Lorentz transforms physical incoherence
_______________________________________

(Based on an example presented by Daryl McCullough)

We assume that a rocket is moving at speed v = 0.866 c
relative to the Earth, and we want to know what is
the relationship between the coordinates of an event,
in the frame of the Earth, and the coordinates of
the same event, in the frame of the rocket.

We assume that the rocket passes the Earth at an
event with Earth-coordinates tR=0, xR=0 and with
rocket-coordinates tR'=0, xR'=0.
(The primed variables are observed in the rocket
frame).

Let's pick an event E, in this case an explosion,
that takes place on a planet, at rest relatively
to the Earth. The planet is situated at a distance xE
form the Earth, and the explosion is observed after
a time interval tE, hence the Earth coordinates of
the event E are (xE, tE), and the corresponding
rocket coordinates are (xE', tE').

For simplicity, let's assume that the Earth, the
planet, and the rocket are all lined up, so that
we only need to consider the x-axis.

In this scenario, the distances are expressed
in light-years (ly), and the times in years.

After a time interval T, the rocket will be at
a distance v*T from the Earth, hence the distance
between the rocket and the event E is D = xE-vT.
In the rocket frame, the corresponding distance
is D' = D/gamma
(as v = 0.866 c, gamma = 1/sqrt(1-v^2/c^2) = 2).

Let xE = 3 ly and tE = 5 years.

Examples:

1) After a time interval T = xE/v, D = 0 and D' = 0.
Let's notice that T' = T/gamma. This is always the
case, as the ratio T/T' depends on the velocity of
the rocket, not on its position.

2) Let's take an arbitrary value T, for instance
T = 10 years.
From the formula D = xE -vT, we get
D = 3-0.866*10 = -5.66 ly, and
D' = D/gamma = -2.83 ly.
T' = T/gamma = 5 years.

3) Let's take T = 9.608 years. Then
D = 3-0.866*9.608 = -5.32 ly
D' = D/gamma = -5.32/2 = -2.66 ly
Of course, T' = 9.608/2 = 4.804 years.

Let's notice that those results have been obtained
by applying "Lorentzian" formulae.

Now let's use the Lorentz (or rather Einstein)
transformations:

t' = gamma(t-vx/c^2) and x' = gamma(x-vt)

Using the above notation, we get

tE' = gamma(tE-v*xE/c^2), thus
= 2(5-0.866*3) = 4.804 years

D' = gamma(xE-v*tE)
= gamma(3-0.866*5) = -2.66 ly,
which is exactly the value obtained in example 3,
by using T = tE'*gamma = 9.608 years.

Thus, gamma(xE-v*tE) = (xE-vT)/gamma.

But, in fact, *there is no physical relation between
time and position*. When the rocket travels an
arbitrary distance v*T wrt the Earth, T' is always
given by T/gamma, in other words, T' is independant
from v*T. If T = tE = 5 years, T' = 5/2 = 2.5 years,
not 4.804 years, and of course,
D = xE-v*tE = 3-0.866*5 = -1.33 ly, and
D'= D/gamma = -0.665 ly, not -2.66 ly.
(notice "en passant" that -0.665*gamma^2 = -2.66)

Let's now illustrate the physical incoherence
of the Lorentz time transformation
tE' = gamma(tE-v*xE/c^2).

We have mathematically seen above that
gamma (xE-v*tE) = (xE-v*T)/gamma, or
gamma^2 (v*tE - xE) = v*T - xE (1)

Let's tE = xE/v + delta t, thus
delta t = tE - xE/v
v*delta t = v*tE - xE
Replacing (v*tE - xE) by v*delta t in relation (1),
one gets
gamma^2 * v*delta t = v*T - xE
v*T = xE + gamma^2 * v*delta t
T = xE/v + gamma^2 * delta t,
T = xE/v + gamma^2 * (tE - xE/v) (2)

And indeed, with xE=3, tE=5 and gamma=2,
equation (2) leads to
T = 3/0.866 + 4(5 - 3/0.866)
= 3.464 + 4(5 - 3.464)
= 9.608 years

Equation (2) shows that the t' in the Lorentz time
transform t' = gamma(t-vx/c^2), expressed in the
Earth frame by T = t'*gamma, corresponds to the
time tau needed by the rocket to travel the
distance xE at the velocity v, increased by the
difference between the time coordinate tE of the
event E and the time tau, multiplied by the
factor gamma^2.

