Natural Science Forum / Physics / Relativity / January 2007

"Dork Van de merde" aka
"Dork Van de psychopath",
"Dork Van de psychotic fumble mumbler",
"Dork Van de fuckhead",
[anip]

 http://users.telenet.be/vdmoortel/dirk/Physics/TwinsEvents.html
"We use 3 inertial reference frames" [because Dorks can't get the result
they want in two].
"In neither of these frames any form of acceleration is felt" [neither one of
all three].
"In order for the travelling twin to make HIS trip, SHE must be in frame S'
while going away".
"if T = 5 years and v = 0.8c, then the stay at home twin will have aged
10 years".

Belgium is where the farts blow.

"Your conclusion is dead wrong.
Start over, but skip the first part and the conclusion." -- Dork Van de
fuckhead.

"You made a mistake" -- Dork Van de psychotic fumble mumbler.

ASSistant professor Paul B. Andersen, tusseladd:

"That is, we can reverse the directions of the frames
which is the same as interchanging the frames,
which - as I have told you a LOT of times,
OBVIOUSLY will lead to the transform:
 t = (tau-xi*v/c^2)/sqrt(1-v^2/c^2)
 x = (xi - v*tau)/sqrt(1-v^2/c^2)
or:
 tau = (t+xv/c^2)/sqrt(1-v^2/c^2)
 xi = (x + vt)/sqrt(1-v^2/c^2)"

On Jan 28, 1:15 pm, "Dirk Van de moortel" <dirkvandemoor...@ThankS-NO-
SperM.hotmail.com> wrote:

Thanks for seeing the light !

It is just that it annoys me that Universities can make such errors.

It reminds me of university grads such as Doctors and specifically
Dentists. I used to run into numerous problems after each time
additional amalgam implants were  added to my teeth.  It caused nasty
myofacial pains that lasted for months and never completely faded
away, and eventually led to myofacial muscle spasms that occurred on
average of every second day. On top of that, body temperature dropped,
the tip of my nose was always blue, and my hands were always ice cold.

But I assumed, while still at a young age, that university grads with
qualifications such as now being a Doctor, in combination to the fact
that the medical association also supported the actions that which my
dentist was practicing, was also constructed out of university grads
with impressive degrees, that they all new exactly what they were
doing, and therefore that what they were doing was completely safe.  
The impression that was quit strong during that time, was that Doctors
were Gods.

And so the problems that I was having, just did not make sense at
all.  This was especially the case when my immune system also
collapsed which led to numbers of other health problems.  But by
chance, I stumbled into someone else who had also experienced these
same problems.  He connected me with Dentist in particular who did
basically nothing but remove amalgam fillings. His office walls were
covered with letters from his patients, thanking him for saving their
lives.  Not one square inch of any of the four walls was left
uncovered.  Letters were even overlapping due to having run out of
room.   I read some of them, and felt much better when I saw that they
said things such as, " My blood circulation has returned to normal.
" , " I can shake hands again without people saying that my hands are
ice cold every damn time. " , " I am no longer being controlled by
massive Candida yeast infections, internally and externally, now that
my immune system has recovered ", , etc., etc.  Their were hundreds
and hundreds of letters saying THANK YOU THANK YOU THANK YOU......

I too recovered after having all those amalgam filling removed which
by the way contain 50% Mercury.

It turns out that the Mercury, a heavy metal, messes with the immune
system, and much more, as it proceeds to replace light metals within
the body, with this heavy metal. Most people however, are not effected
because it is known to have a knee effect, meaning that the health can
be reduced a bit over time, but eventually you hit the knee point
where all hell breaks loose, but for most people, they would not reach
that knee point until they were well over a hundred years old.  But
some are not so lucky, and they can be hit while still just in their
twenties.  Both the Canadian, and American Dental Associations had
refused to release any test results that had proven that the amalgam
filling were safe for all.  That is because they did not have any test
results of this nature, but in fact of the opposite.  So instead they
quietly gradually reduced the use of the metal amalgam fillings.

And so, when I see universities F_CK up, I become concerned about what
the outcome of such mistakes will be in the long run.

