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Old Feb 24th 2019, 01:57 PM   #1
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Twins contradiction with specialized clocks

Almost all teachings in Special Relativity describe time in inertial reference frames as clocks running slower in any inertial reference frame that has a relative velocity with respect to the frame making the measurement. That concept seems to include an implicit re-initialization of clocks as part of the concept. This concept seems contradictory to me. I setup a simple gedanken experiment. I hope that someone will explain how these are interpreted using Einstein's concepts.

Twins Paradox with specialized clocks.
This is the standard twins problem, where there are two identical twins in an inertial reference frame. One twin starts moving at velocity V relative to the initial inertial reference frame. In this variant of the problem, I used specialized clocks to see if the clocks in the other frame run slower. Let V = sqrt(3)/2 * c. This gives a factor of two as the time dilation.
Now the stay at home twin wants to measure if the moving twins clock runs at half the rate as his own. So the stay at home twin makes a clock that runs at twice the rate of a standard clock. He gives this to the moving twin to take on his journey. Similarly, the moving twin wants to verify that his clock is running at twice the rate of the stay at home twin's clock. So the moving twin makes a clock that runs at half the rate of a standard clock and takes that with him on his journey. Obviously, both of the modified clocks traveling with the moving twin do not show the same time since one is running at four times the rate of the other. The clock running at twice the standard rate doesn't show the same elapsed time as the clock running at half the standard rate since they are in the same inertial reference frame (the moving twin's frame), yet the two specialized clocks supposedly each measure exactly how the stay at home twin's clock is running. One view has to be incorrect. Any insights?

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Old Feb 25th 2019, 07:20 AM   #2
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Discussions on the twins "paradox" often centre on the speed difference.
However the key difference is the acceleration difference.

The two twins start in the same reference frame (F0)
One twin accelerates to new speed, and thus a new reference frame F1.
Then decelerates back into reference frame F0.

It is the action of moving from one reference frame to the other and back that generates the seeming paradox.
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Old Feb 25th 2019, 07:25 AM   #3
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The problem has nothing to do with acceleration. The two twins could already have a constant velocity of V = sqrt(3)/2 * c, and then pass each other at the same x coordinate where they have the identical age. The clocks could be set at that point in time and space to the age of each twin. Acceleration is irrelevant to the scenario.
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Old Feb 25th 2019, 08:32 AM   #4
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Twin A in Reference frame FA will see everything in his frame as being "normal",
but looking across to Twin B in Reference frame FB everything will look odd.

Twin B in Reference frame FB will see everything in his frame as being "normal",
but looking across to Twin A in Reference frame FA everything will look odd.

For constant relative velocities between Frame FA and Frame FB the observed oddities will be identical for each of the two twins!

Twin A will see himself as "normal" but his twin being relatavistically slowed.
Twin B will see himself as "normal" but his twin being relatavistically slowed.
The amount of relativistic slowing each will observe in the other will be identical.
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Old Feb 26th 2019, 08:25 AM   #5
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The fast-running clock given to the (assumed male) traveler always correctly tells the traveler what the (assumed female) home twin concludes about her current age at any given time in his life. I.e., the fast-running clock in the spaceship always correctly gives HER conclusion about their respective ages, so it always correctly tells him what HER perspective is. That remains true during his entire round trip.

On the OUTBOUND leg of his trip, the slow-running clock in the spaceship correctly tells him what her current age is, according to HIS perspective. But when he instantaneously reverses course, his conclusion about her current age instantaneously changes ... according to HIM, she instantaneously gets much older. So at that point, and for the remainder of his trip, the slow-running clock in the spaceship no longer gives him correct information about her current age ... it continues to show what her current age would have been IF he had never reversed course.
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Old Feb 26th 2019, 09:01 AM   #6
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The Twins "Paradox" can be viewed as the twins taking different routes through 4D spacetime,
between two events (their separation and their reunion).

One twin takes a route that is longer in space, but shorter in time,
the other twin takes a route that is shorter in space, but longer in time.
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Last edited by Woody; Feb 26th 2019 at 09:06 AM.
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