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# 3. Length Contraction

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Lecture

In this mini-lecture, we discuss the concept of length contraction, that is, moving objects are short. As we move through this mini-lecture, we consider: (i) the length contraction equation that relates the length of an object that is moving in one reference frame as measured by someone in a different reference frame; (ii) the gamma factor in this equation, which is very common in Special Relativity; (iii) an example using this equation, where observers in two different reference frames measure the length of a meter stick in the reference frame they are not in and find it to be short — both are correct due to different notions of simultaneity in different reference frames; (iv) the simple act of how to measure the length of a stationary object; and (v) and how to measure the length of a moving object (the ends need to be measured simultaneously).

Course

In this course, Professor David Griffiths (Reed College) gives an introduction to Einstein’s Theory of Special Relativity. In the first mini-lecture, we discuss Einstein’s two postulates of Special Relativity — the principle of relativity and the universal speed of light — and compare Galileo’s velocity addition rule with Einstein’s velocity addition rule. In the second mini-lecture, we use a thought experiment to understand the relativity of simultaneity, where we see that observers in different reference frames do not agree on what is considered simultaneous. In the third and fourth mini-lectures, we use two more thought experiments to understand length contraction and time dilation, respectively. Finally, in the fifth mini-lecture, we introduce the Lorentz transformations, a set of equations that allows us to translate the coordinates of an event as assigned by an observer in one reference frame into the coordinates assigned to that same event by an observer in a different reference frame.

Lecturer

David Griffiths is an Emeritus Professor from Reed College in Portland, Oregon in the United States. He is known for his highly regarded undergraduate physics textbooks, including Introduction to Elementary Particles (published in 1987, second edition published 2008), Introduction to Quantum Mechanics (published in 1995, third edition published 2018), and Introduction to Electrodynamics (published in 1981, fourth edition published in 2012). He was also the 1997 recipient of the Robert. A Millikan award (renamed the Lillian McDermott Medal in 2021), an American Association of Physics Teachers (AAPT) award that recognises those who have made notable and intellectually creative contributions to the teaching of physics.

#### Cite this Lecture

APA style

Griffiths, D. (2022, January 13). Introduction to Special Relativity - Length Contraction [Video]. MASSOLIT. https://massolit.io/courses/introduction-to-special-relativity/length-contraction

MLA style

Griffiths, David. "Introduction to Special Relativity – Length Contraction." MASSOLIT, uploaded by MASSOLIT, 13 Jan 2022, https://massolit.io/courses/introduction-to-special-relativity/length-contraction