I just wrote them an email asking them to correct this, together
with another mistake.
The other is in the length contraction part. See if you can find it.

Dirk Vdm

A SITE  REVIEW.

Time dilation

In the animations below, Zoe is travelling at speed v as she drives
past Jasper's verandah. She has various clocks on board: clocks that
work using the laws of mechanics and/or electromagnetism. According to
Einstein's principle of special relativity, these laws by which these
clocks operate are the same for her and for Jasper, so it doesn't
matter what sort of clock we choose. So let's choose a very simple
electromagnetic clock. It uses electromagnetic waves and mirrors: it
has a pulse of light going from side to side across her car (whose
width is w). Zoe has timing apparatus to measure the time between
reflections in the windows. So does Jasper, and for this purpose, the
mirrors are only partially reflecting so that some of the light gets
out.

Prior to the experiment, Zoe parks her car  next to Jasper's verandah
so we can observe her clock, shown in the diagram at right.
Coincidentally, the car and the verandah are the same length.

The animation below shows Jasper's and Zoe's observations of the
events. In Jasper's frame, Zoe is travelling left to right at v =
0.8*c, and the pulse of light traces the lines shown, each of which is
the hypotenuse of a right angled triangle. In Zoe's frame, Jasper and
his verandah are travelling right to left at speed v = 0.8*c, and the
light pulse of the clock just goes sideways, to and fro across the
car. The red counters record each time that the light pulse strikes
one of the windows: each window reflection is a tick of the clock.
(You can use the 'step' function to check that this happens.) You can
also check the constancy of the speed of light for the two observers
by checking that the light pulse travels the same distance per frame.

Now the speed of light c in each of the animations is the same -
that's what the principle of relativity is all about. But the
distances are different: for Jasper, each tick of Zoe's clock is the
time T taken for light to trace the hypotenuse of the right angled
triangle. For Zoe, the light pulse covers only w, the width of the
car, in each tick. So the constant speed of light means that the light
beam clock ticks at different rates for Jasper and for Zoe! Jasper
observes Zoe's clock running more slowly than Zoe does. (The red
counters give the number of ticks of the clock as measured by each of
the observers.) Let's call T' the time that Zoe measures for one tick
of the clock, so

75,000 km * 10 = 750,000 km
750,000 km / 2.5 = 300,000 km per sec.

Jasper, on the other hand, has a wrist watch that is running twice as
fast as Zoe's is.  To Jasper, it appeared as thought 5 seconds had
passed for these 10 events to occur.  To Jasper, each hypotenuse path
of the light is measured to be 150,000 km in length.

150,000 km * 10 = 1500,000 km
1500,000 km / 5 = 300,000 km per sec.

So yes, both Zoe and Jasper measure the speed of light to be the
300,000 km per sec., and yes " the constant speed of light means that
the light beam clock ticks at different rates for Jasper and for Zoe!
", but the number of EVENTS or TICKS is still 10 and only 10 when
viewed from either frame, regardless of the fact that they tick at
different rates as Zoe's and Jasper's wrist watches indicate. <<

w = cT'.

c = 300,000 km per sec.
10 clock ticks = 2.5 sec.  ,  therefore   1 tick = 0.25 sec. ,  and
so  T' = 0.25 sec.
w =  c * 0.25sec  = 75,000 km <<

Pythagoras meets Einstein

How to relate, T, the time of a tick on Zoe's clock as Jasper observes
it, to T', the time of a tick on the same clock, as Zoe sees it? Look
at the triangle at the right of the animation above. Light travels at
c, so the hypotenuse has length cT. One side of the triangle is the
width w of the car. The other side is vT, where v is the speed of the
car relative to Jasper. Pythagoras' theorem says that the square of
the hyptenuse is the sum of the squares on the other two sides. Here,
this gives

(cT)^2 = w^2 + (vT)^2.

w^2 = 75,000 * 75,000

(vT)^2. =  ( 260,000 km * 0.5 sec  ) * ( 260,000 km * 0.5 sec  )

(cT)^2 = w^2 + (vT)^2 = 150,000 km  per 0.5 sec.

