Special Relativity Part 3: Length Contraction

Time dilation was pretty weird, huh? Well we aren't done yet! Time is relative, and so is space! Different observers measure different lengths for objects and journeys. It's called length contraction, and it's another important part of special relativity. Weird stuff!

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[robertflores]

heard that ladies, length is relative

[chrissaffran]

This is a really great explanation! But in the comprehension test question in the outro you're asking for the distance as measured from someone on earth, which would mean we're solving for the proper length (L0). So the answer is L0 = L/(sqrt(1-v^2/c^2)) = (100 m)/(sqrt(1-(0.85*c)^2/c^2))) = ~189.83 m.

[christopherhart]

Thank you for these videos. They really help me do so well in my classes, I couldn't do it without your videos. This is still helping me 5 years after you posted it.

[clarissaayres]

for the question at the end of the vid, shouldn't L be 100m since, the inertial reference frame used to measure 100m was the ship?

[upandatom]

Special Relativity is so crazy! I'm going to be doing a series on it so hopefully by the end I'll understand it as well as you do lol. Can't wait to meet you at vidcon!

[jessicaonymous]

No where in my physics text does it explicitly state that the proper observer for time and the proper observer for length may be two different observers, and that was really throwing me off. Thank you for explaining difference between the two! I feel much more confident in my understanding of special relativity!

[lestahass]

Somehow I understood time dilation

But I think this is a step too far, relatively speaking

[santiagomereles]

Dave. Why don't we calculate L0 in checking comprehension? I thought L0 was the proper length

[themi]

I dont know if you read comments on old videos Prof Dave but I was wondering if you could clarify something for me. In the comprehension question you made L0 the length observed by the astronaut but from how you explained it earlier L0 is from the inertial reference frame of earth. Could you maybe explain why in that example L0 is from the astronaut's perspective? Is L0 meant to be the inertial reference frame of the viewer?

[katiehoang]

Thank you so much Professor Dave. I have been struggling for the special relativity theory for a while, and thanks to your explanation; I'm good now.

[rachelmery]

i thought i understood, but the comprehension example made me even more i know you explained it a bunch of time already in the comments but i still don't really understand why we are using the distance measured by the space ship as L0 and not L

[angeliemaebonaobra]

Professor Dave, for the nth time, thank you.

[anwarulmamoon]

Now 'Length Contraction' of the space ship itself as per view from earth.Use the formula L=Lo*root over 1 minus V square by C square.If Lo is the rest length and L is the length seen by observer from Earth, V is speed of space ship and we assume it is equal to 0.8 C. If Lo=100 meter then L is 60 meter as per view from Earth.Thanks.

[desmondbattle]

Knowing that “length is relative” is somehow a really comforting idea. 😂🤷🏿‍♂️

[SolomonUcko]

Unless I'm misunderstanding something, this seems to conflate length (difference in position between two parts of an object, which are at the same time wrt the observer, but might not be the same events for all observers), which does contract, and distance (change in position between two fixed events, which might not be at the same time wrt the observer even if they are for other observers), which dilates.

[jonathanjoestar]

Gotta show this video to anyone complaining about how the Millennium Falcon could do the Kessel Run in only 12 parsecs. When you’re thinking relativisticly it totally makes sense to say a ship traveled a distance of 18.8 ly in only 8.2 ly due to length contraction, so it isn’t that weird to use a unit of distance to describe how fast your ship was able to go.

(The real problem with that quote is that they were using parsecs at all, since a parsec is based on the earth’s distance from the sun and would be completely irrelevant to people in a galaxy far far away.)

[BruinChang]

Wow, the words used to explain are so meaningful and accurate. Thanks.

[eesha_farooq]

Thank you! Your explanation really cleared my concept of Special Relativity. Loved the animation and graphics as well, they really helped.

[anwarulmamoon]

Lets take an example.The space ship has a speed 0.8C meter per sec. It took 100 sec as per its time to reach star X.So the distance as per him 100*0.8C. On the other hand time by Earth will be Ts=Te*square root of 1-(V/C) square.>Ts=Te*square root of 1-0.8C/C square>100=Te*square root of 0.36=Te*0.6>So time by earth Te=100/0.6=167 sec.Therefore If a person throws a light from earth to the star X, the distance traveled up to star X will be 167*C meter. but the distance measured by a person in space ship is 100*0.8C meter. This is LENGTH CONTRACTION. Thanks

[zw]

Wait so in the comprehension, why is L0 now shown as the length as seen from the astronaut’s view when you previously stated that in this scenario, L0 would be from the earth viewer’s perspective?