Twin paradox GRT solution: new questions
Harry
Einstein.
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.
html :
1. "assume that a uniform "gravitational" field suddenly permeates the
universe".
I have a problem with this: It is assumed in GRT that a gravitation field
propagates with speed c. An instantaneously generated field, even if it is
uniform, would propagate from the observer who observes the gravitational
force (the "traveller" in SRT) towards the one who will free-fall (the "stay
at home" in SRT), as the source can only be on the opposite side.
The correct answer (that is, agreeing with SRT) of the Twin paradox is
calculated using GRT with the implicit assumption that the propagation speed
is infinite.
But without full equivalence, the GRT solution of the Twin paradox is in
fact defect, or not?
2. All the GRT solutions that I have seen are incomplete. Starting with the
elaborated Doppler Twin paradox where both Twins send light pulses to each
other, I did not see a GRT calculation of the light transmission arrival
times in the accelerated frame during turn-around:
- for the light pulses that are sent from the freely falling twin (it should
be shown that they arrive at the right times at the observing Twin who feels
the force)
- for the one single light pulse that is sent from the observer who feels
the force.
Does anyone know where such a calculation can be found?
Thanks.
Harald
Harold Ensle
"Harry" <harald.v...@epfl.ch> wrote in message
news:401a6ebc$1...@epflnews.epfl.ch...
Give it up. There is no solution to the twin paradox.
It is definitely not in SR (though some fools would still argue it).
And if one brings in GR, there is simply no sort of justification.
Everything that has been done is not a true solution. It is
all a kind of mathematical propaganda which simply hides
the problem.
How does all this subterfuge benefit anyone?
It doesn't.
H.Ellis Ensle
Dirk Van de moortel
"Harold Ensle" <hee...@ix.netcom.com> wrote in message news:TcGSb.3560$uM2....@newsread1.news.pas.earthlink.net...
[snip]
> Give it up. There is no solution to the twin paradox.
> It is definitely not in SR (though some fools would still argue it).
> And if one brings in GR, there is simply no sort of justification.
> Everything that has been done is not a true solution. It is
> all a kind of mathematical propaganda which simply hides
> the problem.
>
> How does all this subterfuge benefit anyone?
>
> It doesn't.
>
> H.Ellis Ensle
Harold Ellis Ensle The Man Who Hates Monopoly:
http://users.pandora.be/vdmoortel/dirk/Stuff/Monopoly.html
How anyone still bothers trying to educate a piece of dog shit
like you, is beyond every comprehension.
Dirk Vdm
Harold Ensle
"Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote
in message news:d4LSb.909$id2....@phobos.telenet-ops.be...
Dirk just called me a "piece of dog shit". I wonder if the other
SRists in this group have noticed. I wonder if they think that it
is acceptable...or perhaps they actually agree.
If some do, then they definitely need to rethink why they do.
There is a strange psychology playing out here that needs
to be pointed out.
If I am simply wrong, then why is Dirk reacting with such hatred?
If I am wrong, how is it any problem for him? That would be
my problem, not his. Yet he has totally flipped out over my post
to someone else.
Dirk's response here is what would be expected if someone
were defending their religion. You see, religion is a personal
thing and when someone else attacks it, one is threatened
and will often get angry as a response to the threat.
You see, his response is not that of a scientist, but of a religious
fanatic.
I wonder if anyone noticed...........
H.Ellis Ensle
Dirk Van de moortel
"Harold Ensle" <hee...@ix.netcom.com> wrote in message news:AOWSb.5057$uM2....@newsread1.news.pas.earthlink.net...
>
> "Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote
> in message news:d4LSb.909$id2....@phobos.telenet-ops.be...
> >
> > "Harold Ensle" <hee...@ix.netcom.com> wrote in message
> news:TcGSb.3560$uM2....@newsread1.news.pas.earthlink.net...
> >
> > [snip]
> >
> > > Give it up. There is no solution to the twin paradox.
> > > It is definitely not in SR (though some fools would still argue it).
> > > And if one brings in GR, there is simply no sort of justification.
> > > Everything that has been done is not a true solution. It is
> > > all a kind of mathematical propaganda which simply hides
> > > the problem.
> > >
> > > How does all this subterfuge benefit anyone?
> > >
> > > It doesn't.
> > >
> > > H.Ellis Ensle
> >
> > Harold Ellis Ensle The Man Who Hates Monopoly:
> > http://users.pandora.be/vdmoortel/dirk/Stuff/Monopoly.html
> > How anyone still bothers trying to educate a piece of dog shit
> > like you, is beyond every comprehension.