Yep, that all checks out.  <<

Combining the two equations above:

(cT)2 = (cT')^2 + (vT)^2,        then dividing by c and rearranging
gives

T'2 = T2 - (v/c)^2T^2            whence

T' = T(1 - (v/c)^2)1/2 = T/y, where y = 1/(1 - (v/c)^2)^1/2.

So Jasper observes Zoe's clock to tick more slowly by a factor y,
which is always greater than or equal to one. This factor y occurs
regularly in special relativity, so we have plotted it at right. (The
dashed line plots 1/y.) We notice that, unless v is a substantial
fraction of c, y is approximately 1. This of course is why we don't
notice time dilation at ordinary speeds. For an airplane travelling
near the speed of sound, y = 1.0000000000005. Note that 1/y(v/c) is
the equation of a circle, although we
have stretched the horizontal axis so that the dashed line looks like
an elipse. So y (the solid line) is conveniently remembered as the
reciprocal of a circle.

In the animations, Zoe's car travels at 0.8c, so ? = 1.67, so Jasper
measures Zoe's clock to have ticks that are 60% of the time that Zoe
measures.

In my example where  Zoe's car traveling at 0.8666c, or 260,000 km per
second, Jasper would see the clock to have ticks that are 200% of the
time that Zoe measures, for the rate on the ticks seen by Zoe is seen
as a shorter time period since Zoe's clock is ticking half the speed
in comparison with Jasper's.<<

A SITE  REVIEW.

Time dilation

In the animations below, Zoe is travelling at speed v as she drives
past Jasper's verandah. She has various clocks on board: clocks that
work using the laws of mechanics and/or electromagnetism. According to
Einstein's principle of special relativity, these laws by which these
clocks operate are the same for her and
for Jasper, so it doesn't matter what sort of clock we choose. So
let's choose a very simple electromagnetic clock. It uses
electromagnetic waves and mirrors: it has a pulse of light going from
side to side across her car (whose width is w). Zoe has timing
apparatus to measure the time between reflections in the windows. So
does Jasper, and for this purpose, the mirrors are only partially
reflecting so that some of the light gets out.

<< This is true, Zoe and Jasper could also be wearing wrist watches
which will also be affected by velocity of motion, if in motion across
Space.<<

Prior to the experiment, Zoe parks her car  next to Jasper's verandah
so we can observe her clock, shown in the diagram at right.
Coincidentally, the car and the verandah are the same length.

<< Blah blah blah.<<

The animation below shows Jasper's and Zoe's observations of the
events. In Jasper's frame, Zoe is travelling left to right at v =
0.8*c, and the pulse of light traces the lines shown, each of which is
the hypotenuse of a right angled triangle. In Zoe's frame, Jasper and
his verandah are travelling right to left at speed v = 0.8*c, and the
light pulse of the clock just goes sideways, to and fro across the
car. The red counters record each time that the light pulse strikes
one of the windows: each window reflection is a tick of the clock.
(You can use the 'step' function to check that this happens.) You can
also check the constancy of the speed of light for the two observers
by checking that the light pulse travels the same distance per frame.

<< Yes,  " The animation below shows Jasper's and Zoe's observations
of the events."  , it is to be strongly noted that these are
OBSERVATIONS and therefore can not dictate facts. <<

<< Therefore, " In Zoe's ( observational )  frame, Jasper and his
verandah are travelling right to left at speed v = 0.8*c, and the
light pulse of the clock ( apparently ) just goes sideways, to and fro
across the car. ". <<

<< Let's raise the height of the mirrors on Zoe's vehicle, such they
are above Zoe's head.  Now let us position a laser, that is stationary
relative to the ground, in such a position that Zoe will drive under
it at one point while in motion across that same ground.  The mirrors
are at  the same height as the laser. The laser is
pointed just at the appropriate angle, and emits a pulse of light just
at the right time, such that  the pulse of light will hit one of the
mirrors on the vehicle just as it passes by, and will now reflect off
of this mirror just at the appropriate angle such that it will strike
the second mirror on the opposite side of the vehicle even
though the vehicle has moved further away at its constant velocity.
Thanks to the angle of the laser, and the timing of the release of the
pulse being correctly set in time with the movement and position of
the vehicle, these reflections will then continue onward as the
vehicle continues onward. <<

