In the Universe do straight lines exist?

[LightningInAJar]

TL;DR Summary

Do straight lines exist?

In the universe do straight lines exist? I know over long distances like interstellar and even shorter distances like between the Earth and around the gravity of the moon lines tend to curve, but do straight lines exist anywhere? Or just a desire for them to exist in nature if not for gravity and maybe other forces?

 

[Dale]

In any sense that lines exist then straight lines exist too.

 

[phinds]

Summary:: Do straight lines exist?

In the universe do straight lines exist? I know over long distances like interstellar and even shorter distances like between the Earth and around the gravity of the moon lines tend to curve, but do straight lines exist anywhere? Or just a desire for them to exist in nature if not for gravity and maybe other forces?

Actually, they do NOT curve, they travel in straight lines. The source of your error is that the "straight lines" are straight in pseudo-Riemann geometry which is the geometry that describes space-time. These are formally called "geodesics", which is the name for straight lines in that geometry. You are applying Euclidean geometry to movement in space-time where it is not applicable.

We SAY that the lines "curve" or "bend" but physicists understand that it is a simple way of saying what I just described and everyone is familiar w/ Euclidean Geometry so it's just easier to talk about it that way.

In any case, lines are a math thing, so of course Euclidean straight lines exist in space and everywhere else. [see post #9] I was wrong. So do geodesics, it's just that geodesics are the appropriate descirption in the geometry of space-time.

 

[PeroK]

Summary:: Do straight lines exist?

In the universe do straight lines exist? I know over long distances like interstellar and even shorter distances like between the Earth and around the gravity of the moon lines tend to curve, but do straight lines exist anywhere? Or just a desire for them to exist in nature if not for gravity and maybe other forces?

What's your definition of a straight line?

 

[etotheipi]

In any case, lines are a math thing, so of course Euclidean straight lines exist in space and everywhere else. So do geodesics, it's just that geodesics are the appropriate descirption in the geometry of space-time.

What do you mean by "Euclidean straight lines exist in space and everywhere else"? Euclidean geometry only applies to Euclidean spaces, but we do not occupy a Euclidean space

 

[phinds]

What do you mean by "Euclidean straight lines exist in space and everywhere else"? Euclidean geometry only applies to Euclidean spaces, but we do not occupy a Euclidean space

Hm ... OK, but that implies that Euclidean lines don't exist at all in this universe and I don't think that's right. What's wrong with a straight (Euclidean) line from here to the moon, for example. I agree that nothing physical will travel on it unless forced to do so and the math to make that happen would likely be complex, but that doesn't change the fact that such a line exists mathematically does it?

 

[Dale]

A Euclidean straight line implies that the space in which the line exists is Euclidean.

 

[etotheipi]

Hm ... OK, but that implies that Euclidean lines don't exist at all in this universe and I don't think that's right. What's wrong with a straight (Euclidean) line from here to the moon, for example. I agree that nothing physical will travel on it unless forced to do so and the math to make that happen would likely be complex, but that doesn't change the fact that such a line exists mathematically does it?

I think whenever you're trying to do any Physics calculation, you first need to establish some mathematical framework in which to construct your model.

You could start with a Euclidean space, i.e. an affine space with a set of points and an associated vector space, and then you can talk about a straight line between two points in the sense of Euclidean geometry and the 5 postulates. This is the approach taken in Classical Physics, i.e. you model the universe as a Euclidean space (and fill it with planets, and stars, and spherical cows) and you can use concepts from Euclidean geometry. As has been known for a little while, Euclidean space isn't a very good model for the universe, though!

If instead you start with the mathematical structure of a Minkowski space, then you are now dealing with a Lorentzian geometry. I don't know enough about this to comment much on the differences between these two geometries, but one big difference is that now you have a pseudo-Riemannian metric.

In even more general exotic spaces, I'm sure it's significantly more complicated!

 

[phinds]

OK, points taken. I saw the error of my ways almost immediately after posting. I understand now that Euclidean lines do NOT exist in non-Euclidean space. I'll edit my previous post

 

[LightningInAJar]

I am just curious about the true nature of things. I have a retina disease which causes "straight lines" to curve sometimes and was wondering if the brain just uses the cones in the eye to calculate the distances that are shortest to determine what is straight. I think the cones in the central vision are arranged hexagonically so I assume the brain does much of the work. Was just wondering the nature of lines on all scales.

