A Note on Einstein’s Twin Paradox Applied to the Behaviour of Entangled Particles Abstract ~ by Greg Matthews (my brother)

28 01 2011

This essay suggest a gedanken experiment to provide an assessment of the implications of work involving teleportation of entangled particles to a well-known and important result of Special Relativity.

One of the important and most well-known results of Special Relativity [1] concerns the implications of time dilation, per the Lorenz transform, resulting from relativistic effects on twin brothers in different relativistic frames of reference.

In his famous gedanken experiment, Einstein hypothesized on the nature of the rate of time lapse between an Earth bound man with respect to his identical twin accelerated on a rocket ship to very large speeds. Owing to predicted time dilation based on the theory of Special Relativity, in a round trip at relativistic speeds of one of the twin brothers, time would have elapsed at a far slower rate than in the non-relativistic frame of reference of the earth bound brother. These results have been substantiated experimentally by somewhat different means involving, for example, time dilation measured by atomic clocks subjected to different gravitational fields.

In the classic debates between Bohr and Einstein, Bohr made a number of arguments respecting information exchange between entangled particles [2] that were at odds with a fundamental tenet of Einstein’s respecting the absolute value of the speed of light, c. Despite Einstein’s arguments that Quantum Mechanics was an incomplete theory and that Bohr’s arguments were the result of yet to be discovered hidden variables, Bohr’s conjecture respecting behaviors of entangled particles was upheld experimentally [3], and Einstein’s conjecture on hidden variables was disproved mathematically [4] as it led to a contradiction in mathematical form.

More recent experiments not only confirm the seemingly instantaneous transfer of information between entangled particles according to apparent space-like geodesics, at rates far exceeding the speed of light, but also have produced a form of quantum teleportation at instantaneous rates between two entangled particles as Bohr’s theory suggested [5].

In a more recent article, [6], it has been conjectured that a form of time travel may also be developed involving entangled particles. An interesting gedanken experiment may be constructed by accelerating a particle trap, containing one of two entangled particles, on a rocket ship accelerated to relativistic speeds and to very large distances from its other entangled particle held “at rest” in an earthbound particle trap.

According to Special Relativity, time dilation would apply to the particle propagating at relativistic speeds so that having traveled near a light-year in distance from its entangled particle, the clock of the rocket ship transporting the entangled particle at relativistic speeds, would have slowed considerably relative to the clock of the particle trap of the other entangled particle.

Consistent with current experimentation involving quantum teleportation of entangled particles, if the relativistic particle were completely annihilated at a point very distant from its entangled partner, all of its information would be transferred instantaneously to the trapped earthbound particle.

This raises the interesting question as to “at what point in time according to the clock of the earth-bound trapped particle would the earthbound trapped particle receive all of the information from the annihilated relativistic particle in a trap on the rocket ship travelling at relativistic speeds, given the point of time of the rocket ship clock at which the relativistic particle was annihilated?”





One response

21 02 2011
Xavier Terri

Any transformation between two observers is a space-time dialogue between two entities A and B about a third entity C. In the ‘Galileo Transformation’, the third entity C is understood, does not appear in the notation. But the ‘Lorentz Transformation’ completely ignores the entity C, and this is why the twin paradox.
I would like to introduce some new transformations that preserve the local velocity of light. Also resolve the twin paradox.
Relational Transformation: http://vixra.org/abs/0909.0022

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