<< So, even thought we have emitted a pulse of light at just the right
time and angle such that the light continues to reflect off of the
mirrors as the vehicle continues to be on the move, from Zoe's
OBSERVATIONAL point of view,  it APPEARS as thought the light is ONLY
moving  " sideways, to and fro across the car.", even thought this is
not the case.  Hence OBSERVATIONAL findings, do not support the
complete description of the actual event. <<

Now the speed of light c in each of the animations is the same -
that's what the principle of relativity is all about. But the
distances are different: for Jasper, each tick of Zoe's clock is the
time T taken for light to trace the hypotenuse of the right angled
triangle. For Zoe, the light pulse covers only w, the width of the
car, in each tick. So the constant speed of light means that the light
beam clock ticks at different rates for Jasper and for Zoe! Jasper
observes Zoe's clock running more slowly than Zoe does. (The red
counters give the number of ticks of the clock as measured by each of
the observers.) Let's call T' the time that Zoe measures for one tick
of the clock, so w = cT'..

<< Wrong.     It says that  " the speed of light c in each of the
animations is the same ", but in actual fact it is only OBSERVED and
MEASURED to be the same cspeed of light. This does not mean that the
Independent speed of that light itself when related to a moving body
or moving frame, will create a relative
speed equal to c as a total, but may only be OBSERVED and MEASURED to
be so. <<

<< Wrong.     It says that " For Zoe, the light pulse covers only w,
the width of the car ", but in fact, as I pointed out previously, it
is only observed to be such a case. This does not mean that this is
the ACTUAL situation.  <<

<< Wrong.     It says that " So the constant speed of light means that
the light beam clock ticks at different rates for Jasper and for Zoe!
", but this is incomplete.  Each clock tick is an EVENT.  If say 10
events occur on Zoe's vehicle, over a given time period, and then Zoe
stops the clock by blocking the path, then ten events have occurred,
and that is all.   Now if Zoe was wearing a wrist watch, and Zoe had
been moving at a velocity of 260,000 km per sec. , in combination with
the distance between each mirror being a huge 75,000 km, then  Zoe
would see that the 10 events would have occurred in 2.5 seconds, and
this is partially due to the fact that Zoe's watch is running at half
speed while at this specific 260,000 km per sec. velocity.

75,000 km * 10 = 750,000 km
750,000 km / 2.5 = 300,000 km per sec.

Jasper, on the other hand, has a wrist watch that is running twice as
fast as Zoe's is.  To Jasper, it appeared as thought 5 seconds had
passed for these 10 events to occur.  To Jasper, each hypotenuse path
of the light is measured to be 150,000 km in length.

150,000 km * 10 = 1500,000 km
1500,000 km / 5 = 300,000 km per sec.

So yes, both Zoe and Jasper measure the speed of light to be the
300,000 km per sec., and yes " the constant speed of light means that
the light beam clock ticks at different rates for Jasper and for Zoe!
", but the number of EVENTS or TICKS is still 10 and only 10 when
viewed from either frame, regardless of the
fact that they tick at different rates as Zoe's and Jasper's wrist
watches indicate. <<

w = cT'.

<< Yes.   w = cT'.
c = 300,000 km per sec.
10 clock ticks = 2.5 sec.  ,  therefore   1 tick = 0.25 sec. ,  and
so  T' = 0.25 sec.
w =  c * 0.25sec  = 75,000 km <<

Pythagoras meets Einstein

How to relate, T, the time of a tick on Zoe's clock as Jasper observes
it, to T', the time of a tick on the same clock, as Zoe sees it? Look
at the triangle at the right of the animation above. Light travels at
c, so the hypotenuse has length cT. One side of the triangle is the
width w of the car. The other side is vT, where v is the speed of the
car relative to Jasper. Pythagoras' theorem says that the square of
the hyptenuse is the sum of the squares on the other two sides. Here,
this gives

(cT)^2 = w^2 + (vT)^2.