 

[Grinkle]

the true nature of things

That's a tough one to get folks to agree on. Google "geodesics" and see if that description is satisfying.

A red ball looks red to our human eyes because the ball reflects red light, so one wonders if its true nature contains any redness. True nature of things can sometimes involve subjective judgement. Phind's posting in this thread on whether Euclidean straight lines exist in any universe is a perfect example.

 

[phinds]

I am just curious about the true nature of things.

"The true nature of things" is a philosophical question, not a scientific one and cannot be addressed in any meaningful way on this forum (we don't do philosophy). We describe things based on our senses and our instruments and using dimensions that are for the most part completely arbitrary. That's as close as you're going to get.

 

[A.T.]

I am just curious about the true nature of things.

Straight lines are a mathematical concept and therefore an idealization. But they are often a good enough approximation of many things in nature.

 

[FactChecker]

I am just curious about the true nature of things. I have a retina disease which causes "straight lines" to curve sometimes and was wondering if the brain just uses the cones in the eye to calculate the distances that are shortest to determine what is straight. I think the cones in the central vision are arranged hexagonically so I assume the brain does much of the work. Was just wondering the nature of lines on all scales.

To discuss this, you might consider what specific properties you want a "straight" line to have: no curvature, shortest distance, follow the path of light, etc. Consider lines on the surface of the globe. There certainly are lines (paths) of the shortest distance between two points. Would you call them "straight"? Although we see those paths as curved when embedded in three dimensions, a bug on the surface of the globe would not be able to detect that without some mathematical definition of curvature that it can use in that space.

 

[LightningInAJar]

I guess mostly perception of straight. If anything in nature tries to be straight even against the will of other forces. Something that travels along 1 dimension without crossing into 2 dimensions in any direction.

 

[jbriggs444]

I guess mostly perception of straight. If anything in nature tries to be straight even against the will of other forces. Something that travels along 1 dimension without crossing into 2 dimensions in any direction.

Unfortunately, that does not narrow it down much. "1 dimension" just means that position can be described with one number. It does not entail straightness.

For instance, my car's odometer can associate one number with my car's position. That does not entail that my car drives in a straight line.

 

[A.T.]

If anything in nature tries to be straight even against the will of other forces.

This just like the questions about perfect circles in nature (use search). The answer is still what I wrote in post #13.

 

[FactChecker]

If anything in nature tries to be straight even against the will of other forces.

So by a "straight" line you are referring to the path in spacetime that a moving mass would travel due to momentum, with no forces applied. Then the answer is yes, there are straight lines in the universe. But they may not have the properties that you would expect.

 

[phinds]

So by a "straight" line you are referring to the path in spacetime that a moving mass would travel due to momentum, with no forces applied. Then the answer is yes, there are straight lines in the universe. But they may not have the properties that you would expect.

But it seems clear that he's asking about Euclidean straight lines in the actual universe and that question has already been answered as "no".

 

[FactChecker]

But it seems clear that he's asking about Euclidean straight lines in the actual universe and that question has already been answered as "no".

The answer depends on how the OP characterizes "straight". When he characterizes "straight" in different ways, as he did in post #15, the answer changes.

 

[phinds]

The answer depends on how the OP characterizes "straight". When he characterizes "straight" in different ways, as he did in post #15, the answer changes.

Ah. Fair enough.

 

[LightningInAJar]

So by a "straight" line you are referring to the path in spacetime that a moving mass would travel due to momentum, with no forces applied. Then the answer is yes, there are straight lines in the universe. But they may not have the properties that you would expect.

What properties would they have?

 

[jbriggs444]

What properties would they have?

What properties would you expect?

Given any two events in space-time, is there exactly one free-fall trajectory that includes those two events? Not necessarily.

 

[r731]

In Euclidean geometry, a straight line between point A and B is the shortest line from A to B.

 

[phinds]

In Euclidean geometry, a straight line between point A and B is the shortest line from A to B.

True but irrelevant to the question at hand, which is about the physical universe we live in, not abstract math. Please re-read the thread, particularly post #5.