'Twin paradox' paradox
William Owen
argument that this phenomenon will *only* occur as the result of
acceleration.
If a person takes off from this planet, travels through space for a
while then returns home that person will, according to this 'paradox'
find that they, having experienced a rate of acceleration, will have
aged at a slower rate than their twin.
This is not necessarily correct.
If one twin were to board an aeroplane and travel in the opposite
direction to the Earth9s axial spin they would return to the airport
and find that they have aged at a *faster* rate than their twin *not*
at a *slower* rate.
The Hafele-Keating experiment ( Science9 177, 166, 1972) showed that
if atomic clocks are taken around the world in a retrograde orbit,
moving at about 500k-h, those clocks will tick over at a *faster* rate
than the laboratory clocks (back at Washington, as per the HKX).
If the travelling twin followed the same routine as the HKX their age
discrepancy would, admittedly, be *very* tiny (+273 nanoseconds)
however if the travelling twin were in a satellite that orbited the
Earth in a retrograde trajectory for perhaps fifty years at an orbital
velocity of around 1 600k-h relative to the stationary9 twin (at the
equator) there would be a more discernible difference.
We are *not* referring to any doppler shift that either twin may
observe but to the *physical* comparison of their ages (or their
atomic clocks) at the conclusion of the trip.
In the fourth chapter of his special theory of relativity Einstein
suggested that if one clock is made to move in any orthogonal path -
including a circle - with respect to another clock, the moving clock
*will* incur time9 dilation relative to the stationary9 clock9
(this was of course the basis of the Hafele-Keating experiment).
It has been stated, by relativists, that if I were to walk away from a
clock on my desk then return to the desk I would find that my watch has
incurred time dilation with respect to my desk clock but this is *not*
necessarily correct.
If I start walking in an Easterly direction then return to the desk I
could find that the timepieces have *not* incurred time variations.
My watch would lose9 time during the first trip then gain9 time
during the return trip.
- - - - - - -
3Ask an impertinent question and you9re on the way to a pertinent
answer; that is the essence of science.2 (Jacob Bronowski The Ascent
of Man.9)
"Ask an impertinent question and you're on the way out of the science
class; that is the truth of reality." (Bill Owen 'Personal Experiences')
Wayne Throop
: If one twin were to board an aeroplane and travel in the opposite
: direction to the Earth's axial spin they would return to the airport
: and find that they have aged at a *faster* rate than their twin *not*
: at a *slower* rate.
: In the fourth chapter of his special theory of relativity Einstein
: suggested that if one clock is made to move in any orthogonal path -
: including a circle - with respect to another clock, the moving clock
Is there supposed to be some conflict between these statements? I don't
see any, since, indeed, the twin in the terminator-chasing aeroplane is
more nearly stationary in inertial space, and the twin on the ground is
more nearly moving in a circle.
--
Wayne Throop throopw%sheol...@dg-rtp.dg.com
thr...@aur.alcatel.com
Sebastien Lepine
>Extant interpretations of the twin paradox9 comply with Einstein9s
>argument that this phenomenon will *only* occur as the result of
>acceleration.
>If a person takes off from this planet, travels through space for a
>while then returns home that person will, according to this 'paradox'
>find that they, having experienced a rate of acceleration, will have
>aged at a slower rate than their twin.
>
>This is not necessarily correct.
I do not agree, see below.
>If one twin were to board an aeroplane and travel in the opposite
>direction to the Earth9s axial spin they would return to the airport
>and find that they have aged at a *faster* rate than their twin *not*
>at a *slower* rate.
>The Hafele-Keating experiment ( Science9 177, 166, 1972) showed that
>if atomic clocks are taken around the world in a retrograde orbit,
>moving at about 500k-h, those clocks will tick over at a *faster* rate
>than the laboratory clocks (back at Washington, as per the HKX).
This sure seems paradoxical. It is just like the "inertial" twin had aged at a
slower rate than the "non-inertial" twin, contrary to the originally stated
twins paradox. However this really is exactly the twin paradox, and I view
this experiment as a very nice corroboration of special relativity!
According to the twins paradox, the clock in the inertial frame ticks slower
than the clock in the accelerated (at some point) frame. Now, you have to
remember that the surface of the earth IS NOT an inertial frame, because of the
ROTATION of the earth (forget about gravity, we would need general relativity
>:-( ) Now if you stay near the equator (find a good hotel in Quito :-) )
while I jump in a jet travelling clockwise around the earth at a speed of 1600
km/h, guess who would have stayed in an inertial frame? ME! Why? Because you
would have made a trip around the earth by following its rotating surface
(notice the rising and setting sun) while I would have stayed at the same place
(sun over my head all the time) watching the ground going by... Of course, my
atomic clock has run faster than yours, just like stated by the twins paradox!
>It has been stated, by relativists, that if I were to walk away from a
>clock on my desk then return to the desk I would find that my watch has
>incurred time dilation with respect to my desk clock but this is *not*
>necessarily correct.
Of course, you have to take into account the rotation of the earth, as I have
explained. In fact, you should also consider the earth's revolution around the
sun, as well as the motion of the sun and... Mmh well! This is going into the
Mach experiment now ;-) Anyway, my analysis may not be correct since I
neglected gravity. Could someone explain this in Gen.Rel. formalism?
--
Sebastien Lepine
William S. Lawson
A good explanation. GR doesn't change things much because everyone is
subject to pretty much the same gravitational time distortion (but if
you go up in an airplane I think you run into trouble with gravitational
distortion being of similar magnitude to the time dilation). In fact,
the earth going around the sun doesn't matter much because everyone
involved also shares this motion.
-- Bill Lawson
Bronis Vidugiris
William Owen <wo...@extro.ucc.su.oz.au> wrote:
)If one twin were to board an aeroplane and travel in the opposite
)direction to the Earth9s axial spin they would return to the airport
)and find that they have aged at a *faster* rate than their twin *not*
)at a *slower* rate.
)
)The Hafele-Keating experiment ( Science9 177, 166, 1972) showed that
)if atomic clocks are taken around the world in a retrograde orbit,
)moving at about 500k-h, those clocks will tick over at a *faster* rate
)than the laboratory clocks (back at Washington, as per the HKX).
)If the travelling twin followed the same routine as the HKX their age
)discrepancy would, admittedly, be *very* tiny (+273 nanoseconds)
)however if the travelling twin were in a satellite that orbited the
)Earth in a retrograde trajectory for perhaps fifty years at an orbital
)velocity of around 1 600k-h relative to the stationary9 twin (at the
)equator) there would be a more discernible difference.
Yes. Because of the gravitational field of the earth, and the
fact that it's rotating, an observer on the earth does not have
the longest possible time elapsed on a clock.
The total effects are very small, though measurable - and there
is no way to increase the magnitude of the effects beyond
the rate at which the clocks on the geoid (which all
run at the same rate!) are slowed comparison to the reference clock
(which ideally should be well outside of any gravity well).
The "natural" clock to use on the geoid is the one at the
north pole, because it isn't moving. (At least due to the
earth's rotation - there will be similar, but presumably smaller (?)
effects due to the earth's orbit around the sun. I say
presumably because I haven't calculated them out.)
The fact that all the clocks on the geoid (sea level) run at the
same rate is not particularly obvious, but is documented in
"Gravitation" by MTW among other places.
The 207.4 ns discrepancy for clocks traveling around the earth's equator
is well known - see for example "Synchronization and Relativity",
Proc IEEE vol 79, no 6, June 1991 - and it references an April 1985
Science article which I haven't read as well (appears to be later
than your 1972 reference).
Jeffrey Mattox
>According to the twins paradox, the clock in the inertial frame ticks slower
>than the clock in the accelerated (at some point) frame.
Am I the only one who thinks that's backwards? Don't clocks at rest
appear to tick FASTER than those undergoing acceleration?
Jeff
--
Jeffrey Mattox -- je...@heurikon.com
Cartoon of the day: http://www.heurikon.com
William Owen
>Is there supposed to be some conflict between these statements?
No.
William Owen
Sebastian, please accept my apologies if this is a genuine
reponse not one of the usual attempts to ridicule an idea
by creating confusion.
You wrote:
>I jump in a jet travelling clockwise around the Earth...
>guess who would have stayed in an inertial frame? ME!
Shortly after you jump into the jet it *needs* to *accelerate*
in *order* to travel around the world.
An *accelerating* reference frame is *not* an inertial RF.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
You are erroneously, and I trust not deliberately deceitfully,
introducing instantaneous velocity and there ain't NO jet at
*our* airports that are capable of this feat, at least not as
far as I'm aware.
Regarding your comment on the event where I walk away from a
clock on my desk, are you assuming that the relativists' concept
does *not* take place *on this planet*? Alternatively, could it
be possible that relativists are *not* aware of the fact that the
Earth *is* spinning?
Bill Owen
George Herbert
William Owen <wo...@extro.ucc.su.oz.au> wrote:
>Shortly after you jump into the jet it *needs* to *accelerate*
>in *order* to travel around the world.
>
>An *accelerating* reference frame is *not* an inertial RF.
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>
>You are erroneously, and I trust not deliberately deceitfully,
>introducing instantaneous velocity and there ain't NO jet at
>*our* airports that are capable of this feat, at least not as
>far as I'm aware.
>
>Regarding your comment on the event where I walk away from a
>clock on my desk, are you assuming that the relativists' concept
>does *not* take place *on this planet*? Alternatively, could it
>be possible that relativists are *not* aware of the fact that the
>Earth *is* spinning?
Bill, you are missing a critical point here. The surface of the earth
as it rotates is not an inertial reference frame to start with.
You are constantly being accellerated by gravity and the rotation
of the earth and this has a calculatable effect on clock timings.
Moving anti-rotationwise on the surface will lessen the effect.
The "accelleration" of taking off in the jet is looking at the
wrong aspects of the problem.
You almost have it right. The earth IS spinning, and you need to
more thoroughly investegate what that does to the surface coordinate
reference frame. The results of doing that with traditional relativity
explain the phenomena you are trying to explain (more complexly).
-george william herbert
Retro Aerospace
gher...@crl.com
Sebastien Lepine
>In article <DE2yr...@cc.umontreal.ca>, Sebastien Lepine <lepine> wrote:
>>According to the twins paradox, the clock in the inertial frame ticks slower
>>than the clock in the accelerated (at some point) frame.
>
>Am I the only one who thinks that's backwards? Don't clocks at rest
>appear to tick FASTER than those undergoing acceleration?
>
>Jeff
Yes, of course you're right! It should have been read: _ticks faster_ as I
stated elsewhere in my post. Hope this was'nt too confusing... Anyway I think
the rest of the post was clear enough (read it all if you have'nt yet :-)
--
Sebastien Lepine
Sebastien Lepine
>> I jump in a jet travelling clockwise around the Earth...
>> guess who would have stayed in an inertial frame? ME!
>William Owen responded:
>Shortly after you jump into the jet it *needs* to *accelerate*
>in *order* to travel around the world.
>
>An *accelerating* reference frame is *not* an inertial RF.
>^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>You are erroneously, and I trust not deliberately deceitfully,
>introducing instantaneous velocity [...]
I see his point. Darn, this problem ain't easy!
Ok, let's make another thought experiment involving twins.
- Twins A and B are travelling each in a rocket going at relativistic speed.
- They see a star system. B decelerates and land on a planet. A does'nt
stop.
- A continues until he reaches another star system. Finds nothing there. He
decides to go back where B landed.
- As he pass by the first star system, B accelerates again and they head back
to where they're coming from (going home).
Now, which one is older (at the end) according to special relativity? It's A
again!
This is a better analogy to the "clock around the earth" problem. Even though
the clock in the plane experiences some acceleration (deceleration) at the
start (end) of the trip, the point is that the clock in the plane has stayed in
a fixed place in space whereas the clock on the surface of the earth has made a
round trip.
Acceleration/deceleration is not what DOES the trick about time dilation in the
twins paradox, it's only a way of explaining how their trip is different.
>> [ I mentioned that you had to account for the rotation of the earth for
>> a correct description of what happens to time dilation as you move on the >> surface of the earth. ]
>>
> Mr. Owen replied:
>
> [...] are you assuming that the relativists' concept
>does *not* take place *on this planet*? Alternatively, could it
>be possible that relativists are *not* aware of the fact that the
>Earth *is* spinning?
Those poeple *should* be aware of the rotating earth! I guess they drop it
when teaching special relativity because: 1-They may think it's unimportant or
2-they just forget about it, or even 3-They don't want to make things too
complicated :)
--
Sebastien Lepine
William Owen
>>If one twin were to board an aircraft and travel in the opposite
>>direction to the earth9s axial spin they would return to the airport
>>and find that they have aged at a *faster* rate than their twin *not*
>>at a *slower* rate.
>>[...]
>>In the fourth chapter of his special theory of relativity Einstein
>>suggested that if one clock is made to move in any orthogonal
>>path - including a circle - with respect to another clock, the moving
>>clock *will* incur time dilation relative to the stationary clock.
>Is there supposed to be some conflict between these statements?
No, there is not. The confusion in your mind and your attempt to
belittle our promulgation is created because you deliberately omitted
three paragraphs between one of our statements of fact and a later
reference to this phenomenon.
>...the twin in the terminator-chasing aeroplane is more nearly
>stationary in inertial space, and the twin on the ground is more
>nearly moving in a circle.
You either didn9t put much thought into your response or you assume
that people who read these postings are below average intelligence.
The Earth is spinning, it is orbiting the sun which is in turn orbiting
the galaxy and the galaxy is moving through space at an estimated
1 000 kilometres a *second*.
The Earth is moving through space at perhaps 1 100 000m-s and
accelerating yet you consider this to be *stationary* in inertial9
space!
Are you really of the opinion that a difference in velocity of 140m-s
(i.e. 0.01 per cent) is going to have much of an effect? isn9t your
response merely an attempt to ridicule our finding by introducing
totally irrelevant materiel?
The stationary9 twin is moving in a circle with a radius of around
six thousand four hundred kilometres whilst the circle in which the
*moving* twin is travelling has a radius of six thousand four hundred
and *one*! Do you really expect people to believe that a difference
of 1/6400 is going to have much of an effect?
In fact the moving twin, travelling in a *fractionally* larger circle
could well be moving at the *same* velocity as the *stationary* twin.
The *difference* between the two reference frames is that in order
to be travelling around the world the moving twin *has* incurred a
rate of acceleration that the stationary9 twin has *not* experienced.
(the moving twin could be travelling in a very fast train ergo would
be in the *same* gravitational tidal area as the stationary twin thus
incurring the same gravitational acceleration effect as the stationary
twin)
As pointed out at the start of our article; it is said that it is the
twin who experiences *acceleration* who incurs time dilation.
The travelling twin *is* in an accelerated reference frame!
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
They have effectively incurred *negative* acceleration in order that
they are, as you put it, 3more nearly stationary in inertial space2
then must incur *acceleration* in order to return to the same rate of
travel as the stationary9 twin.
The moving twin incurs acceleration!
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
I repeat - the *only* difference is that the moving twin experiences
*acceleration* but, according to the Hafele-Keating experiment, this
person does *not*, as claimed by relativists, incur time dilation -
aging at a slower rate than the stationary twin - but ages at a
*faster* rate.
There *is* a contradiction here but you are either incapable of seeing
it or, possibly due to fanatical bigotry (judging by the sarcastic tone
of your response), you have no *intention* of seeing it.
Bill Owen
William Owen
>Bill, you are missing a critical point here. The surface of the earth
>as it rotates is not an inertial reference frame to start with.
I fully appreciate that fact. OTOH, physicists insist, for the purpose of
'ratifying' special theory, that any given point on the surface of
the Earth *is* a quasi-inertial reference frame *specifically* when
referring to the results of particle acceleration experiments including
muons that are *accelerating* in a *gravitational* field on the surface
of an object in space that is spinning around on its axis; orbiting the
sun which is orbiting the galaxy which is *accelerating* through space
at around 1 000 ks. a *second*!
When amateur 'scientists' such as myself refer to 'my location' as a quasi-
inertial reference frame we are criticised for doing the same thing as 'the
experts'.
A prime example is the fact that whilst the Hafele-Keating experiment has been
fully accepted as 'ratifying' special theory - and *its* concept of inertial
reference frames - and *I* refer to those results I am criticised for implying
that the surface of the Earth is an inertial reference frame. When relativists
talk about walking away from a clock on my desk do you appreciate the fact
that whilst *they* are depicting a special theory-inertial reference frame
situation they must surely also be aware of the fact that my desk is *not*
contained in an inertial reference frame?
Have you, or anyone else to your knowledge, written to relativists objecting
to *their* application of a non-inertial reference frame in order to depict
phenomena relating *to* inertial reference frames? I doubt it.
Irrespective of Sebastian's comment *I* made *no* comment with respect to the
surface of the Earth being an inertial reference frame! I merely replied to
*his* comment.
George, *you* are missing an important point here.
When relativists talk about a twin who accelerates out into space do *they*
take into account the fact that the stay-at-home twin is also *in* a non-
inertial reference frame *or* do they simply refer to a twin who is 'not
moving'? Have you ever read a description of the twin paradox where the author
writes "Of course, the stay-at-home twin is not in an inertial reference
frame."? Of *course* they don't!
It does *not* matter that our stay-at-home twin is not in an inertial reference
frame; the point that you are missing is that the travelling twin experiences
*additional* acceleration!
^^^^^^^^^^^^^^^^^^^^^^^^^
Are you constantly aware, every waking second, of the centripetal acceleration
of the Earth's axial spin? OTOH do *you* notice a rate of acceleration when you
take off in an aircraft in *any* direction?
The travelling twin in our article *notices* and *experiences* a rate of
acceleration that the stay-at-home does *not* notice-experience and *that's*
the critical factor!
>You are constantly being accellerated by gravity and the rotation
>of the earth and this has a calculatable effect on clock timings.
I also appreciate *those* facts which were, of course, taken into account
when the results of the Hafele-Keating experiment were documented however
this makes *no* difference with respect to our article as those effects
*have already been taken into account*!
>Moving anti-rotationwise on the surface will lessen the effect.
>The "accelleration" of taking off in the jet is looking at the
>wrong aspects of the problem.
What do you mean by 'the wrong aspects of the problem."? *What* 'problem'?
Relativists insist that it is the twin who experiences acceleration who
incurs time dilation. The twin who is accelerated in the jet experiences
acceleration *but* they incur time 'contraction' (i.e.their clock ticks over
at a *faster* rate than their twin's) and they age at a *faster* rate.
The only 'problem' that *I* can see is that our article *contradicts*
conventional 'wisdom'!
>You almost have it right. The earth IS spinning, and you need to
>more thoroughly investegate what that does to the surface coordinate
>reference frame. The results of doing that with traditional relativity
>explain the phenomena you are trying to explain (more complexly).
The "phenomena" that I am *explaining* - not *trying* to explain - is that
the travelling twin experiences (*feels*) acceleration whilst the stay-at-
home does *not* experience any *change* in the rate of their normal
conditions.
I *know* what the Earth's rate of spin does to to the surface coordinate
reference frame. This was explained in the fourth chapter of special theory
(one clock moving in a circle around another clock) and in Clifford Will's
book 'Was Einstein Right?' where he wrote about fictitious master clocks at
the centre of the Earth compared with clocks in the surface coordinate system.
Your comments make *no* difference whatsoever to the fact that the travelling
twin *does* experience *additional* effects which the stay-at-home does *not*!
Bill Owen
William Owen
)If one twin were to board an aeroplane and travel in the opposite
)direction to the Earth's axial spin they would return to the airport
)and find that they have aged at a *faster* rate than their twin *not*
)at a *slower* rate.
)
)The Hafele-Keating experiment ('Science' 177, 166, 1972) showed that
)if atomic clocks are taken around the world in a retrograde orbit,
)moving at about 500k-h, those clocks will tick over at a *faster* rate
)than the laboratory clocks (back at Washington, as per the HKX).
)If the travelling twin followed the same routine as the HKX their age
)discrepancy would, admittedly, be *very* tiny (+273 nanoseconds)
)however if the travelling twin were in a satellite that orbited the
)Earth in a retrograde trajectory for perhaps fifty years at an orbital
)velocity of around 1 600k-h relative to the stationary9 twin (at the
)equator) there would be a more discernible difference.
>Yes. Because of the gravitational field of the earth, and the
>fact that it's rotating,
The gravitational field of the Earth *and* the fact that the Earth is
rotating *were* taken into account in the Hafele-Keating experiment and
has similarly been allowed for in our gedanken.
>................................an observer on the earth does not have
>the longest possible time elapsed on a clock.
According to the Hafele-Keating experiment the stationary9 observer
(on the Earth) experiences a *longer* elapsed time than the travelling
twin. When that twin returns to the airport and they compare their
clocks it *will* be found, as proven by the HKX, that the stay-at-home
twin9s clock indicates a *longer* elapsed time than the travelling
twin9s clock. Your statement totally contradicts the results of that
experiment.
