Velocity in Inertial Frames: Lorentz Dilation and Contraction

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SUMMARY

The discussion centers on Lorentz dilation and contraction in special relativity (SR), specifically the equations \grave{l}=l\gamma and \grave{t}=\frac{t}{\gamma}. It clarifies that the velocity in the unprimed system is \frac{l}{t}, while in the primed system it is \frac{l\gamma^{2}}{t}, highlighting that these values differ due to the object's rest frame. The key takeaway is that length contraction and time dilation are observed under specific conditions: length contraction occurs when both ends of an object are measured simultaneously, while time dilation is assessed at the same spatial points from different frames.

PREREQUISITES
  • Understanding of special relativity concepts
  • Familiarity with Lorentz transformations
  • Knowledge of time dilation and length contraction principles
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Study the derivation of Lorentz transformations in detail
  • Explore practical examples of time dilation using high-speed particles
  • Investigate the implications of length contraction in real-world scenarios
  • Learn about the relationship between simultaneity and frame of reference in SR
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This discussion is beneficial for physics students, educators, and anyone interested in the principles of special relativity and their applications in modern physics.

storm4438
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i was looking at the lorentz dilation and contractions for SR. My books says they are [itex]\grave{l}[/itex]=l[itex]\gamma[/itex] and that [itex]\grave{t}[/itex]=[itex]\frac{t}{\gamma}[/itex] .what i don't understand is that the velocity in the unprimed system is then [itex]\frac{l}{t}[/itex] but in the primed system its [itex]\frac{l\gamma^{2}}{t}[/itex] which is not equal to the value in the unprimed system. Shouldnt the velocity in the two frames be the same?
 
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No, one of the frames is the frame in which the object is at rest. Its velocity in that frame, then, is 0.
 
This is probably the most common mistake I've seen with SR...

The length contraction observed is when the both sides of the object are observed at the same instant in time. Time dilation is measured at the same points in space from two different frames. They in no way represent the distance an object is moving over any time.
 

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