View unanswered posts | View active topics It is currently Wed Aug 23, 2017 5:04 pm




Reply to topic  [ 8 posts ] 
 Complete solution of twin paradox 
Author Message
Board Warrior

Joined: Sun Sep 11, 2011 9:22 pm
Posts: 110
Reply with quote
Post Complete solution of twin paradox
https://youtu.be/0iJZ_QGMLD0
I found a video claiming to have complete solution to twin paradox. Basically the difference is due to change of reference. Is this the standard interpretation of SR?

_________________
.start with the end in mind.


Sun Apr 30, 2017 8:02 pm
Profile
Board Warrior

Joined: Sun Sep 11, 2011 9:22 pm
Posts: 110
Reply with quote
Post Re: Complete solution of twin paradox
Imagine if along rocket trajectory we install synchronized clock at every 1 light second. The rocket also bring a clock which is already synchronized before the journey.
When the twin in rocket is passing each clock on the way, what time do they read, and what time shown by his own clock for each passing?

I mean there are six clocks in the same frame of reference, i.e. clock on earth, clock at 1, 2, 3, 4, and 5 light seconds away from earth. They are stationary relative to each other, so after synchronized, they should tick at the same rate.
- When the rocket twin start moving, his clock should show the same value as the earth clock, which is 0 second.
- What would his clock show when he is passing the clock at 1 light second location?
- What would his clock show when he is passing the clock at 2 light second location?
- What would his clock show when he is passing the clock at 3 light second location?
- What would his clock show when he is passing the clock at 4 light second location?
- What would his clock show when he is passing the clock at 5 light second location?
The rocket then turn around. Is there something interesting happens to his clock?
- What would his clock show when he is passing the clock at 4 light second location?
- What would his clock show when he is passing the clock at 3 light second location?
- What would his clock show when he is passing the clock at 2 light second location?
- What would his clock show when he is passing the clock at 1 light second location?
- What would his clock show when he is coming back to earth?

_________________
.start with the end in mind.


Tue May 02, 2017 4:51 am
Profile
Board Warrior

Joined: Sun Sep 11, 2011 9:22 pm
Posts: 110
Reply with quote
Post Re: Complete solution of twin paradox
I'll try to answer those question based on explanation in the video.

According to earth's (and stationary clocks) reference frame:
when the journey start, clock on earth as well as in the rocket show 0 sec.
when the rocket is passing the first clock, it shows 1 sec, while rocket clock shows 0.8 sec.
when the rocket is passing the 2nd clock, it shows 2 sec, while rocket clock shows 1.6 sec.
when the rocket is passing the 3rd clock, it shows 3 sec, while rocket clock shows 2.4 sec.
when the rocket is passing the 4th clock, it shows 4 sec, while rocket clock shows 3.2 sec.
when the rocket is passing the 5th clock, it shows 5 sec, while rocket clock shows 4 sec.
when the rocket is passing the 4th clock, it shows 6 sec, while rocket clock shows 4.8 sec.
when the rocket is passing the 3rd clock, it shows 7 sec, while rocket clock shows 5.6 sec.
when the rocket is passing the 2nd clock, it shows 8 sec, while rocket clock shows 6.4 sec.
when the rocket is passing the first clock, it shows 9 sec, while rocket clock shows 7.2 sec.
when the rocket arrives on earth, earth clock shows 10 sec, while rocket clock shows 8 sec.

