A Symmetric Twins Conundrum
xilog
don't understand, which seems on the face of it to involve strange
consequences of the special and general theories of relativity, and I
would appreciate it if anyone can enlighten me on what the theories
really say happens in these circumstances.
Scenario
The traditional "twins paradox" is asymmetric. One of the twins travels
on a geodesic and the other does not, and the other therefore ages less
in the process. In this case, we arrange for the two twins to undertake
symmetrically opposite journey's which are therefore identical in
relation to time dilation from the point of view of an inertial third
person observing their journeys.
We start with the two twins and an independent observer all at rest
together relative to some inertial frame. All three have clocks which
they synchronise together. The two twins accelerate rapidly to near the
speed of light in opposite directions. They then travel at uniform
velocity for a good long time before turning round, coming back
together at the same speed and decelerating to a stop as they once
again meet.
Analysis
This is my half-baked misunderstanding of what goes on, I'm inviting
people to come up with the correct analysis.
The main part of these journeys is covered by the special theory, the
brief periods of acceleration are covered by the general theory. From
the predictions of special relativity together with considerations of
symmetry we come to some strange ideas about what the general theory
must say about the behaviour of clocks during periods of acceleration.
Considerations of symmetry tell us that the clocks of the two twins
will agree when they meet after their journeys. Special relativity
tells us that each twin observes the other's clock running slowly
during the periods of uniform motion. Ergo, during the periods of
acceleration they must observe the other's clock as running fast.
The periods of uniform motion can be changed arbitrarily without making
any change to the periods of acceleration. If this is done the time
lost during these period will vary, and the time gained during the
periods of acceleration must increase correspondingly for the clocks to
match when they meet up.
Hence the general theory must predict a speed up during acceleration
which is not determined by the amount of acceleration and its duration.
What else could it depend upon? What else does it depend on? What's
wrong with this partial analysis?
Roger Jones
Mike Fontenot
square brackets):
>
> The main part of these journeys is covered by the special theory, the
> brief periods of acceleration are covered by the general theory.
There is no need for general relativity, if there are no large masses
present. Special relativity is all that is needed.
> Hence the [Special] theory must predict a speed up during acceleration
> which is not [SOLELY] determined by the amount of acceleration and its duration.
>
> What else could it depend upon?
The same issue arises in the standard asymetrical twin paradox:
the abrupt increase in the age of the home twin, according to the
traveling twin, during the traveler's turnaround depends on the
acceleration (or, in the instantaneous turnaround case, on the
change in velocity of the traveler), BUT ALSO on their separation.
I quantified this effect in a previous posting. The equation in
that posting applied to an accelerating twin and a stay-at-home
twin. But it can be adapted to handle the symetrical case also.
Here is that posting:
________________________________________________________________
Years ago, I derived a simple equation that
relates the current ages of the twins, ACCORDING
TO EACH TWIN. Over the years, I have found it to
be very useful. Originally, I inferred the equation
while staring at a Minkowski diagram. Then later, I
derived it formally from the Lorentz equations.
To save writing, I write "the
current age of a distant object" (where the
"distant object" is the stay-at-home twin) as
the "CADO". The CADO has a value for each age t of
the traveling twin, written CADO(t). The traveler
and the stay-at-home twin come to DIFFERENT conclusions
about CADO(t), at any given age t of the traveler.
Denote the traveler's conclusion as CADO_T(t), and
the stay-at-home twin's conclusion as CADO_H(t).
(And in both cases, remember that CADO(t) is the age of
the home twin, and t is the age of the traveler).
My simple equation says that
CADO_T(t) = CADO_H(t) - L*v/(c*c),
where
L is their current distance apart, in lightyears,
according to the home twin,
and
v is their current relative speed, in lightyears/year,
according to the home twin. v is positive
when the twins are moving apart.
(Although the dependence is not shown explicitly
in the above equation, the quantities L and v are
to be considered functions of t, the age of the
traveler).
The factor (c*c) has value 1 for these units, and
is needed only to make the dimensionality correct.
The equation explicitly shows how the home twin's
age will change abruptly (according to the traveler,
not the home twin), whenever the relative
speed changes abruptly.
For example, suppose the home twin believes that she
is 40 when the traveler is 20, immediately before
he turns around. So CADO_H(20-) = 40. (Denote his
age immediately before the turnaround as t = 20-,
and immediately after the turnaround as t = 20+.)
Suppose they are 30 ly apart (according to the home
twin), and that their relative speed is +0.9 ly/y (i.e.,
0.9c), when the traveler's age is 20-. Then the traveler
will conclude that the home twin is
CADO_T(20-) = 40 - 0.9*30 = 13 years old
immediately before his turnaround.
Immediately after his turnaround (assumed here
to occur in zero time), their relative speed
is -0.9 ly/y.
The home twin concludes that their distance apart
doesn't change during the turnaround: it's
still 30 ly.
And the home twin concludes that
neither of them ages during the turnaround,
so that CADO_H(20+) is still 40.
But according to the traveler,
CADO_T(20+) = 40 - (-0.9)*30 = 67 years old,
so he concludes that his twin ages 54 years
during his instantaneous turnaround.
In the usual traveling twin scenario, the sudden
change in speed is a negative change: i.e., the
relative speed decreases (becomes more negative, or
less positive), changing from +V to -V (with the
convention that v is positive when the traveler is
moving away from his twin). But note that, if the
sudden speed change is positive, the CADO equation
says that the traveler will then conclude that
his twin suddenly gets YOUNGER, not older.
Since the relative speed v can vary between -1 and +1
lightyear/year, an instantaneous speed change can
be as large as -2 or +2 lightyears/year. So the
CADO equation says that CADO_T can instantaneously
increase or decrease by as much, in years, as
twice the separation L, in lightyears.
For example, if the twins are 30 lightyears apart,
(according to the home twin), then the home twin's
age (according to the traveling twin) can
instantaneously change (positively or negatively) by
as much as 60 years.
The CADO equation works for arbitrary accelerations,
not just the idealized instantaneous speed changes
assumed above. When the separation is sufficiently
great, even 1-g accelerations can produce rapid
changes (positive and negative) in the current age of
the home twin (according to the traveler). The home
twin's maximum (in magnitude) rate of ageing is greater
than the traveler's rate of ageing by a factor
approximately numerically equal to their separation L,
in lightyears. If the traveler is accelerating TOWARD
the home twin, she will be getting older at that
(maximum) rate. If the traveler is accelerating AWAY
from her, she will be getting younger at that (maximum)
rate.
The home twin does not agree with the traveler's
conclusions about their corresponding ages. She
certainly doesn't perceive that the progression of her
own life is in any way affected by the traveler's
accelerations. But the differing conclusions are equally
valid: neither twin is "more correct" than the other,
and neither twin can adopt the other's conclusions
without contradicting their own measurements.
I've got an example with 1-g accelerations
on my web page:
http://home.comcast.net/~mlfasf
The derivation of the CADO equation is given in my paper
"Accelerated Observers in Special Relativity",
PHYSICS ESSAYS, December 1999, p629.
Mike Fontenot
Sorcerer
"xilog" <rb...@rbjones.com> wrote in message
news:1156872280....@i42g2000cwa.googlegroups.com...
It's not your analysis. There is something wrong with the theory.
http://www.androcles01.pwp.blueyonder.co.uk/Rocket/Rocket.htm
Androcles
Russell
> This is a variant on the "twins paradox". It is a situation which I
> don't understand, which seems on the face of it to involve strange
> consequences of the special and general theories of relativity, and I
> would appreciate it if anyone can enlighten me on what the theories
> really say happens in these circumstances.
Did you read the FAQ? See
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
The link to the "General Relativity" explanation is directly
relevant to your question, and also the "Doppler explanation"
will perhaps help you be more careful to define what you
mean by *observe*.
Also I recommend reading the other SR pages, particularly
the one explaining that SR *can* deal with accelerations.
(The distinction you make here between GR and SR is not
the one that most physicists make; most physicists would
call your scenario simply SR because it does not involve
curved spacetime.)
>
> Scenario
>
> The traditional "twins paradox" is asymmetric. One of the twins travels
> on a geodesic and the other does not, and the other therefore ages less
> in the process. In this case, we arrange for the two twins to undertake
> symmetrically opposite journey's which are therefore identical in
> relation to time dilation from the point of view of an inertial third
> person observing their journeys.
>
> We start with the two twins and an independent observer all at rest
> together relative to some inertial frame. All three have clocks which
> they synchronise together. The two twins accelerate rapidly to near the
> speed of light in opposite directions. They then travel at uniform
> velocity for a good long time before turning round, coming back
> together at the same speed and decelerating to a stop as they once
> again meet.
>
> Analysis
>
> This is my half-baked misunderstanding of what goes on, I'm inviting
> people to come up with the correct analysis.
>
> The main part of these journeys is covered by the special theory, the
> brief periods of acceleration are covered by the general theory.
Or, all by the special theory if you do it right.
From
> the predictions of special relativity together with considerations of
> symmetry we come to some strange ideas about what the general theory
> must say about the behaviour of clocks during periods of acceleration.
Symmetry is already implicit in SR theory, it doesn't
have to be added as a separate principle here.
>
> Considerations of symmetry tell us that the clocks of the two twins
> will agree when they meet after their journeys. Special relativity
> tells us that each twin observes the other's clock running slowly
> during the periods of uniform motion. Ergo, during the periods of
> acceleration they must observe the other's clock as running fast.
Just as an aside, you appear to have neglected Doppler
here -- note, when the twins *approach* each other there
is a blue shift and the clocks (through a telescope) will
actually appear to be running *faster*. Just, not as much
faster as the classical theory would have predicted.
Also, you have to be *really* careful when talking about
the observations of periods of acceleration, because they
are happening far away. When the observing twin actually
sees the observed twin accelerate, he will no longer be
accelerating himself (because the light has taken some
time to get to him). The FAQ on the Doppler explanation
does a good job at mapping this all out for you.
>
> The periods of uniform motion can be changed arbitrarily without making
> any change to the periods of acceleration. If this is done the time
> lost during these period will vary, and the time gained during the
> periods of acceleration must increase correspondingly for the clocks to
> match when they meet up.
