Timeline for Can Lorentz-Boosts reach every phase space point?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 2, 2017 at 16:30 | comment | added | FloodLuszt | I guess you're right. In that case the original momentum would always have a component transverse to the boost and not in the direction of the rotated momentum. And this transverse component could not be affected by a boost, which means you can never get the rotated momentum. | |
| Mar 2, 2017 at 16:06 | comment | added | Valter Moretti | My intuition is that if you spatially rotate of $\pi/2$ a momentum, there is no single boost connecting the initial and the final momenta... | |
| Mar 2, 2017 at 16:05 | comment | added | Valter Moretti | Indeed, I think that with two boosts you can connect every pairs of momenta, but it is not possible, in general with one boost. | |
| Mar 2, 2017 at 15:58 | comment | added | FloodLuszt | But then you'd still need more than one boost. | |
| Mar 2, 2017 at 15:25 | comment | added | Valter Moretti | Two pure boosts are always sufficient to connect two given momenta as you wrote in the second part: starting from the first momentum moves to the rest frame by means of a boost and then moves to the second momentum with another boost. No rotations are necessary (even if you may generate rotations by composing boosts as you correctly said). | |
| Mar 2, 2017 at 14:49 | comment | added | FloodLuszt | Thanks for your answers. I was indeed wondering about one single boost, not a Lorentz transformation. So @Marcel's comment suggests that it is possible. I know that the generators of boosts are in fact momentum translation operators but I was hoping to get a more intuitive answer. | |
| Mar 2, 2017 at 14:11 | comment | added | Ben Niehoff | OK, but (as I hinted at slightly in the first sentence), boosts do not form a group. The physically-interesting question is whether two four-momenta are connected by a Lorentz transformation, which includes rotations as well as boosts. | |
| Mar 2, 2017 at 13:49 | comment | added | Valter Moretti | Using both your ideas you prove that two four momenta with the same mass are connected by a sequence of two boosts or more. Instead OP's question refers to one boost if I understand well. I guess the answer is negative. | |
| Mar 2, 2017 at 13:01 | history | answered | Ben Niehoff | CC BY-SA 3.0 |