# Racecar on a Train



## Bullgrit (Aug 26, 2011)

xkcd: Revolutionary

Someone explain the "racecar on a train" idea, and how it's "not even wrong," please. I think I know what it means, but I can't find any insight with a Google search.

Bullgrit


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## jonesy (Aug 26, 2011)

How about their forums:

xkcd • View topic - 0675: "Revolutionary"


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## Stumblewyk (Aug 26, 2011)

xkcd • View topic - 0675: "Revolutionary"

Basically - if you're seated in a racecar, on a train going the speed of light, and you stomp on the gas pedal, you're *NOT* going faster than the speed of light.

"Not even wrong" means that you're so far from anything resembling valid logic, that you're not right, you're not wrong, you're not *even* wrong.

Not even wrong - RationalWiki


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## Bullgrit (Aug 26, 2011)

Yeah, I know/understand "not even wrong."

The xkcd thread on this, (at least the first page), talks about the train and racecar going opposite directions, but my first thought was that the train is going .9c and the racecar on it then goes .9c. How does physics keep this from becoming 1.8c?

I'm not believing this thought experiment breaks physics. I just want to understand how it doesn't. I like this kind of stuff, (see: http://www.enworld.org/forum/media-...geek-stuff/291824-crossing-event-horizon.html), but I'm a total layman on the subject.

Bullgrit


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## Umbran (Aug 26, 2011)

Except, that particular example isn't "not even wrong".  It is perfectly valid logic for a layman - it is just ignorant of how Relativity works.  "Not even wrong" is for things that are really far out in left field, that make no sense whatsoever, even in the speaker's context.  Someone thinking in Newtonian terms makes perfect sense, as that's what they experience.


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## Morrus (Aug 26, 2011)

Of course, if the racecar is a DeLorean then of course the situation changes completely.


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## Janx (Aug 26, 2011)

Maybe the problem is the involvement of light speed and its special rules.

I got a really long train on tracks, with a racecar resting on the caboose facing forward.

The train is rolling at 60MPH.
The car then takes off, also at 60MPH.

Relative to the train, the car is only going 60MPH (as it moves away from the caboose)

Relative to police car sitting at the rail crossing, the racecar is 120MPH as measured from his fixed point in 2 readings when the radar bounces off the race car.

i assume the statements and math to be correct.  Obviously, a physicist could prove me wrong.

Now make it a space train with a spacecar on top.
the train is going .4c to Alpha Centauri from eath
the car takes off again.  the caboose is receding from us at .4c
the car should be receding from us at .8c

Make the train's speed be faster still, and the concept is meant to scale.

Somehow, the magic of relativity and light speed however, make the math all funky.  From the concept of the car driver, time slows down, etc.

But nobody gives a rats ass about the driver.  The point is, does the car go faster because it's starting speed is = train's speed when it takes off?

Therefore, can it, from any vantage point, be going faster than the speed of light?

never mind that it's a short term experiment, as the car will run out of train to race along.  Or that its forward movement will apply some negative movement to the train.


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## jonesy (Aug 26, 2011)

I'll try. I'll probably get corrected too.

It's time dilation and length contraction. The train is moving at .9c from the point of view of someone standing still from the point of view of the train. The racecar is moving at .9c from the point of view of the train, but from the point of view of the person standing still from the point of view of the train time dilation occurs and the racecar on the train wouldn't actually seem to be moving as fast as someone on the train would think it was compared to the train, and both would be contracted in length (not just seemingly, but actually) making them almost the same object (a very very very short train) from the point of view of the person standing still from the point of view of the train making the measurements from the person standing still give both the train and racecar a speed of .9c because of the time dilation affecting all parties in the scenario in a different manner depending on where they are from the point of view of everyone.

In other words, from the pov of the person standing still, they are moving at the same speed. The whole thing is relative to where you are.


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## Janx (Aug 26, 2011)

Bullgrit said:


> Yeah, I know/understand "not even wrong."
> 
> The xkcd thread on this, (at least the first page), talks about the train and racecar going opposite directions, but my first thought was that the train is going .9c and the racecar on it then goes .9c. How does physics keep this from becoming 1.8c?
> 
> ...




one question to ponder:
if I am in fast car and I shoot a gun at the guy in front of me, does my bullet go faster (muzzle velocity + car velocity) or just muzzle velocity?

conceptually, if the motionless car on the train wasn't bolted down, when the train started moving, the car could actually roll off the back of the train.

So steps have to be taken to prevent that (bolt the car down, hold down the brakes, actually acccelerate the car?).

The first layman physics question then, is whether velocity is additive when one object carries another object that is also moving?


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## jonesy (Aug 26, 2011)

jonesy said:


> The train is moving at .9c from the point of view of someone standing still from the point of view of the train.