>The total effects are very small, though measurable - and there
>is no way to increase the magnitude of the effects beyond
>the rate at which the clocks on the geoid (which all
>run at the same rate!) are slowed comparison to the reference clock
>(which ideally should be well outside of any gravity well).
If by 3reference clock2 you are referring to the travelling twin9s clock
then your statement is erroneous. The magnitude of the effects *can*
be increased by changing the HKX orbital velocity from 500k-h to
1 000k-h. Again, the effcets of the gravity well9 *have* been allowed
for so there is no point in further reference to this factor.
>The "natural" clock to use on the geoid is the one at the
>north pole, because it isn't moving. (At least due to the
>earth's rotation - there will be similar, but presumably smaller (?)
>effects due to the earth's orbit around the sun. I say
>presumably because I haven't calculated them out.)
Other than a possible attempt to obfuscate this matter thereby
hoping to confuse other readers and vainly in an attempt to confuse
me why do you feel that it is necessary to introduce your natural9,
and *purely* fictitious, clock at the North pole or the Earth9s orbit
around the sun?
*Neither* of these factors have *any* bearing whatsoever on the
fully documented results of the Hafele-Keating experiment which
showed that, compared with the reference clocks in Washington, the
clocks that were taken around the world in a retrograde orbit *did*,
return to the laboratory indicating a loss9 of 273ns. and this was
*not* dependant on the actions of any clock at the pole *nor* of the
Earth9s orbit of the sun! (i.e. according to the official9
interpretation of those results)
>The fact that all the clocks on the geoid (sea level) run at the
>same rate is not particularly obvious, but is documented in
>"Gravitation" by MTW among other places.
Again, this bit of information has *no* relationship whatsoever to our
article however I assume that you have thrown it in purely for the
sake of general interest and *not* as misleading data.
>The 207.4 ns discrepancy for clocks traveling around the earth's
>equator is well known...
I am fully aware of that fact which is why I referred to it in my
posting.
>.............................- see for example "Synchronization and Relativity",
>Proc IEEE vol 79, no 6, June 1991 - and it references an April 1985
>Science article which I haven't read as well (appears to be later
>than your 1972 reference).
There are *numerous* references to this effect. I nominated the 1972
article due to the fact that it was the *original* publication by the
people who actually *conducted* the first experiment however none
of those later references alter the fact that the accelerated twin *will* age at a *faster* rate than the stay-at-home twin which
*totally* contradicts the claim that it is the twin who experiences
acceleration who incurs time dilation.
If you are sitting at your desk *are* you constantly aware of the fact
that you are incurring centripetal acceleration due to the Earth9s
axial spin and its orbit of the sun and the sun9s orbit of the galaxy
*or* the galaxies rate of travel through space at about 1 000 ks per
*second*?
I believe that *most* people (rather than mentally tear themselves
apart by thinking about all these rates of acceleration) would
consider themselves to be at rest9.
Unless you continuously drop things are you constantly, consciously
aware of the acceleration factor created by the Earth9s gravitational
field which, other than creating pressure on your posterior, is *not* otherwise discernible as a force of acceleration?
If you are standing at an airport are you then consciously aware of
all of these factors of acceleration *or* do you consider yourself to be
standing still9 i.e. at rest9?
When you board the aircraft and it takes off *are* you consciously
aware *of* the force of acceleration that pushes you back in your seat?
In *our* article we pointed out that the twin who is stationary9 at the
airport feels *no* force of acceleration (other than tired feet) whilst
the twin who departs in the aircrfat *does* experience acceleration
and *that9s* the *only* critical and relevant factor.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
The Hafele-Keating experiment *showed* that, *in this case*, the
twin who *physically experiences a rate of acceleration* ages at a
*faster* rate *not* at a *slower rate as depicted by the twin paradox.
I *know* that the twin paradox has been deeply ingrained into
people9s minds for several generations but our example totally
contradicts that claim *in these specific circumstances* and it is
going to take time for *some* people to become aware of, and realise,
that this is so. Of course fanatical bigots will *never* accept this
fact and will arrogantly, deceitfully continue to introduce all manner
of totally irrelevant material.
Some people simply cannot accept the fact that our posting shows a
*specific* contradiction of the long-held law9 that 3it is the twin
who experiences acceleration who actually incurs time dilation2 and in
sheer panic are desperately clutching at *any* straw in a futile
attempt to defend this bit of conventional wisdom9
We have discovered a loophole (no pun intended) in this law9 and
the experts9 are not happy about this fact.
George Herbert
William Owen <wo...@extro.ucc.su.oz.au> wrote:
>George Herbert <gher...@crl.com> wrote:
>>Bill, you are missing a critical point here. The surface of the earth
>>as it rotates is not an inertial reference frame to start with.
>
>I fully appreciate that fact. OTOH, physicists insist, for the purpose of
>'ratifying' special theory, that any given point on the surface of
>the Earth *is* a quasi-inertial reference frame *specifically* when
>referring to the results of particle acceleration experiments including
>muons that are *accelerating* in a *gravitational* field on the surface
>of an object in space that is spinning around on its axis; orbiting the
>sun which is orbiting the galaxy which is *accelerating* through space
>at around 1 000 ks. a *second*!
It is quasi-inertial. Notice the "quasi" there. It is at least accurate
to say that the effects are being applied evenly to all things which
aren't moving much relative to each other, and in roughly even quantities
to things moving around in circles when you average over the whole path
(I think it comes out slightly uneven, but I don't want to double check
that right now). Those effects are predictable calculable and confirmed
under existing theory. Most importantly, they are nth order effects which
aren't going to be noticable in most particle lifetime experiments...
what's the difference between 0.00000000001 second and 0.00000000001000000001
seconds? More than the noise in the instruments? 8-)
>When amateur 'scientists' such as myself refer to 'my location' as a quasi-
>inertial reference frame we are criticised for doing the same thing as 'the
>experts'.
Your location, sitting where you are now, is quasi-inertial in the same
sense as the particle accellerator is. For most measurements, the effects
of the rotation can be ignored.
>A prime example is the fact that whilst the Hafele-Keating experiment has been
>fully accepted as 'ratifying' special theory - and *its* concept of inertial
>reference frames - and *I* refer to those results I am criticised for implying
>that the surface of the Earth is an inertial reference frame. When relativists
>talk about walking away from a clock on my desk do you appreciate the fact
>that whilst *they* are depicting a special theory-inertial reference frame
>situation they must surely also be aware of the fact that my desk is *not*
>contained in an inertial reference frame?
The experiment you are trying to do is one which violates the assumption
that it's a quasi-inertial frame... i.e., you are looking for the effects
of it *not* being inertial, so you *can't possibly* treat it as being inertial.
From a theoretical at-rest frame, the surface of the earth is highly
non-inertial due to its rotation, its orbit around the sun, and the base
velocity of the sun relative to wherever. Let us for the time being assume
that the latter two are not relevant to this investegation. Let us suppose
that we'll simplify this non-inertialness into a pseudo-velocity V,
this being the effects of the rotation and gravity of the earth.
The HK experiment is basically an experiment at determining what the
relativistic effects are of moving at V+v, small v being the velocity
of the vehicle added to V the frame's velocity. This happens to be
very close to the effects of simply moving at v in an inertial frame,
but not exactly, and it is possible to tell the difference.
Your experiment is basically determining what the effects are of moving
at V-v, which is slower in the reference inertial frame, so the effects
should have negative sign compared to the HK experiment.
The key here is recognizing that V, the earth's surface frame velocity,
is not anything close to inertial. Once you understand that, then taking
existing relativity gives you the right answers.
>George, *you* are missing an important point here.
>When relativists talk about a twin who accelerates out into space do *they*
>take into account the fact that the stay-at-home twin is also *in* a non-
>inertial reference frame *or* do they simply refer to a twin who is 'not
>moving'? Have you ever read a description of the twin paradox where the author
>writes "Of course, the stay-at-home twin is not in an inertial reference
>frame."? Of *course* they don't!
That's not the point. When one twin accellerates to large-fraction-of-C,
the non-inertialness of the stay at home twin's frame is negligible
compared to the non-inertialness of the accellerated twin's frame.
You can trivially correct the problem you mention by doing the classic
Physics Professor trick of adding "plus epsilon, for epsilon too small
to care about" to the description.
In our experiment on the earth's surface, the non-inertialness of the
surface frame suddenly is the whole issue when looking at retrograde
motion, and cannot be ignored at all if one wants to get a correct
answer...
>I *know* what the Earth's rate of spin does to to the surface coordinate
>reference frame. This was explained in the fourth chapter of special theory
>(one clock moving in a circle around another clock) and in Clifford Will's
>book 'Was Einstein Right?' where he wrote about fictitious master clocks at
>the centre of the Earth compared with clocks in the surface coordinate system.
>
>Your comments make *no* difference whatsoever to the fact that the travelling
>twin *does* experience *additional* effects which the stay-at-home does *not*!
Again, you are almost right. You are realizing what needs to be factored
in to arrive at the correct answer. You just need to go back and rethink
with a better understanding of what's negligible and what isn't in the
particular experiment you are trying.
-george
Richard A. Schumacher
"Spacetime Physics" by Taylor and Wheeler, and "Introduction to Relativity"
by Resnick and Halliday. That should relieve some of the confusion between
rotating and inertial frames demonstrated here recently.
William Owen
(snip of example)
Let9s *try* to stick to the event on hand OK?
>Acceleration/deceleration is not what DOES the trick about time
>dilation in the twins paradox, it's only a way of explaining how
>their trip is different.
In his article The Twin Paradoxes of Special Relativity: Their
Resolution and Implications.9 (Foundations of Physics, Vol. 19, No. 5.
May, 1989) Prof. Simon Prokhovnik wrote: 3The Dingle Paradox has
been confronted in a number of ways. Most relativists, *including
Einstein himself*, hold that the absolute effect arises from *the
accelerations* required by an out-and-return journey.2
The Dingle Paradox9 was, of course, his argument that special theory
does not identify which one of the clocks is the moving9 clock thus
that on the fully reciprocal basis *of* special theory - *both* clocks
incur time dilation.
In his article in Naturwissenschafen9 in 1925 Einstein introduced the
idea that it was the twin who incurred rates of acceleration that
experienced time dilation hence if one twin is *accelerated* it is
*that* twin which, according to relativists - and *Einstein* - who
incurs time dilation.
I *know* that in our example it is the stay-at-home who incurs time
dilation but now that the facts detailed in our article have been
disseminated it is *now* no longer suitable for relativists to insist
that (under *all* situations) the twin who incurs time dilation is the
one who has experienced acceleration.
We have simply introduced one *minor* paradox within a paradox! Merely
a *snippet* of possible interest!
*Try* to stick to the subject in hand. If you are unable to do that
without introducing extraneous material for the purposes of deliberate
obfuscation then your arguments are not valid nor worthy of response.
William Owen
>It is quasi-inertial. Notice the "quasi" there.
Oh! Thank you! I *hadn<t* been aware of the fact that *I* had used the
word quasi>. How stupid of me not to be aware of what I am writing!
(snip)
>>When amateur 'scientists' such as myself refer to 'my location' as a
>>quasi-inertial reference frame we are criticised for doing the same
>>thing as 'the experts'.
>Your location, sitting where you are now, is quasi-inertial in the same
>sense as the particle accellerator is. For most measurements, the
>effects of the rotation can be ignored.
That<s right, the effects of the rotation can be ignored for most
measurements other than when it suits people not to do so - for
example in relation to our argument.
>The experiment you are trying to do is one which violates the
>assumption that it's a quasi-inertial frame... i.e., you are looking
>for the effects of it *not* being inertial, so you *can't possibly*
>treat it as being inertial.
You have certainly mastered the art of being able to distort
information haven<t you?
In our argument we imply that the stay-at-home twin *is* in a quasi-
inertial reference frame! We are *not* looking for the effects of it
not being inertial and we *are* treating it as being (quasi) inertial.
It was *Sebastien* who argued that it was *not* an inertial reference
frame *not* us!
*Our* argument was it that it was the twin who *accelerates* out of
the quasi-inertial reference frame who is thus no longer *in* that
quasi-inertial reference frame.
>From a theoretical at-rest frame, the surface of the earth is highly
>non-inertial due to its rotation, its orbit around the sun, and the >base velocity of the sun relative to wherever. Let us for the=
time >being assume that the latter two are not relevant to this >investegation.
The fact is that they are *not* relevant to this investigation however
for some reason you found it necessary to *refer* to same. Wasn<t this
simply to confuse and obfuscate the issue?
(snip - irrelevant)
>Your experiment is basically determining what the effects are of moving
>at V-v, which is slower in the reference inertial frame, so the effects
>should have negative sign compared to the HK experiment.
Why can<t you simply stick to the basis of our argument? Relativists
insist that it is the twin who incurs *acceleration* that experiences
time dilation! I *know* that the estationary (quasi-inertial RF) twin
incurs time dilation and I know *why* this is so but all that *we* are
saying is that, under these *particular* circumstances the twin who
experiences acceleration relative to the original quasi-inertial
reference frame does *not* age at a slower rate than the estationary<
twin but ages at a *faster* rate!
>The key here is recognizing that V, the earth's surface frame velocity,
>is not anything close to inertial. Once you understand that, then
>taking existing relativity gives you the right answers.
You stated, above The experiment you are trying to do is one which
violates the assumption that it's a quasi-inertial frame.> *Now* you
are stating that eit<s not anything close to inertial> i.e. that it<s
*not* a quasi-inertial reference frame! Make up your mind.
>>George, *you* are missing an important point here.
>>When relativists talk about a twin who accelerates out into space do
>>*they* take into account the fact that the stay-at-home twin is also
>>*in* a non-inertial reference frame *or* do they simply refer to a
>>twin who is 'not moving'? Have you ever read a description of the
>>twin paradox where the author writes "Of course, the stay-at-home
>>twin is not in an inertial reference frame."? Of *course* they don't!
>That's not the point. When one twin accellerates to large fraction
>of-C, the non-inertialness of the stay at home twin's frame is
>negligible compared to the non-inertialness of the accellerated twin's
>frame. You can trivially correct the problem you mention by doing the
>classic Physics Professor trick of adding "plus epsilon, for epsilon
>too small to care about" to the description.
When one twin accelerates to (a) large fraction of C (sic) the non-
inertialness of the stay at home twin<s frame is negligible.> *Where*
in our original posting, or in any of our responses, do we make any
reference to a velocity *of* a large fraction of c?
If I walk away from the clock on my desk does time dilation *only*
apply if I walk at a large fraction of c?
*I* know that special relativity<s concept of time dilation *really*
applies to relativistic velocities but that does *not* alter the fact
that the Hafele-Keating experiment did *not* involve the large fraction
of c that you have introduced for purposes of obfuscation. *Nor* does
it alter the fact that, as several relativist have *erroneously*
argued, my watch *will* incur time dilation relative to the clock on
my desk.
>In our experiment on the earth's surface, the non-inertialness of the
>surface frame suddenly is the whole issue when looking at retrograde
>motion, and cannot be ignored at all if one wants to get a correct
>answer...
Except when it suits you to do so by arguing that The experiment you
are trying to do is one which violates the assumption that it's a quasi-
inertial frame.> It suddenly *becomes* the whole issue> doesn<t it?
>>I *know* what the Earth's rate of spin does to to the surface
>>coordinate reference frame. This was explained in the fourth chapter
>>of special theory (one clock moving in a circle around another clock)
>>and in Clifford Will's book 'Was Einstein Right?' where he wrote
>>about fictitious master clocks at the centre of the Earth compared
>>with clocks in the surface coordinate system.
>
>>Your comments make *no* difference whatsoever to the fact that the
>>travelling twin *does* experience *additional* effects which the
>>stay-at-home does *not*!
>Again, you are almost right. You are realizing what needs to be
>factored in to arrive at the correct answer. You just need to go back
>and rethink with a better understanding of what's negligible and what
>isn't in the particular experiment you are trying.
Your arrogant condescending and deliberately belittling attitude along
with your deliberate distortion of materiel negates any future response
to any reply to this posting. The questions posed above are purely
rhetorical.
*Nothing* needs to be factored in>!
The only reason why you insist upon this is because you are aware of
the fact that we *have* shown a paradox and you have typically set out
to protect econventional wisdom< using any means at your disposal -
including deception and distortion.
It is an *indisputable fact* that, in the paradox we presented, the
twin who *physically experiences acceleration* ages at a *faster*
rate than the stay-at-home twin *not* at a *slower* rate as insisted
upon by relativists but *only* under those *specific* circumstances.
It is a *minor* paradox within a paradox *nothing more*!
No matter how much intentional obfuscation you introduce - the
travelling twin *physically* experiences acceleration; the other
twin does *NOT*!
When I am estationary< in my quasi-inertial reference frame I am *not*
aware of the fact that the Earth is spinning on its axis OR that it is
moving around the sun OR that the solar system is spinning around the
galaxy OR that the galaxy is accelerating through space. I<m *not*
physically aware of the fact that I<m travelling through space relative
to any 'universal inertial reference frame at something like a
*thousand* kilometres a *second*!
Unless I drop something I am *not* physically aware of the
acceleration created by the Earth<s gravitational field. If a motor
vehicle that had been parked in the street outside is started up and
*accelerates* away then that vehicle is no longer *in* my quasi-
inertial reference frame.
BUT, according to relativists, people in that vehicle age at a *slower*
rate than myself yet, according to the Hafele-Keating experiment, this
is *not* necessarily correct!
Relativists insist that if I walk away from my desk I will, upon
*returning* to my desk, find that my watch has incurred time dilation
compared to the clock on my desk.
This is not necessarily correct!
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
If I walk away to the West my watch *will*, according to the HKX, tick
over at a *faster* rate than the clock and, as I return to the desk,
my watch will then tick over at a *slower* rate than the clock hence I
*could* find (depending on the respective rates of travel) that
*contrary* to the claim by relativists, my watch indicates the *same*
time as the clock!
The claim that it is the twin who *experiences acceleration* who incurs
time dilation is *not* true under all circumstances.
The claim that if I walk away from a clock on my desk my watch *will*
incur time dilation is *not* true under all circumstances.
Wayne Throop
: The gravitational field of the Earth *and* the fact that the Earth is
: rotating *were* taken into account in the Hafele-Keating experiment
: Some people simply cannot accept the fact that our posting shows a
: *specific* contradiction of the long-held law9 that 3it is the twin
: who experiences acceleration who actually incurs time dilation2 and in
: sheer panic are desperately clutching at *any* straw in a futile
: attempt to defend this bit of conventional wisdom9
Hmmmm. Right, right, the twin on the ground experiences GmM/r^2 - v^2/r
acceleration, and the twin in the plane experiences the (greater)
GmM/r^2, thus the twin who has the most local (quantity of) acceleration
actually ages *more*.
But it is pretty trivial to come up with cases here the twin with the
larger local (quantity of) acceleration ages more. Have one twin do
10-g circles for a few years, while the other spends the years on a 1g
trip out-and-back. 10g twin ages more than 1g twin.
So why is this profound?
Why is this "desperation"? Why is this "clutching at straws"?
: Message-ID: <427ml8$5...@metro.ucc.su.OZ.AU>
: Relativists insist that it is the twin who experiences acceleration
: who incurs time dilation. The twin who is accelerated in the jet
: experiences acceleration *but* they incur time 'contraction'
: (i.e.their clock ticks over at a *faster* rate than their twin's) and
: they age at a *faster* rate.
Yes, relativists "say" that the twin who experiences acceleration
is the one who experiences the least time. Yet the mathematical model
for nontrivial cases is actually more complicated than this.
And those mean old nasty gravitationalists "say" that planets follow
eliptical orbits, while the mathematical model for nontrivial cases
is actually more complicated than this.
So?
: The only 'problem' that *I* can see is that our article *contradicts*
: conventional 'wisdom'!
A violation of a heuristic-cast-in-words, but still follows the precise
mathematical formulation that the heuristic attempts to imperfectly capture.
So?
Tor Arntsen
All the ^L in these postings makes them very hard to read.
[Mod Note: I brought this up with Bill some time ago, and apparently
it's some software problem at his site. I may start manually editing
extraneous control characters out, if I have the time... appologies
to the readership. -gwh]
Regards,
--
Tor Arntsen (t...@spacetec.no) Standard disclaimers apply.
WWW kills the Internet. MIME is a braindead evil hack.
Robin van Spaandonk
If time distortion is indeed linked to the direction of travel (east
-> west or west -> east), then wouldn't that mean that a laser beam of
very specific and known frequency, would _increase_ in frequency when
shone in one direction, and _decrease_ in frequency when shone in the
opposite direction?
Regards,
Robin van Spaandonk <rvan...@netspace.net.au>
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
Man is the creature that comes into this world knowing everything,
Learns all his life,
And leaves knowing nothing.
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
Dave Oldridge
William Owen <wo...@extro.ucc.su.oz.au> wrote:
> When one twin accelerates to (a) large fraction of C (sic) the non-
> inertialness of the stay at home twin<s frame is negligible.> *Where*
> in our original posting, or in any of our responses, do we make any
> reference to a velocity *of* a large fraction of c?
