Re: relativity vs velocity addition


lkoluk2003@xxxxxxxxx yazdi:
lkoluk2003@xxxxxxxxx yazdi:
Hi,
Although the symmetric twin paradox can be explaied by ALT(Aether
theory with Lorentz Transformations) , I am a relativist. So after I
was sure SR(special relativity) is incorrect, I started to search
explanation(s) of the paradox in a relativist way. According to me the
starting point ought to be the velocity addition rule, because every
huge leap in physics is achieved by understanding the secrets of
velocity. Galileo set up a new phsics by the concepts of inertia and
independence of velocities in different axes(vector addition). SR and
GR(General Relativity) is also set up by claiming the velocity
additition rule is not a simple algebraic sum. I don't try it, but it
seems that the lorentz transformations can be derived from the velocity
addition rule which is (v+w)/(1+vw/c^2) if v and w have the same
direction. Now I will try to show that if relativity principle(i.e. if
there is no absolute inertial frame) is true, then the speed of light
must be a constant relative to the source.

Let there are two platforms A and B and within each platform there are
two observers Oa and Ob respectively. Let the platforms are two trains
and Ob is in the middle of the train B with a detector D. On each of
the two far sides of the train there is a clock and a light source.
When the clock ticks a predefined times, the light source fires a light
beam such that it will hit the detector on the middle of the train.
I.e. the light source Sf fires light beam from left to right and Sb
fires in opposite direction as shown in the following.

--------------------------------------------------------------------------------
| | | Sf --------> D <--------- Sb |
| Oa | | Cf Ob
Cb |
---------------------------------------------------------------------------------
Train A Train B ----->x axis

The distance between each light source and detector D is the same.
Detector gives two results: the two light beams hit at the same time
or in different times.

My postulates are the followings:

1. The experiments within a train does not affected by the outside
objects which have a constant speed relative to it.
2. The speed of light is direction independent within a train.


Experiment1:
Synchronize the clocks and set up such that the light sources will be
fired after n ticks. So they will fire at the same time according to
observer Ob. The relative speed of trains A and B is zero. So the same
thing is true for observer Oa. Of course , from the Ob's reference
frame the two lights must hit the detector at the same time with the
given postulates. This is the same for Oa.

Experiment2:
Synchronize the clocks and set up such that the light sources will be
fired after n ticks. Place the clocks and light sources on the two far
sides of the train B as mentioned. The relative speed of trains A and
B is zero. So the clocks are synchronized according to both Oa and Ob.
Now let train B accelerates and reach a constant speed v relative to
train A after a while along the x axis. Then wait for the experiment
to be completed. According to Ob the experiment gives the same result.
I.e. the lights hit at the same time. Now examine what Oa see with the
assumption that the speed of light is always the same according to the
observer.

From Ob's reference frame: The clocks are still synchronized since they
share the same movement and so get the same affects. So the two light
beams are fired at the same time. The speed of the light train fired
from Sf is c and from Sb is -c. Still the distance between Sf and D is
the same with the distance between Sb and D although they are shorter
now. Let this distance be x. So, the travel time of the light beam
fired from Sf would be x/(c-v) and the travel time of the light beam
fired from Sb would be x/(c+v). Since v is greater than zero these
times are not equal and Oa predicts a different result from that of Ob.
So relativity principle conflicts with the postulate that the speed of
light is always the same according to the observer.

Actually what above experiments show that if the relativity principle
is true and the speed of light is direction independent, then the speed
of light is direction independent relative to the source. Since the
direction independence of light speed is a proven fact(Michael&Morley
experiment and others), any theory conflicts with this also conflicts
with relativity principle. This means that the Lorentzian velocity
addition law conflicts with relativity principle.

Lokman Kolukisa

Hi,
I think I have managed to find a relativistic speed addition formula
which gives the correct result for the symmetric twin problem. The
formula is v+w-v.w/c where v and w are relative speeds in the same
direction. By relative speed(is this a correct name for this?), I mean
the following. Let x be the distance between two objects at a moment.
After a time interval t, let the distance be x'. Then (x'-x)/t is the
avarage relative speed of these two objects. A velocity addition
formula based on a coordinate system should easily be derived from this
formula. Now I will explain how I got it.

As I have said before, the direction independent time dilation gives
inconsistent result in the twin problem. So either there should not be
a time dilation or it must be dependent on the direction of the speed.
Let t1 and t2 are the total times spend by the twin A in outbound and
inbound movement respectively. While twin A is in outbound movement,
twin B is also in his/her outbound movement. The same thing is true for
inbound movement also. The acceleration affects are ignored. Then let
t1' and t2' are the total times spend by twin B as measured by twin A
in outbound and inbound movements respectively. For the result to be
consistent t1+t2=t1'+t2' must be true. The outbound relative speed of
the twin need not be equal to the inbound relative speed. So we can
write

t1'=t1.B(v1), t2'=t2.B(-v2)

where v1 and v2 are the outbound and inbound relative speeds and B(v)
is the dilation factor. Then we get

t1+t2=t1'+t2'=t1.B(v1)+t2.B(-v2)
(x/v1) + (x/v2) = (x/v1).B(v1) + (x/v2).B(-v2)

where x is the longest distance between the twin A&B. It seems that the
only formula which satisfies this equation is B(v)=1+b.v where b is
unknown.