According to rocket's reference frame:
when the journey start, clock on earth as well as in the rocket show 0 sec.
when the rocket is passing the first clock, it shows 0.64 sec, while rocket clock shows 0.8 sec.
when the rocket is passing the 2nd clock, it shows 1.28 sec, while rocket clock shows 1.6 sec.
when the rocket is passing the 3rd clock, it shows 1.92 sec, while rocket clock shows 2.4 sec.
when the rocket is passing the 4th clock, it shows 2.56 sec, while rocket clock shows 3.2 sec.
when the rocket is passing the 5th clock, it shows 3.2 sec, while rocket clock shows 4 sec.
when the rocket is turning around 5th clock, it shows a jump to 6.8 sec, while rocket clock still shows 4 sec.
when the rocket is passing the 4th clock, it shows 7.44 sec, while rocket clock shows 4.8 sec.
when the rocket is passing the 3rd clock, it shows 8.08 sec, while rocket clock shows 5.6 sec.
when the rocket is passing the 2nd clock, it shows 8.72 sec, while rocket clock shows 6.4 sec.
when the rocket is passing the first clock, it shows 9.36 sec, while rocket clock shows 7.2 sec.
when the rocket arrives on earth, earth clock shows 10 sec, while rocket clock shows 8 sec.

Hence at the end of the journey both twins agree that earth twin is older then rocket twin.
Is my understanding above correct?

_________________
.start with the end in mind.


Tue May 02, 2017 4:55 am
Profile
Board Warrior

Joined: Sun Sep 11, 2011 9:22 pm
Posts: 110
Reply with quote
Post Re: Complete solution of twin paradox
What if right after the rocket twin get back to earth, he repeat his journey?
I'll try to analyze it below.

According to earth's (and stationary clocks) reference frame:
when the journey restart, clock on earth shows 10 sec, while rocket clock shows 8 sec.
when the rocket is passing the first clock, it shows 11 sec, while rocket clock shows 8.8 sec.
when the rocket is passing the 2nd clock, it shows 12 sec, while rocket clock shows 9.6 sec.
when the rocket is passing the 3rd clock, it shows 13 sec, while rocket clock shows 10.4 sec.
when the rocket is passing the 4th clock, it shows 14 sec, while rocket clock shows 11.2 sec.
when the rocket is passing the 5th clock, it shows 15 sec, while rocket clock shows 12 sec.
when the rocket is passing the 4th clock, it shows 16 sec, while rocket clock shows 12.8 sec.
when the rocket is passing the 3rd clock, it shows 17 sec, while rocket clock shows 13.6 sec.
when the rocket is passing the 2nd clock, it shows 18 sec, while rocket clock shows 14.4 sec.
when the rocket is passing the first clock, it shows 19 sec, while rocket clock shows 15.2 sec.
when the rocket arrives on earth, earth clock shows 20 sec, while rocket clock shows 16 sec.

According to rocket's reference frame:
when the journey restart, clock on earth shows 10 sec, while rocket clock shows 8 sec.
when the rocket is passing the first clock, it shows 10.64 sec, while rocket clock shows 8.8 sec.
when the rocket is passing the 2nd clock, it shows 11.28 sec, while rocket clock shows 9.6 sec.
when the rocket is passing the 3rd clock, it shows 11.92 sec, while rocket clock shows 10.4 sec.
when the rocket is passing the 4th clock, it shows 12.56 sec, while rocket clock shows 11.2 sec.
when the rocket is passing the 5th clock, it shows 13.2 sec, while rocket clock shows 12 sec.
when the rocket is turning around 5th clock, it shows a jump to 16.8 sec, while rocket clock still shows 12 sec.
when the rocket is passing the 4th clock, it shows 17.44 sec, while rocket clock shows 12.8 sec.
when the rocket is passing the 3rd clock, it shows 18.08 sec, while rocket clock shows 13.6 sec.
when the rocket is passing the 2nd clock, it shows 18.72 sec, while rocket clock shows 14.4 sec.
when the rocket is passing the first clock, it shows 19.36 sec, while rocket clock shows 15.2 sec.
when the rocket arrives on earth, earth clock shows 20 sec, while rocket clock shows 16 sec.

_________________
.start with the end in mind.


Wed May 03, 2017 6:19 am
Profile
Board Warrior

Joined: Sun Sep 11, 2011 9:22 pm
Posts: 110
Reply with quote
Post Re: Complete solution of twin paradox
At a glance, the analysis above looks fine, with rocket twin aging rate is 80% of earth twin.
That's until we realize that to restart the journey, the rocket has to perform acceleration, which in turn should produce time jump.
In the other hand, if the second journey is done in the opposite direction, there would be no acceleration at restarting moment, hence no time jump.

