The Symmetric Twin Paradox [Physics]

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From: K_h on 17 Jun 2010 21:39

"Transfer Principle" <lwalke3(a)lausd.net> wrote in message
news:bf6929a8-2236-4b82-a181-0b17fe7ebf30(a)s9g2000yqd.googlegroups.com...
On Jun 16, 12:21 am, Koobee Wublee <koobee.wub...(a)gmail.com>
wrote:
> On Jun 15, 11:25 pm, colp <c...(a)solder.ath.cx> wrote:
> > In the symmetric twin paradox both twins leave Earth,
> > setting out in opposite directions and returning to
> > Earth at the same
> > time.
> Thanks, yours truly has brought this up earlier. <shrug>

> that if the universe is closed, the twins travelling
> in opposite directions might end up meeting at the
> other side of the universe -- then which twin would
> be older? (But then I always waved this off by saying,
> therefore, the universe _isn't_ closed...)

No problem for a closed universe. The answer depends on how
mass and energy are distributed throughout the universe and
how each twin moves relative to that matter and energy.
Since the distribution of mass and energy cause the closure
there is no problem with relativity.

_

From: Koobee Wublee on 18 Jun 2010 00:59

On Jun 17, 6:13 am, Tom Roberts wrote:
> Peter Webb wrote:

Oh, good. The big guns like Professor Roberts has decided to come to
the rescue of the pawns of the self-styled physicists like Peter
Webb. I can now ignore these ignorant minions. Thanks for showing
up. <TWO THUMBS UP>

> > GPS will function without any GR effect applied if indeed exists. You
> > can google the previous few posts by yours truly to understand how GPS
> > works.
>
> This is just plain not true. The relativistic effects in the GPS are well known
> and are MEASURED to agree with the predictions of GR to excellent accuracy.

The algorithms in any GPS receivers do not require any relativistic
corrections. <shrug>

> The
> GPS could not possibly work without applying the relativistic effects.

Hmmm... That statement is a wishful thinking from the self-styled
physicists. <shrug>

> Note that the GPS is an ENGINEERED system, and consists of clocks
> both in satellites and on the ground.

Yes. <shrug>

> It is true that a similar system without ground clocks could IN PRINCIPLE be
> designed to work without relativistic corrections;

I hope the Einstein Dingleberry Peter Webb is taking notes on this
one. <shrug>

> IN PRACTICE the engineering
> of such a system would be impossible (e.g. any satellite that missed its orbit
> by a small amount would be useless);

It is funny that a physicists would try to be an engineer on this
one. Please explain what this 'missing the orbit' thing.

> the required perfection does not occur in
> the real world.

It is great that a physicist can put on an engineer's hat.

> Fortunately, the designers of the GPS knew this and designed a
> system that actually works; it requires BOTH relativistic corrections and daily
> parameter updates (the largest corrections are to satellite orbits).

According to the algorithms inside each GPS receiver, there is no
relativistic effect, and no relativistic effect is necessary. Where
is this relativistic effect applied?

> Note that
> the manufactured modification to the satellite clocks (due to relativistic
> effects) completely dwarfs the daily updates.

So, as long as all satellites exhibit the same clock rate that
accumulates the chronological time, the system has to work. So, since
they are all built on the surface of the earth, applying any
relativistic effect whether if it is valid or not is a waste of
effort. <shrug>

From: Koobee Wublee on 18 Jun 2010 01:25

On Jun 17, 6:21 am, Tom Roberts wrote:
> colp wrote:

> > The symmetric twin thought experiment (as described in the OP) is such
> > an experiment.
>
> No. It is a GEDANKEN, not an experiment. There are no actual measurements of
> this situation.

Of course not. I know you would agree that a paradox is not a
physical reality. So, please clarify with professor Drape aka PD who
thinks a paradox is still a possibility in real life.

> > In the experiment SR predicts that the twins will both be younger than
> > each other when they return to Earth, which is of course impossible.
>
> This is just plain not true. You and that paper did not actually use SR. The
> comic book used does not describe the actual theory accurately enough to be useful.

Oh, careful here. You are treading on thin ice while embracing the
principle of relativity. The time dilation in the Lorentz transform
must be mutual. <shrug>

As a on-stage magician, I have called your mathemagical tricks. There
is a slight difference between Larmor's transform and the later
Lorentz transform, but this slight difference is going to determine
what is reality and what is fairy tale. Larmor's and the Lorentz
transforms are different only that Larmor's requires one of the two
observers to be the stationary background of the Aether while the
Lorentz does not. The Lorentz transform can only possibly valid if
and only if these two observers are moving in parallel to each other
against the stationary background of the Aether. Your mathemagical
trick is to show the Lorentz transform in your hand while performing
all calculations/applications with Larmor's transform. That may pass
the Einstein Dingleberries, but you cannot fool the true scholars of
physics since Larmor's transform does not satisfy the principle of
relativity and thus supporting the absolute simultaneity in accordance
with real-life observations in the coherencies of interferometers time
after time. <shrug>

> > Some solutions proposed by the relativists are:
> > [...]
>
> Those are not the real solution. The REAL solution is to actually use SR in the
> analysis of this gedanken.