>
> Dirk just called me a "piece of dog shit". I wonder if the other
> SRists in this group have noticed. I wonder if they think that it
> is acceptable...or perhaps they actually agree.
Perhaps, but I doubt it.
>
> If some do, then they definitely need to rethink why they do.
> There is a strange psychology playing out here that needs
> to be pointed out.
>
> If I am simply wrong,
But dear Harold, you are not "simply wrong". You are simply
"dog shit".
> then why is Dirk reacting with such hatred?
Hatred? Come come, don't overestimate yourself now.
What gave you that idea?
As long as you don't drop yourself in my front yard or on
my doorstep, there will be no such feelings, I assure you.
> If I am wrong, how is it any problem for him? That would be
> my problem, not his. Yet he has totally flipped out over my post
> to someone else.
>
> Dirk's response here is what would be expected if someone
> were defending their religion. You see, religion is a personal
> thing and when someone else attacks it, one is threatened
> and will often get angry as a response to the threat.
Oh boy, I feel *so* threatened :-)
>
> You see, his response is not that of a scientist, but of a religious
> fanatic.
>
> I wonder if anyone noticed...........
Let's hope that everyone who feels an urge to talk about physics
with you and decides to waste his time on educating a dishonest
piece of excrement like you, has noticed.
My advice to you: keep quiet for a while, wait a few months and
then try again, just like you have done during the last six years.
By then there will be some new victims for you. You can also try
to use another name. That usually works, at least for a while.
Good luck!
Dirk Vdm
Tom Roberts
> I have new questions about the GRT Twin Paradox solution as proposed by
> Einstein.
>
> http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.
> html :
>
> 1. "assume that a uniform "gravitational" field suddenly permeates the
> universe".
> I have a problem with this: It is assumed in GRT that a gravitation field
> propagates with speed c. An instantaneously generated field, even if it is
> uniform, would propagate from the observer who observes the gravitational
> force (the "traveller" in SRT) towards the one who will free-fall (the "stay
> at home" in SRT), as the source can only be on the opposite side.
You missed the context -- Stella turns on her thrusters but remains
"motionless" (wrt her coordinate system) -- how can that be unless
"coincidentally" some other force magically appears to cancel the force
of her thrusters, to keep her "motionless"?
This is magic invoked by Stella to "explain" how she can remain
motionless in spite of turning on her thrusters. It is no real
"gravitational force", it is mathematical magic invented by Stella --
analogous to "centrifugal force" in Newtonian mechanics: when one starts
rotating, the "centrifugal force" must turn on INSTANTLY throughout the
universe; it, too, is mathematical magic invented by the rotating
observer to maintain the fiction that in the rotating coordinates
Newton's laws remain valid.
The limit of c on the propagation speed of CHANGES in gravitational
fields does not apply to such mathematical magic.
I use the term "mathematical magic" rather loosely. In reality
this is code words for people fooling themselves. A rotating
system is NOT inertial, and Newton's laws do NOT apply, and
"centrifugal force" is inadequate to the task[#]. Ditto for
Stella and her coordinate system -- she is of course free to
integrate the metric components expressed in terms of her
coordinates, but the shortcuts mentioned above are fooling her.
[#] All valid approaches essentially admit this, apply the
equations in some inertial frame, and transform the
results to the accelerated coordinates. For instance,
this is a description of "centrifugal and Coriolis
forces" for the specific case of constant rotation....
But don't try to rely on them for variable rotation or
other types of motion....
The extended quest in several threads of this newsgroup to "explain"
what the accelerated observer "sees" in the twin scenario is completely
wrong-headed. The quest is basically trying to answer: "how old is the
stay-at-home twin for a given age of the traveling twin, as measured by
the traveling twin?" -- that is hopeless, as it requires a definition of
simultaneity which is intrinsically AMBIGUOUS -- one can define
simultaneity however one likes, subject to the obvious constraints at
the endpoints (it is not ambiguous at a single location). So one can
obtain an infinity of answers for this quest, and there's no definitive
way to distinguish among them.
But that's OK:
Physics is LOCAL -- don't worry how the distant twin is aging during the
trip; all that can be tested experimentally is the comparison of their
clocks when they rejoin; compute that correctly and be happy.
