"Bilge" wrote in message
...
Harold Ensle:

"Bilge" wrote in message
ue-al.net...

[........lies snipped.....]

The postulates lead to the lorentz transforms because those
transforms fulfill the requirement that the laws of physics are the
same
in all inertial frames. Your choice of arguments here is reduced to
one of
the following: (A) You do not accept that the laws of physics are the
same
in all inertial frames, or (B) You do not accept that the lorentz
transforms fulfill that requirement. I just proved that the lorentz
transforms _do_ fulfill that requirement in another thread by deriving
them based upon the assumption that the laws of physics were the same
in
all inertial frames, leaving you with (A) as your only objection. I'm
willing to accept (A) as an argument for a different theory having
different postulatess, but you have no evidence to support that
hypothesis.

Actually, since SR is self contradictory, it then follows that (A) is
wrong.

I'll note that you think the geometry of the conic sections is
inconsistent.

Gad...you are so stupid. I didn't say this! I said (A)!!!! can't
you even understand your own posts?

That is: The absolute rest frame must have some physical significance.
The fact that it has not yet been detected (except possibly by
Silvertooth)
means nothing, since, it could be that the correct experiment simply
has never been done.

If an absolute rest frame existed, it would have physical
significance. If you find an experiment that depends upon
that frame, let me know.

[...]
The acceleration here, since it directly correlates to the
_relative_ velocity of the Lorentz Transformations is a
_relative_ acceleration.

No, it doesn't harold

The acceleration in equation 3 is not relative?
This is a trivial point......again not even controversial.

I've told you precisely how to apply that equation.
I don't care what semantics games you want to play.
Either tell me what's wrong with applying as I told
you, or shut up.

And you snipped everything that follows because you
have no reply.

Face it, you screwed up your previous post
(and this one) royally.

H.Ellis Ensle

"Paul B. Andersen" wrote in message ...

[snip]

So let's see what the equation really has to say about your scenario.
I have run it throught a computer program doing the integration
numerically.

Home twin A, coordinates x,t.
Travelling twin B, coordinates x',t'.

B is accelerating away from A for 1 LY i A's frame,
reversing the direction of the acceleration, until he again
is 1 LY from home in A's frame.
Reversing his acceleration again, to break.
The acceleration is c per year, which happens to be ca. 1g.

In A's inertial frame:

t t' dt'/dt v/c x
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
6.9 5.2 1.00 -0.03 0.00

In B's accelerated frame:

t' t dt/dt' v/c x'
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
5.2 6.9 1.00 0.04 0.00

The twins will obviously agree on the proper times of
their clocks when reunited.
A ages 6.9 years, B ages 5.2 years during the journey.


The equation seems to work just fine.

Of course they work fine ;-)
Arbitrarily accelerated motion:
http://users.pandora.be/vdmoortel/di...eleration.html
Travelling twin B, time coordinate T
t(T) = c/a sinh(aT/c)
T(t) = c/a argsinh(at/c)
Your case:
a/c = 1
4 phases: acceleration, deceleration acceleration, deceleration
4*argsinh(6.90/4) = 5.25
4*sinh(5.25/4) = 6.89
Picture of half trip:
http://users.pandora.be/vdmoortel/di...AccelDecel.gif

Dirk Vdm

"Dirk Van de moortel" wrote in message
...

[snip]

Of course they work fine ;-)
Arbitrarily accelerated motion:
http://users.pandora.be/vdmoortel/di...eleration.html
Travelling twin B, time coordinate T
t(T) = c/a sinh(aT/c)
T(t) = c/a argsinh(at/c)
Your case:
a/c = 1
4 phases: acceleration, deceleration acceleration, deceleration
4*argsinh(6.90/4) = 5.25
4*sinh(5.25/4) = 6.89
Picture of half trip:
http://users.pandora.be/vdmoortel/di...AccelDecel.gif

with slightly different notation of course:
T in text == t' on gif picture
6.90 in text == 4T on gif picture

Dirk Vdm

"Dirk Van de moortel"
escribió en el mensaje ...

"Paul B. Andersen" wrote in message
...

[snip]

So let's see what the equation really has to say about your scenario.
I have run it throught a computer program doing the integration
numerically.

Home twin A, coordinates x,t.
Travelling twin B, coordinates x',t'.

B is accelerating away from A for 1 LY i A's frame,
reversing the direction of the acceleration, until he again
is 1 LY from home in A's frame.
Reversing his acceleration again, to break.
The acceleration is c per year, which happens to be ca. 1g.