<< Yes.   (cT)^2 = w^2 + (vT)^2.      In my example of the velocity
being 260,000 km per second,

w^2 = 75,000 * 75,000

(vT)^2. =  ( 260,000 km * 0.5 sec  ) * ( 260,000 km * 0.5 sec  )

(cT)^2 = w^2 + (vT)^2 = 150,000 km  per 0.5 sec.

Yep, that all checks out.  <<

Combining the two equations above:

(cT)2 = (cT')^2 + (vT)^2,        then dividing by c and rearranging
gives

T'2 = T2 - (v/c)^2T^2            whence

T' = T(1 - (v/c)^2)1/2 = T/y, where y = 1/(1 - (v/c)^2)^1/2.

<< OK <<

So Jasper observes Zoe's clock to tick more slowly by a factor y,
which is always greater than or equal to one. This factor y occurs
regularly in special relativity, so we have plotted it at right. (The
dashed line plots 1/y.) We notice that, unless v is a substantial
fraction of c, y is approximately 1. This of course is why we don't
notice time dilation at ordinary speeds. For an airplane travelling
near the speed of sound, y = 1.0000000000005. Note that 1/y(v/c) is
the equation of a circle, although we
have stretched the horizontal axis so that the dashed line looks like
an elipse. So y (the solid line) is conveniently remembered as the
reciprocal of a circle.

<< Wrong.   Jasper has no idea how fast Zoe's wrist watch is
ticking.   Jasper, as does Zoe, is only watching the 10 light clock
ticks.  The rate of which these ticks occur can only be determined by
monitoring their wrist watches and comparing the watch readings with
the time periods of the 10 Events of the 10 light clock ticks.<<

In the animations, Zoe's car travels at 0.8c, so ? = 1.67, so Jasper
measures Zoe's clock to have ticks that are 60% of the time that Zoe
measures.

<< Wrong.   Zoe's clock and Jaspers clock are one in the same, since
each tick is simply an event that is revealed to both.   However, if
Jasper was able to know of Zoe's measuring of the tick rate, in the
case of Zoe's car traveling at 0.8c, Jasper would see the clock to
have ticks that are 167% of the time that Zoe measures.

In my example where  Zoe's car traveling at 0.8666c, or 260,000 km per
second, Jasper would see the clock to have ticks that are 200% of the
time that Zoe measures, for the rate on the ticks seen by Zoe is seen
as a shorter time period since Zoe's clock is ticking half the speed
in comparison with Jasper's.<<

A SITE  REVIEW.

Time dilation

In the animations below, Zoe is travelling at speed v as she drives
past Jasper's verandah. She has various clocks on board: clocks that
work using the laws of mechanics and/or electromagnetism. According to
Einstein's principle of special relativity, these laws by which these
clocks operate are the same for her and for jasper, so it doesn't
matter what sort of clock we choose. So let's choose a very simple
electromagnetic clock. It uses electromagnetic waves and mirrors: it
has a pulse of light going from side to side across her car (whose
width is w). Zoe has timing apparatus to measure the time between
reflections in the windows. So does Jasper, and for this purpose, the
mirrors are only partially reflecting so that some of the light gets
out.

<< This is true, Zoe and Jasper could also be wearing wrist watches
which will also be affected by velocity of motion, if in motion across
Space. <<

Prior to the experiment, Zoe parks her car  next to Jasper's verandah
so we can observe her clock, shown in the diagram at right.
Coincidentally, the car and the verandah are the same length.

<< Blah blah blah.<<

The animation below shows Jasper's and Zoe's observations of the
events. In Jasper's frame, Zoe is travelling left to right at v =
0.8*c, and the pulse of light traces the lines shown, each of which is
the hypotenuse of a right angled triangle. In Zoe's frame, Jasper and
his verandah are travelling right to left at speed v = 0.8*c, and the
light pulse of the clock just goes sideways, to and fro across the
car. The red counters record each time that the light pulse strikes
one of the windows: each window reflection is a tick of the clock.
(You can use the 'step' function to check that this happens.) You can
also check the constancy of the speed of light for the two Observers
by checking that the light pulse travels the same distance per frame.