One could send signals from twin to twin during the journey,
and THEY can also be tested experimentally (by local
measurements of each twin) -- THEY can be computed
unambiguously, but how the distant twin is aging cannot
(the traveling twin has no way to MEASURE it). One could
come up with other _MEASURABLE_ quantities about the twins;
the computations of such MEASURABLE quantities by either
twin will be unambiguous (and equal); but computations
depending intrinsically on an AMBIGUOUS definition of
simultaneity will be ambiguous. <shrug>
The basic failure is omitting the description of precisely HOW the
traveling twin MEASURES the age of the stay-at-home twin (standard SR
conventions determine the stay-at-home twin's measurements of the
traveling twin's age). Do this precisely and the ambiguity is resolved;
omit it and all is chaos....
> [... further questions rendered irrelevant by the above]
Tom Roberts tjro...@lucent.com
Harry
>
> "Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com> wrote
> in message news:d4LSb.909$id2....@phobos.telenet-ops.be...
> >
> > "Harold Ensle" <hee...@ix.netcom.com> wrote in message
> news:TcGSb.3560$uM2....@newsread1.news.pas.earthlink.net...
> >
> > [snip]
> >
> > > Give it up. There is no solution to the twin paradox.
> > > It is definitely not in SR (though some fools would still argue it).
> > > And if one brings in GR, there is simply no sort of justification.
> > > Everything that has been done is not a true solution. It is
> > > all a kind of mathematical propaganda which simply hides
> > > the problem.
> > >
> > > How does all this subterfuge benefit anyone?
> > >
> > > It doesn't.
> > >
> > > H.Ellis Ensle
> >
> > Harold Ellis Ensle The Man Who Hates Monopoly:
> > http://users.pandora.be/vdmoortel/dirk/Stuff/Monopoly.html
> > How anyone still bothers trying to educate a piece of dog shit
> > like you, is beyond every comprehension.
>
> Dirk just called me a "piece of dog shit". I wonder if the other
> SRists in this group have noticed. I wonder if they think that it
> is acceptable...or perhaps they actually agree.
Dirk, foei toch!
http://www.physics.adelaide.edu.au/~dkoks/Faq/Administrivia/newsgroups.html
> If some do, then they definitely need to rethink why they do.
> There is a strange psychology playing out here that needs
> to be pointed out.
>
> If I am simply wrong, then why is Dirk reacting with such hatred?
> If I am wrong, how is it any problem for him? That would be
> my problem, not his. Yet he has totally flipped out over my post
> to someone else.
>
> Dirk's response here is what would be expected if someone
> were defending their religion. You see, religion is a personal
> thing and when someone else attacks it, one is threatened
> and will often get angry as a response to the threat.
>
> You see, his response is not that of a scientist, but of a religious
> fanatic.
>
> I wonder if anyone noticed...........
Harold, it is a general problem... in fact it is religious tendencies in
"science" that triggered my renewed interest in relativity!
Harald
Harry
"Tom Roberts" <tjro...@lucent.com> wrote in message
news:1ClTb.6991$BA2....@newssvr26.news.prodigy.com...
> Harry wrote:
> > I have new questions about the GRT Twin Paradox solution as proposed by
> > Einstein.
> >
> >
http://www.math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.
> > html :
> >
> > 1. "assume that a uniform "gravitational" field suddenly permeates the
> > universe".
> > I have a problem with this: It is assumed in GRT that a gravitation
field
> > propagates with speed c. An instantaneously generated field, even if it
is
> > uniform, would propagate from the observer who observes the
gravitational
> > force (the "traveller" in SRT) towards the one who will free-fall (the
"stay
> > at home" in SRT), as the source can only be on the opposite side.
>
> You missed the context -- Stella turns on her thrusters but remains
> "motionless" (wrt her coordinate system) -- how can that be unless
> "coincidentally" some other force magically appears to cancel the force
> of her thrusters, to keep her "motionless"?
>
> This is magic invoked by Stella to "explain" how she can remain
> motionless in spite of turning on her thrusters.
In fact it was invoked by Einstein in 1918 in an attempt to justify his
theory, an explanation that is promoted by this newsgroup in the faq as
shown above.
> It is no real
> "gravitational force", it is mathematical magic invented by Stella --
> analogous to "centrifugal force" in Newtonian mechanics: when one starts
> rotating, the "centrifugal force" must turn on INSTANTLY throughout the
> universe; it, too, is mathematical magic invented by the rotating
> observer to maintain the fiction that in the rotating coordinates
> Newton's laws remain valid.