>
> Hence the general theory must predict a speed up during acceleration
> which is not determined by the amount of acceleration and its duration.
>
> What else could it depend upon? What else does it depend on? What's
> wrong with this partial analysis?
It also depends on the distance apart. In GR terms you
could say it depends on the pseudo-gravitational *potential*.
Recall from Physics 1 that gravitational potential energy is
mgh in the (approximately uniform) field at the earth's surface.
Divide by m and you get the potential -- equal parts distance
and acceleration.
>
> Roger Jones
Paul Cardinale
Distance.
Paul Cardinale
Sorcerer
"Mike Fontenot" <mlf...@comcast.net> wrote in message
news:44F489B9...@comcast.net...
| xilog wrote: (with my [mlf] editorial comments and changes between
| square brackets):
| >
| > The main part of these journeys is covered by the special theory, the
| > brief periods of acceleration are covered by the general theory.
|
| There is no need for general relativity, if there are no large masses
| present. Special relativity is all that is needed.
Prove it.
|
| > Hence the [Special] theory must predict a speed up during acceleration
| > which is not [SOLELY] determined by the amount of acceleration and its
duration.
| >
| > What else could it depend upon?
|
| The same issue arises in the standard asymetrical twin paradox:
| the abrupt increase in the age of the home twin, according to the
| traveling twin, during the traveler's turnaround depends on the
| acceleration (or, in the instantaneous turnaround case, on the
| change in velocity of the traveler), BUT ALSO on their separation.
|
| I quantified this effect in a previous posting. The equation in
| that posting applied to an accelerating twin and a stay-at-home
| twin. But it can be adapted to handle the symetrical case also.
| Here is that posting:
| ________________________________________________________________
|
| Years ago, I derived a simple equation that
| relates the current ages of the twins, ACCORDING
| TO EACH TWIN. Over the years, I have found it to
| be very useful.
Oh sure... as useful as a tit on a bull. You often
go on long journeys and come back younger than
your twin, obviously. Does it piss your twin off to
be 75 years old while you are only 74.9999?
Originally, I inferred the equation
| while staring at a Minkowski diagram. Then later, I
| derived it formally from the Lorentz equations.
Yes, but what you cannot do is derive the cuckoo equations.
|
| To save writing,
Noooo.... we don't want you to save writing, I want to see
you derive the cuckoo equations. I'll save your writing
for you.
[snip crap]
Androcles
Sorcerer
"Russell" <rus...@mdli.com> wrote in message
news:1156877762....@74g2000cwt.googlegroups.com...
| xilog wrote:
| > This is a variant on the "twins paradox". It is a situation which I
| > don't understand, which seems on the face of it to involve strange
| > consequences of the special and general theories of relativity, and I
| > would appreciate it if anyone can enlighten me on what the theories
| > really say happens in these circumstances.
|
| Did you read the FAQ?
See
|
|
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
Get your head out of you arse and see
http://www.androcles01.pwp.blueyonder.co.uk/Baez/TwinParadox.htm
Fuckwit.
Androcles
guido
> This is a variant on the "twins paradox".
(...)
> The traditional "twins paradox" is asymmetric. One of the twins travels
> on a geodesic and the other does not, and the other therefore ages less
> in the process. In this case, we arrange for the two twins to undertake
> symmetrically opposite journey's which are therefore identical in
> relation to time dilation from the point of view of an inertial third
> person observing their journeys.
(...)
You announce it nicely but then seem to stick to the classical case, as far
as I can see...
> The main part of these journeys is covered by the special theory, the
> brief periods of acceleration are covered by the general theory. From
not at all, as said already by others.
> the predictions of special relativity together with considerations of
> symmetry we come to some strange ideas about what the general theory
> must say about the behaviour of clocks during periods of acceleration.
GR is not needed for, nor 'affected' by this.
> Considerations of symmetry tell us that the clocks of the two twins
> will agree when they meet after their journeys. Special relativity
> tells us that each twin observes the other's clock running slowly
> during the periods of uniform motion. Ergo, during the periods of
> acceleration they must observe the other's clock as running fast.
OK.
> The periods of uniform motion can be changed arbitrarily without making
> any change to the periods of acceleration. If this is done the time
> lost during these period will vary, and the time gained during the
And so will be total rest time to be compared to.
> periods of acceleration must increase correspondingly for the clocks to
> match when they meet up.
Not at all, depends only upon type of accelerations, not upon uniform
movements before or after.
> Hence the general theory must predict a speed up during acceleration
> which is not determined by the amount of acceleration and its duration.
See previous.
> What else could it depend upon? What else does it depend on? What's
> wrong with this partial analysis?
Again, I don't see the point of the third twin for symmetry.
For a good understanding of the TP, including the 'Lorentz frame' and
'visual' aspects to be well distinguished, and the acceleration-within-SRT
aspect, have a dash at my brand new page
http://home.scarlet.be/~pin12499/paratwin.htm
regards
guido
Russell
> "Russell" <rus...@mdli.com> wrote in message
> news:1156877762....@74g2000cwt.googlegroups.com...
> | xilog wrote:
> | > This is a variant on the "twins paradox". It is a situation which I
> | > don't understand, which seems on the face of it to involve strange
> | > consequences of the special and general theories of relativity, and I
> | > would appreciate it if anyone can enlighten me on what the theories
> | > really say happens in these circumstances.
> |
> | Did you read the FAQ?
>
> See
> |
> |
> http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
Btw, some of the pages there have been edited within the past
year or so, and I'm glad to say they are even better now.
>
>
> Get your head out of you arse and see
> http://www.androcles01.pwp.blueyonder.co.uk/Baez/TwinParadox.htm
My head is already right where I want it, thank you, and
I *have* seen your page. Your mathematical arguments
(all two of them) are silly: (1) "If one of equation is correct,
they all are" -- well sure, but only an idiot would claim they
must all apply *simultaneously* once a coordinate system
is fixed, and (2) the 2AB/(t'A-tA) thing that shows you don't
know the difference between a distance of travel and a
vector displacement.
And your diagram, what is that supposed to prove? It
diagrams what a universe without time dilation would look
like. Assume no dilation, and damn who would have thought,
Stella and Terence meet up both the same age. I'm sorry,
such diagrams have been known for centuries -- the problem
is, they don't agree with experiment.
> Fuckwit.
> Androcles
Androcles, I am very sorry for the loss you recently suffered.
Beyond that, I really have nothing more to say to you. Please
try to stay on your side of the sandbox and I'll stay on mine.
Sorcerer
"guido" <br...@scarlet.be> wrote in message
news:QJudncDkne_...@scarlet.biz...
| "xilog" :
|
| > This is a variant on the "twins paradox".
| (...)
| > The traditional "twins paradox" is asymmetric. One of the twins travels
| > on a geodesic and the other does not, and the other therefore ages less
| > in the process. In this case, we arrange for the two twins to undertake
| > symmetrically opposite journey's which are therefore identical in
| > relation to time dilation from the point of view of an inertial third
| > person observing their journeys.
| (...)
|
| You announce it nicely but then seem to stick to the classical case, as
far
| as I can see...
Yes... what's wrong with that?
|
| > The main part of these journeys is covered by the special theory, the
| > brief periods of acceleration are covered by the general theory. From
|
| not at all, as said already by others.
"baa" is said by other sheep. Say "baa" for me.
|
| > the predictions of special relativity together with considerations of
| > symmetry we come to some strange ideas about what the general theory
| > must say about the behaviour of clocks during periods of acceleration.
|
| GR is not needed for, nor 'affected' by this.
That's right. GR is not needed. Fuckwits are not needed either.
|
| > Considerations of symmetry tell us that the clocks of the two twins
| > will agree when they meet after their journeys. Special relativity
| > tells us that each twin observes the other's clock running slowly
| > during the periods of uniform motion. Ergo, during the periods of
| > acceleration they must observe the other's clock as running fast.
|
| OK.
Is it ok? Well, it is what SR claims.
| > The periods of uniform motion can be changed arbitrarily without making
| > any change to the periods of acceleration. If this is done the time
| > lost during these period will vary, and the time gained during the
|
| And so will be total rest time to be compared to.
|
| > periods of acceleration must increase correspondingly for the clocks to
| > match when they meet up.
|
| Not at all, depends only upon type of accelerations, not upon uniform
| movements before or after.
Yes at all, time and clocks have fuck all to do with acceleration.
|
| > Hence the general theory must predict a speed up during acceleration
| > which is not determined by the amount of acceleration and its duration.
|
| See previous.
Previous: "Baa..."
|
| > What else could it depend upon? What else does it depend on? What's
| > wrong with this partial analysis?
|
| Again, I don't see the point of the third twin for symmetry.
You wouldn't see any time dilation either.
|
| For a good understanding of the TP, including the 'Lorentz frame' and
| 'visual' aspects to be well distinguished, and the acceleration-within-SRT
| aspect, have a dash at my brand new page
| http://home.scarlet.be/~pin12499/paratwin.htm
But that is where you offer no proof, sheep. For a good
understanding of fuckwittery, see my proof at my old web
page:
http://www.androcles01.pwp.blueyonder.co.uk/Rocket/Rocket.htm
|
| regards
| guido
Disregards,
Androcles
Sorcerer
| Sorcerer wrote:
| > "Russell" <rus...@mdli.com> wrote in message
| > news:1156877762....@74g2000cwt.googlegroups.com...
| > | xilog wrote:
| > | > This is a variant on the "twins paradox". It is a situation which I
| > | > don't understand, which seems on the face of it to involve strange
| > | > consequences of the special and general theories of relativity, and
I
| > | > would appreciate it if anyone can enlighten me on what the theories
| > | > really say happens in these circumstances.
| > |
| > | Did you read the FAQ?
| >
| > See
| > |
| > |
| >
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html
|
| Btw, some of the pages there have been edited within the past
| year or so, and I'm glad to say they are even better now.
|
| >
| >
| > Get your head out of you arse and see
| > http://www.androcles01.pwp.blueyonder.co.uk/Baez/TwinParadox.htm
|
| My head is already right where I want it, thank you, and
| I *have* seen your page.
What, you lile your head up your arse? Ok...
Your mathematical arguments
| (all two of them) are silly: (1) "If one of equation is correct,
| they all are" -- well sure,
Where are Baez's mathematical arguments?
