Length contraction and time dilation in relativity

Thread starter Kennedy
Start date Dec 17, 2017
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Contraction Dilation Length Length contraction Relativity Time Time dilation

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SUMMARY

The forum discussion centers on calculating the proper lifetime of an elementary particle traveling at 0.950c, which decays after traveling 0.250 mm in the lab frame. The correct proper lifetime is determined to be 2.74 x 10^-13 seconds, using the Lorentz factor (γ) of 3.2025. The discussion highlights the importance of understanding length contraction and the relativity of simultaneity in special relativity, emphasizing that the lab frame is the rest frame for the distance measurement provided. Misconceptions about which frame to use for calculations are clarified, and the necessity of using Lorentz transformations is reinforced.

PREREQUISITES

Understanding of special relativity concepts, including time dilation and length contraction.
Familiarity with the Lorentz factor (γ) and its calculation.
Knowledge of proper time and how it relates to time measured in different frames.
Ability to apply algebraic manipulation to solve physics problems involving relativistic effects.

NEXT STEPS

Study the derivation and application of the Lorentz transformations in special relativity.
Learn about the implications of the relativity of simultaneity in different reference frames.
Explore examples of length contraction and time dilation in various scenarios involving high-speed particles.
Practice solving problems involving proper time and the Lorentz factor in different inertial frames.

USEFUL FOR

Students of physics, particularly those studying special relativity, as well as educators seeking to clarify common misconceptions about relativistic effects in particle physics.

Dec 17, 2017

Kennedy

Orodruin said:

Alternatively, imagine that the rod is at rest in the particle rest frame and that in the lab frame the other end of the rod passes the position where the particle eventually will decay at the same time as the particle is created. Since the rod is length contracted, it will indeed be longer in the particle's rest frame. However, in the particle's rest frame, the particle creation is not simultaneous to the event that the other end of the rod passes the position in the lab frame where the particle will eventually decay. Therefore the length of the rod divided by the velocity of the lab frame will not give the correct time.I am going to stop you right there because this is a fundamental misunderstanding of relativity. There is no way you can identify a particular frame as a "moving" frame. All movement is relative, in classical mechanics as well as in special relativity. Relative to the lab frame, the particle is moving. Relative to the particle's rest frame, the lab is moving.

I'm very very very confused, but yes I understand that all movement is relative. That was a poor choice of words on my part.