IMHO, in Newtonian theory the centrifugal force is a real and LOCAL reaction
force that only acts on the rotating parts, and therefore the speed of
propagation is irrelevant for that problem, it is NOT claimed to affect the
rest of the universe. To the contrary, rotation is "absolute" in his theory.
Starting from the unexplained existence of inertia, the force is not "magic"
in any way.
> The limit of c on the propagation speed of CHANGES in gravitational
> fields does not apply to such mathematical magic.
Hmm... it does not exactly sound as if you are defending the case for
Einstein's GRT! From your reply and from an earlier discussion that I only
watched , I now here introduce the label GRT-Einstein for that.
GRT-Einstein, according to "Die Naturwissenschaften" 29 Nov. 1918 p.697, A
Einstein:
"Therefore one can neither say, the gravitation field at a certain place is
something "real" nor that it something purely "fictive" is."
And:
"Approximative integration of the gravitation equations gave indeed that
such induction effects of accelerated masses [he meant the other masses of
the universe] really must happen."
(Uncertified translation mine)
I had not noticed that Machian detail myself when I wrote the above
question. But I am still far from convinced that it works, again because the
delay times depend on the distances... I will be surprised to actually SEE
that calculation, I wonder if it was bluff.
> I use the term "mathematical magic" rather loosely. In reality
> this is code words for people fooling themselves. A rotating
> system is NOT inertial, and Newton's laws do NOT apply, and
> "centrifugal force" is inadequate to the task[#]. Ditto for
> Stella and her coordinate system -- she is of course free to
> integrate the metric components expressed in terms of her
> coordinates, but the shortcuts mentioned above are fooling her.
>
> [#] All valid approaches essentially admit this, apply the
> equations in some inertial frame, and transform the
> results to the accelerated coordinates. For instance,
> this is a description of "centrifugal and Coriolis
> forces" for the specific case of constant rotation....
> But don't try to rely on them for variable rotation or
> other types of motion....
>
>
> The extended quest in several threads of this newsgroup to "explain"
> what the accelerated observer "sees" in the twin scenario is completely
> wrong-headed. The quest is basically trying to answer: "how old is the
> stay-at-home twin for a given age of the traveling twin, as measured by
> the traveling twin?" -- that is hopeless, as it requires a definition of
> simultaneity which is intrinsically AMBIGUOUS -- one can define
> simultaneity however one likes, subject to the obvious constraints at
> the endpoints (it is not ambiguous at a single location). So one can
> obtain an infinity of answers for this quest, and there's no definitive
> way to distinguish among them.
I got a different impression from Einstein and later Moller. Using the
equivalence principle, what is ambiguous?
And I guess that at the most (but I'm not sure there is) one approach can
yield the correct solution as I ask in question 2...
> But that's OK:
> Physics is LOCAL -- don't worry how the distant twin is aging during the
> trip; all that can be tested experimentally is the comparison of their
> clocks when they rejoin; compute that correctly and be happy.
Not so, see my question 2: the received light pulses must arrive at each at
the correct local times!
> One could send signals from twin to twin during the journey,
> and THEY can also be tested experimentally (by local
> measurements of each twin) -- THEY can be computed
> unambiguously, but how the distant twin is aging cannot
> (the traveling twin has no way to MEASURE it). One could
> come up with other _MEASURABLE_ quantities about the twins;
> the computations of such MEASURABLE quantities by either
> twin will be unambiguous (and equal); but computations
> depending intrinsically on an AMBIGUOUS definition of
> simultaneity will be ambiguous. <shrug>
I only discussed such measurable quantities.
> The basic failure is omitting the description of precisely HOW the
> traveling twin MEASURES the age of the stay-at-home twin (standard SR
> conventions determine the stay-at-home twin's measurements of the
> traveling twin's age). Do this precisely and the ambiguity is resolved;
> omit it and all is chaos....
>
>
> > [... further questions rendered irrelevant by the above]
It seems you misunderstood my second question: the proof that with the GRT
approach the light signals after the turn-around arrive at the travelling
twin at the correct local times.
Harald
Tom Roberts
> There is no solution to the twin paradox.
Hmmm. This depends on what one means by "solution". As long as one
restricts onseself to a discussion of measurable quantities, it is quite
easy to obtain the solution. Using either SR or GR[#].
[#] The boundary between SR and GR is fuzzy....
