 Physics Help Forum Special Relativity: From an Introduction to Modern Astrophysics by Carroll and Ostlie
 User Name Remember Me? Password

 Special and General Relativity Special and General Relativity Physics Help Forum Jun 23rd 2011, 12:42 PM #1 Junior Member   Join Date: Jun 2011 Posts: 2 Special Relativity: From an Introduction to Modern Astrophysics by Carroll and Ostlie 1. The problem statement, all variables and given/known data Because there is no such thing as absolute simultaneity, two observers in relative motion may disagree on which of two events A and B occurred first. Suppose, however, that an observer in reference frame S measures that event A occurred first and caused event B. For example, event A might be pushing a light switch, and event B might be a light bulb turning on. Prove that an observer in another frame S' cannot measure event B (the effect) occurring before event A (the cause). The temporal order of cause and effect is preserved by the Lorentz transformation equations. Hint: For event A to cause event B, information must have traveled from A to B, and the fastest that anything can travel is the speed of light. 2. Relevant equations Suppose $\displaystyle (x_{A},y_{A},z_{A},t_{A}),(x_{B},y_{B},z_{B},t_{B} )$ are the coordinates in the coordinate system S, and $\displaystyle (x'_{A},y'_{A},z'_{A},t'_{A}),(x'_{B},y'_{B},z'_{B },t'_{B})$ are the coordinates in the coordinate system S', which is traveling at speed $\displaystyle u t_{A}$ Because event A caused event B, $\displaystyle \frac{\sqrt{(x_{B}-x_{A})^{2} + (y_{B}-y_{A})^{2} + (z_{B}-z_{A})^{2}}}{t_{B}-t_{A}} \leq c$ 3. The attempt at a solution I need to prove that $\displaystyle t'_{B} - t'_{A} > 0$ $\displaystyle t'_{B}-t'_{A} = \frac{(t_{B} - t_{A})-(u/c^{2})(x_{B}-x_{A})}{\sqrt{1-(u^{2}/c^{2})}}$ What do I do now?   Jun 23rd 2011, 12:44 PM #2 Junior Member   Join Date: Jun 2011 Posts: 2 Latex doesn't seem to work. So here's the code. I put tex tags instead of math tags. 1. The problem statement, all variables and given/known data Because there is no such thing as absolute simultaneity, two observers in relative motion may disagree on which of two events A and B occurred first. Suppose, however, that an observer in reference frame S measures that event A occurred first and caused event B. For example, event A might be pushing a light switch, and event B might be a light bulb turning on. Prove that an observer in another frame S' cannot measure event B (the effect) occurring before event A (the cause). The temporal order of cause and effect is preserved by the Lorentz transformation equations. Hint: For event A to cause event B, information must have traveled from A to B, and the fastest that anything can travel is the speed of light. 2. Relevant equations Suppose $\displaystyle (x_{A},y_{A},z_{A},t_{A}),(x_{B},y_{B},z_{B},t_{B} )$ are the coordinates in the coordinate system S, and $\displaystyle (x'_{A},y'_{A},z'_{A},t'_{A}),(x'_{B},y'_{B},z'_{B },t'_{B})$ are the coordinates in the coordinate system S', which is traveling at speed $\displaystyle u t_{A}$ Because event A caused event B, $\displaystyle \frac{\sqrt{(x_{B}-x_{A})^{2} + (y_{B}-y_{A})^{2} + (z_{B}-z_{A})^{2}}}{t_{B}-t_{A}} \leq c$ 3. The attempt at a solution I need to prove that $\displaystyle t'_{B} - t'_{A} > 0$ $\displaystyle t'_{B}-t'_{A} = \frac{(t_{B} - t_{A})-(u/c^{2})(x_{B}-x_{A})}{\sqrt{1-(u^{2}/c^{2})}}$ What do I do now?  Tags astrophysics, carroll, introduction, modern, ostlie, relativity, special Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post Astro Special and General Relativity 13 Apr 24th 2017 07:46 AM brentwoodbc Special and General Relativity 0 Jan 19th 2009 05:02 PM ah-bee Special and General Relativity 0 Nov 10th 2008 02:43 AM evabern Special and General Relativity 2 Oct 6th 2008 04:26 AM ah-bee Special and General Relativity 3 Aug 31st 2008 04:49 PM