Travelling faster than the speed of light - SR

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SUMMARY

This discussion centers on the implications of special relativity (SR) regarding velocity and time dilation. Participants explore the misconception that adding velocities directly can yield speeds exceeding the speed of light, specifically addressing the scenario of traveling at 0.75c. The correct application of the velocity addition formula, v = 1.5c/(1+0.75^2), demonstrates that the resultant speed is actually 0.96c. Additionally, the conversation delves into the optimal speed for travel from an observer's frame, concluding that approximately 0.707c minimizes travel time while considering time dilation effects.

PREREQUISITES
  • Understanding of special relativity principles
  • Familiarity with the Lorentz factor and time dilation equations
  • Knowledge of the velocity addition formula in special relativity
  • Basic grasp of frames of reference in physics
NEXT STEPS
  • Study the Lorentz transformation equations in detail
  • Learn about the implications of time dilation and length contraction
  • Research the concept of frames of reference and their significance in physics
  • Explore practical applications of the velocity addition formula in relativistic scenarios
USEFUL FOR

Students of physics, educators teaching special relativity, and anyone interested in understanding the complexities of time and motion at relativistic speeds.

  • #31
which once graphed, shows that optimum time is to go as fast as possible.
 
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  • #32
is this correct?
No.

You can use Earth distance D, then
t=D/v
t'=t/γ.

Or you use spaceship distance D', then
D'=D/γ
t'=D'/v
t=t' γ.

Either way, t'=(D/v)/γ.
 

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