>
> If I walk away from the clock on my desk does time dilation *only*
> apply if I walk at a large fraction of c?
You had better walk pretty briskly if you want it to be measurable. For
instance, if your clock has a resolution of +/- .01 sec per year, you
will just barely be able to detect the dilation if you "walk" at a bit
better than 16000 miles per hour for the whole year!
The effect really DOESN'T get large at all until v > .5c (where it's
about 14%).
Anyway, what are you trying to prove? If you solve the system in
general relativity you get numbers that accord with observed data. If
you constrain general relativity to inertial frames, it reduces to
special relativity.
--
Dave Oldridge
dold...@fox.nstn.ns.ca
Gordon Long
Robin van Spaandonk <rvan...@netspace.net.au> wrote:
>Just a thought on this subject:
>If time distortion is indeed linked to the direction of travel (east
>-> west or west -> east), then wouldn't that mean that a laser beam of
>very specific and known frequency, would _increase_ in frequency when
>shone in one direction, and _decrease_ in frequency when shone in the
>opposite direction?
Yes. That is, if the source of the laser beam was moving with repect to
whatever was measuring the frequency. This effect is known as redshift
(when the frequency decreases, i.e. the source is moving away from the
detector) or blueshift (frequency increase, i.e. the source is moving
toward the detector). It's an important effect in astronomy.
Gordon Long
gl...@vsophd.cern.ch
George Herbert
William Owen <wo...@extro.ucc.su.oz.au> wrote:
>You, and others, have devoted considerable time and bandwidth presenting
>arguments that you *know* have no validity yet you continue to come
>up with asinine objections. *This* is "desperation"; *this* is
>"clutching at straws".
>You *know* that we have presented a valid contradiction ergo you
>automatically defend 'conventional wisdom' using *any* means at your
>disposal - clutching at straws.
William, this is a completely unfair characterization of the counterarguments
to your propositions. Any number of people have looked at your proposal
and properly identified what is really happening, and tried to explain it
to you. We are not trying to cover up some sort of major flaw in physics
as we know it. We see that the actual physical conditions involved
agree with theory when theory is properly applied and are trying to
communicate this to you.
Your proposition rests on a fundamental misunderstanding of what is and
is not an inertial frame, and what effects frames-not-being-inertial
will have on observations. This is not a funamental failure of relativity.
It is perhaps a failure of physicists to be absolutely precise when making
public statements, but when you examine things at the proper level they all
make sense and work. A lab with fixed location on earth is a somewhat
accellerated frame. A plane flying around the earth in the prograde
direction is a more accellerated frame. A plane flying the retrograde
direction is a less accellerated frame. Apply this to time dialation
with the classical relatavistic formula and see what you get out of it.
William Owen
: The gravitational field of the Earth *and* the fact that the Earth is
: rotating *were* taken into account in the Hafele-Keating experiment
: and has similarly been allowed for in our gedanken. [...]
: Some people simply cannot accept the fact that our posting shows a
: *specific* contradiction of the long-held 3law9 that 3it is the twin
: who experiences acceleration who actually incurs time dilation2 and in
: sheer panic are desperately clutching at *any* straw in a futile
: attempt to defend this bit of conventional wisdom9
>Hmmmm. Right, right, the twin on the ground experiences GmM/r^2 - v^2/r
>acceleration, and the twin in the plane experiences the (greater)
>GmM/r^2, thus the twin who has the most local (quantity of) acceleration
>actually ages *more*.
The Hafele-Keating experiment *proved* that the twin in the plane
ages *more* than the other twin during the retrograde trip.
>But it is pretty trivial to come up with cases here the twin with the
>larger local (quantity of) acceleration ages more. Have one twin do
>10-g circles for a few years, while the other spends the years on a 1g
>trip out-and-back. 10g twin ages more than 1g twin.
Once again, totally extraneous material introduced for no other reason
than to deliberately obfuscate the argument. You are obviously totally
incapable of dealing logically with the subject on hand.
>So why is this profound?
I made *no* claim that it was 3profound2 it was merely presented as a
minor point of interest but, as usual, people have mounted their high
horses in order to protect conventional wisdom9 and have blown the
topic out of *all* proportion.
If you believe it to be so trivial why have you expended so much effort
attempting to negate the point?
>Why is this "desperation"? Why is this "clutching at straws"?
You, and others, have devoted considerable time and bandwidth presenting
arguments that you *know* have no validity yet you continue to come
up with asinine objections. *This* is "desperation"; *this* is
"clutching at straws".
You *know* that we have presented a valid contradiction ergo you
automatically defend 'conventional wisdom' using *any* means at your
disposal - clutching at straws.
: Relativists insist that it is the twin who experiences acceleration
: who incurs time dilation. The twin who is accelerated in the jet
: experiences acceleration *but* they incur time 'contraction'
: (i.e.their clock ticks over at a *faster* rate than their twin's) and
: they age at a *faster* rate.
>Yes, relativists "say" that the twin who experiences acceleration
>is the one who experiences the least time.................
Well, finally!
That's what *we* have been saying but you have continously refused
to acknowledge this fact.
>...........................................................................Yet the mathematical model
>for nontrivial cases is actually more complicated than this.
Did I, at any stage, claim that our article *was* anything other than
trivial? Did you get the impression that the posting represented a
*major* contradiction of modern-day physics or have you, in your
*own* mind, typically blown everything out of proportion?
>And those mean old nasty gravitationalists "say" that planets follow
>eliptical orbits, while the mathematical model for nontrivial cases
>is actually more complicated than this.
>
>So?
Grow up can9t you? At least try to stop *exhibiting* your immaturity.
: The only 'problem' that *I* can see is that our article *contradicts*
: conventional 'wisdom'!
>A violation of a heuristic-cast-in-words, but still follows the precise
>mathematical formulation that the heuristic attempts to imperfectly capture.
>So?
This tautology salves your bitter frustration resulting from an
inability to have an original idea of your own does it?
- - - - - - -
"Each progressive spirit is opposed by a thousand men
appointed to guard the past."
(Maeterlink)
george william herbert
>arguments that you *know* have no validity yet you continue to come
>up with asinine objections. *This* is "desperation"; *this* is
>"clutching at straws".
>You *know* that we have presented a valid contradiction ergo you
>automatically defend 'conventional wisdom' using *any* means at your
>disposal - clutching at straws.
William, this is a completely unfair characterization of the counterarguments
Bronis Vidugiris
Dave Oldridge <dold...@fox.nstn.ns.ca> wrote:
)You had better walk pretty briskly if you want it to be measurable. For
)instance, if your clock has a resolution of +/- .01 sec per year, you
)will just barely be able to detect the dilation if you "walk" at a bit
)better than 16000 miles per hour for the whole year!
The earth rotates 25,000 miles in 24 hours at the equator for a
velocity of about 1,000 mph.
This is about 450 meters/sec, 1.5e-6 c which gives a gamma of
about 1 + 1.25e-12. This amounts to 108 ns / day, which is of an
order to be quite measurable with an atomic clock. The actual
figure for circumnavigating the earth is 207ns from my references,
I'm not quite clear on the discrepancy (considering that one could
perform the experiment by flying at about 1000 mi/hr anti-spinwards
for a day). (Did I err?) Actual experiments similar to this were done as
was mentioned, the speed was not quite 1000 mi/hr though
(the speed of a typical jet plane).
george william herbert
Steven B. Harris
It's a bigger figure because the clock on the equator is slowed by
gravity AND by velocity.
Steve Harris, M.D.
DUPREE
> Just a thought on this subject:
> If time distortion is indeed linked to the direction of travel (east
> -> west or west -> east), then wouldn't that mean that a laser beam of
> very specific and known frequency, would _increase_ in frequency when
> shone in one direction, and _decrease_ in frequency when shone in the
> opposite direction?
> Regards,
>
> Robin van Spaandonk <rvan...@netspace.net.au>
Robin, are you sure that in fact this doesn't happen. Have you
calculated the dopple shift for an observer moving with a linear velocity
equal to (radius of earth)*(earth's angular velocity)? I imagine that
the effect is extremly small. On the other hand, how about the doppler
shift of a galaxy rushing away from us? How about the doppler shift of
lines in the solar spectrum because of atoms moving towards or away from
the Earth at the time of emission?
Cool .sig
Craig (cmd...@omega.uta.edu)
ron house
>A lab with fixed location on earth is a somewhat
>accellerated frame. A plane flying around the earth in the prograde
>direction is a more accellerated frame. A plane flying the retrograde
>direction is a less accellerated frame. Apply this to time dialation
>with the classical relatavistic formula and see what you get out of it.
Nothing, because time dilation has nothing to do with acceleration: it
is to do with speed. Saying it is due to acceleration is like saying
that roads are stretched by turning steering wheels. It mistakes cause
and effect. I.e., to follow a shorter-time path, it will (probably) be
necessary to accelerate, but the acceleration is not the cause of the
time dilation: the geometry of the path in space-time is.
[Mod Note: I oversimplified, Ron is correct. -gwh]
--
Ron House. USQ | A nonviolent diet is the
(ho...@usq.edu.au) Toowoomba, Australia. | foundation for a nonviolent world.
William Owen
>:: But it is pretty trivial to come up with cases here the twin with the
>:: larger local (quantity of) acceleration ages more. Have one twin do
>:: 10-g circles for a few years, while the other spends the years on a
>:: 1g trip out-and-back. 10g twin ages more than 1g twin.
>: From: William Owen <wo...@extro.ucc.su.oz.au>
>: Once again, totally extraneous material introduced for no other reason
>: than to deliberately obfuscate the argument. You are obviously
>: totally incapable of dealing logically *with the subject on hand*.
>Oh. Silly me, I thought it was material introduced to illustrate
>why I didn't find the "revelation" of Hafele-Keating results very
>interesting.
If you didn9t find this revelation9 of interest why have you wasted
so much time making several responses to the posting?
>:: So why is this profound?
>: I made *no* claim that it was profound9 it was merely presented as a
>: minor point of interest but, as usual, people have mounted their high
>: horses in order to protect conventional wisdom9 and have blown the
>: topic out of *all* proportion.
>Oh. OK. Then let me rephrase. "Why is this minor point of any >interest?"
Why have *you* found it to be of sufficient interest to warrant your
attempts to negate our argument?
>I gather from this and previous postings that it has something to do
>with "original ideas" and presumably blind and dogmatic scientists,
To the best of my knowledge this minor point has never previously
been promulgated ergo could be considered as being original9.
>but the connection to relativity remains obscure.
I9m certainly not going to waste my time explaining to you what
relationship the twin paradox has to relativity.
Ian Woollard
>In article <4338ng$e...@metro.ucc.su.OZ.AU>,
>William Owen <wo...@extro.ucc.su.oz.au> wrote:
>>You, and others, have devoted considerable time and bandwidth presenting
>>arguments that you *know* have no validity yet you continue to come
>>up with asinine objections. *This* is "desperation"; *this* is
>>"clutching at straws".
>>You *know* that we have presented a valid contradiction ergo you
>>automatically defend 'conventional wisdom' using *any* means at your
>>disposal - clutching at straws.
>
>William, this is a completely unfair characterization of the counterarguments
>to your propositions. Any number of people have looked at your proposal
>and properly identified what is really happening, and tried to explain it
>to you. We are not trying to cover up some sort of major flaw in physics
>as we know it. We see that the actual physical conditions involved
>agree with theory when theory is properly applied and are trying to
>communicate this to you.
Save your breath.
His starting point isn't the axioms of relativity or honestly
investigating how physicists can really believe the things they do.
Wowen's starting point is that every physicist knows that Relativity
is a fraud, or they are stupid. He doesn't listen to any attempt to
defend it. Why should he? ;-)
It may be he isn't very intelligent, or it is equally likely his
prejudices get in the way.
Either way, you can kill his postings in trn by typing: 'wowen/fK:j'.
You might also consider that his postings constitute slander, or
libel...
>-george william herbert
>Retro Aerospace
>gher...@crl.com
-Ian
"The Internet is a horrible monster that has been created and we can't do
anything about it." - Detective Inspector Laverick, on finding school kids
are stealing credit card numbers, rather than 'proper' crimes.
Wayne Throop
: If you didn9t find this revelation9 of interest why have you wasted so
: much time making several responses to the posting?
Because one William Owen was going on and on about it as if it
*ought* to hold some interest. I wondered what the hubub was about.
: To the best of my knowledge this minor point has never previously been
: promulgated ergo could be considered as being original9.
The point that it is possible to arrange things so that an
observer that experiences a greater magnitude of acceleration also
experiences the longer time duration? I've already explained
why I find that trivial.
: I9m certainly not going to waste my time explaining to you what
: relationship the twin paradox has to relativity.
And well you should not, since that wasn't what I was asking.
I was asking what the fact that relativity was found to accurately model
the spinward and anti-spinward trips has to do with some vague claim
that relativists are rejecting new and original ideas.
Van
Wayne Throop <throopw%sheol...@dg-rtp.dg.com> wrote:
>I was asking what the fact that relativity was found to accurately model
>the spinward and anti-spinward trips has to do with some vague claim
>that relativists are rejecting new and original ideas.
What you call trivial seems to answer the question raised in this thread,
IMO, thus my previous answer.
I just came to this thread, so I don't know about the new and original
ideas.
--
Van -- Email: van...@netcom.com
ple...@aztec.co.za
>Save your breath.
>-Ian
I stumbled across the end arguments of this debate. I would really
appreciate posting of the arguments explaining the paradox. That might
save some future bandwdth.
Van
William Owen <wo...@extro.ucc.su.oz.au> wrote:
>throopw%sheol...@dg-rtp.dg.com (Wayne Throop):
>
>>:: But it is pretty trivial to come up with cases here the twin with the
>>:: larger local (quantity of) acceleration ages more. Have one twin do
>>:: 10-g circles for a few years, while the other spends the years on a
>>:: 1g trip out-and-back. 10g twin ages more than 1g twin.
Isn't this reasoning backwards. Time goes slower for those in a higher
grav. field, right? I don't know what this has to do with the twin paradox,
which is about what happens to someone who follows a geodesic, or
stays in his own inertial frame, compared to someone who takes a
path which is not a geodesic, and thus does not have a = 0 at all times,
so his path is longer in spacetime. It really doesn't matter how the
acceleration is distributed over the path, a path with a not = 0
will always have longer proper time than one who has a = 0 the whole time
(a = 0 defines a geodesic).
Someone in a 10g field will age slower than someone in a 1g field.
William S. Lawson
It isn't reasoning backwards. The person going in small 10g circles (perhaps
in a jet airplane, or perhaps just in a centrifuge) never goes very fast. The
person who travels at 1g to another star and back will incur a large time
dilation along the way. One poster put it beautifully, as an analogy with
a road being longer because of the turns, rather than because of the distance.
One fairly gentle turn can make a road much longer than a whole series of
sharp ones. To find the length of the road you must look at more than the
turns.
-- Bill Lawson
Daryl McCullough
>throopw%sheol...@dg-rtp.dg.com (Wayne Throop) writes:
>>Oh. Silly me, I thought it was material introduced to illustrate
>>why I didn't find the "revelation" of Hafele-Keating results very
>>interesting.
>If you didn't find this revelation of interest why have you wasted
>so much time making several responses to the posting?
I think the answer is that Wayne finds the results not to be interesting,
but to be "meta-interesting". There is a distinction. For example,
rap music might be uninteresting to me. However, the *fact* that so
many people are interested in rap music might be interesting to me,
even though rap is not. So I would say that rap music is not interesting
to me, but it is "meta-interesting" (that is, I'm interested in people's
interest in rap). Going further, somebody else might find rap
uninteresting, and the fact that people are interested in rap
uninteresting, but the fact that I am interested in why people are
interested in rap might itself be interesting. Such a person would
find rap "meta-meta-interesting".
If for some subject, you don't find the subject interesting, nor
meta-interesting, nor meta-meta-interesting, nor meta-meta-meta-interesting,
etc. then that means you find the subject "omega-meta-boring". The
theory of levels of interestingness goes further, but it's pretty
boring, to tell the truth.
Daryl McCullough
ORA Corp.
Ithaca, NY
Erik Max Francis
> In article <vanjacDF...@netcom.com>, van...@netcom.com (Van) writes:
>
> |> Isn't this reasoning backwards. Time goes slower for those in a higher
> |> grav. field, right? I don't know what this has to do with the twin paradox
> |> which is about what happens to someone who follows a geodesic, or
> |> stays in his own inertial frame, compared to someone who takes a
> |> path which is not a geodesic, and thus does not have a = 0 at all times,
> |> so his path is longer in spacetime. It really doesn't matter how the
> |> acceleration is distributed over the path, a path with a not = 0
> |> will always have longer proper time than one who has a = 0 the whole time
> |> (a = 0 defines a geodesic).
> |>
> |> Someone in a 10g field will age slower than someone in a 1g field.
>
> It isn't reasoning backwards. The person going in small 10g circles (perhaps
> in a jet airplane, or perhaps just in a centrifuge) never goes very fast. Th
> person who travels at 1g to another star and back will incur a large time
> dilation along the way. One poster put it beautifully, as an analogy with
> a road being longer because of the turns, rather than because of the distance
> One fairly gentle turn can make a road much longer than a whole series of
> sharp ones. To find the length of the road you must look at more than the
> turns.
Correct me if I'm wrong, but isn't Van referring to gravitational time
dilation, rather than simply special relativistic time dilation here?
Erik Max Francis, &tSftDotIotE // uuwest!alcyone!max, m...@alcyone.darkside.com
San Jose, CA, USA // 37 20 07 N 121 53 38 W // GIGO, Omega, Psi // the 4th R!
H.3`S,3,P,3$S,#$Q,C`Q,3,P,3$S,#$Q,3`Q,3,P,C$Q,#(Q.#`-"C`- // 1love // folasade
_Omnia quia sunt, lumina sunt._ // mc2? oo? Nah. // http://www.spies.com/max/
Bronis Vidugiris
)Isn't this reasoning backwards. Time goes slower for those in a higher
)grav. field, right? I don't know what this has to do with the twin paradox,
)which is about what happens to someone who follows a geodesic, or
)stays in his own inertial frame, compared to someone who takes a
)path which is not a geodesic, and thus does not have a = 0 at all times,
)so his path is longer in spacetime.
So far I agree.
)It really doesn't matter how the
)acceleration is distributed over the path, a path with a not = 0
)will always have longer proper time than one who has a = 0 the whole time
)(a = 0 defines a geodesic).
I think you let your fingers type a little too fast here! The geodosic
is only a local maximum. It's quite possible to have a non-geodosic
path have a longer tame than a geodosic path, because the locally
maximum geodosic path isn't globally optimum (perhaps it spends a lot of
time in a deep potential well).
)Someone in a 10g field will age slower than someone in a 1g field.
Not always. For instance, because the potential is a maximum, I
expect that a clock in the center of the earth would "tick" slower in spite
of being in a zero g field than a clock on the surface of the
earth experiencing a 1 g field. (Put the clock on the surface at the
north pole if you're worried about the rotational effects).
William S. Lawson
In article <Z4oPBD...@alcyone.darkside.com>, m...@alcyone.darkside.com (Erik Max Francis) writes:
|> law...@ludwig.llnl.gov (William S. Lawson) writes:
|>
|> > In article <vanjacDF...@netcom.com>, van...@netcom.com (Van) writes:
|> >
|> > |>
|> >
|> > in a jet airplane, or perhaps just in a centrifuge) never goes very fast. Th
|> > person who travels at 1g to another star and back will incur a large time
|> > dilation along the way. One poster put it beautifully, as an analogy with
|> > a road being longer because of the turns, rather than because of the distance
|> > One fairly gentle turn can make a road much longer than a whole series of
|> > sharp ones. To find the length of the road you must look at more than the
|> > turns.
|>
|> Correct me if I'm wrong, but isn't Van referring to gravitational time
|> dilation, rather than simply special relativistic time dilation here?
That was part of the confusion -- the earlier post said, "travelling in
10g circles", and somehow that got turned into a 10g gravitational field.
The point is that acceleration does not cause time dilation, although it is
necessary if two clocks are to be compared at different times.
-- Bill Lawson
Steven B. Harris
>
>
>Excuse me, but could someone please
>summarize (probably in a single short sentence)
>whatever this 3person2 with the broken keyboard
>is trying to say, beyond all the heat about other people
>who don't have original thoughts and are trying to confuse the issue ?
>
>I imagine that it is possible that he has some
>valuable and even important message to deliver,
>but it is not getting through to ME,
>and other than the humor value of reading his 3stylish2 prose,
>it annoys me that he never gets around to saying the thing
>he is 3referring2 3to2.
>
>And why doesn't he fix the wierd-3characters2 problem?
>He reminds me of the guy in the trailer park in Texas
>WHO TYPES IN ALL-CAPS !!!, TAKES EVERYTHING AS A PERSONAL ASSAULT !!!,
>and is the internet-text equivalent of a Deaf Drunken Brawl-Starter.