In A's inertial frame:

t t' dt'/dt v/c x
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
6.9 5.2 1.00 -0.03 0.00

In B's accelerated frame:

t' t dt/dt' v/c x'
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
5.2 6.9 1.00 0.04 0.00

The twins will obviously agree on the proper times of
their clocks when reunited.
A ages 6.9 years, B ages 5.2 years during the journey.


The equation seems to work just fine.

Of course they work fine ;-)
Arbitrarily accelerated motion:
http://users.pandora.be/vdmoortel/di...eleration.html
Travelling twin B, time coordinate T
t(T) = c/a sinh(aT/c)
T(t) = c/a argsinh(at/c)
Your case:
a/c = 1
4 phases: acceleration, deceleration acceleration, deceleration
4*argsinh(6.90/4) = 5.25
4*sinh(5.25/4) = 6.89
Picture of half trip:
http://users.pandora.be/vdmoortel/di...AccelDecel.gif

Dirk Vdm

Which would be perfect if you calculated the ellapsed time for the Earth
twin A from the PoV of the traveller twin and would show that it coincides
with the ellapsed time as measured by A herself.

In the previous thread of this name I asked some questions
which were never answered, so I would like to try again.
I will discuss also a few of the previous replies.

First, concerning some basic requirements of special relativity.
Mathematically, it is defined by the Lorentz Transformations:

x'=g(x-vt) (1)
t'=g(t-vx/c^2) (2)

where g=1/sqrt(1-v^2/c^2)

(x is position, t is time, c is the speed of light
and v is the relative velocity)

Note that the Lorentz Transformations are based solely on
_relative_ velocity. We can derive from these a general
expression that relates the passage of time for two observers:

t'=integral from t_1 to t_2(sqrt(1-v(t)^2/c^2))dt (3)

This can be found in most relevant textbooks such as Moller
or Jackson. Note that this equation incorporates acceleration.
It is important to understand to which acceleration it refers.
The acceleration here, since it directly correlates to the
_relative_ velocity of the Lorentz Transformations is a
_relative_ acceleration. That is, it is the change in
_relative_ velocity over time. It is a purely kinematic value.
It tells us _nothing_ about what forces are present. It tells us
only that the _relative_ velocity between the two observers
is changing.

Now I want to determine the time that has passed for both
twins in the twin paradox. First for the stay-at-home one
can use equation 3. Note that with any non-zero velocity
the integrand is always less than one, therefore the
stay-at-home will see the travelling twin's passage of time
to be less than his own by:

tt=ts/k.
(4)

where tt is the travelling twin's time, ts is the stay-at-home's
time, and k is some value greater than one.
Now the travelling twin has accerated during the trip, so
since the Lorentz transformations are only valid in
an inertial frame, he can't use them.

SO the question is: What equation can the travelling twin
use?

If the travelling twin uses the Lorentz transformations, he
will derive the very same differential form as equation 3.
Of course, if he applies it, he will get:

ts=tt/k
(5)

thus tt=ts*k which is contradictory to equation (4). This is
the mathematical statement of the twin paradox.
Now since equation 3 is the time relation derived in
correspondence to the Lorentz transformations for both
observers, it is evident that the solution of the contradiction
cannot come from the Lorentz transformations. Since
these are the statements of SR, it thus follows that the
twin paradox cannot be resolved at all in the context of SR.

I am not claiming here that there is an ultimate contradiction.
I have shown here only that there is a contradiction that
does arise if SR is used by itself.

Now, in regards to an equation that will work for the
travelling twin. In the last thread I received only one
candidate (from Andersen).

t' = integral from t1 to t2(sqrt(1-v(t)^2/c^2)(1 + ax/c^2))dt (6)
where a is the acceleration of the x-t frame.

In this form, x should actually read x(t), because it changes
over time. Naturally, all variables are as measured in the
accelerating frame.

Since equation 3 is the time dilatation
derived from the Lorentz transformations, this equation is
clearly not derived, or derivable from SR alone.
Because, if it were, it would have to be identical to
equation 3.

Note that equation 3 is only applicable when v is constant
and thus a=0 between t1 and t2. When you fill in a=0 in
equation 6, you get equation 3.

Now, if this equation has a legitimate source, does it
solve the paradox? Well...apparently, it doesn't even do that.
Note that to solve the paradox, this equation must provide
for a round trip a solution for the travelling twin such that:

ts=tt*k (7)

So that both twins will agree on their reunion. Thus at
some point in the travelling twin's trip he must see the
stay-at-home's time accumulating faster than his own.

Imagine a trip where the travelling twin accelerates for the
first half of his outward journey and then deccelerates
for the rest of the way, and then does the same process to
return home.

First 'a' is positive and then 'a' is negative when 'x' is larger.

