Time Dilation: SR Basics & Confusion

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SUMMARY

This discussion centers on the concept of time dilation within the framework of Special Relativity (SR), specifically addressing the confusion surrounding the twin paradox. The participants clarify that while observers in different inertial frames perceive time differently due to the Lorentz Transform, each clock measures its own proper time, which is a function of its four-dimensional path through spacetime. The conversation emphasizes that there is no fundamental frame of reference in SR, and the effects of time dilation and length contraction are merely coordinate effects linked to the Lorentz transformation.

PREREQUISITES
  • Understanding of Special Relativity concepts, including four-vectors and the Lorentz Transform.
  • Familiarity with the metric equation in the context of spacetime.
  • Knowledge of the Doppler effect as it relates to relativistic speeds.
  • Basic grasp of inertial frames and their significance in relativity.
NEXT STEPS
  • Research the twin paradox and its implications in Special Relativity.
  • Study the mathematical formulation of the Lorentz Transform in detail.
  • Explore the concept of proper time and its calculation for moving clocks.
  • Investigate the relationship between time dilation and length contraction in various inertial frames.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in deepening their understanding of Special Relativity and its counterintuitive implications regarding time and motion.

thrush
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Hi everybody,

I'm learning Special Relativity, and probably ok with four vectors, the metric equation, the Lorentz Transform, and the Doppler shift, etc., but enough about me.

I'm still a little confused about time dilation. In several hypothetical examples of SR that I have seen, two spaceships, call them A, and B, are traveling apart. From A's frame, B's velocity is 0.9C, and B's spaceship has contracted in length and increased in mass. From B's frame, A's velocity is 0.9C, and A's spaceship has contracted in length and increased in mass. When both slow down so that the relative velocity becomes zero, all is back to 'normal' and they then occupy the same reference frame (with standard orientation, as some say).

But what about time? From A's frame, time is slowed on B's spacecraft . But from B's frame, time is slowed on A's spacecraft . Would it not then be the case that their clocks would read identically even until their relative velocities became zero again? Which astronaut aged more slowly? Do not these examples about an astronaut aging more slowly on a high speed round-trip imply that she is moving with respect to some more fundamental frame upon which we sit back here on Earth? And does not SR imply that there is no "fundamental frame?"

I know this must be a thread many times here, apologies, but clearly I am missing something. Thank you.
 
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You need to find out about the so called 'twin paradox'. http://en.wikipedia.org/wiki/Twin_paradox.[/PLAIN]

Relativity is not about time-dilation and length contraction. These are just linked coordinate effects of the Lorentz transformation that connects any two inertial frames' coordinates. The important things are those that are *not* dependent on which observer measures them.

The most important ( for some) is the fact that every clock measures its own time, which is a mathematical function of the spacetime length of its four dimensional path through spacetime.
 
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Thanks for the pointer Mentz114! No need to beat a dead horse here, close this thread/delete it. You have given me plenty to chew on!
 

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