# Linearity of the Loentz transformations

1. Jan 19, 2007

### 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'

2. Jan 20, 2007

### pervect

Staff Emeritus
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.

3. Jan 20, 2007

### bernhard.rothenstein

linearity

4. Jan 20, 2007

### robphy

5. Jan 22, 2007

### Meir Achuz

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.

6. Jan 23, 2007

### nakurusil

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.

7. Jan 30, 2007

### 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...

8. Jan 30, 2007

### quantum123

Why linear? Because they are the easiest.
LOL!

Chris: