# If you are walking on a train, can you add your walking speed to the train's speed? **URL:** \ **Category:** Factual Questions\ **Created:** [May 11, 2013, 10:58am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067 "2013-05-11T10:58:11Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [May 11, 2013, 10:58am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/1 "2013-05-11T10:58:11Z")
I was reading a [post](http://opinionator.blogs.nytimes.com/2013/03/22/mary-and-the-zombies-consciousness-revisited/) on the Stone philosophy blog at the NY Times website, finding that the vast majority of commenters seemed smarter than the philosophy professor who wrote the post. But that is just background for my question. One commenter stated the following to illustrate their point: > [@](#): > > The notion that logical inquiry can escape getting entangled in the messy world of empiricisim is not tenable. For instance, until the turn of the century (or so) the argument that " if I walk on a train at 5 miles / h and the train moves at 20 miles/h my speed, relative to the ground, must be 25 mils / hour" would have been considered LOGICALLY necessary, yet today it is understood to be false. What this illustrates is not the trivial fact that conclusions based on logical derivation depend on the validity of their premises but that logical derivations inevitably incorporate an essentially infinite number of “silent” or implicit premises (in addition to the explicitly stated ones) whose validity is being accepted by virtue of unawareness of their existence or relevance. Is that really true, that this is now “understood to be false”? Why \*can’t \*you just add the speeds together? I mean, presumably the person on the train is walking in the same direction as the train is moving, we are discounting wobbles from side to side, and of course there is no issue in terms of approaching the speed of light. So am I failing to grasp something, or is this person way off despite giving the impression of intelligence? ---
**Author:** ![Der\_Trihs](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/der_trihs/32/233_2.png) [@Der\_Trihs](https://boards.straightdope.com/u/Der_Trihs)\ **Post date:** [May 11, 2013, 11:06am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/2 "2013-05-11T11:06:51Z")
Possibly a clumsy reference to relativistic speeds? If you’re on a starship traveling _1_ mph short of the speed of light and you trot down a corridor at _5_ mph, you don’t go past the speed of light. So it’s not true that speeds always add up arithmetically like that, it only seems that way under the conditions people normally live in ---
**Author:** ![Lord\_Mondegreen](https://avatars.discourse-cdn.com/v4/letter/l/91b2a8/32.png) [@Lord\_Mondegreen](https://boards.straightdope.com/u/Lord_Mondegreen)\ **Post date:** [May 11, 2013, 11:12am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/3 "2013-05-11T11:12:25Z")
Without further information, the expression “until the turn of the century (or so)” seems to nod towards relativity. At the actual speeds being talked about, of course you can add the two. I can only imagine the writer is trying (and failing) to make some point about relativistic speeds. ---
**Author:** ![Lord\_Mondegreen](https://avatars.discourse-cdn.com/v4/letter/l/91b2a8/32.png) [@Lord\_Mondegreen](https://boards.straightdope.com/u/Lord_Mondegreen)\ **Post date:** [May 11, 2013, 11:17am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/4 "2013-05-11T11:17:56Z")
I swear I edited my post to say that **Der Trihs** ’s post wasn’t there when I replied. This board acts screwy sometimes. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [May 11, 2013, 11:30am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/5 "2013-05-11T11:30:06Z")
Okay, so I’m not insane, stupid, or both. Whew! I even thought of that issue of approaching light speed, but discarded it immediately given that the speeds used in the example were so infinitesimal by comparison. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [May 11, 2013, 11:56am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/6 "2013-05-11T11:56:58Z")
Just for grins one can work out the discrepancy. at 20mph the Lorentz contraction is sqrt(1 - v[sup]2[/sup]/c[sup]2[/sup]) which is 0.9999999999999995 So your 5mph is actually 4.999999999999998 mph from the reference point of the ground, and thus you are travelling at 24.999999999999998 mph. Infinitesimal is right. ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [May 11, 2013, 12:00pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/7 "2013-05-11T12:00:33Z")
> [@Francis\_Vaughan](#): > > Just for grins one can work out the discrepancy. at 20mph the Lorentz contraction is sqrt(1 - v[sup]2[/sup]/c[sup]2[/sup]) which is 0.9999999999999995 So your 5mph is actually 4.999999999999998 mph from the reference point of the ground, and thus you are travelling at 24.999999999999998 mph. > > Infinitesimal is right. But that result is 9 orders of magnitude larger than 25 mils / hour, which is a very large discrepancy indeed. ---
**Author:** ![hibernicus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hibernicus/32/2802_2.png) [@hibernicus](https://boards.straightdope.com/u/hibernicus)\ **Post date:** [May 11, 2013, 12:04pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/8 "2013-05-11T12:04:14Z")
> [@Lord\_Mondegreen](#): > > I can only imagine the writer is trying (and failing) to make some point about relativistic speeds. I think the author is using relativity to give an example of something that was once thought to be necessarily true and is now known not to be. The principle holds and the example stands even if the difference happens to be small. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [May 11, 2013, 12:34pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/9 "2013-05-11T12:34:35Z")
