Length Contraction Explained

Relativity is the idea that time and space can behave differently depending on your perspective. It is notoriously difficult to understand, but in this series, I explain the methods that helped me understand it to the best of my ability. This episode covers length contraction, where the lengths of objects change depending on velocity.

Intro Song: Chopin's Nocturne op 9 no 2, performed by Frank Levy
Outro Song: Tchaikovsky's Waltz of the Flowers, from youtube's media library

[rafakordaczek]

This is the best explanation of why the speed of light is not a limit on itself. I've seen many times ridicilous explanations like "it takes infinite energy" or "the mass increases". The truth is, that when we are moving close to the speed of light, the contracted lenght becomes so short, that we are able to travel huge "uncontracted" distances. Like entire galaxies. From your perspective, you could travel entire galaxy in any time you like, for instance, 1 day, because you are moving through contracted space with huge speed. But from the observer's perspective, it would still take like years. And at the end, you would realize, that time dilation affected you, and you, in fact, have travelled years, but for you, only 1 day would pass by. Time dilation and lenght contraction might seem to be counterintuitive, but they are direct consequences of light travelling at the same speed for any observer, and nothing more. Your channel is highly underrated, and this video - very well put together in explaining the subject. I subscribed.

[ChadwickMartin-uqsd]

These relativity videos are great! After listening to hours of lectures and reading a ton I was still struggling with some concepts that you cleared up in an hour. I will sleep better tonight! You make me feel like I can almost grasp the math even---thank you for sharing this, I anxiously await the next one!

[demitech]

This is the best explanation I've seen explaining time dilation and length contraction and their direct correlation. I've seen a dozen or more videos and this is the best one. Thanks!

[fifaerbest]

6:30 That was an incredible explanation

[ShopperPlug]

0:35 - 😮Excellent explanation. Makes more sense now.

[zactron]

I find it really interesting that relative simultaneity applies to time, but not to space. Both space and time experience the same "length contraction", dilating them across spacetime. And yet, spacial dilation preserves coincidence within spatial dimensions, but temporaral dilation does not for the time dimension.

Really great video, thanks for sharing!

[SkyGrel]

OMG you are so so talented in explaining stuff and keeping the intrigue, really thank you for your videos!!

[chrismousakli]

love you so much, you explain it better than any teacher:)

[jucom]

This also solves the "direction of the photon clock" paradox from the second video.

[marsaro]

Thank you so much for making this video !!! I’ve been watching three videos about this topic and this one is the best one yet. the equation helps me understand so much

[vaclavtrpisovsky]

Another hint to help figure out the ladder paradox:


(click to reveal)
Imagine that the shack has a door on each side that we can instantly open or close. One of the events is when the tail end of the ladder passes through the entrance door so we cqn close it behind the ladder. What could be the other event?

[BenWard]

Is there any way to move to make something longer? Like if I run backwards? Or can I shake my hips in a certain way? I have heard lots of $$$ can cause certain things to undergo a Lorentz transformation. Asking for a friend...

[dreamwork]

took me a bit but I finally get it. Another great video ❤ thank you & keep up this series please 😊

[vaclavtrpisovsky]

These lectures are really helpful, I would not even mind paying for them. Have you considered Patreon?

[igNights]

Good stuff, please continue this series!

[LoganMarcosSchmidt]

PLEASE MAKE THE ELECTRICITY AND MAGNETISM VIDEO

[massimilianodellaguzzo]

Thank you for your explanation and for your interesting video.

I would like to tell you about this scenario.
A spaceship moves in the frame of the Earth, and travels a distance L. (to reach a star S, suppose the Earth-star distance is L in the frame of the Earth)
The nose of the spaceship (the astronaut twin) and the Earth twin occupy the same position at the initial times (t = t’ = 0)
... and the twins are in relative motion to each other at speed v.

If we consider the uniform linear motion of the spaceship in the frame of the Earth:
1) the astronaut twin reaches the star S at time t = L/v, in the frame of the Earth
2) the star S reaches the astronaut twin at time t’ = L / (gamma*v) in the frame of the spaceship
In the spaceship frame the Earth-star distance is CONTRACTED, YOU'RE RIGHT !

But in my opinion if we consider the uniform linear motion of the Earth in the frame of the spaceship, then we need to consider SOMETHING ELSE: in this case it is necessary to consider the uniform linear motion of the star S in the frame of the spaceship.
And if we consider the uniform linear motion of the star S in the frame of the spaceship:
1) the star S reaches the astronaut twin at time t ’ = L/v in the frame of the spaceship
2) the astronaut twin reaches the star S at time t = L / (gamma*v) in the frame of the Earth

In my opinion the uniform linear motion of the star is hidden but it exists and happens, do you agree ?

[js]

what if the mover was spinning around the stayer but the stayer was in unison with the mover (similar to how the center of a wheel has the same rpms as the outside of the wheel) would this mean that the stayer observing the mover would see the mover contract?

[honzarubes]

Isn't the time dilation formula supposed to be Tmover = Tstationary/square root of 1 - v squared / c squared ???

[siddharthpotti]

I dont really understand how you merge the two theories of length contraction. To my understanding they are explained by different proofs>>

Distance Between Two Planets (Spaceship’s Perspective): When a spaceship moves between two planets at relativistic speeds, the distance between the planets appears contracted from the spaceship's perspective. This seems to be explained by time dilation—the spaceship’s clock runs slower, so to cover the distance in a shorter time (from the ship’s perspective), the distance between the planets must appear shorter.

Length of the Spaceship (Planet’s Perspective): From the planet’s perspective, the spaceship appears contracted in length. This can be explained by the light clock analogy: the spaceship has a light clock, and light must travel at the same speed in all reference frames. However, for the light to travel between two points on the spaceship in the same amount of time, but with the clock’s time dilated, the length of the spaceship must be shorter in the direction of motion to make up for the slower ticking of the clock (since the speed of light is constant and time is dilated).