>
>Thank You.
>
He's obviously not uploading DOS-text or ASCII text, and you're seeing
some kind of word processor symbols for italics or bold which he hasn't
stripped.
As to what his original beef is, I haven't a clue. Perhaps he'd upload
a shorter and simpler version.
Mark Barton
>Subject: Re: 'Twin paradox' paradox
>From: plessey
>Date: Tue, 19 Sep 1995 17:54:44 GMT
>>Ian.Woolla...@bnr.ca (Ian Woollard) wrote:
>
>>In article <433en3$e...@crl8.crl.com>, George Herbert <gher...@crl.com> wrote:
>
>I stumbled across the end arguments of this debate. I would really
>appreciate posting of the arguments explaining the paradox. That might
>save some future bandwdth.
I've been sparring a bit with Bill recently. In fact I had cottoned on
by
about the second post that Bill was all pomposity and empty inside, but I
was curious about the extent. Pretty much totally, I concluded. Here's
my
summary of the related "invalidation of the light clock gedanken" thread.
Bill's argument combines one famous thought experiment and one famous
real
experiment to produce an apparent contradiction. It's really the
well-known "Clock Paradox" recycled, with extra complications so you
don't
notice.
The thought experiment is one where Einstein introduces an atomic clock
to
serve as a standard and then considers a light clock moving relative to
it.
(The thought experiment dates from before lasers, but a laser is exactly
a
practical implementation of a light clock.) By analysing the internals of
the light clock, he concludes that the light clock will show time
dilation.
(This is because the light has to travel further to keep up with the
mirrors etc constituting the clock.)
The real experiment is the Hafele-Keating experiment (Science 177:166 and
177:168 (1972)). Atomic clocks were flown around the world in opposite
directions in aircraft, starting and ending in Washington. The elapsed
times were then compared with a clock that remained on the ground. The
results validated an equation given in the paper which incorporated the
special relativistic prediction plus a general relativistic correction
for
gravity. (Because the aircraft were at a higher altitude their clocks
ran
slower.)
The striking fact is that the clock which went around the world east to
west, that is, opposite to the earth's rotation, actually gained time.
That is, it showed net time contraction. There are several ways of
seeing
why this is the correct SR prediction which I will explain below.
Bill then juxtaposes the two experiments, letting the clock on the ground
in Washington be Einstein's atomic clock, and contrasting the light clock
and the east-to-west atomic clock. It then appears that the light clock
shows time dilation and the atomic clock shows time contraction. This
would be a contradiction of the relativity principal, by which there is
no
local experiment that can tell you your velocity. If there were such a
difference in rates, then harnessing a light clock and an atomic clock
and
comparing the results would give a portable velocity detector. I'm not
sure if that is exactly the way Bill would phrase the conclusion, but
he's
quite sure that this is a fatal contradiction, and he hints at a future
theory in which a light clock and an atomic clock _will_ behave the same.
There are two definitely correct ways of performing the juxtapostion of
the two experiments, and then Bill's which is a hybrid. In all cases we
ignore general relativity and treat gravity as an empirical correction.
The first is to look at everything from the point of view of an observer
stationary relative to the centre of the earth and not rotating. In this
case, the Washington clock is travelling at a constant speed in a circle.
The east-west clock is travelling in much the same circle at a lower
speed.
Thus the east-west clock shows less time dilation than the Washington
clock. The light clock is travelling with the east-west clock, so
obviously you would expect the same time dilation as the east-west clock.
This somewhat begs Bill's question of course, but there is no way of
motivating any difference between a light clock and an atomic clock in
this
picture. When I have presented this picture, Bill has argued that the
light clock running faster than the Washington clock is a contradiction
with the fact that in Einstein's thought experiment, the light clock is
running slower than the Washington clock. Tough. That's just how
relativity works. The relative time dilation between clocks not only
varies but changes sign, depending on the observer. You can find out
more
about it by looking up the "Clock Paradox" in a relativity book. (Or, if
you ask nicely I could mail you a PostScript file with a helpful diagram
that I think says as much as a thousand words.) Bill has argued that
Einstein didn't mention an observer in the particular chapter he (Bill)
was
referring to so that he (Einstein) must necessarily mean that the
comparison was done absolutely, without reference to any observer or any
time standard. I found a very clear Einstein quote that flatly
contradicted the idea that there was any observer independent way of
comparing clocks in relativity, but Bill just accused me of falsifying
the
reference.
The second is to look at everything from the point of view of an observer
moving in a straight line tangent to the earth's surface at Washington,
without rotating. To get a good mental picture of what I mean here,
imagine being a few tens of thousands of kilometres above the north pole
and look down. Pretend Washington is at the equator. You will see the
earth rolling like a bowling ball along this observer's x-axis. Thus
Washington will be moving in a cycloidal path. Once per day, it will
come
to rest, but all the rest of the time it will be moving. In particular,
12
hours after the rest position it will be moving with speed 2v_e. Its
_average_ speed is v_e.
If we do Bill's juxtaposition of the two experiments when Washington is
stationary, we would expect to find both the light clock and the
east-west
clock to show a small amount of time dilation. When I have presented
this
picture, Bill has argued that it cannot be, since the Hafele-Keating
experiment showed time contraction. And so it did. The key to resolving
the paradox in this picture is the fact that the time of the comparison
is
atypical. There only needs to be relative time contraction _when
averaged
over a whole circuit of the earth_. If we do the juxtaposition when
Washington is at the 12 hour position, the Washington clock itself shows
gamma(2_ve) of time dilation, whereas the light clock and the east-west
clock both show gamma(2v_e - v). Now gamma(v) is equal to v^2/(2c^2) for
small v, so gamma(2v_e) is approximately 2v_e^2/c^2 or 4gamma(v_e).
Similarly, gamma(2v_e - v) is 2v_e^2/c^2 - 2v v_e/c^2. We can get a
rough
idea of the true average by averaging these extreme values: the average
time dilation of the Washington clock is v_e^2/c^2 or 2gamma(v_e). This
is
the roughly linear sum of the effects of going at an average velocity of
v_e plus going in circles at v_e. The time dilation of both the other
clocks is v_e^2/c^2 - v v_e/c^2 + v^2/(2c^2). Since v is less than v_e,
the second term is bigger than the third term. Thus both travelling
clocks
are time dilated less on average, and show relative time contraction.
Again, everything is consistent.
Various people have told Bill at one time or another that one just can't
do
relativity on the surface of the earth. This is partly true and partly
false, and unfortunately Bill is not one for subtleties. To do it, one
must invoke the tangentially moving observer as above. SR observers must
without fail move in straight lines at constant speed, so this is the
best
one can do. The trick is an approximation which works well for limited
areas and times, such as all of nuclear physics. The problem is that it
can't be extended to the whole surface at once. As near as I can work
out,
Bill believes simultaneously both that applying special relativity
anywhere
in the universe is impossible (because no finite region of space is
exactly
inertial) and that because everybody else is doing it (applying SR to
bits
of the earth's surface) nobody is going to stop Bill doing it (applying
SR
to the whole earth's surface at once).
Let's see what happens if one tries. If you take the tangentially moving
observer and wrap 40000 km of his/her x-axis around the earth, it seems
to
fit. Where's the problem. The problem is in the Lorentz transformation
for
the time. The time coordinate of the tangentially moving observer, t', is
given in terms of that of the earth centre observer, t, by
t' = gamma(v_e)(t - x v_e/c^2)
If you've never really taken notice of the mysterious second term before,
notice it now. It's saying that if two events happen at the same time a
distance x apart, then the second observer will judge them to be
gamma(v_e)
x v_e/c^2 apart in time. That's weird, but it turns out Nature doesn't
care about that slop, which is always less than the time light would take
to travel between the events. At least Nature doesn't care, _provided
the
events really are x apart_. If you wrap the x-axis round in a circle,
you
bring the two events together! There can be no mistaking whether two
events at the same place are at the same time or not, thus, this is a
really bad idea. The best you can do while preserving the spirit of SR
is
put in a tiny little international dateline of a hundred nanoseconds or
so.
If you do this, you will then find that the light clock and the east-west
clock will be more time dilated than the Washington clock for all points
on
the earth's surface. However in the Hafele-Keating experiment, the moving
clocks cross the mini-date line and have to be put forward.
Alternatively, you can arbitrarily drop the second term in the Lorentz
transform and work with a non-relativistic time coordinate t'. I don't
know if UTC (Universal Time Coordinate) is currently implemented to where
it would be an issue, but this is the sort of time coordinate that the
implementors would be trying for, one with no discontinuities. The price
to be paid is that basic laws of SR physics are no longer expected to
apply. Since relativistic time is defined to _make_ the speed of light
equal to c, _this will not be true with respect to UTC_. The travelling
clocks will show time contraction all over the earth's surface, but this
is no longer SR's problem
I think this has been a very interesting problem and I'm glad Bill
spurred
me to think about it. I worry about him though...
Cheers,
Mark B.
ron house
>Time goes slower for those in a higher
>grav. field, right? I don't know what this has to do with the twin paradox,
>which is about what happens to someone who follows a geodesic, or
>stays in his own inertial frame, compared to someone who takes a
>path which is not a geodesic, and thus does not have a = 0 at all times,
>so his path is longer in spacetime. It really doesn't matter how the
>acceleration is distributed over the path, a path with a not = 0
>will always have longer proper time than one who has a = 0 the whole time
>(a = 0 defines a geodesic).
>Someone in a 10g field will age slower than someone in a 1g field.
Just about everything in this post is wrong. Time dilation has NO RELATION
to the strength of the gravitational field. There are two causes
of time dilation: speed and being LOWER IN GRAVITATIONAL POTENTIAL.
I have explained the accel. thing before. Re LIGP: consider this example: a
massive hollow shell in space. The closer we get to the sphere, the lower
our grav. potential gets and the slower time passes. By PURE COINCIDENCE the
gravitational field is also increasing. Now we pass through a small hole into
the inside of the shell. The gravitational field now falls to zero, yet
time still passes slower because we still have a low grav. potential.
So here we are, completely weightless, with time just barely ticking over.
The answer to all these problems is to recognise that these effects are
geometrical, not 'physical', by which latter term I mean due to dynamic
forces and other such like.
Van
Sorry for the confusion.
======
In article <1995Sep20....@schbbs.mot.com>,
Bronis Vidugiris <b...@areaplg2.corp.mot.com> wrote:
>In article <vanjacDF...@netcom.com>, Van <van...@netcom.com> wrote:
>
>)Isn't this reasoning backwards. Time goes slower for those in a higher
>)grav. field, right? I don't know what this has to do with the twin paradox,
>)which is about what happens to someone who follows a geodesic, or
>)stays in his own inertial frame, compared to someone who takes a
>)path which is not a geodesic, and thus does not have a = 0 at all times,
>>>>)so his path is longer (should be _shorter_) in spacetime.
>
>So far I agree.
>
>)It really doesn't matter how the
>)acceleration is distributed over the path, a path with a not = 0
>>>>)will always have longer (I mean shorter)
> proper time than one who has a = 0 the whole time
>)(a = 0 defines a geodesic).
>
>I think you let your fingers type a little too fast here! The geodosic
>is only a local maximum. It's quite possible to have a non-geodosic
>path have a longer tame than a geodosic path, because the locally
>maximum geodosic path isn't globally optimum (perhaps it spends a lot of
>time in a deep potential well).
Yes.
>)Someone in a 10g field will age slower than someone in a 1g field.
>
>Not always. For instance, because the potential is a maximum, I
>expect that a clock in the center of the earth would "tick" slower in spite
>of being in a zero g field than a clock on the surface of the
>earth experiencing a 1 g field. (Put the clock on the surface at the
>north pole if you're worried about the rotational effects).
I disagree. Both the field and potential, as well as the metric,
correspond to no field, no potential, and a flat space for a hole
of any size in a spherically symmetric mass.
For a star (with no holes), I the potential in
the interior ~ r, as I recall, so it goes to 0 at r = 0.
Van
William S. Lawson <law...@ludwig.llnl.gov> wrote:
>
>In article <vanjacDF...@netcom.com>, van...@netcom.com (Van) writes:
>|> Someone in a 10g field will age slower than someone in a 1g field.
>It isn't reasoning backwards. The person going in small 10g circles (perhaps
>in a jet airplane, or perhaps just in a centrifuge) never goes very fast. The
>person who travels at 1g to another star and back will incur a large time
>dilation along the way. One poster put it beautifully, as an analogy with
>a road being longer because of the turns, rather than because of the distance.
>One fairly gentle turn can make a road much longer than a whole series of
>sharp ones. To find the length of the road you must look at more than the
>turns.
I was referring to the effects of gravity, not velocity here.
If one says that graviational time dilation is negligible, and we are only
considering time dilation due to relative motion in flat space, then the
person going very slowly in a 10g field will have neglible time dilation,
the same a a person at rest in 0 g, so why gring gravity into things?
In the general case, one simply measures the proper time for both twins,
taking into effect the metric if necessary if space is not flat, but this
isn't the twin paradox.
In the twin paradox one has flat space, and both twins start and end
at the same event (pt. in spacetime). One changes inertial frames
and thus follows path with longer proper time.
I agree with the road analogy, but the opposite can also be true:
a person taking a path that looks like a high freq. sine wave
with a large amplitude may have a longer proper time T
than one with a continuous slow curve. If the amplitude of the wave
and frequency is very small (about a geodesic), then this path may be
shorter than the one with a continuous slow curve. All that matters
in the total length,
T = total proper time = Integral{dT;C) = Integral{sqrt|g_ab u^a u^b| dt; C}
Van
Yes, I came late to this thread and thought that gravitational
time dilation was being brought into the problem (as I said,
this is not the twin paradox). I guess I was wrong if no one was
talking about graviational fields, and only non-gravitational forces are
acting. If the centripetal acceleration == a in flat space is
a = 10g = v^2/r,
and r is large enough, v can be very small, so it would be as if
he was the twin who stayed home in his own inertial frame, and the
twin who travels at high speed to a distant star and back will be
younger, as his path will be shorter (I may have said longer before,
I don't recall, but in SR, geodesics are the _longest_ proper time
paths, as opposed to Euclidean space, where geodesics are the shortest
paths between 2 points.)
For the person who asked for an explanation of the twin paradox:
see the sci.phys FAQ posted here and in news.answers monthly
or get it by ftp as follows:
======
Any usenet FAQ can be obtained from rtfm.mit.edu in
pub/usenet/news.answers
Most World Wide Web browsers can handle FTP sites too, so you can just go to
URL
ftp://rtfm.mit.edu/pub/usenet-by-hierarchy
to access MIT's anonymous FTP archive (this URL will put you in the
hierarchical listing by newsgroup name;
ftp://rtfm.mit.edu/pub/usenet-by-group
instead will give you a listing of all the FAQs by group name in one
big directory, which makes it easier to browse at random but harder to
find a specific FAQ). The sci.physics FAQ can be found both under
news.answers and sci.physics.
There is also a full-fledged Web page for Usenet FAQs with URL
http://www.cis.ohio-state.edu/hypertext/faq/usenet/top.html
It isn't updated as scrupulously as the MIT archive. In general the MIT
site is the definitive source.
I get my stuff from the aol mirror, as its always open (note they changed
name from mirrors to mirror:
==========AOL MIRRORS======
ftp://mirror.aol.com/pub/
% /pub/cica winftp.cica.indiana.edu:/pub (Windows files)
% /pub/guitar ftp.nevada.edu:/pub/guitar (guitar info and tablature)
% /pub/info-mac sumex-aim.stanford.edu:/info-mac (Info-Mac Archive)
% /pub/mac mac.archive.umich.edu (Umich Mac Archive)
% /pub/rtfm rtfm.mit.edu:/pub (FAQ files)
William Owen
>: If you didn9t find this revelation of interest why have you wasted so
>: much time making several responses to the posting?
>Because one William Owen was going on and on about it as if it
>*ought* to hold some interest. I wondered what the hubub was about.
I made *one* - and only one - posting detailing this factor.
What you classify as 3going on and on2 was, as you are fully
aware, responses to postings challenging or ridiculing the idea.
Do you *really* think that if someone posts a negative response,
even nonsensical and totally irrelevant comments such as your own
I should have *no* right of reply?
>: To the best of my knowledge this minor point has never previously been
>: promulgated ergo could be considered as 3being original2.
>The point that it is possible to arrange things so that an
>observer that experiences a greater magnitude of acceleration also
>experiences the longer time duration? I've already explained
>why I find that trivial.
Am I writing to an echo?
If you9ve already explained why you find it trivial *why* bother
repeating yourself?
Of course the fact that your comment bears no relationship
whatsoever to the referred quotation exemplifies your lack of
credibility.
>: I9m certainly not going to waste my time explaining to you what
>: relationship the twin paradox has to relativity.
>And well you should not, since that wasn't what I was asking.
>I was asking what the fact that relativity was found to accurately model
>the spinward and anti-spinward trips has to do with some vague claim
>that relativists are rejecting new and original ideas.
Your statement was,:-
Re: 'Twin paradox' paradox
Date:
12 Sep 1995 13:43:16 GMT
From:
throopw%sheol...@dg-rtp.dg.com (Wayne Throop)
Organization:
Alcatel Network Systems (Raleigh, NC)
Wayne Throop throopw%sheol...@dg-rtp.dg.com
thr...@aur.alcatel.com
: 3Oh. OK. Then let me rephrase. "Why is this minor point of any
: interest?" I gather from this and previous postings that it has
: something to do with "original ideas" and presumably blind and
: dogmatic scientists, but the connection to relativity remains obscure.2
The 3minor point2 to which you refer is, of course, the fact that
the twin *can* experience acceleration yet *not* incur time
dilation and you question the connection between a matter
dealing with time dilation and relativity.
Now you are rephrasing again but hoping that the original
question had been forgotten
Your deceit terminates any further response however I assume
that you will just keep going on and on about a topic that you
find trivial. I guess it9s a way of seeing your name up in lights.
William Owen
>> Relativists insist that it is the twin who experiences acceleration
>> who incurs time dilation. The twin who is accelerated in the jet
>> experiences acceleration *but* they incur time 'contraction'
>> (i.e.their clock ticks over at a *faster* rate than their twin's) and
>> they age at a *faster* rate.
>But the clock travelling west in the HKX was *decelerating* at take off.
>The clock, pilot, cabin crew, passengers all experienced *deceleration*.
>They went from rotating at about 1000 miles per hour to rotating at
>about 500 miles per hour. They were facing west (with their backs
>to the direction of the 1000 mph rotation) so the deceleration pushed
>them back into their seats.
>The interesting point here is that within their frame of reference the
>plane's occupants could not distinguish between acceleration and
>deceleration. Both experiences 'feel' exactly the same.
Deceleration is *negative acceleration*.
The clock, pilot, cabin crew, passengers all experience
negative acceleration. The twin at the airport feels *no* rate
of acceleration, positive *or* negative - apart from gravity.
Negative acceleration is an integral aspect of the extant twin
paradox ratification resulting from a mid-journey turn-around
or negative acceleration incurred upon returning to Earth.
Mark Barton
>>)Someone in a 10g field will age slower than someone in a 1g field.
>>
>>Not always. For instance, because the potential is a maximum, I
>>expect that a clock in the center of the earth would "tick" slower in spite
>>of being in a zero g field than a clock on the surface of the
>>earth experiencing a 1 g field. (Put the clock on the surface at the
>>north pole if you're worried about the rotational effects).
>
>I disagree. Both the field and potential, as well as the metric,
>correspond to no field, no potential, and a flat space for a hole
>of any size in a spherically symmetric mass.
>
>For a star (with no holes), I the potential in
>the interior ~ r, as I recall, so it goes to 0 at r = 0.
I think you are mistaken. Two cases:
(i) the body is solid and you make tiny test holes in it - the _field_
goes
as r (because the enclosed mass goes as r^3 and the field law is 1/r^2).
The potential is an arbitrary constant term plus something proportional
to
r^2. You could always choose the constant term to make the potential
zero
at the centre, but this would be incompatible with the usual convention
of
zero at infinity. (Potential outside is conventionally -1/r.)
(ii) the body is hollow - the field is zero and the potential is
constant.
Again, it could be constant anything, but compatibility with the usual
convention means some negative value.
BTW, the connection of any of this to the twin paradox is that when the
astronaut fires the rocket engines to come home, the astronaut doesn't
move, but everything else in the universe accelerates. To account for
this, you have to postulate a fictitious pseudo-gravitational field
temporarily filling the universe. Only the astronaut, who "happens" to
be
firing rockets at the time the field switches on, manages to maintain the
same velocity. The earth falls "down" in this field, back toward the
astronaut. But, being briefly at a much higher position in the field,
the
earth sees a much higher psuedo-gravitational potential. By the
equivalence principle, this causes clocks on the earth to run fast, just
like a real gravitational field.
Cheers,
Mark B.
