Can there really be a truly straight line on the Earth?

[icymist]

I was sitting at a desk last night starring down a long hallway. The floor, walls, and ceiling all protruding away from me in straight lines into a very visually reduced doorway at the end of the hallway. The thought popped into my head that all of this was laid out with care by masons and carpenters, all using proper levels and squares, to make a straight building on a curved sphere (the Earth). If this hallway was built long enough, would it not bend with the Earth? Therefore, every so-called straight line would bend, at least, a little. Another example came to mind of the interstate highway system in the Midwest and Southwestern sections of America where a straight road curves with the Earth on the horizon.

[Warpy]

1. It's theoretically possible to approximate a straight line

along a laser sight above the surface, but you're right, any line using a carpenter's level will curve along with the earth.

[icymist]

6. A lot of questions pop into head from thinking like this.

How in the world could our geometry be correct? Are parallel lines really parallel? Could a perfect square be made outside of the Earth?

[tridim]

9. The only perfect shape in the universe is the sphere

Although technically it's just a bunch of lines following curved space around a point of gravity.

That's why PI is so fascinating.

[flyingfysh]

7. not even light is straight

It is affected by gravity. The earth's mass "bends" space.

Physics experts can explain it better than I can.

So your expensive laser might give you a line a fraction of a wavelength off. Is the rest of your house built to that kind of precision?

[Tesha]

22. The heck with gravity...

> not even light is straight -- It is affected by gravity.
> So your expensive laser might give you a line a fraction of a wavelength off.

The heck with gravity! Your expensive laser level is much
more grossly affected by thermal convection currents in
air. You can probably demonstrate this with a laser level
and a cigarette lighter; I'm sure the effect is far, far
bigger than the "several wavelengths" of offset that
gravity might cause. ;)

Tesha

[TechBear_Seattle]

10. Nope, not even that

Light bends along the "curvature" of spacetime. Mass causes spacetime to curve (this curvature is manifest as gravity.) A light beam near the Earth can not follow a straight line, as it must follow the way spacetime curves due to the Earth's mass.

You would have to get extremely far out from any mass in order to come close to a straight line, and even then, the mass of the experimenter's body and the mass of the equipment conducting and detecting the experiment, would cause curvature of spacetime and thus cause light to not travel in a straight line.

So if you ask a theoretical physicist or mathematician, the answer is a flat out and absolute, "No." If you ask an engineer, however, the answer will be more like, "How straight is 'straight' and what is the distance it must stay within that limit?" :hi:

[Warpy]

12. The operative word was "approximate"

[TechBear_Seattle]

14. Sorry, I was a math major in college

I even belonged to the university's math society. I've been part of too many involved discussions with topics like, "If space is curved, can any of Euclid's postulates still be assumed true?" to let the argument slip by :hi:

You said "approximate", the OP asked about "truly straight lines." Should have replied to the OP.

[Salviati]

15. It depends on what your definition of straight is...

There are those who would say that the path of a light ray through space cannot take any other path than a straight line. That by calling the path curved is merely trying to impose some idea of straightness by an outside observer that is not intrinsic to the space itself.

[Random_Australian]

16. Actually, if you knew what everything about how the mass was distributed,

you could calculate how light would bend, and thus obtain two points, one at the origin of the beam and the other some distance from the end.

However, eventually Heisenberg would get us, but until then, forward! :)

[Ready4Change]

20. Well... define straight.

Yes, the light from a laser is bent by the curvature of space produced by the earths mass.

However, since it is space itself which is curved, which would be a "straighter" line: One which curves to follow space, or one which curves to maintain its own idea of straight in disregard of the space around it?

But I sympathisize regarding the lines in your house. I think those who built mine were drunk, and thus following their own personal interpretations of straightness. ;)

[whistle]

2. I believe the ancient greeks first discovered this and designed

...and constructed their large scale buildings to compensate for the distortions caused by the perception of curving even though something is perfectly level or straight.

http://milan.milanovic.org/math/english/golden/golden4.html

[Kutjara]

3. Don't some of the really long highways in the Midwest...

...have occasional left-then-right turns built into them? I can't remember where I read this, but I remember the reason given for these otherwise pointless changes of direction was so that the highways would appear straight on the interstate highway maps. I'm not sure if this is an urban legend, but the 'fact' was sitting there in the back of my head, so I thought I'd put it out there in case anyone else has heard it.

[mccoyn]

19. I heard that was to prevent highway hypnosis.

The idea is that if you drive on a (relatively) straight road for a long period of time you will become focused on a few things, like the lines on the road and will therefore be more likely to cause a collision. The curves force your mind to deal with something once in a while and stay more alert. This is apparently a problem on some of the old highways in Europe that were built without occasional curves.

[Xipe Totec]

4. Yes

The definition of a straight line is "the shortest distance between two points. On a curved surface such as the earth, a straight line is also called a great circle and the length of that line is the great circle distance.

