Explain xkcd: It's 'cause you're dumb.
This comic, which appeared the day before National Train Day, plays on the fact that a choice of a reference frame is arbitrary, leading to the "Principle of relativity" in Albert Einstein's theories of special relativity and general relativity. But at speeds much lower than the speed of light it also applies to the newtonian mechanics.
Rather than viewing this situation as a train causing itself to move relative to an immobile Earth, Randall provides the unconventional perspective of a train remaining fixed in space while causing the Earth itself and all the stars in the sky to rotate instead. In principle either perspective is equally valid — though in practice different trains often move in mutually-exclusive directions, thus each train would have to define its own frame of reference. It is said that Einstein once asked a ticket collector, "What time does Oxford stop at this train?"
Changing the reference frame into the inside of the train only means that you see the outside world in a different reference, since the train doesn't really move the Earth (the train's engine and the friction of the wheels aren't even remotely powerful enough) it simply appears that way from the inside.
From the Newtonian perspective this choice of frame is valid, but results in unnecessarily complicated math; the equation of motion would include terms for centrifugal, Coriolis and other so-called "fictional forces" see 123: Centrifugal Force. Newton supposes the existence of "inertial frames", in which these forces are zero, and the surface of the Earth approximates an inertial frame well. In General Relativity, the presence of mass in a system curves the spacetime around of it. The train-earth system could be modelled in general relativity, taking the train as fixed. However the resulting equations would be complex, and not amenable to an exact solution.
The title text expands on this to include elevators, which change a person's position relative to the center of the Earth. From a passenger's perspective, it would appear as though the Earth's position was instead being changed in space.
These examples use the train and the elevator as fixed points to define relative travel. The more common method to define movement is to use the Earth's surface as fixed point, but other reference points could be the Earth's center, the Sun, predefined "fixed" stars or the center of our galaxy. Each of these would result in a completely different movement speed:
- The speed of the train (stationary on the equator) relative to the earth's center: 465 m/s (1,674 km/h or 1,040 mph)
- The speed of the train (on earth) relative to the sun: 30 km/s (108,000 km/h or 67,000 mph)
- The speed of the train (on earth) relative the center of our galaxy: 220 km/s (828,000 km/h or 514,000 mph)
The train, as seen from an inertial frame, doesn't seem to rotate the earth, but it does in fact have a minute, immeasurable effect on the Earth's rotation (see what-if? 41: Go West and 162: Angular Momentum).
- [On the upper edge of a circle representing the Earth, Cueball is in a train car looking to his left.]
- [The train tracks run between another person standing at the 2:00 position, and Hairy standing at the 9:30 position. There's yet another person standing at the 6:00 position, between some snow-capped mountains and some low hills.]
- [There's a counterclockwise arrow in the middle of the circle, and motion lines indicate that everyone and everything on the planet is moving counterclockwise, except for the train, which is motionless.]
- A machine that grabs the Earth by metal rails and rotates it until the part you want is near you
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I just did an explanation from scratch for the first time, please could you tell me how I could improve it? Thanks :) Cheeselord99 (talk) 07:02, 9 May 2014 (UTC)
Am I the only one who gets Inflation when going to xkcd.com (without the www)? This comic shows at www.xkcd.com and m.xkcd.com however. 188.8.131.52 07:11, 9 May 2014 (UTC)
- I created an account. The 184.108.40.206 ip address today is me, along with 220.127.116.11 today. Mikemk (talk) 07:16, 9 May 2014 (UTC)
- I thought today's comic was late. http://www.xkcd.com/1366/ kept on displaying "Web-page not available" (browser thing, not server-thing), then I checked here. So. Oh, http://www.xkcd.com/ also... Hmmm... That's not right. Oh, "Ping request could not find host www.xkcd.com. Please check the name and try again." DNS errors? Only those trying via cached details get anything? Things are not working for xkcd.com or m.xkcd.com either. So, DNS poisoning or human error of some kind? Not the place to discuss this, I know, sorry... 18.104.22.168 10:05, 9 May 2014 (UTC)
- Explanation is good, but there are certainly related comics or maybe what-if ... I've found Orbital Speed, but I think there were something mentioning how fast sun goes relatively to galaxy ... -- Hkmaly (talk) 10:14, 9 May 2014 (UTC)
- Found two related comics - any other? Condor70 (talk) 11:33, 9 May 2014 (UTC)
It sounds like the dark matter engine in Futurama:http://futurama.wikia.com/wiki/Dark_matter_engine 22.214.171.124 (talk) (please sign your comments with ~~~~)
- That's just what I was thinking! --126.96.36.199 17:53, 12 May 2014 (UTC)
I think the last paragraph, considering the situation from the point of view of multiple trains, is not relevant. The whole concept of what makes this idea funny and interesting is that you MUST view the situation from the point of view of a single train (or elevator). --RenniePet (talk) 13:24, 9 May 2014 (UTC)
- Second-last paragraph - my comment was written at the same time as another paragraph was added. --RenniePet (talk) 13:26, 9 May 2014 (UTC)
I do not understand what the last paragraph is suggesting as it seems to violate the 3rd Newtonian law of motion.