Actually, I'll be the first to correct me. That should say:

The train is moving at .9c from the point of view of someone _moving away from the train at .9c from the pov of the train_.

There is no such thing as a stable observation location when you are talking about relativity. Everything is moving.


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## Umbran (Aug 26, 2011)

The basic problem is very simple.

"You're on a train moving at the speed of light..."

No, you aren't.  Period.  Only _massless_ particles actually move at the speed of light.  Trains are big, heavy things, and cannot move at the speed of light.  They can move close to the speed of light, but not actually at it.

So, you're on a train moving very close to the speed of light.  Or, more correctly, someone standing on the side of the track says it is moving close to the speed of light.  From the race car's point of view, the train's _motionless_.  You stomp on the race car gas pedal.  The race car takes off, moving say 30 MPH faster than the train. That's fine.  

From the point of view of someone standing on the side of the train track, the train is moving near the speed of light.  The car is moving slightly faster than the train, but still not at the speed of light.  From the point of view of the bystander, the speed of the car and the train do *not* simply add linearly.  

That's relativity - distances and times (and thus speeds) change relative to who is doing the measuring.


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## Pbartender (Aug 26, 2011)

Umbran said:


> So, you're on a train moving very close to the speed of light.  Or, more correctly, someone standing on the side of the track says it is moving close to the speed of light.  From the race car's point of view, the train's _motionless_.  You stomp on the race car gas pedal.  The race car takes off, moving say 30 MPH faster than the train. That's fine.
> 
> From the point of view of someone standing on the side of the train track, the train is moving near the speed of light. The car is moving slightly faster than the train, but still not at the speed of light. From the point of view of the bystander, the speed of the car and the train do *not* simply add linearly.




Or, to put it another way, if the train was moving at 0.9c and the race car started driving (on the train) at 0.2c (relative to the train), the track-side observer would NOT see the race car traveling at 1.1c.  Instead, it would look like it was traveling at something greater than 0.9c but less than 1.0c that I can't computate off the top of my head from memory, since I haven't practically used those equations since 13 years ago in college.

In the finest tradition of collegiate level Physics, I'll leave it as an exercise for the student.


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## Janx (Aug 26, 2011)

jonesy said:


> Actually, I'll be the first to correct me. That should say:
> 
> The train is moving at .9c from the point of view of someone _moving away from the train at .9c from the pov of the train_.
> 
> There is no such thing as a stable observation location when you are talking about relativity. Everything is moving.




but the problem with physics mumbo jumbo is the wash everything out with that clause making it all relative.

I am at the space train station that is doing it's damndest to hold a stable position in the universe.  I am waving good by to you, as your train pulls away on its way to Alpha Centauri which is 4 light years away.

For the purposes of the test, which is very fast, because the train has a very rapid acceleration, (let's say +.1c per second), what do I, the allegedly mostly non-moving observer see?*

*let's seperate the fact that I used the word "see" which has to do with light, and consider the concept as if actual light, the ability to see, and how it travels is magic and not related to the movement of the train.

Do I ever "see" the train reach light speed?  
and arrive there in pretty fast time?**

**if it can only reach light speed, it would take about 4 years + 10 seconds approx to get there.  If it could exceed light speed, by the time 40 seconds elapsed, it would be there (+.1c per second, and math that I don't do).

I suspect that we can all accept that time for the train passengers moves slower by some physics math that we may not understand so to them the trip is faster than those left behind might think it would be.  Therefore, their perspective, while interesting, really never was part of the concern for laymen to grasp whats going on.

I think the challenge for us layfolk is, is getting a physicist to answer that if I launch a 1c rocket to alpha centauri and back, will I will see that rocket in 8 years or not?


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## Umbran (Aug 26, 2011)

Janx said:


> I think the challenge for us layfolk is, is getting a physicist to answer that if I launch a 1c rocket to alpha centauri and back, will I will see that rocket in 8 years or not?




You cannot launch a 1c rocket.  Period.  The law isn't just that you can't go faster than light.  Physical objects with mass cannot even go as fast as light.

If you launch a 0.5c rocket*, you'll see it in 16 years.

The people on the rocket (or any time-recording device) will think something less than 16 years has gone by for them during the journey.  




*Assuming somehow it instantaneously reaches 0.5c without turning any people on it into paste, can stop on a dime, turn around, and come back again.


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## jonesy (Aug 26, 2011)

Janx said:


> I am at the space train station that is doing it's damndest to hold a stable position in the universe.



But that's just it. There is no such thing. First you'd need a universe that isn't expanding. (Or contracting, but that no longer seems to be a possibility for us). Then you'd need the planets, the stars, the galaxies, even gravity itself to stop moving. Every single thing in our universe is moving according to the point of view of something else. And every single thing can use itself as an observation post which it can itself say isn't moving.