I've addressed his last,
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html
and I see no mathematical arguments, just bullshit.
but only an idiot would claim they
| must all apply *simultaneously* once a coordinate system
| is fixed, and (2) the 2AB/(t'A-tA) thing that shows you don't
| know the difference between a distance of travel and a
| vector displacement.
Vector displacement? What is that, shithead?
http://mathworld.wolfram.com/VectorSpace.html
|
| And your diagram, what is that supposed to prove?
Which one, moron?
| It
| diagrams what a universe without time dilation would look
| like. Assume no dilation, and damn who would have thought,
| Stella and Terence meet up both the same age. I'm sorry,
| such diagrams have been known for centuries -- the problem
| is, they don't agree with experiment.
That's right. Stella has never been to Alpha Centauri and
back so it cannot agree with experiment, imbecile.
|
| > Fuckwit.
| > Androcles
|
| Androcles, I am very sorry for the loss you recently suffered.
Thank you.
| Beyond that, I really have nothing more to say to you. Please
| try to stay on your side of the sandbox and I'll stay on mine.
Then get the hell out of my sandbox, go to alt.local.village.idiot
or alt.morons and write there, there ain't room for us both.
Come back when you can derive the cuckoo transformations.
http://www.androcles01.pwp.blueyonder.co.uk/Rocket/Rocket.htm
Androcles.
Russell
John Baez did not write the FAQ. He is one of the people who
hosts it. You might try to get at least that much right.
> I've addressed his last,
> http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html
> and I see no mathematical arguments, just bullshit.
>
>
>
>
> but only an idiot would claim they
> | must all apply *simultaneously* once a coordinate system
> | is fixed, and (2) the 2AB/(t'A-tA) thing that shows you don't
> | know the difference between a distance of travel and a
> | vector displacement.
>
> Vector displacement? What is that, shithead?
> http://mathworld.wolfram.com/VectorSpace.html
>
>
> |
> | And your diagram, what is that supposed to prove?
>
> Which one, moron?
The one that you drew, not the ones that you copied from
the FAQ. I thought that would be obvious.
Sorcerer
Then he should not put his name to it.
| He is one of the people who
| hosts it. You might try to get at least that much right.
So he's a shithead, like you <shrug>
| > I've addressed his last,
| >
http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_vase.html
| > and I see no mathematical arguments, just bullshit.
|
No answer to that, arrogant fuckwit?
I can ignore you too.
Androcles
Harry
> don't understand, which seems on the face of it to involve strange
> consequences of the special and general theories of relativity, and I
> would appreciate it if anyone can enlighten me on what the theories
> really say happens in these circumstances.
>
> Scenario
>
> The traditional "twins paradox" is asymmetric. One of the twins travels
> on a geodesic and the other does not, and the other therefore ages less
> in the process. In this case, we arrange for the two twins to undertake
> symmetrically opposite journey's which are therefore identical in
> relation to time dilation from the point of view of an inertial third
> person observing their journeys.
>
> We start with the two twins and an independent observer all at rest
> together relative to some inertial frame. All three have clocks which
> they synchronise together. The two twins accelerate rapidly to near the
> speed of light in opposite directions. They then travel at uniform
> velocity for a good long time before turning round, coming back
> together at the same speed and decelerating to a stop as they once
> again meet.
>
> Analysis
>
> This is my half-baked misunderstanding of what goes on, I'm inviting
> people to come up with the correct analysis.
>
> The main part of these journeys is covered by the special theory, the
> brief periods of acceleration are covered by the general theory.
No, everything can be dealt with by the special theory. Just describe the
phenomena from inertial frames and you're OK.
> From
> the predictions of special relativity together with considerations of
> symmetry we come to some strange ideas about what the general theory
> must say about the behaviour of clocks during periods of acceleration.
>
> Considerations of symmetry tell us that the clocks of the two twins
> will agree when they meet after their journeys. Special relativity
> tells us that each twin observes the other's clock running slowly
> during the periods of uniform motion.
Only if and when they recalibrate their measurement systems to the temporary
inertial frames in which they are consecutively in rest. In practice it's
more common for astronauts to keep "universal" time, that is, the earth's
time standard.
> Ergo, during the periods of
> acceleration they must observe the other's clock as running fast.
Not necessarily. It won't make much sense for them to continuously
recalibrate while they are being pushed back in their chairs!
> The periods of uniform motion can be changed arbitrarily without making
> any change to the periods of acceleration. If this is done the time
> lost during these period will vary, and the time gained during the
> periods of acceleration must increase correspondingly for the clocks to
> match when they meet up.
If you realise that it's just a mathematical construct, it won't puzzle you.
> Hence the general theory must predict a speed up during acceleration
> which is not determined by the amount of acceleration and its duration.
No, it depends on that as well as on the distance.
> What else could it depend upon? What else does it depend on? What's
> wrong with this partial analysis?
See above.
Harald
G. L. Bradford
"Paul Cardinale" <pcard...@volcanomail.com> wrote in message
news:1156878998.5...@p79g2000cwp.googlegroups.com...
You are the only one to put "distance" into the fray and I'm entirely sure
that even you understand what that means with regard to differing readings
of light time. In none of the posters posts is there any consideration of
distance being between the twins always putting each twin behind in
observable time relative to the other. Or that differentiation in velocity
itself translates to increased distance between twins.
Neither of the twins can possibly observe the current time of the other
twin at a distance. The limitations of the speed of light upon information
transmission, including light born imagery, will never allow it. Thus each
twin will be somewhere ahead in clock time of the clock time observed for
him by the other twin. The greater the distance between, or the greater the
differentiation in velocity between, the farther ahead one will be in clock
time to the clock time observed for him by the other twin. The posters do
not account for this delay in information transmission translating to one
clock being behind the other. Nor do they translate speed into light time
stretching of time based information. They just automatically take what will
be observed -- from a distance in space and time -- to be the IMMEDIATE fact
of the matter on the other end.
A man on Earth knows exactly how old he is right down to the second. A
space station is orbiting Mars and Mars just happens to be 220 light seconds
from Earth at this time. The man on Earth transmits his age (to the second)
at the speed of light to a man on the space station. When the light speed
transmission arrives 220 light seconds away from Earth, is the transmission
correct as to the man on Earth's CURRENT age right down to the second? Or is
it wrong, is it off, by [a minimum] of 220 seconds?
The man on the space station orbiting knows the same thing about his own
age right down to the second and does the same thing, transmitting his age
to the man on Earth. When the light speed transmission arrives to the man on
Earth 220 light seconds away from the station, is the transmission correct
as to the man on the station's CURRENT age right down to the second? Or is
it wrong, is it off, by [a minimum] of 220 seconds?
The posters to the this thread would answer yes to the first question and
no the second, particularly concerning the case of the man on the space
station's age. Why? Because to them there is no distance, and no difference,
in space and time whatsoever between observer and observed. All 220 second
long communication of information is mentally translated by the posters to
be an instantaneous communication of information. The universe -- except for
Earth -- suspends in animation, the man on the station suspends in aging,
until the observer on Earth gets the information, thus making it current.
The man is IMMEDIATELY exactly as old as he says he is, right down to the
second, to the posters, no matter the distance between transmitter and
observer.
No observer can observe a traveler's properly tuned clock to be running
faster than his own properly tuned clock unless the traveler is oncoming
toward him. The faster the traveler comes toward him the faster in running
the observer would observe the oncoming traveler's clock to be. And no
observer in a so-called inertial frame will ever observe a traveler's
properly tuned clock going away from him and his own properly tuned clock --
at any velocity whatsoever -- to be running either in sync with his, or
running faster than. No matter what the traveler's velocity going away, the
traveler's clock would be observed to be running slower than the observer's.
The greater the difference in velocity in the traveler going away, the
greater the distance being gained faster, the slower will be the [apparent]
running of the traveler's clock ([observed to running that much slower],
that is). No matter what direction the traveler will travel, during the
duration of transmission of information to the distant observer he will
continue to be animated and time will continue to pass for him for the
entire length of that "duration" of transmission of information, thus always
putting him and his clock somewhere ahead in both space and TIME of anywhere
the distant observer will -- per observation (per all light speed
information arrived to him) -- place him in [both] space and TIME. The
actual traveler and his actual clock, the real traveler's real spatial
placement and real clock time (current placement and current clock time),
can not and will not be in the distant observer's picture at all. That he
and it will not be is a [constant] disadvantage to the observer of the
timing of the speed of light across any distance whatsoever being ever so
acutely finite in speed rather than infinite in speed.
GLB
Sorcerer
"G. L. Bradford" <glbr...@insightbb.com> wrote in message
news:9NGdnYU1qsc_92jZ...@insightbb.com...
Cardinale is a well-known shithead.
Androcles
xilog
> xilog wrote: (with my [mlf] editorial comments and changes between
> square brackets):
> >
> > The main part of these journeys is covered by the special theory, the
> > brief periods of acceleration are covered by the general theory.
>
> There is no need for general relativity, if there are no large masses
> present. Special relativity is all that is needed.
Thanks for that point.
All the accounts of special relativity I have read give the impression
that special relativiity applies only to inertial frames and that
general relativity is needed to explain the twin "paradox".
Thanks also for your extensive account of what really goes on according
to special relativity.
I now also (think I) understand that this fact that the extent of the
time contraction depends on the distance, which is what most struck me
as odd, is because this is all caused by describing the action from an
accelerating frame of reference, i.e. from continually varying
coordinate systems.
Roger Jones
xilog
> xilog wrote:
> > This is a variant on the "twins paradox". It is a situation which I
> > don't understand, which seems on the face of it to involve strange
> > consequences of the special and general theories of relativity, and I
> > would appreciate it if anyone can enlighten me on what the theories
> > really say happens in these circumstances.
>
> Did you read the FAQ?
Well I did, but evidently not thoroughly enough, and a more thorough
read has been invaluable.
When I first looked I didn't think the twin paradox was a problem, and
thought I understood why, and was interested in the different problem
raised by the symmetric version.
Had I read the explanation of the twin paradox fully I would have also
understood the symmetric case, and now imagine I do.