The last paragraph is not correct, the Earth would also experience an acceleration (albeit a small one).--Sturmonium (talk) 13:54, 9 May 2014 (UTC)
"The logic of the comic also fails when taking acceleration into account. Whether the train or earth is moving can be determined by which one experiences a force due to acceleration or deacceleration when the train starts."
is incorrect, according to the principle of General Relativity. You cannot experimentally distinguish between your own acceleration against a fixed universe, and your position remaining fixed against an accelerating universe. This applies for rotation as well; if you fix the reference frame of the train rider, the acceleration of the universe creates gravity waves that cause any rider on the train to experience what feels like an acceleration. Therefore, the logic of the comic is indeed correct, even for accelerating trains. I will correct this edit.--JB Gnome (talk) 14:12, 9 May 2014 (UTC)
- But the comic doesn't say that the train accelerates the universe: rather, it just accelerates the Earth. Does that make a difference? 188.8.131.52 14:34, 9 May 2014 (UTC)
Does anyone have an idea where "train guy" is heading? He's saying "almost", like he's almost there but wasn't sure if there was something more. Maybe he's timing when he needs to jump off the train? 184.108.40.206 14:58, 9 May 2014 (UTC)Pat
I see this comic as a nice ab absurdo for the many people who think the sun rotates around us, and further to those who claim the earth has 6 thousand years etc... 220.127.116.11 18:12, 9 May 2014 (UTC)
I don't have a citation, but some traditional Polynesian navigation works using this view. Their "maps" are made of a grid of bush materials where intersections are stars or islands (possibly with a pebble tied on to represent the island). They consider the map and the earth to be connected, and you don't move along the map - the map moves. So you don't go to another island, you bring it to you. At night you move the stars to the right place, and during the day you paddle the sea and land so they are in the right place and direction.--DivePeak (talk) 21:15, 9 May 2014 (UTC)
A train rotating the Earth is NOT physically equivalent to a train traversing the Earth. It would be true for a flat Earth, but rotation is absolute, see Newton's bucket argument.  --Gleyshon
I am only a layperson, but as i read it the explanation confuses coordinate systems for the description of motion with physical explanation. The reasons why the train cannot be seen as accelerating the earth/universe are so numerous (even ignoring the other objects moving in different ways) it's just for subjective fun that i'll point out a few: The rest mass of the earth is not relative, so neither is the force needed to accelerate it -- force which the train cannot create by a factor of kajillions (roughly ;^). And if it did, the area would turn into plasma. Sticking to the comic, there isn't enough friction/rigidity/etc for the wheels/rails to "grab the earth". (Notice these are local observations unaffected by any relativity.) If somehow the earth could be accelerated in this manner, the rest of the universe wouldn't go along with it. And if it did, astronomical objects wouldn't change apparent position until their light reached us. Finally, rotation of massive bodies creates Frame-dragging (the twisting of spacetime) which is locally observable. So: the point of the comic isn't that the view presented is counter-intuitively valid (with awkward math); rather the comic is funny because of how badly this view fails. But i don't think i'm the person to rewrite the explanation... Noobgeek (talk) 16:59, 15 May 2014 (UTC)
- That physics are easy to understand:
- At the train you just see the Earth is moving.
- On Earth surface you just see that the train is moving.
- Just get into the train without any knowledge about the size or mass of the Earth, and you just see the surface beyond you is moving. I will try to enhance the explain on this matter. --Dgbrt (talk) 21:39, 15 May 2014 (UTC)
- Hi there! You're right that you can often exclude information and be left with various "relativities". But (to give only one argument) the comic explicitly describes the entire planet being grabbed and rotated to a new orientation. Mountains and all :^) Noobgeek (talk) 15:07, 16 May 2014 (UTC)
It's fun to play with the physics, but the explanation is just wrong re the comic expressing a valid perspective in physics, most directly for the reason supplied by the title text: Multiple trains and elevators are moving relative to each other, so their mode of operation can't be to stay still and shift the earth. (The point of the title text might be to make the false-physics joke extra clear.) I'm going to rewrite the explanation if no one else does -- but this will be my first big edit, so before i do, to be a polite noob, i'm requesting objections. Noobgeek (talk) 19:58, 23 May 2014 (UTC)