Your problem is that you insist on trying to discuss UNMEASURABLE
quantities, such as "how does the stay-at-home twin age as seen by the
traveling twin?" [my statement of the problem, not yours]. Before that
is measurable, you need to specify how the traveling twin measures it,
and that will involve defining simultaneity for the traveling twin
(simultaneity is implicitly defined for the stay-at-home twin, so this
problem in definitions is asymmetric).
As is usual around here, LACK OF PRECISION is the cause of protracted
arguments.
This necessity to restrict discussions to measureable quantities
is QUITE STRIKING, when one compares to quantum mechanics. In
SR/GR it arises for quite different reasons than in QM....
Tom Roberts tjro...@lucent.com
Dirk Van de moortel
"Harry" <harald.v...@epfl.ch> wrote in message news:401e4d8b$1...@epflnews.epfl.ch...
Ik noem de dingen graag bij hun naam.
Dit is er eentje uit ervaring.
Dirk Vdm
Tom Roberts
> IMHO, in Newtonian theory the centrifugal force is a real and LOCAL reaction
> force that only acts on the rotating parts,
Then you don't know what "centrifugal force" is in Newtonian mechanics.
It is a pure coordinate effect, and the only way one could consider it
"real" is via a horrible PUN on that word.
Consider a person on a rotating merry-go-round. The force she
feels from the platform is a centripetal (center-pointing)
force, and is real (in any sense). The "centrifugal force" is
"magic" she must invoke in order to consider herself at rest
in a co-rotating coordinate system -- it exactly counterbalances
the real centripetal force. No such magic is required in any
inertial frame -- only the real centripetal force appears.
IMHO the only sensible meaning for "real" in physics is "suitable for
inclusion in a valid theory of physics". With the Principle of
Relativity in mind, that implies that only invariant quantities can be
"real". "centrifugal force", "Coriolis force" and "gravitational force"
all do not meet that rquirement. In particular, any quantity that
explicitly depends on coordinates cannot have any place in a theory of
physics, as it is clearly a RELATIONSHIP between something and that
coordinate system, and coordinate systems are artificial human
constructs without any physical significance of their own.
Newtonian mechanics violates this. GR does not.
Tom Roberts tjro...@lucent.com
Ken S. Tucker
>On 2/2/2004 8:32 AM, Harry wrote:
>> IMHO, in Newtonian theory the centrifugal force is a real and LOCAL reaction
>> force that only acts on the rotating parts,
>
>Then you don't know what "centrifugal force" is in Newtonian mechanics.
>It is a pure coordinate effect, and the only way one could consider it
>"real" is via a horrible PUN on that word.
>
> Consider a person on a rotating merry-go-round. The force she
> feels from the platform is a centripetal (center-pointing)
> force, and is real (in any sense). The "centrifugal force" is
> "magic" she must invoke in order to consider herself at rest
> in a co-rotating coordinate system -- it exactly counterbalances
> the real centripetal force. No such magic is required in any
> inertial frame -- only the real centripetal force appears.
>
>IMHO the only sensible meaning for "real" in physics is "suitable for
>inclusion in a valid theory of physics". With the Principle of
>Relativity in mind, that implies that only invariant quantities can be
>"real". "centrifugal force", "Coriolis force" and "gravitational force"
My problem with this HO, is the equivalence of
centripetal and gravitational acceleration. While
sitting at my desk I really cannot distinguish
between the two effects, (I could be on a
Merry-Go-Round about some center in outer space)
hence I cannot say one is real and one is not.
>In particular, any quantity that
>explicitly depends on coordinates cannot have any place in a theory of
>physics, as it is clearly a RELATIONSHIP between something and that
>coordinate system, and coordinate systems are artificial human
>constructs without any physical significance of their own.
Commonly the g_00 accounts for g-potential, ie
g_00 = 1 -2M/r
and produces a centripetal acceleration by &g_00/&r.
In free-fall, specifically in a circular orbit, a time
varying velocity (acceleration) acts to negate g_00.
A careful look at the Chistoffel will find &g_tr/&t
((I like the tr designation since I'm talking to TR))
cancels (1/2) g_tt/&r. (g_00/&x^1, r==x^1).
My understanding of GR is : There is NO absolute
(invariant) acceleration (This is sometimes disputed
by Lorentz Force). So notwithstanding Lorentz
and EM herein, I see no mathematical way to define
forces as real or imaginary.
My best guess is to place an accelometer in the
CS, because that reading won't vanish.
If TR or anyone has any ideas of the tensor that
describes accelometer readings please let me know.