If I get on rocket ship to the Moon and reach the vacuum of space where I then shut down my rocket, I can say that the rocket is moving through the vacuum towards the moon. But I would be equally correct in saying that the Moon is moving through the vacuum towards me, and that my rocket is standing still and merely waiting for the Moon to reach it.



Janx said:


> *let's seperate the fact that I used the word "see" which has to do with light, and consider the concept as if actual light, the ability to see, and how it travels is magic and not related to the movement of the train.



That's like saying "let's forget about the laws of physics as we know them, so that we can discuss the laws of physics as we know them". The way you see things by way of light is an intrinsic part of the question of what you would actually see.


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## Pbartender (Aug 26, 2011)

jonesy said:


> But that's just it. There is no such thing. First you'd need a universe that isn't expanding. (Or contracting, but that no longer seems to be a possibility for us). Then you'd need the planets, the stars, the galaxies, even gravity itself to stop moving. Every single thing in our universe is moving according to the point of view of something else. And every single thing can use itself as an observation post which it can itself say isn't moving.
> 
> If I get on rocket ship to the Moon and reach the vacuum of space where I then shut down my rocket, I can say that the rocket is moving through the vacuum towards the moon. But I would be equally correct in saying that the Moon is moving through the vacuum towards me, and that my rocket is standing still and merely waiting for the Moon to reach it.




But, to use your own interjection, that's just it.  Relativity allows you to be your own "stable position", and let the rest of the universe be damned, because you are the center of the universe and everything else is moving but you are not.  Ever.  Unless you want to be.

I am not moving and the space train is moving relative to me, and it doesn't make a lick of difference if anything else in the universe is moving or not, because it too is moving relative to me, because I'm the observer, because I say so.


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## Janx (Aug 26, 2011)

Umbran said:


> You cannot launch a 1c rocket.  Period.  The law isn't just that you can't go faster than light.  Physical objects with mass cannot even go as fast as light.
> 
> If you launch a 0.5c rocket*, you'll see it in 16 years.
> 
> ...




That's a useful answer.

If my rocket can go .9c, will I see it in 4/.9*2 years?

Basically, disregarding the 1c limit, is there anything else intrinsic to speed that affects the mission?  Or is the math still normal like the .5 example?

And of course, we are ignoring the paste problem, which presumably is because lots of acceleration = lots of Gs = lots of paste.  Another simple mechanic us layment can understand without needing math.

Now to the first part of your statement.  Barring the technical issue of fuel and engines for my super fast rocket, why can it not go 1c (relative to me sitting at home on the launch pad)?

What makes it not go that fast, whats so special about going from .8c to .9c to 1c?

if my rocket accelerates in .1c bursts, pauses to recharge the accelerates again, after 10 bursts, is it not going 1c, relative to me sitting on earth on that launchpad?

[MENTION=10324]jonesy[/MENTION], for the purposes of a 40 second or 16 year test, how much drift between my space station and alpha centauri are we talking about?  Is it adding 5 feet, 5 miles, 5 light years?  For the purposes of a short term test, true motionlessness and non-significant drift are good enough.

It's like your example about the capsule going to the moon.  yes, you are correct that the moon is moving towards the capsule from a certain perspective.  But that perspective is functionally useless when we know we launched the capsule at the moon, not the moon at the capsule.  The guys in the capsule know they are riding a capsule that is headed for the moon, which is also moving, but they will catch up to*.  While their eyes tell them the moon is getting bigger, they know that they are moving and the moon is not actually doing all the work and headed for them, they are headed for the moon.  

*NASA guys probably know to aim the capsule into the path of the moon or some such that technically the moon may also be moving through its orbit into a collision course with the capsule.

  it's no different than the thinking that "what if reality was just our souls remote driving our bodies like in the Matrix."  It may be true that that's how reality works, but it is functionally useless.


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## Bullgrit (Aug 26, 2011)

> The people on the rocket (or any time-recording device) will think something less than 16 years has gone by for them during the journey.



This touches on another question I've had for a while. If time for the Traveler slows down, doesn't this mean that the Traveler thinks he moved faster than the Observer thinks?

If the faster the Traveler goes, the more time slows down for him, is there a point where, from the Traveler's point of view, he traveled faster than light? What is the ratio of time slow down to fraction of light speed? Like, if traveling at .5c, does the Traveler's clock slow down to .5 compared to the stationary Observer's clock?