If the Lorentz time transformation were coherent,
the correction by gamma^2 would also apply to tau,
not only to the difference (tE-tau).
Indeed, there is no physical justification for
not treating homogenously the time coordinate tE.

Btw, such fancy correction by gamma^2 leads to
absurdities. For instance, when v is close to the
speed of light, the time corresponding to the
product gamma^2(tE-tau) can exceed the age of the
Universe!

The incoherence of the Lorenz time transform is
very obvious when the event coordinates are
(xE=0, tE=5). Then the transform gives
T = gamma^2 * tE = 4 * 5 = 20 years, instead of
T = 5 years!

Marcel Luttgens

wrote in message ups.com...
Lorentz transforms physical incoherence
_______________________________________

(Based on an example presented by Daryl McCullough)

Marcel Luttgens based on Marcel Luttgens:

Marcel Luttgens' fumbles:
http://www.google.com/search?q=luttg...ers.pandora.be

Marcel Luttgens' home page:
http://perso.wanadoo.fr/mluttgens/

March 2003
"The Lorentz transformation (LT) are false":
http://perso.wanadoo.fr/mluttgens/LTfalse.htm
shot down in
http://groups.google.com/groups?&thr... g.google.com

May 2003
"There is no length contraction"
http://perso.wanadoo.fr/mluttgens/mmx.htm
shot down in
http://groups.google.com/groups?&thr... ng.google.com

Sep 2001
"The Twin paradox falsifies SR"
http://perso.wanadoo.fr/mluttgens/twinpdx1.htm
shot down in
http://groups.google.com/groups?&thr...nso-cl.aol.com

"Newton vs Einstein"
http://redshift.vif.com/JournalFiles...F/V05n1lut.pdf

Dirk Vdm

says...

We assume that a rocket is moving at speed v = 0.866 c
relative to the Earth...

Let's pick an event E, in this case an explosion,
that takes place on a planet, at rest relatively
to the Earth. The planet is situated at a distance xE
form the Earth, and the explosion is observed after
a time interval tE, hence the Earth coordinates of
the event E are (xE, tE), and the corresponding
rocket coordinates are (xE', tE').

This might not be important, but if the Earth
coordinates of the explosion are (xE,tE), that does
not mean that the explosion is *observed* after
a time interval tE. The explosion will not be
observed until a time tE + xE/c, because the
light has to travel from the explosion to the Earth.

After a time interval T, the rocket will be at
a distance v*T from the Earth, hence the distance
between the rocket and the event E is D = xE-vT.
In the rocket frame, the corresponding distance
is D' = D/gamma

No, that's not what relativity says. In the frame of the
rocket, the rocket is not moving, so the distance
between the rocket and the event is *always* xE',
which is

xE' = gamma (xE - v tE)

the time T is irrelevant.

Length contraction D' = D/gamma cannot be used in this
circumstance. Length contraction can only be used in the
following very special circumstances:

If two objects are at rest in the frame of the
Earth, and the distance between the objects is D, as measured
in the frame of the Earth, then the distance between the
objects is D' = D/gamma in the frame of the rocket.

If two objects are at rest in the frame of the
rocket, and the distance between the objects is D', as measured
in the frame of the rocket, then the distance between the
objects is D = D'/gamma in the frame of the Earth.

So length contraction is about the distance between two *objects*
that are at rest relative to each other. It is not used to compute
the distance between an object and an event.

Similarly, time dilation can only be used in very special circumstances:

If two events take place at the same location, as measured
in the frame of the Earth, and the time between the events
is T, as measured in the frame of the Earth, then the time
between the events will be T' = gamma T, as measured in the
frame of the rocket.

If two events take place at the same location, as measured
in the frame of the rocket, and the time between the events
is T', as measured in the frame of the rocket, then the time
between the events will be T = gamma T', as measured in the
frame of the Earth.

In all other circumstances, you have to use the full Lorentz
transformations to compute the times and locations of events
in the two different frames.

--
Daryl McCullough
Ithaca, NY

Moronic crackpot!

Daryl, you didn't follow the demonstration, especially:

3) Let's take T = 9.608 years. Then
D = 3-0.866*9.608 = -5.32 ly
D' = D/gamma = -5.32/2 = -2.66 ly
Of course, T' = 9.608/2 = 4.804 years.

Let's notice that those results have been obtained
by applying "Lorentzian" formulae.

