From: Sue... on
On Jun 19, 7:17 pm, colp <c...(a)solder.ath.cx> wrote:
> On Jun 20, 3:57 am, stevendaryl3...(a)yahoo.com (Dary McCullough) wrote:
>
> > colp says...
>
> > >Then what do you think the circumstances are in which SR predicts that
> > >a twin observes the other to age more quickly, and what mathematical
> > >relationship quantifies this?
>
> > Sure. Let's assume the following set-up. One twin stays at
> > home throughout. The other zips away and comes back.
>
> You are talking about the classic twin paradox, not the symmetric
> paradox. However, you haven't introduced acceleration or deceleration,
> so the issues are the same as in the symmetric case.
>
> Also, you have given a worked example, rather than answering my
> questions directly. A direct answer would be that gamma is always
> larger than or equal to one, so according to SR, time dilation (or
> equivalent time if gamma is equal to one) is always observed, and time
> compression is never observed. Thus the (previously contested) second
> point of the following argument is true:
>

==================

> 1. SR predicts that each twin observes the other twin to age more
> slowly both on the outgoing leg and the return leg.

No...

<<Einstein's 1905 presentation of special relativity was soon
supplemented, in 1907, by Hermann Minkowski, who showed that
the relations had a very natural interpretation[C 5] in terms
of a unified four-dimensional "spacetime" in which absolute
intervals are seen to be given by an extension of the
Pythagorean theorem.>>
http://en.wikipedia.org/wiki/Lorentz_ether_theory#The_shift_to_relativity

<< the four-dimensional space-time continuum of the
theory of relativity, in its most essential formal
properties, shows a pronounced relationship to the
three-dimensional continuum of Euclidean geometrical space.
In order to give due prominence to this relationship,
however, we must replace the usual time co-ordinate t by
an imaginary magnitude

sqrt(-1)

ct proportional to it. Under these conditions, the
natural laws satisfying the demands of the (special)
theory of relativity assume mathematical forms, in which
the time co-ordinate plays exactly the same rĂ´le as
the three space co-ordinates. >>
http://www.bartleby.com/173/17.html

Sue...



>
> 2. In no case does SR predict that a twin observes the other to
> age more quickly.
>
> 3. Points 1 &2 mean that SR predicts that each twin will younger than
> the other at the end of the experiment.
>
>
>
> > Each twin sends out a radio pulse once per second (as
> > measured by his own clock).
>
> > From the point of view of the stay-at-home twin, the traveling twin
> > travels away at 0.866 c for 200 seconds, turns around rapidly,
> > and comes back at 0.866 c for 200 seconds. The traveling twin
> > experiences time dilation of a factor of two, so the trip takes
> > 400 seconds, as measured by the stay-at-home twin, and only
> > 200 seconds, as measured by the traveling twin. According to
> > the stay-at-home twin, the traveling twin sends out pulses at
> > the rate of one pulse every two seconds.
>
> > What about the pulses? The stay-at-home twin will receive signals
> > from the traveling twin at the rate of one signal every 3.73 seconds
> > for the first 373 seconds (for a total of 100 pulses). Then, the
> > stay-at-home twin will receive signals at the rate of one signal
> > every 0.27 seconds for the next 27 seconds, for a total of 100 more
> > pulses.
>
> > Why these numbers? On the way out, each successive pulse from
> > the traveling twin is sent from farther and farther away. Since
> > the traveling twin travels 1.732 light seconds between sending
> > any pulses. That means that the second pulse takes an additional
> > 1.732 seconds to travel back to Earth. Since it is sent 2 seconds
> > later, that means it will arrive at Earth 3.732 seconds later.
>
> > When the traveling twin is on his way back, each pulse is sent
> > from a closer and closer distance. One pulse is sent. Then the
> > next pulse is sent 2 seconds later. But since it is sent from
> > closer in, it takes 1.732 seconds *less* time to travel the
> > distance back to Earth. So the second pulse arrives only
> > 2 - 1.732 = 0.268 seconds later.
>
> A rate faster than the rest rate of pulse reception should not be
> confused with observed time compression, since the decreasing signal
> transit time results in the pulse rate increase.
>
>
>
>
>
> > So the stay-at-home twin sees pulses arrive at rate once per
> > 3.732 seconds for part of the time, and sees pulses arrive at
> > the rate of once per 0.268 seconds for the rest of the time.
> > When does the changeover happen? Well, it happens when the
> > last pulse from the traveling twin's outward journey is sent.
> > Since the traveling twin travels outward for 200 seconds, he
> > is 200*0.866 = 173.2 light-seconds away. So it takes another
> > 173.2 seconds for that pulse to reach the Earth. So the
> > earth only gets that pulse at time 200 + 173.2 = 373.2 seconds.
>
> > So the earth receives at the rate of one per 3.732 seconds for
> > 373.2 seconds, for a total of 100 pulses, and then receives at
> > the rate of one per 0.268 seconds for the next 26.8 seconds,
> > for a total of 100 more pulses. So the Earth twin receives
> > 200 pulses from the traveling twin.
>
> > Now, let's look at the situation from the point of view
> > of the traveling twin:
>
> > The two rates are the same (by relativity): The traveling
> > twin receives pulses from the Earth twin at the rate of one
> > pulse per 3.732 seconds during his outward trip, which lasts
> > 100 seconds (according to his clock) for a total of about 27
> > pulses received. In his return trip, he receives pulses from the
> > Earth at the rate of one pulse per 0.268 seconds for the
> > next 100 seconds, for a total of 373 more pulses. So altogether,
> > the traveling twin receives 373 + 27 = 400 pulses.
>
> > So the traveling twin receives 400 pulses from the stay-at-home
> > twin, while the stay-at-home twin receives only 200 pulses from
> > the traveling twin. By counting pulses, they both agree that
> > the traveling twin is younger.
>
> The standard explanation for the classic twin paradox requires the
> consideration of the role of acceleration and deceleration in the
> experiment. Since you haven't considered this, your example is at odds
> with that explanation in terms of resolving the paradox.
>
> We can treat your example exactly the same as the symmetric case
> because acceleration and deceleration are not an issue in showing the
> paradox, only relative velocity. In other words, we can say that there
> is no significant difference between the motion of the two twins in
> your example. Thus the paradox can be expressed similarly to the
> classic case - looked at one way, one twin receives half as many
> pulses as the other, but looked at in another way the situation is
> reversed, which is clearly paradoxical.