> The link to the "General Relativity" explanation is directly
> relevant to your question,
However, I didn't follow this bit, and my present understanding does
not depend on it.
I have been assured, and now believe, that the explanation does not
depend on the general theory.
> and also the "Doppler explanation"
> will perhaps help you be more careful to define what you
> mean by *observe*.
I was assuming, as is surely usual. that any necessary corrections for
non relativistic observational factors are done.
I probably didn't understand the doppler bit in the FAQ,.
Of course the explanation of doppler effects is of interest, but surely
the phenomenon we are looking to explain here is a relativistic effect
and cannot be explained purely by discussing doppler effects, which
seem a red herring, unless you are really discussing what the observers
see as opposed to what they infer.
> Also I recommend reading the other SR pages, particularly
> the one explaining that SR *can* deal with accelerations.
> (The distinction you make here between GR and SR is not
> the one that most physicists make; most physicists would
> call your scenario simply SR because it does not involve
> curved spacetime.)
That certainly made a big difference to me.
It has changed my perception of the demarcation between special and
general relativity, i.e. I no longer think of the special theory as
dealing only with inertial frames and non-accelerating observers.
However, I think of GR as a theory about gravitation which happens
normally to be formulated using curved space-time, but can also be
formulated in a flat space time (Doran, Lazenby and Gull).
Roger Jones
xilog
Paul Cardinale wrote:
> xilog wrote:
> > Hence the general theory must predict a speed up during acceleration
> > which is not determined by the amount of acceleration and its duration.
> >
> > What else could it depend upon? What else does it depend on?
>
> Distance.
Well that's what I thought, but I couldn't believe it.
Now I see that this is all smoke and mirrors, and that the dependence
on distance is OK because the whole effect is created by continuous
changes to the reference frame rather than anything physical.
Roger Jones
xilog
> "xilog" :
>
> > This is a variant on the "twins paradox".
> (...)
> > The traditional "twins paradox" is asymmetric. One of the twins travels
> > on a geodesic and the other does not, and the other therefore ages less
> > in the process. In this case, we arrange for the two twins to undertake
> > symmetrically opposite journey's which are therefore identical in
> > relation to time dilation from the point of view of an inertial third
> > person observing their journeys.
> (...)
>
> You announce it nicely but then seem to stick to the classical case, as far
> as I can see...
The difference is as advertised.
The situation is symmetric, both twins travel, not just one of them.
Also the problem to be resolved is different.
The problem was, how could the observed time compression during
acceleration vary even though the acceleration and its duration remain
the same (if the duration of the inertial travel is changed).
> > The main part of these journeys is covered by the special theory, the
> > brief periods of acceleration are covered by the general theory. From
>
> not at all, as said already by others.
>
> > the predictions of special relativity together with considerations of
> > symmetry we come to some strange ideas about what the general theory
> > must say about the behaviour of clocks during periods of acceleration.
>
> GR is not needed for, nor 'affected' by this.
>
> > Considerations of symmetry tell us that the clocks of the two twins
> > will agree when they meet after their journeys. Special relativity
> > tells us that each twin observes the other's clock running slowly
> > during the periods of uniform motion. Ergo, during the periods of
> > acceleration they must observe the other's clock as running fast.
>
> OK.
>
> > The periods of uniform motion can be changed arbitrarily without making
> > any change to the periods of acceleration. If this is done the time
> > lost during these period will vary, and the time gained during the
>
> And so will be total rest time to be compared to.
>
> > periods of acceleration must increase correspondingly for the clocks to
> > match when they meet up.
>
> Not at all, depends only upon type of accelerations, not upon uniform
> movements before or after.
The rest of us seem now to agree that it depends upon distance, which
depends itself on the length of the period of uniform motion.
> > Hence the general theory must predict a speed up during acceleration
> > which is not determined by the amount of acceleration and its duration.
>
> See previous.
>
> > What else could it depend upon? What else does it depend on? What's
> > wrong with this partial analysis?
>
> Again, I don't see the point of the third twin for symmetry.
The "third twin" (third person in the original) is irrelevant for the
symmetry.
I could have omitted the stationary observer altogether but as it
happens the description of what the other two are doing is really from
his point of view.
> For a good understanding of the TP, including the 'Lorentz frame' and
> 'visual' aspects to be well distinguished, and the acceleration-within-SRT
> aspect, have a dash at my brand new page
> http://home.scarlet.be/~pin12499/paratwin.htm
Thanks for your help.
Roger Jones
xilog
Thanks for your response, which made clear to me for the first time
that we must distinguish between the frame of reference of the observer
and the frame relative to which he describes what he observed, which
have no need of being the same.
This has made big improvement to my sense of understanding of special
relativity.
I was stuck with this idea that it was the frame of reference of the
observer which mattered, but this is relevant only to the corrections
which the observer makes when he takes his naked observations and tries
to figure out what is actually going on.
When he then comes to describe what happened, he can do this using any
frame of reference he likes, and what he says should be completely
independent of the frame in which he made his observations.
Though it seems natural enough that someone might make observations
from an accelerating space ship, it now seems to me (after your
interjection) that it would be very silly to describe anything in the
(non-inertial) frame of reference in which the space ship is
stationary, and if you do that you can expect the description to look
rather strange.
Roger Jones
Harry
You're welcome, glad it helped. :-)
Harald
Sue...
xilog wrote:
<< What's wrong with this partial analysis? >>
Abstract
Einstein addressed the twin paradox in special relativity
in a relatively unknown, unusual and rarely cited paper
written in 1918, in the form of a dialogue between a
critic and a relativist. Contrary to most textbook versions
of the resolution, Einstein admitted that the special
relativistic time dilation was symmetric for the twins,
and he had to invoke, asymmetrically, the general relativistic
gravitational time dilation during the brief periods
of acceleration to justify the asymmetrical aging.
Notably, Einstein did not use any argument related to
simultaneity or Doppler shift in his analysis. I discuss
Einstein's resolution and several conceptual issues
that arise. It is concluded that Einstein's resolution using
gravitational time dilation suffers from logical and
physical flaws, and gives incorrect answers in a general
setting. The counter examples imply the need to reconsider
many issues related to the comparison of transported
clocks. The failure of the accepted views and
resolutions is traced to the fact that the special relativity
principle formulated originally for physics in empty
space is not valid in the matter-filled universe.
C. S. Unnikrishnan
Gravitation Group,
Tata Institute of Fundamental Research,
Homi Bhabha Road, Mumbai 400 005, India
http://www.iisc.ernet.in/currsci/dec252005/2009.pdf
-----
Sue...
>
> Roger Jones
xilog
Sue... wrote:
<snip>
Thanks for the abstract and the link to the paper, which I am looking
at.
You don't say how this bears upon my symmetric twin conundrum or what
you think of my analysis of it.
Roger Jones
Sue...
Why would I read an analysis of a conundrum that dosen't exist?
Next time, do write about something real. :-)
Einstein observed that that any but the symetric solution is
a mathematical absurdity. Occasioally hucksters will still
try to prop up the asymetic calculation with abuse of 'length
of world lines' ect.
A basic text on complex numbers and Einstein's chapeter
on Minkowski space dispells that illusion.
Here is the correct form:
http://www.aoc.nrao.edu/~smyers/courses/astro12/speedoflight.html
Jupiter's moons can not put on different shows for every observer so
the
symetric solution *has* to be the correct one. The twins have to see
every tick of each others watches regardless of their motion.
So it is 'back to the drawing board' for Ponce deLeon and H.G. Wells.
;-)
Sue...
>
> Roger Jones
guido
> guido wrote:
> > "xilog" :
> > You announce it nicely but then seem to stick to the classical case, as
far
> > as I can see...
>
> The difference is as advertised.
> The situation is symmetric, both twins travel, not just one of them.
> Also the problem to be resolved is different.
> The problem was, how could the observed time compression during
> acceleration vary even though the acceleration and its duration remain
> the same (if the duration of the inertial travel is changed).
But that's between one moving and one home twin. What need of a second mover
there?
> > > The periods of uniform motion can be changed arbitrarily without
making
> > > any change to the periods of acceleration. If this is done the time
> > > lost during these period will vary, and the time gained during the
> >
> > And so will be total rest time to be compared to.
> >
> > > periods of acceleration must increase correspondingly for the clocks
to
> > > match when they meet up.
> >
> > Not at all, depends only upon type of accelerations, not upon uniform
> > movements before or after.
>
> The rest of us seem now to agree that it depends upon distance, which
> depends itself on the length of the period of uniform motion.
Oh, right ho :-)
> > > Hence the general theory must predict a speed up during acceleration
> > > which is not determined by the amount of acceleration and its
duration.
> >
> > See previous.
> >
> > > What else could it depend upon? What else does it depend on? What's
> > > wrong with this partial analysis?
> >
> > Again, I don't see the point of the third twin for symmetry.
>
> The "third twin" (third person in the original) is irrelevant for the
> symmetry.
> I could have omitted the stationary observer altogether but as it
> happens the description of what the other two are doing is really from
> his point of view.
Well, between themselves the situation is symmetric, so they end up the same
age and conclusions. With regard to the homestayer only one mover is needed.
So I still don't get the point of the third man, see?:-)
> > For a good understanding of the TP, including the 'Lorentz frame' and
> > 'visual' aspects to be well distinguished, and the
acceleration-within-SRT
> > aspect, have a dash at my brand new page
> > http://home.scarlet.be/~pin12499/paratwin.htm
>
> Thanks for your help.
Same,
guido
Mike Fontenot
>
> I quantified this effect in a previous posting. The equation in
> that posting applied to an accelerating twin and a stay-at-home
> twin. But it can be adapted to handle the symetrical case also.
I've been trying to do what I claimed (in the last sentence above)
could be done, and it's not as easy as I had expected...so far,
I haven't gotten a consistent result. Has anyone ever seen a
description of the symmetrical twin paradox, in which one of the
twins determines the correspondance between their two ages?
I.e., for each instant in the life of one of the twins, what
is the corresponding age of the other twin (as concluded by
the first twin)? (I'm of course talking here about the DEDUCED
simulataneity, NOT the way a TV image of the other twin would
appear to the first twin to be ageing). What does that plot
look like?
