3 ms·

Ironically, spacetime contains no actual space nor any time. It's actually mostly whole grain wheat and malted barley flour. Edit: Wait, that's Grape-Nuts. Not

Ironically, spacetime contains no actual space nor any time. It's actually mostly whole grain wheat and malted barley flour. Edit: Wait, that's Grape-Nuts. Not spacetime. Anyway, my point still holds.

stcredzero 8y ago
It's actually mostly whole grain wheat and malted barley It's a fusion microbrew?
Koshkin 8y ago
Indeed, this is similar to calling a plane "X-Y plane" - coordinate axes are a part of a reference frame and not of the plane itself.
- chasing 8y ago
  The x-y plane contains zero actual airplanes. Popular misconception.
- raattgift 8y ago
  The tangent vectors at each point in the 2d flat plane are always positive, while those in the flat 3d (Lorentzian) spacetime can be negative, null, or positive. By extension curves can also be classified when the tangent vectors at every point along them are all negative, all null, or all positive. You can't have a negative or null curve in the 2d flat plane, but you can in 3d flat spacetime; likewise, you can't have a negative or null curve in the 3d Euclidean space, but you can in 4d Minkowski spacetime. Strictly speaking, "time" in "spacetime" is superfluous, but it's often useful in physics to distinguish between a generic space and a Lorentzian spacetime -- for example, one frequently decomposes a spacetime into a set of spaces (e.g. in the Hamiltonian formulation of General Relativity) where each space is treated as having evolved causally from its neighbour. Maybe the choice of "time" in spacetime (and "timelike" for negative curves) is just physics chauvinism rather than something deeper, but if so does it really matter? I think you know the following, but for anyone else reading, "time" is tacked on to "space" giving spacetime much the same way that the differently-signed dimension is tacked on to the line element. In Cartesian coordinates, with mostly-plus eigenvalue signs, for flat space --> flat spacetime: dx^2 + dy^2 --> dx^2 + dy^2 - c^2 dt^2 dx^2 + dt^2 + dz^2 --> dx^2 + dy^2 + dz^2 - c^2 dt^2 where c is some arbitrary constant, and x, y, z, and t are the labelled orthogonal axes. The line element between two arbitrarily close points in the space cases will be positive, but in the spacetime cases can be positive, null, or negative. There is enormous freedom to use different systems of coordinates and different slicings, but there's no escaping a change in sign and constant factor for one of the components of the line element in a (Lorentzian) spacetime of dimension n > 1 compared to the components of the line element in an n-1 dimensioned spacelike slice of it.

stcredzero 8y ago

It's actually mostly whole grain wheat and malted barley It's a fusion microbrew?

Koshkin 8y ago

Indeed, this is similar to calling a plane "X-Y plane" - coordinate axes are a part of a reference frame and not of the plane itself.

chasing 8y ago
The x-y plane contains zero actual airplanes. Popular misconception.
raattgift 8y ago
The tangent vectors at each point in the 2d flat plane are always positive, while those in the flat 3d (Lorentzian) spacetime can be negative, null, or positive. By extension curves can also be classified when the tangent vectors at every point along them are all negative, all null, or all positive. You can't have a negative or null curve in the 2d flat plane, but you can in 3d flat spacetime; likewise, you can't have a negative or null curve in the 3d Euclidean space, but you can in 4d Minkowski spacetime. Strictly speaking, "time" in "spacetime" is superfluous, but it's often useful in physics to distinguish between a generic space and a Lorentzian spacetime -- for example, one frequently decomposes a spacetime into a set of spaces (e.g. in the Hamiltonian formulation of General Relativity) where each space is treated as having evolved causally from its neighbour. Maybe the choice of "time" in spacetime (and "timelike" for negative curves) is just physics chauvinism rather than something deeper, but if so does it really matter? I think you know the following, but for anyone else reading, "time" is tacked on to "space" giving spacetime much the same way that the differently-signed dimension is tacked on to the line element. In Cartesian coordinates, with mostly-plus eigenvalue signs, for flat space --> flat spacetime: dx^2 + dy^2 --> dx^2 + dy^2 - c^2 dt^2 dx^2 + dt^2 + dz^2 --> dx^2 + dy^2 + dz^2 - c^2 dt^2 where c is some arbitrary constant, and x, y, z, and t are the labelled orthogonal axes. The line element between two arbitrarily close points in the space cases will be positive, but in the spacetime cases can be positive, null, or negative. There is enormous freedom to use different systems of coordinates and different slicings, but there's no escaping a change in sign and constant factor for one of the components of the line element in a (Lorentzian) spacetime of dimension n > 1 compared to the components of the line element in an n-1 dimensioned spacelike slice of it.