# Half Speed **URL:** \ **Category:** Factual Questions\ **Created:** [April 10, 2009, 6:19pm UTC](https://boards.straightdope.com/t/half-speed/492669 "2009-04-10T18:19:07Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![bintang](https://avatars.discourse-cdn.com/v4/letter/b/8edcca/32.png) [@bintang](https://boards.straightdope.com/u/bintang)\ **Post date:** [April 10, 2009, 6:19pm UTC](https://boards.straightdope.com/t/half-speed/492669/1 "2009-04-10T18:19:07Z")
Is it impossible to go HALF the speed of light? Lets say that there are three objects in space. One object (Object A) is stationary (relatively speaking). Object B takes off in one direction away from A. Object C takes off in the exact opposite direction away from A. The two objects are moving at X speed, but wouldn’t they be travelling at 2X relative to each other? Wouldn’t that assumption mean that if Object A saw Object B going half the speed of light, wouldn’t Object C see B traveling at the speed of light? If that is the case, then shouldn’t 1/2 the speed of light be just as unattainable as the speed of light itself? ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [April 10, 2009, 7:00pm UTC](https://boards.straightdope.com/t/half-speed/492669/2 "2009-04-10T19:00:48Z")
No. Let’s make B and C travel at .9999 light speed relative to A. Observer A sees the separation of B and C increasing as though one of them is traveling away from the other at 1.9998 light speed. But when B or C actually does the measurement of the other’s speed, it’s always less than light speed. In other words, none of the observers measure any of the others traveling at more than light speed **relative to him** (i.e., in his frame of reference). ---
**Author:** ![Wheelz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wheelz/32/5718_2.png) [@Wheelz](https://boards.straightdope.com/u/Wheelz)\ **Post date:** [April 10, 2009, 7:03pm UTC](https://boards.straightdope.com/t/half-speed/492669/3 "2009-04-10T19:03:44Z")
> [@rowrrbazzle](#): > > No. > > Let’s make B and C travel at .9999 light speed relative to A. > > Observer A sees the separation of B and C increasing as though one of them is traveling away from the other at 1.9998 light speed. But when B or C actually does the measurement of the other’s speed, it’s always less than light speed. > > In other words, none of the observers measure any of the others traveling at more than light speed **relative to him** (i.e., in his frame of reference). Can you expand on your answer, **rowrrbazzle**? Why is this so? ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [April 10, 2009, 7:26pm UTC](https://boards.straightdope.com/t/half-speed/492669/4 "2009-04-10T19:26:14Z")
There’s a handy [List of Relativistic Equations](http://en.wikipedia.org/wiki/List_of_relativistic_equations) on Wikipedia. The one involved here is the simple Lorenz Transformation for velocity addition, near the top of the page. Relativity is based on this. Putting any two velocities into the equation always sum to less than C. [Why?](http://en.wikipedia.org/wiki/Theory_of_relativity) > [@](#): > > Special relativity is based on two postulates which are contradictory in classical mechanics: > > The laws of physics are the same for all observers in uniform motion relative to one another (Galileo’s principle of relativity), > > The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light. Once you assume that the speed of light is a constant everything else follows as a consequence. ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [April 10, 2009, 8:11pm UTC](https://boards.straightdope.com/t/half-speed/492669/5 "2009-04-10T20:11:06Z")
> [@](#): > > The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the source of the light. Is this really a postulate? I thought that this was predicted by the ToR and explained the data gained from the Michaelson-Morley experiment. Rob ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [April 10, 2009, 8:29pm UTC](https://boards.straightdope.com/t/half-speed/492669/6 "2009-04-10T20:29:21Z")
[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) ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [April 10, 2009, 8:50pm UTC](https://boards.straightdope.com/t/half-speed/492669/7 "2009-04-10T20:50:45Z")
> [@sweeteviljesus](#): > > Is this really a postulate? I thought that this was predicted by the ToR and explained the data gained from the Michaelson-Morley experiment. > > Rob Today we know that it is a mathematical consequence but at the time Einstein would’t have been able to realize that. He had to treat it as an assumption. It’s also not really clear whether he used the Michaelson-Morley experiment or not. > **[Special Theory of Relativity](https://faraday.physics.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html)** > [@](#): > > Notice that the statement also explains the null result of the Michelson-Morley experiment. However, although the evidence is not certain it seems quite likely that in 1905 Einstein was unaware of the experiment (cf. Gerald Holton, “Einstein, Michelson and the ‘Crucial’ Experiment,” which has appeared in Thematic Origins of Scientific Thought, pg. 261. and also in Isis 60, 1969, pg. 133.). ---
**Author:** ![bintang](https://avatars.discourse-cdn.com/v4/letter/b/8edcca/32.png) [@bintang](https://boards.straightdope.com/u/bintang)\ **Post date:** [April 10, 2009, 8:52pm UTC](https://boards.straightdope.com/t/half-speed/492669/8 "2009-04-10T20:52:34Z")
> [@Exapno\_Mapcase](#): > > Relativity is based on this. Putting any two velocities into the equation always sum to less than C. So this does say that half the speed of light is unattainable since any two velocities always are less than C, right? ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [April 10, 2009, 8:59pm UTC](https://boards.straightdope.com/t/half-speed/492669/9 "2009-04-10T20:59:18Z")