MARC EDWARD FORRESTER
>Negative acceleration is an integral aspect of the extant twin
>paradox ratification resulting from a mid-journey turn-around
>or negative acceleration incurred upon returning to Earth.
Is there any effective difference between positive and negative
acceleration, then? I'd have thought to define an acceleration
as positive or negative, you'd need to know which direction you
were travelling in, and that's not a meaningful question unless
asked w.r.t some other velocity..
Wayne Throop
: From: William Owen <wo...@extro.ucc.su.oz.au>
: I made *one* - and only one - posting detailing this factor.
But nevertheless makes posting after posting accusing me (among others)
of "sheer panic" and "clutching at any straw" and "deliberately
obfuscat[ing] the argument" and "deceit". I still call that "going on and on".
: If you9ve already explained why you find it trivial *why* bother
: repeating yourself?
Because one William Owen keeps insisting that there is something
interesting there, and accusing me of attempting to whitewash this
alleged interesting case. I can't help but be curious in such a
circumstance. I see an obvious triviality. William Owen keeps
shouting in my ear that there's more there. Something "original".
Something to "panic" over. What is this thing I'm missing? Who can say?
:: "Why is this minor point of any interest?"
:: I gather from this and previous postings that it has something to do
:: with "original ideas" and presumably blind and dogmatic scientists,
:: but the connection to relativity remains obscure.
: The 3minor point2 to which you refer is, of course, the fact that the
: twin *can* experience acceleration yet *not* incur time dilation and
: you question the connection between a matter dealing with time
: dilation and relativity.
I do NOT question the connection between a matter of time dilation and
relativity. I am questioning the connection between blind and dogmatic
scientists who are "panicing" and "clutching at straws" and relativity.
I see no such dogmatism, panic, or clutching, and so William Owen's
continued insistance that this relativistic triviality is provoking
such reaction is incongruous.
: Now you are rephrasing again but hoping that the original question had
: been forgotten Your deceit terminates any further response
No, I was hoping to rephrase to make my meaning clear.
In reacting to my original phraseology, William Owen seems to have been
confused as to what two items I was puzzled about. William Owen seems
bound and determined to think I meant "time dilation" and "relativity".
William Owen is wrong. I meant "alleged panic/dogmatism/etc of scientists"
and "relativity". I fail to see how I could have been any simpler
in my attempt to clarify, but for some reason William Owen takes it upon
himself to insult me yet again.
: I guess it9s a way of seeing your name up in lights.
A way to collect irrelevant insults, more like.
David Bert
> >> Relativists insist that it is the twin who experiences acceleration
> >> who incurs time dilation. The twin who is accelerated in the jet
> >> experiences acceleration *but* they incur time 'contraction'
> >> (i.e.their clock ticks over at a *faster* rate than their twin's) and
> >> they age at a *faster* rate.
> >But the clock travelling west in the HKX was *decelerating* at take off.
> >The clock, pilot, cabin crew, passengers all experienced *deceleration*.
> >They went from rotating at about 1000 miles per hour to rotating at
> >about 500 miles per hour. They were facing west (with their backs
> >to the direction of the 1000 mph rotation) so the deceleration pushed
> >them back into their seats.
> >The interesting point here is that within their frame of reference the
> >plane's occupants could not distinguish between acceleration and
> >deceleration. Both experiences 'feel' exactly the same.
> Deceleration is *negative acceleration*.
> The clock, pilot, cabin crew, passengers all experience
> negative acceleration. The twin at the airport feels *no* rate
> of acceleration, positive *or* negative - apart from gravity.
> Negative acceleration is an integral aspect of the extant twin
> paradox ratification resulting from a mid-journey turn-around
> or negative acceleration incurred upon returning to Earth.
It is the *high speed of travel* that creates the time dilation
in the Twin Paradox.
The mention of feeling acceleration was only used to refute the
arguments of Herbert Dingle (astrophysicist). Dingle said that
there would be *no* time variation because from the astronaut's
point of view it was the earth that was accelerating away from
him and back again.
At this point it was stated that the astronaut was experiencing
the higher speed of travel because it was the astronaut who
experienced the acceleration. The acceleration is only important
as it is an indication of which frame is moving at the higher speed.
Any time variation due to the increased gravity felt by acceleration
(or deceleration) in the HKX would be insignificant to the clocks
and also would have been cancelled out as it would have been
experienced by both clocks.
Therefore the question of acceleration or deceleration *is* important
as it indicates which clock is moving to the higher (or lower)
speed and therefore which clock will experience the time dilation
due to their respective speeds.
--
* Meeeow ! Call Spuddy on (01268) 515441 for FREE mail & Usenet access *
son...@utdallas.edu
> > Deceleration is *negative acceleration*.
No, the fact that one of them turns around and then has to accelerate to
catch up with the other one creates the time dilation.
> The mention of feeling acceleration was only used to refute the
> arguments of Herbert Dingle (astrophysicist). Dingle said that
> there would be *no* time variation because from the astronaut's
> point of view it was the earth that was accelerating away from
> him and back again.
> At this point it was stated that the astronaut was experiencing
> the higher speed of travel because it was the astronaut who
> experienced the acceleration. The acceleration is only important
> as it is an indication of which frame is moving at the higher speed.
That's why acceleration is important.
> Any time variation due to the increased gravity felt by acceleration
> (or deceleration) in the HKX would be insignificant to the clocks
> and also would have been cancelled out as it would have been
> experienced by both clocks.
That's true. It's the fact that one of the twins has to turn around and
accelerate to catch up with the other one that's important.
> Therefore the question of acceleration or deceleration *is* important
> as it indicates which clock is moving to the higher (or lower)
> speed and therefore which clock will experience the time dilation
> due to their respective speeds.
Yes!
:)
--
"Somewhere else the tea's getting cold." -- The Doctor
"In science there is only physics; everything else is stamp collectiong."
--Ernest Rutheford
"Politics is for the moment. An equation is for eternity." -- A. Einstein
Wayne Throop
: No, the fact that one of them turns around and then has to accelerate
: to catch up with the other one creates the time dilation.
This is a remarkably poor way of thinking about it. Consider the
properties of the "time dilation" this implies.
First, consider that the acceleration of person A is actually
affecting the age of person B. We can see this by noting that the
acceleration can occur over a small period of time, during which
A's age is largely unaffected. Yet when A rejoins B, B is found
to have an age shift.
Second, the effect is not primarily dependent on the acceleration's
magnitude, but only on the net velocity change times the distance
between A and B.
Third, the "time dilation" alegedly created or "caused" by A's acceleration
can actually cause B to UN-age. We know this must be so, because consider
what happens if A accelerates to rejoin B. The claim is that this
"causes" the age difference. Then A (again with little change in A's age)
changes A's mind and accelerates to resume the trip. And finally, changes
goals again and accelerates to rejoin B. No matter how many times A changes
goals, the age relationship when A and B rejoin is the same. Which means
that some of the age changes alegedly "caused" by the acceleration must
be negative, to "cancel out" all the positive ones allegedly "caused"
by A accelerating to rejoin B.
IMHO, the best way of understanding this is to remember that what's going
on to make the twin's ages different is NOT "time dilation", but rather
failure of simultaineity at a distance.
David Bert
> David Bert (be...@spuddy.mew.co.uk) wrote:
> > It is the *high speed of travel* that creates the time dilation
> > in the Twin Paradox.
> No, the fact that one of them turns around and then has to accelerate to
> catch up with the other one creates the time dilation.
Oh great! Just when I think I have got it all sorted out in my own mind
you come in with a sliding tackle! :-)
I thought that bit about the dilation when heading back on the return
journey was just a way of explaining the effect.
ie the astronaut is experiencing time dilation due to high speed
travel all through the journey but it only becomes *apparent*
when he turns around and starts to return. So that the dilation
does not *occur* because he turns around but is *noticed* because
he turns around.
Every time I get to a stage where I can logically fit all the pieces
together in an intuitive way along comes another bit that makes me
go "WHAT!?". You know, it sometimes seems to me that the whole
theory of relativity was invented just to try and make me believe
absolutely anything.
Nathan Urban
> : From: son...@utdallas.edu
> : No, the fact that one of them turns around and then has to accelerate
> : to catch up with the other one creates the time dilation.
> This is a remarkably poor way of thinking about it. Consider the
> properties of the "time dilation" this implies.
> First, consider that the acceleration of person A is actually
> affecting the age of person B. We can see this by noting that the
> acceleration can occur over a small period of time, during which
> A's age is largely unaffected. Yet when A rejoins B, B is found
> to have an age shift.
I am assuming B is the stay-home person and A is the travelling person.
Of _course_ B is going to have an age shift. (Well, I don't know what
an ``age shift'' is. I assume you mean B is going to age?) A finite
amount of time elapses, so B must age. What the acceleration affects
is the relative clock rates of A and B. It does not affect the actual
clock rate of B.
> Second, the effect is not primarily dependent on the acceleration's
> magnitude, but only on the net velocity change times the distance
> between A and B.
So? It can still be explained as an acceleration effect. It is an easy
way to see how the symmetry between the two observers is broken.
> Third, the "time dilation" alegedly created or "caused" by A's acceleration
> can actually cause B to UN-age. We know this must be so, because consider
> what happens if A accelerates to rejoin B. The claim is that this
> "causes" the age difference. Then A (again with little change in A's age)
> changes A's mind and accelerates to resume the trip. And finally, changes
> goals again and accelerates to rejoin B. No matter how many times A changes
> goals, the age relationship when A and B rejoin is the same. Which means
> that some of the age changes alegedly "caused" by the acceleration must
> be negative, to "cancel out" all the positive ones allegedly "caused"
> by A accelerating to rejoin B.
No, you don't un-age. What happens is that when B accelerates and then
travels out, its clock is running slower than A's, so it measures a
shorter duration of time. If A then accelerates to catch up with B, now
it is A's clock that is running slower, so B ages faster and things
cancel out over the same duration of time.
> IMHO, the best way of understanding this is to remember that what's going
> on to make the twin's ages different is NOT "time dilation", but rather
> failure of simultaineity at a distance.
I'm not sure exactly what failure of simultaneity at a distance is, but
it is true that in SR there are often several ways of looking at things,
so maybe you're right. I just say that thinking in terms of
acceleration is a perfectly good way of doing it.
By the way, I took this followup out of sci.space.policy, sci.astro,
and alt.sci.time-travel. It doesn't belong in any of those.
--
-----------------------------------------------------------------------------
Nathan Urban | e-mail: nur...@mail.vt.edu
Undergraduate {CS,Physics}, Virginia Tech | WWW: http://nurban.campus.vt.edu/
-----------------------------------------------------------------------------
son...@utdallas.edu
> David Bert <be...@spuddy.mew.co.uk> wrote:
> >It is the *high speed of travel* that creates the time dilation
> >in the Twin Paradox.
> This is the weird bit about the twin paradox..
> How do you know which twin is travelling fast, and which is stationary?
You don't and can't until the twins come in contact with one another. In
fact -- it doesn't even make a hill of beans until they come in contact
with one another. The whole point is that one of the twins has to turn
around and "catch up" with the other one. That's what determines which
is travelling fast and which is stationary. The twin that turned around
and went back to the other one was the one moving while the other one was
the one that was stationary.
Wayne Throop
:: affecting the age of person B. We can see this by noting that the
:: acceleration can occur over a small period of time, during which A's
:: age is largely unaffected. Yet when A rejoins B, B is found to have
:: an age shift.
: From: nur...@csugrad.cs.vt.edu (Nathan Urban)
: Of _course_ B is going to have an age shift. (Well, I don't know what
: an ``age shift'' is. I assume you mean B is going to age?) A finite
: amount of time elapses, so B must age. What the acceleration affects
: is the relative clock rates of A and B. It does not affect the actual
: clock rate of B.
What I mean by "age shift" is that, since A and B are in relative motion,
and since there is no way in SR to state which one is "really" moving
and which is "really" motionless, then A (just prior to turnaround) considers
B to have aged *LESS* then A. A then turns around, and during the return
trip, *ALSO* considers B to have aged less then A. But the net result in
SR is that B ages *MORE* than A. The difference between the naive summation
of A's aging process counted by B, and the actual age of B when A and B
rejoin, is what I meant by an "age shift".
But note closely what my claims are. I'm *not* claiming that the
acceleration doesn't affect things. I'm merely claiming that it is a
poor explanation to say that the acceleration "causes" or "creates" the
time dilation. Because, given only the acceleration magnitude and
timing, you can't calculate the age difference. You need to know the
trajectory and relative velocities. Even if you have a timewise log of
the acceleration *vector* the only way you can calculate the age
difference is by accounting for the velocity and distance this implies.
: It can still be explained as an acceleration effect. It is an easy
: way to see how the symmetry between the two observers is broken.
I completely agree that the acceleration is how you can see that the
symmetry is broken, and is the reason, or even the "cause" of one twin's
age being different than the other's. Again, I just think that saying that the
acceleration "creates" or "causes" the time dilation is misleading. For
example, muons created by cosmic ray interactions in the upper
atmosphere DO actually reach the ground despite not (under newtonian
physics) having enough lifetime to do so. Yet no (significant)
acceleration exists in this case at all; since we have a case of time
dilation with no acceleration, saying that the latter creates the former
is (IMHO) not a good explanation.
How to I reconcile that with the fact that I just said I agreed that the
acceleration is the "cause" of the twin's ages being different? Because
their ages differ because A can't get B's age just by summing up the
two segments of B's ageing during the two legs of A's trip; this in turn
is because of the acceleration. But the reason you can't to the sum
legitimately is because of failure of simultaineity, not because of
time dilation.
: I'm not sure exactly what failure of simultaneity at a distance is,
: but it is true that in SR there are often several ways of looking at
: things, so maybe you're right. I just say that thinking in terms of
: acceleration is a perfectly good way of doing it.
I agree that concentrating on the acceleration is a good way of showing
the asymmetry. Also, showing that the time dilations from A's original
frame mean A's return trip takes a long, long time and is only time-dilated
to seem short to A, and this explains the age difference. BUT. It is equally
legitimate to say that A's *outward* trip is the one that takes a long, long
time and is only time-dilated to seem short, and the *return* trip is the
one where B only ages a small amount. And of course, saying that the
acceleration *causes* or creates the time dilation on the trip segment
that happened *before* the acceleration is... well, a poor way of looking
at it, and prone to confuse people eventually.
As to failure of ... oh, let me just say FoSaaD. As to FoSaaD, it is
the difference in time coordinate between two SR coordinate systems due
to the distance between two events. In the twin paradox, FoSaaD comes
into it because the reference frame of B just before turnaround is
different from that just after turnaround. The time shift in the event
of what-A-is-doing-Right-Now between these two reference frames of B is
one way of accounting for A's greater age when they get back together.
To me, it is a much better way to think about the situation. Because
the cause of the asymmetry (the acceleration) is what causes there to be
two referencne frames from which B models things, and the FoSaaD between
these two reference frames, when added to the time dilation that B
thinks has *slowed* A's ageing, exactly accounts for A's actual greater
age when they meet up again. Saying that the acceleration "causes" the
event in A's timeline which B considers simultaneous to turnover to
change has fewer puzzling issues, and is, all in all, a much neater
account IMHO.
See "The Feynman Lectures on Physics", Vol I, section 15-6,
where Feynman names the effect and gives the formula for FoSaaD.
The point is, in SR, reference frames can differ about the time interval
between events, but the proper time along a worldline is always the same.
But explaining *why* these two features fit together without resulting
in contradictions requires one to note that when you talk about what's
happening "now" at a distance is ambiguous, and the time offsets by which
different coordinate systems displace simultaneity over distance is exactly
what makes it all work. This is especially apparent when viewed geometrically.
Note well: the mathematics of it just *is*. I'm talking entirely about mental
*models* of the mathematics used for learning or explaining or motivating.
Nathan Urban
> What I mean by "age shift" is that, since A and B are in relative motion,
> and since there is no way in SR to state which one is "really" moving
> and which is "really" motionless, then A (just prior to turnaround) considers
> B to have aged *LESS* then A. A then turns around, and during the return
> trip, *ALSO* considers B to have aged less then A. But the net result in
> SR is that B ages *MORE* than A. The difference between the naive summation
> of A's aging process counted by B, and the actual age of B when A and B
> rejoin, is what I meant by an "age shift".
When A turns around, he sees B start to age faster all of a sudden.
All those lagged photons catch up all at once.
This is easy to see with spacetime diagrams. As I'm sure you've done.
More people should actually draw out what's happening.. there would be
fewer debates on sci.physics..
> But note closely what my claims are. I'm *not* claiming that the
> acceleration doesn't affect things. I'm merely claiming that it is a
> poor explanation to say that the acceleration "causes" or "creates" the
> time dilation. Because, given only the acceleration magnitude and
> timing, you can't calculate the age difference. You need to know the
> trajectory and relative velocities. Even if you have a timewise log of
> the acceleration *vector* the only way you can calculate the age
> difference is by accounting for the velocity and distance this implies.
The existence of the acceleration is what allows for the difference.
True, you need an exact acceleration profile to calculate exactly what
happens, but the mere existence of acceleration allows one to resolve
the twin paradox (although not necessarily provide exact figures.)
So that's all I'm trying to say.
> : It can still be explained as an acceleration effect. It is an easy
> : way to see how the symmetry between the two observers is broken.
> I completely agree that the acceleration is how you can see that the
> symmetry is broken, and is the reason, or even the "cause" of one twin's
> age being different than the other's. Again, I just think that saying that the
> acceleration "creates" or "causes" the time dilation is misleading. For
> example, muons created by cosmic ray interactions in the upper
> atmosphere DO actually reach the ground despite not (under newtonian
> physics) having enough lifetime to do so. Yet no (significant)
> acceleration exists in this case at all; since we have a case of time
> dilation with no acceleration, saying that the latter creates the former
> is (IMHO) not a good explanation.
No, that's not what I was trying to say! I think we are agreed,
actually. It is true that merely a difference in velocity produces time
dilation. No acceleration necessary. It's just the acceleration which
breaks the symmetry in the twin paradox.. if you didn't have it, than
both A and B would see the other as aging less than themselves.
> How to I reconcile that with the fact that I just said I agreed that the
> acceleration is the "cause" of the twin's ages being different? Because
> their ages differ because A can't get B's age just by summing up the
> two segments of B's ageing during the two legs of A's trip; this in turn
> is because of the acceleration. But the reason you can't to the sum
> legitimately is because of failure of simultaineity, not because of
> time dilation.
I prefer say that you can't do the sum legitimately is because you switched
inertial frames in the middle of the problem. That is equivalent to FoSaaD.
> As to failure of ... oh, let me just say FoSaaD. As to FoSaaD, it is
> the difference in time coordinate between two SR coordinate systems due
> to the distance between two events. In the twin paradox, FoSaaD comes
> into it because the reference frame of B just before turnaround is
> different from that just after turnaround. The time shift in the event
> of what-A-is-doing-Right-Now between these two reference frames of B is
> one way of accounting for A's greater age when they get back together.
Right. It comes into it because the reference frames are different just
before and just after turnaround. Which is equivalent to saying that
there was an acceleration.
> age when they meet up again. Saying that the acceleration "causes" the
> event in A's timeline which B considers simultaneous to turnover to
> change has fewer puzzling issues, and is, all in all, a much neater
> account IMHO.
Isn't that what I said?
> The point is, in SR, reference frames can differ about the time interval
> between events, but the proper time along a worldline is always the same.
> But explaining *why* these two features fit together without resulting
> in contradictions requires one to note that when you talk about what's
> happening "now" at a distance is ambiguous, and the time offsets by which
> different coordinate systems displace simultaneity over distance is exactly
> what makes it all work. This is especially apparent when viewed geometrically.
Yes, you can look at it that way. I kind of feel uncomfortable with
simultaneity in SR right now, so I like my way. They are both
equivalent anyway. It's just a matter of which one explains things more
clearly to you.
> Note well: the mathematics of it just *is*. I'm talking entirely about mental
> *models* of the mathematics used for learning or explaining or motivating.
I wish other people would realize this.
Wayne Throop
:: B considers simultaneous to turnover to change has fewer puzzling
:: issues, and is, all in all, a much neater account IMHO.
: From: nur...@csugrad.cs.vt.edu (Nathan Urban)
: Isn't that what I said?
I still don't think so, for a couple of reasons. First, just a terminology
issue: I don't count that as a "time dilation". Second, because the time
offsets caused by this effect can be negative (depending on the direction
of the acceleration), and have the other effects I pointed out before
that makes me wary of calling the effect "time dilation".
: When A turns around, he sees B start to age faster all of a sudden.
: All those lagged photons catch up all at once.
SR effects as calculated by lorentz transforms or as shown in space-time
diagrams have nothing to do with visual efffects due to lightspeed
delay. (Nathan probably knows this already, but I'd like to reinforce
that the simultaineity effects I'm talking about at turnover are not
visual or message-delay effects.
Mark Barton
>: From: nur...@csugrad.cs.vt.edu (Nathan Urban)
>: When A turns around, he sees B start to age faster all of a sudden.