Now let's use the Lorentz (or rather Einstein)
transformations:

t' = gamma(t-vx/c^2) and x' = gamma(x-vt)

Using the above notation, we get

tE' = gamma(tE-v*xE/c^2), thus
= 2(5-0.866*3) = 4.804 years

D' = gamma(xE-v*tE)
= gamma(3-0.866*5) = -2.66 ly,
which is exactly the value obtained in example 3,
by using T = tE'*gamma = 9.608 years.

Take a little more time!

Marcel

wrote in message ups.com...
Daryl, you didn't follow the demonstration, especially:

But you were wrong before you even started, silly.
You still don't understand coordinates and events.

You talk about
"the distance between the rocket and event E"
but you should say
"the distance between the rocket and the planet"

You say:
"Let's notice that T' = T/gamma. This is always the
case, as the ratio T/T' depends on the velocity of
the rocket, not on its position."
but this is clearly not always the case. It is only the
case if T' happens to be a time interval between two
*two physical ticks of the rocket clock*, and if T is
the same time between those same rocket ticks, but
now measured on the Earth clock. But that was not
the way you defined T' and T. In stead, you defined
T as the time measured on the *Earth clock* between
the tick of departure of the rocket, and another tick
on the Earth clock, namely the tick that is simultaneous
with the event where the rocket is at distance vT as
seen in the Earth frame. So you are talking about a
proper time on the *Earth clock*, so you should be
using the expression T' = T*gamma.
Remember, Marcel? Many of us explained that to
you just as many times as the number of times you
miserably failed to understand it. Difficult, isn't it?
Shouldn't you turn your attention to collecting poodle
droppings or something?


3) Let's take T = 9.608 years. Then
D = 3-0.866*9.608 = -5.32 ly
D' = D/gamma = -5.32/2 = -2.66 ly
Of course, T' = 9.608/2 = 4.804 years.

Let's notice that those results have been obtained
by applying "Lorentzian" formulae.

But you don't even understand the concept of
coordinates. What could you possible do with
advanced stuff like that?


Now let's use the Lorentz (or rather Einstein)
transformations:

t' = gamma(t-vx/c^2) and x' = gamma(x-vt)

Using the above notation, we get

tE' = gamma(tE-v*xE/c^2), thus
= 2(5-0.866*3) = 4.804 years

D' = gamma(xE-v*tE)
= gamma(3-0.866*5) = -2.66 ly,
which is exactly the value obtained in example 3,
by using T = tE'*gamma = 9.608 years.

Take a little more time!

Take *much* more time.

Dirk Vdm

:
Lorentz transforms physical incoherence
_______________________________________

If you can't understand a simple coordinate transformation after
years of explanations, you need to find a hobby that doesn't
involve science. You need to be realistic and accept your limitations,
unless you just enjoy drawing attention to your deficiencies.

In article . com,
says...

Daryl, you didn't follow the demonstration, especially:

3) Let's take T = 9.608 years. Then
D = 3-0.866*9.608 = -5.32 ly
D' = D/gamma = -5.32/2 = -2.66 ly
Of course, T' = 9.608/2 = 4.804 years.

Let's notice that those results have been obtained
by applying "Lorentzian" formulae.

Now let's use the Lorentz (or rather Einstein)
transformations:

t' = gamma(t-vx/c^2) and x' = gamma(x-vt)

Using the above notation, we get

tE' = gamma(tE-v*xE/c^2), thus
= 2(5-0.866*3) = 4.804 years

D' = gamma(xE-v*tE)
= gamma(3-0.866*5) = -2.66 ly,
which is exactly the value obtained in example 3,
by using T = tE'*gamma = 9.608 years.

Take a little more time!

Marcel

Another SR worshipper!

Like always, you are "parroting" what you read in textbooks, you can't
think by yourself. You are a typical example of those religious SR
crackpots
whose mind closes when they are confronting with a dissident opinion.
If you want to be taken seriously, try at least to refute my
demonstration
of the LT incoherence, or at least to explain why gamma(xE-v*tE) =
(xE-vT)/gamma.
is wrong, according to your faithful follower thinking.

Don't forget that when xE=3, v=0.866, tE=5, T=9.608 (T is obtained from
the LT),
one gets 2(3-0.866*5) = (3-0.866*9.608)/2 , or -2.66 = -2.66 !
Use your brain, not your prejudices!

Of course, abuse (your specialty) is easier.

Marcel Luttgens