I haven't found any reference anywhere to this
problem. The best I've been able to come up with
is a tensor Q_u in the thread "Einstein's Nonsymmetrical
Field Theory", but relies on Maxwell's Equations.
Ken S. Tucker
Tom Roberts
> Tom Roberts <tjro...@Lucent.com> wrote in message news:<401FB6E6...@Lucent.com>...
>>inclusion in a valid theory of physics". With the Principle of
>>Relativity in mind, that implies that only invariant quantities can be
>>"real". "centrifugal force", "Coriolis force" and "gravitational force"
>>all do not meet that requirement.
>
> My problem with this HO, is the equivalence of
> centripetal and gravitational acceleration. While
^^^^^^^^^^^ -- TYPO: should be "centrifugal"
> sitting at my desk I really cannot distinguish
> between the two effects, (I could be on a
> Merry-Go-Round about some center in outer space)
> hence I cannot say one is real and one is not.
What's the problem?? -- NEITHER ONE is "real" (as I use the word).
> My understanding of GR is : There is NO absolute
> (invariant) acceleration
Clearly false. An object can quite clearly have a nonzero 4-acceleration
(e.g. a rocket, or a charged particle in an external E-field). In the
instantaneously-comoving inertial frame of the object, this is the
proper force on the object.
[Technically this really only applies to a pointlike object.]
> (This is sometimes disputed
> by Lorentz Force). So notwithstanding Lorentz
> and EM herein, I see no mathematical way to define
> forces as real or imaginary.
Non-zero 4-force or 4-acceleration => real. In GR neither "gravitational
force" nor "centrifugal force" is related to any 4-force at all (they
are both merely components of the connection -- in the equation of
motion DP/d\tau=F they are both hidden inside the covariant derivative).
> My best guess is to place an accelometer in the
> CS, because that reading won't vanish.
That's OK, too. An accelerometer measures its own proper acceleration,
and that is the projection of its 4-acceleration onto its
instantaneously-comoving inertial frame.
> If TR or anyone has any ideas of the tensor that
> describes accelometer readings please let me know.
See above.
Tom Roberts tjro...@lucent.com
Harold Ensle
"Tom Roberts" <tjro...@Lucent.com> wrote in message
> On 1/30/2004 10:31 PM, Harold Ensle wrote:
> > There is no solution to the twin paradox.
>
> Hmmm. This depends on what one means by "solution". As long as one
> restricts onseself to a discussion of measurable quantities, it is quite
> easy to obtain the solution. Using either SR or GR[#].
SR cannot possibly solve it, since the Lorentz transformations cannot be
applied in an accelerating frame. So, by definition SR must be excluded.
> [#] The boundary between SR and GR is fuzzy....
No.
> Your problem is that you insist on trying to discuss UNMEASURABLE
> quantities, such as "how does the stay-at-home twin age as seen by the
> traveling twin?" [my statement of the problem, not yours].
And how does this statement differ from mine? BTW I also asked how
the travelling twin viewed his own time, which turns out to be even more
problematic.
>Before that
> is measurable, you need to specify how the traveling twin measures it,
> and that will involve defining simultaneity for the traveling twin
> (simultaneity is implicitly defined for the stay-at-home twin, so this
> problem in definitions is asymmetric).
Yes and then it becomes MEASUREABLE. However, if you define the
simultaneity based on the stay-at-home's view, the paradox is not resolved.
(BTW this is a common trick employed by those who try and hide the
contradiction in relativity.)
> As is usual around here, LACK OF PRECISION is the cause of protracted
> arguments.
No. The cause of protacted arguments is the endless subterfiuge of
those who would deny any argument merely because it opposes relativity.
[...]
H.Ellis Ensle
Cesar Sirvent
Then it must be a compliment that you call me by my name? :-)
> Dirk Vdm
Tom Roberts
> "Tom Roberts" <tjro...@Lucent.com> wrote in message
> news:401E612C...@Lucent.com...
>>On 1/30/2004 10:31 PM, Harold Ensle wrote:
>>>There is no solution to the twin paradox.
>>
>>Hmmm. This depends on what one means by "solution". As long as one
>>restricts onseself to a discussion of measurable quantities, it is quite
>>easy to obtain the solution. Using either SR or GR[#].
>
> SR cannot possibly solve it, since the Lorentz transformations cannot be
> applied in an accelerating frame. So, by definition SR must be excluded.
SR includes more than the Lorentz transforms. Specifically, it includes
elementary mathematical manipulation of them, such as integration.