>: All those lagged photons catch up all at once.
>
>SR effects as calculated by lorentz transforms or as shown in space-time
>diagrams have nothing to do with visual efffects due to lightspeed
>delay. (Nathan probably knows this already, but I'd like to reinforce
>that the simultaineity effects I'm talking about at turnover are not
>visual or message-delay effects.
Hear, hear. It's possibly a lost cause, but I'd like to see a ban on the
word "see" used in explanations of relativity except possibly in such
collocations as "see, visually, with the eye".
That would create a need for a good substitute to replace the misleading
"see" and the unwieldy "measured in accordance with the protocols of
special relativity". I would like to propose "log" as descriptive of
what
actually has to happen nearly all the time if you think about it - that
some automatic bit of equipment has to log a value and timestamp it. The
actual human observer, if any, can't be everywhere at once, not even in
principle. Any better ideas?
Cheers,
Mark B.
awi...@iquest.com
twin paradox. I'm not singling you out, it's just I can't find a way to address
this post to "all".
Anyway, the twin paradox is posed to physics students while they are taking
Special Relativity. This means acceleration is zero (!). So the twin paradox
has nothing to do with acceleration.
The paradox is as follows:
Some guy goes to some star that is about 20 light-years away at a
constant speed (!) of near speed of light. He leaves his twin brother
on earth. So a round trip for the astronaut would be slightly over 40
years as seen by his twin brother. Now due to the fact that the time
dilation formula is
t = t0 Sqrt[ 1 - v^2/c^2 ]
with t0 = 40 years, we can see that the astronaut hardly ages because
v is nearly c.
Now here's the "paradox" part:
Einstein derived this equation to be covariant. That means that it should
work equally well for the guy travelling to the star. Einstein's response
was yes. He sees his twin on earth aging less than him, but then we have
to realize that the trip itself undergoes a Lorentz transformation, so that
the star and earth very nearly coexist in the same space for the astronaut.
The distance that the astronaut sees to the star is
l = l0 Sqrt[ 1 - v^2/c^2 ]
with l0 = 20 light-years.
Solution:
The guy on earth ages forty years, where the astronaut hardly ages at all.
The guy on earth swears the trip was to a star 20 light-years away, where
the astronaut swears it was very, very near.
Of course all this ignores any effect acceleration may have!
Andy
awi...@iquest.com
>David Bert <be...@spuddy.mew.co.uk> wrote:
>>It is the *high speed of travel* that creates the time dilation
>>in the Twin Paradox.
>
>This is the weird bit about the twin paradox..
>How do you know which twin is travelling fast, and which is stationary?
According to Einstein, it doesn't matter. That's because it's the relative
speed that counts. That is the speed that one is moving with respect to
the other.
Andy
Christopher R. Volpe
You're avoiding the question. You just said it doesn't matter, but it really
does matter, because when the twins meet again, it will be the one in the
spaceship who has barely aged, not the one who rode away from the spaceship
and back on that high velocity planet. Since it is perfectly valid for the guy
in the spaceship to claim that the earth and distant star are moving very fast
in the other direction, which is consistent with his observation that the guy
on earth is aging slowly, the following question immediately comes to mind:
"Why is it *NOT* the case that the guy in the spaceship, who considers himself
stationary, and who sees the earth and distant star make a very fast round
trip, ends up meeting a barely-aged earth-bound traveller after all is done?"
The answer is not "because the spaceship accelerated", because, from the
spaceship's frame of reference, it is the planet and stars that accelerated.
Although I'm no expert, I presume the answer lies in General Relativity, which
probably claims that the acceleration of all the mass in the universe away
from the spaceship induces a gravitational field that acts on the spaceship,
causing his clock to tick slower than that of the earth observer, who is in
freefall in this gravitational field.
--
Chris Volpe Phone: (518) 387-7766 (Dial Comm 8*833
GE Corporate R&D Fax: (518) 387-6560
PO Box 8, Schenectady, NY 12301 Email: vol...@crd.ge.com
Halibut
: >This is the weird bit about the twin paradox..
: >How do you know which twin is travelling fast, and which is stationary?
: According to Einstein, it doesn't matter. That's because it's the relative
: speed that counts. That is the speed that one is moving with respect to
: the other.
I thought there WAS a "preferred twin".
The twin that accelerates is the one fothat ends up aged less
when they meet again.
Halibut
: The answer is not "because the spaceship accelerated", because, from the
: spaceship's frame of reference, it is the planet and stars that accelerated.
: Although I'm no expert, I presume the answer lies in General Relativity, which
: probably claims that the acceleration of all the mass in the universe away
: from the spaceship induces a gravitational field that acts on the spaceship,
: causing his clock to tick slower than that of the earth observer, who is in
: freefall in this gravitational field.
Actually, I believe the answer *is* "because the spaceship
accelerated", since it is a very easy matter to determine which one
accelerated. It was the one where the guy was squished into his chair at
5G for a few hours.
Nathan Urban
> It's clear that somehow some really wrong info is being disseminated about the
> twin paradox. I'm not singling you out, it's just I can't find a way to
> address this post to "all".
existing ones..
> Anyway, the twin paradox is posed to physics students while they are taking
> Special Relativity. This means acceleration is zero (!). So the twin paradox
> has nothing to do with acceleration.
See below.
> The paradox is as follows:
> Some guy goes to some star that is about 20 light-years away at a
> constant speed (!) of near speed of light. He leaves his twin brother
[...]
> Now here's the "paradox" part:
> Einstein derived this equation to be covariant. That means that it should
> work equally well for the guy travelling to the star. Einstein's response
> was yes. He sees his twin on earth aging less than him, but then we have
[...]
> Of course all this ignores any effect acceleration may have!
Well, no, acceleration does have something to do with this. As you say,
the paradox is that you should get the same result for both twins,
because there is total symmetry between the two cases. Thus it cannot
be the case that one twin is younger than the other. Now, the trip out
and back can be nice constant velocity trips, but to get back, you have
to undergo some acceleration to reverse your velocity, if only for an
instant. That is the asymmetry -- the travelling twin switched inertial
frames. The only way you can do that is to undergo acceleration.
Some people here will probably argue that you shouldn't be looking at this
from an acceleration point of view, but from a simultaneity-at-a-distance
point of view. Nevertheless, it is perfectly valid to say that
acceleration has something to do with it.
son...@utdallas.edu
> It's clear that somehow some really wrong info is being disseminated about the
> twin paradox. I'm not singling you out, it's just I can't find a way to address
> this post to "all".
> Anyway, the twin paradox is posed to physics students while they are taking
> Special Relativity. This means acceleration is zero (!). So the twin paradox
> has nothing to do with acceleration.
Or . . . this is an example of "things to come" -- GR. One way of
looking at this "paradox" is that it arises out of SR and is answered by GR.
> The paradox is as follows:
> Some guy goes to some star that is about 20 light-years away at a
> constant speed (!) of near speed of light. He leaves his twin brother
> on earth. So a round trip for the astronaut would be slightly over 40
> years as seen by his twin brother. Now due to the fact that the time
> dilation formula is
> t = t0 Sqrt[ 1 - v^2/c^2 ]
> with t0 = 40 years, we can see that the astronaut hardly ages because
> v is nearly c.
> Now here's the "paradox" part:
> Einstein derived this equation to be covariant. That means that it should
> work equally well for the guy travelling to the star. Einstein's response
> was yes. He sees his twin on earth aging less than him, but then we have
> to realize that the trip itself undergoes a Lorentz transformation, so that
> the star and earth very nearly coexist in the same space for the astronaut.
> The distance that the astronaut sees to the star is
> l = l0 Sqrt[ 1 - v^2/c^2 ]
> with l0 = 20 light-years.
> Solution:
> The guy on earth ages forty years, where the astronaut hardly ages at all.
> The guy on earth swears the trip was to a star 20 light-years away, where
> the astronaut swears it was very, very near.
But you forgot to do it for the "stationary" brother! This -- as well as
the previous time dilation equation -- *can* be applied to *both*
inertial reference frames. And we still have the same paradox. This
problem cannot be answered by SR. One can say that the traveling twin,
after turning around, must travel at a higher velocity than the
stationary twin in order to catch up, but one can say the same for the
stationary twin since both are experiencing a constant velocity
throughout the "experiemnt". The thing is that the traveling twin *must*
accelerate to at least turn around, causing him to experience a point
where his reference frame is *not* an inertial reference frame.
> Of course all this ignores any effect acceleration may have!
> Andy
Christopher R. Volpe
He accelerated with respect to what? A preferred or absolute reference frame?
There is none. Relative to his own frame of reference, he did not accelerate,
in fact, he did not even move. The fact that he was squished into his chair
could just as easily be described as a gravitational effect. I'm getting
squished in my chair at 1G right now. By your reasoning, I'm accelerating at
9.8 m/s^2, and if I sit here long enough, I should eventually be travelling at
pretty darn close to c.
Tim Dugan
I think a valid point is being missed:
First, the twin accellerates away,
apparently slowing aging ("red shift")
Then, to return, the twin accellerates toward,
apparently increasing aging ("blue shift")
Am I wrong or am I wrong?
-t
Tim Dugan
>It's clear that somehow some really wrong info is being disseminated about the
>twin paradox. I'm not singling you out, it's just I can't find a way to address
>this post to "all".
>
>Anyway, the twin paradox is posed to physics students while they are taking
>Special Relativity. This means acceleration is zero (!). So the twin paradox
>has nothing to do with acceleration.
>
>Some guy goes to some star that is about 20 light-years away at a
>constant speed (!) of near speed of light. He leaves his twin brother
>on earth. So a round trip for the astronaut would be slightly over 40
>years as seen by his twin brother. Now due to the fact that the time
>dilation formula is
>
> t = t0 Sqrt[ 1 - v^2/c^2 ]
>
>with t0 = 40 years, we can see that the astronaut hardly ages because
>v is nearly c.
>
>Now here's the "paradox" part:
>Einstein derived this equation to be covariant. That means that it should
>work equally well for the guy travelling to the star. Einstein's response
>was yes. He sees his twin on earth aging less than him, but then we have
>to realize that the trip itself undergoes a Lorentz transformation, so that
>the star and earth very nearly coexist in the same space for the astronaut.
>The distance that the astronaut sees to the star is
>
> l = l0 Sqrt[ 1 - v^2/c^2 ]
>
>with l0 = 20 light-years.
>
>Solution:
>The guy on earth ages forty years, where the astronaut hardly ages at all.
Not exactly. FROM THE PERSPECTIVE of the guy on earth, the astronaut
hardly ages at all. From the perspective of the astronaut, the guy
on earth hardly ages at all.
>The guy on earth swears the trip was to a star 20 light-years away, where
>the astronaut swears it was very, very near.
Not sure about this point.
Wayne Throop
: From: ti...@Starbase.NeoSoft.COM (Tim Dugan)
: Not exactly. FROM THE PERSPECTIVE of the guy on earth, the astronaut
: hardly ages at all. From the perspective of the astronaut, the guy on
: earth hardly ages at all.
No. Remember, we're talking about when they meet up again, and are
standin side by side. Their perspectives on the here-and-now are the
same perspective then. And they both agree, the guy who stayed on earth
aged 40 years, the astronaut aged some (perhaps vastly) lesser amount.
And this is unambiguous, not a matter of perspective. One of them has
had many times as many heartbeats as the other, many time the number
of seconds tick of on their wristwatch, many times as many respirations,
many times as many ATP cycles gone through at the molecular level in
their cells. And no, it isn't due to one getting more exercise, either.
Mark Matis
throopw%sheol...@dg-rtp.dg.com says...
>
>: From: ti...@Starbase.NeoSoft.COM (Tim Dugan)
>: First, the twin accellerates away, apparently slowing aging ("red
>: shift") Then, to return, the twin accellerates toward, apparently
>: increasing aging ("blue shift")
>: Am I wrong or am I wrong?
>
>
>Doppler shifts are, therefore, another kettle of fish of a different color.
Is that red or blue? }:-]
Tae W Son
|> In article <44vcak$3...@cnct.com>, Halibut <hal...@cnct.com> wrote:
|> >awi...@iquest.com wrote:
|> >
|> >: >This is the weird bit about the twin paradox..
|> >: >How do you know which twin is travelling fast, and which is stationary?
|> >
|> >: According to Einstein, it doesn't matter. That's because it's the relative
|> >: speed that counts. That is the speed that one is moving with respect to
|> >: the other.
|> >
|> > I thought there WAS a "preferred twin".
|> >
|> > The twin that accelerates is the one fothat ends up aged less
|> >when they meet again.
|>
|> I think a valid point is being missed:
|>
|> apparently slowing aging ("red shift")
|>
|> Then, to return, the twin accellerates toward,
|> apparently increasing aging ("blue shift")
|>
|> Am I wrong or am I wrong?
Wrong, even if negative acceleration means an increase in age. The
point is that the travelling twin has to accelerate to overcome the
stationary twin -- in short, his *net* acceleration is still greater.
Here's a rough and simple example. 1) Twin A decelerates away. Then
he turns around and accelerates back towards the Twin B. In order to
catch up, the acceleration must be greater than the deceleration in
order for Twin A to "catch up" with Twin B. 2) Twin A accelerates
away. Then he turns around and decelerates back towards Twin B. At
some point, his deceleration has to become negative in order for him
to "catch up" with Twin B. In other words, his deceleration must turn
into an acceleration -- and, as in case 1, his acceleration must be
greater than the deceleration in order for him to catch up with Twin
B.
Wayne Throop
: First, the twin accellerates away, apparently slowing aging ("red
: shift") Then, to return, the twin accellerates toward, apparently
: increasing aging ("blue shift")
: Am I wrong or am I wrong?
Well, I'm not sure which "wrong" you mean, but you are, indeed, wrong.
The age-rate effects discussed in the twin paradox have nothing to do
with doppler shifts. (Well... exact details of doppler shifts may have
to do with the age-rate effects discussed in the twin paradox, but not
the other way 'round, if you see what I mean. Hrm. Well. What I mean
is, when we say that (given a coordinate frame) a person in motion "ages
slower" than one at rest, we're talking about the rate of the person's
physiological ageing process in that coordinate system, not the rate
that photons reach some stationary observer.)
Doppler shifts are, therefore, another kettle of fish of a different color.
wil...@hg.uleth.ca
>Christopher R. Volpe (vo...@bart.crd.ge.com) wrote:
>
>: The answer is not "because the spaceship accelerated", because, from the
>: spaceship's frame of reference, it is the planet and stars that accelerated.
>: Although I'm no expert, I presume the answer lies in General Relativity, which
>: probably claims that the acceleration of all the mass in the universe away
>: from the spaceship induces a gravitational field that acts on the spaceship,
>: causing his clock to tick slower than that of the earth observer, who is in
>: freefall in this gravitational field.
>
> Actually, I believe the answer *is* "because the spaceship
>accelerated", since it is a very easy matter to determine which one
>accelerated. It was the one where the guy was squished into his chair at
>5G for a few hours.
The best way to look at this is with a construction called a Brehme
diagram. You will see that the invariant interval of the stay-at-home
twin is necessarily longer than that of the travelling twin. I'm not
going to try to explain it here but if you can find a book by Shadowitz,
he explains it better than I can. Strictly speaking the twin paradox
is not a consequence of the acceleration other than in the sense that
the world line of the stay at home twin is straight, whereas the world
line of the travelling twin is bent. A variation of the twin paradox
(thought up by a student in a course I taught, who had never heard of the
twin paradox), is to have the travelling twin travel in a circle.
The effect is the same.
twin fly in a large circle.
Halibut
: > Actually, I believe the answer *is* "because the spaceship
: >accelerated", since it is a very easy matter to determine which one
: >accelerated. It was the one where the guy was squished into his chair at
: >5G for a few hours.
: So, if the other twin were in a 5G gravity field, then this would be
: negated?
No. If the other twin were in a 5G gravity field, and then all of
a suddne foudn himself in a 10G field, then both are travelling away from
each other. Just being in a 5G field is not the same.
Wayne Throop
: He accelerated with respect to what? A preferred or absolute reference frame?
With respect to any inertial frame. Inertial frames are coordinate systems
that are set up so that there are no inertial (or "ficticious") forces.
: I'm getting squished in my chair at 1G right now. By your reasoning,
: I'm accelerating at 9.8 m/s^2, and if I sit here long enough, I should
: eventually be travelling at pretty darn close to c.
Nnnnnnnnooooooo, not quite. In special relativity, gravity hasn't yet
been made a ficticious force. (I'm simplifying somewhat, but that's one
way of looking at it; that is, that we can get away with treating
gravity as a newtonian force field if it isn't too strong). Therefore,
in this model, sitting on the planet here, electromagnetic forces are
keeping the atoms from collapsing on each other, and gravitational
forces are squishing everything together, but you are (in the relevant
in-this-model-inertial frame) not accelerating. Your distance from the
earth isn't changing, nor is it's rate of change changeing, which means
no acceleration. (Well, the earth's rotation and revolution about the
sun (and galaxy (and whatnot)) means you *are* accelerating, but all
these effects (while detectable) are very very small compared to the
effects of the motions of the traveling twin.)
Now, GR introduces the notion that gravity is an inertial force, but at
the same time shows how to deal with physics from non-inertial frames.
And the way you deal with physics from non-inertial frames is that
inertial forces cause time dilation and so on and on. From this
perpective, the traveling and stay-at-home twins are *still* not
equivalent, because the global geometry of the inertial forces
introduced by their coordinate systems aren't symmetric. The traveling
twin is way, WAY deep in an inertial force potential during turnaround,
which introduces the same FoSaaD that switching inertial frames does.
The inertial force potential of the earth's gravity is miniscule by
comparison, even if the traveling twin only does a 1-g turnaround,
because gravity drops off inverse-square, while the inertial force in
the traveling twin's frame does not.
More or less. Anecdotes for comparison purposes only. Actual anecdotes
may vary. Anecdotes packed by bytecount. Some bloating may occur during
network transit. Void where prohibited. No purchase necessary.
State or local restricitons may apply. No physicists were harmed
in the filming of this episode.
son...@utdallas.edu
> In <44lb60$o...@utdallas.edu>, son...@utdallas.edu writes:
> >MARC EDWARD FORRESTER (me...@aber.ac.uk) wrote:
> >> >It is the *high speed of travel* that creates the time dilation
> >> >in the Twin Paradox.
> >
> >> How do you know which twin is travelling fast, and which is stationary?
> >
> >fact -- it doesn't even make a hill of beans until they come in contact
> >with one another. The whole point is that one of the twins has to turn
> >around and "catch up" with the other one. That's what determines which
> >is travelling fast and which is stationary. The twin that turned around
> >and went back to the other one was the one moving while the other one was
> >the one that was stationary.
> No Marc. The speed the Lorentz time dilation equation is refering to is
> *relative* speed. That is how fast one person is travelling with respect
> to the other. It is clear that one considers himself at rest and the other
> travelling at near speed of light. All of the perspective problem illusions
> become a wash in relativity. That is why relativity is so beautiful.
> The one that turned around after reaching his destination is just as much at
> rest in his frame of reference as the guy on earth is in his frame. It's always
> the "other" guy that is in motion. So no matter which frame you take to be
> at "absolute" rest, the laws of nature always turn out the same as long as
> you take "proper measurements" consistently; *this* is the essence of
> relativity!
That's true -- but you're forgetting to take into account that the twin
that turned around was temporarily not in an inertial reference frame.
In that moment where he turned around, he wasn't at constant velocity and
therefore he is the one that ages slower because of it.
--
"Somewhere else the tea's getting cold." -- The Doctor
"In science there is only physics; everything else is stamp collectiong."
--Ernest Rutherford
William S. Lawson
In article <44uos9$o...@rdsunx.crd.ge.com>, vo...@bart.crd.ge.com (Christopher R. Volpe) writes:
|> In article <44ulp4$c...@polo.iquest.com>, awi...@iquest.com writes:
|> >In <44h12n$3...@osfa.aber.ac.uk>, me...@aber.ac.uk (MARC EDWARD FORRESTER) writes:
|> >>>It is the *high speed of travel* that creates the time dilation
|> >>>in the Twin Paradox.
|> >>
|> >>This is the weird bit about the twin paradox..
|> >>How do you know which twin is travelling fast, and which is stationary?
|> >
|> >the other.
|>
|> does matter, because when the twins meet again, it will be the one in the
|> spaceship who has barely aged, not the one who rode away from the spaceship
|> and back on that high velocity planet. Since it is perfectly valid for the guy
|> in the spaceship to claim that the earth and distant star are moving very fast
|> in the other direction, which is consistent with his observation that the guy
|> on earth is aging slowly, the following question immediately comes to mind:
|> "Why is it *NOT* the case that the guy in the spaceship, who considers himself
|> stationary, and who sees the earth and distant star make a very fast round
|> trip, ends up meeting a barely-aged earth-bound traveller after all is done?"
|> spaceship's frame of reference, it is the planet and stars that accelerated.
|> Although I'm no expert, I presume the answer lies in General Relativity, which
|> probably claims that the acceleration of all the mass in the universe away
|> from the spaceship induces a gravitational field that acts on the spaceship,
|> causing his clock to tick slower than that of the earth observer, who is in
|> freefall in this gravitational field.
Special relativity postulates the existence of inertial frames. The
difference between the twins here arises because one of them changes from
one inertial frame to another in order to go back to the place he came from.
If you want to explain the existence of inertial frames, then you must
resort to Mach's principle and General Relativity.
-- Bill Lawson
Tim Dugan
and such, there is a term something like:
_____________
\/
1 - (v/c)**2
But, the truth is that v is actually a VECTOR. The term
(v/c)**2
is really the vector V V
- dot -
c c
There is another equation about adding velocities, v1 & v2
v = v1 + v2
----------
<some factor>
I generally see these equations written as scalar equations
which seems misleading to me.
Also, the point(s) of reference is(are) often omitted.
To every observer, I assume that each observer experiences time
at a rate of 1 second every second.
The other entity appears to experience a sort of
doppler shift in time...(someone emailed me that this is not
anything like a doppler affect, but I beg to differ, moving
toward observer is speeded up, away is slowed.)
I tried to restate the twin paradox in more objective terms,
but have trouble. The end result would be something to the
effect of two paths through space-time such that the start
and end points are the same but delta t is different. Does
that make sense? (May be if gravity is taken into account?)
More importantly, what is the scientific evidence? I've heard
hearsay that, say, the clock on the space shuttle looses minute
but measurable amounts of time because of relativistic effects.
Is this true? Is it published somewhere?
-t
Christopher R. Volpe
>In article <450rvv$j...@rdsunx.crd.ge.com>, vo...@ausable.crd.ge.com wrote:
>> He accelerated with respect to what? A preferred or absolute reference frame?
>> in fact, he did not even move. The fact that he was squished into his chair
>> squished in my chair at 1G right now. By your reasoning, I'm accelerating at
>> 9.8 m/s^2, and if I sit here long enough, I should eventually be travelling at
>> pretty darn close to c.
>
>Saying ``relative to his own frame of reference, he did not accelerate''
>can be misleading, because you are talking about a frame that is
>co-accelerating with him, which is noninertial. There is no inertial
>frame in which he did _not_ accelerate.
I'm not talking about intertial frames here. I'm saying that the relativity
principle suggests that any observer can consider himself to be at rest, and
all the laws of physics remain the same. I agree that the spaceship observer
is not in an inertial frame. But this fact can be viewed as a result of two
distinct possible explanations: 1) He's not in an inertial frame, because he's
accelerating. 2) He's not accelerating, everyone else is accelerating, but
he's in a gravitational field, so that makes his reference frame non-inertial.
>
>In the twin paradox, you can say that the Earth twin remained in the
>same inertial frame, while the travelling twin changed inertial frames
>at least once. We define that as acceleration.
Ok I see the trouble. We have a difference of terminology. I was considering
acceleration, as well as velocity, to be relative. Tha is, it's meaningless to
say something is accelerating without saying with respect to what. Therefore
it is correct to say that relative to the earth reference frame, the spaceship
observer is accelerating, but relative to the spaceship, the observer inside
the spaceship is not accelerating, and is at rest. Note that I didn't say
anything about whether each reference frame was an inertial frame or not.
William S. Lawson
In article <450rg3$9...@Starbase.NeoSoft.COM>, ti...@Starbase.NeoSoft.COM (Tim Dugan) writes:
|> In article <44ulp4$c...@polo.iquest.com>, <awi...@iquest.com> wrote:
|> >In <44h12n$3...@osfa.aber.ac.uk>, me...@aber.ac.uk (MARC EDWARD FORRESTER) writes:
|> >>David Bert <be...@spuddy.mew.co.uk> wrote:
|> >>>It is the *high speed of travel* that creates the time dilation
|> >>>in the Twin Paradox.
|> >>
|> >>This is the weird bit about the twin paradox..
|> >>How do you know which twin is travelling fast, and which is stationary?
|> >
|> >According to Einstein, it doesn't matter. That's because it's the relative
|> >speed that counts. That is the speed that one is moving with respect to
|> >the other.
|>
|>
|> When the twins are reunited, will they once again be the same age?
Einstein did not do away with the notion that some frames are special.
Inertial frames are special, and when you change inertial frames you
may not ignore the fact, and pretend that the rest of the universe
is what changed. Among inertial frames, none are preferred, and this
is the postulate of relativity. This postulate predates Einstein by
centuries. It is the constancy of the speed of light that introduces
all the weirdness.
-- Bill Lawson
Nathan Urban
> In article <44vfjb$8...@cnct.com>, hal...@cnct.com (Halibut) writes:
> > Actually, I believe the answer *is* "because the spaceship
> >accelerated", since it is a very easy matter to determine which one
> >accelerated. It was the one where the guy was squished into his chair at
> >5G for a few hours.
> He accelerated with respect to what? A preferred or absolute reference frame?
> There is none. Relative to his own frame of reference, he did not accelerate,
> in fact, he did not even move. The fact that he was squished into his chair
> could just as easily be described as a gravitational effect. I'm getting
> squished in my chair at 1G right now. By your reasoning, I'm accelerating at
> 9.8 m/s^2, and if I sit here long enough, I should eventually be travelling at
> pretty darn close to c.
The answer is: he accelerated with respect to some inertial frame.
Saying ``relative to his own frame of reference, he did not accelerate''
can be misleading, because you are talking about a frame that is
co-accelerating with him, which is noninertial. There is no inertial
frame in which he did _not_ accelerate.
In the twin paradox, you can say that the Earth twin remained in the
same inertial frame, while the travelling twin changed inertial frames
at least once. We define that as acceleration.
Nathan Urban
> In article <4512ul$g...@csugrad.cs.vt.edu>, nur...@csugrad.cs.vt.edu (Nathan Urban) writes:
> >In article <450rvv$j...@rdsunx.crd.ge.com>, vo...@ausable.crd.ge.com wrote:
> >> He accelerated with respect to what? A preferred or absolute reference
> >> frame? There is none. Relative to his own frame of reference, he did not
> >> accelerate, in fact, he did not even move. The fact that he was squished
> >> into his chair could just as easily be described as a gravitational effect.
> >> I'm getting squished in my chair at 1G right now. By your reasoning, I'm
> >> accelerating at 9.8 m/s^2, and if I sit here long enough, I should
> >> eventually be travelling at pretty darn close to c.
> >The answer is: he accelerated with respect to some inertial frame.
> >Saying ``relative to his own frame of reference, he did not accelerate''
> >can be misleading, because you are talking about a frame that is
> >co-accelerating with him, which is noninertial. There is no inertial
> >frame in which he did _not_ accelerate.
> I'm not talking about intertial frames here. I'm saying that the relativity
> principle suggests that any observer can consider himself to be at rest, and
> all the laws of physics remain the same. I agree that the spaceship observer
This is not true in SR. It is true in GR, though. SR only says all the
laws are the same in inertial frames.
> is not in an inertial frame. But this fact can be viewed as a result of two
> distinct possible explanations: 1) He's not in an inertial frame, because he's
> accelerating. 2) He's not accelerating, everyone else is accelerating, but
> he's in a gravitational field, so that makes his reference frame non-inertial.
I say that not being in an inertial frame implies acceleration and vice
versa. See below. Terminology difference, as you say.
> >In the twin paradox, you can say that the Earth twin remained in the
> >same inertial frame, while the travelling twin changed inertial frames
> >at least once. We define that as acceleration.
> Ok I see the trouble. We have a difference of terminology. I was considering
> acceleration, as well as velocity, to be relative. Tha is, it's meaningless to
> say something is accelerating without saying with respect to what. Therefore
> it is correct to say that relative to the earth reference frame, the spaceship
> observer is accelerating, but relative to the spaceship, the observer inside
> the spaceship is not accelerating, and is at rest. Note that I didn't say
> anything about whether each reference frame was an inertial frame or not.
Well, there is a perfectly well-defined way of saying something is
accelerating without saying with respect to what. If you are
accelerating, i.e. are in a noninertial frame, you will experience an
outside force. Whether that force is caused by rocket engines or
gravity or being spun around in a circle is irrelevant. Sitting here
on the surface of the Earth, I am accelerating -- I am deviating from
normal geodesic motion. I can tell, because I am being pulled down by
a force. (Of course, in a coordinate system that is co-accelerating, I
measure no change in position.)
In orbital free-fall, I am moving in normal geodesic motion, experience
no outside force, and hence am not accelerating. Weird viewpoint,
huh? In Newtonian mechanics, you would say that in orbital motion, I
would be experiencing a continual inward acceleration. And, in fact, I
am accelerating with respect to an inertial frame moving with the Earth
(except the Earth is moving noninertially.. ignore that..) :) But in
some sense, acceleration can be defined as an absolute concept -- by my
criterion, you can always determine whether or not you are accelerating.
You know, I think I may have thought of a reason why it might be bad to
say that acceleration is the central issue in the twin paradox. Is it
possible for the travelling twin to go out and come back, all the while
experiencing geodesic motion? That is, could the twin go out, for
example, do a gravity slingshot around the far star, and come back,
while remaining in free-fall for the whole trip? The twin would still
have changed inertial frames during the trip, but you can't say that he
accelerated in the way that I am talking about. Anyone care to
comment?
awi...@iquest.com
>MARC EDWARD FORRESTER (me...@aber.ac.uk) wrote:
>> >It is the *high speed of travel* that creates the time dilation
>> >in the Twin Paradox.
>
>> This is the weird bit about the twin paradox..
>> How do you know which twin is travelling fast, and which is stationary?
>
>fact -- it doesn't even make a hill of beans until they come in contact
>with one another. The whole point is that one of the twins has to turn
>around and "catch up" with the other one. That's what determines which
>is travelling fast and which is stationary. The twin that turned around
>and went back to the other one was the one moving while the other one was
>the one that was stationary.
No Marc. The speed the Lorentz time dilation equation is refering to is
*relative* speed. That is how fast one person is travelling with respect
to the other. It is clear that one considers himself at rest and the other
travelling at near speed of light. All of the perspective problem illusions
become a wash in relativity. That is why relativity is so beautiful.
The one that turned around after reaching his destination is just as much at
rest in his frame of reference as the guy on earth is in his frame. It's always
the "other" guy that is in motion. So no matter which frame you take to be
at "absolute" rest, the laws of nature always turn out the same as long as
you take "proper measurements" consistently; *this* is the essence of
relativity!
David Bert <be...@spuddy.mew.co.uk> seems to have a grasp of the
theory.
Respectfully,
Andy
awi...@iquest.com
>awi...@iquest.com wrote:
>
>: >This is the weird bit about the twin paradox..
>: >How do you know which twin is travelling fast, and which is stationary?
>
>: speed that counts. That is the speed that one is moving with respect to
>: the other.
>
> I thought there WAS a "preferred twin".
>
> The twin that accelerates is the one fothat ends up aged less
>when they meet again.
No, this is a common misperception. I don't know where it came from,
especially if you consider that the twin paradox was posed as an
"apparent contradiction" of special relativity where acceleration is assumed
to be equal to zero. The solution depends on the fact that both time and
distance are Lorentz contracted for the one that is considered to be moving,
whether he be on earth or in the spacecraft. For this reason Einstein and
Minkowski started refering to "proper time" (German: Eigenzeit) as the time
for which Newtonian Physics is true. Proper time is the time for which the
motion is zero. For the guy on earth, his proper time is whatever his clock
says. The spacecraft for him is moving at near speed of light with respect
to him. However for the guy in the spacecraft, his proper time is the time
he sees (which is Lorentz contracted with respect to earth). But then he
sees earth moving at near the speed of light. This implies that the distance
between earth and the star is also Lorentz contracted as seen from the space-
craft. When you work out the details in the equations, it all becomes a wash
and there is no paradox after all. The interesting thing is that the traveller
ages less than the guy on earth no matter who you take at rest. So some of
the early relativists thought that this could be a way to determine absolute
motion. As it turns out the absolute motion can not be determined while the
relative motion is going on. Only after the whole scenario is over, can one
compare what has happened and determine that one had been moving with
respect to the other which was taken to be at rest and thus was the possessor
of the resulting proper time at the end of the scenario.
A famous verification of this explaination of the twin paradox is the Frisch-
Smith experiment involving muons ("American Journal of Physics" 31, p342
(1963) ). Muons have a half life of 3.1 micro-seconds in their own frame
of reference. They are created in the upper atmosphere by cosmic radiation
and travel about 98%c. If we go up a 5000 meter mountain and count the
number of muons there we find out that there are about 10^6 muons in a
given time period in a frame of reference at rest with respect to earth.
During the same earth-time we find that 4.7*10^5 muons survive the
trip to sea level. This is about 21 times the amount that should survive
under Newtonian physics. The reason is that the muons aren't aging as
fast because they are going a fast speed. But this is the explaination as
seen from earth.
Looking from the muon's perspective, they are aging normally and earth
is the one not aging as fast. But then the earth is rushing at them at a
reckless speed of 98%c. Everything then pans out and the laws of nature
are satisfied. But the interesting fact is that there are more muons at
sea level than Newton would expect.
Andy
Wayne Throop
: The spacecraft for him is moving at near speed of light with respect
: to him. However for the guy in the spacecraft, his proper time is the
: time he sees (which is Lorentz contracted with respect to earth). But
: then he sees earth moving at near the speed of light. This implies
: that the distance between earth and the star is also Lorentz
: contracted as seen from the space- craft. When you work out the
: details in the equations, it all becomes a wash and there is no
: paradox after all.
I'm sorry, but this explanation is a load of fetid dingoes kidneys.
It's sorriest feature is that it totally ignores the paradox, to wit,
if it's legitimate for the earth to apply time dilation to get the
traveler's proper time, why isn't it legitimate for the traveler to
apply time dilation to get the stay-at-home's proper time? In this
so-called "explanation", it is completely waved away, swept under
the rug, the hand is quicker than the eye, and so on.
It doesn't suffice to simply say "time time he sees (which is Lorentz
contracted with respect to the earth)". You must answer the question,
if the traveler's time iscontracted WRT the earth, why isn't it an
equally legitimate point of view to suppose the earth's time is contracted
WRT the spacecraft?
This so-called explanation says, "we do time contraction from earth's POV,
and space contraction from the traveler's POV... see, no problem", without
any hint of a reason why it shouldn't be the other way 'round.
: A famous verification of this explaination of the twin paradox is the
: Frisch- Smith experiment involving muons ("American Journal of
: Physics" 31, p342 (1963) ).
While it is a nice verification of SR predictions, it's hardly a
verification of this as an explanation of the twin paradox. Among other
reasons, the muons aren't making a round trip, as in the twin paradox.
Sigh. Please excuse my grumpiness. But really, it Just Won't Do.
root
question at hand is an example of Special relitivity, Which some of you
have gotten mixed up with general. To set the record straight:
General relitivity makes two real claims:
1) Light always travels in a straight path.
2) It is impossible to distinguish any particular uniform accelaration
With the gravatational accelaration; with out outside referance.
special relitivity makes one claim:
1) the quaitity (dl)^2=(dx)^2+(dy)^2+(dz)^2+(ds)^2 is invairent from
all inertial frames of referance. ds is defined to be i*c*(dt).
Now given the twin paradox, the key point is when the traveling twin
turns around. At that point he undergoes an accelaration an his frame of
referance is no longer inertial.
Thanks,
Ian
--
*************************************************************************
*Ian Spielman *
*ispi...@uoknor.edu *
*http://129.15.140.250 *
*************************************************************************
John W. D. Anderson
On 4 Oct 1995, Halibut wrote:
> Christopher R. Volpe (vo...@bart.crd.ge.com) wrote:
>
> : The answer is not "because the spaceship accelerated", because, from the
> : spaceship's frame of reference, it is the planet and stars that accelerated.
> : Although I'm no expert, I presume the answer lies in General Relativity, which
> : probably claims that the acceleration of all the mass in the universe away
> : from the spaceship induces a gravitational field that acts on the spaceship,
> : causing his clock to tick slower than that of the earth observer, who is in
> : freefall in this gravitational field.
>
> Actually, I believe the answer *is* "because the spaceship
> accelerated", since it is a very easy matter to determine which one
> accelerated. It was the one where the guy was squished into his chair at
> 5G for a few hours.
>
>
The twin paradox does not depend on acceleration
or general relativity as can be seen from the
following example.
Take 3 observers, A, B, and C.
In A's rest frame, B has velocity
v and C has velocity -v. Let
gamma = (1 - (v/c)*(v/c))^-1/2.
Say that at some time, A and B are
at the same position. Since they
are coincident, they can synchronize
their clocks to t = 0.
B continues on for some time T as measured
in B's rest frame. The elapsed time as
measured by A is T * gamma.
At this time, C which has been coming
the other way happens to be at the same
place as B. Since they are coincident,
C can set his clock to be the same as B's.
By symmetry, C takes time T as measured
in his rest frame to get back to where
A is. The elapsed time as measured by
A is T * gamma.
When A and C are in the same position,
they compare the times on their clocks.
C's reads 2T and A's reads 2T * gamma.
So A's clock is further along than C's.
The important thing about this way of
thinking about things is that you see
that the discrepancy of A and C's clocks
is just a kinematic effect that is a
consequence of the equality of the speed
of light in all frames. There is no
paradox, since I used 3 observers and
synchronized B and C's clocks part way
through. I am dealing with 3 frames of
reference and not 2 so there isn't a
simple reciprocity between 2 frames.
If you really want to get A and B back
together again, you need to accelerate
B (in A's frame) of course, but this
is not central to the basic example.
This post is my personal contribution and
not related to my employer.
son...@utdallas.edu
That's acceleration. C has to accelerate or decelerate in order for him
to be in the same inertial reference frame as B so that they can
synchronize their respective clocks.
> By symmetry, C takes time T as measured
> in his rest frame to get back to where
> A is. The elapsed time as measured by
> A is T * gamma.
> When A and C are in the same position,
> they compare the times on their clocks.
> C's reads 2T and A's reads 2T * gamma.
> So A's clock is further along than C's.
Once again, another acceleration by C.
> The important thing about this way of
> thinking about things is that you see
> that the discrepancy of A and C's clocks
> is just a kinematic effect that is a
> consequence of the equality of the speed
> of light in all frames. There is no
> paradox, since I used 3 observers and
> synchronized B and C's clocks part way
> through. I am dealing with 3 frames of
> reference and not 2 so there isn't a
> simple reciprocity between 2 frames.
The important thing is that the one that doesn't experience a inertial
reference frame uniformly throughout the "experiment" is the one that
ages slower.
> If you really want to get A and B back
> together again, you need to accelerate
> B (in A's frame) of course, but this
> is not central to the basic example.
The whole point is that you get them together in order to compare their
relative elapsed times.
Nathan Urban
> Yes, that's why I invoked GR: Because SR itself is incomplete and yields the
> wrong result in the thought experiment where a spaceship stays at rest and the
> remainder of the universe accelerates away and back. According to SR, if the
> universe accelerates away and comes back, the universe should have hardly
> aged, while the stationary guy in the stationary spaceship should have aged a
> lot. This doesn't happen, and GR explains why.
I'm not sure if I agree with this.. you basically get GR if you
consider SR in a bunch of successively/continuously transformed
inertial frames, so I wouldn't say that SR is incomplete like that..
I think that SR still works. The reason? The Earthbound twin remained
in one inertial frame, while (in the ideal case) the travelling twin
switched from one inertial frame to another. You can do SR in each of
the two piecewise cases and patch them together. This breaks the
symmetry; if you do it from the Earthbound twin's perspective, you
are in one inertial frame and the other twin switches, and vice versa.
> >You know, I think I may have thought of a reason why it might be bad to
> >say that acceleration is the central issue in the twin paradox. Is it
> >possible for the travelling twin to go out and come back, all the while
> >experiencing geodesic motion? That is, could the twin go out, for
> >example, do a gravity slingshot around the far star, and come back,
> >while remaining in free-fall for the whole trip? The twin would still
> >have changed inertial frames during the trip, but you can't say that he
> >accelerated in the way that I am talking about. Anyone care to
> >comment?
> I'll take a shot at it: Any gravitational forces strong enough to do that to
> the spaceship would impart such strong tidal forces on the earth that the
> earth would be in a (very) non-inertial frame, and would therefore be the one
> who was accelerating for all intents and purposes. The spaceship twin, who
> remained inertial, would see the earth observer age slowly (due to SR time
> dilation), and remain younger than the spaceship observer upon return (due to
> the lack of change in inertial frame of the spaceship). So the acceleration is
> necessary, otherwise the roles would be reversed.
I don't think that it would impart strong tidal forces on the Earth.
This is a distant star that the twin is slingshotting around.
So you are saying that in this case, the Earthbound twin will be
younger? My gut instinct is that this is going to have the same result
as the standard twin paradox -- the travelling twin will be younger.