During the first half of the outward journey, the travelling twin
feels an outward acceleration, while he sees the stay-at-home
twin move in the opposite direction. This means that a and x
have opposite signs (ax 0) in this phase.
The next phase, the accelerating force is reversed and points
in the same direction as the stay-at-home twin, so a and x
have the same sign (ax 0).
So the term ax in equation 6 is positive for the 'far away' part
of the journey, where the absolute value of x is the greatest.

When you apply equation 6 correctly, with the right sign of
the term ax, you will find that it does resolve the paradox.

And when you find a different result, you'd better ask where
you went wrong yourself, instead of blaming the formula or SR.


H.Ellis Ensle


Benno Muilwijk

"Cesar Sirvent" wrote in message s...

"Dirk Van de moortel"
escribió en el mensaje ...

"Paul B. Andersen" wrote in message
...

[snip]

So let's see what the equation really has to say about your scenario.
I have run it throught a computer program doing the integration
numerically.

Home twin A, coordinates x,t.
Travelling twin B, coordinates x',t'.

B is accelerating away from A for 1 LY i A's frame,
reversing the direction of the acceleration, until he again
is 1 LY from home in A's frame.
Reversing his acceleration again, to break.
The acceleration is c per year, which happens to be ca. 1g.

In A's inertial frame:

t t' dt'/dt v/c x
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
6.9 5.2 1.00 -0.03 0.00

In B's accelerated frame:

t' t dt/dt' v/c x'
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
5.2 6.9 1.00 0.04 0.00

The twins will obviously agree on the proper times of
their clocks when reunited.
A ages 6.9 years, B ages 5.2 years during the journey.


The equation seems to work just fine.

Of course they work fine ;-)
Arbitrarily accelerated motion:
http://users.pandora.be/vdmoortel/di...eleration.html
Travelling twin B, time coordinate T
t(T) = c/a sinh(aT/c)
T(t) = c/a argsinh(at/c)
Your case:
a/c = 1
4 phases: acceleration, deceleration acceleration, deceleration
4*argsinh(6.90/4) = 5.25
4*sinh(5.25/4) = 6.89
Picture of half trip:
http://users.pandora.be/vdmoortel/di...AccelDecel.gif

Dirk Vdm

Which would be perfect if you calculated the ellapsed time for the Earth
twin A from the PoV of the traveller twin and would show that it coincides
with the ellapsed time as measured by A herself.

.... which is what Paul did numerically :-)

Dirk Vdm

Harold Ensle:


Gad...you are so stupid. I didn't say this! I said (A)!!!! can't
you even understand your own posts?

I do understand my own posts, harold, so let's just look at what I
wrote in (A):

(A) You do not accept that the laws of physics are the same
in all inertial frames,

Since this statement also gives the lorentz transforms known as
rotations:

x' = x cos(A) + y sin(A)
y' = y cos(A) - y sin(A)

I have to assume you mean that this coordinate transformation also
is invalid, since you have given no other theory in which the laws
of physics would be identical in inertial frames which differ by a
rotation in the x-y plane but would differ in frames which would be
rotations in the x-t plane:

x' = x cosh(A) - t sinh(A)
t' = t cosh(A) - x sinh(A)

The point here harold, is that you don't understand the physics in
special relativity. All you know are that some equations exist for
transforming coordinates, but you don't know what they mean or how
they are derived in any way doesn't appear to be some variation on
lorentz' original derivation.

I've told you precisely how to apply that equation.
I don't care what semantics games you want to play.
Either tell me what's wrong with applying as I told
you, or shut up.

And you snipped everything that follows because you have no reply.

No, I snipped it because there is no point in addressing numerous
objections based upon the same misunderstanding. Surely you can resolve
one of those points at a time. I'll address each and every one in
turn, upon resolving the ones preceeding it, if that's what you wish.
I'm only going to address one thing at a time, however, so that you
focus on it and don't digress.

Face it, you screwed up your previous post (and this one) royally.

You always say something to that effect, so you should put it in
your signature block.

"Dirk Van de moortel"
escribió en el mensaje ...

"Cesar Sirvent" wrote in message
s...

"Dirk Van de moortel"
escribió en el mensaje
...

"Paul B. Andersen" wrote in message
...

[snip]

So let's see what the equation really has to say about your
scenario.
I have run it throught a computer program doing the integration
numerically.

Home twin A, coordinates x,t.
Travelling twin B, coordinates x',t'.

B is accelerating away from A for 1 LY i A's frame,
reversing the direction of the acceleration, until he again
is 1 LY from home in A's frame.
Reversing his acceleration again, to break.
The acceleration is c per year, which happens to be ca. 1g.

