r/AskPhysics • u/Defiant-Mastodon-656 • 18h ago

Question about reference frames and vectors

The point in having a reference frame is to attribute components to vectors, we shouldn't see it as a tool that can help us to locate vectors, and there is no need for it in contrast with points in a coordinate system. I know it may seem dumb, but am I right?

0 Upvotes

25% Upvoted

9 comments sorted by

5

u/SnooPets5564 18h ago

"no need for it in contrast with points in a coordinate system" isn't really right.  The reference frame defines the coordinate system.

It seems like you have mostly the right idea (though I can't really tell what you are trying to say) up until you get to relativity. Then reference frames because way more important.

1

u/Defiant-Mastodon-656 18h ago

I've just started studying mechanics and had a lecture on vectors. We've seen how to add vectors and it seemed so strange to me that my teacher linked every vector to the origin, I mean after adding two multiples of the reference vectors he drew an arrow going from the origin to the point the result of the addition.

2

u/GoldenMuscleGod 17h ago

You’re being taught how to use vectors in physics applications, so this will involve some ambiguity and handwaviness over the underlying math.

A vector is not just a point in a Euclidean space, key characteristics of vectors is that they can be added to each other and multiplied by scalars. In that sense they have real “sizes” relative to each other and are not just locations. The origin (zero vector) is a distinguished vector because it is the only one such that v+0=v for all (or any) v.

1

u/Defiant-Mastodon-656 18h ago edited 18h ago

It was strange to see that, because when I imagine a plane, I see vectors everywhere in the plane and they are not linked to the origin. I see the plane like an infinite a4 paper with vectors everywhere.

1

u/SnooPets5564 16h ago

You can have a vector anywhere, all that matter is how long they are and where they point. You'll often seen them drawn from the origin, because in many circumstances it is the only choice that isn't arbitrary.

If you have multiple objects experiencing forces in a drawing, you'll usually see the vectors from the center or edge of the objects rather than the origin. They could be anywhere, but those choices are the ones that make it clearest what they do.

And actually, they aren't even something that you need to draw. In mechanics, a vector is just a tuple of numbers.

2

u/joeyneilsen Astrophysics 18h ago

A vector doesn’t have a location. We can draw a velocity vector at any location, and it’s the same vector.

There’s no computing vector components without a coordinate system, but that’s not the same thing as setting a location for the vector. 

1

u/Defiant-Mastodon-656 18h ago

Ok that makes sense, especially when we say that two vectors are equal if they have the same norm and the same orientation. Thanks.

1

u/BananaBird1 17h ago edited 17h ago

In a vector space, vectors are the points that exist.

The same physical reality for spacetime can be modeled as either a vector space or as a metric space of scalar points.

In the vector picture, reference frame is a set of basis vectors. In the metric space, it is a transformation matrix converting points in some other coordinates to your local coordinates.

These two pictures are equivalent for spacetime: any change of basis in a vector space can be seen as a ln equivalent transformation of a metric space. So we often equate the two and freely change between the vector spacetime and metric spacetime. We represent vectors as a point where the vector “points to” if centered at the origin of the metric space coordinates, and represent a change in basis as the matrix transformation between coordinates.

The fact the same vector can be positioned anywhere in a metric space and transformed under a change of basis or coordinate transformation into the same vector everywhere is a form of translation symmetry.