Linearity of the Loentz transformations

[bernhard.rothenstein]

Please give a plausibile justification for the linearity of the Lorentz transformations. Would you accept: The Lorentz transformations should be linear because to one event in I should correspond a single event in I'

 

[pervect]

Homgoneity -distance and time intervals must be independent of the choice of origin. This is mentioned but not explained in detail in Einstine's 1905 paper, I believe.

 

[bernhard.rothenstein]

linearity

Homgoneity -distance and time intervals must be independent of the choice of origin. This is mentioned but not explained in detail in Einstine's 1905 paper, I believe.

Thanks. Could that be better: The transformations should be linear because straight worldlines (i.e. constant velocity worldlines) in one frame must transform into stright worldlines in all other?

 

[robphy]

Homgoneity -distance and time intervals must be independent of the choice of origin. This is mentioned but not explained in detail in Einstine's 1905 paper, I believe.

Thanks. Could that be better: The transformations should be linear because straight worldlines (i.e. constant velocity worldlines) in one frame must transform into stright worldlines in all other?

That's better [since your previous justification allows (say) conformal transformations, which need not preserve lines]. You may recall this earlier thread: https://www.physicsforums.com/showthread.php?p=1079973

 

[Meir Achuz]

Please give a plausibile justification for the linearity of the Lorentz transformations. Would you accept: The Lorentz transformations should be linear because to one event in I should correspond a single event in I'

In physical terms, I would say LT ius linear so that constant velocity in one frame will not lead to acceleration in another frame. That is equivalent to straight world lines.

 

[nakurusil]

Please give a plausibile justification for the linearity of the Lorentz transformations. Would you accept: The Lorentz transformations should be linear because to one event in I should correspond a single event in I'

The linearity of the Lorentz transforms comes from the way Einstein derived them in his 1905 paper. He starts with the clock synchronisation condition, uses a Taylor expansion in order to produce a PDE. Solving the PDE produces the LT. By stopping the Taylor expansion to the rank one terms, Einstein forces the LT to be linear.
What if Einstein continued the Taylor expansion to higher terms? It can be proven that the resulting LT transforms are STILL linear! i.e. the coefficients of the higher order terms intervening in the LT's derived this way are zero.

 

[Chris Hillman]

Careful, Shubee is linking to (apparently) his own website, everythingimportant.org which generally runs counter to mainstream physics/math. Unfortunately, this is only one of literally hundreds of such websites which pretend to describe relativistic physics... sigh...

 

[quantum123]

Why linear? Because they are the easiest.
LOL!

Chris:
Please define "mainstream".

 

[bernhard.rothenstein]

linearity

Why linear? Because they are the easiest.
LOL!

Wich are the harder?