Now back to the experiment testing speed addition formulas. With this
experiment, it is shown that the light speed must be direction
independent relative to the source.
Note that this result does not exlude the time& length dilation. The
only difference is that the dilation factor must be applied to all
coordinates now not just x and t. Let k(v) is the speed of light
relative to the source. Of course k(0)=c and if k(v)=c then the correct
transformations would be that of the Galilean type. For an observer in
the train B the time required by a light beam to travel a distance x
is x/c. From the point of view of the observer Oa, the time required
is t=x'/k(v) for the same event where x'=x.B(v). Since x'/t'=c , the
formula becomes t=t'.c/k(v) where t' is the time measured by the
observer in the train B. From this and t'=t.B(v), we get
c/k(v)=1/B(v) and then k(v)=c.(1+b.v). So the speed of light with
respect to the observer Oa would be as v+k(v)=v+c.(1+b.v)=v+c+b.v.c.

To obtain speed formula, do the same experiment but replace light
sources with identical guns which gives a speed w' to the bullets when
fired. By using two identical guns directed to opposite directions and
identical bullets, we avoid a change in the speed of the train B due to
a momentum change. However, we only need one bullet for the
calculations. By similar logic, we find w'=w(1+b.v) where w' is the
speed of the bullet relative to the source with respect to the observer
Oa. Thus the speed of the bullet relative to the observer is found as
v+w.(1+b.v)

Now what is the value of b? The phsicists say that there are many
experimental evidences showing c as an upper limit for the speed. So
the formula would be

v+w-v.w/c

It also has the associative property. So if the calculations and the
logic I have used are correct, this is the relativistic speed formula.
However, if E=m.c^2 could not be derived from it, it has no value. One
way of doing is to repeat the Einstein's study in his 1905 paper.
However, to do this one needs the energy formula of light. As now the
light speed is varying with respect to the observer, I wonder whether
the correct formula is known. Anyway, I neither have sufficient
experience to go beyond nor desire to go. Also I don't deal with a
career in Physics. This is a relativistic solution to the twin
paradox and as a logician and relativist it seems sufficient to me.
However, in any case, I will form a full text consisting of what I
write about this subject here and put somewhere. After the formula is
verified by someone(s), I may send it to a journal.

Lokman Kolukisa


It seems that the assumption that the maximum distances between the
twins during inbound and outbound part are equal is not generally true.
I.e. the most general formula is t1=x1/v1 and t2=x2/v2 where x1 is not
equal to x2. In this case, the only explanation is that the clock rates
of both twins are the same even from the point of view of the twins.

On the other hand, the relativity principle is fully compatible with
this. I copied the following from my text in another threat.
"Each tick in a clock is an event and an event's observed time can be
different from time dilation. For example one can set a clock by using
a light pulse
and two mirrors. The pulse is reflected between the mirrors and the
time interval between the reflection times of mirror 1 can be
considered as one tick of this clock. If the light speed is source
dependent then the duration of each tick is the same regardless of the
speed of the clock and the time delation."

Assume there is a platform with the clock mentioned above and two
observers A&B. The tick time of this clock would be t=2.x/c where x is
the distance between the mirrors.

Now let the platform carrying the observer B is moving with a constant
speed v with respect to the observer A. The clock is placed in such a
way that the light pulse movement is in the same direction with the
platform's speed. Assume there is a time dilation B. I.e. t'=t.B where
t' is the time measured by observer B and t is the time measured by the
observer A. Since according to the observer B, there is nothing
changed, so (s)he will observe the tick time as t'=2x'/c or 2.x'=c.t'.

The relativity principle requires that the light speed is source
dependent. Let this relative speed is k(v). Then the tick time for
observer A would be
t=2.x'/k(v) = c.t'/k(v ) = c.t.B/k(v)

From here we deduce k(v)=B.c. On the other hand x'/t'=x/t must be true.
I.e. x'=x.B. So from here

t=2.x'/k(v) = 2.x.B/(c.B) = 2.x/c

same with if the speed was zero. As seen the observed tick time is
independent from the speed and from the dilation factor. The same thing
is true for any event including the movement of someting or at least
any event whose time is measured by distance/speed. This is a perfect
result because the twin paradox is fully resolved now(assuming the time
measure always involves something which has a movement) and the
dilation factor can be choosen without considering it.

Best regards,
Lokman Kolukisa

.

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