3 ms·

Said vector doesn’t span all of 3D space though. It is a one dimensional vector. x, y, and z are just shorthand for orthonormal basis vectors. What you’ve desc

Said vector doesn’t span all of 3D space though. It is a one dimensional vector. x, y, and z are just shorthand for orthonormal basis vectors. What you’ve described isn’t “traveling in all three dimensions” simultaneously, it’s traveling along on of the dimensions with a different basis.

gizmo686 4y ago
But this is true in relativity as well. In an appropriate coordinate system, you are also moving in only 1 of the 4 dimensions. If you are not accelerating, then this coordinate system is an inertial reference frame, and the fact that you appear to be a stationary object moving through time is not mere mathematical curiosity, but the core insight of relativity.
ickelbawd 4y ago
That might be true from my own frame of reference but not so to an observer, right? How can we say there are 3 spatial dimensions at all if what you say is true? What you’re describing suggests there are an infinite number of dimensions based on the different frame of reference for all observers. Why do we then believe there to be 3 dimensions? Is this just one of the cases where 3 dimensions is a useful model for calculation but not really true in reality? Undoubtedly there must be something I’m missing here—I’ve taken physics courses but clearly I’m no expert. :)
- wbsss4412 4y ago
  Unfortunately I am not well versed in relativity, my response was completely rooted in linear algebra. That is, any vector is going to be inherently one dimensional, regardless of its coordinates. Dimension is a property of a set of vectors, dependent upon how many are linearly independent of the rest of the vectors in the set. What I described doesn’t imply that there are infinite dimensions. The vector [0,0,1] is traveling through three dimensions just the same as [1,1,1].
  - rexer 4y ago
    Not quite, though, right? Because the magnitude of those two vectors is different: the magnitude of the latter one is 1.7. I agree with the rest of your statement.
    - wbsss4412 4y ago
      Yes exactly, I was only focused on the direction, not the magnitude.

gizmo686 4y ago

But this is true in relativity as well. In an appropriate coordinate system, you are also moving in only 1 of the 4 dimensions. If you are not accelerating, then this coordinate system is an inertial reference frame, and the fact that you appear to be a stationary object moving through time is not mere mathematical curiosity, but the core insight of relativity.

ickelbawd 4y ago

That might be true from my own frame of reference but not so to an observer, right? How can we say there are 3 spatial dimensions at all if what you say is true? What you’re describing suggests there are an infinite number of dimensions based on the different frame of reference for all observers. Why do we then believe there to be 3 dimensions? Is this just one of the cases where 3 dimensions is a useful model for calculation but not really true in reality? Undoubtedly there must be something I’m missing here—I’ve taken physics courses but clearly I’m no expert. :)

wbsss4412 4y ago
Unfortunately I am not well versed in relativity, my response was completely rooted in linear algebra. That is, any vector is going to be inherently one dimensional, regardless of its coordinates. Dimension is a property of a set of vectors, dependent upon how many are linearly independent of the rest of the vectors in the set. What I described doesn’t imply that there are infinite dimensions. The vector [0,0,1] is traveling through three dimensions just the same as [1,1,1].
- rexer 4y ago
  Not quite, though, right? Because the magnitude of those two vectors is different: the magnitude of the latter one is 1.7. I agree with the rest of your statement.
  - wbsss4412 4y ago
    Yes exactly, I was only focused on the direction, not the magnitude.