# Why do we apply gamma to all components of an object?

1. May 12, 2015

### bolognie1

So it seems straightforward to me that if time dilated, then so would size, mass and energy, but I don't know how to prove that mathematically. I understand the concepts of special relativity and the lorentz transform, and why it is applied to time, but I can't recall or figure out why Einstein would decide to apply it to all properties of an object.
Thanks guys.

2. May 12, 2015

### robphy

3. May 12, 2015

### PAllen

One way it arises, for a large class (but not all) of objects, is going from time derivatives to derivatives by proper time along a world line. Any change from time derivative to proper time derivative introduces a factor gamma. As a result, all 4-velocity (the world line tangent vector with derivative by proper time) and anything based on it get this factor. That includes 4-momentum. From the latter, it applies to energy which is the time component of 4-momentum (in standard coordinates).

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