From: train on
On Jun 19, 6:06 pm, "Inertial" <relativ...(a)rest.com> wrote:
> "train" <gehan.ameresek...(a)gmail.com> wrote in message
>
> news:8848af8d-c47c-4d28-b572-cfd072537de9(a)s4g2000prh.googlegroups.com...
>
>
>
>
>
> > On Jun 19, 1:11 pm, "Inertial" <relativ...(a)rest.com> wrote:
> >> "colp" <c...(a)solder.ath.cx> wrote in message
>
> >>news:81c945d7-ef5d-4905-bc17-ff691d4025fd(a)z15g2000prh.googlegroups.com....
>
> >> > On Jun 19, 7:34 pm, "Inertial" <relativ...(a)rest.com> wrote:
> >> >> "colp" <c...(a)solder.ath.cx> wrote in message
>
> >> >>news:3f27a5b2-6fe9-4f52-9d45-033de8e4f473(a)g39g2000pri.googlegroups.com...
>
> >> >> > On Jun 19, 3:27 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> >> >> >> colp wrote:
> >> >> >> > It is not necessary for me to showing you the math in order for
> >> >> >> > you
> >> >> >> > to
> >> >> >> > identify the errors in the article.
>
> >> >> >> The basic error in that article is that they DID NOT use the math
> >> >> >> of
> >> >> >> SR.
>
> >> >> > That isn't necessarily an error. Can you show how their math
> >> >> > resulted
> >> >> > in coming to an incorrect conclusion?
>
> >> >> >> Instead
> >> >> >> they used a comic-book description of SR such as "moving clocks run
> >> >> >> slow" -- SR
> >> >> >> does NOT say that;
>
> >> >> > The truth is not determined by what SR says
>
> >> >> The truth about what SR says IS determinets by what SR says
>
> >> > Circular reasoning.
>
> >> Nope.  Your LACK of reasoning.  You say the truth of SR is determined by
> >> what SR does NOT say.  SR does NOT say the twins are less than each other
> >> over the whole experiment .. it says they have the same ages.
>
> > Even if the twins both show the same age after te symmetric travel, I
> > made the point earlier that twin A has moved relative to twin B and
> > twin B has moved relative to twin A.
>
> Of course they have
>
> >  When realtive motion occurs, time
> > dilation occurs.
>
> Yeup
>
> > The additional paradox is
>
> > how can both twins show the same age when relative movement between
> > them has occurred?
>
> Same way as one twin can be younger than the other in the usual twins
> paradox.