_________________
.start with the end in mind.


Wed May 03, 2017 6:20 am
Profile
Board Warrior

Joined: Sun Mar 12, 2017 4:00 pm
Posts: 177
Reply with quote
Post Re: Complete solution of twin paradox
The video says that there is time lost at the turnabout even if done instantly.
How can u loose over 3 sec if the turnabout is instant ???

Also there is a version out there where instead of turningabout the clock exchanges the time with a clock going the other way already.
Here the Einsteinian crowd can do no better that to say that it is impossible to synchronise clocks when travelling at different velocity.


Wed May 03, 2017 11:44 pm
Profile
Obsessed With the Question

Joined: Sat Dec 13, 2014 4:00 pm
Posts: 619
Reply with quote
Post Re: Complete solution of twin paradox
McMac wrote:
The video says that there is time lost at the turnabout even if done instantly.
How can u loose over 3 sec if the turnabout is instant ???

Also there is a version out there where instead of turningabout the clock exchanges the time with a clock going the other way already.
Here the Einsteinian crowd can do no better that to say that it is impossible to synchronise clocks when travelling at different velocity.


No. You can synchronize two clocks with a different velocity when the clocks are located at the same point in space.
The clock observer changes frames when the clocks are being synchronized. Two clocks synchronized at one point are logically equivalent to an observer that passes through that point.

The synchronization is performed with mechanical forces. Mechanical forces have to satisfy the dynamics of relativity. So in order for the kinematics of relativity to hold true, meaning the measurements, the kinetics of relativity have to old true, meaning the forces.

A clock acts by means of oscillatory forces. These forces have to be consistent with relativity.

The clock that meets the other clock moving in the same direction effectively bounces off the other clock. The physical description of a synchronized clock is closely analogous to if two equal masses bounced off each other elastically. So one can construct a noninertial frame using a clock that bounces off a wall at the turn around point. The contact force on the wall has to transform by a Lorentz transformation, just like the readings of time on the clock.

The idea is to follow the noninertial frame that follows the clock. When the two clocks are synchronized, the observer in this noninertial frame follows the synchronization. If you do it this way, the Lorentz invariance of the mechanical forces are maintained.

Relativitistic mechanics is about forces, just like any other mechanics. The measurements are made with forces. The essential assumption in special relativity is that the mechanical force laws are invariant to the Lorentz transformation. This is because forces can't move faster than the speed of light in a vacuum.


Fri May 05, 2017 6:57 pm
Profile
Board Warrior

Joined: Sun Mar 12, 2017 4:00 pm
Posts: 177
Reply with quote
Post Re: Complete solution of twin paradox
Einstein’s Third Postulate -- W W Englehardt -- 2015
WWE says re Einstein & his STR................
...............In order to give this new concept of “relative time” a solid foundation, he discussed in §1 of his paper at great length the term “simultaneous events” and the synchronization of clocks. It was there where he raised a third postulate that is not fully recognized in the literature as a sine qua non:

3) “We assume that this definition of synchronism is free from contradictions and possible for any number of points;”

This seemingly innocent assumption was never justified by Einstein in detail, but following from the local time derived in §3 a severe problem appears to emerge. More than thirty years later, in Einstein’s book with L. Infeld [6] a simplification is employed, which, intentionally or not, circumnavigates this issue. In this note we review Einstein’s synchronization procedure and discuss its implication with respect to the Lorentz transformation. To guard against potential misunderstandings, Einstein’s own demonstration of the variable “rhythm” of clocks dependent on their motion, as sketched in Fig. 36 of his book [6], is strictly adhered to.........................

https://www.researchgate.net/publicatio ... _Postulate


Sun May 07, 2017 9:48 pm
Profile
Display posts from previous:  Sort by  
Reply to topic   [ 8 posts ] 

Who is online

Users browsing this forum: Bing [Bot] and 1 guest


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group.
Designed by STSoftware.