# 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:** 15\ **Page:** 2
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [April 11, 2009, 2:44pm UTC](https://boards.straightdope.com/t/half-speed/492669/21 "2009-04-11T14:44:27Z")
> [@Chronos](#): > > Relativity, sure, that’s easy once you get used to it. Now, quantum mechanics, nobody actually understands that. “We are all agreed that your theory is crazy. The question that divides us is whether it is crazy enough to have a chance of being correct.” – Niels Bohr to Wolfgang Pauli. Stranger ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [April 11, 2009, 2:44pm UTC](https://boards.straightdope.com/t/half-speed/492669/22 "2009-04-11T14:44:40Z")
In special relativity the formula for adding speeds is: ```auto u + v w = --------- 1 + uv/c2 ``` It is just that at our low everyday speeds the term uv/c2 can be neglected and the formula taken as w = u + v but that is only an approximation. ---
**Author:** ![Chessic\_Sense](https://avatars.discourse-cdn.com/v4/letter/c/7c8e57/32.png) [@Chessic\_Sense](https://boards.straightdope.com/u/Chessic_Sense)\ **Post date:** [April 11, 2009, 3:31pm UTC](https://boards.straightdope.com/t/half-speed/492669/23 "2009-04-11T15:31:11Z")
Ok, look people…some of us here are rather dumb about this stuff. You can´t just say “Here´s an equation for this stuff” and just bank on us knowing what the hell those variables are. ---
**Author:** ![Santo\_Rugger](https://avatars.discourse-cdn.com/v4/letter/s/e95f7d/32.png) [@Santo\_Rugger](https://boards.straightdope.com/u/Santo_Rugger)\ **Post date:** [April 11, 2009, 4:24pm UTC](https://boards.straightdope.com/t/half-speed/492669/24 "2009-04-11T16:24:52Z")
u is the speed of B relative to A, v is the speed of C relative to A, and W is the speed of C relative to A. The part I don’t understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not? ---
**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 11, 2009, 4:31pm UTC](https://boards.straightdope.com/t/half-speed/492669/25 "2009-04-11T16:31:04Z")
> [@Chessic\_Sense](#): > > Ok, look people…some of us here are rather dumb about this stuff. You can´t just say “Here´s an equation for this stuff” and just bank on us knowing what the hell those variables are. That’s the equation I used to calculate what would happen if both speeds were .99C. So I set u = .99 and v = .99 and C = 1. You can set u to any value and v to any value to calculate the outcome. I used .99 because it’s the most dramatic and least obvious that w will still be less than 1. If you use half light speed, then u = v = .5 and w = .8. If u = .99 and v = .5, w = .9966. But if u = v = .000001 (or 670 mph, around the speed of sound), then w = .000002 just as you’d expect. And sound is much faster than any normal human process. The equation is amazingly simple and straightforward. You can calculate it by putting the terms into the Google search bar. And to explain Chronos’ joke. You can never achieve infinity. So any finite number, no matter how large, is essentially 0% of infinite. Extremely loosely speaking. For all real world purposes, a few nines in the .999 expansion is pretty damn close. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [April 11, 2009, 4:45pm UTC](https://boards.straightdope.com/t/half-speed/492669/26 "2009-04-11T16:45:33Z")
**Chronos** wasn’t quite joking, though. No matter how fast you’re going relative to another observer, you will both measure the speed of light as the same value. If you plug in c for one of the terms in the equation, you get (v + c)/(1 + v/c), which rearranges to c(v + c)/(v + c), or c. Note that this happens regardless of the value of v, so even if v = c, the relative velocity is still c. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [April 11, 2009, 5:41pm UTC](https://boards.straightdope.com/t/half-speed/492669/27 "2009-04-11T17:41:43Z")
> [@Santo\_Rugger](#): > > The part I don’t understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not? They’ll be 1 ly from each other, as measured by an observer at A. What B and C see as distance to each other (or any other point) is dependent upon the relative velocity. One way to think about this is that you have velocity along four orthogonal directions; x, y, z, and t. Your total scalar of velocity is always **c**. If you are fixed (relative to an inertial reference frame), your velocity is \<0,0,0, **c** \>. If you are moving at half the speed of light in the x direction, your velocity is \<0.5 **c** ,0,0,√(0.75)· **c** \> and so forth. And of course as your direction along the t-axis changes, all of your measurements that pertain to intervals of time (i.e. how long it takes to go from here to there, and how far that makes it) also change. Fundamentally, all Special Relativity really says is that **c** is the invariant ruler of the space-time plenum against which all other scales are measured. When you adjust the length of **c** in a given direction, you have to adjust everything else accordingly to make the math come out. General Relativity–now that stuff’s a bit more tricky. It’s the same basic concept, but now it factors in the effect of mass on time and the interval you travel in space, which requires a far more complex model. I dub the o.p.'s apparent (fallicious) paradox Zeno’s Relativity Paradox, and for his next trick he needs to show why the tortoise is both ahead of and behind Achilles, but the group velocity of his decoherence quantum probability cloud is always just a little bit ahead. Stranger ---