A straight line, in the conventional way you mean, also exists on earth. It is called the Stanford Linear Accelerator (SLAC).

In space, a straight line follows the curvature of space.

An alternative way to ask your question is: Can there be a truly flat space anywhere?

To which the answer is no.

[tridim]

5. Gravity can simulate a nearly perfect line

Hang a weight on a string and the string will straighten out in the direction of gravitational force. I've always wondered if any line is truly straight due to the curvature of space around the earth. What we perceive as perfectly straight might actually be a curve conforming to curved space.

I don't think a straight line can exist without the aid of gravity (ie, not possible in space), which is why the monolith in the 2001 books was so mind blowing to the characters, it was impossibly perfect. I think about stuff like this constantly.

[icymist]

8. What about light? Does light travel in straight lines?

Or is light constantly emanating from itself as it travels, in all directions? Would a macroscopic universe be as strange as a micro-quantum one?

[Canuckistanian]

11. Something I noticed on the prairies in Canada

The roads in the prairies are all laid out in perfect squares. The east/west roads were called "concessions" and the north/south roads were called "lines".

About every fifth "line" or so, there was a road called a "correction line". I asked someone what a "correction line" was.

They told me it was a special "line" road with a slightly different angle to allow for the curvature of the earth.

Because when you think about it, you can't keep laying out perfectly square boxes on a sphere and expect them to stay at the same longitude. Eventually, they'll veer off to the south.

[Salviati]

13. Just to offer a bit of perspective here:

The curvature of the earth would have an utterly negligable effect on what you'd percieve as a straight line using gravity as a guide. When we're talking about the scale of human sized buildings, the surface of the Earth is for all intents and purposes completely flat.

For example, if we look at the Karl-Marx-Hof in Vienna, Austria which, according to wikipedia,is the longest single residential building in the world at 1100m in length, the direction of "straight down" on one end differs from the direction of "straight down" on the other end by only .01 degrees.

[Nihil]

17. Buildings maybe but other structures need to compensate

Large suspension bridges have their piers aligned slightly out of parallel
in order that they remain perpendicular to the surface.

[TechBear_Seattle]

18. On the other hand....

My grandfather was involved in the design and construction of the Stanford Linear Accelerator Center (SLAC) in Palo Alto, California. The accelerator is a research tool that accelerates subatomic particles and smashes them into other bits of matter, just to see what interesting things pop up. The building of the accelerator was a technical challenge, as it had to be STRAIGHTER than the surface of the earth. When you have electrons being shot one at a time for two miles down a tube that is barely 1/4 inch in diameter aiming for a target that is only a few dozen atoms wide, 0.1 degree off will miss the target completely. (The target has to be that small, because the equipment looking for the result of the collision needs to focus on an extremely tiny volume of space in order to detect anything.)

Again, it comes down to "straight line" as defined by a theorist and "straight line" as defined by an engineer. The theorist will say that there is no such thing as a straight line, throw up his hands in disgust, then go off for a beer. The engineer will pull out a pencil and paper, ask you to define "straight line" and then ask about the distance your light beam must stay within that definition.

[Bill McBlueState]

21. So theorists must be happier than engineers

since the threshhold to go get drunk is much lower.

Personally, I'm an observational astronomer. We're satisifed with getting the answer to within an order of magnitude. So there's plenty of opportunity for beer.

[TechBear_Seattle]

25. Theorists may be drunker, but engineers get laid more

An example one of my college math professors used to illustrate the difference:

Take a group of 20 engineers and 20 mathematicians. Put 10 of each in each endzone of a football field. Put 40 centerfold models at the 50 yard line. Then tell the men in the endzones that if they can make it to the middle of the field, they can do what mathematicians and engineers don't get to do anywhere near as often as they'd like.

The mathematicians will throw their hands up in disgust and leave the field, feeling cheated. They know that it is impossible to ever arrive at the middle of anything. The engineers sprint forward, clothes flying as they run. They know that it is possible to get close enough to the middle as to make no difference.

[Tesha]

23. Actually, I've heard it said that the Infinite Corridor at MIT...

Actually, I've heard it said that the Infinite Corridor at MIT
is long enough to demonstrate the curvature of the Earth, but
I see no obvious "officiated" claim to that rumor.

http://en.wikipedia.org/wiki/Infinite_Corridor

On the other hand, there's *NO DOUBT* that quite a few suspension
bridges are long enough that the curvature of the Earth had to be
taken into account when their towers were designed.

Tesha

[Salviati]

24. according to my back o' the envalope calc...

If the floor is built following the surface of the Earth, if you aligned a laser at floor level parallel to the floor at one end of the hallway, it would hit the wall about half a centimeter higher at the other end 250 meters away.

[bemildred]

26. No.

Probably cannot even agree on what that would mean. Euclidean space is an abstraction that does not coincide with experiment. You could have a geodesic (theoretically), but not a Euclidean "straight line", because you are not in a Euclidean space.