Second opinions, anyone?
Christopher R. Volpe
>In article <4539n7$j...@rdsunx.crd.ge.com>, vo...@ausable.crd.ge.com wrote:
>
>> Yes, that's why I invoked GR: Because SR itself is incomplete and yields the
>> wrong result in the thought experiment where a spaceship stays at rest and the
>> remainder of the universe accelerates away and back. According to SR, if the
>> universe accelerates away and comes back, the universe should have hardly
>> aged, while the stationary guy in the stationary spaceship should have aged a
>> lot. This doesn't happen, and GR explains why.
>
>I'm not sure if I agree with this.. you basically get GR if you
>consider SR in a bunch of successively/continuously transformed
>inertial frames, so I wouldn't say that SR is incomplete like that..
>
>I think that SR still works. The reason? The Earthbound twin remained
>in one inertial frame, while (in the ideal case) the travelling twin
>switched from one inertial frame to another. You can do SR in each of
>the two piecewise cases and patch them together. This breaks the
>symmetry; if you do it from the Earthbound twin's perspective, you
>are in one inertial frame and the other twin switches, and vice versa.
So if the earth and entire universe fly away from the spaceship and back while
the spaceship really stays at rest, what is it about SR that says the
spaceship's reference frame is not inertial? (Answer: Nothing. You need GR to
show the spaceship's frame is not inertial).
>
>> >You know, I think I may have thought of a reason why it might be bad to
>> >say that acceleration is the central issue in the twin paradox. Is it
>> >possible for the travelling twin to go out and come back, all the while
>> >experiencing geodesic motion? That is, could the twin go out, for
>> >example, do a gravity slingshot around the far star, and come back,
>> >while remaining in free-fall for the whole trip? The twin would still
>> >have changed inertial frames during the trip, but you can't say that he
>> >accelerated in the way that I am talking about. Anyone care to
>> >comment?
>
>> I'll take a shot at it: Any gravitational forces strong enough to do that to
>> the spaceship would impart such strong tidal forces on the earth that the
>> earth would be in a (very) non-inertial frame, and would therefore be the one
>> who was accelerating for all intents and purposes. The spaceship twin, who
>> remained inertial, would see the earth observer age slowly (due to SR time
>> dilation), and remain younger than the spaceship observer upon return (due to
>> the lack of change in inertial frame of the spaceship). So the acceleration is
>> necessary, otherwise the roles would be reversed.
>
>I don't think that it would impart strong tidal forces on the Earth.
>This is a distant star that the twin is slingshotting around.
But think about how strong that field is going to have to be to completely
turn around a spaceship traveling almost at the speed of light. In order to
not be sucked up by that field he'd have to stay pretty far away from it. He
would, in fact, have to be in an orbit around it, an orbit that passes
through the earth's position if his frame is to be completely inertial. But
then something has to keep the stationary earth from falling into this
gravitational well, so imagine a gigantic steel beam holding the earth "up",
so to speak. Now the earth is being held up by this gigantic pole against an
enormous gravitational pull, enough to bring a tangential light beam
(practically) all the way back to the starting point. (I know the gigantic
pole thing sounds silly, but I think that's just an indication of how
ill-posed this question really is.)
>
>So you are saying that in this case, the Earthbound twin will be
>younger?
Without a doubt. Just to remove all aspects of spaceship acceleration from
this problem (because in the above problem the spaceship changes its inertial
frame when it leaves the earth and rejoins the earth), let's make the
following variation: The spaceship starts off moving at high speed before it
gets to the earth. It zips past the earth close enough for the ship observer
(S) and the earthbound observer (E) to synchronize their clocks. (Ideally
they'd have to actually meet, but we'll assume they are close enough that the
ssimultineity differences are negligable.) S zips along in an
inertial frame and is eventually brought back to earth (through the big
gravitational force out there) and comes close enough to E to agree upon an
instant to compare elapsed clock ticks. When they do, they find that E's clock
has ticked far *fewer* times than S's clock, and S has aged more in the
process. This is completely the opposite result as in the original twin
paradox, and the reason is that this time it is S who remains in an inertial
frame. We know this because we constructed his frame that way. Since they
can't both be in an inertial frame if their relative velocities changed so
drastically (separating at almost c, to approaching at almost c), so it must
be E whose frame is so non-inertial.
>My gut instinct is that this is going to have the same result
>as the standard twin paradox -- the travelling twin will be younger.
>Second opinions, anyone?
I disagree, as I said above. I'm also very interested in what others have to
say.
Christopher R. Volpe
Nathan Urban and render an opinion on what would happen in the proposed
scenario. The subject is a variation of the twin paradox in which the high
speed traveller leaves the earth and returns to the earth, but stays in an
inertial frame the entire time by using a distant star to "slingshot" him back
towards the earth. Nathan maintains that the guy in the ship will be the one
who "remaines young" when the two observers meet again, just as in the
traditional twin paradox. I maintain that since the guy in the ship is, by
construction of the scenario, in the inertial reference frame, then the guy on
the earth cannot be in an inertial frame. The guy in the ship therefore "sees"
the earth guy aging slowly, relative to him, during the whole trip and should
end up being the younger one when they meet. Who is right?
In article <453rkm$8...@csugrad.cs.vt.edu>, nur...@csugrad.cs.vt.edu (Nathan Urban) writes:
>In article <453n1d$4...@rdsunx.crd.ge.com>, vo...@ausable.crd.ge.com wrote:
>> So if the earth and entire universe fly away from the spaceship and back while
>> the spaceship really stays at rest, what is it about SR that says the
>> spaceship's reference frame is not inertial? (Answer: Nothing. You need GR to
>> show the spaceship's frame is not inertial).
>
>It is not SR or GR that defines what an inertial frame is. SR states
>that it applies to inertial frames, but you already have to have some
>definition of `inertial frame' to define SR.
>
>So I say that neither SR nor GR is required to say that the spaceship's
>frame is not inertial.
The point is that it is perfectly valid to assume that the spaceship is
constantly at rest. It is perfectly valid to consider an enormous spaceship
the size of all the mass in the universe, except for some guy's cylindrical
metal cabin. The SR twin paradox *assumes* that the earth is an inertial frame
and that therefore all the acceleration is on the part of the spaceship. The
twin paradox doesn't say anything about what the rest of the mass in the
universe is doing. But what the rest of the mass is doing plays a critical
role in deciding which frame is inertial. If the rest of the mass is following
the spaceship (say it's a huge spaceship made up of most of the mass in the
universe), then the earth is really accelerating relative to it and is
non-inertial.
>
>> But think about how strong that field is going to have to be to completely
>> turn around a spaceship traveling almost at the speed of light. In order to
>
>I haven't said anything about the ship travelling almost at the speed of
>light. The twin paradox applies any time, even at 1 m/s.
Yeah, well you're not going to get much dilation that way. Gravitational
effects would completely overpower any SR time dilation.
>
>> not be sucked up by that field he'd have to stay pretty far away from it. He
>> would, in fact, have to be in an orbit around it, an orbit that passes
>> through the earth's position if his frame is to be completely inertial. But
>
>Whose frame? I'm not saying that the travelling twin is inertial. Or
>do you mean the Earthbound twin?
I thought you *were* saying that the travelling twin is inertial. That was the
whole point! To use gravity as a means of returning a high speed traveller to
his starting point while remaining effectively in "free fall".
>
>I agree that he would have to orbit it.. a hyperbolic orbit that will
>throw him back out to the Earth's future position.
ok
>
>> then something has to keep the stationary earth from falling into this
>> gravitational well, so imagine a gigantic steel beam holding the earth "up",
>> so to speak. Now the earth is being held up by this gigantic pole against an
>
>I don't see the Earth falling into Alpha Centauri anytime soon, by the
>way.. certainly not before the travelling twin gets back, even with a
>very low-speed trip..
And I don't see how a spaceship leaving the earth towards alpha centauri with
some initial high velocity is going to make it back to earth without using his
engines at all. Forget about low speed trips, because the effects wont be
measurable. If the earth is receding from alpha-centauri at a similarly slow
speed, then part of your away-from-earth motion is actually due to the
earth's motion, not yours.
>
>> enormous gravitational pull, enough to bring a tangential light beam
>> (practically) all the way back to the starting point. (I know the gigantic
>> pole thing sounds silly, but I think that's just an indication of how
>> ill-posed this question really is.)
>
>Ill-posed? How so?
Because it assumes that a ship leaving the earth in an inertial frame at a
high speed relative to the earth can return to the earth due to external
gravitational forces that don't affect the status of the earth as an inertial
frame. The problem constructs a means for the spaceship to remain inertial,
assumes that the earth is inertial, and then permits a great relative
acceleration to occur between the spaceship and the earth (going from a fast
separation to a fast approach). This is a logical inconsistency. They can't
separate and rejoin while both remain inertial.
>
>> >So you are saying that in this case, the Earthbound twin will be
>> >younger?
>
>> Without a doubt. Just to remove all aspects of spaceship acceleration from
>[...]
>
>Well, with some doubts. :) I read what you said, and it seems to make
>sense, but I still can't help wondering if there isn't something
>missing that we're both not thinking of.
Maybe. I'll wait to hear from others.
>
>> >My gut instinct is that this is going to have the same result
>> >as the standard twin paradox -- the travelling twin will be younger.
>> >Second opinions, anyone?
>
>> I disagree, as I said above. I'm also very interested in what others have to
>> say.
>
>Maybe one of us should repost the question under a different subject so
>all the experts who killfiled this thread can see it..
Good idea.
Nathan Urban
> The point is that it is perfectly valid to assume that the spaceship is
> constantly at rest. It is perfectly valid to consider an enormous spaceship
> the size of all the mass in the universe, except for some guy's cylindrical
> metal cabin. The SR twin paradox *assumes* that the earth is an inertial frame
> and that therefore all the acceleration is on the part of the spaceship. The
> twin paradox doesn't say anything about what the rest of the mass in the
> universe is doing. But what the rest of the mass is doing plays a critical
> role in deciding which frame is inertial. If the rest of the mass is following
> the spaceship (say it's a huge spaceship made up of most of the mass in the
> universe), then the earth is really accelerating relative to it and is
> non-inertial.
This is pretty Machian. I don't really like interpretations that
involve the rest of the universe. I don't know if it is necessary.
> >> But think about how strong that field is going to have to be to completely
> >> turn around a spaceship traveling almost at the speed of light. In order to
> >I haven't said anything about the ship travelling almost at the speed of
> >light. The twin paradox applies any time, even at 1 m/s.
> Yeah, well you're not going to get much dilation that way. Gravitational
> effects would completely overpower any SR time dilation.
So maybe by insisting that the travelling twin travel along a geodesic
we just messed up the problem so it is no longer like the standard twin
problem. Gravitational effects would certainly come into play.. I
don't know what order of magnitude compared to the roughly constant
velocity motion far from the star.
> >> not be sucked up by that field he'd have to stay pretty far away from it.
> >> He would, in fact, have to be in an orbit around it, an orbit that passes
> >> through the earth's position if his frame is to be completely inertial. But
> >Whose frame? I'm not saying that the travelling twin is inertial. Or
> >do you mean the Earthbound twin?
> I thought you *were* saying that the travelling twin is inertial. That was the
> whole point! To use gravity as a means of returning a high speed traveller to
> his starting point while remaining effectively in "free fall".
Well, yeah, I guess I am saying the travelling twin is inertial. (Maybe
I need a good definition of `inertial'.) So, if I'm using the correct
definition and geodesic motion is inertial, then this is different from
the standard twin paradox, because you are in inertial motion always.
But it is similar, because you are still going to have to change your
coordinate system continuously to get frames co-moving with the
travelling twin at all times.
Looking in Ellis and Williams, section 5.3, I see the following quote:
``When we move from the special to the general principle of relativity
... inertial motion no longer has a clear physical meaning, because
motion that is inertial in one reference frame will not be inertial in
another that is accelerating with respect to the first. However, we can
assign a clear physical meaning to the notion of a particle in free fall
...''
> And I don't see how a spaceship leaving the earth towards alpha centauri with
> some initial high velocity is going to make it back to earth without using his
> engines at all. Forget about low speed trips, because the effects wont be
> measurable. If the earth is receding from alpha-centauri at a similarly slow
> speed, then part of your away-from-earth motion is actually due to the
> earth's motion, not yours.
It doesn't really matter if the effects are measurable. There should
still be a difference, and I want to know which.
I think you can get some sort of compromise situation where the
Earth-Alpha Centauri acceleration is negligible and you can still make a
round-trip hyperbolic path. Of course, it might turn out to be the case
that the Earth-Alpha Centauri acceleration is the whole key to the issue.
Nathan Urban
> the spaceship really stays at rest, what is it about SR that says the
> spaceship's reference frame is not inertial? (Answer: Nothing. You need GR to
> show the spaceship's frame is not inertial).
that it applies to inertial frames, but you already have to have some
definition of `inertial frame' to define SR.
So I say that neither SR nor GR is required to say that the spaceship's
frame is not inertial.
> But think about how strong that field is going to have to be to completely
> turn around a spaceship traveling almost at the speed of light. In order to
I haven't said anything about the ship travelling almost at the speed of
light. The twin paradox applies any time, even at 1 m/s.
> not be sucked up by that field he'd have to stay pretty far away from it. He
> would, in fact, have to be in an orbit around it, an orbit that passes
> through the earth's position if his frame is to be completely inertial. But
Whose frame? I'm not saying that the travelling twin is inertial. Or
do you mean the Earthbound twin?
I agree that he would have to orbit it.. a hyperbolic orbit that will
throw him back out to the Earth's future position.
> then something has to keep the stationary earth from falling into this
> gravitational well, so imagine a gigantic steel beam holding the earth "up",
> so to speak. Now the earth is being held up by this gigantic pole against an
I don't see the Earth falling into Alpha Centauri anytime soon, by the
way.. certainly not before the travelling twin gets back, even with a
very low-speed trip..
> enormous gravitational pull, enough to bring a tangential light beam
> (practically) all the way back to the starting point. (I know the gigantic
> pole thing sounds silly, but I think that's just an indication of how
> ill-posed this question really is.)
Ill-posed? How so?
> >So you are saying that in this case, the Earthbound twin will be
> >younger?
> Without a doubt. Just to remove all aspects of spaceship acceleration from
[...]
Well, with some doubts. :) I read what you said, and it seems to make
sense, but I still can't help wondering if there isn't something
missing that we're both not thinking of.
> >My gut instinct is that this is going to have the same result
> >as the standard twin paradox -- the travelling twin will be younger.
> >Second opinions, anyone?
> I disagree, as I said above. I'm also very interested in what others have to
> say.
Maybe one of us should repost the question under a different subject so
all the experts who killfiled this thread can see it..
Mark Barton
ti...@Starbase.NeoSoft.COM writes:
>Subject: Re: 'Twin paradox' paradox
>From: Tim Dugan, ti...@Starbase.NeoSoft.COM
>Date: 5 Oct 1995 10:00:08 -0500
>>
>>: >This is the weird bit about the twin paradox..
>>: >How do you know which twin is travelling fast, and which is stationary?
>>
>>: According to Einstein, it doesn't matter. That's because it's the relative
>>: speed that counts. That is the speed that one is moving with respect to
>>: the other.
>>
>> I thought there WAS a "preferred twin".
>>
>> The twin that accelerates is the one fothat ends up aged less
>>when they meet again.
>
>
> apparently slowing aging ("red shift")
>
> Then, to return, the twin accellerates toward,
> apparently increasing aging ("blue shift")
>
>Am I wrong or am I wrong?
Well, there's no particular need to bring Doppler shifts into an already
complicated problem, but you can if you want. The prescribed measurement
procedure in SR uses large numbers of presynchronized clocks moving in
formation with the master clock at different distances. The time and
position of an event are logged not by comparing it directly to the
master
clock, but to whichever of the slave clocks it happens to be next to. No
signals travel across space and the Doppler effect is not relevant. You
are free to substitute some other time/position measurement, such as
radar,
provided you can show it would give the same results. In this case you
would have to subtract the Doppler effect explicitly. The proportion of
the net slowing that you call Doppler effect and the proportion you call
time dilation depends on the value you assume for speed of light.
According to the speed of light postulate, you must calculate the Doppler
effect separately for each observer assuming the speed of light is c in
each case. Thus different observers will divide up the net slowdown or
speedup between a particular source and receiver differently.
If we suppose that the twins are continually exchanging light of an
agreed
frequency, they will both see the same amount of net slowdown on the
first
leg of the trip and the same net speedup on the second leg of the trip.
The Doppler effect that they calculate will be identical and so will the
time dilation they attribute to their partners.
The assymetry is that when the travelling twin turns around, the signals
from earth will immediately go up in frequency. Thus the traveller will
see red and blue shifted light for equal amounts of time. However the
twin
on earth will not see the frequency change until somewhat after halftime.
Thus the stay-at-home will see red shifted light for somewhat longer than
blue. If you count up the total number of cycles sent and received, it
turns out that all cycles are properly accounted for and that the number
earth->traveller is greater than traveller->earth by gamma(v) as required.
Cheers,
Mark B.
Mark Barton
>Date: 6 Oct 1995 01:29:33 GMT
>>: From: awi...@iquest.com
>: The spacecraft for him is moving at near speed of light with respect
>: to him. However for the guy in the spacecraft, his proper time is the
>: time he sees (which is Lorentz contracted with respect to earth). But
>: then he sees earth moving at near the speed of light. This implies
>: that the distance between earth and the star is also Lorentz
>: contracted as seen from the space- craft. When you work out the
>: details in the equations, it all becomes a wash and there is no
>: paradox after all.
>
>I'm sorry, but this explanation is a load of fetid dingoes kidneys.
>
>It's sorriest feature is that it totally ignores the paradox, to wit,
>if it's legitimate for the earth to apply time dilation to get the
>traveler's proper time, why isn't it legitimate for the traveler to
>apply time dilation to get the stay-at-home's proper time? In this
>so-called "explanation", it is completely waved away, swept under
>the rug, the hand is quicker than the eye, and so on.
See if you like the following version. Suppose that the elapsed time on
earth is 2T and the roundtrip distance (as measured by the earth twin
with
an earth-stationary ruler) is 2L. On the outward leg, the earth twin
puts
T of earth time into 1-1 correspondence with T/gamma of traveller time.
The
traveller agrees that his/her elapsed time to the turnaround point is
only
T/gamma because the distance of L, being specified in the earth frame is
length contracted to L/gamma. Thus the relative velocity is the same:
v = L/T = (L/gamma)/(T/gamma)
(The accounting for the case where the travelling twin drags a tape
measure
behind is left as a challenge to the reader!)
The traveller puts this T/gamma into 1-1 correspondence with T/gamma^2 of
earth time. Specifically, as you can check on a Minkowski diagram, it is
the _first_ T/gamma^2 that gets paired off. If the traveller continued
in
a straight line, he/she would have the opportunity to match up T/2 and
T/gamma but this project is cut short.
On the way back, things are almost exactly the same. The earth twin puts
T
of earth time into 1-1 correspondence with T/gamma of traveller time, and
the traveller puts the same T/gamma into correspondence with the _last_
T/gamma^2 of earth time.
>It doesn't suffice to simply say "time time he sees (which is Lorentz
>contracted with respect to the earth)". You must answer the question,
>if the traveler's time iscontracted WRT the earth, why isn't it an
>equally legitimate point of view to suppose the earth's time is contracted
>WRT the spacecraft?
It's not a stupid thing to want to know and I sympathize. In fact thus
far
we do have symmetry, at least as far as the rates of exchange at which
things get put into 1-1 correspondence are concerned.
>This so-called explanation says, "we do time contraction from earth's POV,
>and space contraction from the traveler's POV... see, no problem", without
>any hint of a reason why it shouldn't be the other way 'round.
The trick is that the traveller does not put the middle 2T(1-1/gamma^2)
of
earth time into 1-1 correspondence with anything! In the process of
accelerating, and thereby changing from one SR frame to another, the
definition of "now" relative to the traveller is moved forward by
2T(1-1/gamma^2) at the position of the earth. That amount of earth
history
has to be just dropped on the floor because there is no place for it in
the
traveller's view of things.
There is no justification or rationalization for this within SR. Turning
around was a forbidden, silly thing to do, with a obvious silly
consequence. More precisely, there is no problem with the traveller or
his/her clock accelerating, but having done so he/she is not entitled to
a
coherent opinion about what time is doing elsewhere relative to
him/herself.
>: A famous verification of this explaination of the twin paradox is the
>: Frisch- Smith experiment involving muons ("American Journal of
>: Physics" 31, p342 (1963) ).
>
>While it is a nice verification of SR predictions, it's hardly a
>verification of this as an explanation of the twin paradox. Among other
>reasons, the muons aren't making a round trip, as in the twin paradox.
You're right. The standard experimental reference for the twin paradox
is
two papers by Hafele and Keating, Science 177:166 and the following in
the
same volume.
Cheers,
Mark B.