Mike Fontenot
Paul Cardinale
G. L. Bradford wrote:
[snip]
> You are the only one to put "distance" into the fray and I'm entirely sure
> that even you understand what that means with regard to differing readings
> of light time. In none of the posters posts is there any consideration of
> distance being between the twins always putting each twin behind in
> observable time relative to the other.
Look at the Lorentz transform for time. Notice the x.
[snip]
> Neither of the twins can possibly observe the current time of the other
> twin at a distance. The limitations of the speed of light upon information
> transmission, including light born imagery, will never allow it. Thus each
> twin will be somewhere ahead in clock time of the clock time observed for
> him by the other twin. The greater the distance between, or the greater the
> differentiation in velocity between, the farther ahead one will be in clock
> time to the clock time observed for him by the other twin.
You're confusing 'observing' (which accounts for delayed signals) with
'seeing' (which doesn't).
Paul Cardinale
Sorcerer
|
| G. L. Bradford wrote:
|
| [snip]
Snipping moron.
Androcles
xilog
I think there is just one problem between us at present, which is the
question of why I have two moving twins, so I'll just try to explain
that more carefully.
In the classic twin paradox there is no symmetry, but there is still
suppose to be an issue as to why one twin ages more than the other. I
guess this is because during the intertial phases the time dilation is
symmetric. The simple answer to why they age differently is that when
they are not both inertial, just the moving twin accelerates, and this
acceleration therefore causes him to age differently to the other.
(that's not a good explanation, but it will do for present purposes).
(i.e. they are not symmetric when acceleration takes place)
Accepting this explanation, I then ask myself, but what if we construct
a symmetric scenario in which both twins do the same thing except in
mirror image, including symmetric periods of acceleration.
In that case, during the inertial periods they both observe dilation,
but when they get together by symmetry they must have the same age, so
during the acceleration they must observe time compression. Symmetry
is essential to this argument. Then we note that the amount of
compression depends upon the duration of the inertial period, which is
the bit which seems really odd. You can't make this argument without
the symmetry, which is not present in the normal twin paradox.
The "resolution" is that the time/distance dependence is caused by the
fact that the compression arises not as a physical effect of
acceleration, but as a book keeping adjustment as the observer changes
reference frame, (its the observer's acceleration which does it, not
the acceleration of the observed twin) and the moral is, if you want a
description to make sense, don't change your reference frame half way
through. There is a second moral too, which is that you should talk
about what happens relative to a frame of reference NOT relative to an
observer, because the observer always has to correct what he sees to
get a true description, and he always has to do this relative to some
frame of reference, but he does not actually have to do it relative to
a frame of reference in which he is at rest, and he especially doesn't
hvae to try and do it relative to an accerating frame of reference if
he happens to be accelerating.
As to your own question about how it appears to each of the symmetric
twins after correcting for observational errors, this is how it now
seems to me.
For simplicity let's assume that the turnaround is instantaneous.
At the start of the journey the observed twin ages slowly according to
the separation velocity using the usual formula. When the observing
twin turns round the observed twin suddenly ages by eactly the amount
that his aging will be reduced by dilation on both the inward and the
outward journeys. The chunk of his life which the observed twin seems
to have lost during this instant turnaround includes his own
turnaround, so the observing twin then observes him returning with
exactly the same time dilation as before, so that by the time they meet
again they have resynchronised.
Do you agree with that?
Roger Jones
xilog
Sue... wrote:
> Why would I read an analysis of a conundrum that dosen't exist?
> Next time, do write about something real. :-)
And why would I read a response to my message from someone who claims
not to have read it?
Roger Jones
Sue...
You would read it because C. S. Unnikrishnan has put a lot of careful
work into the same subject you titled your post with. In this newsgroup
one needs only see the words 'paradox' and 'acceleration' to know the
poster's confusion. IOW... if you know the shortest way from Rome
to Athen's, it isn't necessary to read a gazillion alternate routes,
before
you convey to someone, the shortest route from Rome to Athens. :o)
Sue...
>
> Roger Jones
xilog
Sue... wrote:
> In this newsgroup
> one needs only see the words 'paradox' and 'acceleration' to know the
> poster's confusion. IOW...
I see the words "paradox" and "acceleration" in your recent posting.
Should I conclude that you are confused?
Roger Jones
Sue...
in his calculations or analysis, then you can conclude that the
author is confused.
Sue...
>
> Roger Jones
jem
Well there's no such thing as a "symmetrical twin paradox", since in any
symmetric scenario, the twins ages will obviously remain the same, but
if both twins accelerate, just take the relationships you say you
already have, between each twin and a "stay-at-home observer" (e.g. the
transformation equations that relate their time and distance
measurements) and factor out the middle-man to get the relationship
between the twins (i.e. if S(x,t) = T1(x1,t1) and S(x,t) = T2(x2,t2),
then T1(x1,t1) = T2(x2,t2)).
Mike Fontenot
I found the error I was making when I tried to adapt my CADO
equation to the symmetrical twin paradox (that was causing
results that were inconsistent). My initial conjecture about
the correspondance between the ages of the two twins (according
to one of the twins) is correct: a plot of twin 2's age, versus
twin 1's age, according to twin 1, starts from the origin as
a straight line (of some positive slope 1/gamma < 1). Working
from the other end (when the twins are reunited, say, at ages
40 and 40), the plot is another straight line with the same
slope 1/gamma, ending at the point (40,40). At the midpoint
(age 20 years old for twin 1), the plot jumps discontinuously
from the lower straight line to the upper straight line.
This plot is just like the plot for the standard (aymmetrical)
twin paradox (plotting the home twin's age versus the traveler's
age, according to the traveler), except that the magnitude of the
discontinuity is smaller.
But I had wanted to adapt my CADO equation to handle the symmetrical
problem so that I could obtain the plot without having to work
from both ends. (In a more complicated scenario (with multiple
speed changes), the twins would not necessarily be reunited, so
that working backward from the reunion wouldn't be possible).
That's one of the advantages of my CADO equation (for problems
in which one of the twins is perpetually inertial): it allows
the magnitude of the discontinuity to be computed directly, without
using information about the future parts of the trip.
I wanted to be able to do the same thing in the symmetrical problem,
but when I tried to adapt the CADO equation to do that, my first
attempt produced inconsistent results (because of mistakes I made).
It MAY be possible to adapt the CADO equation to handle the
symmetrical case, but my first attempt was incorrect. It may be that
any such adaptation might not be very useful...the utility of the
CADO equation in the standard (asymmetrical) case lies in the fact
that the quantities on the RHS of the equation are all based on the
conclusions of the home twin, which are much easier to compute than
the corresponding quantities based on the conclusions of the
accelerating twin. But in the symmetrical case, both twins
accelerate, so most or all of the utility of the CADO equation may
be lost.
Mike Fontenot
_______________________________________________________________
xilog
Mike Fontenot wrote:
> But in the symmetrical case, both twins
> accelerate, so most or all of the utility of the CADO equation may
> be lost.
I don't think the fact that both twins accelerate matters much because
its only the acceleration (or turnaround) of the observing twin that
makes a difference and it does so only because of the change of frame
it entails if you are measuring all from the frame of the observer.
If its an instant turnaround you just have to make the mid-flight
correction for change of frame, the turnaround of the observed twin has
no effect on his age (not at least from SR).
Roger Jones
Mike Fontenot
But in trying to use the CADO equation, acceleration of the
observed object DOES make a difference, because two of the
quantities on the RHS of the CADO equation (CADO_H and L) are
from the point of view of the observed twin; when the observed
twin accelerates, CADO_H and L both change rapidly. In the
standard asymmetrical case, when the observer accelerates,
but the observed object doesn't, the quantities CADO_H and L
don't change during the observer's instantaneous speed change,
and that is what makes the use of the equation so simple: the
observer's conclusion about the CADO (CADO_T), which varies
in a complicated way, is expressed in terms of several quantities
which are much simpler.
Another way to say it is this: the CADO equation allows the
CADO according to the traveling twin (CADO_T), which is
complicated to compute directly, to be computed from
quantities that are much simpler to compute (quantities
that are the conclusions of the home twin). But when both
twins accelerate, neither of their viewpoints is simpler
than the other, so the equation may lose some or all of
its utility.
As time permits, I still plan to try to see how the CADO
equation can be adapted to the case where both twins
accelerate. But it may well turn out that some other
approach is better suited to that problem.
Mike Fontenot
Mike Fontenot
wugi
> I think there is just one problem between us at present, which is the
> question of why I have two moving twins, so I'll just try to explain
> that more carefully.
>
> In the classic twin paradox there is no symmetry, but there is still
> suppose to be an issue as to why one twin ages more than the other. I
> guess this is because during the intertial phases the time dilation is
> symmetric. The simple answer to why they age differently is that when
> they are not both inertial, just the moving twin accelerates, and this
> acceleration therefore causes him to age differently to the other.
> (that's not a good explanation, but it will do for present purposes).
> (i.e. they are not symmetric when acceleration takes place)
No mystery here.
Moreover, the amount of time dilation (inertial bits) is independent of the
amount of time gap, or compression if you like (the acceleration bit). If
you take
instant acceleration then you get my picture
http://home.scarlet.be/~pin12499/MySRT/RelatyTravtwin2.TIF
whereas if there is some continuous acceleration you get a picture like
http://home.scarlet.be/~pin12499/MySRT/PhysicsNmtRaymond.png
(courtesy of http://physics.nmt.edu/~raymond/classes/ph13xbook/node46.html )
The smoother the acceleration bit, the less time compression and the less
difference in total time.
> Accepting this explanation, I then ask myself, but what if we construct
> a symmetric scenario in which both twins do the same thing except in
> mirror image, including symmetric periods of acceleration.
> In that case, during the inertial periods they both observe dilation,
> but when they get together by symmetry they must have the same age, so
> during the acceleration they must observe time compression. Symmetry
> is essential to this argument. Then we note that the amount of
> compression depends upon the duration of the inertial period, which is
> the bit which seems really odd. You can't make this argument without
> the symmetry, which is not present in the normal twin paradox.
Oh, what I understand now is this:
in the usual case you have the time gap DE, see picture first mentioned
above.