In A's inertial frame:

t t' dt'/dt v/c x
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
6.9 5.2 1.00 -0.03 0.00

In B's accelerated frame:

t' t dt/dt' v/c x'
[Y] [Y] [LY]
0.0 0.0 1.00 0.00 0.00
[snip]
5.2 6.9 1.00 0.04 0.00

The twins will obviously agree on the proper times of
their clocks when reunited.
A ages 6.9 years, B ages 5.2 years during the journey.


The equation seems to work just fine.

Of course they work fine ;-)
Arbitrarily accelerated motion:
http://users.pandora.be/vdmoortel/di...eleration.html
Travelling twin B, time coordinate T
t(T) = c/a sinh(aT/c)
T(t) = c/a argsinh(at/c)
Your case:
a/c = 1
4 phases: acceleration, deceleration acceleration, deceleration
4*argsinh(6.90/4) = 5.25
4*sinh(5.25/4) = 6.89
Picture of half trip:
http://users.pandora.be/vdmoortel/di...AccelDecel.gif

Dirk Vdm

Which would be perfect if you calculated the ellapsed time for the Earth
twin A from the PoV of the traveller twin and would show that it
coincides
with the ellapsed time as measured by A herself.

... which is what Paul did numerically :-)

Dirk Vdm

So the analytical solution must be quite hard? In any case, where is dt_A /
dt_B ? I am curious.

John Anderson:
Bilge wrote:

I've already explained to you that you can apply that to
both twins. Both twins perform the calculation with respect
to the same inertial frame in which they started.

That unduly restricts the answer. It doesn't matter whichframe you
use to do the calculation. The result is Lorentz invariant.

Sure, but harold provided the restriction. He insists that the equation
has to apply to both twins equivalently _and_ that the acceleration be
considered only relative, to try and find a semantics loophole to exploit.
The simplest way to avoid the semantics arguement was to take the starting
frame to be inertial an put both twins in it and then compute the elapsed
time of each twin relative to the starting frame, which is inertial by
definition.

The inertial
frame in which both twins begin, is the frame from which their
proper times are calculated. You simply insist on using equations
it incorrectly. Using equations correctly isn't new to relativity,
harold. If you apply newtonian mechanics incorrectly, you will
get non-sense for an answer, too.


Yes, that's the real point of Ensle's error. He's using equationsthat are
correct and assigning the wrong meaning to the symbols
in the equations. He wrote down valid equations and then
made incorrect claims about how the variables in those equations
are related to measurements that are made in experiments.

Right. I simply provided the means to render his objections moot
rather than try to convice him of anything more general. He seems
to have difficulty if the meanings of the variables are not what
he thinks they are.

"Benno Muilwyk" wrote in message ...
In the previous thread of this name I asked some questions
which were never answered, so I would like to try again.
I will discuss also a few of the previous replies.

First, concerning some basic requirements of special relativity.
Mathematically, it is defined by the Lorentz Transformations:

x'=g(x-vt) (1)
t'=g(t-vx/c^2) (2)

where g=1/sqrt(1-v^2/c^2)

(x is position, t is time, c is the speed of light
and v is the relative velocity)

Note that the Lorentz Transformations are based solely on
_relative_ velocity. We can derive from these a general
expression that relates the passage of time for two observers:

t'=integral from t_1 to t_2(sqrt(1-v(t)^2/c^2))dt (3)


[snip]


t' = integral from t1 to t2(sqrt(1-v(t)^2/c^2)(1 + ax/c^2))dt (6)
where a is the acceleration of the x-t frame.

In this form, x should actually read x(t), because it changes
over time. Naturally, all variables are as measured in the
accelerating frame.

Since equation 3 is the time dilatation
derived from the Lorentz transformations, this equation is
clearly not derived, or derivable from SR alone.
Because, if it were, it would have to be identical to
equation 3.

Note that equation 3 is only applicable when v is constant
and thus a=0 between t1 and t2. When you fill in a=0 in
equation 6, you get equation 3.

Hm, I do't go along with that. Eq. 3 is valid for any v, provided
t is the time coordinate used by an inertial observer and t' is the
time read on an arbitrarily accelerated clock, that has velocity
v(t) at time t according to the inertial observer. This velocity
can be any function since the clock can be arbitrarily
accelerated.

Eq. 6 is valid provided t is the time kept by an arbitrarily
accelerated observer and t' is the proper time of the
inertial observer.
Actually, keeping the same convention as in eq 3, eq. 6
should be
t = integral from t1' to t2'(sqrt(1-v'(t')^2/c^2)(1 + ax'/c^2))dt' (6')
where a=0 would again not imply v'(t') = 0.

Dirk Vdm