<< Yes,  " The animation below shows Jasper's and Zoe's observations
of the events."  , it is to be strongly noted that these are
OBSERVATIONS and therefore can not dictate facts. <<

<< Therefore, " In Zoe's ( observational )  frame, Jasper and his
verandah are travelling right to left at speed v = 0.8*c, and the
light pulse of the clock ( apparently ) just goes sideways, to and fro
across the car. ". <<

<< Let's raise the height of the mirrors on Zoe's vehicle, such they
are above Zoe's head.  Now let us position a laser, that is stationary
relative to the ground, in such a position that Zoe will drive under
it at one point while in motion across that same ground.  The mirrors
are at  the same height as the laser. The laser is pointed just at the
appropriate angle, and emits a pulse of light just at the right time,
such that  the pulse of light will hit one of the mirrors on the
vehicle just as it passes by, and will now reflect off of this mirror
just at the appropriate angle such that it will strike the second
mirror on the opposite side of the vehicle even though the vehicle has
moved further away at its constant velocity. Thanks to the angle of
the laser, and the timing of the release of the pulse being correctly
set in time with the movement and position of the vehicle, these
reflections will then continue onward as the vehicle continues onward.
<<

<< So, even thought we have emitted a pulse of light at just the right
time and angle such that the light continues to reflect off of the
mirrors as the vehicle continues to be on the move, from Zoe's
OBSERVATIONAL point of view,  it APPEARS as thought the light is ONLY
moving  " sideways, to and fro across the car.", even thought this is
not the case.  Hence OBSERVATIONAL findings, do not support the
complete description of the actual event. <<

Now the speed of light c in each of the animations is the same -
that's what the principle of relativity is all about. But the
distances are different: for Jasper, each tick of Zoe's clock is the
time T taken for light to trace the hypotenuse of the right angled
triangle. For Zoe, the light pulse covers only w, the width of the
car, in each tick. So the constant speed of light means that the light
beam clock ticks at different rates for Jasper and for Zoe! Jasper
observes Zoe's clock running more slowly than Zoe does. (The red
counters give the number of ticks of the clock as measured by each of
the observers.) Let's call T' the time that Zoe measures for one tick
of the clock, so w = cT'.

<< 1 Wrong.     It says that  " the speed of light c in each of the
animations is the same ", but in actual fact it is only OBSERVED and
MEASURED to be the same cspeed of light. This does not mean that the
independent speed of that light itself when related to a moving body
or moving frame, will create a relative speed equal to c as a total,
but may only be OBSERVED and MEASURED to be so.<<

<< 2 Wrong.     It says that " For Zoe, the light pulse covers only w,
the width of the car ", but in fact, as I pointed out previously, it
is only observed to be such a case. This does not mean that this is
the ACTUAL situation.  <<

<< 3 Wrong.     It says that " So the constant speed of light means
that the light beam clock ticks at different rates for Jasper and for
Zoe! ", but this is incomplete.  Each clock tick is an EVENT.  If say
10 events occur on Zoe's vehicle, over a given time period, and then
Zoe stops the clock by blocking the path, then ten events have
occurred, and that is all.   Now if Zoe was wearing a wrist watch, and
Zoe had been moving at a velocity of 260,000 km per sec. , in
combination with the distance between each mirror being a huge 75,000
km, then  Zoe would see that the 10 events would have occurred in 2.5
seconds, and this is partially due to the fact that Zoe's watch is
running at half speed while at this specific 260,000 km per sec.
velocity.

75,000 km * 10 = 750,000 km
750,000 km / 2.5 = 300,000 km per sec.

Jasper, on the other hand, has a wrist watch that is running twice as
fast as Zoe's is.  To Jasper, it appeared as thought 5 seconds had
passed for these 10 events to occur.  To Jasper, each hypotenuse path
of the light is measured to be 150,000 km in length.

150,000 km * 10 = 1500,000 km
1500,000 km / 5 = 300,000 km per sec.

So yes, both Zoe and Jasper measure the speed of light to be the
300,000 km per sec., and yes " the constant speed of light means that
the light beam clock ticks at different rates for Jasper and for Zoe!
", but the number of EVENTS or TICKS is still 10 and only 10 when
viewed from either frame, regardless of the fact that they tick at
different rates as Zoe's and Jasper's wrist watches indicate. <<

w = cT'.