**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, 5:48pm UTC](https://boards.straightdope.com/t/half-speed/492669/28 "2009-04-11T17:48:43Z")
> [@](#): > > The part I don’t understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not? After one year in whose reference frame? And distances measured in whose reference frame? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [April 11, 2009, 5:54pm UTC](https://boards.straightdope.com/t/half-speed/492669/29 "2009-04-11T17:54:44Z")
Now I’m all at _c_. ---
**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 11, 2009, 7:02pm UTC](https://boards.straightdope.com/t/half-speed/492669/30 "2009-04-11T19:02:23Z")
> [@Santo\_Rugger](#): > > u is the speed of B relative to A, v is the speed of C relative to A, and W is the speed of C relative to A. > > The part I don’t understand is that, after one year, A will be half a light year from B, and A will be half a light year from C. Will B and C, then, not be half a light year away from each other? Why or why not? B and C are moving at opposite directions to one another. If we were on earth, we’d say that one moves a half-mile west from A and the other a half-mile east from A so at the end they are one mile apart. B \< = 1/2 light year \< A \> 1/2 light year =\> C B \<= 1 light year =\> C ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [April 11, 2009, 8:14pm UTC](https://boards.straightdope.com/t/half-speed/492669/31 "2009-04-11T20:14:59Z")
I personally think Einstein must have been one conceited SOB. I mean who else thinks their theory a is a _special_ theory? Did Schrodinger call his equation The _Special_ Wave Equation”? What about Heisenberg, did he think his Uncertainty Principle should be called “The _Special_ Uncertainty Principle”? What about Pauli? Etc. etc. etc. (Say this with a Cary Grant accent) No! Only big Al was pompous enough to think his damn theory was special. Screw you Al. Poincare almost beat you to it anyway ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [April 11, 2009, 8:22pm UTC](https://boards.straightdope.com/t/half-speed/492669/32 "2009-04-11T20:22:50Z")
> [@Ring](#): > > I personally think Einstein must have been one conceited SOB. > > I mean who else thinks their theory a is a _special_ theory? > > Did Schrodinger call his equation The _Special_ Wave Equation”? > > What about Heisenberg, did he think his Uncertainty Principle should be called “The _Special_ Uncertainty Principle”? > > What about Pauli? Etc. etc. etc. (Say this with a Cary Grant accent) > > No! Only big Al was pompous enough to think his damn theory was special. > > Screw you Al. Poincare almost beat you to it anyway 😉 I once knew a German girl who said the Brits were so conceited to call their country “Great Britain”. I had to explain to her the origin and meaning of the name. ---
**Author:** ![Stranger\_On\_A\_Train](https://avatars.discourse-cdn.com/v4/letter/s/13edae/32.png) [@Stranger\_On\_A\_Train](https://boards.straightdope.com/u/Stranger_On_A_Train)\ **Post date:** [April 12, 2009, 1:26am UTC](https://boards.straightdope.com/t/half-speed/492669/33 "2009-04-12T01:26:46Z")
> [@Ring](#): > > I personally think Einstein must have been one conceited SOB. > > I mean who else thinks their theory a is a _special_ theory?..Screw you Al. Poincare almost beat you to it anyway Actually, Special Relativity is “special” in the short bus sense of the word; it is the retarded little brother of the more jingoistic “General Relativity”. Poincare really did beat Albert to the punch in terms of developing the theory, but he was a little too scattered to publish. It’s the whole Newton and Liebniz thing all over again. Stranger ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [April 12, 2009, 1:56am UTC](https://boards.straightdope.com/t/half-speed/492669/34 "2009-04-12T01:56:08Z")
Actually, **Sailor** , now that I think about it all physicists must be pompous asses. It’s not the Wave Equation, it’s the “_Schrodinger_ Wave Equation”. It’s not the Uncertainty Principle it’s the “_Heisenberg_ Uncertainty Principle”, and then there’s “_Feynman_ Diagrams”, and the ‘_Pauli_ Principle”, and on and on. Pretty soon we’ll be hearing about “_ **Chronos’** _ General Theory of Nano Dongers” or something or other. BTW what does the Great in Great Britain stand for? A sop to Scotland and Wales? **Stranger** , I knew that - I was just being a silly ass. ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [April 12, 2009, 2:47am UTC](https://boards.straightdope.com/t/half-speed/492669/35 "2009-04-12T02:47:02Z")
> [@Ring](#): > > Actually, **Sailor** , now that I think about it all physicists must be pompous asses. > > It’s not the Wave Equation, it’s the “_Schrodinger_ Wave Equation”. It’s not the Uncertainty Principle it’s the “_Heisenberg_ Uncertainty Principle”, and then there’s “_Feynman_ Diagrams”, and the ‘_Pauli_ Principle”, and on and on. > > Pretty soon we’ll be hearing about “_ **Chronos’** _ General Theory of Nano Dongers” or something or other. > > BTW what does the Great in Great Britain stand for? A sop to Scotland and Wales? > > **Stranger** , I knew that - I was just being a silly ass. “Great” Britain as opposed to Lesser Britain, as in what we now call Brittany, a part of France. [Previous page](https://boards.straightdope.com/t/half-speed/492669.md?page=1)