Bullgrit


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## GSHamster (Aug 26, 2011)

It basically comes out of the math. The thing about the racecar on a train is that a layman using classical physics thinks the race car's velocity = race car's speed + train's speed or

velocity = u + v

But that is not the correct equation. The real equation is

velocity = (u + v) / (1 + (uv/c^2))

Where c is the speed of light.  if u and v are very small, then that last term in the denominator goes to 0, and the equation simplifies to u + v.  But when you're at .9c, and you jump another .9c, the equation is

velocity = (.9c + .9c ) / (1 + (.9 * .9))
 = 1.8c / 1.81
 = 0.9945c


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## Pbartender (Aug 27, 2011)

Janx said:


> What makes it not go that fast, whats so special about going from .8c to .9c to 1c?




As GSHamster says, this is another one that falls out of the math...

M=m/√(1-v2/c2)

With m being the rest mass and M being the apparent relativistic mass.

So, as velocity approaches the speed of light, the mass of the object approaches infinity.  In other words, it would take an infinite amount of energy to make a massive object go light speed.


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## jonesy (Aug 27, 2011)

Janx said:


> for the purposes of a 40 second or 16 year test, how much drift between my space station and alpha centauri are we talking about?  Is it adding 5 feet, 5 miles, 5 light years?  For the purposes of a short term test, true motionlessness and non-significant drift are good enough.



That's not quite what I was talking about, but the universe is expanding at the speed of 74.2 kilometers/second/megaparsec (this is from 2009).



Bullgrit said:


> What is the ratio of time slow down to fraction of light speed?



Roughly, at .7c you are adding months to the time that the observer experiences versus what the traveller does during a few years of travel time. At .9c you are adding years. And after .999c it starts getting crazy.


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## Bullgrit (Aug 27, 2011)

> Roughly, at .7c you are adding months to the time that the observer experiences versus what the traveller does during a few years of travel time. At .9c you are adding years. And after .999c it starts getting crazy.



So it does get to the point that from the Traveler's point of view, he traveled a lightyear distance in less than a year of time? Maybe even to the point of instantaneous?

Starman: I laughed out loud at your xp awards above. I get the reference. 

Bullgrit


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## jonesy (Aug 27, 2011)

Bullgrit said:


> So it does get to the point that from the Traveler's point of view, he traveled a lightyear distance in less than a year of time? Maybe even to the point of instantaneous?



That close to 1c the distance you can travel increases almost at the same ratio as the difference in time experienced by the observer.

In other words, I have no idea how to calculate what you're asking.


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## Janx (Aug 27, 2011)

jonesy said:


> That close to 1c the distance you can travel increases almost at the same ratio as the difference in time experienced by the observer.
> 
> In other words, I have no idea how to calculate what you're asking.




is it sufficient to say, that the super faster you go, the slower time goes in the spacecraft (clock and passenger).

Thus, the faster you get there, you will spend even less of your life on the trip


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## Starman (Aug 27, 2011)

For those curious about time dilation, Wikipedia has a good page on it. I won't repost any of the formulas here in an effort to keep readership from declining further.


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## Bullgrit (Aug 27, 2011)

Wikipedia said:
			
		

> Time dilation can arise from:
> 
> 1.    the relative velocity of motion between two observers



Wait a minute. Wait a minute. The relative velocity between the two observers? So if Traveler A is traveling at .5c "east" and Traveler B is traveling at .5c "west"... they will see each others time differently from each other *and* from how stationary Observer sees their time? Even though they are going the same speed, but in opposite directions. Will each see the other's clock stopped because their relative velocity is 1.0c?

I find these discussions on this kind of subject absolutely fascinating.

I just bought _The Universe in a Nutshell_, but I'm waiting to read it on my vacation in 2 weeks.

Bullgrit


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## Relique du Madde (Aug 27, 2011)

Morrus said:


> Of course, if the racecar is a DeLorean then of course the situation changes completely.




The strange thing about DeLoreans is that you can never speed past 89 mph without accidently finding yourself at your destination extremely late or extremely early compared to the time it would take to arrive at the location in a Veyron.


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## Pbartender (Aug 29, 2011)

Bullgrit said:


> Wait a minute. Wait a minute. The relative velocity between the two observers? So if Traveler A is traveling at .5c "east" and Traveler B is traveling at .5c "west"... they will see each others time differently from each other *and* from how stationary Observer sees their time?




Yes.



Bullgrit said:


> Even though they are going the same speed, but in opposite directions. Will each see the other's clock stopped because their relative velocity is 1.0c?




No, because they have mass, their relative velocity is not 1.0c, but (using GSHamster's equation above) 0.8c.

In the interest of saving people's sanity, spoilered mathematics:

[sblock]velocity = (u + v) / (1 + (uv/c2))

velocity = (0.5c + 0.5c) / (1 + ((0.5c * 0.5c)/c2))

velocity = 1.0c / (1 + (0.25c2/c2))

velocity = 1.0c / 1.25

velocity = 0.8c[/sblock]


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