Recent content by lvirany

You can get the gradient in spherical (or any other) coordinates by direct substitution, using basic linear algebra. From there you can get div, curl, and the Laplacian just by vector operations:

I would consider the two masses to be connected by a spring of infinite spring constant at the point of collision.

Minkowski 4-Force = dP/d-tau where P is 4-momentum; or 4-Force = gamma(3-Force, id/dt(mc)) where m is relativistic mass.

(x,y,z,ct) and (x',y',z',ct') do describe the same point but the question is, can you get to another point which is a '4-distance' ds away through a linear transformation? As an example of a case in which this does not hold, consider the differential elements in spherical coordinates. They are...

Another thing about Minkowski and 4-forces. Is he not actually defining an 8-dimensional space? There's (x,y,z,ct) and (x',y',z',ct').

"I was wondering if this law could be expressed more simply, or at least using different terminology like four-acceleration, four-momentum, proper time, etc." No. It can't. I'm (quite) certain Minkowski's derivation does not define a single differentiable 4-manifold in the Einsteinian sense...

This is where Minkowski differs from Einstein & Lorentz. Minkowski explains the observed length contraction without having to use the concept of mass. Space-time as measured by the moving observer is uniformly dilated in a sheet-like way through the concept of 'proper space' as well as 'proper...

What you can do is map the ellipse to the real axis and map the real axis to a regular 4-sided polygon using Schwartz-Christoffel.