<< Yes.   w = cT'.
c = 300,000 km per sec.
10 clock ticks = 2.5 sec.  ,  therefore   1 tick = 0.25 sec. ,  and
so  T' = 0.25 sec.
w =  c * 0.25sec  = 75,000 km <<

Pythagoras meets Einstein

How to relate, T, the time of a tick on Zoe's clock as Jasper observes
it, to T', the time of a tick on the same clock, as Zoe sees it? Look
at the triangle at the right of the animation above. Light travels at
c, so the hypotenuse has length cT. One sideof the triangle is the
width w of the car. The other side is vT, where v is the speed of the
car relative to Jasper. Pythagoras' theorem says that the square of
the hyptenuse is the sum of the squares on the other two sides. Here,
this gives

(cT)^2 = w^2 + (vT)^2.

w^2 = 75,000 * 75,000

(vT)^2. =  ( 260,000 km * 0.5 sec  ) * ( 260,000 km * 0.5 sec  )

(cT)^2 = w^2 + (vT)^2 = 150,000 km  per 0.5 sec.

Yep, that all checks out.  <<

Combining the two equations above:

(cT)2 = (cT')^2 + (vT)^2,    then dividing by c and rearranging gives

T'2 = T2 - (v/c)^2T^2        whence

T' = T(1 - (v/c)^2)1/2 = T/y, where y = 1/(1 - (v/c)^2)^1/2.

<< OK <<

So Jasper observes Zoe's clock to tick more slowly by a factor y,
which is always greater than or equal to one. This factor y occurs
regularly in special relativity, so we have plotted it at right. (The
dashed line plots 1/y.) We notice that, unless v is a substantial
fraction of c, y is approximately 1. This of course is why we don't
notice time dilation at ordinary speeds. For an airplane travelling
near the speed of sound, y = 1.0000000000005. Note that 1/y(v/c) is
the equation of a circle, although we have stretched the horizontal
axis so that the dashed line looks like an elipse. So y (the solid
line) is conveniently remembered as the reciprocal of a circle.

<< Wrong.   Jasper has no idea how fast Zoe's wrist watch is
ticking.   Jasper, as does Zoe, is only watching the 10 light clock
ticks.  The rate of which these ticks occur can only be determined by
monitoring their wrist watches and comparing the watch readings with
the time periods of the 10 Events of the 10 light clock ticks.<<

In the animations, Zoe's car travels at 0.8c, so ? = 1.67, so Jasper
measures Zoe's clock to have ticks that are 60% of the time that Zoe
measures.

<< Wrong.   Zoe's clock and Jaspers clock are one in the same, since
each tick is simply an event that is revealed to both.   However, if
Jasper was able to know of Zoe's measuring of the tick rate, in the
case of Zoe's car traveling at 0.8c, Jasper would see the clock to
have ticks that are 167% of the time that Zoe measures.

In my example where  Zoe's car traveling at 0.8666c, or 260,000 km per
second, Jasper would see the clock to have ticks that are 200% of the
time that Zoe measures, for the rate on the ticks seen by Zoe is seen
as a shorter time period since Zoe's WRIST WATCH is ticking half the
speed in comparison with Jasper's.<<

On Jan 30, 4:01 am, "harry" <harald.vanlintelButNotT...@epfl.ch>
wrote:

True, but it is basically nothing but an equivalent of the wrist watch
that I have mentioned, which was also used to measure the time between
the reflection from one mirror to the other mirror.

Still, the number of counts, or ticks of the LIGHT CLOCK, would still
be the same for both observers.

The difference noted, is that each timing apparatus in each frame,
will measure different time periods between each LIGHT CLOCK tick.

THE_ONE

On Jan 30, 4:01 am, "harry" <harald.vanlintelButNotT...@epfl.ch>
wrote:

True, but it is basically nothing but an equivalent of the two wrist
watches that I have mentioned, which were also used to measure the
time between the reflection from one mirror to the other mirror.

Still, the number of counts, or ticks of the LIGHT CLOCK, would still
be the same for both observers.

The difference noted, is that each timing apparatus in each frame,
will measure different time periods between each LIGHT CLOCK tick.

THE_ONE