# Two neutrinos travelling in opposite directions **URL:** \ **Category:** Factual Questions\ **Created:** [April 12, 2013, 10:40am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487 "2013-04-12T10:40:48Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![Willcross](https://avatars.discourse-cdn.com/v4/letter/w/b2d939/32.png) [@Willcross](https://boards.straightdope.com/u/Willcross)\ **Post date:** [April 12, 2013, 10:40am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/1 "2013-04-12T10:40:48Z")
If neutrinos have mass and travel very close to the speed of light, could one not exceed c in reference to the other if they were the only two objects in the frame of reference? It seems that if two space ships are travelling opposite directions at 10mph, its just as correct to say that one is stationary and the other is travelling at 20mph away from it. Although this must be incorrect thinking on my part. Because I know any object with mass cannot exceed c in any frame of reference. ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [April 12, 2013, 10:48am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/2 "2013-04-12T10:48:35Z")
> [@Willcross](#): > > If neutrinos have mass and travel very close to the speed of light, could one not exceed c in reference to the other if they were the only two objects in the frame of reference? No. Much of the point of Relativity Theory, and relativistic effects like time dilation, is to rule out such possibilities. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [April 12, 2013, 10:51am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/3 "2013-04-12T10:51:21Z")
> [@Willcross](#): > > It seems that if two space ships are travelling opposite directions at 10mph, its just as correct to say that one is stationary and the other is travelling at 20mph away from it. That would be an indictment of all of relativity if correct. Fortunately it is not. In relativity, when switching reference frames, the formula to transform velocities is not simple addition. The addition of velocity formula for two speeds u and v is (u + v)/(1+uv/c^2), which stays below c for all reference frames even if u and v are close to c. ---
**Author:** ![Earl\_Snake-Hips\_Tucker](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/earl_snake-hips_tucker/32/3269_2.png) [@Earl\_Snake-Hips\_Tucker](https://boards.straightdope.com/u/Earl_Snake-Hips_Tucker)\ **Post date:** [April 12, 2013, 10:51am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/4 "2013-04-12T10:51:24Z")
[An earlier thread](http://boards.straightdope.com/sdmb/showthread.php?t=569183) that touches on some of this. ---
**Author:** ![Willcross](https://avatars.discourse-cdn.com/v4/letter/w/b2d939/32.png) [@Willcross](https://boards.straightdope.com/u/Willcross)\ **Post date:** [April 12, 2013, 10:59am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/5 "2013-04-12T10:59:36Z")
> [@leahcim](#): > > That would be an indictment of all of relativity if correct. Fortunately it is not. > > In relativity, when switching reference frames, the formula to transform velocities is not simple addition. The addition of velocity formula for two speeds u and v is (u + v)/(1+uv/c^2), which stays below c for all reference frames even if u and v are close to c. Ah! Thank you! I knew it wasn’t correct since reaching or exceeding c never happens for objects with mass. I did not know about this formula! Thanks! ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [April 12, 2013, 12:22pm UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/6 "2013-04-12T12:22:52Z")
[The Master Speaks](http://www.straightdope.com/columns/read/418/if-i-fire-a-gun-while-near-light-speed-will-the-bullet-exceed-light-speed) on relative speeds in special relativity. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [April 13, 2013, 4:36am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/7 "2013-04-13T04:36:11Z")
Note that, for low speeds like 10 MPH, the simple addition rule is an excellent approximation, and the relative speed will be very, very close to 20 MPH. When you get to things moving at almost c, though, the approximation has very thoroughly broken down. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [April 13, 2013, 8:53am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/8 "2013-04-13T08:53:04Z")
I want to know what happens when the neutrinos walk into a bar… ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [April 13, 2013, 9:13am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/9 "2013-04-13T09:13:07Z")
> [@dtilque](#): > > I want to know what happens when the neutrinos walk into a bar… No charge. ---
**Author:** ![Baron\_Greenback](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/baron_greenback/32/48_2.png) [@Baron\_Greenback](https://boards.straightdope.com/u/Baron_Greenback)\ **Post date:** [April 13, 2013, 9:21am UTC](https://boards.straightdope.com/t/two-neutrinos-travelling-in-opposite-directions/655487/10 "2013-04-13T09:21:04Z")
> [@njtt](#): > > No charge. _polite ripple of applause_