On this basis the conclusion that space time
is Euclidean appears to be convincing and reasonable enough, since with
imaginary time it has a Euclidean metric.

*=* bm of
frame S in Fig. 1 becomes Lorentz contracted as OO' = m in going from frame S' to S in Fig.
1. This reveals another aspect of Euclidean space time that when rest
clock at O' registers

t'=-1 in Fig. 1, the observer at O adjusts itself spatially as well
as temporally on moving from S' to S so that the rest clock at O in
S registers t = -1.

**CONCLUSION (2)**

^{2} + PS^{2}]^{ 0.5}

^{2}) -------(11)

**(3)
CONCLUSION (3)**

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Rajan Dogra, Instructor, Wireless Operator Trade Industrial Training Institute, Chandigarh.

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