In your symmetry case, I came up with this version:
http://home.scarlet.be/~pin12499/MySRT/SymTwins2.PNG
The same gap window DE, extended to the mirror traveler, now shows a gap
D'B'E'. The nicety is, as we know (1) AB'C represents the same age as
observer's ABC, (2) AD' + E'C represents the age observed (and D'B'E' the
"blind" bit), we can conclude that the observing twin's system(s) allot his
own age to AD' + E'C = time dilation (and zero time to D'B'E').
Maybe that's what you were trying to tell.
It's a nicety of the symmetry, but no special feature for helping understand
Tw.P.
> The "resolution" is that the time/distance dependence is caused by the
> fact that the compression arises not as a physical effect of
It *is* a physical effect by its own right.
> acceleration, but as a book keeping adjustment as the observer changes
> reference frame, (....)
>
> As to your own question about how it appears to each of the symmetric
> twins after correcting for observational errors, this is how it now
> seems to me.
> For simplicity let's assume that the turnaround is instantaneous.
Here too, I extended the usual case (only to be seen 'completely' in my own
site, from what I saw elsewhere:-)
http://home.scarlet.be/~pin12499/MySRT/RelaseeTravtwin.TIF .......
......to
http://home.scarlet.be/~pin12499/MySRT/SymTwinSee7.PNG .
> At the start of the journey the observed twin ages slowly according to
> the separation velocity using the usual formula. When the observing
> twin turns round the observed twin suddenly ages by eactly the amount
> that his aging will be reduced by dilation on both the inward and the
> outward journeys. The chunk of his life which the observed twin seems
> to have lost during this instant turnaround includes his own
yes
> turnaround, so the observing twin then observes him returning with
> exactly the same time dilation as before, so that by the time they meet
> again they have resynchronised.
>
> Do you agree with that?
Look at the last picture.
First stage: recession AR, perceived as AR+, 'slow' aging
Instant turnback: R is perceived 'warped' (from R+) to R- when starting the
backtrip.
Second stage: RB', perceived as R- B'- with *zero* speed ! 'Equal' aging as
if rest system.
Third stage: comeback approach B'C, perceived as B'- C, 'fast' aging.
The first and third stages have the same "seeing" duration as one can see.
guido
http://home.scarlet.be/~pin12499/paratwin.htm
Sorcerer
"wugi" <br...@scarlet.be> wrote in message
news:kIOdnaSkB6PtEGHZ...@scarlet.biz...
| "xilog" :
|
| > I think there is just one problem between us at present, which is the
| > question of why I have two moving twins, so I'll just try to explain
| > that more carefully.
| >
| > In the classic twin paradox there is no symmetry, but there is still
| > suppose to be an issue as to why one twin ages more than the other. I
| > guess this is because during the intertial phases the time dilation is
| > symmetric. The simple answer to why they age differently is that when
| > they are not both inertial, just the moving twin accelerates, and this
| > acceleration therefore causes him to age differently to the other.
| > (that's not a good explanation, but it will do for present purposes).
| > (i.e. they are not symmetric when acceleration takes place)
|
| No mystery here.
| Moreover, the amount of time dilation (inertial bits) is independent of
the
| amount of time gap, or compression if you like (the acceleration bit). If
| you take
| instant acceleration then you get my picture
| http://home.scarlet.be/~pin12499/MySRT/RelatyTravtwin2.TIF
Get my picture:
http://www.androcles01.pwp.blueyonder.co.uk/Baez/twin-non-paradox.JPG
Yours is terrible, the twins remain the same age.
| whereas if there is some continuous acceleration you get a picture like
| http://home.scarlet.be/~pin12499/MySRT/PhysicsNmtRaymond.png
Mine already had acceleration.
Do you idiots reverse the x and t axes so that you can call a
distance/time chart a "spacetime diagram"?
Sexy term for little boys who want to be space-travelling chrononauts,
I suppose.... <yawn>
| (courtesy of
http://physics.nmt.edu/~raymond/classes/ph13xbook/node46.html )
Bloody useless. I made my own.
| The smoother the acceleration bit, the less time compression and the less
| difference in total time.
The drool is dripping off your chin, son.
| > Accepting this explanation, I then ask myself, but what if we construct
| > a symmetric scenario in which both twins do the same thing except in
| > mirror image, including symmetric periods of acceleration.
| > In that case, during the inertial periods they both observe dilation,
| > but when they get together by symmetry they must have the same age, so
| > during the acceleration they must observe time compression. Symmetry
| > is essential to this argument. Then we note that the amount of
| > compression depends upon the duration of the inertial period, which is
| > the bit which seems really odd. You can't make this argument without
| > the symmetry, which is not present in the normal twin paradox.
|
| Oh, what I understand now is this:
| in the usual case you have the time gap DE, see picture first mentioned
| above.
You do not understand physics.
http://www.androcles01.pwp.blueyonder.co.uk/Rocket/Rocket.htm
Yawn... Have a nice day.
Androcles
| In your symmetry case, I came up with this version:
| http://home.scarlet.be/~pin12499/MySRT/SymTwins2.PNG
| The same gap window DE, extended to the mirror traveler, now shows a gap
| D'B'E'. The nicety is, as we know (1) AB'C represents the same age as
| observer's ABC, (2) AD' + E'C represents the age observed (and D'B'E' the
| "blind" bit), we can conclude that the observing twin's system(s) allot
his
| own age to AD' + E'C = time dilation (and zero time to D'B'E').
| Maybe that's what you were trying to tell.
| It's a nicety of the symmetry, but no special feature for helping
understand
| Tw.P.
|
| > The "resolution" is that the time/distance dependence is caused by the
| > fact that the compression arises not as a physical effect of
|
| It *is* a physical effect by its own right.
Bullshit. Einstein took you in and you fell for it.
Mike Fontenot
>
> I found the error I was making when I tried to adapt my CADO
> equation to the symmetrical twin paradox (that was causing
> results that were inconsistent). My initial conjecture about
> the correspondance between the ages of the two twins (according
> to one of the twins) is correct: a plot of twin 2's age, versus
> twin 1's age, according to twin 1, starts from the origin as
> a straight line (of some positive slope 1/gamma < 1). Working
> from the other end (when the twins are reunited, say, at ages
> 40 and 40), the plot is another straight line with the same
> slope 1/gamma, ending at the point (40,40). At the midpoint
> (age 20 years old for twin 1), the plot jumps discontinuously
> from the lower straight line to the upper straight line.
I'm now not so sure that my above solution is correct. Continuing
with the gamma = 2 case above, I think the correct solution may
be that the initial straight line starting from the origin (with
slope 1/gamma = 1/2) only reaches the point (10, 5) before it
jumps vertically to (10, 20), then is horizontal from (10, 20)
until (30, 20), then jumps vertically to (30, 35), and then
is a final straight line (again of slope 1/gamma = 1/2) between
(30, 35) and (40, 40).
Anyone care to "weigh in" on the question?
Mike Fontenot
Mike Fontenot
>
> Mike Fontenot wrote:
>
> > [...] Has anyone ever seen a
> > description of the symmetrical twin paradox, in which one of the
> > twins determines the correspondance between their two ages?
> > I.e., for each instant in the life of one of the twins, what
> > is the corresponding age of the other twin (as concluded by
> > the first twin)? (I'm of course talking here about the DEDUCED
> > simulataneity, NOT the way a TV image of the other twin would
> > appear to the first twin to be ageing). What does that plot
> > look like?
>
> if both twins accelerate, just take the relationships you say you
> already have, between each twin and a "stay-at-home observer" (e.g. the
> transformation equations that relate their time and distance
> measurements) and factor out the middle-man to get the relationship
> between the twins (i.e. if S(x,t) = T1(x1,t1) and S(x,t) = T2(x2,t2),
> then T1(x1,t1) = T2(x2,t2)).
This is fine, as far as it goes. In fact, it may be a better appraoch
to this problem than trying to adapt the CADO equation. But a LOT
of work is required to go from your equation above, to a plot of
twin 2's age, versus twin 1's age, according to twin 1. As time
permits, I'll try to carry out that work. But if you already
have the result, what does that plot look like (for example,
for the case where gamma = 2 (beta = 0.866 for the relative
speed between the two twins, which implies a relative speed
between each twin and the earth of 0.577), and where each twin
reverses course when they are 20 years old, and are reunited
when they are each 40 years old).
Mike Fontenot
Sue...
Sure...
Try applying the Lorentz transfom where you have some matter
to interact with the light, like the nearfield of the coupling
structures.
http://farside.ph.utexas.edu/teaching/em/lectures/node50.html
Sue...
>
> Mike Fontenot
jem
> jem wrote:
>
>>Mike Fontenot wrote:
>>
>>
>>>[...] Has anyone ever seen a
>>>description of the symmetrical twin paradox, in which one of the
>>>twins determines the correspondance between their two ages?
>>>I.e., for each instant in the life of one of the twins, what
>>>is the corresponding age of the other twin (as concluded by
>>>the first twin)? (I'm of course talking here about the DEDUCED
>>>simulataneity, NOT the way a TV image of the other twin would
>>>appear to the first twin to be ageing). What does that plot
>>>look like?
>>
>>[...] but
>>if both twins accelerate, just take the relationships you say you
>>already have, between each twin and a "stay-at-home observer" (e.g. the
>>transformation equations that relate their time and distance
>>measurements) and factor out the middle-man to get the relationship
>>between the twins (i.e. if S(x,t) = T1(x1,t1) and S(x,t) = T2(x2,t2),
>>then T1(x1,t1) = T2(x2,t2)).
>
>
> This is fine, as far as it goes. In fact, it may be a better appraoch
> to this problem than trying to adapt the CADO equation. But a LOT
> of work is required to go from your equation above, to a plot of
> twin 2's age, versus twin 1's age, according to twin 1.
How do you figure that? Determining the relationships between t1 and t2
from T1=T2 is as straightforward as it gets. The symbol pushing might
be tedious depending on the form of the Tn's, but if those functions are
known, it's hard to see how any other approach could be easier.
As time
> permits, I'll try to carry out that work. But if you already
> have the result, what does that plot look like (for example,
> for the case where gamma = 2 (beta = 0.866 for the relative
> speed between the two twins, which implies a relative speed
> between each twin and the earth of 0.577), and where each twin
> reverses course when they are 20 years old, and are reunited
> when they are each 40 years old).
