Yes.
Damn that was fast I was just going to link a picture of my mons wagnus
Your mom’s what??
His mom’s wangus, pay attention.
When you zoom in on those pristine facets it looks like a gravel driveway
It depends on where you draw the line (heh) on “straightness” and “flatness”. Some planes on gems or geodes are pretty flat, but probably not perfectly flat. Another example is a spider’s web between two points. That’s a pretty straight line if it’s taut, but again, probably not exactly perfect.
Nothing is perfectly flat, neither in nature nor man made. It’s purely a mathematical concept as every surface has some form of texture if you look close enough.
Well, yes. My point exactly.
Right, atoms are not flat
A string with weight will be a pulled under gravity. Yes even a taut spider web.
Orient it vertically
Perhaps
Lines and planes in the mathematical sense are 1 and 2 dimensional. They don’t have any height (and lines also no width). So they can’t exist as a physical object made out of atoms as they are already 3 dimensional.
They only exist as a concept.
Then, o pedant, do straight or flat objects (thus linelike, planelike) exist?
Why ask a pedantic question and be upset by a pedantic answer?
You are merely seeing through pedantic eyes.
Graphene is a great example of a planar molecule, within 1 atom of tolerance. Graphene is found in naturally occurring graphite rocks.
You could get serious Van der Waals off a couple sheets of that.
Their manifestation in our world was limited, they have already gone to another plane of existence
No, they are mathematical constructs. Everything in nature is composed of matter and the like, so there are no perfectly straight lines or flat planes.
Even a beam of light curves and refracts as it interacts with matter and space over a long enough distance.
Light is going straight from it’s point of view . It is following the shortest path between two points. The transform from different reference frames is why we see it as curved.
But if that’s your definition, then there are no straight lines in mathematics either because you could transform the straight line from one system into a curved line in another system.
Yes, nature is not objective - it is relative. Mathematics is a discipline that is based around an objective framework. Lines and planes are mathematical constructs. Mathematics gives us an objective framework that can be used to model a natural world, but they are just models.
Some things are “line-like” or “plane-like,” in that modeling them as lines or planes is helpful to describe them. You can measure a distance “as the bird flies” because birds fly in lines compared to how humans travel along roads and paths. You can describe a dense, heavy, falling object as traveling in a straight line, because air resistance may be negligible over short distances.
A model is only useful insofar as it accurately represents reality. Lines and planes are mathematical constructs, and they may be incorporated into models that describe real things. “A beam of light crossing a room travels in a straight line” is probably a useful construct because the effects of gravity and refraction of the air are probably negligible for nearly all purposes. “The surface of a pond is a plane” is probably an acceptable model for a cartographer, since the height of ripples and the curvature of the earth are negligible at that scale.
The initial question was not “Do straight lines and flat planes model anything in nature,” but whether they exist in nature. They do not. They only exist in mathematics.
They only exist in mathematics.
The curved light path is because a mathematical transform is done between two different frames of reference.
It’s no different than taking a mathematically straight line and performing a transform function to map it to a curved coordinate system. Because you allow transformation functions, there would also be no straight lines in math.
Unless the light is in a vacuum like space
Light bends in space all the time. Our sun has enough gravity to bend light.
I asked my good friend gravitational lensing about light in space, and they said that light can go and get bent
Space is not empty
There is no perfect vacuum, even in deep space. In the space of our Solar System, there is on average 5 atoms in every cubic centimeter. In interstellar space, there is on average 1 atom every cubic centimeter. In intergalactic space, there is on average 1 atom every 100 cubic centimeters. It’s a gradient, but much like the perfectly straight lines and flat planes in the original question, perfect vacuum is a theoretical construct that is impossible to achieve in our reality.
Neutrinos travel in a straight line.
Unfortunately (fortunately?) the space they’re traveling through is curved. It was a good attempt though neutrinos.
Edwin A. Abbott has entered the chat…
It appears curved to us because we mathematically transformed the reference frame.
If you are allowed to transform your geometric space to say “no straight lines” then there are no straight lines in math either. Because you could perform a transform on the straight line into a curved geometry.
Not to mention quantum fuzzing
They don’t, although they
do not“rarely” interact with other particles, they move as waves, like all other energy in the universe.“I want to emphasize that light comes in this form-particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you were probably told something about light behaving like waves. I’m telling you the way it does behave- like particles.”
Richard Feynman, “QED The Strange Theory of Light and Matter.” Introduction, Page 15.
You’re talking to somebody that studies particle physics okay.
Cubed pyrite is one of my favorite examples of this.
That’s very cool, I see why you like it
You really have to declare to what degree you are asking. You could take a very carefully grown crystal and define a plane based on its lattice structure. But the atoms are not all perfectly placed on the lattice once you zoom in far enough. There’s even gaps between the atoms! A “plane” of carbon looks more like a net to an observer on the scale of those atoms.
Is an electron a perfect sphere? Scientists probably thought so in 1900 but now ask a physicist and they will say “No, probably not”.
And yes, as others have stated, our space time is not perfectly Euclidean so that’s another level of uncertainty. How do you measure the small imperfections in a Euclidean model when actual space time isn’t Euclidean?
As a professor used to tell my class, there are no 0s.
According to mathematical platonism, yes.
Otherwise we have no idea. We have some models of physics, none perfectly describing our universe. We don’t know the structure of space, or the structure of time.
Even if we did: what would it mean for a line or a plane to exist? There could be equivalent descriptions of our universe, some including those as objects and some only as emergent properties.
Short answer, depends on perspective. For example surface of perfectly still lake could be considered flat, but on macro level it follows curvature of the earth. But we still use water to level our buildings, because radius of a planet is so big. On microscopic level it’s anything but flat.
Someone else mentioned spider silk danging. It’s also another great example, but the same perspective clause applies. But usually crystals and some geological features tend to have flat features.
Simple answer: no
Is the Higgs Field a flat plane?
Right after they mow, otherwise it’s rather fluffy.
Depending on scale. Is the surface of the lake flat?
Once you experience true level you will never go back.
Yes they do
What are some examples?
A spider web dangling down.
Curved space, perturbations from air currents, molecular irregularities, quantum fuzz
I was thinking a ray of light. But even then.