So you’re saying the speeds cannot simply be added even at speeds nowhere approaching the speed of light–that there is some very slight degree to which the whole is less than the sum of the parts? I was not aware of that. ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [May 11, 2013, 12:40pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/10 "2013-05-11T12:40:44Z")
This is whatp ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [May 11, 2013, 12:50pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/11 "2013-05-11T12:50:31Z")
This is what I find very funny: the poster you cite–or perhaps in the spirit of things I should say Dr. Gutting’s interlocutor–rites good but is blithely oblivious to the dings in his puzzler. Granted, he is talking physics to someone who publishes on post-1960s French philosophy, who surely is aware of the _[l’affaire Sokal](http://en.m.wikipedia.org/wiki/Sokal_affair)._ ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [May 11, 2013, 2:56pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/12 "2013-05-11T14:56:54Z")
I think the author was trying to make the point that we wouldn’t normally say that a person walking through a train car was walking at 25 mph just as we wouldn’t say that a person walking on a plane was walking at 805 mph. Because we would normally think of our walking speed in terms of the environment we’re walking in - the train or the plane. But the writer screws up his point by explicitly adding “relative to the ground”. When you add the specific detail, then you are walking at 25 mph in a train and the writer is wrong. ---
**Author:** ![Little\_Nemo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/little_nemo/32/3120_2.png) [@Little\_Nemo](https://boards.straightdope.com/u/Little_Nemo)\ **Post date:** [May 11, 2013, 3:00pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/13 "2013-05-11T15:00:27Z")
A better example would have been that when you’re driving your car down the highway, you’re moving at 65,000 mph relative to the sun. But you probably won’t get ticketed. ---
**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:** [May 11, 2013, 3:00pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/14 "2013-05-11T15:00:42Z")
In fact, you probably have equipment in your house that can detect relativistic effects from speeds far lower than that train. The electrons in a current-carrying wire, under reasonable conditions, have average velocities of only centimeters per second or less, and yet a simple compass will detect the magnetic field, which is a purely relativistic effect. ---
**Author:** ![jtur88](https://avatars.discourse-cdn.com/v4/letter/j/e9c0ed/32.png) [@jtur88](https://boards.straightdope.com/u/jtur88)\ **Post date:** [May 11, 2013, 3:25pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/15 "2013-05-11T15:25:47Z")
Well, yes. If you board the train in the back, and during the journey you walk to the front of the train, then you can get off the train at the front when it arrives at the station, and not have to walk there along the platform. So you have actually arrived earlier at your destination turnstile than if you had deboarded the train at the back, where you got on. I.e , you “went faster” for the duration of the journey. ---
**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:** [May 11, 2013, 5:13pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/16 "2013-05-11T17:13:41Z")
> [@hibernicus](#): > > But that result is 9 orders of magnitude larger than 25 mils / hour, which is a very large discrepancy indeed. Nine orders of magnitude larger than 25 mph is 25,000,000,000 mph. That’s impossible, since it’s much faster than the speed of light. An order of magnitude is ten times more. I’m not sure what you were thinking of. ---
**Author:** ![Francis\_Vaughan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/francis_vaughan/32/3093_2.png) [@Francis\_Vaughan](https://boards.straightdope.com/u/Francis_Vaughan)\ **Post date:** [May 11, 2013, 5:39pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/17 "2013-05-11T17:39:57Z")
> [@Exapno\_Mapcase](#): > > An order of magnitude is ten times more. I’m not sure what you were thinking of. I assume he was poking fun at the mistyping of miles as mils. One mil per hour is 0.00000001578 miles per hour. ---
**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:** [May 11, 2013, 5:54pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/18 "2013-05-11T17:54:24Z")
> [@Francis\_Vaughan](#): > > I assume he was poking fun at the mistyping of miles as mils. One mil per hour is 0.00000001578 miles per hour. Ah. It wasn’t anywhere in your post that he quoted and it didn’t occur to me to look for it elsewhere. Never mind. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [May 11, 2013, 6:29pm UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/19 "2013-05-11T18:29:13Z")
You could argue that (if we keep things 1-D, i.e. all velocities parallel) then the quantity we should be adding is V = c\*arctanh(v/c) and if v\<\ **Author:** ![appleciders](https://avatars.discourse-cdn.com/v4/letter/a/85f322/32.png) [@appleciders](https://boards.straightdope.com/u/appleciders)\ **Post date:** [May 12, 2013, 12:05am UTC](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067/20 "2013-05-12T00:05:14Z") Honestly, at that speed, the relativistic differences are smaller than the Newtonian differences; that is, as you walk forward on the train, you push it backwards. If the train weighs ten million times more than you do, you still slow it more than the relativistic effects do. [Next page](https://boards.straightdope.com/t/if-you-are-walking-on-a-train-can-you-add-your-walking-speed-to-the-trains-speed/658067.md?page=2)