Computing the values of MEASUREMENTS in the twin scenario is quite
simple in SR using the inertial coordinates of the stay-at-home twin. It
is significantly more complex using the accelerated coordinates of the
traveling twin, but can be done for simple forms of her acceleration.
From the form of the equations involved, it is QUITE CLEAR that the two
computations yield the same values, for MEASUREMENTS.
As I repeatedly point out, all measurements yield invariant
values. This is merely one more instance of that general
truth (which, BTW, transcends SR/GR).
SR can handle accelerated observers, as is shown in numerous
intermediate and advanced textbooks on SR (and GR). The complexities of
GR that SR cannot handle relate to spacetime curvature and/or nontrivial
topologies.
>>Your problem is that you insist on trying to discuss UNMEASURABLE
>>quantities, such as "how does the stay-at-home twin age as seen by the
>>traveling twin?" [my statement of the problem, not yours].
>
> And how does this statement differ from mine?
I dunno -- you never state things precisely, so I stated what I
_THOUGHT_ you were trying to ask, and pointed out this was my statement,
not yours.
In any case, attempts to discuss such UNMEASURABLE quantities are doomed
to failure.
> BTW I also asked how
> the travelling twin viewed his own time, which turns out to be even more
> problematic.
Not at all. The traveling twin always views his time as corresponding to
his own clock. <shrug>
>>Before that
>>is measurable, you need to specify how the traveling twin measures it,
>>and that will involve defining simultaneity for the traveling twin
>>(simultaneity is implicitly defined for the stay-at-home twin, so this
>>problem in definitions is asymmetric).
>
> Yes and then it becomes MEASUREABLE. However, if you define the
> simultaneity based on the stay-at-home's view, the paradox is not resolved.
To compute MEASUREMENTS, one need not define simultaneity at all. One
simply computes what the measurements yield (which may be simple but
non-trivial (:-)). Since the result of any measurement is an invariant,
one is guaranteed that the two twins will compute the same values for
each MEASUREMENT. This is so regardless of the coordinates used by
either twin (the ambiguity I mention occurs in the selection of
coordinates by the traveling twin).
Asking "how does the stay-at-home twin age as seen by the
traveling twin?" is not discussing measurements. Instead one
must ask the following type of question:
Twin T leaves twin H at t=0 on both their clocks;
At time t0 on clock T a light ray is emitted by
Twin T towards twin H, who detects it at time t1
on clock H. What is the value of t1 given all the
relevant quantities? One must, of course, include
the velocity profile of T wrt H, etc. Here T and H
refer to the Traveling and the stay-at-Home twins.
Such questions invlove only invariant quantities (e.g. the
intersection of a specific light ray with a specific clock's
trajectory) -- so they have invariant answers. The
all-too-nebulous "how fast does the other twin age?" is too
ill-specified to have an answer.
> (BTW this is a common trick employed by those who try and hide the
> contradiction in relativity.)
You still don't understand relativity. The contradiction is in your
MISUNDERSTANDING of relativity, not in relativity itself. A major part
of your misunderstanding is your insistence on stating things too
loosely, so they have no answer. But to you that is invisible. <shrug>
Tom Roberts tjro...@lucent.com
Eric Baird
> ...
>1. "assume that a uniform "gravitational" field suddenly permeates the
>universe".
> ...
>2. All the GRT solutions that I have seen are incomplete.
> ...
>Does anyone know where such a calculation can be found?
I tried looking a few years ago and only found two papers on the
subject:
: C. Møller, "Motion of Free Particles in Discontinuous Gravitational Fields"
: Am.J.Phys. [27] 491-493 (1959) ::
:: " IN a recent paper in the American Journal of
:: Physics, Leffert and Donahue[1] have noticed
:: and discussed a somewhat surprising feature of
:: the motion of one of the famous twin clocks
:: entering in the discussion of the well-known
:: "clock paradox."[2] In fact, it seems that the
:: solution of the original clock paradox, as
:: presented by the present author, introduces a
:: new paradox as regards the motion of the clocks,
:: and some doubts have been raised as to the
:: legitimacy of using the particular non-inertial
:: system of reference in which the gravitational
:: field at definite times is abruptly switched on
:: and off. In the present note, I want to point out
:: that the mentioned pecularities of the motion
:: can be given a simple physical interpretation if
:: we use the 3-dimensional form of the equations
:: of motion,[3] in which the mass of a particle
:: moving through a gravitational field appears to
:: depend on the gravitational potential as well
:: as on the velocity.