The Keating experiment did not show a mutual time dilation thus is a
valid proof to SR. Remember that no experiment can possibly prove a
paradox valid. <shrug>

From: Koobee Wublee on 18 Jun 2010 01:35

On Jun 17, 7:50 am, stevendaryl3...(a)yahoo.com wrote:
> Transfer Principle says...

> >Still, I admit that I've once thought about this
> >"symmetric twin paradox." I also once asked myself
> >that if the universe is closed, the twins travelling
> >in opposite directions might end up meeting at the
> >other side of the universe -- then which twin would
> >be older? (But then I always waved this off by saying,
> >therefore, the universe _isn't_ closed...)
>
> No, a closed cylindrical universe is no more a problem for
> Special Relativity than the existence of cylinders is for
> Euclidean geometry.

A closed cylindrical universe is no more a problem for any theory that
does not satisfy the principle of relativity either. So? <shrug>

> For a flat infinite sheet, all directions are equivalent, but
> if you wrap that paper into a cylinder, then there is suddenly
> a big difference between the direction around the circumference
> and the direction parallel to the axis.

Nonsense. There is still no difference. <shrug>

> Similarly for a cylindrical universe in SR. For a flat
> infinite universe, all inertial frames are equivalent.
> But if you wrap the universe into a cylinder, there is
> a difference between the inertial frame of an observer
> traveling out the circumference and the inertial frame
> of an observer traveling parallel to the axis of the
> cylinder.

DITTO. <shrug>

From: Koobee Wublee on 18 Jun 2010 01:41

On Jun 17, 7:14 am, stevendaryl3...(a)yahoo.com wrote:
> colp says...

> >The classic twin paradox is asymmetric in that one twin remains on
> >Earth while the other leaves (i.e. only one of them accelerates and
> >deaccelerates). In the symmetric twin paradox both twins leave Earth,
> >setting out in opposite directions and returning to Earth at the same
> >time. The conventional explanation for the classic twin paradox is
> >since only one twin accelerates, the ages of the twins will be
> >different. In the symmetric case this argument cannot be applied.
>
> >The paradox of the symmetric twins is that according to special
> >relativity (SR) each twin observes the other twin to age more slowly
> >both on the outgoing leg and the return leg, so SR paradoxically
> >predicts that each twin will be younger than
> >the other when they return to Earth.
>
> This is only a paradox to those incompetent at mathematics.

Gee! It shows how ignorant you are with the mathematics of the
Lorentz transform. <shrug>

> Let's
> look at an analogous "paradox" in Euclidean geometry:
>
> You have two cities, Startville and Endville. Endville lies 1000 miles
> due west of Startville. There are two different routes to get from
> Startville to Endville: One route goes straight west for 1000 miles.
> The other route starts off traveling northwest then at the halfway
> point turns to travel southwest the rest of the way.
>
> From the point of view of a traveler following the straight path,
> the bent path looks longer: it travels away to the north for a
> while, and then it travels south for a while, and the total length
> is given by the Pythagorean theorem.
>
> From the point of view of a traveler following the bent path,
> it might seem that it is the *first* traveler who travels away
> to the *south* for the first half of the trip, and then travels
> to the *north* for the second half of the trip. So is it right
> for the second traveler to claim that the *other* traveler is
> following the bent path? Clearly no.
>
> In Euclidean geometry there is a "relativity" of directions.
> You pick any direction you like and call it your coordinate
> axis. There is nothing special about traveling west: you can
> let your axis travel to the northwest just as well.
>
> But there is *no* relativity when it comes to bent paths
> versus straight paths. All observers, regardless of how
> they set up their coordinate systems, can tell the difference
> between a straight path and a bent path.
>
> In SR, the analogy of "straight path" is "unaccelerated path"
> and the analogy of "bent path" is "accelerated path".

Oh, where is the math that shows this? Want to apply GR to an SR
problem? Go right ahead and show me. I call your bluff. <shrug>

> Whether
> an observer is at rest or not is a matter of relativity, but
> whether an observer is accelerated or not is not relative:
> all observers agree about who it is that accelerates.

Handwaving is not physics. <shrug>