Well, the special case where the accelerations are instantaneous and
symmetrical seems pretty easy. With gamma=2, each twin decides the
other ages half as fast on both the way out, and the way back, and
consequently ages 20 = 40 - 2*20/2 years "during" the turnaround.
>
> Mike Fontenot
Mike Fontenot
>
> Well, the special case where the accelerations are instantaneous and
> symmetrical seems pretty easy. With gamma=2, each twin decides the
> other ages half as fast on both the way out, and the way back, and
> consequently ages 20 = 40 - 2*20/2 years "during" the turnaround.
>
That was my 1st prospective solution, and it may indeed be the
correct solution. But what has started to bother me, when I
try to apply my CADO equation to this problem, is that when
twin 1 reverses course (when she is 20), she regards twin 2's
age at that instant to be 10, and so she concludes that part
of her speed change will occur BEFORE twin 2 begins his speed
change when he is 20. (According to twin 1, as her speed changes
abruptly, twin 2's age will increase abruptly, so that part way
through her speed change, twin 1 will make his sudden speed change).
It MAY be that all this complexity somehow conspires to produce
the outcome you gave above, but I haven't been able to sort all that
out yet.
Mike Fontenot
jem
> jem wrote:
>
>>Well, the special case where the accelerations are instantaneous and
>>symmetrical seems pretty easy. With gamma=2, each twin decides the
>>other ages half as fast on both the way out, and the way back, and
>>consequently ages 20 = 40 - 2*20/2 years "during" the turnaround.
>>
>
>
> That was my 1st prospective solution, and it may indeed be the
> correct solution. But what has started to bother me, when I
> try to apply my CADO equation to this problem, is that when
> twin 1 reverses course (when she is 20), she regards twin 2's
> age at that instant to be 10,
and 15, 20, and 25, as well. In fact, she regards twin 2 at that
instant to be every age between 10 and 30.
and so she concludes that part
> of her speed change will occur BEFORE twin 2 begins his speed
> change when he is 20. (According to twin 1, as her speed changes
> abruptly, twin 2's age will increase abruptly, so that part way
> through her speed change, twin 1 will make his sudden speed change).
> It MAY be that all this complexity somehow conspires to produce
> the outcome you gave above, but I haven't been able to sort all that
> out yet.
>
Yes, such complexities are accounted for in the relative aging at the
turnarounds. To see that this must be the case, note that whenever the
twins aren't accelerating (i.e. everywhere but at the turnarounds) their
measurements are related by a Lorentz transformation.
> Mike Fontenot
Mike Fontenot
I finally figured out how to determine twin 2's age, according
to twin 1, as a function of twin 1's age, for the case where
both twins are accelerating arbitrarily and independently.
I arrived at the solution by staring for quite a while at
a Minkowski diagram...the same way I inferred the CADO
equation quite a few years ago. (The CADO equation
applies to the case where twin 2 never accelerates (the
stay-at-home twin)).
Using that procedure for the special case of the symmetrical
"twin paradox" problem, the result turns out to be what I had
initially guessed would be the answer (which was also the
solution given by jem). My incorrect attempt to adapt my
CADO equation to that problem produced my second guess as
to the solution, which differed from my first guess, and which
I now definitely know to be incorrect.
The procedure I've found for determining the age correspondences
of the two twins, when they both accelerate, is not an adaptation
of the CADO equation (i.e., there is no one equation which replaces
the CADO equation, in the general case). But the new procedure
has a graphical interpretation on a Minkowski diagram which is
a generalization of the graphical interpretation on a Minkowski
diagram which originally led me to the CADO equation. The
new procedure is conceptually straightforward, but it is more
involved computationally. It does allow idealized problems
with instantaneous speed changes ("twin paradox"-type problems)
to be solved by hand. But more complicated problems, like
those with piecewise-constant (e.g., 1 g) accelerations, or
those with arbitrary acceleration profiles, require more
extensive calculations on a computer.
I'll post an outline of the procedure as soon as time permits.
For readers who don't remember what my first prospective solution
to the symmetrical "twin paradox" problem was, here's a repeat
of that description:
> A plot of twin 2's age, versus
> twin 1's age, according to twin 1, starts from the origin as
> a straight line (of some positive slope 1/gamma < 1). Working
> from the other end (when the twins are reunited, say, at ages
> 40 and 40), the plot is another straight line with the same
> slope 1/gamma, ending at the point (40,40). At the midpoint
> (age 20 years old for twin 1), the plot jumps discontinuously
> from the lower straight line to the upper straight line.
>
> This plot is just like the plot for the standard (asymmetrical)
> twin paradox (plotting the home twin's age versus the traveler's
> age, according to the traveler), except that the magnitude of the
> discontinuity is smaller.
> But I had wanted to adapt my CADO equation to handle the symmetrical
> problem so that I could obtain the plot without having to work
> from both ends. (In a more complicated scenario (with multiple
> speed changes), the twins would not necessarily be reunited, so
> that working backward from the reunion wouldn't be possible).
> That's one of the advantages of my CADO equation (for problems
> in which one of the twins is perpetually inertial): it allows
> the magnitude of the discontinuity to be computed directly, without
> using information about the future parts of the trip.
Mike Fontenot
shuba
> I finally figured out how to determine twin 2's age, according
> to twin 1
Despite your single-minded obsession with the "current age of a
distant object", it remains a concept devoid of any practical or
theoretical value.
---Tim Shuba---
Russell
I second that. My reaction to his posts is a big ho-hum, which
on second thought is rather sad, because Mike is clearly an
intelligent and conscientious chap -- and how we need people
like that around here -- who wants to be taken seriously.
A better use of his time might be to read through Spacetime
Physics and then explain, in his own words, what you (Tim)
might possibly mean by your posting.
jem
Do you think the Lorentz Transformation (which relates the clock
measurements of Inertial observers) warrants being called a "concept
devoid of any practical or theoretical value"? Presumably not, so why
would you think a transformation which relates the clock measurements of
a broader class of observers, does warrant it?
shuba
> Do you think the Lorentz Transformation (which relates the clock
> measurements of Inertial observers) warrants being called a "concept
> devoid of any practical or theoretical value"? Presumably not, so why
> would you think a transformation which relates the clock measurements of
> a broader class of observers, does warrant it?
I think you'll have to consider the basics of group theory to
realize how utterly naive that question is. For starters, try
defining precisely what is being transformed with this CADO
nonsense, and then determine which important properties of
transformations apply (or not).
---Tim Shuba---
jem
That "naive question" was rhetorical, since any correct expression of
the relationships between clock measurements in Relativity is
*obviously* not "devoid of any practical or theoretical value".
However, if it's not obvious to you, feel free to point out exactly what
criteria you think should serve as the basis for determining which
measurement relationships have some value, and which don't.
shuba
It's always instructive to mention something like group theory
and watch the reaction.
---Tim Shuba---
jem
And it's always amusing to watch your evasive maneuvering when you're
challanged to back-up your critical-tone, no-substance posts.
You need to do more than mention a term, Shuba. Demonstrate exactly
*how* "the basics of [G]roup [T]heory" indicate that Fontenot's results
are valueless. And don't worry about overwhelming me with the
complexity of your explanation - I'm quite familiar with the mathematics
involved.
shuba
> >>shuba wrote:
> >>>I think you'll have to consider the basics of group theory to
> >>>realize how utterly naive that question is. For starters, try
> >>>defining precisely what is being transformed with this CADO
> >>>nonsense, and then determine which important properties of
> >>>transformations apply (or not).
> You need to do more than mention a term, Shuba.
I did exactly that. I gave the considerations above.
> I'm quite familiar with the mathematics
> involved.
Then, presumably, your inability to address any part of the
content of my post was due to other reasons.
---Tim Shuba---
jem
> jem wrote:
>
>
>>>>shuba wrote:
>
>
>>>>>I think you'll have to consider the basics of group theory to
>>>>>realize how utterly naive that question is. For starters, try
>>>>>defining precisely what is being transformed with this CADO
>>>>>nonsense, and then determine which important properties of
>>>>>transformations apply (or not).
>
>
>>You need to do more than mention a term, Shuba.
>
>
> I did exactly that. I gave the considerations above.
Give me a break, Shuba - Seto says stuff that makes more sense than your
"considerations".
>
>
>>I'm quite familiar with the mathematics
>>involved.
>
>
> Then, presumably, your inability to address any part of the
> content of my post was due to other reasons.
The "content" of your post is its clear indication that you don't know
what you're talking about - I addressed that.
Fontenot's equations relate the clock readings of observers according to
Special Relativity; the *only* "important propert[y]" those equations
must satisfy is a correct correspondence with the theory, and that
correspondence gives them "theoretical value", by definition.
And your juvenile attempt to redirect my response only serves to confirm
my opinion of you.
Russell
Note, Tim did not say the *LT* is devoid of practical or
theoretical value.
The LT is of theoretical value to SR for the same reason that
2+2=4 is of theoretical value to arithmetic. And it's of practical
value because it transforms coordinates that physicists have
found to be useful.
No physicist in their right mind would use the coordinates that Mike
Fontenot is trying, with impressive effort, to do calculations with.
At least, no physicist who has recourse to easier coordinates, i.e.
in this case the coordinates of some inertial frame, take your pick
which.
"The current age of a distant object" is not invariant, indeed it is
not
observable. You have to *calculate* it based on some coordinate
system that you adopt. And, contrary to what Mike and you seem
to be assuming, there is no necessary coordinate system here --
no coordinate system that represents what "really is". Indeed, by
making such an assumption you are working against the whole
spirit of relativity.
shuba
> Fontenot's equations relate the clock readings of observers according to
> Special Relativity; the *only* "important propert[y]" those equations
> must satisfy is a correct correspondence with the theory, and that
> correspondence gives them "theoretical value", by definition.
That pathetic statement also does not address what I posted.
---Tim Shuba---
jem
Note, I didn't say that he did.
>
> The LT is of theoretical value to SR for the same reason that
> 2+2=4 is of theoretical value to arithmetic. And it's of practical
> value because it transforms coordinates that physicists have
> found to be useful.
>
> No physicist in their right mind would use the coordinates that Mike
> Fontenot is trying, with impressive effort, to do calculations with.