:: In order to state the new paradox, we need
:: only consider the first two stages of the motions
:: of the clocks in the treatment of the clock
:: paradox. ...
:: ... "
The other paper (also cited by Møller) was
:C.B. Leffert and T.M. Donahue,
: Am.J.Phys. [26] 514 (1958)
, but my copy of that one is still buried in a mass of paper
somewhere, so I'm afraid that I can't give you the title, I don't seem
to have indexed it in my files.
At the time, I couldn't find anything more recent than the Møller
paper, but perhaps there's been something since (or perhaps the
citation indexes have thrown up some new leads since).
Regards,
=Erk= (Eric Baird)
: " ... They were urged on by the delirium of trying to reach the books
: in the Crimson Hexagon: books whose format is smaller than usual,
: all-powerful, illustrated and magical. "
: -- "The Library of Babel", Jorge Luis Borges
Harold Ensle
> Harold Ensle wrote:
> > "Tom Roberts" <tjro...@Lucent.com> wrote in message
> > news:401E612C...@Lucent.com...
> >>On 1/30/2004 10:31 PM, Harold Ensle wrote:
> >>>There is no solution to the twin paradox.
> >>
> >>Hmmm. This depends on what one means by "solution". As long as one
> >>restricts onseself to a discussion of measurable quantities, it is quite
> >>easy to obtain the solution. Using either SR or GR[#].
> >
> > SR cannot possibly solve it, since the Lorentz transformations cannot be
> > applied in an accelerating frame. So, by definition SR must be excluded.
>
> SR includes more than the Lorentz transforms. Specifically, it includes
> elementary mathematical manipulation of them, such as integration.
How is that more than the Lorentz transformations? When I say the
"Lorentz transformations" that automatically includes any possible
mathematical manipulation of them. (That should be obvious.)
Put forth a bit of effort and try and understand. You can manipulate the
Lorentz equations all you want and the best you can do is get the
stay-at-home's view of the travelling twin's acceleration. Without
_additional_ information the travelling twin's view of the stay-at-home
is based on the same acceleration. His view is thus identical and
ultimately contradictory.
> Computing the values of MEASUREMENTS in the twin scenario is quite
> simple in SR using the inertial coordinates of the stay-at-home twin. It
> is significantly more complex using the accelerated coordinates of the
> traveling twin, but can be done for simple forms of her acceleration.
It is not that difficult. While Andersen provided an additional acceleration
term that solved the travelling twin's view of the stay-at-home's time
_generally_, the travelling twin's own time still is forcefully determined
by the stay-at-home's view.
And if that were not failure enough, the acceleration term he used could
not possibly come from the Lorentz transformations to begin with.
> From the form of the equations involved, it is QUITE CLEAR that the two
> computations yield the same values, for MEASUREMENTS.
Only when you trick yourself at some point in the process by surreptitiously
making the travelling twin's time based on the stay-at-home's time, and
then claim that it is the travelling twin's view. It is really quite
obvious.
BTW when I say "view", it is the same as your "measurements" which
should be obvious from the context.
[......]
> trajectory) -- so they have invariant answers. The
> all-too-nebulous "how fast does the other twin age?" is too
> ill-specified to have an answer.
What is this BS? I have never asked "how fast does the other twin age?"
So this is your own made up question. I have _always_ asked
how each twin _observes_ the aging of the other (and themselves).
In this simple word problem "observes" would automatically (since
we are talking about physics) indicate that a measurement is made.
There is nothing wrong with the wording of this question and any
real theory would provide a self-consistent answer(#). For example,
this problem, exactly as it is worded, could be described consistently
by classical physics with no fuziness what-so-ever. (It turns out
that experimentally it would be shown to be wrong, but there would
be no contradiction in the theory itself.)
(#) this assumes, of course, that the typical twin paradox scenario
has already been introduced as the context.
> > (BTW this is a common trick employed by those who try and hide the
> > contradiction in relativity.)
>
> You still don't understand relativity.
No.....you do not understand relativity. Because if you did, you would
know with complete confidence that the theory was impossible.
[.....]
H.Ellis Ensle
Harry
"Eric Baird" <eric_...@compuserve.com> wrote in message
news:2umd20psv8r39hd4f...@4ax.com...
Thanks, I will look them up (that is, likely the Moller paper has been
superseded by his book).
But I am very pessimistic that they address the issues of speed of gravity
and speed of light!
Harald