> [@bintang](#): > > So this does say that half the speed of light is unattainable since any two velocities always are less than C, right? Not really, there’s no problem reaching half the speed of light. You can’t apply normal math to this. Normal math doesn’t work at relativistic speeds. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 10, 2009, 8:59pm UTC](https://boards.straightdope.com/t/half-speed/492669/10 "2009-04-10T20:59:25Z")
> [@bintang](#): > > So this does say that half the speed of light is unattainable since any two velocities always are less than C, right? No, it says that as you approach the speed of light, the formula for computing relative velocities starts to deviate from simple addition. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [April 10, 2009, 9:05pm UTC](https://boards.straightdope.com/t/half-speed/492669/11 "2009-04-10T21:05:18Z")
> [@bintang](#): > > So this does say that half the speed of light is unattainable since any two velocities always are less than C, right? No, what it’s saying is that everything is relative. You can’t say “Bob is going half the speed of light.” You can only say “Bob is going half the speed of light _relative to Alice_” Let’s go back to the OP’s example. B and C are both traveling away from A in opposite directions. From A’s point of view, both B and C are traveling at 0.5C. Similarly, from B and C’s point of view, A is traveling away from them at 0.5C. What about B’s view of C? According to Newtonian physics, the apparent velocity _should_ be exactly 1C. But Einstein postulated (and experiment later proved) that when relativistic velocities are encountered, simple Newtonian math breaks down and no longer works. To find the apparent velocity, you have to use the Lorentz equation: 1 / sqrt( 1 - ( v[sup]2[/sup] / c[sup]2[/sup] ) ) B is traveling away from A at (for the sake of simplicity) 150,000 km/sec. That gives us a Lorentz change factor of roughly 1.15. That means three things: 1. If A could observe B’s mass, it would be 1.15 times heaver than when B was at rest. 2. If A could observe B’s length in the direction of travel, it would be 1.15 times shorter than when B was at rest 3. If A could observe a clock on B, it would be going 1.15 times slower than when B was at rest. Similarly, an observer on B would notice the same thing about A. Because of this time and length dilation, any observations that B makes about C would be likewise affected. The net result is that to an observer on B, C appears to be traveling away at something less than the speed of light. ---
**Author:** ![bintang](https://avatars.discourse-cdn.com/v4/letter/b/8edcca/32.png) [@bintang](https://boards.straightdope.com/u/bintang)\ **Post date:** [April 10, 2009, 9:12pm UTC](https://boards.straightdope.com/t/half-speed/492669/12 "2009-04-10T21:12:03Z")
Thanks so much! Especially Friedo. You guys really cleared that up for me! ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [April 10, 2009, 9:12pm UTC](https://boards.straightdope.com/t/half-speed/492669/13 "2009-04-10T21:12:11Z")
> [@bintang](#): > > So this does say that half the speed of light is unattainable since any two velocities always are less than C, right? And to third it, particles are known that travel at .99 many nines % C. If you do the math, two particles moving away from one another at .99 C have a relative velocity of .999949 C. Any speed short of C is attainable in theory. ---
**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 10, 2009, 9:55pm UTC](https://boards.straightdope.com/t/half-speed/492669/14 "2009-04-10T21:55:12Z")
On the other hand, you can’t really say that you can approach the speed of light, since no matter how fast you’re going, you’re always just as far away from c as when you started. ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [April 10, 2009, 9:57pm UTC](https://boards.straightdope.com/t/half-speed/492669/15 "2009-04-10T21:57:49Z")
> [@Chronos](#): > > On the other hand, you can’t really say that you can approach the speed of light, since no matter how fast you’re going, you’re always just as far away from c as when you started. Oh, c’mon, don’t confuse the poor sod. 🙂 ---
**Author:** ![Reply](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/reply/32/15952_2.png) [@Reply](https://boards.straightdope.com/u/Reply)\ **Post date:** [April 11, 2009, 1:43am UTC](https://boards.straightdope.com/t/half-speed/492669/16 "2009-04-11T01:43:35Z")
:eek: People can actually understand this sort of stuff?! ---
**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 11, 2009, 1:55am UTC](https://boards.straightdope.com/t/half-speed/492669/17 "2009-04-11T01:55:08Z")
Relativity, sure, that’s easy once you get used to it. Now, quantum mechanics, nobody actually understands that. ---
**Author:** ![friedo](https://avatars.discourse-cdn.com/v4/letter/f/8edcca/32.png) [@friedo](https://boards.straightdope.com/u/friedo)\ **Post date:** [April 11, 2009, 2:56am UTC](https://boards.straightdope.com/t/half-speed/492669/18 "2009-04-11T02:56:34Z")
> [@Chronos](#): > > Relativity, sure, that’s easy once you get used to it. Now, quantum mechanics, nobody actually understands that. At least people know what quantum mechanics is, though. Nobody can even define string theory. ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [April 11, 2009, 4:44am UTC](https://boards.straightdope.com/t/half-speed/492669/19 "2009-04-11T04:44:41Z")
Why bother? Definitions just get in the way. 😃 ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [April 11, 2009, 2:14pm UTC](https://boards.straightdope.com/t/half-speed/492669/20 "2009-04-11T14:14:00Z")
> [@Chronos](#): > > On the other hand, you can’t really say that you can approach the speed of light, since no matter how fast you’re going, you’re always just as far away from c as when you started. That makes my brain hurt. [Next page](https://boards.straightdope.com/t/half-speed/492669.md?page=2)