> At least, no physicist who has recourse to easier coordinates,
This is about *what* is being determined, not *how* it's being
determined - the easiest possible determination method can always be used.
i.e.
> in this case the coordinates of some inertial frame, take your pick
> which.
The measurements being discussed in this thread aren't from the
perspective of Inertial reference frames.
>
> "The current age of a distant object" is not invariant,
So?
indeed it is
> not
> observable. You have to *calculate* it based on some coordinate
> system that you adopt.
Calculated values based on some coordinate system correspond to measured
values based on the perspective of some observer.
And, contrary to what Mike and you seem
> to be assuming, there is no necessary coordinate system here --
And where did anyone but you, say anything about a "necessary coordinate
system"?
> no coordinate system that represents what "really is".
In any viable physical theory, every coordinate system "really is"
representing the measurements of some observer.
Indeed, by
> making such an assumption you are working against the whole
> spirit of relativity.
One of a pair of co-located twins accelerates at a given rate to a given
speed relative to the other, and then decelerates at a given rate until
they're again co-moving. If you believe there's no value in being able
to determine the twins' ages from the twins' perspective, I'm not going
to try to persuade you from that belief.
jem
Well, it does, but not quite as succintly as that other statement where
I said you don't know what you're talking about.
And speaking of pathetic, I see baby Shuba's still trying to get the
grown-ups to fall for that redirection trick. Keep trying, Baby.
Russell
Fine, so what Tim and I are saying is that the *what* that
Mike is considering here is of no practical or theoretical
interest.
If, for example, Mike were to calculate twin B's age at
a certain event at which twin B is present -- say, twin B's
age when he receives a birthday greeting from twin A --
then of course that would be a practical result. It is
indeed practical for twin A to predict whether his birthday
wishes will arrive at the desired time, or not.
But it is not an issue of practical interest to calculate
what twin B's age is, according to A's coordinates,
when A *sends* the card. Or, what A's age is when
B receives the card -- who the heck cares? These
are examples of "current age of a distant object".
Now, it *could* be of practical interest if it were some
intermediate calculation on the way to some practical
result. But here, it never would be, because easier
coordinates are available to us for doing any practical
calcs that we might like to do, and being smart physicists,
we would be using *those* coordinates. Something like
that is what I was thinking when I unwisely stressed the
"how" in my previous posting.
>
> i.e.
> > in this case the coordinates of some inertial frame, take your pick
> > which.
>
> The measurements being discussed in this thread aren't from the
> perspective of Inertial reference frames.
They aren't even *measurements*, and that's pretty much
the crux of the matter.
A measurement is some reading on some instrument; a
photograph that somebody has taken; some observation
made by someone's eye or other sensory organ. These
are invariant -- if my voltmeter reads 1.0 V at an event at
which my watch reads 12:00, this fact does not depend
on observer. All observers, regardless of what their *own*
instruments read, will nevertheless agree that *my*
voltmeter reads 1.0 V and *my* watch reads 12:00 at
the event in question.
> >
> > "The current age of a distant object" is not invariant,
>
> So?
So it isn't a measurement.
>
> indeed it is
> > not
> > observable. You have to *calculate* it based on some coordinate
> > system that you adopt.
>
> Calculated values based on some coordinate system correspond to measured
> values based on the perspective of some observer.
The point being discussed here is whether they "correspond",
as you put it, in any way that has practical or theoretical value.
You haven't shown that they do.
>
> And, contrary to what Mike and you seem
> > to be assuming, there is no necessary coordinate system here --
>
> And where did anyone but you, say anything about a "necessary coordinate
> system"?
Probably it would have been clearer if I'd said there is no
*one* coordinate system that corresponds to twin A's
(or twin B's) perspective. There are conventions, yes --
Rindler coords, to be specific -- but Mike seems unaware
that this is convention, not something real. Change the
convention, and you change the "current age of a distant
object". That rather drives home the futility of his program.
>From what I have seen so far, I think you suffer from a
similar confusion. But perhaps I have not read carefully
enough; there is much that I've skipped over.
>
> > no coordinate system that represents what "really is".
>
> In any viable physical theory, every coordinate system "really is"
> representing the measurements of some observer.
Well, it's true that you can construct coordinate systems by
stating what measurements are to be done, and what conventions
are to be applied (e.g. such and such a clock is to be transported
from event A to event B by such and such a method of physical
transport) and that any coords that are useful in physics are of
this kind, at least in principle.
Where you go wrong is in thinking that this has to do with
some "observer". A coordinate system must be everywhere
in spacetime (or at least, everywhere of interest) but an
observer is only in one place. The key word in Shuba's
critique is "distant".
>
> Indeed, by
> > making such an assumption you are working against the whole
> > spirit of relativity.
>
> One of a pair of co-located twins accelerates at a given rate to a given
> speed relative to the other, and then decelerates at a given rate until
> they're again co-moving. If you believe there's no value in being able
> to determine the twins' ages from the twins' perspective, I'm not going
> to try to persuade you from that belief.
There is no value in determining the current age of a distant
object (or person). Except insofar as this determination is
an intermediate result in some other practical or theoretical
determination. Or, except insofar as it serves pedagogical
needs.
Are those sufficient provisos to satisfy you?
Mike might argue that there is pedagogical value to what
he is doing; but if that is his point, I (and I think Tim) would
say that Mike fails to achieve that aim. Ok, maybe do it
once, to satisfy yourself that it all works out correctly, but
after that, it's better pedagogy to learn not to obsess over
irrelevancies.
jem
Of course the clock interval comparisons in this thread are
measurements. *Any* quantitative comparison of one thing and another
thing is a measurement.
>
> A measurement is some reading on some instrument; a
> photograph that somebody has taken; some observation
> made by someone's eye or other sensory organ. These
> are invariant -- if my voltmeter reads 1.0 V at an event at
> which my watch reads 12:00, this fact does not depend
> on observer. All observers, regardless of what their *own*
> instruments read, will nevertheless agree that *my*
> voltmeter reads 1.0 V and *my* watch reads 12:00 at
> the event in question.
>
>
>>>"The current age of a distant object" is not invariant,
>>
>>So?
>
>
> So it isn't a measurement.
>
Once it's been measured, it's a measurement.
In SR, the length of a distant object isn't invariant either, but it can
certainly be measured.
And, of course, both of those measurements will be invariant in the
sense of your voltmeter example, since all observers will agree on
what's indicated by any specific set of measuring instruments.
>
>> indeed it is
>>
>>>not
>>>observable. You have to *calculate* it based on some coordinate
>>>system that you adopt.
>>
>>Calculated values based on some coordinate system correspond to measured
>>values based on the perspective of some observer.
>
>
> The point being discussed here is whether they "correspond",
> as you put it, in any way that has practical or theoretical value.
> You haven't shown that they do.
In order to have theoretical value, all they have to do is agree with
the theory.
>
>
>> And, contrary to what Mike and you seem
>>
>>>to be assuming, there is no necessary coordinate system here --
>>
>>And where did anyone but you, say anything about a "necessary coordinate
>>system"?
>
>
> Probably it would have been clearer if I'd said there is no
> *one* coordinate system that corresponds to twin A's
> (or twin B's) perspective. There are conventions, yes --
> Rindler coords, to be specific -- but Mike seems unaware
> that this is convention, not something real.
Do you think conventions aren't real?
Change the
> convention, and you change the "current age of a distant
> object".
Change the meter standard and you change the length of the bridge - so
what? Changing the convention amounts to changing the way measurements
are done.
> That rather drives home the futility of his program.
>
>>From what I have seen so far, I think you suffer from a
> similar confusion. But perhaps I have not read carefully
> enough; there is much that I've skipped over.
>
>
>>>no coordinate system that represents what "really is".
>>
>>In any viable physical theory, every coordinate system "really is"
>>representing the measurements of some observer.
>
>
> Well, it's true that you can construct coordinate systems by
> stating what measurements are to be done, and what conventions
> are to be applied (e.g. such and such a clock is to be transported
> from event A to event B by such and such a method of physical
> transport) and that any coords that are useful in physics are of
> this kind, at least in principle.
>
> Where you go wrong is in thinking that this has to do with
> some "observer".
In the context of physical theories, a coordinate system is a framework
for representing the measurements of an observer (i.e. the entity that
effects the measurements).
A coordinate system must be everywhere
> in spacetime (or at least, everywhere of interest) but an
> observer is only in one place.
That's irrelevant - the instrumentation an observer uses to make
measurements isn't restricted to one place (e.g. rulers, e.g.
synchronized clocks, e.g. etc.).
The key word in Shuba's
> critique is "distant".
>
>
>> Indeed, by
>>
>>>making such an assumption you are working against the whole
>>>spirit of relativity.
>>
>>One of a pair of co-located twins accelerates at a given rate to a given
>>speed relative to the other, and then decelerates at a given rate until
>>they're again co-moving. If you believe there's no value in being able
>>to determine the twins' ages from the twins' perspective, I'm not going
>>to try to persuade you from that belief.
>
>
> There is no value in determining the current age of a distant
> object (or person). Except insofar as this determination is
> an intermediate result in some other practical or theoretical
> determination. Or, except insofar as it serves pedagogical
> needs.
>
> Are those sufficient provisos to satisfy you?
Like I said, it's trivially obvious that *any* tool that can be used to
generate some theoretical results has theoretical value, but I'm done
arguing the point.
shuba
> Mike might argue that there is pedagogical value to what
> he is doing; but if that is his point, I (and I think Tim) would
> say that Mike fails to achieve that aim. Ok, maybe do it
> once, to satisfy yourself that it all works out correctly, but
> after that, it's better pedagogy to learn not to obsess over
> irrelevancies.
It would be detrimental to use it as a teaching tool. There are
already quite enough bad appoaches to the twin paradox. But it's
irrelevant anyway, as it will never happen. Fontenot wrote a
paper some seven years ago in a low-level journal. From what I
can tell, there are no citations to the paper, and the only other
person cheerleading for this approach on usenet is unwilling or
incapable of addressing the simplest of theoretical issues.
Since Mike Fontenot does not appear to be a crackpot, I hope he
invests his energy in other things. This one is a dead end.
---Tim Shuba---