Intuition: Why the Lorentz Transformation is Linear

One of the most important starting points for deriving the Lorentz transformation is the fact that it is a linear transformation. Why do we get to assume that? Here we explain the intuition behind why we expect the Lorentz transformation to be linear, using the coordinate systems of special relativity and how rulers and clocks change between inertial reference frames.

0:00 Introduction
4:48 T(u+v) = T(u)+T(v)
15:13 T(cv) = cT(v)

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Music: OcularNebula - The Lopez

[ritilranjan]

This is by far the best explanation of the linearity of lorentz transformation, which I dont know why people just assume implicitly, but there is still a scope of improvement for this video

[sardanapale]

The clocks being synchronised in a frame does NOT mean that being stationnary in that frame and looking at them they will read the same time. They wont. The further away they are the 'older' the time they will read will be : a light signal will take time to reach you.

Clocks being synchronised means that if you had the hability to be at every point of the space, all the clocks would read the same time. It means that for any pair of clocks, if you put yourself in the middle point between them, the time you read is the same : it does not mean that the clock were you stand reads the same time as the two others.

[rodericksibelius]

In simpler terms:

Length Contraction: The length of objects appears to "shrink" or contract when they are moving at speeds close to the speed of light, as observed from a stationary frame.

Time Dilation: Time appears to "slow down" or "elongate" for objects in motion compared to a stationary observer. Clocks on the moving object tick more slowly when viewed from the stationary frame.

[haushofer]

Nice video. Just a nitpick: the emphasis in the name Lorentz is on the first syllable: LOrentz. Sorry, i'm Dutch :P

[markkennedy]

One thing you might be able to answer quickly for me.
When we talk about relative velocity v, why is it that: v of coordinate system 1 as measured in coordinate system 2 means -v of coordinate system 2 as measure in coordinate system 1.

[markkennedy]

Isn't it simply that if we have a body moving with uniform velocity in one coordinate system, that body will have to have a uniform velocity in a second coordinate system. Otherwise, we would have a force in one and no force in the other (but since forces involved interactions, this would be a contradiction).

So If x is linear in t in one coordinate system, x' must be linear in t' in the second coordinate system.

So x and t are both linear in x' and t' and vice versa.

[kleinpca]

Is c an arbitrary constant or the speed of light?

[tomkerruish]

Glad to see they're still using Taylor & Wheeler. That book (and this diagram in particular) really drove home for me just what a reference frame actually is.
Also, please remember that you are now in the fourth dimension.
(x)²+(y)²+(z)²+(cit)² = (x')²+(y')²+(z')²+(cit')²