What is the Lorentz Transformation?

What is the Lorentz Transformation? It is a tool we use to relate the different experiences of different observers in special relativity. It is also one of the defining features of special relativity and what differentiates it from Galilean relativity. In this video, we will derive the Lorentz Transformation (as well as its inverse) from a simple thought experiment using the principles of length contraction, time dilation and spacetime invariance.

[toaj]

I think we have to apply the transformation to find the new x, y and z basis vectors and then express the position intervals in terms of the new bases.

[ThisisBarris]

I would assume that's it doesn't matter the direction Albert goes because Isaac would according to Albert, always go to the - of that direction.

[lolosum]

Hands down best video on Special Relativity:)

[fierce-green-fire]

This assumes the star is fixed, which is not the case. Since no star is fixed...unless by chance some particular star is traveling at the exact same velocity in an expanding universe as earth...does this impact relativity at all, conceptually? Or is it simply another term to be modified and/or transformed and can be accounted for in the math? Thanks for the video.

[ResurrectingJiriki]

"we will derive the Lorentz Transformation (as well as its inverse) from a simple thought experiment using the principles of length contraction, time dilation and spacetime invariance."

So "a simple thought experiment" where length is no longer the same length, nor is time the same time nor the relation of the two i.e. spacetime? Did I get that right, or?

Then, is it me or is this far from a simple thought experiment, but more some elaborate mental gymnastics trying to explain an even more mental gymnastic concept of 'spacetime'?
As in, how do you even fit those two in one word to begin with? Something with a physical length, just glued on something non physical?

And why do we 'need' to 'bend' all that stuff, which from my simple minded perspective, makes absolutely no sense, defies any logic. Sincere question.

[vincegilligan]

At 1:46 Why is the formula for relative length different for relative momentum?

[Misada]

this video is amaizing thank you so much!

[greenbug]

XYZW is incorrect way of looking at Relative time. XuYvZw is a more correct view of relative time. Where (uvw) is portioned index of time, as time is a single dimension in space's three dimensional depiction of it.

The problem is time is not static for every single space dimension. Nor is its expanse or contraction the same when moving frames at different values of v, up to and including c.

Einstein saw this and corrected special relativity with general relativity ten years later. Lorentz Transformations have the same problem in quantum realm as well, wave transformations correct for this.

[rpgee]

If you are looking for a different perspective or equation on the Lorentz Transformation then check out this video:

[RileyGHunter]

I don’t think that for Albert, Isaac is moving at the same velocity in the other direction. If for Albert, the distances and the times are transformed then for Albert, Isaac is travelling at a different speed and for a different time than Albert is travelling for Isaac. There is so much stuff like this in Relativity that is just overlooked. I think the whole thing is junk science.

[georgedishman]

Very disappointing, the transforms should be applied to event coordinates and this does nothing to explain how to use them. I know one person who imagines they only apply to durations and this would only reinforce his misunderstanding.