My point is that the assertion that the twins show the same age is in
contradiction with the fact that the twins have moved relative to each
other. I cannot make it more simple than that

The moving clock runs slow

The stay at home twin ages faster means that all stay at home twins
age faster than the all traveling twins that follow the exact same
flight profile.

But a particular traveling twin`s clock is always in motion with
respect to another traveling twins clock if they move in paths 90
degrees to each other for example.

Is this not true?

oh maybe as AE said we have to give up common sense. And reason?

T

>
> > Acceleration?
>
> Yes. . or more exactly .. chagne of rest inertial frame
>
> > put a value a for the time dilation during acceleration,
> > and by symmetry in cancels out.
>
> Yes .. the symmetrical change in frame cancels out the time dilation
>
> > 1. If relative motion occurs between two clocks, there is no
> > difference between their times when the relative motion between them
> > becomes zero
>
> It depends on what happens in-between
>
> > or
>
> > 2. If relative motion occurs between two clocks, when they are brought
> > together when the relative motion between them becomes zero they show
> > the same time  ( oh yes there are special case symmetric etc)
>
> It depends on what happens in-between
>
> > Which one is it?
>
> > or
>
> > 3. There is no answer
>
> No single answer as you propose.  What happens depends on the velocity
> profiles of the two clocks between the events in question.

From: Daryl McCullough on
colp says...
>
>On Jun 20, 3:57=A0am, stevendaryl3...(a)yahoo.com (Dary McCullough) wrote:
>> colp says...
>>
>> >Then what do you think the circumstances are in which SR predicts that
>> >a twin observes the other to age more quickly, and what mathematical
>> >relationship quantifies this?
>>
>> Sure. Let's assume the following set-up. One twin stays at
>> home throughout. The other zips away and comes back.
>
>You are talking about the classic twin paradox, not the symmetric
>paradox. However, you haven't introduced acceleration or deceleration,
>so the issues are the same as in the symmetric case.

The symmetric case works similarly: From the point of view
of each of the twins:

Time period 1. Up until turnaround, the pulses from the other twin come
delayed (less than one pulse per second).

Time period 2. After turnaround, and for a while, the pulses from
the other twin come at exactly one pulse per second.

Time period 3. After the twin receives the last pulse from the other
twin sent before the other twin turned around, the pulses start
coming more frequently than one per second.

The net effect in the symmetric case is that each twin sends and
receives the exact same number of pulses.

>Also, you have given a worked example, rather than answering my
>questions directly. A direct answer would be that gamma is always
>larger than or equal to one, so according to SR, time dilation (or
>equivalent time if gamma is equal to one) is always observed, and time
>compression is never observed.

That's not correct. The Lorentz transformations do not
say that the relationship between the time coordinates
of the two observers is as simple as one time coordinate
being a multiple of the other time coordinate.

If you look at the Lorentz transformation for time, you
find:

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

So t' does not simply depend on t and gamma, it depends on v and
x as well. If v is changing, then that will affect the relationship
between t and t'.

You have to actually use the equations.

>Thus the (previously contested) second
>point of the following argument is true:
>
>1. SR predicts that each twin observes the other twin to age more
>slowly both on the outgoing leg and the return leg.

False. I just explained it to you. If by "observing the other
twin aging" you mean looking at the other twin through a powerful
telescope and seeing how old he *looks*, then what you would find
is:

(1) During the outward journey, each twin will see the other twin
aging more slowly.

(2) During the return journey, each twin will see the other twin
aging more rapidly.

Whether they end up the same age, or different ages depends on
how long the fast aging period lasts compared with the slow aging
period.

>2. In no case does SR predict that a twin observes the other to
>age more quickly.

That's not correct.

>A rate faster than the rest rate of pulse reception should not be
>confused with observed time compression, since the decreasing signal
>transit time results in the pulse rate increase.

That's true, but you can reliably figure out how old each twin is
when they get back together by counting the number of pulses sent
by each twin that is received by the other twin.

>The standard explanation for the classic twin paradox requires the
>consideration of the role of acceleration and deceleration in the
>experiment. Since you haven't considered this, your example is at odds
>with that explanation in terms of resolving the paradox.

The main point is that there *is* no paradox. There are many
different ways to compute the age of each twin when they get
back together, and they *all* give the same answer.

Acceleration *does* spoil the symmetry in the asymmetric case.
In the asymmetric case, both twins experience two different
periods:

Period 1: Pulses from the other twin arrive at less than 1
pulse per second.

Period 2: Pulses from the other twin arrive at greater than 1
pulse per second.

The asymmetry is that for the stay-at-home twin, Period 1
is much longer than Period 2, so the total number of pulses
he receives from the other twin is less than 1 per second,
on the average.

For the traveling twin, Period 1 and Period 2 are the same
length of time. So he sees fewer pulses from the earth during
Period 1, but many more pulses during Period 2, with the net
effect being that he receives, on the average, more than 1
pulse per second from the stay-at-home twin.

When the traveling twin turns around, he *immediately*
encounters quicker pulses from the stay-at-home twin.
But the stay-at-home twin won't see quicker pulses until
much later---they are delayed by the time it takes light
to travel from the turnaround spot back to Earth.



>We can treat your example exactly the same as the symmetric case
>because acceleration and deceleration are not an issue in showing the
>paradox, only relative velocity. In other words, we can say that there
>is no significant difference between the motion of the two twins in
>your example. Thus the paradox can be expressed similarly to the
>classic case - looked at one way, one twin receives half as many
>pulses as the other, but looked at in another way the situation is
>reversed, which is clearly paradoxical.

No, that's WRONG. You have to compute how many pulses each twin
receives from the other. In the symmetric case, there are three
periods:

Period 1: Each twin receives pulses from the other twin at less
than 1 per second. (Red-shifted)

Period 2: Each twin receives pulses from the other twin at exactly
1 per second.

Period 3: Each twin receives pulses from the other twin at greater
than 1 per second. (Blue-shifted)

The effects of Period 1 and Period 3 cancel exactly, so that, on
the average, each twin receives 1 pulse per second from the other
twin.

If you want to make a mathematical claim, then you have to actually
do the mathematics. If you do, you'll find that SR consistently
predicts that in the symmetric case, the two twins will be the
same age when they reunite, and consistently predicts that in
the asymmetric case, the stay-at-home twin will be older.

--
Daryl McCullough
Ithaca, NY

From: Peter Webb on

<kado(a)nventure.com> wrote in message
news:87999400-7cac-47bc-b8c4-fe5750451eda(a)s9g2000yqd.googlegroups.com...
On Jun 18, 8:45 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
>
snip
>
> In this case, the usual "twin paradox" has been implemented
> experimentally, and
> the result is as predicted by SR. The "symmetric twin paradox" has not
> been
> implemented experimentally AFAIK, but can be considered as a
> straightforward
> extension of the usual one.
>
> > Nevertheless, what you do not seem to realize and be able to
> > accept is that the whole of Einstein's SR and GR are based
> > on gedankens, and not a bit of these are based on empirical
> > experimentation!
>
> This is WILDLY untrue. There are HUNDREDS of experiments that confirm
> various
> predictions of SR, and directly refute Newtonian mechanics.

I hope you understand that both SR and GR were formulated before
these experiments were conducted.

___________________________________
(a) Irrelevant. There is no need for experimental verification of a theory
to occur *before* the theory is formulated.

(b) Incorrect. At least two experiments - Michelson Morley and the
precession of Mercury - were conducted prior to the formulation of the
theories that explained them. Of course, there were also many experiments
conducted after the theories were derived, as is common in science.

Is there a single prediction of SR that you believe to be false, and if so
what is it? Or do you believe all predictions of SR are correct?


From: colp on
On Jun 20, 12:32 pm, stevendaryl3...(a)yahoo.com (Daryl McCullough)
wrote:
> colp says...

> >The standard explanation for the classic twin paradox requires the
> >consideration of the role of acceleration and deceleration in the
> >experiment. Since you haven't considered this, your example is at odds
> >with that explanation in terms of resolving the paradox.
>
> The main point is that there *is* no paradox. There are many
> different ways to compute the age of each twin when they get
> back together, and they *all* give the same answer.

In other words, you deny that there is a problem with your explanation
for the classic twin paradox, but you can't say why the standard
explanation claims that consideration of acceleration is necessary to
resolve the paradox when your own explanation of the paradox makes no
mention of it.
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